Finite element simulation of stresses in cutting tools during tapping

Tapping is inherently more complex than other machining processes. The main reason for this complexity is that the chip removal process takes place in a closed environment. For this reason, in order to use the tap tools more efficiently, it is necessary to know the cutting conditions and the stresses that occur in the tool during cutting. In this study, holes of different diameters were drilled in the AISI 1050 material and threaded with M10 taps with three different geometries. Uncoated HSS and TiN coated HSS taps were used in the study. The tapping operations were carried out in dry conditions. The simulation conditions were chosen exactly the same as the experimental conditions. Stresses during tapping were analyzed using the Third Wave AdvantEdge program based on the finite element method (FEM). The tapping tools were modeled by reverse engineering method and then imported in the program. In general, the coating applied to the tools positively affected the stresses on the cutting tool.


Introduction
Cutting tool costs constitute a significant part of the machining cost. In addition, it is not possible to achieve the desired dimensional accuracy and surface quality in cutting processes that are not made under ideal cutting conditions. Therefore, it is a must to determine the appropriate tool and ideal cutting conditions for the workpiece quality and production costs in machining. Choosing cutting tools is very important along with ideal cutting conditions. Inappropriate tool geometry may cause tool wear, damage or even breakage during cutting. To prevent such undesirable situations and to choose the appropriate tool geometry, it has become important to determine the cutting forces and stresses that occur during cutting. For this reason, studies on determining the cutting forces and stresses that occur during drilling operations are quite common in the literature. Although these studies are common, studies on the determination of stresses occurring in tapping are very few. Studies on tapping have been carried out mostly experimentally.
Monka et al. investigated tapping errors in tapping process. They tried to determine the effect of cutting parameters and tool geometry on tool wear. They observed that the torque increased when the drill hole diameter was drilled smaller than the thread diameter. 1 Uzun and Korkut 2 tapped AISI 304 stainless steel at four different cutting speeds and four different depths of cut. They examined the torque and forces that occur during tapping. They concluded that the chips adhering to the cutting tool cutting edge and the depth of cut in the screw cutting process affect the tool life. Kayır 3 investigated the effect of hole diameter on cutting forces and torque in tapping machining. In the study, he tapped the AA5083 material with TiN coated and uncoated HSS machine taps. The study concluded that increasing hole diameters reduce cutting forces and torque. Kayır 4 investigated the effect of drill diameter on tapping of AISI 1050 steel with tapping tools. He concluded that the drill diameter reduces the torque and cutting forces that occur during the tapping process. Gu¨nay, 5 investigated the effects of infeed angles on thread quality in his study. He performed thread cutting on CNC lathe at 0°, 14.5°, 15°, 27.5°, and 30°infeed angles with single point cutters at constant cutting speed. In the analysis according to the experimental results and the machined surface, he concluded that the optimum infeed angle for external threading is 30°. Fernandes et al. 6 aimed to analyze the wear mechanisms acting on High Speed Steels -HSS-E, Diamond Like Carbon -DLC coated tools during tapping of AA6351 T6 aluminum alloy. They used a thread cutting tap with four helical flutes, diameter 12 mm, and 1.5 mm thread pitch. They concluded that the entry teeth of the cutting tap showed aluminum stickiness, plastic deformations, and more pronounced side wear. Pereira et al. 7 in their study evaluated the torque behavior for tapping as a function of the number of threads, the tool manufacturer, and the angle of the tool taper region of tool. Experimental tests were carried out using M10x1.5 taps and cutting speeds of 10 and 25 m/min. They concluded that there is a difference in torque distribution along the threads of the tapered part between the taps. Bhowmick et al. 8 investigated the effects of cooling method on tapping Al-6.5%Si alloy. They reached that in dry tapping performed with HSS DLC coated tapping, edge formation is prevented thanks to the low coefficient of friction. Along with experimental studies, the number of studies in which various analysis and modeling methods are used has started to increase. Tanaka et al. 9 have proposed a method for measuring tool edge temperature during tapping. The infrared ray from the edge of the tap was measured using a twocolor pyrometer with an optical fiber. They used AISI 1045 based free machining steel, AISI 303 and AISI 304 stainless steel as workpiece material. They found that the cutting temperature of AISI 303 was approximately 100°C lower than that of AISI 304. Oezkaya and Biermann 10 developed an automated software module geometric torque prediction method (GTPM) to determine the torque generated in different tapping tools. They used AISI 1045 and AISI 304 as workpiece material. In M3, M6, M8, and M10 taps, the feed rates were determined as 0.5, 1, 1.25, and 1.5 mm, respectively. Experimental tests were performed to validate the simulation results. In the GPTM method they developed, they estimated the torque values that will occur in M12, M14, M16 and M18 taps with the results they obtained from these four taps. Araujo and Fromentin 11 machined two biomaterials with the milling method and drilled M2 internal threads into the mini-holes. The geometrical analysis of the thread milling process and the mechanical modeling of the cutting force associated with the experiments were created. In his experiments, Ti6Al4V titanium alloy workpiece and water-based emulsified Cr-Co alloy Ramor 400 were used. They stated that the average forces occurring at different feed rates of both materials analyzed did not differ much. Yıldız et al. 12 performed the finite element simulation of the drilling process and the theoretical analysis of the drilling stresses with Deform 3D program. They concluded that most of the simulated results were within 65% of the test results. Oezkaya and Biermann 13 developed a mathematical model for 3D FEM tapping simulation to predict the relative torque before tool manufacturing. They reached that the computation time could be reduced by approximately 97% compared to a normal 3D tapping simulation along the entire chamfer length. Warrington et al. 14 used FEM for tap design improvement in form tapping. The effects of various tap design parameters and tapping conditions on the formation of split crests were investigated to arrive at an optimal tap design. They concluded that cryogenically treated tools performed better. Chede et al. 15 compared the performance of conventional tools and cryogenically treated tools. They tapped holes drilled with an M2 HSS drill. M3 TiN coated tapping tools were used in the experiments. They investigated the effects of cutting speed and feed rate on tool life. Wu et al. 16 performed optimization of tool geometric parameters for a small fluteless forming tap (FFT). They used DEFORM-3D (finite element model) and MINITAB (regression analysis) in the study. A 5 mm thick 7075-T6 aluminum alloy was chosen as the test material. With the ANOVA results, they concluded that the coefficients of determination (R 2 ) for f1 and T1 were 97.0% and 90.6%. Ren and Yan, 17 tapping simulation has been realized to reduce the radial pitch diameter difference of the threads. In the study, they developed a quasi-static model to estimate the radial pitch diameter difference in tapping and simulated the radial pitch diameter difference at different chamfer lengths and spindle speeds through this model. Together with the simulation results, they concluded that the chamfer length and spindle speed have an effect on the radial pitch diameter difference. Barooah et al. 18 investigated the wear mechanism in tapping Al-Si alloy. Ten different PVD coated tapping tools were used in the study. In the progressive wear tests, they concluded that the average torque increases with the increase in the number of tapped holes for all taps, and the average torque of the TiAlN-coated tap is lower than that of the ZrNcoated tap. Dogrusadik et al. 19 carried out optimization of the tool design parameters for thread tapping process of Ti-6Al-4V. They selected the most effective tool design parameters on the process as rake angle, helical flute angle, chamfer angle, and tool coating. Taguchi L8 orthogonal array was used as the experimental design. They found optimized tool design parameters as 6°rake angle, 12°helical flute angle, 14°chamfer angle and TiCN coating.
In addition to these studies, studies such as highaccuracy classification of thread quality in tapping processes, 20 fatigue analysis of threaded connections using the local strain approach, 21 and use of the coolant 22 are available in the literature. In addition, finite element analysis and cutting zone temperatures are also among the subjects investigated. [23][24][25] When the studies in the literature are evaluated in general, it is seen that the finite element method is used in both hole drilling and tapping operations. However, there are not many studies examining the stresses that occur in the tapping cutting tools during the tapping process. In this study, the stresses during tapping were analyzed using the Third Wave AdvantEdge program based on the FEM.

Material method
Test specimens were drilled with diameters of 8.3, 8.4, 8.5, and 8.6 mm and tapped with an M10x1.5 machine tap. The hole diameters must be of a certain value for the dimensions of the screws to be drilled. For standard metric screws in the manufacturing industry, the screw pitch is subtracted from the major diameter to practically find the drill diameter. In theoretical calculations, the screw pitch is multiplied by 1.0825 and this value is subtracted from the major diameter to find the drill diameter. Using this formula, drill diameter = 102(1.0825 3 1.5) = 8.376 for M10 screw. The recommended drill diameter for the M10 tap is between 8678 and 8376 mm. 3,4 In the experiments, the hole diameters were taken between the recommended minimum and maximum values, and 4 different drill diameters with 0.1 mm increments between 8.3 and 8.6 were used for this. HSS and TiN coated HSS, were used in the analysis. In the analysis, the first tap was coded as A303, the second as A320 and the third as A330. A303 coded tap is straight flute. The helix angle of the A320 code tap is 15°and the helix angle of the A330 code tap is 30°.
A three-dimensional (3D) laser scanner was used to model the tapping tools and point clouds of taps were generated. Point clouds data transferred to Geomagic Design X software has been converted to STL format. Then, STL format was transferred to Catia program and 3D models of point clouds of taps were obtained. 26 3D images of the tapping tools created with point clouds are given in Figure 1.
Third Wave AdvantEdge is a widely used software for improving manufacturing processes, especially in the aerospace industry. By examining similar studies in the literature, 12,27,28 the maximum element size of 0.2 mm and the minimum element size of 0.012 mm were selected for mesh formation. To determine how many turns the tap will be rotated after the meshing, three simulations were run and a rotation of 1080°w as given to the tap in such a way that the screw with a length of three steps was opened. The simulation process performed in this way took 36 days, approximately 12 days for each. Three trial simulations were performed by rotating the tapping tools 60°. This process took 6 days in total. An acceptable variation of 1.5%-3.5% was observed in the data obtained by rotating the tap 60°and 1080°. For this reason, the rotation movement of the tap is chosen as 60°in the simulations within the scope of the study (the tap rotates 60°). To control the reliability of the maximum and minimum element size selected by considering the meshing in the literature, 12 trial simulations were run. These simulations were performed with uncoated HSS and TiN coated HSS for 8.3 and 8.6 mm hole diameters (the highest thrust forces and torques were obtained for a hole diameter of 8.3 mm, while the lowest values were obtained for a hole diameter of 8.6 mm). Each simulation took an average of 2 days. Then, the maximum and minimum element size values were changed, and 12 more simulations were made by taking the maximum element size of 0.1 mm and the minimum element size of 0.005 mm. The simulation results with the specified parameters were compared, and it was determined that the results did not change significantly, but the solution time was extended by an average of 18 h for each simulation. As a result of this situation, the maximum element size of 0.2 mm and the minimum element size of 0.012 mm were selected as meshing parameters in terms of optimum time utilization. The workpiece dimensions are determined as 15 3 8 3 15 mm so that all the teeth of the tap are in full contact with the workpiece. The speed was chosen as 318 rpm and the starting temperature was 20°C. A series of iterative experiments were performed to determine the Johnson-Cook material model parameters for AISI 1050. As a result of the simulations made by trialand-error, it was found that as the thermal softening value m decreases, the thrust force decreases, and the C value affects the torque values. As a result of trial-and-error simulations, the model parameters in Table 1 were determined and these parameters were used in the study. In this study, the coefficient of friction is 0.5 and the heat transfer coefficient of the refrigerant is 10,000 W/m 2 K and the cooling temperature is 20°C to simulate the effect of the coolant. These parameters are the values that the AdvantEdge program provides to the user to keep the operating environment temperature constant at room temperature.
Playing the simulation and viewing the simulation results were obtained through the Tecplot interface integrated with AdvantEdge software.
During the cutting operation, it was investigated in which regions the maximum and minimum principal stresses and equivalent (von Mises) stress occurred in the tapping tools.

Results and discussion
The stresses occurring in the cutting tool can be monitored step-by-step during the entire simulation period from the first time the simulation starts to the end. In Figure 2, stresses generated on the TiN coated A330 coded tap for 8.3 mm hole diameter simulation taken from a 4 s simulation video, a few frames of film for an example illustration given as. The stress distributions at each cutting edge are repeated cyclically. Figure 3 gives the values of s 1 , s 3 , and s e for uncoated HSS taps. In general, it is seen that the highest values for s 1 occur with a hole diameter of 8.3 mm. Stress values of 7842 MPa for A303 coded tap, 2344 MPa for A320 coded tap and 4193 MPa for A330 coded tap were obtained with 8.3 mm hole diameter. This can be attributed to the increasing chip volume as the hole diameter gets smaller. It is seen that as the hole diameter increases, the stress values decrease depending on the decrease in the chip volume. The lowest values for s 1 are 2982 MPa when machining a hole diameter of 8.4 mm for A303 coded tap, and 554 and 1173 MPa when machining a hole diameter of 8.6 mm for taps coded A320 and A330, respectively.
Looking at the graph (Figure 3), the highest values for s 3 are 6989 MPa when machining a hole diameter of 8.5 mm for A303 coded tap. In taps coded A320 and A330, the s 3 stresses are 6224 and 7094 MPa, respectively, when machining a hole diameter of 8.3 mm. The highest compressive stresses occurred at different hole diameters compared to the tensile stresses. Depending on the drill diameters, the increasing chip volume causes an increase in the stresses. Studies in the literature also support this result. 29 When the equivalent stresses (von Mises stress, s e ) were examined, the highest value for s e was 8640 MPa when machining a hole diameter of 8.5 mm for the A303 coded tap. In taps coded A320 and A330, the s e stresses are 5878 and 6098 MPa, respectively, when machining a hole diameter of 8.3 mm.
The stresses occurring in the TiN coated tools are given in Figure 4. The highest values for s 1 occurred as 4151 MPa with a hole diameter of 8.5 mm for the A303 coded tap, and 1779 and 1046 MPa when machining a hole diameter of 8.4 mm for taps coded A320 and A330, respectively.
The highest values for s 3 occurred as 4333 and 2642 MPa, respectively, for taps coded A303 and A330 when machining a hole diameter of 8.6 mm. It is 5104 MPa with 8.3 mm hole diameter for tap coded A320.
The highest value for s e is 5092 MPa when machining a hole diameter of 8.4 mm for the A303 coded tap. In taps coded A320 and A330, the highest s e stresses are 3706 and 2342 MPa, respectively. These are values when machining a hole diameter of 8.3 and 8.6 mm, respectively.
It is seen from Figures 3 and 4 that the highest stress values for A303, A320, and A330 coded taps occur at different diameters. Although this is expected, it can be attributed to partial degeneration in the mesh structure while running the simulation. It is also considered as the fact that the tool does not absorb any energy because of determining it as rigid. 10,[30][31][32] While running simulatingre using FEM, that is, during the chip formation process, degeneration of elements can occur due to the continuous resizing and shaping of the elements, which is very common. This degeneration in the mesh structure causes a sudden/instantaneous increase or decrease in the values of force and torque generated during the simulation and, indirectly, the stress. Figure 5 shows distributions of the maximum principal stress s 1 that occur on uncoated HSS taps when machining a hole diameter of 8.3 mm with taps coded A303, A320, and A330. Stress value of 7842 MPa for A303 coded tap occurred at the cutting edge just above the first cutting thread. It was 2344 MPa at the cutting edge of the second cutting thread for the A320 coded tap and 4193 MPa at the third and fourth full thread for the A330 coded tap. Figure 6 shows distributions of the minimum principal stress s 3 that occur on uncoated HSS taps. The highest s 3 for A303 coded tap when machining a hole diameter of 8.5 mm is 6989 MPa in the middle of the second thread and the first full thread, close to the bottom of the thread. The highest s 3 values were obtained when machining a hole diameter of 8.3 mm in the taps coded A320 and A330. The highest s 3 for A320 coded tap is on the cutting edge of the first and second flute thread and the cutting edge of the first full thread. In the A330 coded tap, it occurred in the third and fourth full thread. The highest s 3 values for taps coded A320 and A330 are 6224 and 7094 MPa, respectively.
Distributions of the equivalent stress s e that occur on uncoated HSS taps are given in Figure 7. The     highest equivalent stress values for all tap types were obtained when machining a hole diameter of 8.3 mm. In the taps coded A303, the highest s e , which was 7402 MPa, was observed between the first flute and the second flute, close to the thread base diameter. It occurred at the cutting edge of the second flute thread for the A320 coded tap (5878 MPa). It was seen at the third and fourth full thread for the A330 coded tap (6098 MPa).
Stress distributions vary depending on the helix angle of the flute in the tap. It has been observed that the cutting edges of the A303 coded tap do not form the full thread depth, and it is forced from the first thread. In the tap coded A320 where the helix angle is 158, the stress was transferred to the second thread. In the tap coded A330 where the helix angle is 30°, the stress occurs at the full thread depth and is carried to the third and fourth teeth. This indicates that the taps with helical flute facilitate the cutting process. This may be due to easier chip breaking and easier chip evacuation in the helical flute. 2,4 Stress distributions on TiN coated HSS taps are given in Figures 8 to 10. It can be seen in Figure 8 that the maximum principal stress (s 1 ) in the A303 coded tap, which is 4151 MPa, is formed at the diameter of the thread base where the second flute tooth and the first full thread meet. It occurred at the thread base diameter where the fourth and fifth full threads meet while machining a hole diameter of 8.4 mm on tap coded A320 (1779 MPa). It occurred on the cutting edge of the third full thread while machining a hole diameter of 8.4 mm in tap coded A330 (1046 MPa).
When the minimum principal stresses (s 3 ) in Figure 9 are examined, the stress (4333 MPa) in the tap coded A303 occurred at the cutting edge of the second flute thread. In tap coded A320 (5104 MPa), it occurred at the cutting edge of the second full thread. In tap coded A330 (2642 MPa), it appears on the entire cutting edge of the fourth full thread and in specific areas on the cutting edge of the second, third, and fifth full thread.
When the equivalent stresses (s e ) in Figure 10 are examined, the highest se stress in A303 coded tap occurs at the top of the cutting edge of the first flute thread (5092 MPa). In the tap coded A320, it is at the cutting edge of the first full thread (3706 MPa).
It has been determined that the stress distributions on TiN coated HSS taps move toward the upper thread compared to uncoated HSS taps. In other words, the coating facilitated the cutting process by reducing the friction on the cutting tool rake surface during cutting, and thus the smaller stresses occurred. 33

Conclusions
Interactions between cutting forces and cutting tools are of great importance in terms of cutting tool wear or breakage. For this reason, the stresses occurring in the cutting tool should be carefully examined. This becomes more important, especially for operations that take place in a closed environment such as drilling and tapping. For this purpose, the simulation and analysis of tapping on AISI 1050 steel with TiN coated and uncoated HSS taps in three different forms were carried out. After tapping simulation, the stresses on the cutting tool were investigated. It has been determined in which regions the stress distributions, which are important in terms of cutting tool life, occur. The findings of the study and suggestions for future studies are as follows: The highest stresses occurring in cutting tools were reached with uncoated tools.  Smaller stresses occur in helical flute taps compared to straight flute taps. The highest tensile and compressive stresses, which are the maximum and minimum principal stresses, respectively, occurred as 7842 and 7094 MPa in the uncoated HSS taps coded A303 and A330. The highest equivalent stress was 7402 MPa in the uncoated HSS taps coded A303. Using AdvantEdge software, researchers can in the future examine parameters such as cutting zone temperature, cutting forces and tool stresses for different tools in different operations. In this study, stresses occurring in cutting tools during tapping through length were determined. In the future, tool stresses can be investigated for a more difficult tapping blind hole. In the following stages, the tool wear can be determined in experimental studies and a connection can be made with the stresses obtained as a result of the simulation. Optimum values for cutting parameters can be estimated by using the parameters used in the experiments in simulation programs using the finite element method. However, costly experimental research is avoided.