Next Article in Journal
Analysis of Threshold Voltage Shift for Full VGS/VDS/Oxygen-Content Span under Positive Bias Stress in Bottom-Gate Amorphous InGaZnO Thin-Film Transistors
Next Article in Special Issue
Positioning Accuracy Determination of the Servo Axes for Grinding Wavy-Tilt-Dam Seals Using a Four-Axis Grinder
Previous Article in Journal
A Magnetically Actuated Superhydrophobic Ratchet Surface for Droplet Manipulation
Previous Article in Special Issue
Research on Precision Blanking Process Design of Micro Gear Based on Piezoelectric Actuator
 
 
Font Type:
Arial Georgia Verdana
Font Size:
Aa Aa Aa
Line Spacing:
Column Width:
Background:
Article

Cutting Force Prediction Models by FEA and RSM When Machining X56 Steel with Single Diamond Grit

College of Mechanical and Electrical Engineering, Harbin Engineering University, Nantong Ave 145, Harbin 150001, China
*
Author to whom correspondence should be addressed.
Micromachines 2021, 12(3), 326; https://doi.org/10.3390/mi12030326
Submission received: 1 February 2021 / Revised: 14 March 2021 / Accepted: 15 March 2021 / Published: 19 March 2021
(This article belongs to the Special Issue Micro and Nano Machining Processes)

Abstract

:
In the field of underwater emergency maintenance, submarine pipeline cutting is generally performed by a diamond wire saw. The process, in essence, involves diamond grits distributed on the surface of the beads cutting X56 pipeline steel bit by bit at high speed. To find the effect of the different parameters (cutting speed, coefficient of friction and depth of cut) on cutting force, the finite element (FEA) method and response surface method (RSM) were adopted to obtain cutting force prediction models. The former was based on 64 simulations; the latter was designed according to DoE (Design of Experiments). Confirmation experiments were executed to validate the regression models. The results indicate that most of the prediction errors were within 10%, which were acceptable in engineering. Based on variance analyses of the RSM models, it could be concluded that the depth of the cut played the most important role in determining the cutting force and coefficient the of friction was less influential. Despite making little direct contribution to the cutting force, the cutting speed is not supposed to be high for reducing the coefficient of friction. The cutting force models are instructive in manufacturing the diamond beads by determining the protrusion height of the diamond grits and the future planning of the cutting parameters.

1. Introduction

Submarine pipelines play a major role in the transportation of offshore oil and gas, but they fail from time to time due to various reasons [1]. It is necessary to remove the faulty part for maintenance, yet conventional means are not as effective as desired. In the past few decades, diamond wire saws have become the top choice for cutting hard material [2] and those designed for submarine pipeline cutting are already in practical use [3]. The study of the factors influencing submarine pipeline cutting is of great significance for the planning of the cutting parameters. The reasonable feed speed range of the diamond wire saw cutting submarine pipelines was defined [4]. Considering that both the service life and the working efficiency of the brazed diamond grits are superior to the sintered ones, the former was chosen as subject of this work [5]. The primary wear form of the diamond beads is pulled-out grits, and the breakages of the diamond wire were mainly due to fatigue failure [6,7]. Therefore, the planning of the cutting parameters is crucial to diamond wire saw cutting.
Numerous models were proposed to explain the mechanism of the cutting force [8,9,10,11]. The issues become more complicated in micromachines. Conventional models need adjustment for not being able to capture its behavior in microscale [12,13]. The chip formation mechanism varies considerably [14]. The factors that are significant in micromachines might be of little significance in conventional machining [15]. Chip formation models combining cutting tool geometries and materials microstructures were developed [16,17,18]. The chip formation mechanism of both the single diamond grit and the diamond beads was analyzed in the previous work [19].
FEM has proven to be an effective method of studying friction and cutting force [20,21]. The authors compared various pieces of FEM software and found that the performance of DEFORM-2D is superior to the others in large deformation cutting [22]. FEM was also applied to predict the tool wear evolution and tool life in orthogonal cutting [23]. To derive the magnitude and distribution of stress/strain in the metal matrix material, the authors used ANSYS/LS-DYNA software to simulate the cutting process of SiC particle-reinforced aluminum-based metal materials and the results indicated that the contact between the cutting tool and the particles was the main cause of particle fracture and dislodgement [24]. The experimental work is substituted for virtual experiments carried out using a finite element method model of the cutting process to obtain the specific cutting coefficients [25].
The response surface methodology (RSM) is convenient for predicting the interaction and the main effects of the different influential combinations of the machining parameters [26,27]. The prediction models of the cutting forces were established using the FEM and RSM methods, respectively, and the results indicate that both methods can be used for the accurate prediction of the cutting forces [28]. Besides, it is feasible to use the RSM method to model the cutting force based on the FE data [29].
In this work, two means were used to obtain the regression equation of the cutting force. One was to use AdvantEdge software to simulate the single grit cutting steel, the virtual experiment data of which was applied to fit the empirical equation of the cutting force; the other obtained the regression equation of the cutting force and corresponding response surface by Design of Experiments. The effect of the different parameters on the cutting force was analyzed. Finally, experiments were conducted to verify the reliability of the cutting force equations.

2. Finite Element Modeling

Virtual experiments using FEM have proved to be an effective means of substituting experiments [25]. The chief advantage of FEM is the convenience of obtaining machining information that is difficult to obtain without massive experiments [30]. The mechanisms of diamond grits cutting and the procedural steps involved in the modeling were discussed as follows:

2.1. The Mechanisms of Diamond Grits Cutting

To analyze the mechanisms of diamond grits cutting, an experimental platform (Figure 1) of diamond wire saw was adopted.
In the process of X56 steel cutting, the bond on the surface of diamond grits was worn away and the diamond grits revealed themselves afterward because the matrix of the diamond beads was softer. Figure 2 describes the change in the surface topography of the brazed diamond beads. The initial state of diamond beads’ surface observed by SEM is shown in Figure 2a, and the bond on the surface was worn away after cutting, as shown in Figure 2b.
Periodic extrusion and friction result in fatigue cracks and abrasive wear on the one hand, yet, on the other hand, subtly changed the positions of the diamond grits, thus avoiding complete abrasion. Figure 3 shows the abrasive wear and position change of a single diamond grit during cutting. The protrusion heights of the brazed diamond beads are higher than those of the sintered ones. Additionally, the bonds between the diamond grits and the matrix of beads are so strong that the dropping of grits is rare. Therefore, a brazed diamond wire saw is an ideal choice for X56 steel pipeline cutting.
The machined chips and the corresponding grooved surface are of significance for the understanding of the cutting process. It would be much too difficult to capture and precisely measure the chips produced by single diamond grits because they are relatively small-scale. Therefore, the chips and scratches produced by diamond beads, instead of single diamond grits, were observed in our previous work [19]. The microscopic observation of the chips and corresponding grooved surfaces are shown in Figure 4a,b, respectively.

2.2. Modeling of the Single Diamond Grit

The diamond grits on the diamond beads are artificial. According to the diamond beads observed by SEM in Figure 2 and Figure 3, the diamond grits have a relatively regular octahedral hexakis shape, and more than 70% of them are wrapped. The prism length ranges from 150 μm to 250 μm and the value is set as 200 μm for simplicity. The two-dimensional model of the diamond grit is shown in Figure 5.
A two-dimensional finite element machining model for X56 steel was performed by AdvantEdge as the 2D machining model has diverged from the 3D machining process [31]. Therefore, the approach features few uncertainties present with this conversion is economical and highly reliable [32]. AdvantEdge is a software designed for metal cutting simulation [32,33], the finite element simulation process diagram of which is shown in Figure 6. Diamond (polycrystalline diamond) was picked as the material of the diamond grits, and X56 steel was chosen as the workpiece material.

2.3. Modeling of the Cutting Force

There was an empirical formula describing the relationship between cutting force, friction coefficient, depth of cut and cutting speed. The virtual experiment was conducted by AdvantEdge FEM software to obtain the mathematical model of cutting force.
The range of cutting speed of diamond wire saw is 960–1500 m/min [4], and the cutting depth ranges from 0.01 mm to 0.04 mm. The range of common friction coefficient value is 0.1–0.8. Parameters of the virtual experiments are shown in Table 1, according to which the cutting virtual experiments were carried out to fit the empirical formula and the data is shown in the table of Appendix A.
There is a complex exponential relationship between the cutting force and each factor [34]. During the simulation, it was found that the friction coefficient, cutting speed and depth of cut were the main factors affecting the magnitude of the cutting force. By analogy with the diamond wire cutting model [3], an empirical equation for single grit cutting force can be derived as follows:
F   =   k v b 1 h b 2 μ b 3
where v, h and μ represent cutting speed, depth of cut and coefficient of friction, respectively. Moreover, k ,   b 1 , b 2 and b 3 denote constants.
The cutting forces obtained by performing 64 sets of simulations according to the virtual experimental scheme in Table 1 are shown in the Appendix A Table A1 at the end of the paper. According to the mathematical model of the cutting force in Equation (1), the equation obtained by least-squares fitting is as follows:
F   =   79 . 4941 v 0 . 0977 h 0 . 7145 μ 0 . 2020

3. Response Surface Regression Modeling

3.1. Principle of Tribometer and Experiments

The principle of the tribometer is shown in Figure 7. In the work, the SFT-2M tribometer shown in Figure 8 was used to conduct the experiments providing the data RSM needs.
According to the operation manual, the feed depth of the machine is about 0.01 mm every 10 min under a certain load. The initial feed depth varies as the knob on the top of the machine rotates. The cutting speed is controlled by adjusting the rotate speed ω of the workpiece and the offset distance of the fixture.
The diamond grits were made of polycrystalline diamond, and the material of the workpiece was X56 steel, The X56 steel was machined into a thin round sheet with a thickness of 2 mm and fixed by the fixture.
The tribometer used for the microcutting experiments was connected to an industrial computer as shown in Figure 9a. The force was output in the form of the curve and sampling points. Figure 9b shows the curve of the output cutting force drawn according to the sampling points. To make it easier for further comparison, the mean value of the small-scale bandwidth fluctuations is chosen as the cutting force.

3.2. Response Surface Methodology and Design of Experiment

The range of friction coefficient and cutting speed is identical to the previous FEM, but the range of cutting depth is modified to 0.02–0.04 mm as oxide film was found on the surface of the steel sheet. Therefore, a certain depth of the steel sheet needs to be removed before the experiment to improve the accuracy.
A central composite face centered design with six center points was used in this study, and the three levels of the experimental input parameters (cutting speed, depth of cut and friction coefficient) are shown in Table 2. The responses obtained after the experiments are given in Table 3. ANOVA analysis was used to obtain significant parameters with their effects, and a response cutting force model was developed. The purpose of this study was to investigate the relationship between the obtained responses and the input variables.
In this work, the mathematical regression equation of the cutting force was found using the response surface method and the relationship between the input parameters was investigated. The experimental results of the cutting force analysis using ANOVA are shown in Table 4.
As can be seen in Table 4, a statistical cubic model is more suitable for analyzing the factors influencing the cutting force of a single diamond grit. The mathematical regression model of the cutting forces generated using Design Expert-12.0 can be expressed as Equation (3).
FrictionForce = 2.79 − 0.0585A + 0.646B + 0.4895C − 0.0131AB − 0.0106AC + 0.1179BC + 0.0079A2
−0.0306B2 − 0.1671C2 − 0.00260ABC − 0.0391A2B − 0.0041 A2C + 0.0039AB2
where A is cutting speed, B is depth of cut, C is coefficient of friction.
Figure 10 shows the estimated response surface for the cutting force concerning the coefficient of the friction and the depth of the cut. The effect of the depth of the cut and cutting speed on the cutting force is shown in Figure 11. By comparing Figure 10 and Figure 11, it could be concluded that with an increase in the depth of the cut and the coefficient of friction, the cutting force shows an increasing trend. The depth of the cut is the most significant factor that affects cutting force among the three. However, lowering the protrusion height could enlarge the area of the diamond–workpiece contact surface [35]. Therefore, the protrusion heights of the diamond grits deserve high priority when manufacturing diamond beads that serve different purposes. Despite making little direct contribution to the cutting force, the cutting speed is not supposed to be high in the cutting process for reducing the coefficient of friction [36].

4. Confirmation Experiment

Besides ANOVA analysis for cutting force by RSM, the tribometer used in the response surface regression modeling was also employed in the validation of the developed models since the instrument was convenient in precise measurement. The confirmation experiment results are shown in Table 5. The comparison between the predicted values for cutting force obtained by RSM, FEA and experimental data indicates that predictions were in close agreement with each other (Table 5). The prediction errors of the FEM model and experimental results vary from −11.7% to −6.4%, while the errors between the RSM model and the experimental results range from −9.99% to 10.02%. The results indicate that the prediction errors of both models are acceptable in engineering [4,37], in view of the randomly distributed diamond grits on the beads in our research [5]. It can also be observed that most of the actual cutting force is less than those calculated by the empirical formula. This phenomenon may be ascribed to the graphitization of the steel, which is not taken into consideration because the diamond wire saw in our research works underwater.

5. Conclusions

Conventional research on the diamond wire saw cutting process concentrated on a macroscale, which was not helpful enough to understand the nature of the machining process, and henceforth, the cutting force prediction model of the single diamond grit was necessary. In this work, the relationship between the cutting force and the different parameters (depth of cut, cutting speed and coefficient of friction) was found through FEA and RSM modelling and experimental substantiation. The subsequent conclusions are as follows:
  • Two means were used to obtain the equation of the cutting force. In the first approach, AdvantEdge was used to simulate the cutting process, and the virtual experiment data were applied to fit the empirical equation of the cutting force. In the second one, the regression equation of the cutting force and the corresponding response surface was obtained by Design of Experiments.
  • Twelve confirmation experiments were conducted, and the results indicate that both derived models can predict the cutting force with fair accuracy. The prediction errors of the developed models and experimental results vary from −11.7% to 10.02%, which are acceptable in engineering. Additionally, the predicted values of the regression model using FEM were generally lower than the experimental results because graphitization was not included in FEM.
  • The results of RSM reveal that with increasing depth of cut and coefficient of friction, cutting force shows an increasing trend. High cutting speed increases cutting efficiency while reducing the coefficient of friction. Hence, the cutting speed needs to be restricted to a specified range. The influence of the depth of the cut is the most significant among the three factors. However, high protrusion contributes to less grit–workpiece contact. Therefore, the protrusion heights of the diamond grits deserve first priority when manufacturing diamond beads that serve different purposes.
In summary, the derived models are effective in the parametric programming of diamond wire saw cutting and manufacturing.

Author Contributions

Conceptualization, L.Z. and X.S.; methodology, M.L. and X.S; software, X.S. and Y.P.; validation, L.W., M.L. and L.Z.; formal analysis, X.S.; investigation, X.S.; resources, L.W.; data curation, L.Z.; writing—original draft preparation, X.S.; writing—review and editing, M.L.; visualization, L.W.; supervision, M.L.; project administration, L.Z.; funding acquisition, L.Z. All authors have read and agreed to the published version of the manuscript.

Funding

This work was supported by the National Natural Science Foundation of China (Grant No. 5167051260), the State Key Laboratory of Ocean Engineering, China (Grant No. 1804) and the Provincial Natural Science Foundation of Heilongjiang (Grant No. JJ2019LH1520).

Conflicts of Interest

The authors declare no conflict of interest.

Appendix A

Table A1. Results of the virtual experiment.
Table A1. Results of the virtual experiment.
Num of Experimentν
(m/min)
f
(mm/r)
µF
(N)
19600.010.10.9178
20.31.2018
30.51.4041
40.71.4081
50.020.11.5144
60.31.9554
70.52.3423
80.72.3861
90.030.12.0514
100.32.5581
110.53.0224
120.73.0845
130.040.12.5614
140.33.1344
150.53.5284
160.73.6851
1711400.010.10.8922
180.31.1736
190.51.3336
200.71.3224
210.020.11.5044
220.31.9422
230.52.2216
240.72.2826
250.030.12.0472
260.32.5521
270.52.9478
280.73.0292
290.040.12.5468
300.33.0598
310.53.4636
320.73.5468
3313200.010.10.8794
340.31.1662
350.51.3014
360.71.2626
370.020.11.4896
380.31.9056
390.52.2318
400.72.2416
410.030.12.0496
420.32.5364
430.52.9374
440.72.9072
450.040.12.5484
460.33.0478
470.53.4502
480.73.5606
4915000.010.10.8728
500.31.1494
510.51.2626
520.71.2232
530.020.11.4896
540.31.8744
550.52.1764
560.72.2094
570.030.12.0292
580.32.5174
590.52.8846
600.72.9058
610.040.12.5443
620.33.0476
630.53.4006
640.73.5346

References

  1. Bai, Y.; Bai, Q. Risk Analysis for Subsea Pipelines. In Subsea Pipeline Integrity and Risk Management, 1st ed.; Gulf Professional Publishing: Oxford, UK, 2014; pp. 169–212. [Google Scholar]
  2. Maeda, H.; Takanabe, R.; Takeda, A.; Matsuda, S.; Kato, T. High-Speed Slicing of SiC Ingot by High-Speed Multi Wire Saw. Mater. Sci. Forum. 2014, 778, 771–775. [Google Scholar] [CrossRef]
  3. Cao, L.; Meng, Q.; Wang, L.; Tong, W. Research on Underwater Diamond Wire Saw. In Proceedings of the 2006 IEEE International Conference on Mechatronics and Automation, Luoyang, China, 25–28 June 2006; pp. 1695–1700. [Google Scholar]
  4. Wang, Z.; Zhang, B.; Wang, L.Q.; Xu, D. Research on Experimentation of Diamond Wire Saw Cutting Compound Pipes Underwater. Mater. Sci. Forum. 2009, 626, 303–308. [Google Scholar] [CrossRef]
  5. Horita, Z.; Xiao, B.; Fu, Y.; Su, H.; Xu, J.; Xu, H. Machining Performance of Brazed Diamond Wire Saw with Optimum Grain Distribution. Key. Eng. Mat. 2006, 304, 43–47. [Google Scholar] [CrossRef]
  6. Ge, P.Q.; Gao, Y.F.; Li, S.J.; Hou, Z.J. Study on Electroplated Diamond Wire Saw Development and Wire Saw Wear Analysis. Key. Eng. Mat. 2009, 416, 311–315. [Google Scholar] [CrossRef]
  7. Huang, G.Q.; Xu, X.P. Analysis of the Breakage of Diamond Wire Saws in Sawing of Stone. Key. Eng. Mat. 2006, 4, 123–126. [Google Scholar] [CrossRef]
  8. Maity, K.P.; Das, N.S. A class of slipline field solutions for metal machining with slipping and sticking contact at the chip-tool interface. J. Mech. Sci. 2001, 43, 2435–2452. [Google Scholar] [CrossRef]
  9. Behrens, B.-A.; Bouguecha, A.; Hadifi, T.; Mielke, J. Advanced friction modeling for bulk metal forming processes. Prod. Eng. 2011, 5, 621–627. [Google Scholar] [CrossRef]
  10. Schulze, V.; Michna, J.; Schneider, J.; Gumbsch, P. Modelling of cutting induced surface phase transformations considering friction effects. Proc. Eng. 2011, 19, 331–336. [Google Scholar] [CrossRef]
  11. Özel, T.; Zeren, E. A Methodology to Determine Work Material Flow Stress and Tool-Chip Interfacial Friction Properties by Using Analysis of Machining. J. Manufac. Sci. Eng. Trans. ASME 2006, 128, 119–129. [Google Scholar] [CrossRef]
  12. Rahman, M.A.; Rahman, M.; Mia, M.; Gupta, M.K.; Sen, B.; Ahmed, A. Investigation of the specific cutting energy and its effect in shearing dominant precision micro cutting. J. Mater. Process. Tech. 2020, 283, 116688. [Google Scholar] [CrossRef]
  13. Wu, X.; Li, L.; He, N. Investigation on the burr formation mechanism in micro cutting. Precis. Eng. 2017, 47, 191–196. [Google Scholar] [CrossRef]
  14. Woon, K.S.; Rahman, M. Extrusion-like chip formation mechanism and its role in suppressing void nucleation. CIRP Annals 2010, 59, 129–132. [Google Scholar] [CrossRef]
  15. Rahman, M.; Rahman, M.; Anantharajan, S.K. Material perspective on the evolution of micro- and nano-scale cutting of metal alloys. J. Micromanuf. 2018, 1. [Google Scholar] [CrossRef]
  16. Rahman, M.A.; Woon, K.S.; Venkatesh, V.C.; Rahman, M. Modelling of the combined microstructural and cutting edge effects in ultraprecision machining. CIRP Ann. 2018, 67, 129–132. [Google Scholar] [CrossRef]
  17. Rahman, M.A.; Amrun, M.R.; Rahman, M.; Kumar, A.S. Variation of surface generation mechanisms in ultra-precision machining due to relative tool sharpness (RTS) and material properties. Int. J. Mach. Tool. Manu. 2017, 115, 15–28. [Google Scholar] [CrossRef]
  18. Rahman, M.A.; Rahman, M.; Kumar, A.S. Modelling of flow stress by correlating the material grain size and chip thickness in ultra-precision machining. Int. J. Mach. Tool. Manu. 2017, 123, 57–75. [Google Scholar] [CrossRef]
  19. Zhang, L.; Sun, Y.; Liu, M.; Liu, M.; Wang, L. Research on the influence of cutting parameters on chips in the process of diamond bead cutting pipeline steel. Diam. Relat. Mater. 2021, 111, 108220. [Google Scholar] [CrossRef]
  20. Markopoulos, A.P. Application of FEM in Metal Cutting. In Finite Element Method in Machining Processes, 1st ed.; Markopoulos, A.P., Ed.; Springer: London, UK, 2013; pp. 59–69. [Google Scholar]
  21. Umbrello, D. Finite element simulation of conventional and high speed machining of Ti6Al4V alloy. J. Mater. Process. Tech. 2008, 196, 79–87. [Google Scholar] [CrossRef]
  22. Bil, H.; Kılıç, S.E.; Tekkaya, A.E. A comparison of orthogonal cutting data from experiments with three different finite element models. Int. J. Mach. Tool. Manu. 2004, 44, 933–944. [Google Scholar] [CrossRef]
  23. Yen, Y.-C.; Söhner, J.; Lilly, B.; Altan, T. Estimation of tool wear in orthogonal cutting using the finite element analysis. J. Mater. Process. Tech. 2004, 146, 82–91. [Google Scholar] [CrossRef]
  24. Pramanik, A.; Zhang, L.C.; Arsecularatne, J.A. An FEM investigation into the behavior of metal matrix composites: Tool–particle interaction during orthogonal cutting. Int. J. Mach. Tool. Manu. 2007, 47, 1497–1506. [Google Scholar] [CrossRef]
  25. Gonzalo, O.; Jauregi, H.; Uriarte, L.G.; López de Lacalle, L.N. Prediction of specific force coefficients from a FEM cutting model. Int. J. Adv. Manuf. Tech. 2008, 43, 348. [Google Scholar] [CrossRef]
  26. Jeyakumar, S.; Marimuthu, K.; Ramachandran, T. Prediction of cutting force, tool wear and surface roughness of Al6061/SiC composite for end milling operations using RSM. J. Mech. Sci. Technol. 2013, 27, 2813–2822. [Google Scholar] [CrossRef]
  27. Kathiravan, S.; Sathees, T. Application of RSM in the optimization of cutting conditions in metal matrix composites. Int. J. App. Eng. 2015, 10, 11018–11022. [Google Scholar]
  28. Kadirgama, K.; Abou-El-Hossein, K.; Mohammad, B.; Al-Ani, H.; Noor, M.M. Cutting force prediction model by FEA and RSM when machining Hastelloy C-22HS with 90° holder. J. Sci. Ind. Res. India 2008, 67, 421–427. [Google Scholar]
  29. Setia, S. Comparative analysis and optimization of FEM and RSM based regression model with experimental results for the dry turning of SiCp- Al7075 composite. Silicon 2020. [Google Scholar] [CrossRef]
  30. Sartkulvanich, P.; Altan, T.; Göcmen, A. Effects of flow stress abd friction models in finite element simulation of orthigonal cutting. Mach. Sci. Tech. 2005, 9, 1–26. [Google Scholar] [CrossRef]
  31. Wang, J.; Ye, R.; Tang, Y.; Bin, H. 3D dynamic finite element simulation analysis of single abrasive grain during surface grinding. Diam. Abras. Eng. 2009, 173, 41–45. [Google Scholar]
  32. Franchi, R.; del Prete, A.; Umbrello, D.; Mariano, E. Inverse analysis procedure to determine flow stress and friction data for metal cutting Finite Element Modeling. Key Eng. Mat. 2015, 651, 1345–1350. [Google Scholar] [CrossRef]
  33. Kwiatkowska, E.; Niesłony, P.; Grzesik, W. The numerical investigation of stress distribution on the rake face for grooved cutting tool inserts. Adv. Mater. Res. 2011, 223, 304–313. [Google Scholar] [CrossRef]
  34. Knight, W.A.; Boothroyd, G. Fundamentals of Metal Machining and Machine Tools, 3rd ed.; I K International Publishing House Pvt. Ltd.: New Delhi, India, 2019. [Google Scholar]
  35. Xu, X.P.; Zhang, G.Q.; Huang, H. Face Grinding of Granite with Brazed Diamond Grits. Key Eng. Mater. 2004, 259, 26–32. [Google Scholar] [CrossRef]
  36. Sterle, L.; Pušavec, F.; Kalin, M. Determination of Friction Coefficient in Cutting Processes: Comparison between Open and Closed Tribometers-Sciencedirect. Procedia CIRP 2019, 82, 101–106. [Google Scholar] [CrossRef]
  37. Cao, L. Research on Cutting Technology of Underwater Diamond Wire Saw. In Proceedings of the 2008 IEEE International Conference on Automation and Logistics, Qingdao, China, 1–3 September 2008; pp. 2751–2756. [Google Scholar]
Figure 1. Experimental platform of diamond wire saw cutting.
Figure 1. Experimental platform of diamond wire saw cutting.
Micromachines 12 00326 g001
Figure 2. Surface topography of brazed diamond beads: (a) before the cutting, (b) after the cutting.
Figure 2. Surface topography of brazed diamond beads: (a) before the cutting, (b) after the cutting.
Micromachines 12 00326 g002
Figure 3. Change of single diamond grit: (a) initial state (b) abrasive wear and pose change.
Figure 3. Change of single diamond grit: (a) initial state (b) abrasive wear and pose change.
Micromachines 12 00326 g003
Figure 4. Microscopic observation of the (a) grooved surface and (b) chips.
Figure 4. Microscopic observation of the (a) grooved surface and (b) chips.
Micromachines 12 00326 g004
Figure 5. Two-dimensional model of the diamond grit.
Figure 5. Two-dimensional model of the diamond grit.
Micromachines 12 00326 g005
Figure 6. Finite element simulation process diagram of AdvantEdge.
Figure 6. Finite element simulation process diagram of AdvantEdge.
Micromachines 12 00326 g006
Figure 7. Principle of tribometer.
Figure 7. Principle of tribometer.
Micromachines 12 00326 g007
Figure 8. SFT-2M tribometer.
Figure 8. SFT-2M tribometer.
Micromachines 12 00326 g008
Figure 9. Experimental setup with (a) output of SFT-2M tribometer (b) cutting force measurement.
Figure 9. Experimental setup with (a) output of SFT-2M tribometer (b) cutting force measurement.
Micromachines 12 00326 g009
Figure 10. Response surface of the depth of cut and coefficient of friction on cutting force.
Figure 10. Response surface of the depth of cut and coefficient of friction on cutting force.
Micromachines 12 00326 g010
Figure 11. Response surface of the depth of cut and cutting speed on cutting force.
Figure 11. Response surface of the depth of cut and cutting speed on cutting force.
Micromachines 12 00326 g011
Table 1. Process parameters and their limits.
Table 1. Process parameters and their limits.
Levels Parameters1234
Cutting speed (m/min)960114013201500
Depth of cut (mm)0.010.020.030.04
Coefficient of friction0.10.30.50.7
Table 2. Process parameters and their limits.
Table 2. Process parameters and their limits.
ParametersLevel 1Level 2Level 3
Cutting Speed (m/min)96012301500
Depth of Cut (mm)0.020.030.04
Coefficient of Friction0.10.40.7
Table 3. Design layout and experimental results.
Table 3. Design layout and experimental results.
Run OrderCutting Speed (m/min)Depth of Cut (mm)Coefficient of FrictionCutting Force (N)
112300.030.42.791
212300.030.12.134
315000.040.12.55
412300.020.42.114
59600.020.11.66
69600.040.73.892
712300.030.42.791
815000.020.11.593
99600.040.12.659
109600.020.72.411
1112300.030.42.791
1215000.020.72.312
1312300.030.73.113
1412300.030.42.79
1512300.030.42.792
1612300.030.42.789
179600.030.42.857
1815000.030.42.74
1915000.040.73.73
2012300.040.43.406
Table 4. Results of ANOVA for cutting force by response surface method (RSM).
Table 4. Results of ANOVA for cutting force by response surface method (RSM).
SourceSum of SquaresDOFMean SquareF-Valuep-ValueSignificance
Model6.46130.49655.566   × 10 5 <0.0001Significant
A-Cutting Speed0.006810.00687672.82<0.0001-
B-Depth of cut0.834610.83469.356 × 10 5 <0.0001
C-Coefficient of Friction0.479210.47925.372   × 10 5 <0.0001
AB0.001410.00141544.90<0.0001
AC0.000910.00091012.42<0.0001
BC0.111210.11121.246   × 10 5 <0.0001
A20.000210.0002192.84<0.0001
B20.002610.00262884.90<0.0001
C20.076810.076886069.91<0.0001
ABC0.000110.000161.800.0002
A2B0.002410.00242745.63<0.0001
A2C0.000010.000030.520.0015
AB20.000010.000026.930.0020
AC20.00000---
B2C0.00000
BC20.00000
A30.00000
B30.00000
C30.00000
Residual5.352   × 10 6 68.920   × 10 7
Lack of Fit1.894   × 10 8 11.894   × 10 8 0.01780.8992Not significant
Pure Error5.333   × 10 6 51.067   × 10 6 ---
Cor Total6.4619-
Table 5. Results of the confirmation experiment.
Table 5. Results of the confirmation experiment.
Numbers of ExperimentsCutting Speed (m/min)Depth of Cut (mm)Coefficient of FrictionCutting Force (N)RSM ResultsError%FEM ResultsError%
113000.020.51.7961.99610.022.096−11.7
210000.030.212.2112.1025.192.411−8.3
311000.040.513.112.839.893.51−11.4
415000.020.521.9832.203−9.992.083−6.9
511500.030.482.6112.761−5.432.811−7.11
612400.040.373.0012.8017.143.251−7.69
713400.020.611.8251.985−8.061.675−8.96
89800.030.42.6022.54.082.752−6.81
912800.040.312.9272.7775.43.127−6.4
1011600.020.491.9611.837.162.111−7.11
1114000.030.22.112.311−8.72.31−8.66
1213400.040.352.8913.191−9.43.105−9.23
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Share and Cite

MDPI and ACS Style

Zhang, L.; Sha, X.; Liu, M.; Wang, L.; Pang, Y. Cutting Force Prediction Models by FEA and RSM When Machining X56 Steel with Single Diamond Grit. Micromachines 2021, 12, 326. https://doi.org/10.3390/mi12030326

AMA Style

Zhang L, Sha X, Liu M, Wang L, Pang Y. Cutting Force Prediction Models by FEA and RSM When Machining X56 Steel with Single Diamond Grit. Micromachines. 2021; 12(3):326. https://doi.org/10.3390/mi12030326

Chicago/Turabian Style

Zhang, Lan, Xianbin Sha, Ming Liu, Liquan Wang, and Yongyin Pang. 2021. "Cutting Force Prediction Models by FEA and RSM When Machining X56 Steel with Single Diamond Grit" Micromachines 12, no. 3: 326. https://doi.org/10.3390/mi12030326

Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.

Article Metrics

Back to TopTop