**1. Introduction**

Achieving good surface quality in final parts is a widespread concern among manufacturers of all kinds. The milling of thin parts is an especially critical issue [1], since the stiffness of these parts is low, which eases the appearance of vibration, as chatter and forced vibration, which negatively affect final surface quality and tool life [2]. This problem can lead to the rejection of these parts or to the necessity of reprocessing, which entails high costs in terms of material, time, and energy.

However, as Kolluru and Axinte [3] and Irene Del Sol et al. [4] have pointed out, chatter avoidance in thin parts has traditionally focused on thin wall milling, whereas thin floor milling has been relegated, even though its importance is high in fields such as aeronautic and aerospace industries, where pockets are milled in parts as aircraft structures in order to lighten them and must comply with stringent surface requirements. Precisely, mechanical milling appears as an alternative to chemical milling for thin floors, which is hazardous and pollutant [5,6].

Chatter is a self-excited vibration that appears due to the dynamic excitation produced as a consequence of the chip thickness variation caused by the periodic irregular surface

**Citation:** Casuso, M.; Rubio-Mateos, A.; Veiga, F.; Lamikiz, A. Influence of Axial Depth of Cut and Tool Position on Surface Quality and Chatter Appearance in Locally Supported Thin Floor Milling. *Materials* **2022**, *15*, 731. https://doi.org/10.3390/ ma15030731

Academic Editors: Gilles Dessein and J. Antonio Travieso-Rodriguez

Received: 14 December 2021 Accepted: 17 January 2022 Published: 19 January 2022

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**Copyright:** © 2022 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 (https:// creativecommons.org/licenses/by/ 4.0/).

generated by the precedent tool tooth pass [7]. Mainly, three types of solutions have been proposed to cope with vibrations in mechanical milling of thin floors: fixture design aiming to increase the stiffness of the part, damping systems aiming to dissipate vibration energy, and the prediction of stable machining conditions [8]. Both fixture and damping systems can be ad hoc for a given geometry or flexible and adjustable for different ones. On the one hand, if they are ad hoc, they are able to avoid vibrations as they completely support thin floors, but they also require investments that are neither feasible nor profitable when manufacturing low batches, as it is usual in aeronautic and aerospace sectors [9]. On the other hand, flexible fixtures usually consist of actuators that support the part by means of vacuum cups. In such a layout, due to the distance between actuators, some zones of the part may be without back support. Chatter vibration can appear easily in this situation of extremely low stiffness. Due to this fact, this kind of fixture is usually discarded for high precision milling, as it is usual in aeronautic and aerospace sectors, and they are employed only for other operations, such as drilling, trimming, or for milling processes that do not require demanding tolerances [10]. As a consequence, the potential of flexible fixtures has not been fully harnessed yet. A deeper analysis consisting of predicting and selecting proper cutting conditions and areas leading to a stable and precise machining can be a solution [2]. It would make feasible thin floor milling even in the situation of such a low stiffness that happens in flexible fixtures.

In this line, F.J. Campa et al. [11] suggest the mathematical analysis of the cutting process for thin floors, by means of stability lobes diagram (SLD) determination, which allows the selection of the pair of values of spindle speed and axial depth of cut leading to the most stable and productive machining. In the case of parts with low stiffness, as thin floors are, the dynamic parameters of the part continuously vary during milling, since both mass and stiffness decrease. So, in addition to the depth of cut and spindle speed, Bravo et al. [12] suggest taking into account the geometric state of the part during milling, thus leading to three-dimensional SLD. This approach is followed in the present study, due to the low stiffness and the relatively high material removal rate that thin floors undergo.

The experimental setup has been planned to test different cutting conditions in a context of extremely low stiffness, which is a thin floor simply screwed in its corners and without back support. It emulates a thin floor supported by four clamping vacuum cups, as it happens in flexible fixtures. The objective is to analyze the milling of thin floors aiming to optimize the surface quality achieved and to avoid chatter vibration. For that purpose, thin plates have been pocket milled. Vibration and surface roughness results have been measured, discussed, and compared to the available bibliography. Finally, some guidelines are proposed to make such thin floor milling feasible.

## **2. Materials and Methods**

#### *2.1. Tested Parts*

Aiming to emulate a real industrial case, a series of pocketing tests were carried out in metal thin plates. Each thin plate is a square metal sample of 85 × 85 mm<sup>2</sup> and 2 mm thick, very similar to the samples used by Del Sol et al. [13] and Rubio-Mateos et al. [14]. The material is aluminum alloy UNS 2024-T3, widely employed in the aeronautic industry.

Prior to any machining operation, each thin floor was drilled near its corners to make holes of 7 mm in order to screw it to an intermediate rigid block that maintains the stability of the process. Each thin floor was elevated, so the screws were its only support and clamping during the entire machining process, which causes a reduction of stiffness in the axial direction of the mill. The centers of the screws form a square of 69 × 69 mm2. This layout is an extrapolation of the milling of a thin floor locally supported by four vacuum cups. The general setup is shown in Figure 1.

**Figure 1.** General setup of a sample to be machined, with the accelerometer below.

#### *2.2. Methodology*

The methodology employed in the present study of the pocket machining of thin plate samples comprises various steps.

First, the frequency response function (FRF) of the tool was measured prior to the machining, as well as the FRFs of the thin plates in four consecutive stages of the machining, in order to calculate the three-dimensional stability lobe diagrams (3D-SLD) of the system. Besides, the vibration of the sample during machining was continuously monitored, and it is used to calculate its Fast Fourier Transform (FFT). To this point, the methodology is similar to the one followed by Kolluru and Axinte [15] to analyze the impact dynamics in the machining of low rigidity workpieces, by means of the determination of dominant modes.

In addition, a roughness analysis was conducted at the end of the present study, in order to correlate it to the vibrations of the samples during machining. The general overview of the tasks is shown in Table 1.

**Table 1.** Conducted tasks.


#### *2.3. Machining Operation*

The machining operation that was performed in each thin floor consisted in a dry milling of a pocket of 50 × 50 mm<sup>2</sup> by an outward helicoidal strategy, which is one of the most suitable machining strategies regarding final roughness, accuracy, and process time, as Del Sol et al. [16] have proved. This strategy follows the guidelines of Herranz et al. [7] taking advantage of the rigidity of the uncut part, which is higher near the screws.

The strategy comprised 33 straight cutting passes, consecutively numbered in Figure 2, plus an initial brief drilling in the center in order to start the milling.

The pocket machining was performed in a 5-axis NC center Ibarmia ZV 25U600 EXTREME, with a two flutes bull-nose end-mill Kendu 4400, which has a 10 mm diameter, 30◦ helix angle and 2.5 mm edge radius (*r*).

Regarding the cutting conditions, conservative ones were selected, as they lead to lower part distortion and lower surface roughness in an aluminum alloy [17,18]. Even though the machining time is higher, this factor is out of the scope of the present study. So, the spindle spins at 4000 rpm and the feed rate was 800 mm/min (0.1 mm/tooth). The radial immersion of the mill was 5 mm.

**Figure 2.** Followed outward helicoidal machining strategy.

A different axial depth of cut was employed for pocketing each thin floor (1, 0.8, 0.4 and 0.2 mm), in order to compare the influence of different material removal rates both in vibrations and in achieved final roughness. Due to the depths of cut employed, the thin plates can be named as shown in Table 2. Their remaining features, both in material and in machining operation, are identical.


**Table 2.** Thin plates according to the depth of cut.

## *2.4. Vibration Monitoring, FRF Obtention and SLD Calculation*

SLDs of the thin plate samples are calculated from their FRFs, which quantify the response of the sample–tool–spindle–machine system to an excitation. Nevertheless, the calculation of the SLDs of parts with low thickness as employed thin plates entails two phenomena. The first one is that the stiffness of the part is lower than the stiffness of the cutting tool, so chatter vibration is mostly affected by the dynamic properties and critical modes of the part [19]. The second phenomenon is the ratio of material removal, which is high compared to the global volume of the part and that leads to a continuous change in its modal parameters and FRF during machining [20]. In order to consider this feature, there are two possibilities. The first one is the use of Finite Element Analysis (FEA) that aims to simulate the FRFs of the samples. This option was used and validated by Dang et al. [21], who consider the second possibility impractical, that is, the Experimental

Modal Analysis (EMA), which aims to measure the FRFs of the samples conducting several impact hammer tests during machining and measuring the response of the system with an attached accelerometer [22]. Nevertheless, FEA also entails the requirement of high computational resources and time expended, so EMA is a suitable option, especially for short machining with a simple setup as the one presented in this study. This option was also followed by Qu et al. [23].

Consequently, aiming to obtain the SLDs of the system, several FRF tests were conducted at different stages of the machining. In each test, an impact hammer hit the sample at its top center, while an accelerometer placed at the bottom center registers the corresponding data. The first test was performed prior to any machining operation, the second one was performed after cutting pass 5, the third one after cutting pass 17, and the last one with the pocket completed, so four FRF tests were performed in each sample. As a consequence of performing each test in different stages of the machining, the calculated SLDs take into account not only the axial depth of cut and the spindle speed, but also the position reached by the tool along the cutting path.

The accelerometer is a uniaxial PCB model 352C22 with a measuring range from 1 to 10 kHz and a sensitivity of 1.0 mV/(m/s2), located at the bottom center of the thin floor. This accelerometer was also used to continuously monitor vibrations during machining.

The FRF was obtained only in the thick direction or Z direction of the sample, which is considered to be overwhelmingly less rigid than the others, so it is regarded that the workpiece only moves along this direction, an assumption also followed by Seguy et al. [24] and Arnaud et al. [25].

In the case of the tool, the FRF was obtained in its three spatial directions, gluing the accelerometer to the tool. As the FRF of the tool does not vary during machining, a single impact test before machining suffices for obtaining it.

Aiming to determine the machining conditions leading to chatter vibration, stability lobes were calculated. Since modal parameters of the samples vary during material removal, several stability lobes were obtained corresponding to different machining stages, precisely, the machining stages where FRF tests were undertaken, enabling the calculation of SLDs that also take into account the position reached by the tool along the cutting path. This kind of 3D-SLD was also obtained by Campa et al. [11], analyzing thin floor milling.

Thus, these SLDs show the maximum chatter-free axial depth of cut regarding each spindle speed for a given stage of the machining. They have been obtained by applying the three-dimensional mono-frequency model [26,27], and combining the FRF of the samples with the FRF of the tool.

The forces used in this calculation have been obtained employing the mechanistic approach [28,29], which relates the force components (tangential [*Ft*], radial [*Fr*] and axial [*Fa*]) acting in each differential element *j* of the edge of the mill during machining to the feed per tooth (*fz*), and length (*dS*), angular position (Φ) and axial depth of cut (*dz*) of the element *j*.

$$
\begin{bmatrix} dF\_t(\Phi, z) \\ dF\_t(\Phi, z) \\ dF\_{\tilde{a}}(\Phi, z) \end{bmatrix}\_j = \begin{bmatrix} K\_{t\varepsilon} \\ K\_{t\varepsilon} \\ K\_{a\varepsilon} \end{bmatrix} \cdot dS(z) + \begin{bmatrix} K\_{t\varepsilon} \\ K\_{t\varepsilon} \\ K\_{t\varepsilon} \end{bmatrix} \cdot f\_z \cdot \sin\Phi(\Phi\_j, z) \cdot dz \tag{1}
$$

This relation is based on the friction (*Kte*, *Kre*, *Kae*) and shearing (*Ktc*, *Krc*, *Kac*) cutting coefficients, which have been obtained prior to the pocketing operation. Precisely, they were obtained solving the equations using force values measured in a previous grooving test, taking a constant value for the spindle speed of 4000 rpm, which is the speed employed in the pocketing tests.

Bull-nose end mills have a lead angle that varies from 0◦ to 90◦. For the case of the mill employed in the present study, these values would correspond to 0 and 2.5 mm of the axial depth of cut, respectively. Altintas [26] suggested that an average value of 45◦ could be taken. Since in the present study the axial depth of cut varies only from 0.2 mm to 1 mm, a lower constant lead edge angle could be considered. Following Rubio-Mateos et al. [30], a constant lead edge angle of 20◦ is taken.
