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Surface integrity optimization for ball-end hard milling of AISI D2 steel based on response surface methodology

Surface integrity optimization for ball-end hard milling of AISI D2 steel based on response... a1111111111 a1111111111 This study focuses on systematically revealing how cutting parameters influence the surface integrity of ball-end hard milled surface of AISI D2 steel and proposing optimization scheme from surface integrity, wear resistance and fatigue resistance perspective based on response surface methodology respectively. Results can be summarized into three aspects. OPENACCESS Firstly, radial depth of cut with percent contribution ratio (PCR) 62.05% has a decisive influ- ence on surface roughness, followed by spindle speed 13.25% and feed per tooth 6.63%. Citation: Huang W, Wan C, Wang G, Zhang G (2023) Surface integrity optimization for ball-end The work hardening degree was raised from 12.5% to 38.4% when spindle speed changed hard milling of AISI D2 steel based on response from 8000 rpm to 2000 rpm. Spindle speed and radial depth of cut are the most significant surface methodology. PLoS ONE 18(8): e0290760. factor influencing residual stress. The PCR of spindle speed and radial depth of cut reached https://doi.org/10.1371/journal.pone.0290760 73.47% and 18.63% for residual stress in feed direction, 47.11% and 37.51% in step-over Editor: Antonio Riveiro Rodrıguez, University of direction, respectively. High residual compressive stress can be generated by lowering spin- Vigo, SPAIN dle speed and radial depth of cut benefiting from the aggravated squeeze between ball-end Received: April 17, 2023 milling cutter and workpiece. Secondly, too small feed per tooth or too small radial depth of Accepted: August 15, 2023 cut should be avoided from wear resistance point because though the surface microhard- Published: August 25, 2023 ness can be improved, the surface quality will also be deteriorated. The combination of high Copyright:© 2023 Huang et al. This is an open spindle speed, small feed per tooth together with small radial depth of cut can meet the wear access article distributed under the terms of the resistance and the machining efficiency requirement. Finally, a medium-sized cutting Creative Commons Attribution License, which parameter combination should be adopted to realize satisfying material removal rate and permits unrestricted use, distribution, and fatigue resistance. This study can be used to guide the selection of cutting parameters dur- reproduction in any medium, provided the original author and source are credited. ing ball-end milling of hardened AISI D2 steel for dies/molds manufacturing industries. Data Availability Statement: All relevant data are within the paper and its Supporting Information files. Funding: This work was supported by the National Introduction Natural Science Foundation of China (52105463), In virtue of the good blends of hardness, toughness and strength, cold working steel AISI D2 is the Natural Science Foundation of Shandong widely used for the manufacture of dies and molds, taking drawing dies, extrusion molds, and Province (ZR2020QE182, ZR2022QE015) and the Elite Program of Shandong University of Science plastic injection molds for example [1]. This kind of material contains high amount of hard and Technology (0104060540413). carbide particles and can maintain high strength and hardness under high temperature condi- tion, which is beneficial for fatigue resistance and wear resistance. However, these characteris- Competing interests: The authors have declared that no competing interests exist. tics are also responsible for high temperature, deteriorated surface and tendency to cutting PLOS ONE | https://doi.org/10.1371/journal.pone.0290760 August 25, 2023 1 / 23 PLOS ONE Surface integrity optimization for ball-end hard milling of AISI D2 steel Abbreviations: n, Spindle speed; f , Feed per tooth; z tool wear generated in cutting process leading to hardened AISI D2 steel a typical hard-to- a , Radial depth of cut; a , Axial depth of cut;β , e p f machine material [2]. Lead angle;β , Tilt angle; ϕ, Diameter of ball-end In general, the traditional manufacturing process for dies and molds contains milling of milling cutter;γ, Rake angle Clearance angle;α, AISI D2 steel in annealed condition, quenching and tempering treatments, electrical discharge Clearance angle;β, Helix angle; Z, Tooth number of machining, grinding and manual polishing [3, 4]. This is a time-consuming process and seri- ball-end milling cutter; Ra, Surface roughness; HV, Microhardness;σ , Residual stress in feed ously affects the production efficiency and market competitiveness of enterprises [5]. With the feed direction;σ , Residual stress in step-over cross-feed rapid development of advanced coatings, cutting tool material and lubrication/cooling tech- direction. nology, the feasibility and advantage of applying hard milling technology to the die and mold manufacturing industry is becoming more and more obvious [6, 7]. This is because the appli- cation of hard milling technology can reduce manufacturing cost and shorten production period [8]. However, this process may introduce unsatisfactory surface integrity taking large surface roughness, tensile residual stress, and surface pits for example [9]. It is well known that the excessive wear and the fatigue spalling or fracture are the common typical failure modes for dies and molds. The failure mechanism is always closely correlated with the surface integ- rity. Hence, it is necessary to systematically reveal the relationship between cutting parameters and surface integrity during ball-end milling process of hardened AISI D2 steel. Furthermore, proposing optimum process scheme is also of great importance to improve the wear and fatigue resistance of dies and molds in actual production. Many experimental studies have been performed to illustrate the machinability of hardened AISI D2 steel. Sahinoglu et al. [10] explored the machinability of hardened AISI S1 steel (60HRC) by hard turning process using CBN cutting inserts and found that feed rate has sig- nificant influence on surface roughness. Carreira et al. [11] performed hard milling experi- ments of hardened AISI D2 steel and concluded that the combination of high milling speed and small feed per tooth contributed to small surface roughness. However, the variation trends of surface microhardness and residual stress along with the cutting parameters was not obvi- ous because of the rough surface. Kara et al. [12] investigated the influence of cutting parame- ters on the tool wear and surface roughness during dry cutting of hardened AISI D2 steel. They found that the coated cutting tool performed better compared with the uncoated cutting tool from surface roughness and tool wear standpoint. Abbas A T et al. [13] used an artificial neural network with Edgeworth-Pareto method to optimize the cutting parameter during face milling process of high-strength grade-H steel and established neural network models for dif- ferent surface roughness and unit-volume machining time requirements. Markopoulos A P et al. [14] conducted face milling tests of hardened cold work steel AISI O1 and revealed the influence of cutting parameters (depth of cut, cutting speed and feed rate) on surface rough- ness, cutting forces, cutting power and machining cost based on Taguchi design of experi- ments method. Aqib et al. [15] compared the influence of minimum quantity lubrication (MQL) and nanofluids-based MQL (NFMQL) on cutting temperature and surface roughness during face milling process of hardened AISI D2 steel based on response surface methodology. They found that NFMQL performed better in terms of the ability to reduce cutting tempera- ture and surface roughness than MQL. Mac et al. [16] put forward a novel method to improve the prediction accuracy of cutting force and chip shrinkage coefficient for end milling of cold work steel SKD11 with the method of simulation and experiment. The wear and fatigue resistance of machined surface is closely correlated with the surface integrity. Zheng et al. [17] studied the wear resistance of hardened Cr12MoV surfaces with quadrangular pits feature formed by ball-end milling process. They found that the smaller the size of pits feature is, the better the wear resistance will be. Carreira et al. [11] found that cer- met inserts led to higher compressive residual stress and lower surface roughness compared with cemented tungsten carbide inserts in end milling process of hardened AISI D2 steel, which is beneficial for the improvement of adhesion characteristics. Tang et al. [18] PLOS ONE | https://doi.org/10.1371/journal.pone.0290760 August 25, 2023 2 / 23 PLOS ONE Surface integrity optimization for ball-end hard milling of AISI D2 steel investigated the influence of hardness on wear behavior of hardened D2 steel. They concluded that wear resistance was sensitive to hardness and the discrepancy in hardness is responsible for the difference in wear mechanisms. Gong et al. [19] investigated the influence of rolling times on the wear resistance of ultrasonic rolled surface of Cr12MoV steel. They found that the thickness of plastic deformation layer increased and the surface carbide decreased with the increase of rolling times. This variation can inhibit the crack initiation and propagation and then improve the wear resistance. It is well known that the fatigue performance is related to work hardening and the state of residual stress for machined surfaces. Different processing techniques lead to different surface integrity and then the discrepancy in fatigue performance for the same surface. Turned surfaces have better fatigue resistance than those generated by EDM and electrochemical machining pro- cess because of a higher residual compressive stress [20, 21]. Jesus et al. [4] compared the fatigue resistance of AISI D2 steel subjected to electrical discharging machining (EDM) and conventional grinding techniques, respectively. They found that large dendritic primary carbides were gener- ated after EDM process, which is detrimental to the fatigue resistance. In addition, the specimens machined by EDM process showed higher fatigue notch sensitivity than the ones machined by grinding process. Zhang et al. [22] studied the surface and subsurface characteristics and mechan- ical properties of ground surface of LPBF 304L stainless steel. The results showed that grinding process can significantly improve the surface roughness and grinding induced grain refinement can improve the fatigue resistance of the workpiece. Zhang et al. [23] compared the fatigue resis- tance of gear suffered four typical manufacturing processes: carburizing and grinding, shot peen- ing, barrel finishing, and barrel finishing after shot peening. They found that compared with the carburized and ground process, the gear contact fatigue life of shot peening, barrel finishing, and barrel finishing after shot peening can significantly improve the surface roughness, residual stress gradient and hardened layer, thus improving the fatigue resistance of gear contact surfaces. Taken together, the influence of cutting tool material, cutting parameters, coating types and lubrication methods on the machinability of hardened AISI D2 steel has been studied by many researchers from surface finish, tool life, cutting force and cutting temperature standpoint. The mainly findings are that the increase of cutting speed contributes to good surface finish and the coated carbide tool is competent for hard cutting. However, these reported studies are mainly focused on high speed hard turning and end/face milling process. Little attention was paid on the ball-end hard milling process of hardened AISI D2 steel. Moreover, though the influence of surface roughness, residual stress and hardness on the wear or fatigue perfor- mance has been reported by many literatures, the systematic investigations for the selection of cutting parameters from wear resistance and fatigue resistance perspective is scarcely found during ball-end hard milling process of hardened AISI D2 steel. Hence, this study aims to systematically investigate the influence of cutting parameters on surface integrity, especially considering that the ball-end milling operation always take place at the end of dies or molds manufacturing process, and then put forward specific selection scheme of cutting parameters for specific surface integrity requirement, good wear resistance and satisfying fatigue resistance, respectively. The findings in this study can provide guidance for the selection of cutting parameters during ball-end milling of hardened AISI D2 steel and contribute to the high-efficiency and high-performance manufacturing of dies and molds. Experimental procedures Material preparation The workpiece material selected in this study is high carbon and high chromium cold working steel AISI D2 with dimensions of 120 × 80 × 30 mm. In virtue of satisfying wear resistance, this PLOS ONE | https://doi.org/10.1371/journal.pone.0290760 August 25, 2023 3 / 23 PLOS ONE Surface integrity optimization for ball-end hard milling of AISI D2 steel Table 1. Chemical compositions of AISI D2 tool steel. Elements C Mn Si Cr Mo P S V Fe wt% 1.5 0.45 0.25 12 1.0 0.025 0.025 0.35 Balance https://doi.org/10.1371/journal.pone.0290760.t001 kind of steel has been widely used in the dies and molds manufacturing industry. The chemical composition of the as-received AISI D2 steel is given in Table 1. After heat treatment, the Rockwell hardness of the used workpiece reached approximately 61±1 HRC. The substrate is composed of retained carbides, tempered martensite and retained austenite, as shown in Fig 1. Design of experiments based on response surface methodology Response surface methodology (RSM) is usually used for modeling and analyzing the relation- ship between a response and several factors based on relatively small test numbers. A second- order mathematical model will be developed to realize the prediction of responses. This model considers not only the influence of independent factors but also the influence of interaction effect with each other. Response surface experiments were designed by using Box-behnken method. This method is commonly used during response surface design and does not arrange all test factors into a high-level test combination at the same time and then contributes to a sat- isfying cutting tool life. According to our preliminary experiments regarding of the relation- ship between cutting parameters and surface integrity, spindle speed n, feed per tooth f , and radial depth of cut a were identified as the input factors. Three levels of the three selected Fig 1. Microstructure of hardened AISI D2 steel. https://doi.org/10.1371/journal.pone.0290760.g001 PLOS ONE | https://doi.org/10.1371/journal.pone.0290760 August 25, 2023 4 / 23 PLOS ONE Surface integrity optimization for ball-end hard milling of AISI D2 steel Table 2. Parameters configuration of response surface experiments. No. Spindle speed Cutting speed Feed per tooth Radial depth of cut a , mm Axial depth of cut a , mm e p n, rpm v , m/min f , mm/z c z 1 8000 251 0.30 0.3 0.2 2 8000 251 0.18 0.5 0.2 3 5000 157 0.18 0.3 0.2 4 8000 251 0.18 0.1 0.2 5 5000 157 0.18 0.3 0.2 6 2000 63 0.06 0.3 0.2 7 5000 157 0.30 0.1 0.2 8 5000 157 0.06 0.5 0.2 9 2000 63 0.18 0.5 0.2 10 5000 157 0.18 0.3 0.2 11 2000 63 0.30 0.3 0.2 12 5000 157 0.06 0.1 0.2 13 2000 63 0.18 0.1 0.2 14 8000 251 0.06 0.3 0.2 15 5000 157 0.30 0.5 0.2 16 5000 157 0.18 0.3 0.2 17 5000 157 0.18 0.3 0.2 https://doi.org/10.1371/journal.pone.0290760.t002 factors are determined based on the existing research and the recommendation from the tool manufacturer. Furthermore, during the ball-end milling process, axial depth of cut was main- tained a constant value 0.2 mm. 17 runs were designed based on the Design Expert 8.0 soft- ware. This software can provide highly efficient design of experiments and convenient response analysis. Table 2 shows the parameters configuration of the three factors and three levels response surface experiments designed based on Box-Behnken method. Then, the hard milling operations of AISI D2 tool steel were performed by using a five-axis high speed machining center DMU60P duoBlock. The maximum spindle speed of the machin- ing center can reach 12000 rpm. New coated solid tungsten carbide ball-end milling cutter (Serial number SECO: TORNADO JH111L100-MEGA-64) was used during the unlubricated milling process. The geometrical parameter of the used ball-end milling cutter is given in Table 3. During the milling process, the lead angleβ and the tilt angleβ were set as 0˚ and f n 20˚, respectively. According to previous studies [24, 25], this kind of combination can avoid the nose of ball-end milling cutter from cutting and contributes to a satisfying tool life. The schematic diagram of tool path strategy in ball-end hard milling process is shown in Fig 2. Characterization of surface integrity Before the characterization of surface integrity, the ball-end hard milled surface was cleaned carefully by using an ultrasonic cleaner for about 10 min to avoid the influence of oil contami- nation on detection accuracy. Surface roughness of milled surfaces was obtained by using white light interferometer Veeco NT9300. Three different areas on the ball-end milled surface were selected and the average value was used as the final surface roughness. Surface Table 3. Geometrical parameter of ball-end milling cutter. Diameter ϕ Rake angleγ Clearance angleα Helix angleβ Tooth number Z 10 mm 0˚ 1˚ 17˚ 2 https://doi.org/10.1371/journal.pone.0290760.t003 PLOS ONE | https://doi.org/10.1371/journal.pone.0290760 August 25, 2023 5 / 23 PLOS ONE Surface integrity optimization for ball-end hard milling of AISI D2 steel Fig 2. Schematic diagram of tool path strategy in ball-end hard milling process. https://doi.org/10.1371/journal.pone.0290760.g002 microhardness was measured through microhardness tester MH-6. The dwell time and the indentation load were set as 10 s and 0.1 kg, respectively. The singular results were eliminated and the microhardness was obtained by averaging at least five measurements. Residual stress was measured by using X-stress 3000 in the light of sin ψ technique. Two directions, namely the feed direction and step-over direction, were adopted during the measuring process. At least five measurements were performed for each test and the average value was recorded as the final residual stress. Results and discussion Surface roughness, surface microhardness, and surface residual stress were chosen as the three responses. The response surface analysis was conducted by using software Design Expert 8.0. The software can easily compare which polynomial model is the most suitable, and give the recommended model. This kind of software can compare different models and show the most significant one. By this way, the accuracy of the proposed prediction model can be improved to some extent. Response surface analysis for surface roughness The analysis of variance (ANOVA) can be used to investigate the influence of input factors on output response [26]. Table 4 shows the result of variance analysis for surface roughness. Results show that spindle speed, radial depth of cut, feed per tooth and interaction between spindle speed and radial depth of cut are significant factors. The percent contribution ratio (PCR) on surface roughness reached 13.25%, 62.05%, 6.63% and 10.24%, respectively. Radial depth of cut is the most significant factor influencing surface roughness. The two factors inter- action model was recommended for illustrating the results of surface roughness. It can be seen that the proposed model is significant as it exhibits a very small P value. The prediction model 2 2 with R 93%, R -adjusted 88.6% and R2-predicted 82.4% can be expressed by the following Eq. PLOS ONE | https://doi.org/10.1371/journal.pone.0290760 August 25, 2023 6 / 23 PLOS ONE Surface integrity optimization for ball-end hard milling of AISI D2 steel Table 4. Variance analysis for surface roughness: Two factor interaction model. Source Sum of squares PCR(%) df Mean square F value P value Prob>F Remarks Model 1.54 6 0.26 21.75 < 0.0001 Significant A-n 0.22 13.25 1 0.22 18.56 0.0015 B-a 1.03 62.05 1 1.03 86.72 < 0.0001 C-f 0.11 6.63 1 0.11 9.17 0.0127 AB 0.17 10.24 1 0.17 14.01 0.0038 AC 0.019 1.14 1 0.019 1.63 0.2301 −3 −3 BC 5.15×10 0.31 1 5.15×10 0.44 0.5243 Residual 0.12 10 0.012 −3 Lack of fit 0.039 6 6.58×10 0.33 0.8884 Not significant Pure error 0.079 4 0.02 Cor total 1.66 16 https://doi.org/10.1371/journal.pone.0290760.t004 (1). 5 4 Ra ¼ 0:305þ 1:17917� 10 nþ 3:75521a 1:48175f 3:39167� 10 na e z e ð1Þ þ1:93056� 10 nf 1:49479a f z e z Fig 3 shows the 3-D response surface for surface roughness. Generally, surface roughness for ball-end milled surfaces mainly determined by two types of scallops: Feed-interval scallops induced by the feed movement and pick-interval scallops induced by the step-over movement. The difference in value between feed per tooth and radial depth of cut leads to the increase of heterogeneity of surface topography and then the increase of surface roughness. As indicated in Fig 3(A) and 3(B), radial depth of cut has the most significant influence on surface rough- ness compared with feed per tooth and spindle speed. This is because the pick-interval scallop height is usually higher than the feed-interval scallop. In addition, surface roughness decreases with the increase of spindle speed, but this effect is the least obvious. Though improving spin- dle speed contributes to the decrease of cutting force and the increase of cutting temperature, which is beneficial for cutting stability and surface roughness, this effect is negligible compared to the two types of scallops controlled by feed per tooth and radial depth of cut. Taken together, selecting small radial depth of cut and high spindle speed contributes to small rough- ness at given feed per tooth condition. Response surface analysis for microhardness Analysis of variance for microhardness of ball-end hard milled surface is given in Table 5. Results show that spindle speed, radial depth of cut, feed per tooth, the interaction between spindle speed and radial depth of cut and quadratic terms of feed per tooth are significant fac- tors. Feed per tooth (PCR 25.14%) and spindle speed (PCR 24.79%) are the most significant factor influencing surface microhardness relatively. The quadratic model was recommended for illustrating the results of surface microhardness. As shown in Table 5, the proposed model is significant because of the small P value 0.0037. The quadratic model with R value 92.3%, R -adjusted 82.5% and R2-predicted 84.3% shown in Eq (2) can be used to describe the rela- tionship between the three input factors and microhardness. HV ¼ 1113:333 0:010167n 613:333a 613:888f þ 0:074167na 0:02nf e z e z ð2Þ 2 2 2 708:33a f 2� 10 n þ 462:5a þ 1770:8f e e z PLOS ONE | https://doi.org/10.1371/journal.pone.0290760 August 25, 2023 7 / 23 PLOS ONE Surface integrity optimization for ball-end hard milling of AISI D2 steel Fig 3. 3-D response surface for surface roughness of ball-end milled AISI D2 steel under dry cutting condition, (a) n×a , (b) f ×a , (c) e z e f ×n. https://doi.org/10.1371/journal.pone.0290760.g003 Table 5. Variance analysis for microhardness: Quadratic model. Source Sum of squares PCR(%) df Mean square F value P value Prob>F Remarks Model 38088.56 9 4232.06 9.39 0.0037 Significant A-n 10224.5 24.79 1 10224.5 22.69 0.0021 B-a 2738 6.64 1 2738 6.08 0.0432 C-f 10368 25.14 1 10368 23.01 0.002 AB 7921 19.21 1 7921 17.58 0.0041 AC 256 0.62 1 256 0.57 0.4756 BC 1156 2.8 1 1156 2.57 0.1533 A 1364.21 3.31 1 1364.21 3.03 0.1254 B 1441.05 3.49 1 1441.05 3.2 0.1169 C 2737.89 6.64 1 2737.89 6.08 0.0432 Residual 3154.5 7 450.64 Lack of fit 3154.5 3 1051.5 0.15 0.9216 Not significant Pure error 0 4 0 Cor total 41243.06 16 https://doi.org/10.1371/journal.pone.0290760.t005 PLOS ONE | https://doi.org/10.1371/journal.pone.0290760 August 25, 2023 8 / 23 PLOS ONE Surface integrity optimization for ball-end hard milling of AISI D2 steel Fig 4. 3-D response surface for microhardness of ball-end milled AISI D2 steel under dry cutting condition, (a) n×a , (b) f ×n, (c) e z f ×a . z e https://doi.org/10.1371/journal.pone.0290760.g004 Fig 4 depicts the 3-D response surface of microhardness considering the interaction effect of input factors. As a result of the coupling effect of strain hardening and thermal softening, obvious work hardening occurred after ball-end milling process of hardened AISI D2 steel, especially for the low spindle speed condition. Compared with the original hardness approxi- mate 720 HV, the work hardening degree reached about 12.5% for the combination of n = 8000 rpm, a = 0.1mm, f = 0.18mm/z, and 38.4% for n = 2000 rpm, a = 0.1 mm and f = e z e z 0.18 mm/z condition. The reason can be explained from the following two aspects. On the one hand, due to the high hardness and high strength of hardened AISI D2 steel, a larger cutting force was needed compared with the traditional cutting process and lead to more severe plastic deformation. On the other hand, the good toughness of AISI D2 steel contributes to the accu- mulation of strain during hard milling process. As indicated in Fig 4, the microhardness of ball-end milled surface decrease with the increase of spindle speed and feed per tooth. This is because more heat was generated and the degree of thermal softening was strengthened under the circumstances. When a small spindle speed was adopted, microhardness of hard milled surface decreased with the increase of radial depth of cut due to the increased temperature. However, it is noteworthy that a slight increase of microhardness was presented for a high spindle speed condition. As spindle speed was set as 8000 rpm and feed per tooth 0.18 mm/z, the work hardening degree changed only from 12.9% to 15.7% when radial depth of cut PLOS ONE | https://doi.org/10.1371/journal.pone.0290760 August 25, 2023 9 / 23 PLOS ONE Surface integrity optimization for ball-end hard milling of AISI D2 steel increases from 0.1mm to 0.5mm. The reason for this is that though more heat was generated for the high spindle speed condition, the contact time between the tool flank face and machined surface was obviously reduced, and the cutting force was strengthened with radial depth of cut increase. Response surface analysis for residual stress The variance analysis for residual stress in feed and step-over direction is shown in Tables 6 and 7, respectively. Results reveal that spindle speed, radial depth of cut and quadratic terms of feed per tooth are significant factors for residual stress in either direction. Furthermore, feed per tooth, the interaction between spindle speed and radial depth of cut, the interaction between spindle speed and feed per tooth and quadratic terms of spindle speed are also signifi- cant factors for residual stress in step-over direction. Overall, spindle speed and radial depth of cut are the most significant factor influencing residual stress. The PCR of spindle speed and radial depth of cut reached 73.47% and 18.63% for residual stress in feed direction, 47.11% and 37.51% for residual stress in step-over direction, respectively. The quadratic model was recom- mended for illustrating the results of residual stress. As shown in Tables 6 and 7, the proposed 2 2 model is significant because of the very small P value. Eq (3) with R value 97.6%, R -adjusted 2 2 94.6% and R2-predicted 96.3%, and Eq (4) with R value 99.8%, R -adjusted 99.5% and R2-predicted 99.7% can be used to predict residual stress in feed direction and step-over direc- tion, respectively. s ¼ 1284:125þ 0:0928nþ 1674:375a þ 1751:041f þ 3:204� 10 na feed e z e ð3Þ 6 6 2 2 2 1:036� 10 nf þ 2:458� 10 n 553:125a 4487:847f e z s ¼ 2162:771þ 0:18825nþ 4932:292a þ 2002:778f þ 0:14417na step over e z e ð4Þ 2 2 2 0:28681nf þ 770:8333a f 4:79167� 10 n 6709:375a 1536:4583f z e z e z Figs 5 and 6 show the 3-D response surface for residual stress in feed and step-over direc- tion, respectively. It can be seen that spindle speed and radial depth of cut are the most notable influencing factors on surface residual stress among the three input factors. A combination of Table 6. Variance analysis for residual stress in feed direction: Quadratic model. Source Sum of squares PCR(%) df Mean squares F value P value Prob>F Remarks 6 5 Model 1.32×10 9 1.47×10 32.29 < 0.0001 Significant 5 5 A-n 9.96×10 73.47 1 9.96×10 218.71 < 0.0001 5 5 B-a 2.52×10 18.63 1 2.52×10 55.45 0.0001 C-f 10296.13 0.76 1 10296.13 2.26 0.1763 −4 AB 4 0 1 4 8.79×10 0.9772 AC 0 0 1 0 0 1 −5 BC 0.25 0 1 0.25 5.493×10 0.9943 A 5180.02 0.38 1 5180.02 1.14 0.3215 B 4960.87 0.37 1 4960.87 1.09 0.3312 C 49864.76 3.68 1 49864.76 10.96 0.0129 Residual 31860.95 7 4551.56 −4 Lack of fit 3.75 3 1.25 1.57×10 1 Not significant Pure error 31857.2 4 7964.3 Cor total 1.36×10 16 https://doi.org/10.1371/journal.pone.0290760.t006 PLOS ONE | https://doi.org/10.1371/journal.pone.0290760 August 25, 2023 10 / 23 PLOS ONE Surface integrity optimization for ball-end hard milling of AISI D2 steel Table 7. Variance analysis for residual stress in step-over direction: Quadratic model. Source Sum of squares PCR(%) df Mean squares F value P value Prob>F Remarks 6 5 Model 2.66×10 9 2.95×10 415.52 < 0.0001 significant 6 5 A-n 1.25×10 47.11 1 1.25×10 1764.85 < 0.0001 5 5 B-a 9.98×10 37.51 1 9.98×10 1405.26 < 0.0001 C-f 7021.13 0.26 1 7021.13 9.88 0.0163 AB 29929 1.12 1 29929 42.1 0.0003 AC 42642.25 1.6 1 42642.25 60.03 0.0001 BC 1369 0.05 1 1369 1.93 0.2077 A 7830.59 0.03 1 7830.59 11.02 0.0128 2 5 5 B 3.03×10 11.4 1 3.03×10 426.9 < 0.0001 C 2061.12 0.08 1 2061.12 2.9 0.1323 Residual 4972.75 7 710.39 −3 Lack of fit 6.75 3 2.25 1.81×10 0.9999 Not significant Pure error 4966 4 1241.5 Cor total 2.66×10 16 https://doi.org/10.1371/journal.pone.0290760.t007 low spindle speed and low radial depth of cut contributes to high residual compressive stress because of the extended heat dissipation time and the aggravated squeeze between ball-end milling cutter and workpiece material. Conversely, the combination of high spindle speed and Fig 5. 3-D response surface for residual stress in feed direction of ball-end milled AISI D2 steel under dry cutting condition, (a) n×a , (b) f ×n, (c) f ×a . e z z e https://doi.org/10.1371/journal.pone.0290760.g005 PLOS ONE | https://doi.org/10.1371/journal.pone.0290760 August 25, 2023 11 / 23 PLOS ONE Surface integrity optimization for ball-end hard milling of AISI D2 steel Fig 6. 3-D response surface for residual stress in step-over direction of ball-end milled AISI D2 steel under dry cutting condition, (a) n×a , (b) f ×n, (c) f ×a . e z z e https://doi.org/10.1371/journal.pone.0290760.g006 large radial depth of cut can bring about residual tensile stress due to the obviously increased cutting temperature. In addition, the effect of feed per tooth on residual stress in both direc- tions is negligible especially at high spindle speed condition. Reasons for that can be explained as following. The thickness of chips changes continuously during the up milling process and reaches the maximum value as the exit of ball-end milling cutter from the workpiece surface. The heat accumulation also reaches the most severe level at this point. Due to the high spindle speed and the characteristics of intermittent cutting, most of heat is carried away by chips and little heat is diffused into the machined surface. Optimization of cutting parameters According to the above analysis, the interaction of spindle speed and radial depth of cut has significant effect on surface integrity on the whole. Then the response surface of desirability function was established based on the two parameters aiming at specific goal of surface integ- rity, wear resistance and fatigue resistance, respectively. Cutting parameters optimization for satisfying surface integrity. Fig 7 depicts the response surface of desirability for different requirements of surface integrity. Two aspects can be summarized as following. On the one hand, desirability for minimizing surface roughness of ball-end milled surface is sensitive to radial depth of cut, especially for the low spindle speed condition as indicated in Fig 7(A). High desirability can be obtained when radial depth of cut PLOS ONE | https://doi.org/10.1371/journal.pone.0290760 August 25, 2023 12 / 23 PLOS ONE Surface integrity optimization for ball-end hard milling of AISI D2 steel Fig 7. Response surface of desirability function for the goal of (a) Minimizing surface roughness, (b) Maximizing surface microhardness, and (c) Maximizing residual compressive stress. https://doi.org/10.1371/journal.pone.0290760.g007 is no larger than 0.2 mm. On the other hand, increasing spindle speed contributes to the improvement of desirability on the whole. When a small radial depth of cut is adopted, the desirability is basically maintained at a larger constant value. Then the combination of high spindle speed and small radial depth of cut can guarantee not only satisfying material removal rate but also high desirability for minimum surface roughness. The recommended cutting parameter configuration is given in Table 8. In actual production, the most reasonable param- eter configuration should be selected comprehensively considering the cutting tool perfor- mance, the machine tool stability and the specific requirements of machined surface quality. Secondly, the desirability response surface is shown in Fig 7(B) for the goal of maximizing surface microhardness. It can be seen that there are two regions with relatively high desirabil- ity, namely the combination of small spindle speed and small radial depth of cut followed by the combination of large spindle speed and large radial depth of cut. However, for the later condition, large surface roughness and severe cutting tool wear will be introduced because of the increased cutting force and cutting temperature. For the former condition, though high desirability can be obtained, the material removal rate is too small to be suitable for mass pro- duction, but only for small batch production. Table 9 shows the recommended cutting param- eter configuration for maximizing surface microhardness with high desirability. In actual production, the cutting parameter configuration should be determined taking production type into consideration. PLOS ONE | https://doi.org/10.1371/journal.pone.0290760 August 25, 2023 13 / 23 PLOS ONE Surface integrity optimization for ball-end hard milling of AISI D2 steel Table 8. Cutting parameter configuration for minimizing surface roughness with high desirability. No. Spindle speed n, rpm Radial depth of cut a , mm Feed per tooth f , mm/z Ra Desirability e z 1 4049 0.10 0.29 0.347 1 2 4548 0.10 0.30 0.353 1 3 4041 0.10 0.27 0.358 1 4 4238 0.10 0.29 0.357 1 5 4107 0.10 0.29 0.344 1 6 4002 0.10 0.28 0.355 1 7 4233 0.10 0.29 0.355 1 8 4105 0.11 0.30 0.351 1 9 4011 0.11 0.29 0.355 1 10 4393 0.10 0.30 0.349 1 11 4387 0.10 0.29 0.358 1 12 4097 0.10 0.29 0.352 1 13 4008 0.10 0.27 0.358 1 14 4440 0.10 0.30 0.351 1 15 4355 0.10 0.29 0.358 1 16 4145 0.11 0.30 0.349 1 17 4000 0.11 0.29 0.360 0.999 18 4000 0.12 0.30 0.365 0.995 19 4000 0.10 0.26 0.366 0.994 20 4990 0.10 0.30 0.368 0.992 21 4000 0.10 0.26 0.370 0.991 22 4000 0.10 0.23 0.391 0.973 23 5858 0.10 0.30 0.399 0.966 24 6428 0.10 0.30 0.420 0.948 25 6489 0.10 0.30 0.422 0.946 26 6779 0.10 0.30 0.432 0.937 27 5186 0.10 0.20 0.439 0.932 28 7199 0.10 0.30 0.447 0.925 29 7549 0.10 0.30 0.460 0.914 30 7567 0.10 0.30 0.460 0.913 31 7911 0.10 0.29 0.473 0.902 32 7981 0.10 0.30 0.475 0.901 33 7273 0.10 0.13 0.488 0.890 34 7868 0.10 0.13 0.491 0.887 https://doi.org/10.1371/journal.pone.0290760.t008 Finally, it is well known that surface residual compressive stress contributes to fatigue resis- tance of service parts bearing alternate load. Fig 7(C) shows the desirability response surface for maximizing surface residual compressive stress in both feed direction and step-over direc- tion simultaneously. It can be seen that the desirability gradually decreases with the increase of spindle speed no matter what radial depth of cut was used. Moreover, selecting a small radial depth of cut contributes to high desirability. The combination of small spindle speed and small radial depth of cut can bring about high desirability. However, this condition will seriously influence the material removal rate. It is noteworthy that the discrepancy in desirability is not obvious for surfaces ball-end milled with small radial depth of cut when different spindle speeds are used. Then selecting relatively high spindle speed and small radial depth of cut can guarantee not only high residual compressive stress but also a satisfying machining efficiency. PLOS ONE | https://doi.org/10.1371/journal.pone.0290760 August 25, 2023 14 / 23 PLOS ONE Surface integrity optimization for ball-end hard milling of AISI D2 steel Table 9. Cutting parameter configuration for maximizing surface microhardness with high desirability. No. Spindle speed n, rpm Radial depth of cut a , mm Feed per tooth f , mm/z HV Desirability e z 1 2091 0.10 0.07 1001 1 2 2041 0.10 0.07 1001 1 3 2287 0.10 0.06 1001 1 4 2067 0.10 0.06 1002 1 5 2116 0.11 0.06 1001 1 6 2013 0.10 0.06 1004 1 7 2109 0.10 0.06 1003 1 8 2037 0.11 0.06 1000 1 9 2226 0.10 0.06 1000 1 10 2013 0.10 0.07 1000 1 11 2054 0.10 0.07 1000 1 12 2000 0.10 0.08 998 0.991 13 2000 0.12 0.06 998 0.989 14 2588 0.10 0.06 998 0.989 15 2000 0.10 0.09 993 0.962 16 2000 0.10 0.1 990 0.945 17 2018 0.10 0.3 983 0.913 18 2000 0.10 0.3 983 0.908 19 2000 0.10 0.3 982 0.905 20 2237 0.10 0.3 980 0.892 21 3710 0.10 0.06 979 0.891 22 2000 0.19 0.06 973 0.859 23 2000 0.19 0.06 971 0.845 24 2000 0.10 0.21 968 0.832 25 6388 0.50 0.06 952 0.749 26 6434 0.50 0.06 952 0.749 27 6349 0.50 0.06 952 0.749 28 6201 0.50 0.06 952 0.749 29 6051 0.50 0.06 952 0.748 30 5330 0.50 0.06 950 0.737 31 5718 0.47 0.06 944 0.705 32 3611 0.50 0.06 937 0.668 33 4128 0.37 0.06 935 0.659 34 4140 0.38 0.06 935 0.659 https://doi.org/10.1371/journal.pone.0290760.t009 Table 10 shows the recommended cutting parameter configuration for maximizing residual compressive stress with high desirability. Cutting parameters optimization for wear resistance. According to our previous research, surface work hardening occurred during ball-end milling process of hardened AISI D2 steel contributes to the improvement of wear resistance. This is because work hardening can improve the ability to resist abrasive wear and plastic deformation on the surface, and also enhance the stability of the oxide film formed on the friction interface, thereby reducing the friction coefficient to a certain extent and improving wear resistance [1, 27]. Though the com- bination of small feed per tooth and small radial depth of cut is beneficial for high microhard- ness, the machining efficiency is greatly reduced. Furthermore, the surface quality will be deteriorated due to the occurrence of micro-pits defect caused by too small feed per tooth or too small radial depth of cut. Therefore, considering the above factors and the recommended PLOS ONE | https://doi.org/10.1371/journal.pone.0290760 August 25, 2023 15 / 23 PLOS ONE Surface integrity optimization for ball-end hard milling of AISI D2 steel Table 10. Cutting parameter configuration for maximizing residual compressive stress with high desirability. No. Spindle speed n, rpm Radial depth of cut a , mm Feed per tooth f , mm/z Residual stress σ , MPa Residual stress σ , MPa Desirability e z feed cross-feed 1 4000 0.10 0.06 -633 -952 0.884 2 4000 0.10 0.06 -630 -945 0.880 3 4000 0.11 0.06 -625 -925 0.871 4 4000 0.10 0.07 -610 -944 0.870 5 4131 0.10 0.06 -617 -933 0.870 6 4000 0.11 0.06 -620 -907 0.862 7 4337 0.10 0.06 -591 -903 0.848 8 4000 0.11 0.07 -593 -895 0.846 9 4000 0.10 0.10 -560 -924 0.840 10 4000 0.10 0.11 -540 -916 0.827 11 4000 0.10 0.30 -561 -861 0.819 12 4033 0.10 0.30 -557 -859 0.816 13 4000 0.10 0.13 -518 -905 0.813 14 4000 0.10 0.30 -556 -843 0.811 15 4000 0.10 0.28 -537 -862 0.808 16 4000 0.10 0.28 -535 -862 0.807 17 4157 0.10 0.30 -541 -849 0.806 18 4000 0.10 0.27 -526 -863 0.803 19 4000 0.10 0.26 -514 -864 0.797 20 4000 0.10 0.18 -488 -884 0.792 21 4000 0.10 0.24 -497 -867 0.791 22 4000 0.10 0.23 -492 -870 0.789 23 4000 0.16 0.06 -560 -718 0.770 24 5769 0.10 0.30 -351 -738 0.676 25 7863 0.10 0.30 -134 -630 0.525 26 4000 0.47 0.06 -294 -311 0.507 https://doi.org/10.1371/journal.pone.0290760.t010 cutting parameters of the tool manufacturer, two constraints are proposed as follows: 4500 rpm�n�8000 rpm, 0.12 mm/z�f �0.3 mm/z. The desirability response surface for the goal of maximizing surface microhardness was obtained by Design Expert 8.0, as shown in Fig 8. The range of desirability is 0 to 1. It can be seen that the desirability decreases obviously with the increase of radial depth of cut and spindle speed. The satisfying solution with high desirability mainly exists in the condition of small radial depth of cut and low spindle speed. The optimiza- tion scheme of cutting parameters with high desirability for satisfying wear resistance is given in Table 11. In actual production, the cutting parameter combination with high desirability should be prioritized on condition that the ball-end milling cutter and machine tool perfor- mance meet the requirements. Cutting parameters optimization for fatigue resistance. In the light of our previous research [28], the superposition of machining induced surface residual compressive stress and alternate load changes the ultimate stress level, average stress and stress ratio on the surface of the workpiece, and then affects the initiation and propagation process of fatigue cracks. The influence of surface work hardening on fatigue resistance is two-sided and moderate degree of work hardening is beneficial for the impediment of shear slip and then provides a strengthened resistance to fatigue crack initiation. However, excessive work hardening will also decrease the surface toughness and improve the sensitivity of surface notch under alternate load. This is detrimental to fatigue resistance because of the influence on crack propagation life. In PLOS ONE | https://doi.org/10.1371/journal.pone.0290760 August 25, 2023 16 / 23 PLOS ONE Surface integrity optimization for ball-end hard milling of AISI D2 steel Fig 8. Desirability response surface for wear resistance of ball-end milled surface of AISI D2 steel under dry cutting condition. https://doi.org/10.1371/journal.pone.0290760.g008 addition, the microscopic stress concentration, which can affect the rate of fatigue crack propa- gation significantly, is closely related with the surface defect and the surface topography of ball-end milled surfaces [29]. Based on the above conclusions, three aspects are considered before optimization of cutting parameters. Firstly, select relatively small radial depth of cut a or large feed per tooth f to e z decrease the microscopic stress concentration phenomenon. Secondly, choose a high spindle speed n or a large feed per tooth f or a large radial depth of cut a to ensure the machining effi- z e ciency. Lastly, increase the spindle speed n or feed per tooth f to restrain surface defects. To satisfy the above requirements, the constraints of cutting parameters are set as following: 4500 rpm�n�8000 rpm, 0.12 mm/z�f �0.3 mm/z, 0.1 mm�a �0.3 mm. Furthermore, combined z e with our previous findings [28], ball-end hard milled surfaces with microhardness approxi- mate HV 900 show better fatigue resistance than the other condition. Then, high residual com- pressive stress together with surface microhardness close to HV 900 are identified as the optimization goal and the degrees of importance for the two responses is set to be the same. Fig 9 gives the response surface and the contour map of desirability for the goal of high resid- ual compressive stress in feed direction and microhardness HV 900. This situation is defined as case 1. Fig 10 gives the response surface and the contour map of desirability for the goal of high residual compressive stress in step-over direction and microhardness HV 900. This situa- tion is defined as case 2. Comparing Figs 9 and 10, it can be found that the areas with high desirability for the two cases are very similar. This is because the residual stress in the feed direction and step-over direction has the similar trend with the change of spindle speed and radial depth of cut as shown in Figs 5 and 6. As shown in Figs 9 and 10, the area with high desirability occurs when a PLOS ONE | https://doi.org/10.1371/journal.pone.0290760 August 25, 2023 17 / 23 PLOS ONE Surface integrity optimization for ball-end hard milling of AISI D2 steel Table 11. Cutting parameter configuration for wear resistance with high desirability. No. Spindle speed n, rpm Feed per tooth f , mm/z Radial depth of cut a , mm HV Desirability z e 1 4500 0.12 0.10 926 0.618 2 4500 0.12 0.11 925 0.614 3 4566 0.12 0.10 925 0.614 4 4500 0.12 0.10 925 0.613 5 4520 0.12 0.11 924 0.612 6 4618 0.12 0.10 924 0.61 7 4500 0.12 0.12 924 0.61 8 4503 0.13 0.10 924 0.609 9 4665 0.12 0.10 924 0.607 10 4500 0.13 0.10 924 0.607 11 4715 0.12 0.10 923 0.604 12 4500 0.13 0.10 923 0.604 13 4500 0.12 0.13 923 0.602 14 4511 0.13 0.10 921 0.595 15 4500 0.12 0.17 919 0.585 16 5036 0.12 0.10 919 0.584 17 4500 0.12 0.23 914 0.555 18 4500 0.17 0.10 910 0.533 19 4500 0.12 0.27 910 0.533 20 6010 0.12 0.10 908 0.521 21 4500 0.12 0.31 906 0.515 22 4500 0.12 0.33 905 0.506 23 4523 0.24 0.10 889 0.424 24 6717 0.12 0.50 862 0.279 https://doi.org/10.1371/journal.pone.0290760.t011 low spindle speed and a small radial depth of cut are adopted. The optional range and the maxi- mum value of radial depth of cut decrease with the increase of spindle speed. Similarly, the optional range and the maximum value of spindle speed decrease with the increase of radial depth of cut. The optimization scheme of cutting parameters for fatigue resistance purpose con- sidering the two aforementioned cases is given in Tables 12 and 13, respectively. In actual produc- tion, the optimization scheme should be chosen based on comprehensive analysis of the requirement of surface roughness, the alternate load direction, the metal removal rate and so on. Fig 9. Optimization of cutting parameters for high residual compressive stress in feed direction and microhardness HV 900 purpose, (a) Response surface of desirability, (b) Contour map of desirability. https://doi.org/10.1371/journal.pone.0290760.g009 PLOS ONE | https://doi.org/10.1371/journal.pone.0290760 August 25, 2023 18 / 23 PLOS ONE Surface integrity optimization for ball-end hard milling of AISI D2 steel Fig 10. Optimization of cutting parameters for high residual compressive stress in step-over direction and microhardness HV 900 purpose, (a) Response surface of desirability, (b) Contour map of desirability. https://doi.org/10.1371/journal.pone.0290760.g010 In the future, the physical mechanism during the machining of AISI D2 steel should be fur- ther investigated to better explain the relationship between cutting parameters and surface integrity. In addition, the influence of tilt angle and lead angle on wear resistance and fatigue resistance should also be revealed. Conclusions During the manufacturing process of dies or molds with large size and complex curved sur- faces, ball-end milling operation is usually used as the final process. The influence mechanism of cutting parameters on surface integrity and the optimization scheme from surface integrity, wear resistance and fatigue resistance perspective were studied during ball-end hard milling process of AISI D2 steel. In this study, the range of cutting speed, feed per tooth and radial Table 12. Optimization scheme of cutting parameters for case 1. No. Spindle speed n, rpm Feed per tooth f , mm/z Radial depth of cut a , mm σ , MPa HV Desirability z e feed 1 4500 0.21 0.10 -424 900 0.829 2 4593 0.20 0.10 -412 900 0.823 3 4637 0.20 0.10 -407 900 0.819 4 4500 0.20 0.11 -411 900 0.816 5 4500 0.20 0.12 -399 900 0.815 6 4500 0.20 0.12 -396 900 0.813 7 4500 0.19 0.15 -369 900 0.798 8 5007 0.18 0.10 -364 900 0.795 9 5253 0.18 0.10 -339 900 0.779 10 4507 0.18 0.19 -320 900 0.768 11 4500 0.17 0.21 -309 900 0.761 12 4500 0.20 0.10 -423 902 0.761 13 4500 0.16 0.25 -270 900 0.737 14 6031 0.14 0.10 -270 900 0.736 15 4500 0.16 0.26 -266 900 0.734 16 4500 0.15 0.29 -243 900 0.716 17 6481 0.13 0.10 -238 900 0.716 18 4504 0.14 0.30 -237 900 0.715 19 5088 0.12 0.30 -189 900 0.683 https://doi.org/10.1371/journal.pone.0290760.t012 PLOS ONE | https://doi.org/10.1371/journal.pone.0290760 August 25, 2023 19 / 23 PLOS ONE Surface integrity optimization for ball-end hard milling of AISI D2 steel Table 13. Optimization scheme of cutting parameters for case 2. No. Spindle speed n, rpm Feed per tooth f , mm/z Radial depth of cut a , mm σ , MPa HV Desirability z e cross-feed 1 4500 0.21 0.10 -824 900 0.904 2 4589 0.20 0.10 -816 900 0.901 3 4501 0.20 0.10 -811 900 0.900 4 4680 0.20 0.10 -807 900 0.898 5 4501 0.20 0.11 -783 900 0.890 6 5194 0.18 0.10 -757 900 0.881 7 4500 0.21 0.10 -824 899 0.868 8 5603 0.16 0.10 -715 900 0.866 9 5942 0.15 0.10 -680 900 0.854 10 6052 0.14 0.10 -668 900 0.849 11 6190 0.14 0.10 -653 900 0.844 12 4500 0.19 0.15 -637 900 0.838 13 6366 0.13 0.10 -634 900 0.837 14 6441 0.13 0.10 -625 900 0.834 15 6617 0.12 0.10 -606 900 0.826 16 4500 0.18 0.19 -499 900 0.785 17 4500 0.18 0.20 -468 900 0.772 18 4500 0.17 0.20 -459 900 0.769 19 4500 0.17 0.21 -428 900 0.750 20 4500 0.16 0.26 -310 900 0.703 21 4500 0.16 0.24 -351 899 0.697 22 4500 0.15 0.29 -259 900 0.679 23 4938 0.13 0.30 -182 900 0.641 24 5087 0.12 0.30 -162 900 0.631 25 7473 0.12 0.10 -519 890 0.557 https://doi.org/10.1371/journal.pone.0290760.t013 depth of cut are 63 m/min to 251 m/min, 0.06 mm/z to 0.3 mm/z and 0.1 mm to 0.5 mm, respectively. Taken together, the main findings in this study can be drawn as following: 1. Radial depth of cut with percent contribution ratio (PCR) 62.05% is the most significant factor influencing surface roughness, followed by spindle speed 13.25% and feed per tooth 6.63%. Surface roughness decreases with the increase of spindle speed, but this effect is the least obvious. The combination of small radial depth of cut and high spindle speed contrib- utes to good surface finish and a satisfying material removal rate simultaneously. 2. Severe work hardening occurred on ball-end milled surface of hardened AISI D2 steel, especially for the low spindle speed condition. The work hardening degree was raised from 12.5% to 38.4% when spindle speed changed from n = 8000 rpm to n = 2000 rpm for a = 0.1 mm, a = 0.2 mm and f = 0.18 mm/z condition. Moreover, the influence of radial depth p z of cut on surface microhardness is not obvious when a high spindle speed is adopted. The work hardening degree changed from 12.9% to 15.7% when spindle speed radial depth of cut increases from 0.1 mm to 0.5 mm. Feed per tooth (PCR 25.14%) and spindle speed (PCR 24.79%) are the most influential factor on surface microhardness relatively. The microhardness of machined surface can be improved significantly by selecting small spindle speed and small radial depth of cut during finish machining process. 3. Spindle speed and radial depth of cut are the most significant factor influencing residual stress. The PCR of spindle speed and radial depth of cut reached 73.47% and 18.63% for PLOS ONE | https://doi.org/10.1371/journal.pone.0290760 August 25, 2023 20 / 23 PLOS ONE Surface integrity optimization for ball-end hard milling of AISI D2 steel residual stress in feed direction, 47.11% and 37.51% for residual stress in step-over direc- tion, respectively. High residual compressive stress can be generated by using low spindle speed and low radial depth of cut combination during ball-end milling process. This is mainly because the squeeze between the ball-end milling cutter and workpiece was aggra- vated. Conversely, the combination of high spindle speed and large radial depth of cut can bring about residual tensile stress due to the obviously increased cutting temperature. 4. Too small feed per tooth or too small radial depth of cut should be avoided from wear resis- tance point of view during ball-end milling process. This is because though the surface microhardness can be improved, the surface quality will also be deteriorated which is detri- mental to wear resistance. Overall, the combination of relatively high spindle speed, small feed per tooth together with small radial depth of cut can meet the wear resistance and the machining efficiency requirement. 5. Cutting parameters can influence the formation of surface defects, the state of residual stress and the degree of microscopic stress concentration. It is unrealistic to ascertain the best cutting parameter combination to satisfy all requirements at the same time and then improve the fatigue resistance of ball-end milled surface. Taken together, the material removal rate and the fatigue resistance can be obtained by using medium-sized cutting parameter combination. Moreover, the optional range and the maximum value of radial depth of cut decrease with the increase of spindle speed. 6. The proposed optimization scheme from surface integrity, wear resistance and fatigue resis- tance perspective respectively in this study can be used to guide the selection of cutting parameters during ball-end milling of hardened AISI D2 steel for dies/molds manufactur- ing industries. Supporting information S1 Data. (PDF) S1 File. (PDF) Author Contributions Funding acquisition: Weimin Huang. 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Tool path selection for high-speed ball-end milling process of hardened AISI D2 steel based on fatigue resistance. The International Journal of Advanced Manufactur- ing Technology, 2020, 110(7): 2239–2247. PLOS ONE | https://doi.org/10.1371/journal.pone.0290760 August 25, 2023 23 / 23 http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png PLoS ONE Public Library of Science (PLoS) Journal

Surface integrity optimization for ball-end hard milling of AISI D2 steel based on response surface methodology

Huang, Weimin; Wan, Cong; Wang, Guijie; Zhang, Guosong
PLoS ONE , Volume 18 (8) – Aug 25, 2023
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Copyright: © 2023 Huang et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Data Availability: All relevant data are within the paper and its Supporting Information files. Funding: This work was supported by the National Natural Science Foundation of China (52105463), the Natural Science Foundation of Shandong Province (ZR2020QE182, ZR2022QE015) and the Elite Program of Shandong University of Science and Technology (0104060540413). Competing interests: The authors have declared that no competing interests exist. Abbreviations: n, Spindle speed; fz, Feed per tooth; ae, Radial depth of cut; ap, Axial depth of cut; βf, Lead angle; βn, Tilt angle; ϕ, Diameter of ball-end milling cutter; γ, Rake angle Clearance angle; α, Clearance angle; β, Helix angle; Z, Tooth number of ball-end milling cutter; Ra, Surface roughness; HV, Microhardness; σfeed, Residual stress in feed direction; σcross-feed, Residual stress in step-over direction
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Abstract

a1111111111 a1111111111 This study focuses on systematically revealing how cutting parameters influence the surface integrity of ball-end hard milled surface of AISI D2 steel and proposing optimization scheme from surface integrity, wear resistance and fatigue resistance perspective based on response surface methodology respectively. Results can be summarized into three aspects. OPENACCESS Firstly, radial depth of cut with percent contribution ratio (PCR) 62.05% has a decisive influ- ence on surface roughness, followed by spindle speed 13.25% and feed per tooth 6.63%. Citation: Huang W, Wan C, Wang G, Zhang G (2023) Surface integrity optimization for ball-end The work hardening degree was raised from 12.5% to 38.4% when spindle speed changed hard milling of AISI D2 steel based on response from 8000 rpm to 2000 rpm. Spindle speed and radial depth of cut are the most significant surface methodology. PLoS ONE 18(8): e0290760. factor influencing residual stress. The PCR of spindle speed and radial depth of cut reached https://doi.org/10.1371/journal.pone.0290760 73.47% and 18.63% for residual stress in feed direction, 47.11% and 37.51% in step-over Editor: Antonio Riveiro Rodrıguez, University of direction, respectively. High residual compressive stress can be generated by lowering spin- Vigo, SPAIN dle speed and radial depth of cut benefiting from the aggravated squeeze between ball-end Received: April 17, 2023 milling cutter and workpiece. Secondly, too small feed per tooth or too small radial depth of Accepted: August 15, 2023 cut should be avoided from wear resistance point because though the surface microhard- Published: August 25, 2023 ness can be improved, the surface quality will also be deteriorated. The combination of high Copyright:© 2023 Huang et al. This is an open spindle speed, small feed per tooth together with small radial depth of cut can meet the wear access article distributed under the terms of the resistance and the machining efficiency requirement. Finally, a medium-sized cutting Creative Commons Attribution License, which parameter combination should be adopted to realize satisfying material removal rate and permits unrestricted use, distribution, and fatigue resistance. This study can be used to guide the selection of cutting parameters dur- reproduction in any medium, provided the original author and source are credited. ing ball-end milling of hardened AISI D2 steel for dies/molds manufacturing industries. Data Availability Statement: All relevant data are within the paper and its Supporting Information files. Funding: This work was supported by the National Introduction Natural Science Foundation of China (52105463), In virtue of the good blends of hardness, toughness and strength, cold working steel AISI D2 is the Natural Science Foundation of Shandong widely used for the manufacture of dies and molds, taking drawing dies, extrusion molds, and Province (ZR2020QE182, ZR2022QE015) and the Elite Program of Shandong University of Science plastic injection molds for example [1]. This kind of material contains high amount of hard and Technology (0104060540413). carbide particles and can maintain high strength and hardness under high temperature condi- tion, which is beneficial for fatigue resistance and wear resistance. However, these characteris- Competing interests: The authors have declared that no competing interests exist. tics are also responsible for high temperature, deteriorated surface and tendency to cutting PLOS ONE | https://doi.org/10.1371/journal.pone.0290760 August 25, 2023 1 / 23 PLOS ONE Surface integrity optimization for ball-end hard milling of AISI D2 steel Abbreviations: n, Spindle speed; f , Feed per tooth; z tool wear generated in cutting process leading to hardened AISI D2 steel a typical hard-to- a , Radial depth of cut; a , Axial depth of cut;β , e p f machine material [2]. Lead angle;β , Tilt angle; ϕ, Diameter of ball-end In general, the traditional manufacturing process for dies and molds contains milling of milling cutter;γ, Rake angle Clearance angle;α, AISI D2 steel in annealed condition, quenching and tempering treatments, electrical discharge Clearance angle;β, Helix angle; Z, Tooth number of machining, grinding and manual polishing [3, 4]. This is a time-consuming process and seri- ball-end milling cutter; Ra, Surface roughness; HV, Microhardness;σ , Residual stress in feed ously affects the production efficiency and market competitiveness of enterprises [5]. With the feed direction;σ , Residual stress in step-over cross-feed rapid development of advanced coatings, cutting tool material and lubrication/cooling tech- direction. nology, the feasibility and advantage of applying hard milling technology to the die and mold manufacturing industry is becoming more and more obvious [6, 7]. This is because the appli- cation of hard milling technology can reduce manufacturing cost and shorten production period [8]. However, this process may introduce unsatisfactory surface integrity taking large surface roughness, tensile residual stress, and surface pits for example [9]. It is well known that the excessive wear and the fatigue spalling or fracture are the common typical failure modes for dies and molds. The failure mechanism is always closely correlated with the surface integ- rity. Hence, it is necessary to systematically reveal the relationship between cutting parameters and surface integrity during ball-end milling process of hardened AISI D2 steel. Furthermore, proposing optimum process scheme is also of great importance to improve the wear and fatigue resistance of dies and molds in actual production. Many experimental studies have been performed to illustrate the machinability of hardened AISI D2 steel. Sahinoglu et al. [10] explored the machinability of hardened AISI S1 steel (60HRC) by hard turning process using CBN cutting inserts and found that feed rate has sig- nificant influence on surface roughness. Carreira et al. [11] performed hard milling experi- ments of hardened AISI D2 steel and concluded that the combination of high milling speed and small feed per tooth contributed to small surface roughness. However, the variation trends of surface microhardness and residual stress along with the cutting parameters was not obvi- ous because of the rough surface. Kara et al. [12] investigated the influence of cutting parame- ters on the tool wear and surface roughness during dry cutting of hardened AISI D2 steel. They found that the coated cutting tool performed better compared with the uncoated cutting tool from surface roughness and tool wear standpoint. Abbas A T et al. [13] used an artificial neural network with Edgeworth-Pareto method to optimize the cutting parameter during face milling process of high-strength grade-H steel and established neural network models for dif- ferent surface roughness and unit-volume machining time requirements. Markopoulos A P et al. [14] conducted face milling tests of hardened cold work steel AISI O1 and revealed the influence of cutting parameters (depth of cut, cutting speed and feed rate) on surface rough- ness, cutting forces, cutting power and machining cost based on Taguchi design of experi- ments method. Aqib et al. [15] compared the influence of minimum quantity lubrication (MQL) and nanofluids-based MQL (NFMQL) on cutting temperature and surface roughness during face milling process of hardened AISI D2 steel based on response surface methodology. They found that NFMQL performed better in terms of the ability to reduce cutting tempera- ture and surface roughness than MQL. Mac et al. [16] put forward a novel method to improve the prediction accuracy of cutting force and chip shrinkage coefficient for end milling of cold work steel SKD11 with the method of simulation and experiment. The wear and fatigue resistance of machined surface is closely correlated with the surface integrity. Zheng et al. [17] studied the wear resistance of hardened Cr12MoV surfaces with quadrangular pits feature formed by ball-end milling process. They found that the smaller the size of pits feature is, the better the wear resistance will be. Carreira et al. [11] found that cer- met inserts led to higher compressive residual stress and lower surface roughness compared with cemented tungsten carbide inserts in end milling process of hardened AISI D2 steel, which is beneficial for the improvement of adhesion characteristics. Tang et al. [18] PLOS ONE | https://doi.org/10.1371/journal.pone.0290760 August 25, 2023 2 / 23 PLOS ONE Surface integrity optimization for ball-end hard milling of AISI D2 steel investigated the influence of hardness on wear behavior of hardened D2 steel. They concluded that wear resistance was sensitive to hardness and the discrepancy in hardness is responsible for the difference in wear mechanisms. Gong et al. [19] investigated the influence of rolling times on the wear resistance of ultrasonic rolled surface of Cr12MoV steel. They found that the thickness of plastic deformation layer increased and the surface carbide decreased with the increase of rolling times. This variation can inhibit the crack initiation and propagation and then improve the wear resistance. It is well known that the fatigue performance is related to work hardening and the state of residual stress for machined surfaces. Different processing techniques lead to different surface integrity and then the discrepancy in fatigue performance for the same surface. Turned surfaces have better fatigue resistance than those generated by EDM and electrochemical machining pro- cess because of a higher residual compressive stress [20, 21]. Jesus et al. [4] compared the fatigue resistance of AISI D2 steel subjected to electrical discharging machining (EDM) and conventional grinding techniques, respectively. They found that large dendritic primary carbides were gener- ated after EDM process, which is detrimental to the fatigue resistance. In addition, the specimens machined by EDM process showed higher fatigue notch sensitivity than the ones machined by grinding process. Zhang et al. [22] studied the surface and subsurface characteristics and mechan- ical properties of ground surface of LPBF 304L stainless steel. The results showed that grinding process can significantly improve the surface roughness and grinding induced grain refinement can improve the fatigue resistance of the workpiece. Zhang et al. [23] compared the fatigue resis- tance of gear suffered four typical manufacturing processes: carburizing and grinding, shot peen- ing, barrel finishing, and barrel finishing after shot peening. They found that compared with the carburized and ground process, the gear contact fatigue life of shot peening, barrel finishing, and barrel finishing after shot peening can significantly improve the surface roughness, residual stress gradient and hardened layer, thus improving the fatigue resistance of gear contact surfaces. Taken together, the influence of cutting tool material, cutting parameters, coating types and lubrication methods on the machinability of hardened AISI D2 steel has been studied by many researchers from surface finish, tool life, cutting force and cutting temperature standpoint. The mainly findings are that the increase of cutting speed contributes to good surface finish and the coated carbide tool is competent for hard cutting. However, these reported studies are mainly focused on high speed hard turning and end/face milling process. Little attention was paid on the ball-end hard milling process of hardened AISI D2 steel. Moreover, though the influence of surface roughness, residual stress and hardness on the wear or fatigue perfor- mance has been reported by many literatures, the systematic investigations for the selection of cutting parameters from wear resistance and fatigue resistance perspective is scarcely found during ball-end hard milling process of hardened AISI D2 steel. Hence, this study aims to systematically investigate the influence of cutting parameters on surface integrity, especially considering that the ball-end milling operation always take place at the end of dies or molds manufacturing process, and then put forward specific selection scheme of cutting parameters for specific surface integrity requirement, good wear resistance and satisfying fatigue resistance, respectively. The findings in this study can provide guidance for the selection of cutting parameters during ball-end milling of hardened AISI D2 steel and contribute to the high-efficiency and high-performance manufacturing of dies and molds. Experimental procedures Material preparation The workpiece material selected in this study is high carbon and high chromium cold working steel AISI D2 with dimensions of 120 × 80 × 30 mm. In virtue of satisfying wear resistance, this PLOS ONE | https://doi.org/10.1371/journal.pone.0290760 August 25, 2023 3 / 23 PLOS ONE Surface integrity optimization for ball-end hard milling of AISI D2 steel Table 1. Chemical compositions of AISI D2 tool steel. Elements C Mn Si Cr Mo P S V Fe wt% 1.5 0.45 0.25 12 1.0 0.025 0.025 0.35 Balance https://doi.org/10.1371/journal.pone.0290760.t001 kind of steel has been widely used in the dies and molds manufacturing industry. The chemical composition of the as-received AISI D2 steel is given in Table 1. After heat treatment, the Rockwell hardness of the used workpiece reached approximately 61±1 HRC. The substrate is composed of retained carbides, tempered martensite and retained austenite, as shown in Fig 1. Design of experiments based on response surface methodology Response surface methodology (RSM) is usually used for modeling and analyzing the relation- ship between a response and several factors based on relatively small test numbers. A second- order mathematical model will be developed to realize the prediction of responses. This model considers not only the influence of independent factors but also the influence of interaction effect with each other. Response surface experiments were designed by using Box-behnken method. This method is commonly used during response surface design and does not arrange all test factors into a high-level test combination at the same time and then contributes to a sat- isfying cutting tool life. According to our preliminary experiments regarding of the relation- ship between cutting parameters and surface integrity, spindle speed n, feed per tooth f , and radial depth of cut a were identified as the input factors. Three levels of the three selected Fig 1. Microstructure of hardened AISI D2 steel. https://doi.org/10.1371/journal.pone.0290760.g001 PLOS ONE | https://doi.org/10.1371/journal.pone.0290760 August 25, 2023 4 / 23 PLOS ONE Surface integrity optimization for ball-end hard milling of AISI D2 steel Table 2. Parameters configuration of response surface experiments. No. Spindle speed Cutting speed Feed per tooth Radial depth of cut a , mm Axial depth of cut a , mm e p n, rpm v , m/min f , mm/z c z 1 8000 251 0.30 0.3 0.2 2 8000 251 0.18 0.5 0.2 3 5000 157 0.18 0.3 0.2 4 8000 251 0.18 0.1 0.2 5 5000 157 0.18 0.3 0.2 6 2000 63 0.06 0.3 0.2 7 5000 157 0.30 0.1 0.2 8 5000 157 0.06 0.5 0.2 9 2000 63 0.18 0.5 0.2 10 5000 157 0.18 0.3 0.2 11 2000 63 0.30 0.3 0.2 12 5000 157 0.06 0.1 0.2 13 2000 63 0.18 0.1 0.2 14 8000 251 0.06 0.3 0.2 15 5000 157 0.30 0.5 0.2 16 5000 157 0.18 0.3 0.2 17 5000 157 0.18 0.3 0.2 https://doi.org/10.1371/journal.pone.0290760.t002 factors are determined based on the existing research and the recommendation from the tool manufacturer. Furthermore, during the ball-end milling process, axial depth of cut was main- tained a constant value 0.2 mm. 17 runs were designed based on the Design Expert 8.0 soft- ware. This software can provide highly efficient design of experiments and convenient response analysis. Table 2 shows the parameters configuration of the three factors and three levels response surface experiments designed based on Box-Behnken method. Then, the hard milling operations of AISI D2 tool steel were performed by using a five-axis high speed machining center DMU60P duoBlock. The maximum spindle speed of the machin- ing center can reach 12000 rpm. New coated solid tungsten carbide ball-end milling cutter (Serial number SECO: TORNADO JH111L100-MEGA-64) was used during the unlubricated milling process. The geometrical parameter of the used ball-end milling cutter is given in Table 3. During the milling process, the lead angleβ and the tilt angleβ were set as 0˚ and f n 20˚, respectively. According to previous studies [24, 25], this kind of combination can avoid the nose of ball-end milling cutter from cutting and contributes to a satisfying tool life. The schematic diagram of tool path strategy in ball-end hard milling process is shown in Fig 2. Characterization of surface integrity Before the characterization of surface integrity, the ball-end hard milled surface was cleaned carefully by using an ultrasonic cleaner for about 10 min to avoid the influence of oil contami- nation on detection accuracy. Surface roughness of milled surfaces was obtained by using white light interferometer Veeco NT9300. Three different areas on the ball-end milled surface were selected and the average value was used as the final surface roughness. Surface Table 3. Geometrical parameter of ball-end milling cutter. Diameter ϕ Rake angleγ Clearance angleα Helix angleβ Tooth number Z 10 mm 0˚ 1˚ 17˚ 2 https://doi.org/10.1371/journal.pone.0290760.t003 PLOS ONE | https://doi.org/10.1371/journal.pone.0290760 August 25, 2023 5 / 23 PLOS ONE Surface integrity optimization for ball-end hard milling of AISI D2 steel Fig 2. Schematic diagram of tool path strategy in ball-end hard milling process. https://doi.org/10.1371/journal.pone.0290760.g002 microhardness was measured through microhardness tester MH-6. The dwell time and the indentation load were set as 10 s and 0.1 kg, respectively. The singular results were eliminated and the microhardness was obtained by averaging at least five measurements. Residual stress was measured by using X-stress 3000 in the light of sin ψ technique. Two directions, namely the feed direction and step-over direction, were adopted during the measuring process. At least five measurements were performed for each test and the average value was recorded as the final residual stress. Results and discussion Surface roughness, surface microhardness, and surface residual stress were chosen as the three responses. The response surface analysis was conducted by using software Design Expert 8.0. The software can easily compare which polynomial model is the most suitable, and give the recommended model. This kind of software can compare different models and show the most significant one. By this way, the accuracy of the proposed prediction model can be improved to some extent. Response surface analysis for surface roughness The analysis of variance (ANOVA) can be used to investigate the influence of input factors on output response [26]. Table 4 shows the result of variance analysis for surface roughness. Results show that spindle speed, radial depth of cut, feed per tooth and interaction between spindle speed and radial depth of cut are significant factors. The percent contribution ratio (PCR) on surface roughness reached 13.25%, 62.05%, 6.63% and 10.24%, respectively. Radial depth of cut is the most significant factor influencing surface roughness. The two factors inter- action model was recommended for illustrating the results of surface roughness. It can be seen that the proposed model is significant as it exhibits a very small P value. The prediction model 2 2 with R 93%, R -adjusted 88.6% and R2-predicted 82.4% can be expressed by the following Eq. PLOS ONE | https://doi.org/10.1371/journal.pone.0290760 August 25, 2023 6 / 23 PLOS ONE Surface integrity optimization for ball-end hard milling of AISI D2 steel Table 4. Variance analysis for surface roughness: Two factor interaction model. Source Sum of squares PCR(%) df Mean square F value P value Prob>F Remarks Model 1.54 6 0.26 21.75 < 0.0001 Significant A-n 0.22 13.25 1 0.22 18.56 0.0015 B-a 1.03 62.05 1 1.03 86.72 < 0.0001 C-f 0.11 6.63 1 0.11 9.17 0.0127 AB 0.17 10.24 1 0.17 14.01 0.0038 AC 0.019 1.14 1 0.019 1.63 0.2301 −3 −3 BC 5.15×10 0.31 1 5.15×10 0.44 0.5243 Residual 0.12 10 0.012 −3 Lack of fit 0.039 6 6.58×10 0.33 0.8884 Not significant Pure error 0.079 4 0.02 Cor total 1.66 16 https://doi.org/10.1371/journal.pone.0290760.t004 (1). 5 4 Ra ¼ 0:305þ 1:17917� 10 nþ 3:75521a 1:48175f 3:39167� 10 na e z e ð1Þ þ1:93056� 10 nf 1:49479a f z e z Fig 3 shows the 3-D response surface for surface roughness. Generally, surface roughness for ball-end milled surfaces mainly determined by two types of scallops: Feed-interval scallops induced by the feed movement and pick-interval scallops induced by the step-over movement. The difference in value between feed per tooth and radial depth of cut leads to the increase of heterogeneity of surface topography and then the increase of surface roughness. As indicated in Fig 3(A) and 3(B), radial depth of cut has the most significant influence on surface rough- ness compared with feed per tooth and spindle speed. This is because the pick-interval scallop height is usually higher than the feed-interval scallop. In addition, surface roughness decreases with the increase of spindle speed, but this effect is the least obvious. Though improving spin- dle speed contributes to the decrease of cutting force and the increase of cutting temperature, which is beneficial for cutting stability and surface roughness, this effect is negligible compared to the two types of scallops controlled by feed per tooth and radial depth of cut. Taken together, selecting small radial depth of cut and high spindle speed contributes to small rough- ness at given feed per tooth condition. Response surface analysis for microhardness Analysis of variance for microhardness of ball-end hard milled surface is given in Table 5. Results show that spindle speed, radial depth of cut, feed per tooth, the interaction between spindle speed and radial depth of cut and quadratic terms of feed per tooth are significant fac- tors. Feed per tooth (PCR 25.14%) and spindle speed (PCR 24.79%) are the most significant factor influencing surface microhardness relatively. The quadratic model was recommended for illustrating the results of surface microhardness. As shown in Table 5, the proposed model is significant because of the small P value 0.0037. The quadratic model with R value 92.3%, R -adjusted 82.5% and R2-predicted 84.3% shown in Eq (2) can be used to describe the rela- tionship between the three input factors and microhardness. HV ¼ 1113:333 0:010167n 613:333a 613:888f þ 0:074167na 0:02nf e z e z ð2Þ 2 2 2 708:33a f 2� 10 n þ 462:5a þ 1770:8f e e z PLOS ONE | https://doi.org/10.1371/journal.pone.0290760 August 25, 2023 7 / 23 PLOS ONE Surface integrity optimization for ball-end hard milling of AISI D2 steel Fig 3. 3-D response surface for surface roughness of ball-end milled AISI D2 steel under dry cutting condition, (a) n×a , (b) f ×a , (c) e z e f ×n. https://doi.org/10.1371/journal.pone.0290760.g003 Table 5. Variance analysis for microhardness: Quadratic model. Source Sum of squares PCR(%) df Mean square F value P value Prob>F Remarks Model 38088.56 9 4232.06 9.39 0.0037 Significant A-n 10224.5 24.79 1 10224.5 22.69 0.0021 B-a 2738 6.64 1 2738 6.08 0.0432 C-f 10368 25.14 1 10368 23.01 0.002 AB 7921 19.21 1 7921 17.58 0.0041 AC 256 0.62 1 256 0.57 0.4756 BC 1156 2.8 1 1156 2.57 0.1533 A 1364.21 3.31 1 1364.21 3.03 0.1254 B 1441.05 3.49 1 1441.05 3.2 0.1169 C 2737.89 6.64 1 2737.89 6.08 0.0432 Residual 3154.5 7 450.64 Lack of fit 3154.5 3 1051.5 0.15 0.9216 Not significant Pure error 0 4 0 Cor total 41243.06 16 https://doi.org/10.1371/journal.pone.0290760.t005 PLOS ONE | https://doi.org/10.1371/journal.pone.0290760 August 25, 2023 8 / 23 PLOS ONE Surface integrity optimization for ball-end hard milling of AISI D2 steel Fig 4. 3-D response surface for microhardness of ball-end milled AISI D2 steel under dry cutting condition, (a) n×a , (b) f ×n, (c) e z f ×a . z e https://doi.org/10.1371/journal.pone.0290760.g004 Fig 4 depicts the 3-D response surface of microhardness considering the interaction effect of input factors. As a result of the coupling effect of strain hardening and thermal softening, obvious work hardening occurred after ball-end milling process of hardened AISI D2 steel, especially for the low spindle speed condition. Compared with the original hardness approxi- mate 720 HV, the work hardening degree reached about 12.5% for the combination of n = 8000 rpm, a = 0.1mm, f = 0.18mm/z, and 38.4% for n = 2000 rpm, a = 0.1 mm and f = e z e z 0.18 mm/z condition. The reason can be explained from the following two aspects. On the one hand, due to the high hardness and high strength of hardened AISI D2 steel, a larger cutting force was needed compared with the traditional cutting process and lead to more severe plastic deformation. On the other hand, the good toughness of AISI D2 steel contributes to the accu- mulation of strain during hard milling process. As indicated in Fig 4, the microhardness of ball-end milled surface decrease with the increase of spindle speed and feed per tooth. This is because more heat was generated and the degree of thermal softening was strengthened under the circumstances. When a small spindle speed was adopted, microhardness of hard milled surface decreased with the increase of radial depth of cut due to the increased temperature. However, it is noteworthy that a slight increase of microhardness was presented for a high spindle speed condition. As spindle speed was set as 8000 rpm and feed per tooth 0.18 mm/z, the work hardening degree changed only from 12.9% to 15.7% when radial depth of cut PLOS ONE | https://doi.org/10.1371/journal.pone.0290760 August 25, 2023 9 / 23 PLOS ONE Surface integrity optimization for ball-end hard milling of AISI D2 steel increases from 0.1mm to 0.5mm. The reason for this is that though more heat was generated for the high spindle speed condition, the contact time between the tool flank face and machined surface was obviously reduced, and the cutting force was strengthened with radial depth of cut increase. Response surface analysis for residual stress The variance analysis for residual stress in feed and step-over direction is shown in Tables 6 and 7, respectively. Results reveal that spindle speed, radial depth of cut and quadratic terms of feed per tooth are significant factors for residual stress in either direction. Furthermore, feed per tooth, the interaction between spindle speed and radial depth of cut, the interaction between spindle speed and feed per tooth and quadratic terms of spindle speed are also signifi- cant factors for residual stress in step-over direction. Overall, spindle speed and radial depth of cut are the most significant factor influencing residual stress. The PCR of spindle speed and radial depth of cut reached 73.47% and 18.63% for residual stress in feed direction, 47.11% and 37.51% for residual stress in step-over direction, respectively. The quadratic model was recom- mended for illustrating the results of residual stress. As shown in Tables 6 and 7, the proposed 2 2 model is significant because of the very small P value. Eq (3) with R value 97.6%, R -adjusted 2 2 94.6% and R2-predicted 96.3%, and Eq (4) with R value 99.8%, R -adjusted 99.5% and R2-predicted 99.7% can be used to predict residual stress in feed direction and step-over direc- tion, respectively. s ¼ 1284:125þ 0:0928nþ 1674:375a þ 1751:041f þ 3:204� 10 na feed e z e ð3Þ 6 6 2 2 2 1:036� 10 nf þ 2:458� 10 n 553:125a 4487:847f e z s ¼ 2162:771þ 0:18825nþ 4932:292a þ 2002:778f þ 0:14417na step over e z e ð4Þ 2 2 2 0:28681nf þ 770:8333a f 4:79167� 10 n 6709:375a 1536:4583f z e z e z Figs 5 and 6 show the 3-D response surface for residual stress in feed and step-over direc- tion, respectively. It can be seen that spindle speed and radial depth of cut are the most notable influencing factors on surface residual stress among the three input factors. A combination of Table 6. Variance analysis for residual stress in feed direction: Quadratic model. Source Sum of squares PCR(%) df Mean squares F value P value Prob>F Remarks 6 5 Model 1.32×10 9 1.47×10 32.29 < 0.0001 Significant 5 5 A-n 9.96×10 73.47 1 9.96×10 218.71 < 0.0001 5 5 B-a 2.52×10 18.63 1 2.52×10 55.45 0.0001 C-f 10296.13 0.76 1 10296.13 2.26 0.1763 −4 AB 4 0 1 4 8.79×10 0.9772 AC 0 0 1 0 0 1 −5 BC 0.25 0 1 0.25 5.493×10 0.9943 A 5180.02 0.38 1 5180.02 1.14 0.3215 B 4960.87 0.37 1 4960.87 1.09 0.3312 C 49864.76 3.68 1 49864.76 10.96 0.0129 Residual 31860.95 7 4551.56 −4 Lack of fit 3.75 3 1.25 1.57×10 1 Not significant Pure error 31857.2 4 7964.3 Cor total 1.36×10 16 https://doi.org/10.1371/journal.pone.0290760.t006 PLOS ONE | https://doi.org/10.1371/journal.pone.0290760 August 25, 2023 10 / 23 PLOS ONE Surface integrity optimization for ball-end hard milling of AISI D2 steel Table 7. Variance analysis for residual stress in step-over direction: Quadratic model. Source Sum of squares PCR(%) df Mean squares F value P value Prob>F Remarks 6 5 Model 2.66×10 9 2.95×10 415.52 < 0.0001 significant 6 5 A-n 1.25×10 47.11 1 1.25×10 1764.85 < 0.0001 5 5 B-a 9.98×10 37.51 1 9.98×10 1405.26 < 0.0001 C-f 7021.13 0.26 1 7021.13 9.88 0.0163 AB 29929 1.12 1 29929 42.1 0.0003 AC 42642.25 1.6 1 42642.25 60.03 0.0001 BC 1369 0.05 1 1369 1.93 0.2077 A 7830.59 0.03 1 7830.59 11.02 0.0128 2 5 5 B 3.03×10 11.4 1 3.03×10 426.9 < 0.0001 C 2061.12 0.08 1 2061.12 2.9 0.1323 Residual 4972.75 7 710.39 −3 Lack of fit 6.75 3 2.25 1.81×10 0.9999 Not significant Pure error 4966 4 1241.5 Cor total 2.66×10 16 https://doi.org/10.1371/journal.pone.0290760.t007 low spindle speed and low radial depth of cut contributes to high residual compressive stress because of the extended heat dissipation time and the aggravated squeeze between ball-end milling cutter and workpiece material. Conversely, the combination of high spindle speed and Fig 5. 3-D response surface for residual stress in feed direction of ball-end milled AISI D2 steel under dry cutting condition, (a) n×a , (b) f ×n, (c) f ×a . e z z e https://doi.org/10.1371/journal.pone.0290760.g005 PLOS ONE | https://doi.org/10.1371/journal.pone.0290760 August 25, 2023 11 / 23 PLOS ONE Surface integrity optimization for ball-end hard milling of AISI D2 steel Fig 6. 3-D response surface for residual stress in step-over direction of ball-end milled AISI D2 steel under dry cutting condition, (a) n×a , (b) f ×n, (c) f ×a . e z z e https://doi.org/10.1371/journal.pone.0290760.g006 large radial depth of cut can bring about residual tensile stress due to the obviously increased cutting temperature. In addition, the effect of feed per tooth on residual stress in both direc- tions is negligible especially at high spindle speed condition. Reasons for that can be explained as following. The thickness of chips changes continuously during the up milling process and reaches the maximum value as the exit of ball-end milling cutter from the workpiece surface. The heat accumulation also reaches the most severe level at this point. Due to the high spindle speed and the characteristics of intermittent cutting, most of heat is carried away by chips and little heat is diffused into the machined surface. Optimization of cutting parameters According to the above analysis, the interaction of spindle speed and radial depth of cut has significant effect on surface integrity on the whole. Then the response surface of desirability function was established based on the two parameters aiming at specific goal of surface integ- rity, wear resistance and fatigue resistance, respectively. Cutting parameters optimization for satisfying surface integrity. Fig 7 depicts the response surface of desirability for different requirements of surface integrity. Two aspects can be summarized as following. On the one hand, desirability for minimizing surface roughness of ball-end milled surface is sensitive to radial depth of cut, especially for the low spindle speed condition as indicated in Fig 7(A). High desirability can be obtained when radial depth of cut PLOS ONE | https://doi.org/10.1371/journal.pone.0290760 August 25, 2023 12 / 23 PLOS ONE Surface integrity optimization for ball-end hard milling of AISI D2 steel Fig 7. Response surface of desirability function for the goal of (a) Minimizing surface roughness, (b) Maximizing surface microhardness, and (c) Maximizing residual compressive stress. https://doi.org/10.1371/journal.pone.0290760.g007 is no larger than 0.2 mm. On the other hand, increasing spindle speed contributes to the improvement of desirability on the whole. When a small radial depth of cut is adopted, the desirability is basically maintained at a larger constant value. Then the combination of high spindle speed and small radial depth of cut can guarantee not only satisfying material removal rate but also high desirability for minimum surface roughness. The recommended cutting parameter configuration is given in Table 8. In actual production, the most reasonable param- eter configuration should be selected comprehensively considering the cutting tool perfor- mance, the machine tool stability and the specific requirements of machined surface quality. Secondly, the desirability response surface is shown in Fig 7(B) for the goal of maximizing surface microhardness. It can be seen that there are two regions with relatively high desirabil- ity, namely the combination of small spindle speed and small radial depth of cut followed by the combination of large spindle speed and large radial depth of cut. However, for the later condition, large surface roughness and severe cutting tool wear will be introduced because of the increased cutting force and cutting temperature. For the former condition, though high desirability can be obtained, the material removal rate is too small to be suitable for mass pro- duction, but only for small batch production. Table 9 shows the recommended cutting param- eter configuration for maximizing surface microhardness with high desirability. In actual production, the cutting parameter configuration should be determined taking production type into consideration. PLOS ONE | https://doi.org/10.1371/journal.pone.0290760 August 25, 2023 13 / 23 PLOS ONE Surface integrity optimization for ball-end hard milling of AISI D2 steel Table 8. Cutting parameter configuration for minimizing surface roughness with high desirability. No. Spindle speed n, rpm Radial depth of cut a , mm Feed per tooth f , mm/z Ra Desirability e z 1 4049 0.10 0.29 0.347 1 2 4548 0.10 0.30 0.353 1 3 4041 0.10 0.27 0.358 1 4 4238 0.10 0.29 0.357 1 5 4107 0.10 0.29 0.344 1 6 4002 0.10 0.28 0.355 1 7 4233 0.10 0.29 0.355 1 8 4105 0.11 0.30 0.351 1 9 4011 0.11 0.29 0.355 1 10 4393 0.10 0.30 0.349 1 11 4387 0.10 0.29 0.358 1 12 4097 0.10 0.29 0.352 1 13 4008 0.10 0.27 0.358 1 14 4440 0.10 0.30 0.351 1 15 4355 0.10 0.29 0.358 1 16 4145 0.11 0.30 0.349 1 17 4000 0.11 0.29 0.360 0.999 18 4000 0.12 0.30 0.365 0.995 19 4000 0.10 0.26 0.366 0.994 20 4990 0.10 0.30 0.368 0.992 21 4000 0.10 0.26 0.370 0.991 22 4000 0.10 0.23 0.391 0.973 23 5858 0.10 0.30 0.399 0.966 24 6428 0.10 0.30 0.420 0.948 25 6489 0.10 0.30 0.422 0.946 26 6779 0.10 0.30 0.432 0.937 27 5186 0.10 0.20 0.439 0.932 28 7199 0.10 0.30 0.447 0.925 29 7549 0.10 0.30 0.460 0.914 30 7567 0.10 0.30 0.460 0.913 31 7911 0.10 0.29 0.473 0.902 32 7981 0.10 0.30 0.475 0.901 33 7273 0.10 0.13 0.488 0.890 34 7868 0.10 0.13 0.491 0.887 https://doi.org/10.1371/journal.pone.0290760.t008 Finally, it is well known that surface residual compressive stress contributes to fatigue resis- tance of service parts bearing alternate load. Fig 7(C) shows the desirability response surface for maximizing surface residual compressive stress in both feed direction and step-over direc- tion simultaneously. It can be seen that the desirability gradually decreases with the increase of spindle speed no matter what radial depth of cut was used. Moreover, selecting a small radial depth of cut contributes to high desirability. The combination of small spindle speed and small radial depth of cut can bring about high desirability. However, this condition will seriously influence the material removal rate. It is noteworthy that the discrepancy in desirability is not obvious for surfaces ball-end milled with small radial depth of cut when different spindle speeds are used. Then selecting relatively high spindle speed and small radial depth of cut can guarantee not only high residual compressive stress but also a satisfying machining efficiency. PLOS ONE | https://doi.org/10.1371/journal.pone.0290760 August 25, 2023 14 / 23 PLOS ONE Surface integrity optimization for ball-end hard milling of AISI D2 steel Table 9. Cutting parameter configuration for maximizing surface microhardness with high desirability. No. Spindle speed n, rpm Radial depth of cut a , mm Feed per tooth f , mm/z HV Desirability e z 1 2091 0.10 0.07 1001 1 2 2041 0.10 0.07 1001 1 3 2287 0.10 0.06 1001 1 4 2067 0.10 0.06 1002 1 5 2116 0.11 0.06 1001 1 6 2013 0.10 0.06 1004 1 7 2109 0.10 0.06 1003 1 8 2037 0.11 0.06 1000 1 9 2226 0.10 0.06 1000 1 10 2013 0.10 0.07 1000 1 11 2054 0.10 0.07 1000 1 12 2000 0.10 0.08 998 0.991 13 2000 0.12 0.06 998 0.989 14 2588 0.10 0.06 998 0.989 15 2000 0.10 0.09 993 0.962 16 2000 0.10 0.1 990 0.945 17 2018 0.10 0.3 983 0.913 18 2000 0.10 0.3 983 0.908 19 2000 0.10 0.3 982 0.905 20 2237 0.10 0.3 980 0.892 21 3710 0.10 0.06 979 0.891 22 2000 0.19 0.06 973 0.859 23 2000 0.19 0.06 971 0.845 24 2000 0.10 0.21 968 0.832 25 6388 0.50 0.06 952 0.749 26 6434 0.50 0.06 952 0.749 27 6349 0.50 0.06 952 0.749 28 6201 0.50 0.06 952 0.749 29 6051 0.50 0.06 952 0.748 30 5330 0.50 0.06 950 0.737 31 5718 0.47 0.06 944 0.705 32 3611 0.50 0.06 937 0.668 33 4128 0.37 0.06 935 0.659 34 4140 0.38 0.06 935 0.659 https://doi.org/10.1371/journal.pone.0290760.t009 Table 10 shows the recommended cutting parameter configuration for maximizing residual compressive stress with high desirability. Cutting parameters optimization for wear resistance. According to our previous research, surface work hardening occurred during ball-end milling process of hardened AISI D2 steel contributes to the improvement of wear resistance. This is because work hardening can improve the ability to resist abrasive wear and plastic deformation on the surface, and also enhance the stability of the oxide film formed on the friction interface, thereby reducing the friction coefficient to a certain extent and improving wear resistance [1, 27]. Though the com- bination of small feed per tooth and small radial depth of cut is beneficial for high microhard- ness, the machining efficiency is greatly reduced. Furthermore, the surface quality will be deteriorated due to the occurrence of micro-pits defect caused by too small feed per tooth or too small radial depth of cut. Therefore, considering the above factors and the recommended PLOS ONE | https://doi.org/10.1371/journal.pone.0290760 August 25, 2023 15 / 23 PLOS ONE Surface integrity optimization for ball-end hard milling of AISI D2 steel Table 10. Cutting parameter configuration for maximizing residual compressive stress with high desirability. No. Spindle speed n, rpm Radial depth of cut a , mm Feed per tooth f , mm/z Residual stress σ , MPa Residual stress σ , MPa Desirability e z feed cross-feed 1 4000 0.10 0.06 -633 -952 0.884 2 4000 0.10 0.06 -630 -945 0.880 3 4000 0.11 0.06 -625 -925 0.871 4 4000 0.10 0.07 -610 -944 0.870 5 4131 0.10 0.06 -617 -933 0.870 6 4000 0.11 0.06 -620 -907 0.862 7 4337 0.10 0.06 -591 -903 0.848 8 4000 0.11 0.07 -593 -895 0.846 9 4000 0.10 0.10 -560 -924 0.840 10 4000 0.10 0.11 -540 -916 0.827 11 4000 0.10 0.30 -561 -861 0.819 12 4033 0.10 0.30 -557 -859 0.816 13 4000 0.10 0.13 -518 -905 0.813 14 4000 0.10 0.30 -556 -843 0.811 15 4000 0.10 0.28 -537 -862 0.808 16 4000 0.10 0.28 -535 -862 0.807 17 4157 0.10 0.30 -541 -849 0.806 18 4000 0.10 0.27 -526 -863 0.803 19 4000 0.10 0.26 -514 -864 0.797 20 4000 0.10 0.18 -488 -884 0.792 21 4000 0.10 0.24 -497 -867 0.791 22 4000 0.10 0.23 -492 -870 0.789 23 4000 0.16 0.06 -560 -718 0.770 24 5769 0.10 0.30 -351 -738 0.676 25 7863 0.10 0.30 -134 -630 0.525 26 4000 0.47 0.06 -294 -311 0.507 https://doi.org/10.1371/journal.pone.0290760.t010 cutting parameters of the tool manufacturer, two constraints are proposed as follows: 4500 rpm�n�8000 rpm, 0.12 mm/z�f �0.3 mm/z. The desirability response surface for the goal of maximizing surface microhardness was obtained by Design Expert 8.0, as shown in Fig 8. The range of desirability is 0 to 1. It can be seen that the desirability decreases obviously with the increase of radial depth of cut and spindle speed. The satisfying solution with high desirability mainly exists in the condition of small radial depth of cut and low spindle speed. The optimiza- tion scheme of cutting parameters with high desirability for satisfying wear resistance is given in Table 11. In actual production, the cutting parameter combination with high desirability should be prioritized on condition that the ball-end milling cutter and machine tool perfor- mance meet the requirements. Cutting parameters optimization for fatigue resistance. In the light of our previous research [28], the superposition of machining induced surface residual compressive stress and alternate load changes the ultimate stress level, average stress and stress ratio on the surface of the workpiece, and then affects the initiation and propagation process of fatigue cracks. The influence of surface work hardening on fatigue resistance is two-sided and moderate degree of work hardening is beneficial for the impediment of shear slip and then provides a strengthened resistance to fatigue crack initiation. However, excessive work hardening will also decrease the surface toughness and improve the sensitivity of surface notch under alternate load. This is detrimental to fatigue resistance because of the influence on crack propagation life. In PLOS ONE | https://doi.org/10.1371/journal.pone.0290760 August 25, 2023 16 / 23 PLOS ONE Surface integrity optimization for ball-end hard milling of AISI D2 steel Fig 8. Desirability response surface for wear resistance of ball-end milled surface of AISI D2 steel under dry cutting condition. https://doi.org/10.1371/journal.pone.0290760.g008 addition, the microscopic stress concentration, which can affect the rate of fatigue crack propa- gation significantly, is closely related with the surface defect and the surface topography of ball-end milled surfaces [29]. Based on the above conclusions, three aspects are considered before optimization of cutting parameters. Firstly, select relatively small radial depth of cut a or large feed per tooth f to e z decrease the microscopic stress concentration phenomenon. Secondly, choose a high spindle speed n or a large feed per tooth f or a large radial depth of cut a to ensure the machining effi- z e ciency. Lastly, increase the spindle speed n or feed per tooth f to restrain surface defects. To satisfy the above requirements, the constraints of cutting parameters are set as following: 4500 rpm�n�8000 rpm, 0.12 mm/z�f �0.3 mm/z, 0.1 mm�a �0.3 mm. Furthermore, combined z e with our previous findings [28], ball-end hard milled surfaces with microhardness approxi- mate HV 900 show better fatigue resistance than the other condition. Then, high residual com- pressive stress together with surface microhardness close to HV 900 are identified as the optimization goal and the degrees of importance for the two responses is set to be the same. Fig 9 gives the response surface and the contour map of desirability for the goal of high resid- ual compressive stress in feed direction and microhardness HV 900. This situation is defined as case 1. Fig 10 gives the response surface and the contour map of desirability for the goal of high residual compressive stress in step-over direction and microhardness HV 900. This situa- tion is defined as case 2. Comparing Figs 9 and 10, it can be found that the areas with high desirability for the two cases are very similar. This is because the residual stress in the feed direction and step-over direction has the similar trend with the change of spindle speed and radial depth of cut as shown in Figs 5 and 6. As shown in Figs 9 and 10, the area with high desirability occurs when a PLOS ONE | https://doi.org/10.1371/journal.pone.0290760 August 25, 2023 17 / 23 PLOS ONE Surface integrity optimization for ball-end hard milling of AISI D2 steel Table 11. Cutting parameter configuration for wear resistance with high desirability. No. Spindle speed n, rpm Feed per tooth f , mm/z Radial depth of cut a , mm HV Desirability z e 1 4500 0.12 0.10 926 0.618 2 4500 0.12 0.11 925 0.614 3 4566 0.12 0.10 925 0.614 4 4500 0.12 0.10 925 0.613 5 4520 0.12 0.11 924 0.612 6 4618 0.12 0.10 924 0.61 7 4500 0.12 0.12 924 0.61 8 4503 0.13 0.10 924 0.609 9 4665 0.12 0.10 924 0.607 10 4500 0.13 0.10 924 0.607 11 4715 0.12 0.10 923 0.604 12 4500 0.13 0.10 923 0.604 13 4500 0.12 0.13 923 0.602 14 4511 0.13 0.10 921 0.595 15 4500 0.12 0.17 919 0.585 16 5036 0.12 0.10 919 0.584 17 4500 0.12 0.23 914 0.555 18 4500 0.17 0.10 910 0.533 19 4500 0.12 0.27 910 0.533 20 6010 0.12 0.10 908 0.521 21 4500 0.12 0.31 906 0.515 22 4500 0.12 0.33 905 0.506 23 4523 0.24 0.10 889 0.424 24 6717 0.12 0.50 862 0.279 https://doi.org/10.1371/journal.pone.0290760.t011 low spindle speed and a small radial depth of cut are adopted. The optional range and the maxi- mum value of radial depth of cut decrease with the increase of spindle speed. Similarly, the optional range and the maximum value of spindle speed decrease with the increase of radial depth of cut. The optimization scheme of cutting parameters for fatigue resistance purpose con- sidering the two aforementioned cases is given in Tables 12 and 13, respectively. In actual produc- tion, the optimization scheme should be chosen based on comprehensive analysis of the requirement of surface roughness, the alternate load direction, the metal removal rate and so on. Fig 9. Optimization of cutting parameters for high residual compressive stress in feed direction and microhardness HV 900 purpose, (a) Response surface of desirability, (b) Contour map of desirability. https://doi.org/10.1371/journal.pone.0290760.g009 PLOS ONE | https://doi.org/10.1371/journal.pone.0290760 August 25, 2023 18 / 23 PLOS ONE Surface integrity optimization for ball-end hard milling of AISI D2 steel Fig 10. Optimization of cutting parameters for high residual compressive stress in step-over direction and microhardness HV 900 purpose, (a) Response surface of desirability, (b) Contour map of desirability. https://doi.org/10.1371/journal.pone.0290760.g010 In the future, the physical mechanism during the machining of AISI D2 steel should be fur- ther investigated to better explain the relationship between cutting parameters and surface integrity. In addition, the influence of tilt angle and lead angle on wear resistance and fatigue resistance should also be revealed. Conclusions During the manufacturing process of dies or molds with large size and complex curved sur- faces, ball-end milling operation is usually used as the final process. The influence mechanism of cutting parameters on surface integrity and the optimization scheme from surface integrity, wear resistance and fatigue resistance perspective were studied during ball-end hard milling process of AISI D2 steel. In this study, the range of cutting speed, feed per tooth and radial Table 12. Optimization scheme of cutting parameters for case 1. No. Spindle speed n, rpm Feed per tooth f , mm/z Radial depth of cut a , mm σ , MPa HV Desirability z e feed 1 4500 0.21 0.10 -424 900 0.829 2 4593 0.20 0.10 -412 900 0.823 3 4637 0.20 0.10 -407 900 0.819 4 4500 0.20 0.11 -411 900 0.816 5 4500 0.20 0.12 -399 900 0.815 6 4500 0.20 0.12 -396 900 0.813 7 4500 0.19 0.15 -369 900 0.798 8 5007 0.18 0.10 -364 900 0.795 9 5253 0.18 0.10 -339 900 0.779 10 4507 0.18 0.19 -320 900 0.768 11 4500 0.17 0.21 -309 900 0.761 12 4500 0.20 0.10 -423 902 0.761 13 4500 0.16 0.25 -270 900 0.737 14 6031 0.14 0.10 -270 900 0.736 15 4500 0.16 0.26 -266 900 0.734 16 4500 0.15 0.29 -243 900 0.716 17 6481 0.13 0.10 -238 900 0.716 18 4504 0.14 0.30 -237 900 0.715 19 5088 0.12 0.30 -189 900 0.683 https://doi.org/10.1371/journal.pone.0290760.t012 PLOS ONE | https://doi.org/10.1371/journal.pone.0290760 August 25, 2023 19 / 23 PLOS ONE Surface integrity optimization for ball-end hard milling of AISI D2 steel Table 13. Optimization scheme of cutting parameters for case 2. No. Spindle speed n, rpm Feed per tooth f , mm/z Radial depth of cut a , mm σ , MPa HV Desirability z e cross-feed 1 4500 0.21 0.10 -824 900 0.904 2 4589 0.20 0.10 -816 900 0.901 3 4501 0.20 0.10 -811 900 0.900 4 4680 0.20 0.10 -807 900 0.898 5 4501 0.20 0.11 -783 900 0.890 6 5194 0.18 0.10 -757 900 0.881 7 4500 0.21 0.10 -824 899 0.868 8 5603 0.16 0.10 -715 900 0.866 9 5942 0.15 0.10 -680 900 0.854 10 6052 0.14 0.10 -668 900 0.849 11 6190 0.14 0.10 -653 900 0.844 12 4500 0.19 0.15 -637 900 0.838 13 6366 0.13 0.10 -634 900 0.837 14 6441 0.13 0.10 -625 900 0.834 15 6617 0.12 0.10 -606 900 0.826 16 4500 0.18 0.19 -499 900 0.785 17 4500 0.18 0.20 -468 900 0.772 18 4500 0.17 0.20 -459 900 0.769 19 4500 0.17 0.21 -428 900 0.750 20 4500 0.16 0.26 -310 900 0.703 21 4500 0.16 0.24 -351 899 0.697 22 4500 0.15 0.29 -259 900 0.679 23 4938 0.13 0.30 -182 900 0.641 24 5087 0.12 0.30 -162 900 0.631 25 7473 0.12 0.10 -519 890 0.557 https://doi.org/10.1371/journal.pone.0290760.t013 depth of cut are 63 m/min to 251 m/min, 0.06 mm/z to 0.3 mm/z and 0.1 mm to 0.5 mm, respectively. Taken together, the main findings in this study can be drawn as following: 1. Radial depth of cut with percent contribution ratio (PCR) 62.05% is the most significant factor influencing surface roughness, followed by spindle speed 13.25% and feed per tooth 6.63%. Surface roughness decreases with the increase of spindle speed, but this effect is the least obvious. The combination of small radial depth of cut and high spindle speed contrib- utes to good surface finish and a satisfying material removal rate simultaneously. 2. Severe work hardening occurred on ball-end milled surface of hardened AISI D2 steel, especially for the low spindle speed condition. The work hardening degree was raised from 12.5% to 38.4% when spindle speed changed from n = 8000 rpm to n = 2000 rpm for a = 0.1 mm, a = 0.2 mm and f = 0.18 mm/z condition. Moreover, the influence of radial depth p z of cut on surface microhardness is not obvious when a high spindle speed is adopted. The work hardening degree changed from 12.9% to 15.7% when spindle speed radial depth of cut increases from 0.1 mm to 0.5 mm. Feed per tooth (PCR 25.14%) and spindle speed (PCR 24.79%) are the most influential factor on surface microhardness relatively. The microhardness of machined surface can be improved significantly by selecting small spindle speed and small radial depth of cut during finish machining process. 3. Spindle speed and radial depth of cut are the most significant factor influencing residual stress. The PCR of spindle speed and radial depth of cut reached 73.47% and 18.63% for PLOS ONE | https://doi.org/10.1371/journal.pone.0290760 August 25, 2023 20 / 23 PLOS ONE Surface integrity optimization for ball-end hard milling of AISI D2 steel residual stress in feed direction, 47.11% and 37.51% for residual stress in step-over direc- tion, respectively. High residual compressive stress can be generated by using low spindle speed and low radial depth of cut combination during ball-end milling process. This is mainly because the squeeze between the ball-end milling cutter and workpiece was aggra- vated. Conversely, the combination of high spindle speed and large radial depth of cut can bring about residual tensile stress due to the obviously increased cutting temperature. 4. Too small feed per tooth or too small radial depth of cut should be avoided from wear resis- tance point of view during ball-end milling process. This is because though the surface microhardness can be improved, the surface quality will also be deteriorated which is detri- mental to wear resistance. Overall, the combination of relatively high spindle speed, small feed per tooth together with small radial depth of cut can meet the wear resistance and the machining efficiency requirement. 5. Cutting parameters can influence the formation of surface defects, the state of residual stress and the degree of microscopic stress concentration. It is unrealistic to ascertain the best cutting parameter combination to satisfy all requirements at the same time and then improve the fatigue resistance of ball-end milled surface. Taken together, the material removal rate and the fatigue resistance can be obtained by using medium-sized cutting parameter combination. Moreover, the optional range and the maximum value of radial depth of cut decrease with the increase of spindle speed. 6. The proposed optimization scheme from surface integrity, wear resistance and fatigue resis- tance perspective respectively in this study can be used to guide the selection of cutting parameters during ball-end milling of hardened AISI D2 steel for dies/molds manufactur- ing industries. Supporting information S1 Data. (PDF) S1 File. (PDF) Author Contributions Funding acquisition: Weimin Huang. 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Published: Aug 25, 2023

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