**Theoretical and Experimental Studies of Over-Polishing of Silicon Carbide in Annular Polishing**

#### **Junjie Zhang 1,\*, La Han <sup>1</sup> , Haiying Liu <sup>2</sup> , Yikai Shi <sup>3</sup> , Yongda Yan <sup>1</sup> and Tao Sun <sup>1</sup>**


Received: 7 February 2018; Accepted: 3 April 2018; Published: 4 April 2018

**Abstract:** Annular polishing technology is an important optical machining method for achieving a high-precision mirror surface on silicon carbide. However, the inevitable over-polishing of the specimen edge in annular polishing deteriorates achieved surface quality. In the present work, we first analytically investigate the kinematic coupling of multiple relative motions in the annular polishing process and subsequently derive an analytical model that addresses the principle of material removal at specimen edge based on the Preston equation and the rigid body contact model. We then perform finite element simulations and experiments involving annular polishing of silicon carbide (SiC), which jointly exhibit agreement with the derived analytical model of material removal.

**Keywords:** silicon carbide; annular polishing; material removal; over-polishing; finite element

#### **1. Introduction**

Silicon carbide (SiC) is one of the preferred materials for manufacturing optical mirrors due to its unique characteristics of low density, high strength, low thermal expansion, high thermal conductivity and high chemical inertness [1,2]. According to the theory of total integrated scattering (TIS), the total surface scattering of a mirror is closely related to its surface roughness. Specifically, with the increase of surface roughness, the TIS rises sharply in conjunction with the decrease of reflectivity, which accordingly results in the degradation of the imaging quality of the optical system [3]. Therefore, achieving an ultra-smooth surface by optical machining methods is critical for the performance of SiC mirrors. At present, annular polishing technology is one of the main methods that has been widely used to obtain high-precision SiC mirrors [4–7].

The inevitable over-polishing of specimen edge that occurs during annular polishing significantly deteriorates machined surface qualities, such as flatness. Additionally, a fundamental understanding of material removal is required to minimize over-polishing. Material removal during the annular polishing process is complex due to the kinematic coupling of multiple relative motions between the specimen and polishing disc. At present, the Preston equation is widely used to describe the material removal process in annular polishing. For instance, Ji et al. [8] investigated the relationship between surface quality and polishing condition and consequently established the trajectory equation for a point on the single-side polishing part relative to the polishing pad by the coordinate transformation method. Wenski et al. [9] obtained improved non-uniformity for material removal at specimen edge by optimizing the trajectory of the polishing machine. However, the Preston equation still needed to be refined. Nanz et al. [10,11] found, through polishing experiments, that although the product of surface pressure of the specimen and its rotate

speed is zero, the polishing removal rate is not zero due to chemistry action. Consequently, a compensation parameter must be introduced to correct underestimation by the Preston equation and which fits well with specific values in the experiments. Luo et al. [12] modified the Preston equation according to the results of both experiments and theoretical calculations.

Although previous analytical and experimental studies have qualitatively analyzed average material removal in the annular polishing process, there is limited work focusing on the over-polishing of specimen edge. In particular, there is no model of a material removal equation that takes into account the phenomenon of edge over-polishing, as the Preston equation only considers the average pressure of the polishing process. Therefore, in the present work, we first analyze the kinematic coupling of multiple relative motions between the specimen and polishing disc in the annular polishing process. Subsequently, based on the Preston equation and the rigid body contact model, we derive an analytical model that addresses the principle of material removal at specimen edge. Finally, finite element (FE) simulations and experiments of annular polishing of SiC are performed to evaluate the accuracy and efficiency of the derived analytical model.

#### **2. Analytical Investigation of Annular Polishing**

#### *2.1. Kinematic Coupling of Motions*

Figure 1a illustrates a typical annular polisher, which consists of a polishing disc, a carrier disc and a swinging bracket. The specimen is pasted on the carrier disc with paraffin, which means that the specimen has a synchronous speed with the carrier disc. The applied pressure is provided by the weight of the carrier disc. Accordingly, Figure 1b illustrates the simplified motion diagram of the annular polishing, which indicates that the kinematic coupling of relative motions includes the rotation of the polishing disc and the rotation of the carrier disc. We note that the swinging of the carrier disc leads to back and forth movements by the specimen, which consequently reduce the propensity of over-polishing of specimen edge. Therefore, to magnify the over-polishing phenomenon, in the present work the back and forth swinging motions are not considered in the kinematic coupling. As indicated in Figure 1b, the speed of the carrier disc is *ω* and the speed of the polishing disc is *δ*. The distance from the center of specimen *O*<sup>2</sup> to point A on the carrier disc is *r* and the distance from the center of the polishing disc *O*<sup>1</sup> to the center of carrier disc *O*<sup>2</sup> is *R*. The angle between the line segments *AO*<sup>2</sup> and *O*1*O*<sup>2</sup> is *θ*. The speed at point A on the polishing disc relative to *O*<sup>1</sup> is *V*<sup>1</sup> and the speed at point A on the specimen relative to *O*<sup>2</sup> is *V*2, so the relative speed of the specimen and the polishing disc at point A is *V*, which can be derived from Equation (1) [13]:

$$V(r,\theta) = \left[\mathbb{R}^2 \delta^2 + r^2(\delta - \omega)^2 + 2r\mathbb{R}\delta(\delta - \omega)\cos\theta\right]^{1/2} \tag{1}$$

**Figure 1.** Illustration of annular polishing. (**a**) Model of annular polisher; (**b**) motion analysis of annular polishing.

#### *2.2. Preston Equation*

Both material removal rate and surface quality of the specimen in the annular polishing process are strongly affected by processing parameters, which have complex interactions. Preston et al. simplified the Preston equation to characterize the relationship between material removal and polishing speed *V*, applied pressure *P*, and other external factors, as shown in Equation (2) [14]:

$$\frac{dh}{dt} = kPV = kP\frac{ds}{dt} \tag{2}$$

where *h* is the amount of material removal and *k* is a proportional constant that is related to various environmental factors. Therefore, the amount of material removal at one specific point can be derived according to Equation (2) [15,16]. However, contact between the specimen and polishing disc changes dynamically with polishing time, which induces uncertainties in analytical investigation of the annular polishing process. Therefore, three main assumptions are made to simplify the operation: (1) The specimen and polishing disc are completely in contact without separation; (2) the applied pressure does not change over polishing time; and (3) the proportional constant *k* does not change over polishing time.

According to the Preston equation, the amount of material removal within a specific polishing time can be derived by integrating time *T*, as shown in Equation (3):

$$h(r) = k \int\_0^T P(r, t) \cdot V(r, t) dt \tag{3}$$

It can be seen from Equation (3) that material removal is only dependent on the resultant speed *V*, given that *k* and *P* are constant. By substituting the relative velocity derived from Equation (1) into Equation (3), material removal at point *A* can be derived, as shown in Equation (4):

$$h(r) = k \int\_0^T P(r, t) \cdot \left[\mathcal{R}^2 \delta^2 + r^2 (\delta - \omega)^2 + 2r \mathcal{R} \delta (\delta - \omega) \cos \theta\right]^{1/2} dt \tag{4}$$

#### *2.3. Rigid Body Contact Model*

It can be seen in Equation (4) that the pressure of each point on the specimen must be accounted for precisely when deriving material removal. Contact between the specimen and polishing disc in annular polishing can be analyzed by using the rigid body contact model, as illustrated in Figure 2 [17].

**Figure 2.** Illustration of the rigid body contact model.

The rigid body contact model, as a two-dimensional plane strain model, can be used to analyze the distribution of contact pressure on the contact surface between the specimen and polishing disc. Considering the much higher stiffness (Mohs hardness of 9.5 and elastic modulus of 360 GPa) of SiC compared to that of a polishing disc made of cast iron (Mohs hardness of 4.5 and elastic modulus of 170 GPa), the SiC specimen is treated as a rigid body and the polishing disc is treated as an elastic

material with small elastic modulus (elastic modulus of 3 MPa). Therefore, the shape of the SiC specimen does not change after being pressed into the polishing disc. Furthermore, it is assumed that the deformation of the polishing disc does not affect the result. The distribution of contact pressure on the specimen surface is expressed in Equations (5) or (6):

$$P(\mathbf{x}) = \frac{P\_{app}}{\pi (\mathbf{R}^2 - \mathbf{x}^2)^{1/2}} \tag{5}$$

$$P(\mathbf{x}) = \frac{P\_{app}\cos(\pi\gamma)}{\pi(\mathbf{R}^2 - \mathbf{x}^2)} (\frac{\mathbf{R} + \mathbf{x}}{\mathbf{R} - \mathbf{x}})^\gamma \tag{6}$$

where *Papp* is the pressure applied to the upper surface of specimen and *R* is the radius of specimen. *γ* can be expressed by:

$$
\cot \pi \gamma = -\frac{2(1-v)}{f(1-2v)}\tag{7}
$$

where *f* is the friction coefficient between the specimen and the polishing pad and *v* is the Poisson's ratio of the polishing pad. While Equation (5) does not consider the friction between contacting surfaces, Equation (6) provides a more accurate description of the contact by considering the frictional force between the two surfaces. By substituting Equation (6) into Equation (4), the removal equation for the specimen in annular polishing can be derived, as seen in Equation (8):

$$h(\mathbf{r}) = k \int\_0^\Upsilon \frac{P\_{app}\cos(\pi r \chi)}{\pi (\mathbf{R}^2 - \mathbf{x}^2)^{1/2}} \left(\frac{\mathbf{R} + \mathbf{x}}{\mathbf{R} - \mathbf{x}}\right)^\gamma \cdot \left[\mathbf{R}^2 \delta^2 + r^2 (\delta - \omega)^2 + 2r \mathbf{R} \delta (\delta - \omega) \cos \theta\right]^{1/2} dt \tag{8}$$

It can be seen from Equations (5) and (6) that contact pressure near specimen edge (i.e.,*r* approaching *R*) increases sharply. Therefore, Equation (8) also applies to the qualitative description of material removal when considering over-polishing of specimen edge.

#### **3. FE Simulation of Annular Polishing**

#### *3.1. FE Modeling*

To verify the accuracy of the derived model of material removal presented in Equation (8), FE simulations of annular polishing of SiC were performed by using ABAQUS software, with an emphasis on the distribution of contact pressure on specimen surface. Similarly to the analytical investigation, in the FE simulations the motion of carrier swing was not considered. Accordingly, the swing bracket was omitted in the FE model. Figure 3 shows that the FE model of annular polishing consisted of a SiC specimen colored in blue, a polishing pad in red and a polishing disc in gray, which were treated as deformable parts. The upper surface of the polishing disc and the lower surface of the polishing pad were bound entirely. The polishing disc had a synchronous speed with the polishing pad. Table 1 lists material properties of the three parts. Furthermore, it was assumed that the properties of the SiC specimen were isotropic.



It is known that grid configuration greatly affects the accuracy of prediction results in FE simulations. The three aspects of cell type, cell shape and grid density need to be considered when configuring grids. In the present work, a structured mesh was used to divide meshes by using a linear hexahedral C3D8I element with eight nodes. Grid density increased with increasing distance from the center of specimen. Furthermore, the mesh of the polishing pad was denser than that of the polishing disc, as shown in Figure 3.

**Figure 3.** Finite element model of annular polishing of silicon carbide (SiC).

In the FE simulation, an explicit dynamical analysis step with a total time of 3 s was used. The selection of 3 s was to ensure that the specimen rotated more than two revolutions, which enabled us to obtain more accurate polishing results. It should also be noted that the time cannot be too long due to high computational costs and minimal change in results. The contact between the specimen and polishing pad was set as a general contact with a friction coefficient of 0.1. A uniform pressure of 0.068 MPa was imposed on the specimen.

#### *3.2. Simulation Results and Discussion*

Figure 4 presents the distribution of contact pressure and deformation of the SiC specimen surface after FE simulation of annular polishing, in which the polishing disc and specimen have the same speed of 100 r/min. In Figure 4a, distributions of contact pressure in three random radial directions highlighted by the three randomly selected red dash lines are analyzed. For each direction, 30 uniformly-spaced points along the red lines are selected. Accordingly, Figure 4c plots variations of contact pressure along the three directions as a function of off-center distance, which shows that the contact pressure in the vicinity of the center of the specimen is distributed uniformly. However, when the off-center distance is higher than 10 mm, the contact pressure gradually increases with increasing off-center distance, and finally reaches the maximum value at the specimen edge. Figure 4b shows the contour of normal strain after polishing, which is related to the material removal of specimen surface. It can be seen in Figure 4b that the material removal at specimen edge is significantly higher than in the middle of the specimen.

**Figure 4.** *Cont.*

**Figure 4.** Distributions of contact pressure and normal strain in finite element (FE) simulations of annular polishing of SiC. (**a**) Contour of contact pressure; (**b**) contour of normal strain; and (**c**) variations of contact pressures.

We further evaluated the influence of the typical parameters (speed, Poisson's ratio and elastic modulus of polishing pad) on the distribution of contact pressure. Figure 5 plots variations of contact pressure along three directions as a function of off-center distance under different parameters. It was found, as shown in Figure 5, that for each parameter, the contact pressure of the specimen showed similar trends, first remaining stable and then increasing sharply when near the edge. The above results verify the pressure distribution equation obtained by the rigid body contact model presented in Equations (5), (6) and (8).

**Figure 5.** Distribution of contact pressure on the SiC specimen surface at different parameters. (**a**) Speed (specimen and polishing plate rotate at equal speed); (**b**) speed (keeping the speed of the polishing disc as 100 r/min, changing the speed of the specimen); (**c**) Poisson's ratio of polishing pad; and (**d**) elastic modulus of polishing pad.

#### **4. Experimental Study of Annular Polishing of SiC**

In addition to the FE simulations that verified the occurrence of over-polishing of specimen edge, annular polishing experiments of SiC were also carried out to further verify the derived model of material

removal presented in Equation (8). All the annular polishing experiments were performed by using the UNIPOL-802 precision auto lapping and polishing machine, as shown in Figure 6. The specific parameters used in the annular polishing experiments were: That the velocities of the polyurethane polishing pad and specimen were the same at 100 r/min, the polishing time was 60 min, and a diamond suspension solution was used. After polishing, the obtained surface was measured by using a surface profiler.

**Figure 6.** Precision auto lapping and polishing machine.

Figure 7 plots the variation of measured relative surface height with off-center distance. The relative surface height is defined as the change in measured surface height after polishing with respect to surface height before polishing. In order to show the mutual verification of the experimental results and the FE simulation results, Figure 7 further plots the variations of contact pressure shown in Figure 4. It can be seen in Figure 7 that within the off-center distance ranging from 0 to 13 mm, the relative surface height of the specimen remains relatively unchanged. Upon a further increase of off-center distance from 13 to 15 mm, which approaches to the specimen edge, however, the relative surface height of the specimen dropped sharply. This indicates that the amount of material removal also increased sharply. Figure 7 also demonstrates that the experimental results are in agreement with the FE simulation results, as material removal during polishing is proportional to contact pressure. Specifically, there is sharp increase in both pressure and material removal at specimen edge, indicating the occurrence of an over-polishing phenomenon. Therefore, it is indicated by both the simulation and experimental results that the derived analytical model of material removal presented in Equation (8) is indeed capable of describing material removal particularly related to the over-polishing of specimen edge during annular polishing of SiC.

**Figure 7.** Distributions of material removal by experiment and contact pressure by FE simulation.

## **5. Conclusions**

In the present work, we performed an analytical investigation, FE simulation and an experimental study to investigate the fundamentals of material removal during annular polishing of SiC, with an emphasis on the underlying mechanisms of over-polishing of specimen edge. According to the analytical investigations of the kinematic coupling of multiple relative motions between the specimen and polishing disc, an analytical model of material removal during the annular polishing process that further accounts for the over-polishing of specimen edge was derived based on the Preston equation and the rigid body contact model. Subsequent FE modeling and simulation showed the non-uniform distribution of contact pressure and the normal strain of the specimen in the annular polishing, i.e., the occurrence of over-polishing at specimen edge, which was further verified by the polishing experiments.

**Acknowledgments:** The authors acknowledge financial support from the National Natural Science Foundation of China (NSFC) and the German Research Foundation (DFG) International Joint Research Program (51761135106).

**Author Contributions:** J.Z., L.H. and T.S. conceived and designed the experiments; L.H. performed the analytical investigation and FE simulations, Y.S. performed the experiments; J.Z., L.H. and Y.Y. analyzed the data; J.Z. and L.H. wrote the paper.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## *Article* **Effects of Setting Errors (Insert Run-Outs) on Surface Roughness in Face Milling When Using Circular Inserts**

## **Csaba Felh ˝o \* ID and János Kundrák**

Institute of Manufacturing Science, University of Miskolc, Egyetemvaros, 3515 Miskolc, Hungary; janos.kundrak@uni-miskolc.hu

**\*** Correspondence: csaba.felho@uni-miskolc.hu; Tel.: +36-46-565-160

Received: 6 March 2018; Accepted: 27 March 2018; Published: 2 April 2018

**Abstract:** In face milling, the roughness of the machined surface varies due to the movement of the cutting edge. Changes in roughness parameter values in the axis of rotation (symmetry plane) have been examined at a constant depth of cut for symmetrical milling. In this paper, the effect of increasing feed per tooth on the topography of the surface is studied in fly-cutting and in multi-point face milling. The study takes into account the axial run-out of the inserts. Theoretical roughness values were modelled, the real values were tested in experiments and in both cases the impact of the run-out of the cutting edges and the change of the chip cross-section were also taken into account. Based on the performed experiments it can be stated that the accuracy of the introduced roughness prediction method increases with the increase in feed and therefore the application of the method in the case of high-feed milling is particularly effective. The results have also shown that the run-out of the insert significantly effects the roughness of the milled surfaces and therefore the measurement and minimization of these setting errors is essential.

**Keywords:** face milling; surface roughness; feed; insert run-out

#### **1. Introduction**

Increasing the productivity of machining requires more intensive material separation. This can be characterized by increasing both the values of the cutting data (the removed chip cross-sections) and the Material Removal Rate (MRR) and the Surface Rate (SR) values. At the same time, consideration should be given to the rigidity of the Machine/Fixture/Tool/Workpiece (MFTW) system and to the required/expected quality of the machined surface. Among the cutting data, increasing the feed directly affects the material removal rate (MRR) but due to its increased value, the roughness of the machined surfaces may deteriorate, since it primarily determines the height of the roughness peaks on the surface. Therefore, the experimental examination and estimation of the expected roughness characteristics for the machined surface, which may limit the applicable feed values, becomes increasingly important. The relevance of this topic is demonstrated by the fact that many researchers are concerned with the investigation of the roughness of milled surfaces, using different approaches and test methods.

The simplest machining process for modelling surface roughness is turning. Numerous studies deal with the simulation of theoretical roughness in turning, the most recent ones being briefly presented here. He et al. [1] introduced a systematic review of influencing factors and theoretical modelling methods of surface roughness in turning process. They found that the most important factors are the kinematic and dynamic properties of the machine tool, the geometrical parameters of the cutting tool, the properties of the workpiece material and the applied coolant. They have classified

these factors as easy and difficult to modelling and the coolant and workpiece material properties belong to the second group. Tomov et al. [2] presented a methodology for modelling and predicting the roughness shape in longitudinal turning that is utilized for both the kinematical-geometrical replication of the cutting tool geometry onto the machined surface and other cutting conditions and factors that are considered a black box—the latter include mechanical properties, thermal preparation, the material of the inserts, the positioning of the tool, the working conditions of the machine, the cutting force, the cutting temperatures, the tool wear, the vibrations of the workpiece and so forth. In the case of milling, it is more difficult to precisely map the theoretical topography due to the multi-point tool design and to the more complex kinematic conditions. Nevertheless, there are many studies on this topic too, some of which are described here in brief. Grzenda and Bustillo [3] proposed a hybrid algorithm which combines a Genetic Algorithm (GA) with Artificial Neural Networks (ANN) for the selection of major parameters for the prediction of surface roughness in high-torque face milling operations. The input data set includes the following parameters: cutting tool geometry, technological parameters and cutting phenomena. Colak et al. [4] used a Gene Expression Programming (GEP) method to predict the surface roughness of end-milled surfaces from cutting parameters such as cutting speed, feed and depth of cut. El-Sonbaty et al. [5] used Artificial Neural Network (ANN) models to analyse and predict the relationship between the cutting conditions and the corresponding fractal parameters of machined surfaces in face milling. The input parameters of the ANNs were the following: rotational speed (n), feed (f), depth of cut (ap), pre-tool flank wear and vibration level. The output parameters were the corresponding calculated fractal parameters: fractal dimension "D" and vertical scaling parameter "G." Tseng et al. [6] used design of experiments (DoE) to determine the significant factors and then fuzzy logic approach for the prediction of surface roughness. The factors considered for DoE were the depth of cut (ap), feed per tooth (fz), cutting speed (vc), tool nose radius (rε), the use of cutting fluid and the three components of the cutting force (Fx, Fy, Fz). The impact of the most important factors on the surface roughness in semi-solid AA 7075 face milling were investigated in Reference [7]. The considered factors were the spindle speed (n), feed rate (v<sup>f</sup> ) and depth of cut (ap) and it was found that the surface roughness was mostly affected by the feed rate ratio and the speed, while the impact of the depth of cut was insignificant. A surface reconstruction model is introduced in Reference [8] that is based on a methodology developed for the prediction of cutting forces in freeform milling. From the global and local geometry of the tool, initial surface and tool path, this approach allows the prediction of cutting forces, surface form and roughness directly from CAM data. A generalized mathematical model of roughness formation is introduced in Reference [9] for surfaces generated by round-nose tools. The model enables the calculation of surface roughness taking into account the tool characteristics, undeformed chip thickness, tool vibrations, tool runout (for multi-point tools) and tool wear. The developed mathematical model was verified by surfaces sculptured by face milling. A statistical model is presented in Reference [10] for surface roughness estimation in high-speed flat end milling using machining variables such as spindle speed (n), feed rate (v<sup>f</sup> ), depth of cut (ap) and width of cut (ae). In Reference [11] optimal cutting parameters were determined, resulting in minimal surface roughness in up peripheral milling of Ti-6Al-4V alloys. Theoretical roughness indexes (Ra) were determined by a model utilizing an artificial neural network. RSM and ANOVA were used to determine the input and output parameters. Miko et al. [12] used an experimental verification method to analyse the of cusp height evolution in end ball milling. The relationship which describe the effect of the direction of milling cutter motion on cusp heights has been derived from the geometrical interpretation of inclined elementary surface.

Shyha et al. [13] studied the microstructure of machined surfaces and chip formation in step-shoulder down-milling, using Ti-6Al-4V material with water-miscible vegetable oil-based coolant and lubricant. It has been found that the micro-geometry of machined surfaces largely depends on the cutting speed and the flow rate of the cutting fluid. Kilickap et al. [14] investigated the effect of cutting speed, feed rate and depth of cut on cutting force, surface roughness and tool wear when milling Ti-6242S alloy. The experimental data were compared with values determined by ANN and RSM methods.

A so-called desirability approach was applied in Reference [15] for the modelling of the following output responses by Response Surface Methodology (RMS): surface roughness (Ra), cutting force (Fc), cutting power (Pc), specific cutting force (Ks) and metal removal rate (MRR), during the face milling of the austenitic stainless steel X2CrNi18-9 with coated carbide inserts (GC4040). A full factorial design (L27) is selected for the experiments and ANOVA is used in order to evaluate the influence of the cutting parameters of cutting speed (vc), feed per tooth and depth of cut (ap) on the out-put responses. Nguyen and Hsu [16] investigated the effect of the cutting parameters on the surface roughness parameter Ra with a combination of the Taguchi method and the RSM. They have used quadratic mathematical modelling to estimate and the desirability function to minimize the Ra parameter. The effects of the insert runout errors and the variation of the feed rate on the surface roughness and the dimensional accuracy were analysed in Reference [17] in a face-milling operation using a surface roughness model. Schmitz et al. [18] investigated the effect of milling cutter teeth runout on surface topography, surface location error and stability in end milling. They pointed out that the cutter runout is an important issue in machining as commercially-available cutter bodies often exhibit significant deviations in milling insert locations in axial and radial directions; therefore, the chip load on the individual cutting teeth varies periodically. A numerical calculation model is presented in Reference [19] for predicting the profile of the surface and surface roughness values (Ra) as a function of feed (f), cutting tool geometry and tool errors. The research was focused on cutting with inserts that had a relatively large nose radius (r), and the influence of such tool errors were described in-depth as radial (εr) and axial (εa) runouts.

The investigations in many directions also point to the fact that face milling is characterized by inhomogeneity of roughness and its values differ in the different planes and surface elements of the surface. There are different roughness values measured in the direction of feed in the direction of the rotational axis of the tool and at different distances to the symmetry line. Theoretically, the highest roughness of the milled surface is in the symmetry plane. Therefore, in this study, the effect of increasing the feed is examined for the topography of the surface in the symmetry plane while analysing the change in the roughness values for single and multi-point milling operations. In the meantime, the axial setting errors of the inserts were also considered. For estimating roughness parameters, surface topography modelling is used that allows the determination and analysis of the theoretical values of 2D and 3D roughness parameters and that can take setting errors into account [20]. This article focuses on how the two- and three-dimensional surface roughness characteristics are affected when using a constant depth of cut. The considered 2D roughness parameters are the following: Ra—arithmetical average of the profile heights; Rz—average value of the absolute values of the heights of five highest profile peaks and the depths of five deepest valleys; Rq—root mean square average of the profile heights. The investigated 3D roughness parameters are the following: Sa—arithmetic mean height of the surface; Sz—maximum height of the surface; Sq—root mean squared height of the surface.

#### **2. Materials and Methods**

The aim of the conducted experiments was to investigate the effect of feed increase on the topography of the surface in face milling with one or more inserts by analysing the theoretical and real values of the 2D and 3D roughness parameters. The analysis is performed in the direction of feed in the rotational axis of the tool. The studies also take into account the axial run-outs of the inserts.

#### *2.1. Investigation Method*

The analysis of topography was performed by analysing the theoretical and real values of 2D and 3D roughness parameters and studying the relationship between the two value sets (Figure 1). The 2D and 3D surface roughness was measured on an AltiSurf 520 surface roughness tester device using a CL2 confocal chromatic probe. The data was evaluated using AltiMap software.

**Figure 1.** The applied investigation method.

#### *2.2. Experimental Conditions*

The milling tests were performed on C45 (1.0503 or AISI-1045) normalized plain carbon steel workpieces. The chemical composition of this material grade is summarized in Table 1. According to the material certification data sheet obtained from the manufacturer, the hardness of the material is 250 HB, its tensile strength is 700 Mpa, while its 0.2% proof stress (Rp0.2) is 400 N/mm<sup>2</sup> . The specimens were prepared as simple blocks with the dimensions of 100 × 50 × 50 mm<sup>3</sup> . The cutting data of the experiments and the characteristics of the machine tool and the tool can be found in Table 2.




**Table 2.** The applied technological data.

During the experiments, a single insert was used in the first stage, while in the second series four inserts were clamped into the milling head. The position of inserts (cutting edges) was checked by a Zoller Hyperion tool pre-setter device, which has a measurement accuracy of around 2 µm and display accuracy of 1 µm. As the effect of radial run-outs on the machined surface is negligible with the investigated insert geometry, they were not investigated.

For the four inserts, the axial run-out values were the following: Insert1: 0 (the deepest one), Insert2: 14 µm, Insert3: 13 µm, Insert4: 4 µm.

#### *2.3. Determination of Roughness Values by CAD Modelling*

The analyses were carried out using a method for determining the theoretical values of surface roughness measurements [21]. Its essence is the CAD modelling of the machined surface. In this process, first the geometric model of the workpiece and the tool was created and then the imprints of the tool were made on the workpiece surface according to the kinematics characteristic of the process. The points of the surface (x, y and z coordinates)—i.e., the theoretical surface—were transferred to a professional surface topography analysis software using an interface software that performs evaluations based on standard two- or three-dimensional roughness parameters to the theoretical values. The AltiMap commercial surface roughness evaluation software was used to evaluate the desired two- and three-dimensional surface roughness parameters as well as visualization of roughness profiles.

One of the great advantages of this method is that both two-dimensional roughness profiles and three-dimensional surfaces can be generated in any measuring position and direction. The novelty of the method is that it is possible to analyse the complex surface topography created by any tool and the workpiece motion combination using the applied principle and the adjustment errors can be taken into account when using multi-point tools. Another great advantage is that it is relatively easy to introduce additional factors into the model. In this research, the option of modelling axial and radial differences between individual inserts has been used.

#### *2.4. Examination of Roughness of the Machined (Milled) Surface*

Examination of the machined surface is based on the 2D and 3D images from the topography and on the values of the measurements. For the evaluation of the surfaces of milling experiments the same topography measurement system is used; therefore, the data obtained by theoretical modelling can be validated on the same basis with the measured roughness profiles and values. The two-dimensional profiles, which are recorded in the feed direction at the centreline of the milling head, are measured in accordance with ISO 4287: 1997 [22] and ISO 4288: 1998 [23] standards. Three-dimensional surfaces are measured and evaluated in accordance with ISO 25178-2: 2012 [24].

#### **3. Results**

The tests were performed with either one or four circular inserts and the roughness parameters were analysed in 2D and 3D systems. Parameters measured in the 2D system: Ra, Rq and Rz. In the 3D system, their equivalents were measured: Sa, Sq and S10z. In each case a profile chart was taken in the 2D system and a topographic graph in the 3D system.

#### *3.1. Roughness of the Modelled (Theoretical) Surface*

Input parameters of the modelling (material quality, geometrical and technological parameters, etc.) were matched to the intended machining experiments and the ranges to be examined. After the modelling steps were completed, both the 2D and 3D profiles and the previously calculated theoretical values were available. From the theoretical values obtained by modelling, Figure 2 shows the results of three feed values for the simulation performed with a single circular insert (iC = 12 mm). Based on the presented topographic graphs, it can be seen, that profiles and three-dimensional surfaces obtained by modelling show a regular periodicity and accurately characterize the increase in surface roughness by increasing the feed.

A similar conclusion can be drawn from Figure 3, where four inserts are applied, with the exception that both profiles are more irregular. The periodicity can be observed here for one tool rotation. Within a revolution, traces of the inserts vary in depth, which is the consequence of the setting error (run-out). If there were no setting errors, then the profiles theoretically would be the same for the same feed per tooth when using one and four inserts. At this time and in this sense, cutting with a single insert can be considered as machining without a setting error.

**Figure 2.** The modelled theoretical 2D (**a**) and 3D (**b**) surfaces when applying a single insert.

**Figure 3.** Modelled theoretical 2D (**a**) and 3D (**b**) surfaces when using four inserts.

#### *3.2. Roughness of Milled Surfaces*

Figures 4 and 5 show the measured roughness of the surfaces machined at the same feed but with one and four inserts respectively. If there were no insert run-outs, then the theoretical roughness would be the same in these cases. However, there are no multi-point milling tools without runout in the reality, so these should be considered in the modelling phase as well.

By comparing the theoretical and the measured profiles, it can be stated that the profiles are in good agreement and with the increasing value of the feed the theoretical profile more closely follows the real profile. This is typical for both single- and four-insert milling. In the case of four circular inserts, imprints of the successive non-coplanar inserts are clearly visible.

From the theoretical and measured values of roughness parameters, the values of Ra, Rq, Rz and Sa, Sq, S are summarized in Tables 3 and 4. In the tables bold values are used to indicate the same feed values for both cases.

**Figure 4.** Roughness profiles (**a**) and topographic images (**b**) of face milling with one insert.

**Figure 5.** Milled 2D profiles (**a**) and 3D surfaces (**b**) when four inserts were applied.


**Table 3.** Roughness values on surfaces milled by a single insert.

**Table 4.** Roughness values on surfaces milled by four inserts.


#### **4. Discussion**

The analysis should be started by comparing the roughness values of milled surfaces machined by one and four inserts. In both cases, values of all parameters increase with increasing feeds and the change is of the same nature. It was also observed, that the Ra and Rq parameters as well as the Sa and Sq ones are varying in the same way and their values are very close to each other. So, only one of them, namely the much more widely used Ra (and Sa in 3D) will be evaluated in the following. Along with the same feed per tooth, the roughness is always lower for cutting with a single insert. After machining with four inserts, the roughness of the surface has increased considerably compared to machining with a single insert. For f<sup>z</sup> = 0.5 mm, the theoretical values are 3.81 times greater for Ra, 3.31 times for Rz, 3.79 times for Sa and Sz is 3.45 times larger when machining with four inserts. Table 5 shows that the differences in measured values are even greater.

**Table 5.** The degree of increase in roughness values when changing the number of inserts.


When using feed per tooth of f<sup>z</sup> = 0.9 mm, this difference is reduced by nearly 1.5-fold and the difference between the measured and the theoretical values is smaller. This means that the accurate setting of the insert is at least as important as changing feed values. It also shows that due to smaller deviations at higher feed, roughness can be more easily predicted. It can also be stated that the greater the value of the feed per tooth, the better the correlation between theoretical and the real roughness. One explanation for this is that in the range of lower feed values the additional effects of chip removal (such as vibrations in the milling cutter, tearing of the workpiece material during the chip removal, built-up edge, defects in the homogeneity of the workpiece material, undeformed chip thickness and tool wear) and the influence of the edge radius and the roughness of the cutting edge are greater in proportion.

Analysing the complete investigation range of one and four inserts, it is also found that the difference between the theoretical and the real roughness values is smaller for one insert than when cutting with four inserts (Figures 6 and 7).

**Figure 6.** The roughness results of single-insert face milling: (**a**) 2D roughness parameters; (**b**) 3D roughness parameters.

**Figure 7.** Comparison diagrams of four-insert roughness: (**a**) 2D roughness parameters; (**b**) 3D roughness parameters.

However, it is worth noting that, especially with respect to the Ra and Sa parameters, the theoretical methods described above have provided slightly greater roughness values than those found on the measured surfaces. This is caused by the relatively large radius (related to the roughness) and here the plastic deformation is more dominant because the cutting effect (material separation) on the tool edge is insufficiently applied, thus the roughness profile is distorted related to the theoretical one. Previous experience has shown that—as it was already mentioned before—the Ra and Rq parameters vary in the same way and their values are almost the same. Therefore, using only one of them—the more general Ra—is enough during the measurements. It has also been observed that neither Ra nor Rq reflects the change of roughness with sufficient sensitivity. Rz responds much more sensitively and more accurately to roughness than Ra. The tendency in the 2D profiles seems to increase the number of deep grooves forming by increasing the feed per tooth (fz). This is unfavourable from a fatigue stress viewpoint but it is beneficial for oil storage. On the 3D profile pictures, however, there is a characteristic embossment which can be explained by the setting errors of the edges. In 3D images, the microgeometric shape of the surface can be said to be regular. A "bump" corresponds to a revolution of the tool.

When studying the data, it is apparent that the roughness parameters are considerably worse in the case of the four-insert milling tool with unchanged feed per tooth. This significant deterioration is clearly due to the run-out errors of the successive inserts. The result of axial run-out is that the inserts engage at different depths, resulting in a similar change in roughness amplitudes. By illustrating the measurement results, it can be established that when using four inserts, roughness can be increased up to seven times at low feed rates. This result is worse than expected. The main reason for this significant roughness deterioration is the setting inaccuracy of the inserts. The roughness peaks and the periodicity that correspond to a revolution of the tool can be easily tracked on the 3D topographic figures.

#### **5. Summary and Outlook**

The method of the study described in this article—simultaneously examining the roughness of the modelled surface and the machined surface—provides a good opportunity to analyse the topography of the machined surface. Based on the experiments carried out it can be stated that the accuracy of the approximation increases with the increase in feed and therefore the application of the method in the case of high-feed milling is particularly effective. Overall, it is therefore suitable for determining the theoretical values of the surface roughness and for estimating the expected roughness of the surfaces machined under the given conditions. In the case of single-insert face milling (fly-cutting), the roughness is gradually deteriorating with the increasing of the feed per tooth fz. This change is most strongly reflected by the change in roughness parameters Rz and Sz. By comparing these roughness values and the four-insert experimental results, it was found that, depending on the feed

rate—for the investigated settings—the surface had a 1.44–7.71 times worse roughness, which can be explained by the run-outs of the inserts. Commercial milling heads and commercial inserts were used in the experiments. The insert setting errors can be much higher in case of using non-standard cutter heads with special design, for example, in Reference [25]. Since tool assembly may result in a run-out that has a significant impact on the topography, it is advisable to check the run-out every time the inserts are replaced. Comparative analysis of modelled and measured roughness data showed that there is good compliance between the two values. Therefore, the roughness of the surfaces milled with various feeds can be well estimated in advance.

**Acknowledgments:** The authors greatly appreciate the support of the National Research, Development and Innovation Office—NKFIH (No. of Agreement: OTKA K 116876). The described article was carried out as part of the EFOP-3.6.1-16-00011 "Younger and Renewing University—Innovative Knowledge City—institutional development of the University of Miskolc aiming at intelligent specialisation" project implemented in the framework of the Szechenyi 2020 program. The realization of this project is supported by the European Union, co-financed by the European Social Fund.

**Author Contributions:** János Kundrák and Csaba Felh˝o conceived and designed the experiments; Csaba Felh˝o performed the experiments; János Kundrák and Csaba Felh˝o analysed the data; Csaba Felh˝o contributed reagents/materials/analysis tools; János Kundrák wrote the paper.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## *Article* **Comparative Analysis of Machining Procedures**

#### **Janos Kundrak <sup>1</sup> , Viktor Molnar 2,\* and Istvan Deszpoth <sup>1</sup>**


Received: 28 February 2018; Accepted: 22 March 2018; Published: 28 March 2018

**Abstract:** The in-depth analysis of cutting procedure is a topic of particular interest in manufacturing efficiency because in large-scale production the effective use of production capacities and the revenue-increasing capacity of production are key conditions of competitiveness. That is why the analysis of time and material removal rate, which are in close relation to production, are important in planning a machining procedure. In the paper three procedures applied in hard cutting are compared on the basis of these parameters and a new parameter, the practical parameter of material removal rate, is introduced. It measures not only the efficiency of cutting but also that of the whole machining process because it includes the values measured by time analysis as well. In the investigations the material removal rate was analyzed, first on the basis of geometrical data of the component. After that different machining procedures (hard machining) were compared for some typical surfaces. The results can give some useful indications about machining procedure selection.

**Keywords:** hard turning; grinding; combined procedure; material removal rate; operation time

#### **1. Introduction**

Machining procedures for machining industry components have developed rapidly in the last decade thanks to new, powerful machines with high load bearing capacities, the materials used in their structures, and their ever more advanced control systems. This technological development facilitates the machining of components with higher accuracy and better surface quality in shorter time. Due to the shorter machining time, more components can be produced within a given time and therefore more profit can be earned. Exact determination of time parameters directly connected to machining is critical, considering that the time decrease of one component is significant if the sum of these time values is considered over a year. This can result in a high revenue surplus in mass production. In the time of Industry 4.0, when the conception of computer controlled automated plants is being extended, automatic data collection and analysis can be utilized to help in intelligent decision-making. This means the time data of production processes are available in a shorter time and at a higher level of accuracy [1–4]. For a given technology the machining time and cost can basically be optimized by the cutting data (cutting speed, depth-of-cut, feed, etc.). Additionally, rationalization of supporting activities of a production process can decrease the times connected directly or indirectly to the machining. This means that decreases can be made in the preparation time or the time needed for material handling among the workplaces, for instance. Several plant management solutions for this purpose have evolved in recent decades, e.g., lean production, six sigma or the theory of constraints [5,6].

Beyond changes in cutting data and the rationalization of manufacturing organization, another essential factor in increasing of production efficiency is the choice of procedures or procedure versions used in machining a given component. If the same surface quality and accuracy can be achieved by two procedures using completely different technologies, the two versions [7] can be considered as perfectly replaceable alternatives from the point of view of machining [8]. In addition to that, of course, the investment volume and other costs related to the machine and equipment needs of the procedures have to be compared, like a skilled workforce or maintenance. Three machining procedures are compared in the paper for finishing hardened surfaces. Conventional grinding is considered as the base point and hard turning and a combined procedure are compared to it. Hard turning and the combined procedure are new solutions in machining but several aspects of conventional grinding are still researched [9,10] In the latter procedure hard turning and grinding are applied in one clamping of the workpiece in order to exploit the advantages of both procedures. This begins with hard turning, whose material removal efficiency is relatively high but which forms a periodic topography, which is not always suitable for requirements for in-built components. Thus, grinding is necessary after cutting with a single-point cutting tool. In this case including grinding in the combined procedure reduces the material removal efficiency compared to hard turning by only a small extent, because to remove periodic topography it is sufficient to remove only a minimal depth of material (*Rmax* scale of the hard turned surface). As this is done in one clamping with hard turning, it leads to little increase in machining time, or even a decrease [11,12].

#### **2. Method of Analysis**

The investigation was carried out for gear wheel finish machining operations. These machine parts have three geometrically distinct surfaces that must be machined. Thus, with the introduced calculation method, the analysis can be applied reliably and simply not only for the different procedures but for the different typical surfaces too. Our earlier experiments dealt with the increase in material removal efficiency achievable by changing technological data, comparing also these three procedures [13,14]. In this study the machining time (*Tm*), the operation time (*Top*), the theoretical value of material removal rate (*Qw*) and the practical material removal rate (*Qwp*) were analyzed in the three machining procedures. After that the effect of changes in geometrical data (bore length and diameter) on the practical material removal rate in machining internal cylindrical surface were analyzed. In the first step the efficiency of material removal was analyzed using the theoretical material removal rate. This parameter can be determined on the basis of the cutting and geometrical data of a component, but a more accurate picture of efficiency can be gained if a time base characterized by real production circumstances is considered.

For this purpose we define a parameter that considers these times, naming it of the practical material removal rate. This practical indicator is also suitable for characterizing production processes (machining and connecting production organization). Thus, calculations by this parameter are suitable to support more complex technological decisions. The logic of this is outlined in Figure 1.

**Figure 1.** Logic of the analysis.

#### **3. Material Removal Efficiency Measurement Parameters**

#### *3.1. Time Parameters*

A relatively inflexible feature of machining is the machining time, i.e. the time the workpiece spends in machining on a machine tool. Reduction of this is possible as long as the quality requirements can still be fulfilled. The other useful parameter is the operation time, which includes the preparation and finishing time of machining, the supplementary times, and other times of operations and processes that are directly needed to produce a component. Projecting the times beyond machining time to one workpiece can also be significant, therefore the reduction of such times is also important for the planners of production process. In our experiments we analyzed machining of the internal cylindrical surface (ICS), plain surface (PS) and shaped surface (SS)—a cone. In the analysis hard turning performed by a single-point tool (ICS, PS, SS), face grinding (PS) and in-feed grinding (ICS, SS) were compared. Calculations were performed by the following formulas. The variables of the formulas are summarized in Table 1.

Bore grinding (roughing and smoothing passes):

$$T\_m = \frac{2\mathcal{L}}{v\_{f\mathcal{L},R}} \cdot \frac{Z\_R}{a\_{e,R}} + \frac{2\mathcal{L}}{v\_{f\mathcal{L},S}} \cdot \left(\frac{Z\_S}{a\_{e,S}} + i\_{so}\right) \tag{1}$$

In-feed bore and cone grinding (roughing and smoothing passes):

$$T\_m = \frac{Z\_A}{v\_{fR,A}} + \frac{Z\_R}{v\_{fR,R}} + \frac{Z\_S}{v\_{fR,S}} + t\_{so} \tag{2}$$

Face grinding (roughing and smoothing passes):

$$T\_m = \frac{1}{n\_w} \cdot \left(\frac{Z\_R + 0.1}{a\_{p,R}} + \frac{Z\_S}{a\_{p,S}} + i\_{so}\right) \tag{3}$$

Hard turning of bore, cone and face (roughing and smoothing passes):

$$T\_m = \frac{L\prime}{f\_R n\_w} + \frac{L\prime}{f\_S n\_w} = \frac{d\_w L\prime \pi}{1000 v\_c f\_R} + \frac{d\_w L\prime \pi}{1000 v\_c f\_S} \tag{4}$$

Combined procedure (hard turning and then in-feed grinding):

$$T\_m = \frac{d\_w L \ell \pi}{1000 v\_c f\_R} + \frac{Z\_A}{v\_{fR,A}} + \frac{Z\_S}{v\_{fR,S}} + t\_{so} \tag{5}$$

Several methods exist for the calculation of operation time of machining. Here we present the formulas applied in the plant where the analyzed gears are machined.

$$T\_{op} = \frac{T\_{prop}}{n} + T\_{pice} \tag{6}$$

$$T\_{\text{piece}} = T\_{\text{base}} + T\_{\text{suppl}} \tag{7}$$

$$T\_{base} = T\_m + T\_{mamp} \tag{8}$$

$$T\_{suppl} = kT\_{base} \tag{9}$$

$$T\_{op} = \frac{T\_{prop}}{n} + (1+k)\left(T\_m + T\_{manip}\right) \tag{10}$$

where *Top* is operation time, *Tprep* time of preparation and finish, *Tpiece* piece time, *Tbase* base time, *Tsuppl* supplementary time, *T<sup>m</sup>* machining time, *Tmanip* workpiece manipulation time, and *k* is a coefficient whose value here is 0.2.


**Table 1.** Geometrical and cutting data applied in the formulas of machining time.

#### *3.2. Material Removal Rate*

The theoretical material removal rate (*Qw*) defines what material volume can be removed from the surface in a time unit. It does not consider the time of machining during which the workpiece is not physically cut (e.g., manipulation). That is why it only shows the effect of change of technological data. This parameter can be calculated in the different procedures. Since it does not include all factors (e.g., sparking out, tool overrun), it cannot be considered as a sufficiently exact parameter in comparing different procedures. The calculation method of the theoretical parameter is summarized in Table 2.

**Table 2.** Calculation of the theoretical parameter of the material removal rate in different procedures.


In the calculation of the practical parameter the removed material volume is divided by a certain time data (*Tx*) characterizing the production of a surface element/surface/component. This value will be the specific material volume, i.e. the parameter measures the material removal rate while considering the time components of machining. If the preferred technological decision factor is the specific material volume removed while the workpiece is clamped, the machining time is considered. If other supplementary times significantly influence the production, the piece time is considered, and so on. In our analyses operation time was included in the calculations. Since the operation time is what expresses the real time consumption, we can also draw conclusions on the efficiency of the whole production process. The practical material removal rates calculated by the operation time are given by Equations (11)–(13).

Bore:

$$Q\_{wp,op} = \frac{\text{Ld}\pi\text{Z}}{60T\_{\text{x}}}\tag{11}$$

Face:

$$Q\_{wp\,\rho p} = \frac{L(d-L)\pi Z}{60T\_{\text{x}}} \tag{12}$$

Cone:

$$Q\_{wp,op} = \frac{L \cos a (d - L \text{tga}) \pi Z}{2 \cdot 60 T\_x} \tag{13}$$

where *L* is machined bore length, *d* workpiece diameter, *Z* allowance, *α* half cone-angle, and *T<sup>x</sup>* considered time.

The rate of theoretical to practical parameters shows the rate of extra time necessary for machining compared to the machining time. We note that the surface rate is a similar parameter. That differs from the material removal rate in showing the specific area of removed surface. The value of the parameter is equal to that of the material removal rate if material removal is performed in one pass.

#### **4. Basic Data of Comparison Analyses**

In the study calculations were made for the machining of an analyzed gear wheel. The component is comprised of one plain surface, one conical surface and one internal cylindrical surface to be machined. The material of the component was 16MnCr5 (HRC 62). Its geometrical and cutting data are summarized in Figure 2 and Table 3, where the symbols are:


**Figure 2.** Geometrical and cutting data.

#### **Table 3.**Cutting data.


#### **5. Results and Discussion**

#### *5.1. Theoretical Material Removal Rate*

The theoretical values of the material removal rate are summarized in Table 4. Machining of the typical surfaces of the component cannot be compared directly with the theoretical values but certain conclusions can be made. For example the bore (S2) can be machined more effectively by hard turning (P2) than by grinding (P1) because 6.75 > 3.32 and 0.72 > 0.3 in the same time. Concerning the machining of the face (S1) the two procedures cannot be compared because in grinding the material removal is carried out in two passes and in hard turning in only one pass.


**Table 4.** Values of the theoretical material removal rate (*Qw*).

#### *5.2. Practical Parameter of Material Removal*

In Table 5 the machining time, the operation time and the practical values of material removal rate (*Qwp,op*) are summarized for a given component. The rate of machining time to operation time was analyzed and is illustrated in Figure 3a. Operation time is considered as 100 percent. While in grinding the operation time is 1.56 times higher than the machining time, this value is 1.7 in hard turning and 2.57 in the combined procedure. The arcs representing the procedures also give the absolute time values. This figure highlights that there is a relatively large difference between the machining and the operation times and that is why it is worth focusing on the role of operation time in efficiency analyses. The values of the practical material removal parameter are given in Figure 3b. The values of grinding and the combined procedure are lower than those of hard turning for the analyzed component. In the figure it can be seen that despite this great difference the *Qwp,op* value of the combined procedure exceeds that of grinding. It is noted that in selection of the procedures not only the machining efficiency but also the costs of the procedures have to be calculated (e.g., machine tool investment).

**Table 5.** Machining time, operation time and *Qwp,op*.


**Figure 3.** (**a**) rate of machining times within operation time (*Top* = 100%); (**b**) practical material removal rates of the three procedures.

#### *5.3. Effect of Bore Length and Diameter*

The practical material removal rates of the three procedures are summarized in Figures 4–6.

In Figure 7 the practical parameters of hard turning and the combined procedure are compared to those of grinding for different bore diameters and bore lengths when machining internal cylindrical surfaces, since this type of surfaces is hard to machine.

**Figure 4.** *Qwp,op* values of grinding.

**Figure 5.** *Qwp,op* values of hard turning.

**Figure 6.** *Qwp,op* values of the combined procedure.

**Figure 7.** Rates of material removal rates of hard turning (**a**) and the combined procedure (**b**) compared to grinding.

In both procedures the difference is clear, namely the value of the practical material removal rate for hard turning exceeds that of the combined procedure but the value of the combined procedure is considerably better than that of grinding. Although the practical material removal rate is the highest in hard turning, the operation circumstances of the component can require the application of the combined procedure. In Figures 5 and 6 it can be seen that with the increase of both the diameter and the bore length the practical value of material removal rates increases. In hard turning when the bore length and the diameter are between 20 and 50 mm, the *Qwp,op* values are between 4.48 and 17.47 mm3/s. In the combined procedure these values are between 2.33 and 13.12 mm3/s. In Figure 7 the rates of *Qwp,op* compared to that of grinding (P1) are given for the introduced procedures (P2, P3). In hard turning the values of practical material removal rate are 2.05–3.99 times higher than those of the grinding. In the combined procedure these values are between 1.25 and 2.36. Application of the practical material removal rate analysis for geometrical data can supports the construction design of components.

#### **6. Conclusions**

Through analyzing the material removal rate the efficiency of machining procedures was calculated. This parameter characterizes the efficiency of the different machining procedures well but it does not facilitate the comparison of different procedures or procedure versions. To compare the procedures the practical parameter was analyzed. The *Qwp,op* value of grinding is 23 percent that of hard turning for the analyzed gear wheels. The practical material removal rate of the combined procedure is 47 percent that of hard turning. That is why the combined procedure is expedient to substitute for grinding if it is necessary to form a random topography. The practical value of the material removal rate *Qwp,op* is suitable for technological decision support within certain limits. It allows more analysis possibilities than the theoretical value because it provides more information than simple time data. However, it does not consider the direct and indirect costs related to machining, which can modify the

decision made for the procedure choice. In the analysis of bore length and diameter, the increase of these two variables results in an increase in the practical material removal rate in case of fixed cutting data. In our tests both geometrical data were varied between 20 and 50 mm. In increasing both the bore length and bore diameter the *Qwp,op* increases 1.83–2.13-fold in hard turning. For smaller diameters and bore lengths the extent of increase is higher if only one parameter is changed at one time. In the combined procedure the *Qwp,op* value increases 2.32-2.42-fold when the diameter or the length are increased. This analysis can be useful in construction design of machined components. In summary, the method introduced here can be applied in the comparison of three separate aspects: different machining procedures; machining of components that contain different types of surfaces and identical types of surfaces with different geometrical values. These comparisons provide information not only about the efficiency of the applied procedures but also about the organization efficiency of production.

**Acknowledgments:** Project no. NKFI-125117 has been implemented with the support provided from the National Research, Development and Innovation Fund of Hungary, financed under the K\_17 funding scheme.

**Author Contributions:** Janos Kundrak and Viktor Molnar conceived and designed the experiments; Viktor Molnar and Istvan Deszpoth performed the experiments; Istvan Deszpoth and Janos Kundrak analyzed the data; Janos Kundrak and Viktor Molnar wrote the paper.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## *Article* **Precision CNC Machining of Femoral Component of Knee Implant: A Case Study**

**Angelos P. Markopoulos \* ID , Nikolaos I. Galanis ID , Nikolaos E. Karkalos and Dimitrios E. Manolakos**

Section of Manufacturing Technology, School of Mechanical Engineering, National Technical University of Athens, Heroon Politechniou 9, 15780 Athens, Greece; ngalanis@central.ntua.gr (N.I.G);

nkark@mail.ntua.gr (N.E.K.); manolako@central.ntua.gr (D.E.M.) **\*** Correspondence: amark@mail.ntua.gr; Tel.: +30-210-772-4299

Received: 13 February 2018; Accepted: 28 February 2018; Published: 2 March 2018

**Abstract:** The design and manufacturing of medical implants constitutes an active and highly important field of research, both from a medical and an engineering point of view. From an engineering aspect, the machining of implants is undoubtedly challenging due to the complex shape of the implants and the associated restrictive geometrical and dimensional requirements. Furthermore, it is crucial to ensure that the surface integrity of the implant is not severely affected, in order for the implant to be durable and wear resistant. In the present work, the methodology of designing and machining the femoral component of total knee replacement using a 3-axis Computer Numerical Control (CNC) machine is presented, and then, the results of the machining process, as well as the evaluation of implant surface quality are discussed in detail. At first, a preliminary design of the components of the knee implant is performed and the planning for the production of the femoral component is implemented in Computed Aided Manufacturing (CAM) software. Then, three femoral components are machined under different process conditions and the surface quality is evaluated in terms of surface roughness. Analysis of the results indicated the appropriate process conditions for each part of the implant surface and led to the determination of optimum machining strategy for the finishing stage.

**Keywords:** femoral component; medical implant; total knee replacement; CNC machining; implant machining; sculptured surface; bio-engineering; surface quality

#### **1. Introduction**

Partial or total replacement of a human knee with an implant can be achieved by a common surgical procedure, namely knee arthroplasty or knee replacement. Only in United States, over 500,000 knee replacement surgeries are reported each year [1], which are mostly for patients between 50 and 80 years old. One of the main reasons for the popularity of this type of surgery is the considerably high percentage of artificial knees still functioning even 20 years after the surgery. During this surgical operation, it is intended to replace damaged or worn components of the knee joint with artificially produced components or implants in order to facilitate proper knee motion of the patients and reduce disability problems and severe pain caused by joint diseases, usually osteoarthritis or rheumatoid arthritis. Apart from patients with advanced osteoarthritis, knee replacement may be suggested for younger patients with damage in the knee joint or bone or some type of deformity. Partial knee replacement is suggested in cases when damage is located only in a specific compartment of the knee. The specific purpose of this type of surgery is essentially to cap the end parts of the bones of the knee joint as well as the kneecap, by means of artificial components. More specifically, during knee replacement surgery, the main knee parts that are replaced are pertinent to the femoral and tibial surfaces near the knee

*Machines* **2018**, *6*, 10

joint as well as a part of the patella. For the components of the replacement implant, suitable metals or non-metallic materials are chosen and properly machined in order to resemble the natural shape of the knee as much as possible and allow for proper joint motion, resistance to wear and corrosion and biocompatibility. The machined components should adhere to highly restrictive regulations and exhibit considerable durability [2–6].

Knee replacement surgery and the design of implant components is currently considerably important and constitutes a part of ongoing research in the medical and engineering scientific communities. However, the first reported attempts to create and use artificial knee components in an actual knee replacement surgery date back to the end of the 19th century, when Gluck created the first artificial joint by ivory [7]. From that period, research is concentrated on the improvement of knee replacement components with a view to decrease considerably their failure rate and replicate proper joint motion as close as possible to the actual. In the 1950s, several new designs, such as the Waldius [8] and GUEPAR [9] knee implants were created; their basic characteristic was the bending-extending capabilities of the joint. During the next two decades, significant advances regarding the knee implant design were observed but still, artificial knee designs such as Geomedic [10] and Geometric [11] suffered from the inability to perform rotational motion and other types of knees such as Marmor [12] and Gunston [13] were exhibiting premature failure due to high contact stresses and material overloading. The ICLH (Imperial College-London Hospital) knee implant design, which was introduced by Freeman and Swanson in 1971 [14], exhibited a lower deformation and wear rate. Other designs presented during the 1970s include Total Condylar and Townley [15], which involved also the kneecap (patella) replacement and Oxford [16] and New Jersey LCS (Low Contact Stress) [17] knee designs, which used mobile bearings. In particular, the latter designs proved to possess capabilities, such as greater mobility and improved compatibility as they employed a secondary moving support surface.

Later, during the 1990s, designs employing moving bearings were also developed which were further enhanced by the use of newly developed materials and alloys and assistive guidelines from previous designs. A representative example of knee implant designs of this period is the B-P (Buechel-Pappas) Mark V which was created from Ti alloy with TiN coating or alternatively, from Co–Cr alloy in order to improve its wear resistance [18]. During this period, Walker et al. [19] introduced a new knee simulating machine with a view to test the kinematics of total knee implants, as well as the wear of these implants. Their machine was able to perform in a more realistic way than its predecessor models, which exhibited several disadvantages such as reduced accuracy in representing the forces exerted on various components of the knee implant or inadequate constraints. More recently, Harrysson et al. [20] proposed a new design method for knee implants, based on patient-specific Computed Tomography (CT) data which can provide among other, more accurate replication of the actual geometries of knee components and the reduced possibility of implant loosening. Lee et al. [21] also employed CT data in order to design the femoral component and afterwards, they created femoral components using rapid prototyping and Computer Numerical Control (CNC) machining methods. Finally, Song et al. [22] presented a thorough work related to the rapid manufacturing of femoral component using Selective Laser Melting (SLM) method which can provide a reliable way to produce customized implants. Results from all the aforementioned works can lead to useful guidelines regarding the design of knee implants. For example, it is crucial to avoid including redundant kinematic constraints for the knee implant components, to enable normal knee motion, to include moving bearings to the design, and to plan the rather copious machining process of the geometrically complex implant in an effective way.

In the present work, the methodology of designing and machining of the femoral component of total knee replacement using a 3-axis Computer Numerical Control (CNC) machining center is presented in several steps and is discussed in detail. After the machining processes take place, an evaluation of machined surface is performed by means of surface roughness measurements in order to determine the optimum process parameters for the machining of various parts of the implant. The present work is related to previous works by the members of the same scientific group, including

studies on machining of femoral heads [23,24] and extends the preliminary work on the machining of knee implant, as reported in [25].

#### **2. Design of the Implant Geometry and Machining Processes**

#### *2.1. Design of the Knee Implant Components*

Despite the fact that the main focus of the present work is set on the design and machining process of the femoral component, it is considered to be crucial to study the design of the whole knee implant at the initial stage in order to determine the appropriate dimensions of this part in relation to the total knee assembly and then study the femoral component separately. The design of the knee implant components was conducted by means of Solidworks TM software in which both the design and manufacturing of the knee implant is able to be studied. As with every engineering design, design constraints should be properly defined in order for the implant to comply with the desired shape of implant parts and allow for normal motion of the implant components so as to provide a satisfying replacement of the damaged knee.

The design of the knee implant parts complies with the international standard ISO 7207-1 [26], in which the geometry of both total and partial knee implant components is defined in detail. More specifically, for the present work, it is assumed that the total knee implant, which is designed, corresponds to the left knee of a male human with constrained rotational movement. In Figure 1, a schematic of the bones near the knee joint is presented, along with a schematic indicating the position of the implant after the surgery. The knee implant components, which will be designed as an assembly, include the femoral component, the tibial component, the tibial articulating surface, and the patellar component, as can be seen in Figure 2.

**Figure 1.** Bones around the knee joint and position of knee replacement after the knee arthroplasty.

**Figure 2.** Parts of the designed knee replacement assembly.

The design of the femoral component contains two different steps, namely the design of its outer and inner surface. This approach is required due to the considerably different geometries of the outer and inner surfaces. More specifically, the outer surface is essentially a sculptured surface that is composed of various curved areas, as this shape is necessary for the contact between the femoral component and the tibial and patellar components of the implant and facilitates normal knee motion. In the outer surface, a groove is also formed, resembling the trochlear groove of the actual human femur bone. As for the design of the inner surface, it is required that it should be strongly fixed on the bone; it is usually achieved by the use of acrylic cement between the implant and the bone during the surgery. The fixation of this surface to the bone is further enhanced by two conical stems on the inner surface, intended to be inserted into two holes in the bone. Although the design of the inner surface is generally simpler, there is an important restriction regarding the thickness of the inner surfaces, as they should have the least possible thickness in order to reduce the need of material removal from the bone during the insertion of the implant.

The design of the tibial component includes the design of two different structural elements, a stem and a platform. The stem is intended to aid to the fixation of the tibial component to the tibia and the platform is essential for the connection of the tibial component to the tibial articulating surface. For the stem, it is required that its thickness is large enough to withstand the relatively high forces will be exerted on it whereas the dimensions of the platform, namely its width and depth should closely match the actual dimensions of the upper part of human tibia. As for the design of the tibial articulating surface it is subjected to two main requirements, namely to withstand the loading from the femur and implement the fixation on the tibial component. In order to fulfill these requirements, the size of the contact surface with the tibial components is designed sufficiently large so as to protect the joint from receiving excessive loading and enable normal knee motion.

Finally, the design of the patellar component aims at the facilitation of the movement of the patella on the trochlear groove of the femur. Thus, a dome-like shape for the lower surface of the patellar component is adopted in order to be able to assist to the sliding movement of this component in the trochlear groove. As for the upper surface of the patellar component, its geometrical shape is properly adjusted so that it provides strong fixation on the patella bone.

#### *2.2. Design of the Machining Process of the Femoral Component*

After the components of the total knee implant were carefully designed according to the international standards and relevant requirements, the focus is set on the machining process of the femoral component of the knee implant. The design of the machining process of this component, which includes complex geometrical shapes, is essential to be conducted on a specialized Computer Aided Manufacturing (CAM) software, such as SolidCAM, which can be accessed through SolidWorks software.

Machining of complex, "sculptured" surfaces is important in various industries such as automotive, aerospace and optical components industry, as well as bioengineering. One of the main challenges concerning the machining of such surfaces is the reduction of machining time, as it is considerably difficult to achieve the required dimensional accuracy and surface quality. Apart from the use of cutting tools with special geometry, the machining strategy needs to be carefully planned in order to achieve the desired geometrical features and suitable process parameters are required to be determined as well. Thus, all of these tasks need to be appropriately addressed by the use of CAM software in order to perform the machining process of the femoral component.

CAM software are specialized to assist in various stages of product manufacturing. Most commonly, they involve the use of an integrated Computer Aided Design (CAD) editor or, such as the case of SolidCAM software, are themselves integrated in the framework of a CAD software and their purpose is eventually to produce the code (G-Code) in order to control CNC machine tools for manufacturing the desired parts. Using this type of software, details about the machining process such as the definition of appropriate cutting tools for the machining process and their characteristics, the desired operations on the workpiece, such as hole drilling, contour, etc., process parameters during the various stages of the

process and machining strategies can be input at first. Then, G-code can be generated, in respect to the type of CNC machine used, given that an appropriate post-processor exists. Furthermore, a simulation of the intended machining operations can be performed in order to verify that the machining will be performed safely and according to the desired goals or detect possible mistakes and perform the necessary adjustments.

The basic challenge which exists in the present work is that, due to the fact that the outer and inner surface of the femoral component contain sculptured surfaces, mounting of the workpiece on the machining center bed is difficult to be performed. For that reason, it is considered more appropriate to perform the machining process in two separate phases; during the first phase, it is intended to create the internal surface of the femoral component and during the second phase, the workpiece will be reverted, and then, machining of the outer surface will occur. Thus, in the CAM software, different coordinate systems will be defined for the two stages as well as different Stock and Target materials.

#### 2.2.1. First Phase of Machining

During the first phase of machining, the emphasis is set on the creation of the inner surfaces. This phase constitutes the main material removal phase and the cutting tools will remove material up to a specific height until the second phase will take place. For the first phase, four cutting tools, both flat and ball end, will be employed, as can be also seen in Table 1. It is important to note that, in the early stages of the machining process, tools with flat end and a larger diameter are preferred in order to remove large bulk of material quickly (roughing stage) without requirements for high accuracy of produced shape. However, at the final stages of the machining process, cutting tools with smaller diameter and ball end are selected in order to render appropriately the final sculptured surface according to the desired dimensional and geometrical requirements (finishing stage). The initial dimensions of the cylindrical workpiece are: 50 mm diameter and 39.3 mm height. The workpiece material, which was chosen is stainless steel 316L, which is appropriate for the femoral component [27,28].


**Table 1.** Characteristics of the cutting tools employed in the present work.

In order to achieve the creation of the desired shape of the inner surface of the femoral component, the 16 mm diameter cutting tool was first employed in order to reduce the initial height of the workpiece at several passes, as can be seen in Figure 3a. Afterwards, a cavity was formed in the region where the inner surfaces of the implant will later be created. Using the same cutting tool, a contour cutting process was also performed in order to create the front and back sculptured surfaces. The next stage, as depicted in Figure 3b, involved the use of 6 mm flat end cutting tool in order to continue the contour cutting process with the rendering of more features of the implant surface, and then, the 6 mm ball end tool was employed to create the final shape of the front sculptured surface. Finally, the finishing stage was implemented by using the 4 mm diameter cutting tool both for the front and the back sculptured surfaces, as can be seen in Figure 3c.

#### 2.2.2. Second Phase of Machining

The second phase of machining is related to the machining of the outer surface of the femoral component. For this phase of machining, three cutting tools are selected, both the flat and ball end. Initially, as can be seen in Figure 4a,b, a 16 mm flat end cutting tool is used to perform contour cutting at a fixed height at each pass, and then, a 6 mm flat end cutting tool performed cutting with fixed y coordinate at each pass (roughing phase). In the end, the finishing process was implemented using a 4

mm ball end cutting tool using the same strategy as with the 6 mm diameter cutting tool, as can be seen in Figure 4c.

**Figure 3.** Snapshots from the simulation of the first machining stage: (**a**) Machining of the front surface of the femoral component using 16 mm diameter tool; (**b**) Machining of the back surface of the femoral component using 6 mm diameter tool; and, (**c**) Machining of inner surfaces of the femoral component using 4 mm ball end tool.

#### *2.3. Initial Machining Test*

After the definition of machining operations and production of G-code in the CAM software and after the simulation of the machining processes was successfully finished, it was decided that a test run, replicating the machining process in the actual CNC machining, was necessary before the final machining process in order to ensure that the generated G-code was producing an accurate and reliable outcome and verify the simulation results. Furthermore, it is important to test the behavior of the cutting tools during the machining process in order to choose the appropriate process parameters that lead to avoidance of chattering, as it is impossible to be determined from the simulation in the CAM software. The test run was performed on a cylindrical bulk of polymer material, and was concluded successfully, indicating that the actual machining process can be performed without problems.

**Figure 4.** Snapshots from the simulation of the second machining stage: (**a**) Roughing stage of the second machining phase using 16 mm diameter tool; (**b**) Machining of sculptured surface of the femoral component using 6 mm ball end tool; and, (**c**) Finishing stage of the second machining phase, using 4 mm diameter ball end tool.

#### **3. Machining of the Implant and Measurement of Surface Roughness**

#### *3.1. Machining Process of the Implant*

After the various stages of the machining process were designed in the CAM software and successfully verified by the test run, the setup of the 3-axis CNC machining center was performed. As the initial bulk is a cylindrical workpiece, it was fixed on the machine with a chuck, as depicted in Figure 5.

After the cutting tools were selected and the necessary setup was performed on the CNC machine, the first phase of the machining process took place. The first phase was expected to last for a relatively long time, as it is required to select small depths of cut and low cutting speed when machining stainless steel workpieces. After the machining process was completed, the inner surface of the implant was created, as can be seen in Figure 6. It is worth noting that the existence of several markings on the produced surfaces was observed, created by the contact of the upper part of the cutting tool with these surfaces when material removal was performed on the lower parts of the inner surface of the implant.

**Figure 5.** Clamping of workpiece on the machining center bed.

**Figure 6.** Views of the workpiece after the first machining stage.

During the second phase of the machining process the workpiece is mounted on the machine tool bed after it is reverted, by using a specially designed platform, as can be seen in Figure 7. The use of this platform is required as it is impossible to fix otherwise the workpiece appropriately on the machine tool. In order to ensure the stability of fixation of the implant, it is required that the internal surfaces of the workpiece are properly aligned on the platform surfaces, parallel to the machining center bed. After the implant is mounted on the platform and fixation is properly performed by two screws, the platform is clamped on a chuck.

**Figure 7.** The platform for mounting the workpiece on the machining center bed for the second machining stage.

When the aforementioned procedure for the machining of the outer surface of the implant is completed, as can be seen in Figure 8. This process was repeated two times with different process parameters at various zones of the implant during finishing stage, in order to investigate the effect of process parameters on surface quality. The process parameters that were employed for the machining of all three implant during the finishing stage are presented in Table 2.

**Figure 8.** Views of the implant after the second machining stage.


**Table 2.** Machining parameters values for each zone and each component.

#### *3.2. Surface Quality Evaluation*

μm and accuracy of parameters is given as 2% of reading plus least significant digit in μm. After the machining process of the femoral component is completed, it is considered important to evaluate the quality of the produced surfaces, as it is directly connected to the tribological behavior and wear resistance of the implant. Inappropriate machining conditions, leading to excessive surface roughness, can prevent not only the adequate performance and reliability of the implant but also its life cycle [29]. Furthermore sufficient surface quality after machining of the implant reduces the need for further processes, such as polishing. For that reason, surface roughness measurements were conducted on the three different implants with a view to determine the optimum process parameters for the finishing stage of the implant machining process. Due to the fact that the implant contains sculptured surfaces, the measurement of the surface roughness with a profilometer is a demanding process and special care has to be paid for the positioning of the measuring device and also for correct sampling length (Ln) and cut-off length (Lc) values. In the present work, a Surtronic 3+ Taylor Hobson profilometer was employed and a sampling length (Ln) of 2.4 mm was selected, as well as a cut-off length (Lc) of 0.8 mm. As per the manufacturer manual, the used profilometer has a resolution of 0.01 µm and accuracy of parameters is given as 2% of reading plus least significant digit in µm. Surface roughness was performed in each of the five zones presented in Figure 9, both in the left and the right side (or inner and outer side) of the upper surface of the implant (the region of the lateral and medial condyles, respectively) and the measurements are repeated three times. In the following analysis the lateral and medial condyles are referred to as inner and outer sides, respectively.

**Figure 9.** Zones of surface roughness measurement.

The evaluation of surface roughness was performed by Ra, Rq, Rt, which represent the arithmetic average surface roughness, root mean squared roughness, and maximum height of the profile, respectively. Especially, Ra is the most popular indicator of surface roughness in industrial practice until today. As for the first femoral component, which was machined with the same conditions in every zone, it can be seen from Figure 10a,b, that there are some differences in the Ra values in the different zones.

**Figure 10.** Surface roughness measurement results for the first femoral component for (**a**) outer and (**b**) inner side.

– μm – μm These differences can be directly attributed to the different geometry of each zone, as zones 1, 2, and 5 are more curved, whereas region 3 and 4 are almost flat. Thus, it is observed that the finishing

process is more effective in the flat regions with values of Ra of about 6–7 µm, whereas Ra exceeds 8 µm in the other regions. Similar trends can be observed in the case of Rq and Rt measurement with the exception of zone 1, which has a relatively low value of Rt when compared to the other zones.

A comparison of surface roughness measurements between the different components, machined with different conditions, can reveal the effect of process parameters to the surface quality of each zone of the femoral component. For zone 1, comparison between results depicted in Figures 10–12 show that, a reduction of feed rate resulted in an increase of Ra and subsequent reduction of both feed rate and spindle speed resulted in a further small increase of Ra. For zone 2, the change of process parameters resulted in almost unchanged values of Ra. For zone 3, a decrease of feed rate resulted in a considerable decrease of average surface roughness, whereas a decrease of spindle speed resulted in an increase of Ra. For zone 4, a decrease of spindle speed resulted in an increase of Ra, whereas a further increase of spindle speed with a slight decrease of feed rate led to a slight decrease of Ra. Finally, for zone 5, it was observed that the reduction of both feed rate and spindle speed resulted initially in higher Ra and a subsequent reduction of both the parameters resulted in slightly lower Ra. –

**Figure 11.** Surface roughness measurement results for the second femoral component for (**a**) outer and (**b**) inner side.

As usually, the effect of feed rate on Ra is that a decrease of feed rate leads to a decrease of Ra and also an increase of spindle speed is beneficial to the surface quality, the results for some of the five zones seem somewhat unexpected. However, these discrepancies can be attributed to the different curvature of each zone; results consistent with the aforementioned behavior are exhibited in zones which are fairly flat, such as zones 3 and 4, but in zones that are more curved different trends exist. The same trends are observed in the case of Rq and Rt measurements on the three femoral components.

The difference between measurements in the inner and the outer side of the upper surface of the femoral component was also investigated during the analysis of surface roughness of the implants. Regarding Ra values, it was found that, with the exception of one zone for the 2nd and 3rd component and two zones for the 1st, the general trend of variations of Ra in respect to different geometry and process parameters was similar. Furthermore, it was observed Ra values were larger in the vast majority of measurements in the outer side rather than the inner side.

Finally, the previous analysis allowed for the determination of optimum process parameters, namely feed rate and spindle speed for the finishing stage. Within the examined range of process parameters values the optimum values for each zone regarding Ra, were observed in the first component for zones 1, 4, 5, and for the second component for zones 2 and 3. Similar conclusions were drawn when examining the values of Rq and Rt.

**Figure 12.** Surface roughness measurement results for the third femoral component for (**a**) outer and (**b**) inner side.

#### **4. Conclusions**

In the present work, various stages of manufacturing the femoral component of knee prosthesis are presented, including the design of geometry and machining operations, as well as the actual machining process and the subsequent determination of surface quality.

The specific requirements for the design of the femoral component in respect to the total knee replacement assembly were determined, and particular situations that require special attention during machining were identified. These particularities were properly taken into consideration during the design of the required machining operations using SolidCAM software.

Furthermore, after machining three different femoral components with variable process parameters values during the finishing stage several important conclusions were drawn. Especially, surface roughness was shown to vary considerably with changes in the surface curvature and the

effect of process parameters to the surface quality was also shown to be dependent of the curvature of the surface. Finally, the optimum parameters, namely feed rate and spindle speed, for the reduction of surface roughness for various zones of the femoral implant were determined.

**Author Contributions:** Nikolaos I. Galanis and Dimitrios E. Manolakos conceived and designed the experiments; Nikolaos I. Galanis performed the experiments; Nikolaos I. Galanis and Nikolaos E. Karkalos analyzed the data; Angelos P. Markopoulos contributed materials and analysis tools; Nikolaos E. Karkalos and Angelos P. Markopoulos wrote the paper.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## *Article* **The Dimensional Precision of Forming Windows in Bearing Cages**

#### **Marius Rîpanu, Gheorghe Nagî¸t, Lauren¸tiu Slătineanu and Oana Dodun \* ID**

Department of Machine Manufacturing Technology, "Gheorghe Asachi" Technical University of Ias,i, Blvd. D. Mangeron, 59 A, Ias,i 700050, Romania; ripanumariusionut@yahoo.com (M.R.); nagit@tcm.tuiasi.ro (G.N.); slati@tcm.tuiasi.ro (L.S.)

**\*** Correspondence: oanad@tcm.tuiasi.ro; Tel.: +40-747-144-604

Received: 5 February 2018; Accepted: 24 February 2018; Published: 1 March 2018

**Abstract:** In the case of double row tapered roller bearings, the windows found in bearing cages could be obtained using various machining methods. Some such machining methods are based on the cold forming process. There are many factors that are able to affect the machining accuracy of the windows that exist in bearing cages. On the dimensional precision of windows, the clearance between punches and die, the work stroke length, and the workpiece thickness could exert influence. To evaluate this influence, experimental research was developed taking into consideration the height and the length of the cage window and the distance between the contact elements of the cage. By mathematical processing of the experimental results, empirical mathematical models were determined and analyzed. The empirical models highlighted the intensity of the influence exerted by the considered forming process input factors on the dimensional precision of the windows obtained in bearing cages.

**Keywords:** double row tapered roller bearing; bearing cage; window forming; dimensional precision; clearance between punch and die; work stroke length; workpiece thickness; mathematical empirical model

#### **1. Introduction**

The rolling bearings are machine elements usually intended to support parts found in a rotation movement. Essentially, they include *rolling elements* and *rings*. To separate the rolling elements, *bearing cages* could be used, as sometimes *sealing elements* are provided to prevent the penetration of foreign objects or substances between bearing elements found in a relative movement to one another.

A category of roller bearings that are used in difficult service conditions, when there is the necessity of compensating the eventual deviations of the coaxiality of supporting bearings or the shaft bending, are the double row tapered roller bearings (Figure 1a). These roller bearings are characterized by a certain self-regulation on the raceway of the outer ring.

The bearing cages presented in the bearings have generally the role of preventing the contact between rolling elements (rolls or balls). There are various methods of manufacturing the bearing cages, considering their shapes and materials. Thus, for example, in the case of cylindrical rolls, the bearing cages could be achieved essentially by successive processes of drawing, perforating the central hole, and cutting the windows. As workpieces, metallic plates that have circular shapes could be taken into consideration before drawing.

**Figure 1.** (**a**) Double row tapered roller bearing; (**b**) details of bearing cage.

The main requirements for bearing cages refer to their accuracy, their surface roughness, and material resistance to wear processes.

If the cage machining accuracy is analyzed, in addition to the accuracy of the overall dimensions, the precision of the dimensions corresponding to the windows in which the rolling elements could be placed is important. The concept of *dimensional precision* refers to the deviation of the real dimensions from their nominal values.

Over the years, the results of certain research concerning the accuracy and the surface state of bearing cages or generally of the windows obtained in sheet type workpieces by forming methods were published.

Thus, Kibe et al. considered that the general position of the punch in the die could exert a significant influence on the machining accuracy in the case of shearing processes [1]. They proposed a method that was able to increase the precision of measuring and adjusting the position of the punching tool, especially when processing metallic thin sheets. The experiments were achieved on workpieces made of phosphor bronze and aluminum that had a thickness of 0.2 mm. The researchers highlighted the influence exerted by the clearance between punch and die on the machining accuracy, taking into consideration the shape of the cross-section and the diameter of the hole obtained by punching.

Subsequently, Kibe and Mitsui investigated the influence exerted by the misalignment of the punch and die positions on the cross-section diameter of the hole and on the out of the roundness in the case of punching applied to workpieces made of phosphor bronze [2].

Istiawan and Mahardika studied the influence exerted by the clearance and the punch speed on the surface quality evaluated by means of burnish area, fracture, and burr zone, in the case of punching a hole with the diameter of 800 µm in a workpiece with a thickness of 300 µm [3]. They noticed the low influence exerted by the punch speed on the surface quality.

Ardeshana and Mehta took into consideration the problem of designing a punch and a die for manufacturing of a bearing cage specific to a taper roller bearing [4]. They considered that the simultaneous cutting of all the windows in the bearing cage could contribute significantly to the decrease of the production time, and thus to the increase of the productivity.

Zhao et al. considered that an improvement of the precision manufacturing of bearing cages by the stamping process could be possible by using the reliability theory to adequately establish the thickness of the plate used as the workpiece in the process of the manufacture of the bearing cage [5]. They modeled the behavior of the bearing cage during the punching process by using the ANSYS finite element analysis.

Various solutions were also considered in patents that referred to the producing windows in roller bearings cages by distinct manufacturing processes [6–10]. Within these patents, only the processes and equipment for obtaining windows in bearing cages were discussed, without offering details

about the dimensional precision of the cages' windows that were obtainable by such manufacturing processes. Even the roller bearings are not complex systems; they could be incorporated in such systems, and principles corresponding to the mechanical systems could be taken into consideration when analyzing the roller bearing and its manufacture [11–15].

The main aim of the research presented in this work was to highlight the influence exerted by the workpiece thickness, punch work stroke, side clearance, and axial clearance between punch and die on the precision of the main dimensions of the windows that exist in the bearings cages in the case of the double row tapered roller bearings. Empirical mathematical models that were able to offer information concerning the intensity of the influences of the abovementioned forming process input factors on three main dimensions of the bearing cage windows were determined.

#### **2. Theoretical Analysis**

In order to achieve the windows in the bearing cage from Figure 1b, a stamping process is applied. On could consider that the stamping process develops on hydraulic pressing equipment (Figure 2a) and using a mold that supposes the axial movement of a central conical mandrel. Due to this movement and to the conical shape of the central conical mandrel, the punches that have an approximate L shape are forced to radially move, materializing the process of window cutting (Figure 2b,c). Since there is a number of punches that is equal to the number of windows that exist in the bearing cage, at a single work stroke of the central conical mandrel, all of the windows are cut.

**Figure 2.** Achieving the windows in bearing cages: (**a**) LVD 600 hydraulic pressing equipment used for cutting the windows in bearings cages; (**b**) components of the cutting tool; (**c**) cutting of a window.

In Figure 3, the shape and the main dimensions specific to a window that exists in the bearing cage could be seen. The main dimensions of the window are the window width *Ww*, the window height *Hw*, and the distance *Drt* between the retention thresholds belonging to the same window. As a consequence of the punch movement, a part of the workpiece material is detached, and a hole is thus generated in the bearing cage (Figure 4).

During the rolling bearing service, especially the window height *Hw*, and the distance *Drt* between retention thresholds are important, since they determine the clearance between the bearing rolls and the bearing cage. These dimensions are determined during the rolling bearing design activity by taking into consideration the recommended or imposed values for the length and the maximum diameter of the bullet roll, the axial, the side, and the tangential clearance between the roll and the bearing cage.

There are many factors that are able to exert influence on the precision of the dimensions *Hw*, *Ww*, and *Drt* during the process of window cutting in accordance with the machining scheme presented in Figure 2b.

**Figure 3.** Shape and main dimensions of the window existing in the bearing cage.

**Figure 4.** Window in the bearing cage after withdrawal of the punch.

The factors that are able to influence the precision of the window cutting in the bearing cage could be grouped in the following way:


The clearance between the punch and the die could be determined as a half of the difference between the dimension of the hole that exists in the die and the conjugate dimension of the punch, both in cross-sections. For example, in the case of windows height *Hw*, the relation for determining the axial clearance *c<sup>a</sup>* (clearance measured along the roller axis) is the following:

$$\mathcal{C}\_a = \frac{D\_{da} - d\_{pa}}{2},$$

in which *Dda* is the axial dimension of the cross section of the hole existing in the die, and *dpa* is the adequate dimension of the punch cross section.

As hypothesized, one can consider that the increase of the clearance between the active zones of punches and die and wear level of these main components will determine the decrease of the cutting process accuracy and of the burr height.

On could suppose a monotone influence exerted by the clearance *c* between punch and die, by the workpiece thickness *t<sup>w</sup>* and by the length of punch work stroke *l<sup>s</sup>* on the accuracy of the dimensions that characterize the window cut in the bearing cage. Accepting such a hypothesis, one could consider that a power type equation could be able to highlight the intensity of the influence exerted by the workpiece thickness *tw*, the length *l<sup>s</sup>* of work stroke, the side clearance *c<sup>s</sup>* , and axial clearance *c<sup>a</sup>* on the deviation ∆*D<sup>i</sup>* of the investigated dimension *D<sup>i</sup>* from its nominal value:

$$
\Delta D\_{\dot{l}} = \mathbb{C}\_0 \cdot t\_w^{\mathbb{C}\_1} \cdot l\_s^{\mathbb{C}\_2} \cdot c\_a^{\mathbb{C}\_3} \cdot c\_s^{\mathbb{C}\_4} \,\tag{2}
$$

in which the coefficient *C*<sup>0</sup> and the exponents *C*1, *C*2, *C*3, and *C*<sup>4</sup> could be experimentally determined. The values of the exponents *C*1, *C*2, *C*3, and *C*<sup>4</sup> will characterize the intensity of the influence exerted by the considered process input factors on the cutting accuracy of the bearing cage window.

#### **3. Materials and Methods**

In order to test the hypotheses concerning the influence exerted by the considered input factors of the window cutting process on window cutting accuracy, experimental research was designed and carried out [16,17].

The experiments were made on the LVD 600 type hydraulic pressing equipment (Figure 2a). The punch and the die correspond to the schematic representation from Figure 2b.

As material of the bearing cage, the steel DD13 (SR EN 10111: 2008) was considered. In the chemical composition of this steel, there are the following main components: 0.034% C, 0.015% Si, 0.25% Mn, 0.02% P, 0.0130% S, etc. The tensile strength of this steel is about 400 MPa.

The possibility was considered of developing an experimental research in which the results could be mathematically processed by means of software based on the method of last squares so that, finally, empirical mathematical models could be determined and analyzed. These empirical mathematical models have to highlight the intensity of the influence exerted by considered process input factors on the sizes of the parameters of technological interest, from the point of view of cutting accuracy.

Regarding cutting process input factors (independent variables), the followings were considered: the workpiece thickness *tw*, the length of the punch work stroke *l<sup>s</sup>* , the side clearance *c<sup>s</sup>* (clearance measured in a plane perpendicular on the axis of the virtual roller), and the axial clearance *c<sup>a</sup>* between the punch and die.

The values of the process input factors *tw*, *l<sup>s</sup>* , *cl* , and *ca*, and of the output parameters (deviation ∆*H<sup>w</sup>* of the window height *Hw*, deviation ∆*W<sup>w</sup>* of the window width *Ww*, and deviation ∆*Drt* of the distance *Drt* between the cage retainer thresholds, were measured using the MarSurf XC 2 contour measuring station. The station guide deviation is lower than 1 µm/120 mm.

As experimental result, the deviations of the measured dimensions from their nominal values were considered.

The experimental conditions and results were presented in Table 1. In the column nos. 2, 3, 4, and 5, the values of the process input factors were included, while in the columns nos. 6, 7, and 8, the sizes of the process output parameters were mentioned.


**Table 1.**Experimental conditions and results.

#### **4. Results**

The experimental results were mathematically processed by means of software based on the use of the method of least squares [18]. The software allows for the consideration of five distinct mathematical empirical models. The adequacy of these empirical models for the experimental results could be estimated by means of the so-called Gauss's criterion. The value of the Gauss's criterion could be determined as a sum of squares of the differences between the measured values and the values determined using the empirical mathematical models, for the same experimental points.

As results of experimental mathematical processing, the following mathematical empirical relations were determined:

$$
\Delta H\_{\rm w} = 0.0311 \cdot t\_{\rm w} \,\, ^{-0.877} \cdot l\_{\rm s} \,\, ^{1.853} \cdot c\_{\rm s} \,\, ^{3.811} \cdot c\_{\rm a} \,\, ^{-11.423} \,\, \, \, \, \tag{3}
$$

in this case the Gauss's criterion has the value *S<sup>G</sup>* = 0.0008970296,

$$
\Delta W\_w = 0.04346 \cdot t\_w \, ^{-0.385} \cdot l\_s \, ^{0.437} \cdot c\_s \, ^{3.051} \cdot c\_a \, ^{-10.115} \, \tag{4}
$$

for which the Gauss's criterion has the value *SG*=0.00000848762, and

$$
\Delta D\_l = 0.142 \cdot t\_w \stackrel{-0.242}{\cdot} \cdot l\_s^{0.303} \cdot \mathcal{c}\_s^{-0.0933} \cdot \mathcal{c}\_a^{1.384} \tag{5}
$$

the Gauss's criterion has the value *S<sup>G</sup>* = 0.000007217791.

On the base of the empirical mathematical models expressed by the Equations (3)–(5), the graphical representations from Figures 5–8 were elaborated.

*Δ Δ Δ* **Figure 5.** Influence exerted by the workpiece thickness *t<sup>w</sup>* on the deviations ∆*Hw*, ∆*Ww*, and ∆*Drt* (*l<sup>s</sup>* = 6.5 mm, *cs* = 0.14 mm, *ca* = 0.54 mm). *Δ Δ Δ*

*Δ Δ Δ* **Figure 6.** Influence exerted by the work stroke length *<sup>l</sup> Δ Δ Δ <sup>s</sup>* on the deviations ∆*Hw*, ∆*Ww*, and ∆*Drt* (*t<sup>w</sup>* = 4 mm, *cs* = 0.14 mm, *ca* = 0.54 mm).

*Δ Δ Δ* **Figure 7.** Influence exerted by the side clearance *c<sup>s</sup>* on the deviations ∆*Hw*, ∆*Ww*, and ∆*Drt* (*t<sup>w</sup>* = 4 mm, *ls* = 6.5 mm, *ca* = 0.54 mm). *Δ Δ Δ*

*Δ Δ Δ*

*Δ Δ Δ* **Figure 8.** Influence exerted by the axial clearance *c<sup>a</sup>* on the deviations ∆*Hw*, ∆*Ww*, and ∆*Drt* (*t<sup>w</sup>* = 4 mm, *ls* = 6.5 mm, *cs* = 0.14 mm).

#### **5. Discussion**

The analysis of the empirical mathematical models (3)–(5), and of the graphical representations from Figures 5–8, facilitated the formulation of some general remarks concerning the influence exerted by the process input factors on the dimensional precision of windows cut in bearing cages.

*Δ Δ Δ Δ Δ Δ Δ Δ* Thus, one can notice that the increase of the workpiece thickness *t<sup>w</sup>* determines an increase of the machining accuracy (a diminishing of the deviations ∆*Hw*, ∆*Ww*, and ∆*Drt*, Figure 5), and this could be justified by the increase of the workpiece rigidity, which has as an effect a more precise cutting of the windows. In all the three mathematical empirical models, the exponents attached to the factor *t<sup>w</sup>* have a negative value, and the highest influence is exerted on the deviation ∆*H<sup>w</sup>* of the window height *H<sup>w</sup>* when the exponent has a maximum value.

*Δ Δ Δ Δ Δ Δ Δ Δ Δ Δ* If the influence of the work stroke length *l<sup>s</sup>* is analyzed, one could notice that in all the three cases the increase of this factor value determines an increase of the deviations ∆*Hw*, ∆*Ww*, and ∆*Drt* (a decrease of the machining precision, Figure 6). The fact could be justified by the longer contact between the workpiece and the cutting punch, which could contribute to a supplementary material removal from the workpiece, inclusively by developing an intense friction phenomenon. The maximum influence is exerted on the deviation ∆*H<sup>w</sup>* of the window height, this meaning that the exponent attached to the factor *l<sup>s</sup>* has the maximum value in the mathematical empirical model that corresponds to the deviation ∆*H<sup>w</sup>* of the window height.

*Δ Δ Δ Δ Δ Δ Δ Δ Δ Δ* As expected, the increase of the side clearance *c<sup>s</sup>* determines a decrease of the machining precision in the case of the deviations ∆*Hw*, ∆*W<sup>w</sup>* (Figure 7), when the exponents attached to the factor *c<sup>s</sup>* has values higher than 3. Indeed, the increase of the side clearance *c<sup>s</sup>* could change the behavior of the workpiece material during the cutting process, and this could determine an increase of the deviations ∆*H<sup>w</sup>* and ∆*Ww*. In the case of the of the deviation ∆*Drt* of the distance *Drt* between the retention thresholds, the influence is practically insignificant, with the value of the exponent attached to the factor *c<sup>s</sup>* being close to zero.

For relatively large values of the axial clearance *c<sup>a</sup>* (0.51–0.58 mm), one notices that the increase of this factor leads to a decrease of the deviations ∆*Hw*, ∆*W<sup>w</sup>* (the exponents attached to the factor *c<sup>a</sup>* in the empirical mathematical models having negative values) and exerts a relatively low influence on the deviation ∆*Drt* of the distance between the retention thresholds, as can be seen in Figure 8. The strongest influence is exerted on the deviation ∆*Drt* of the distance between the retention thresholds, the fact being highlighted both by the exponent attached to the factor *c<sup>a</sup>* in the empirical mathematical model of ∆*Drt* (Equation (5)) and by the graphical representation from Figure 8.

#### **6. Conclusions**

The windows that exist in the bearing cage could be obtained by a forming process that involves the use of a punch and a die. Over the years, researchers have become concerned with the influence exerted by distinct factors on the machining precision that corresponds to punching processes. Only a few experimental results referred to the machining precision of the bearings cage windows. In this paper, the problem of investigating the machining precision in case of the cutting process of windows in cages for double row tapered roller bearings was addressed. The theoretical analysis highlighted that the workpiece thickness, the length of punch work stroke, and the clearance between the punch and die could be factors that are able to affect the dimensional precision of the windows cut in the bearing cage. Experimental research was developed to identify the influence exerted by the above-mentioned process input factors on the precision of some of the windows' overall dimensions and on the so-called distance between the retention thresholds. By mathematical processing of the experimental results, power type empirical mathematical relations were determined. These empirical mathematical models and the graphical representations were analyzed to obtain information concerning the influence of some process input factors on the machining precision of obtaining certain dimensions of the cage windows. Essentially, the increase of the workpiece thickness determines the increase of the machining precision, while the increase of the punch work stroke length contributes to a decrease in the machining accuracy. The increase of the side clearance leads to an increase of the cutting deviation, and the increase of the axial clearance determines the decrease of the overall dimension deviations. In the future, there is the intention to extend the experimental research so that the empirical mathematical models will be used to optimize the punching process of window cutting in bearing cages.

**Acknowledgments:** The experimental research benefited from the material support offered by the company S.C. "Rulment,i" S.A. Bârlad (România).

**Author Contributions:** M.R. conceived and materialized the experimental research, G.N. had the idea of studying the influence exerted by the experimental conditions of the dimensional accuracy of the windows achieved in bearing cages and established the experimental conditions, L.S. proposed and selected the empirical mathematical models and proposed the general structure of the paper, and O.D. achieved the mathematical processing of the experimental results and edited the paper.

**Conflicts of Interest:** The authors declare no conflict of interests.

#### **References**


the 7th International Conference on Mechanical and Manufacturing Engineering, Sustainable Energy Towards Global Synergy, Jogjakarta, Indonesia, 1–3 August 2016; Volume 1831.


© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## *Article* **Numerical and Experimental Characterization of a Railroad Switch Machine**

**Dario Croccolo, Massimiliano De Agostinis, Stefano Fini \* ID , Giorgio Olmi and Francesco Robusto ID**

Department of Industrial Engineering, University of Bologna, Viale del Risorgimento 2, 40136 Bologna, Italy; dario.croccolo@unibo.it (D.C.); m.deagostinis@unibo.it (M.D.A.); giorgio.olmi@unibo.it (G.O.); francesco.robusto2@unibo.it (F.R.)

**\*** Correspondence: stefano.fini@unibo.it; Tel.: +39-051-2093455

Received: 15 January 2018; Accepted: 12 February 2018; Published: 17 February 2018

**Abstract:** This contribution deals with the numerical and experimental characterization of the structural behavior of a railroad switch machine. Railroad switch machines must meet a number of safety-related conditions such as, for instance, exhibiting the appropriate resistance against any undesired movements of the points due to the extreme forces exerted by a passing train. This occurrence can produce very high stress on the components, which has to be predicted by designers. In order to assist them in the development of new machines and in defining what the critical components are, FEA models have been built and stresses have been calculated on the internal components of the switch machine. The results have been validated by means of an ad-hoc designed experimental apparatus, now installed at the facilities of the Department of Industrial Engineering of the University of Bologna. This apparatus is particularly novel and original, as no Standards are available that provide recommendations for its design, and no previous studies have dealt with the development of similar rigs. Moreover, it has wide potential applications for lab tests aimed at assessing the safety of railroad switch machines and the fulfilment of the specifications by many railway companies.

**Keywords:** railroad switch; railway junction; FEA; experimental; points

#### **1. Introduction**

A railroad switch machine (RSM), turnout or set of points is a mechanical installation enabling railway trains to be guided from one track to another, such as at a railway junction or where a spur or siding branches off. One of the key safety requirements of railroad switches is related to achieving a suitable resistance against any undesired movements of the points, due, for instance, to the extreme forces exerted by a passing train in the case of the needle leaned to the rail (force F in Figure 1).

Many railway companies assume a force F = 100 kN as standard. This work deals with the development of FEA models aimed at accomplishing the structural design of the RSM under the aforementioned operating load. In order to validate such models, an experimental test bench has been designed and manufactured. This comprises two ad-hoc designed fixtures that allow the accommodation of the test piece on a standard INSTRON 8500 500 kN standing press and the application of forces up to a maximum of F = 300 kN. Issues of novelty arise from the lack of studies both in the scientific and in the technical literature dealing with the development of similar fixture devices. The developed testing rig can be used not only for FEA validation purposes, but also for experimental tests aimed at warranting the safety of the RSM and the accomplishment of design requirements by most railway companies. The originality of the performed non-trivial design task arises also from the lack of specific Standards providing recommendations or reference schemes for the execution of lab tests aimed at assessing the structural response of RSM under high loads.

**Figure 1.** Geometry of a railroad switch.

#### **2. Materials and Methods**

The Alstom RSM object of the present investigation is shown in Figure 2, along with some balloons highlighting the key structural components of the machine.

**Figure 2.** 3d model of the Alstom RSM: (**1**) body; (**2**) lower plate; (**3**) pin; (**4**) hammer; (**5**) switching rod; (**6**) cam; (**7**) detection rod; (**8**) arm.

Due to confidentiality-related issues, the working principles of the machine cannot be described in detail. The analysis was limited to the verification of the mechanism against unwanted movements of the points caused by a passing train since the system is equipped with two interlocking devices. In fact, once the full stroke has been travelled, and the points are in the open (or closed) position, the switching rod (5) is secured to the body (1) by means of a hammer (4); at the same time, the detection rod (7) is secured to the lower plate (2) by means of a slider, not represented in the picture. Therefore the locking devices come into effect preventing any movement of the rods, when an external force is applied along z-axis to the points, and thereby to the arms (8).

According to the requirements set by railway companies, the RSM should be validated under the action of a force F = 100 kN. The load application rate surely affects the response of the structure. The testing force of F = 100 kN is set by the railway company in order to account for dynamic effects. In order to attain an adequate stiffness of the test fixture, it has been dimensioned for a maximum load of 300 kN. The overall dimensions of the test piece are 900 × 300 × 210 mm; therefore, the fixture was conceived in two separate parts, a lower and an upper grip, so as to achieve a certain flexibility during mounting and unmounting operations on the standing press. In order not to transmit any unwanted bending moment at the arms, the test fixture was shaped as shown in Figure 3. While the lower grip is a simple C-shaped interface between the actuator thread and the arms, the upper grip has to retain the whole RSM by means of four M20 8.8 class bolts. The bolted joint is doubly overlapped: this provision allows doubling the frictional surfaces and hence the transmissible load for a given bolt size and class [1,2]. Except for a few details, the fixture has to be arc welded, therefore a structural steel S275JR according to [3] has been chosen for its construction. All the welds were statically dimensioned according to Standard EN 1993-1-8 [4]. In order to assess the stresses and the deformations on the fixture under maximum design load (F = 300 kN), some FEA have been performed by means of the commercial code Ansys Workbench.

**Figure 3.** Loading scheme: (**1**) test piece (switch machine); (**2**) lower grip; (**3**) upper grip.

Figure 4a shows the boundary conditions applied to the model: the upper grip has been fixed at the upper end and loaded by two equal forces Fz = 150 kN, one at each arm. The model has been meshed with SOLID187 Tetrahedral and Hexahedral elements, Figure 4b. The material is a structural steel, whereas the bonded contacts are managed by means of the pure penalty contact algorithm, with the normal stiffness factor set to FKN = 0.01, following the lines suggested by [5,6]. The analysis and model parameters are summarized in Table 1.

**Figure 4.** FEA on the fixture upper grip: (**a**) Boundary conditions; (**b**) mesh; (**c**) total deformation; (**d**) equivalent von Mises stress.


**Table 1.** Analysis and model parameters.

As can be appreciated by looking at Figure 4c, the total deformation is ∆tot\_max = 1.3 mm, whereas the maximum von Mises equivalent stress remains below 190 MPa (see Figure 4d); such a stress level is well below the material yield point SY = 275 MPa. Since the model is linear, a maximum deformation of about ∆tot\_nom = 0.4 mm can be expected at nominal load, which is deemed acceptable. Δtot deformation of about Δtot

The assembly procedure of the test rig requires quite a number of subsequent operations, briefly summarized in Figure 5. In particular, Figure 5d shows a detailed view of the arms of the machine when these are clamped by the lower grip. When the assembly is done, the load cell undergoes zero calibration and the test can begin. The main goal of the experiment is to provide a validation of the FEA models of the RSM that will be described in the following. A secondary aim of the experimentation is to determine how much of the total load is borne by the switching rod and how much by the detection rod. In order to accomplish this twofold task, three components of the RSM were instrumented by strain gauges: the two arms and the pin (see Figure 6).

**Figure 5.** Test arrangement: (**a**) Placement of the lower grip, (**b**) pre-mounting of the upper grip with the test piece; (**c**) placement of the upper grip with a forklift; (**d**) details of the assembly; (**e**) final configuration.

**Figure 6.** (**a**) Placement of the strain gauges on the arm and (**b**) on the reworked pin.

– The pin and arms had been previously reworked in order to accommodate the sensors (Vishay Precision Group J2A-XXS047K-350); in particular, the pin required both milling and boring operations in order to achieve a plane surface for the application of the strain gauge, as well as a passage for the cables. The arms were instrumented by means of two strain gauges each; the strain gauges were connected in a half-bridge fashion to the Wheatstone circuit. The pin was instrumented by means of a single strain gauge; a dummy gauge, which served as a temperature drift compensator, was glued to an identical, unloaded pin placed in the testing room. The adhesive used for the installation was the M-BOND 200 by Vishay Precision Group. All the sensors were installed by a certified operator, following the guidelines suggested by the Standards [7–9]. Data acquisition was managed by means of the NI 9237 sampling card plugged into a NI cDAQ-9184 carrier. The FEA model of the RSM was developed by means of the Ansys code V.17. Due to the complexity of the assembly, submodeling was leveraged, by considering half a model at a time, as if the machine were cut along its mid-plane, normal to the *x*-axis. In this way, it was possible to find a satisfactory balance between accuracy and computational cost. Both models were meshed with tetrahedral elements SOLID187, switching rod side (Figure 7), and detection rod side (Figure 8). The analysis and model parameters are summarized in Table 2. –

**Figure 7.** Boundary conditions for the half model comprising the switching rod.

**Figure 8.** Boundary conditions for the half model comprising the detection rod.


**Table 2.** Analysis and model parameters.

In the case of the switching rod, the stresses on the pin and those on the hammer were sampled, and subsequently compared with the experimental outcomes. In the case of the detection rod, the stresses on the pins that connect the lower plate to the body were examined, as a function of the actual bolt preload of the joint.

#### **3. Results and Discussion**

The results from a tensile test carried out on the ad-hoc developed test bench are shown in Figure 9.

**Figure 9.** (**a**) View of the test bench and (**b**) plot of the results in terms of stresses on the pin and on the arms and force at the load cell.

Figure 9 reports the data relevant to a test run until a maximum force of F = 160 kN. At the peak load, one of the pins connecting the lower plate with the body failed. The first outcome of the experiment is the knowledge of the force distribution on the two arms: the great majority of the total force (82%) reaches the body by passing through the chain of components named the switching rod, the pin and the hammer. The remaining part (18%) passes through the detection rod, the slider and the lower plate, eventually reaching the body. Running each of the FEA models by applying the appropriate fraction of the total load to the arm under investigation, it was possible to validate the numerical results. For example, looking at Figure 10a, it is possible to observe the equivalent stresses calculated according to the von Mises criterion on the half machine comprising the switching rod. Figure 10b reports the σY bending stresses on the pin that supports the hammer, when this sub-system is loaded with 82% the total load F = 160 kN. reports the σY bending stresses on the pin that supports the hammer, when this sub

— ) bending σY **Figure 10.** (**a**) von Mises stress plot on the half machine—switching rod side, and (**b**) bending σY stresses on the pin.

(σY\_FEA component (σY\_EXP As can be appreciated from Figure 10b, the numerical peak of the bending stress on the pin (σY\_FEA = 477 MPa) is very close to that measured during the experimental test on the same component (σY\_EXP = 450 MPa, see Figure 9). The error, calculated according to Equation (1), is acceptable.

$$\mathcal{C}\% = \frac{\sigma\_{Y\_{\text{\\_}}FEA} - \sigma\_{Y\_{\text{\\_}}EXP}}{\sigma\_{Y\_{\text{\\_}}EXP}} \cdot 100 = 6\% \tag{1}$$

ot of the amount of shearing force borne by the switching rod side pin (T'swi) and by the detection rod side pin (T'det) as functions of the actual screw preload Fv. Each of the Once the FEA model has been validated, it can be used for carrying out some comparisons considering, for example, the joint between the lower plate and the body. Such joints comprise a pattern of eight M8 8.8. screws, working in parallel with a couple of parallel pins of d = 6 mm diameter, manufactured according to Standard [10]. It can be assumed that this joint must withstand the shearing load transmitted by the slider to the body via the lower plate. These pins are coupled with interference (H7/m6). Since the screws are tightened under preload control upon assembly, and some uncertainties with regard to the friction coefficients cannot be avoided [11,12], the load borne by the parallel pins may vary depending on the effective preload of the screws and on the friction coefficient at the interface between the body and the plate. In order to estimate such variation, some parametric analyses were run, for example by imposing different preload levels on the screws. The screw preload was assigned via the preload tool available in the Ansys Workbench environment. Figure 11 reports a plot of the amount of shearing force borne by the switching rod side pin (T'swi) and by the detection rod side pin (T'det) as functions of the actual screw preload Fv. Each of the dashed lines represents the force acting on the relevant parallel pin, whereas the solid lines represent the fraction of load borne by the generic pin.

**Figure 11.** Shearing force on the switching/detection rod side parallel pin versus screw preload.

It can be seen that the most loaded pin is that on the detection rod side (closer to the slider), regardless of the screw preload. Nonetheless, the magnitude of the load borne by the pins decreases as the screw preload increases: a preload limit of Fv = 20 kN is assumed based on the provisions of Standard [13] for M8, 8.8 class screws. Based on different preload levels, it is also possible to extract a plot of the von Mises stresses on the most loaded parallel pin, as shown in Figure 12.

**Figure 12.** von Mises stress plot on the detection rod side parallel pin at a screw preload of (**a**) 10 kN; (**b**) 15 kN; (**c**) 20 kN.

– designer's standpoint, the present work achieved a twofold result: (i) an experimental – The equivalent stress calculated by FEA on the most loaded parallel pin is compatible with the failure event, which took place during the experiment at a total load of F = 160 kN. The strength of the pins could be modified by changing the coupling system, increasing the interference or adopting a different coupling technique. Based on the literature, a valid alternative could be making use of anaerobic or epoxy adhesives, which would make it possible to significantly increase the actual mating area with a positive outcome in terms of the overall strength. This point has been tackled experimentally in papers [14–16], which also provide tips regarding the proportioning of the joint upon its design.

#### **4. Conclusions**

From a designer's standpoint, the present work achieved a twofold result: (i) an experimental setup has been designed, manufactured and calibrated, which is novel and original and will be useful for subsequent experimentations on other products of the same family; (ii) numerical tools have been developed and validated, with respect to experimental data. These models allow the designer to evaluate the effect of structural changes early, hence reducing the time to market of new machines.

designer's standpoint, the present work achieved a twofold result: (i) an experimental

**Acknowledgments:** The authors gratefully acknowledge Eng. Marcello Andrenacci, Eng. Leonardo Bozzoli, Eng. Francesco Muscatello and Eng. Francesca Sopranzetti at Alstom Ferroviaria SpA for having made this research possible. The authors would also like to acknowledge Eng. Francesco Vai, laboratory director at the Department of Industrial Engineering, University of Bologna, for his fundamental contribution to the experimental activities.

**Author Contributions:** D.C. and M.D.A. conceived and designed the experiments; S.F. and M.D.A. performed the experiments; M.D.A., S.F., and F.R. performed the numerical analyses; G.O. analyzed the data; S.F., and M.D.A. provided reagents, materials and analysis tools; G.O. and M.D.A. wrote the paper.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## *Article* **A Methodology for the Lightweight Design of Modern Transfer Machine Tools**

**Dario Croccolo <sup>1</sup> , Omar Cavalli <sup>1</sup> , Massimiliano De Agostinis <sup>1</sup> , Stefano Fini 1,\*, Giorgio Olmi <sup>1</sup> , Francesco Robusto <sup>1</sup> ID and Nicolò Vincenzi <sup>2</sup>**


Received: 10 December 2017; Accepted: 11 January 2018; Published: 14 January 2018

**Abstract:** This paper deals with a modern design approach via finite elements in the definition of the main structural elements (rotary table and working unit) of an innovative family of transfer machine tools. Using the concepts of green design and manufacture, as well as sustainable development thinking, the paper highlights the advantages derived from their application in this specific field (i.e., the clever use of lightweight materials to allow ruling out high-consumption hydraulic pump systems). The design is conceived in a modular way, so that the final solution can cover transfers from four to 15 working stations. Two versions of the machines are examined. The first one has a rotary table with nine divisions, which can be considered as a prototype: this machine has been studied in order to set up the numerical predictive model, then validated by experimental tests. The second one, equipped with a rotary table with 15 divisions, is the biggest of the range: this machine has been entirely designed with the aid of the previously developed numerical model. The loading input forces for the analyses have been evaluated experimentally via drilling operations carried out on a three-axis CNC unit. The definition of the design force made it possible to accurately assess both the rotary table and the working units installed in the machine.

**Keywords:** transfer machine; rotary table; working unit; green design; finite element; machine tool; minimal quantity lubrication

#### **1. Introduction: Green Design Applied to Machine Tools**

In order to be competitive in today's business world, more and more companies have to plan their activities by thinking about energy consumption and resource saving. The themes of green design are compelling in the modern design of machine tools. In practical aspects, up to 10 years ago the goal of machine tool manufacturers was to improve the performance of machine tools in terms of availability, reliability, dimensional accuracy, and precision. To achieve these targets, machine tools have become increasingly complex and automated in their design. These changes resulted in increasing energy requirements, which lead to rising power costs and limited access to resources (particularly fossil fuels), and run counter to increasing environmental consciousness among customers and stricter government regulations. For instance, specifications for the purchase of machine tools set out by automotive companies have dedicated chapters dealing with energy consumption and the correct design of electrical motors, compressed air circuit, hydraulic pumps, etc., in order to optimize the energy-related costs and the environmental impact of the production. Under the label of "energy management", the following points are usually found:

1. No compressed-air motors should be used;


Machine tool energy consumption may be reduced in any of the four areas of its life cycle: (i) manufacturing (design and production of the parts), (ii) transportation (design for assembly/disassembly to allow standard transport), (iii) use (energy used to produce parts), or (iv) end of life (recycled materials). The most important phases are (i) and (iii): design-level changes are able to provide the greatest flexibility and therefore potentially offer the best opportunities for energy savings. The modern approach to the metal cutting operations such as the use of Minimal Quantity Lubrication (MQL) or the dry cutting [2–12] are able to dramatically cut consumption by nearly eliminating the impact of cutting fluids. Just for reference, it is possible to compare the need for a *Ø* = 12 mm standard drill in the presence of emulsion at *p* = 30 bar coolant pressure and for a MQL drill: 900 L/h versus 15 mL/h. Furthermore, the presence of the emulsion needs a dedicated system for the filtration of the fluid from the chips and of volumetric (high consumption) pumps to supply the high-pressure internal coolant. A breakdown of the consumption, split between the different power units in a machining center, is shown in Figure 1. –

**Figure 1.** Breakdown of the average power supply needed for the production of a reference component: (**a**) roughing; (**b**) finishing. Gray shaded arrows represent energy consumption shares other than the main spindle of the machine.

#### *Machines* **2018**, *6*, 2

Based on this scenario, a new line of drilling/milling machines has been conceived in order to fulfill the aforementioned requirements. Particularly, the main topics of the new solution can be summarized as follows:


A new family of transfer machine tools has been designed by Giuliani, based on the guidelines mentioned above. A high performance torque motor is mounted on each transfer machine: it makes it possible to reach high values of torque with limited energy consumption. Every component involved in the motion of the transfer is designed to be as light as possible, according to the required stiffness, to preserve the required tolerances on the finished parts. Each transfer machine consists of a number of machining stations being equipped with a three-axis reconfigurable tooling unit. The three-axis unit geometry has been recently redesigned, in order to improve its performance: this optimization is based on the reduction of the carriage weight, achieved using aluminum alloys, rather than cast iron for these parts, while keeping the stiffness of the parts unchanged. The MQL machining approach has been followed as well, to achieve both energy and coolant saving.

Leveraging the concepts of green design and manufacture, as well as sustainable development thinking, the paper highlights the advantages derived from their application in this specific field: Two versions of the machines are examined. The first one, with nine divisions, which can be considered as a prototype: this machine has been studied in order to set up the numerical predictive model, then validated by experimental tests. The second one, equipped with a bigger rotary table with 15 divisions, has been entirely designed with the aid of the previously developed numerical model. To the best of the authors' knowledge, limited to the case of transfer machine tools, no works based on the same approach are currently available in the literature.

#### **2. Setup of the FE Models for the Transfer Machine with Nine Divisions**

#### *2.1. Experimental Determination of the Operating Loads*

The three-axis unit has been designed, so that it is able to efficiently withstand a spindle thrust force in the order of *F* = 1 kN. This reference value has been chosen, following a preliminary experimental campaign, aimed at the estimation of the maximum thrust forces during the most frequent as well as the most demanding machining operations on the workpiece. In particular, a highly critical task, in terms of the load acting on the transfer, is drilling a hole under an MQL strategy. The outcome of the experiment was that 1 kN could be regarded as a proper threshold, considering for instance the drilling of a 7-mm hole on a round bar made of 16MnCrS5 steel or of a 12-mm hole on a CuZn39Pb3 brass component. In all the studied cases, which can be considered within the conventional applications of the transfer machine, the most recommended values of feed rate have been selected, also based on [13]. The estimated reference force *F* is going to be assumed in the following numerical analyses, in order to calculate the displacements of the transfer machine under load application.

#### *2.2. Experimental Characterization of the Stiffness of the Reference Transfer*

The transfers involved in the investigation consist of two tables (Figure 2), whose outer diameter is *Dout* = 1680 mm. The lower one spins around the *y*-axis, actuated by the torque motor; whereas the upper one is fixed to the frame and supports the three-axis units. In the following, they will be referred to as the "rotating table" and "fixed table," Respectively. Supports are bolted under the rotating table in a number equal to the workstations. Each support carries a pneumatic vise that enables to safely grip the workpiece. The mechanical group described above is fixed to the ground at the base of the column.

**Figure 2.** Fixed and rotary tables of the Transfer Machine with nine divisions.

Some experimental measurements have been carried out, in order to evaluate the vertical displacements of the supports of the Transfer Machine with nine divisions, when a vertical load is applied on a support along *y*-axis: the measured displacements would then be useful for the validation of the numerical model. Three dial gauges with a resolution of 0.01 mm have been placed at the positions shown in Figure 3.

**Figure 3.** (**a**) Dial gauges at positions 1 and 3 and (**b**) at position 2.

Then, a mass *m* = 50 kg has been applied on the support object of investigation. The position of each dial gauge and the position of the mass are shown in Figure 4. The experimental data are shown in Table 1.

**Figure 4.** Positions of the dial gauges and of the applied mass.


**Table 1.** Dial gauge readings.

#### *2.3. Tuning of the Stiffness Parameter of the FE Model*

At first, the CAD geometry of the Transfer Machine with nine divisions has been simplified, in order to reduce the computational effort without significantly affecting the accuracy of the results: it must be remarked that the accurate evaluation of the stresses at notches or joints is beyond the scope of the present analysis. In fact, previous investigations carried out on similar machines showed that no significant stresses are generated on the key components of the frame during operation. Hence, the present analysis focuses just on the stiffness performance of the structure. Due to geometrical and loading symmetry conditions, a half of the geometry has been considered. A frictionless support has been applied on the symmetry plane, as shown in Figure 5a, in order to enforce the symmetry condition. Moreover, the base of the column has been constrained by means of a fixed support (Figure 5b): in the actual application, such a surface is constrained to the lower part of the frame, which can be considered perfectly rigid.

**Figure 5.** (**a**) Frictionless support on the symmetry plane; (**b**) fixed support at the base of the column.

*ν ν* ≈ The materials assigned to the parts are AlMg0.7Si (*E* = 69.5 GPa, *ν* = 0.33) for the rotating table and a structural steel (*E* = 200 GPa, *ν* = 0.30) for any other part. The geometry has been meshed with SOLID187 tetrahedral and hexahedral elements, for a total node count *n* ≈ 95,000. All the contacts in the model are set as bonded, assuming a pure penalty formulation and a normal stiffness factor controlled by the software (FKN = 1, [14,15]). The applied force *F*<sup>y</sup> is calculated according to Equation (1), where term 2 in the denominator is due to the symmetry of the model.

$$F\_y = \frac{9.81 \times 50}{2} = 245.25 \text{ N} \tag{1}$$

 

*F<sup>y</sup>* acts on the upper surface of the reference support, as shown in Figure 6. 

**Figure 6.** Application of *Fy* to the reference support.

The displacements yielded by the numerical simulation and measured at the same positions of the dial gauges, are shown in Figure 7 and summarized in Table 2, along with the percentage error with respect to the experimental ones.

model the bearing by means of a single ring made of an elastic, isotropic material, whose Young's *δ δ* μm; (iv) the Young's modulus of the ring is adjusted until the FE calculated displacement matches the The results reveal that the numerical model, defined according to the basic settings reported above, is stiffer than the actual machine: hence, it has been decided to improve the model, by tuning the key parameters that affect its stiffness. The rotating table is supported by a double-row angular contact roller bearing. In the previous analysis, the bearing has been modeled as a unique ring made of steel: this approximation leads to overestimating its stiffness. Therefore, it has been decided to model the bearing by means of a single ring made of an elastic, isotropic material, whose Young's modulus has to be determined upfront by the following steps. First, (i) a FE analysis of the ring alone is prepared, by assuming its elastic modulus as a parameter and the ring is constrained, replicating the actual application and loaded by an axial thrust; (ii) the displacement of the force application surface is recorded; (iii) the experimental displacement provided by the bearing manufacturer is read-in. The manufacturer usually provides plots like that shown in Figure 8, where several curves express the axial displacement of the bearing as a function of the applied thrust load. Each curve is relevant to a value of the assembly preload *δ* of the bearing: for the present application, *δ* = 15 µm; (iv) the Young's modulus of the ring is adjusted until the FE calculated displacement matches the experimental axial displacement for given axial thrust. model the bearing by means of a single ring made of an elastic, isotropic material, whose Young's *δ δ* μm; (iv) the Young's modulus of the ring is adjusted until the FE calculated displacement matches the

**Figure 7.** FE displacements (scale factor ×1000).


**Table 2.** FEM displacements and percentage errors with respect to the experimental data.

**Figure 8.** Thrust–displacement diagram of the double-row angular contact roller bearing, supplied by – the manufacturer. –

The static structural analysis has been carried out on a half-ring geometry, as shown in Figure 9a: the ring has been constrained with a fixed support on its lower external surface Figure 9b; the upper inner surface of the ring has been loaded with a 10 kN load (Figure 9c).

**Figure 9.** *Cont*.

**Figure 9.** (**a**) Symmetry region, (**b**) fixed support, (**c**) load application surface.

Young's modulus of the ring) until the displacement of the loaded surface equaled 8.5 and a preload of 15 μm. Such a displacement value was reached by setting an equivalent Young's modulus of substantially unvaried with respect to the previous simulation, with differences smaller than 1 μm in As explained above, a set of FE analyses have been run varying the input parameter (equivalent Young's modulus of the ring) until the displacement of the loaded surface equaled 8.5 × 10 <sup>−</sup><sup>4</sup> mm, which is the value reported in Figure 8 for a thrust load of 10 kN and a preload of 15 µm. Such a displacement value was reached by setting an equivalent Young's modulus of *Ering* = 39 GPa. Then, a finite element analysis (FEA) of the whole Transfer Machine with nine divisions, including the ring with the above specified *Ering* , was run. The displacements at the reference points (Figure 10) are substantially unvaried with respect to the previous simulation, with differences smaller than 1 µm in terms of displacement. Therefore, another modification had to be made to the numerical model in order to make it more consistent to the actual machine stiffness.

– Since a correct estimate of the stiffness of a complex assembly is often related to an accurate modeling of its mechanical joints [16–18], the contact conditions between the support and the rotating table have been modified in order to achieve a more accurate FE model. Hence, the bonded contact between the rotary table and the support has been replaced by a set of four M12 12.9 class screws (Figure 11): this bolt pattern replicates that being actually used on the Transfer Machine with nine divisions. The screws have been modeled as solids, and the axial preload has been imposed by the bolt preload tool available in the Ansys Workbench environment.

*μ* factor controlled by the software (FKN = 1). The terminal portion of the shank and the "threaded" *μ* – as for the company's assembl The contact at the interface between the support and the rotating table, as well as the one between the underhead of the screws and the support, has been set as frictional, with a friction coefficient *µ* = 0.2 [19]. The contact formulation has been set as pure penalty with a normal stiffness factor controlled by the software (FKN = 1). The terminal portion of the shank and the "threaded" hole on the rotating table have been joined by means of a bonded contact. The analysis has been divided into two steps: at the first step, a preload of *F<sup>i</sup>* = 70 kN has been assigned to each screw: this preload is calculated, based on a tightening torque *T* = 106 Nm and oiled surfaces, *µ<sup>m</sup>* = 0.10 [20–23], as for the company's assembly specification. The displacements retrieved at this step are shown in Figure 12a. A vertical force *F* = 245.25 N has been added at the second step of the analysis with the bolt preload still acting (lock option set as active in the Ansys WB bolt preload tool). The difference between the displacements recorded at the end of the second step (Figure 12b) and at the end of the first step gives the displacements due to the effect of the external load only, as explained by Equation (2):

$$
\Delta y\_{FEM} = \Delta y\_{step2} - \Delta y\_{step1} \tag{2}
$$

−

Looking at the data in Table 3, relevant to the new FE model, the maximum absolute value of the percentage error is 5% and it is normalized with respect to the displacement at position 2, which is not located on the loaded support but on the adjacent one. Conversely, the errors recorded at the loaded support are of a small entity and stay lower than 3%. In light of the results above, the FE model can now be deemed as validated.

#### *Machines* **2018**, *6*, 2

**Figure 10.** FE displacements of the Transfer Machine with nine divisions with *Ering* = 39 GPa.

**Figure 11.** Detail of the bolted connection between the rotary table and the support.

**Figure 12.** *Cont*.

**Figure 12.** (**a**) FE displacements at first step (bolt preload); (**b**) displacements at second step (bolt preload plus external force).

**n Δ ) Δ ) Δ ) Δ ) -) Table 3.** FE displacements of the modified model at the end of the two steps, ∆*yFEM* and errors with respect to the experimental data.

FE displacements of the modified model at the end of the two steps, Δ


#### *2.4. Modal Analysis*

Based on the settings reported in the previous sections, considering the bolts as bonded contacts with a reduced stiffness, a modal analysis has been carried out in order to predict the first five modes of vibration of the assembly. The natural frequencies are reported in Table 4 and the first two modes are shown in Figure 13a,b.

The natural frequencies and the associated modes reported above will be useful for a vibration assessment, which should take the following points into account: (i) the match between the deformation induced by the generic excitation force and one of the modes shown above; (ii) the match between the frequency of the excitation force and the frequency of the relevant mode. The source of excitation could either be due to the movement of the carriages or to the cutting operation itself. (iii) A further point is the energy associated to the source of excitation: e.g., it must be carefully assessed if the energy associated to the cutting operation is high enough to bring the structure into resonation, provided that there is compatibility between the modes and frequencies. All these checks have been carried out in a separate study [24].

**Table 4.** FE calculated natural frequencies of the Transfer Machine with nine divisions.


**Figure 13.** Modes of vibration of the Transfer Machine with nine divisions: (**a**) first mode; (**b**) second mode.

#### **3. Structural Design of the Transfer Machine with 15 Divisions**

#### *3.1. FEA and Structural Optimization*

The Transfer Machine with 15 divisions is represented in Figure 14: it has six more divisions, thus, if compared to the same machine with nine divisions, a greater diameter (*Dout* = 2940 mm) and one more component (stiffening rib) under the support.

**e # )** 

7 The analysis takes three different load scenarios into account: two radial drilling operations along *x*-axis, positively or negatively oriented, and a vertical (*y*-axis) downwards drilling operation. The purpose of the study is to determine the displacement of the component being clamped under the machining conditions. The same FEM settings validated on the Transfer Machine with nine divisions have been adopted for the analysis of the same machine with 15 divisions, where the same bearing and joining techniques are utilized (see also below). After geometry simplification, the model has been treated again as a symmetrical structure. The materials assigned to the transfer are AlMg0.7Si (*E* = 69.5 GPa, *ν* = 0.33) for the rotating table and a generic structural steel (*E* = 200 GPa, *ν* = 0.30) for all other components. The geometry has been meshed with SOLID187 tetrahedral and hexahedral elements, for a total node count *n* ≈ 160,000. Every contact between the parts has been set as bonded, except the one between the reference support and the rotating table, which is obtained by means of a set of screws. In particular, the Transfer Machine with 15 divisions has a screw pattern made of six M12 12.9 classes, instead of the four-screw pattern utilized in the same machine with nine divisions, as shown in Figure 15. The modeling strategy is the same adopted for the machine with nine divisions.

**Figure 14.** Transfer Machine with 15 divisions: a rib under each support helps increase its stiffness.

**Figure 15.** Bolted connection between the support and the rotary table of the Transfer Machine with 15 divisions.

Three types of machining scenarios have been studied, so three different simulations had to be performed. Each load has been simulated by a remote force *F*<sup>1</sup> = 500 N acting on the upper surface of a support. Symmetry has been enforced as described above. In order to better approximate the actual area of force application (roughly corresponding to the contact area between the vise and the support) a portion of surface has been isolated by a division line (red area in Figure 16) and the machining force applied thereof. The point of application of the force is the center of gravity of the clamped lock, as shown in Figure 17.

Figure 18 shows the displacements along the *y*-axis due to the sole bolt preload, whereas Figure 19 displays the values of *y*-axis displacement for the three load scenarios. The flagged spot always represents the projection of the center of gravity of the clamped lock on the support: the displacements measured at this point in the three different load cases are summarized in Table 5, along with the calculation of the displacements caused by the sole external loads (the displacement due to the bolt preload has been ruled out by applying Equation (2)).

(−) (−) (−) (−) **Figure 17.** Boundary conditions with forces (**a**) *Fz* (−) (**b**) *Fz* (+) (**c**) *Fy* (−). Bolt preload forces.


(−) −0.002 −0.012 −0.010 −0.01

**Table 5.** FE displacements under different machining conditions for the Transfer Machine with 15 divisions.

**Figure 18.** FE displacements of the Transfer Machine with 15 divisions after bolt preloading (scale factor 1000×).

**Figure 19.** *Cont*.

(−) Δ (−) and (−) load case only, has been compared with the experimental outcome, retrieved by means of the The greatest displacement on the reference point is caused by the force *Fy* (−) (∆*y* = 0.01 mm), while both *Fz* (−) and *Fz* (+) cause a displacement of 0.008 mm. The result reported in Table 5, for the *Fy* (−) load case only, has been compared with the experimental outcome, retrieved by means of the test setup shown in Figure 20. The FEA outcome perfectly matches the experimental result. It is noteworthy that the vertical displacement of the Transfer Machine with 15 divisions is less than 17% of that for the same machine with nine divisions, under the same loading condition of vertical downwards drilling, even though the first has a much larger (and thus more flexible) rotary table. Such an outcome has been achieved thanks to a dynamic stiffening system developed by the authors. In fact, the stiffening ribs do not spin around the *y*-axis together with the rotary table; they are instead fixed to the ground. The ribs and the supports at the outer diameter of the rotary table (Figure 21a: in blue shades the moving parts) are clamped together just for the machining time, by means of a hydraulic clamp whose operating principle is quite the same of a disc brake (Figure 21b). This simple device allows for keeping the rotary table comparatively light, as well as achieving enough bending stiffness when needed. (−) Δ (−) and (−) load case only, has been compared with the experimental outcome, retrieved by means of the

(−) (−) **Figure 20.** Experimental measurement of the vertical displacement of the support in the case of *Fy* (−) = 500 N.

*Machines* **2018**, *6*, 2

— — **Figure 21.** Hydraulic locking clamp (**a**) nomenclature and geometry and (**b**) operating principle and hydraulic schematic (P—pressure line, T—tank line).

(−) In order to assess the possibility of further weight savings on the moving parts, further FEA have been run by changing the material assigned to the supports: e.g., lightweight alloys: aluminum, titanium, and magnesium. The comparison between the different solutions has been made in the case of *Fy* (−).The vertical displacements have been sampled along the path illustrated in Figure 22. The results in terms of vertical displacement for different choices of the support material, normalized with respect to the steel support are shown in the plot of Figure 23, whereas Figure 24 shows the displacements obtained with different materials combinations of the support and of the rotary table, normalized with respect to the steel-steel combination.

**Figure 22.** Sampling path defined along an edge of the loaded support.

(−) (−) **Figure 23.** FE displacements of the loaded support (normalized with respect to the steel support) with *Fy* (−) force: comparison between different materials of the support. (−)

(−) (−) **Figure 24.** FE displacements of the loaded support (normalized with respect to the steel-steel combination.) with *Fy* (−) force: comparison between different material combinations of the rotary table and the supports.

(−)

As can be appreciated by looking at Figure 23, besides Ti-alloys, which would have been impractical due to cost and manufacturing reasons, both Al-alloy and Mg-alloy supports negatively affect the bending stiffness of the assembly, especially at the outer edge where machining operations take place: a steel support is therefore the best option. On the other hand, looking at Figure 24, it can be seen that a combination of Al-alloy table and steel support would not be much more compliant than the base case with both components made of steel. The displacement at the outer end would increase by just 10 <sup>−</sup><sup>3</sup> mm, should the lighter construction be adopted. −

Based on these premises, an aluminum alloy has been chosen for the construction of the rotary table, whereas the supports have been built of steel.

#### *3.2. Modal Analysis*

Based on the settings reported in the previous sections for the Transfer Machine with nine divisions, a modal analysis has been carried out in order to determine the first five modes of vibration of the same machine with 15 divisions. The natural frequencies are reported in Table 6 and the first two modes are shown in Figure 25a,b.

**Table 6.** FE calculated natural frequencies of the Transfer Machine with 15 divisions.

**Figure 25.** Modes of vibration of the Transfer Machine with 15 divisions: (**a**) first mode; (**b**) second mode.

## **4. Discussion**

In light of the results presented in the previous sections, some general guidelines for the structural design of a modern transfer machine tool can be drawn.


#### **5. Conclusions**

An experimentally validated numerical model for transfer machine tools has been defined, which allows for forecasting the structural as well as the vibrational response of this kind of machine under typical operating loads. The models helped develop a bigger machine, evaluating different scenarios in terms of materials and design solutions. Through this approach, it has also been possible to optimize the structure in terms of flexural stiffness at a very early stage of the design. A proper choice of the materials and the introduction of an ad hoc designed stiffening solution made it possible to achieve even greater stiffness than with the smaller machine, thus ensuring the desired manufacturing tolerance of the finished parts. This choice will ultimately lead to higher speed and a more efficient machine whose performance is aligned with the values of green design.

**Author Contributions:** D.C. and N.V. conceived and designed the experiments; O.C. performed the experiments; M.D.A., S.F., and F.R. performed the numerical analyses; G.O. analyzed the data; N.V. provided reagents, materials and analysis tools; O.C., S.F. and M.D.A. wrote the paper.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **List of Symbols**


#### **References**


© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

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