Modeling of Cutting Force Distribution on Tool Edge in Turning Process

Procedia Manufacturing Volume 1, 2015, Pages 454–465 43rd Proceedings of the North American Manufacturing Research Institution of SME http://www.sme.org/namrc Modeling of Cutting Force Distribution on Tool Edge in Turning Process Guicai Zhang1 and Changsheng Guo2 1 2 United Technologies Research Center (China), Shanghai, China United Technologies Research Center, East Hartford, CT, USA ZhangG@utrc.utc.com, GuoC@utrc.utc.com Abstract Machining process models can be used to predict cutting force/power and further optimize the process parameters. In this work, a mechanistic cutting force model for turning processes is developed. In order to accurately predict cutting forces, the cutting tool edge is discretized and an approach for calculating the chip load corresponding to each discretized edge segment is developed. Approach for calculating effective tool angles is also developed considering effects of the tool corner radius and the change of feed direction. By using the yield shear stress of the work material, the friction angle between work and tool material, the chip load and the effective tool angles for each tool edge segment, the distributions of the turning forces and force intensity along the tool edge can be predicted. Turning cases of straight turning, contour turning, taper turning and facing are tested and the model outputs include the distributions of the instantaneous effective tool angles, chip load, cutting force coefficients and force intensity. Test results for straight turning and contour turning operations are analyzed to demonstrate the model capability. The distributions of force and force intensity on tool edge provide useful information for prediction of turning forces/power and potential further prediction of tool wear/life. Keywords: Modeling, Cutting force, Turning process 1 Introduction Turning is one of the most widely used processes in manufacturing operations. With the everincreasing applications to precision machining and the machining of difficult-to-machine materials, it is more and more important to model turning process thus to predict cutting forces and to optimize the process parameters. Merchant pioneered the metal cutting mechanics for orthogonal cutting in about 70 years ago (Merchant, 1944). His work laid down a solid foundation for the theoretical modeling of metal cutting thereafter. Most of the fundamental work in early stage was on orthogonal metal cutting (Lee & 2351-9789 © 2015 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the NAMRI Scientific Committee doi:10.1016/j.promfg.2015.09.001 Modeling of Cutting Force Distribution on Tool Edge in Turning Process Zhang and Guo Shaffer, 1951) (Palmer & Oxley, 1959). Results on orthogonal cutting can be easily transformed to that of oblique cutting which is the basis of models for all practical machining processes including turning. In the past twenty years, the modeling of turning processes attracted more and more attention due to the motivation of reduction of machining cost and improving product quality (Chandrasekharan, Kapoor, & DeVor, 1995) (Reddy, DeVor, & Kapoor, 2001) (Song, 2006) (Kaymakci, 2009) (Gencoglu, 2011). In most of the published work, the chip load was divided into several zones and one or more of the zones were discretized (Endres, 1990; Budak, 2007; Altintas, 2012). For the cutting force coefficient models, some researchers used empirical model in which major factors such as rake angle, cutting speed and chip thickness was considered and the coefficients for these factors were determined by cutting experiments (Reddy, DeVor, & Kapoor, 2001). Some others used analytical models incorporating tool rake angle and inclination angle, shear angle, friction angle between the tool and the chip, yield shear stress of the work material, etc. (Altintas, 2012) (Song, 2006) (Kaymakci, 2009). There is no literature available on investigating the distributions of cutting force and force intensity along the tool edge, although this is useful for evaluating or modeling the detailed tool wear status. Major factors affecting cutting forces include tool/work material properties, cutting process parameters (chip load and cutting speed), and tool geometry. Effective tool angles change with the changing of the feed direction and they also change drastically near the tool corner. In precision machining or finishing machining, the depth of cut is small and the tool corner part may take most of the work. It is desirable to model the turning process for predicting the distributions of effective tool angles and the chip load along the tool edge, and thus to accurately predict the cutting forces. In this work, a mechanistic cutting force model for turning processes is developed. In order to accurately predict cutting forces, the cutting tool edge is discretized and an approach for calculating the chip load corresponding to each discretized edge segment is developed. Approach for calculating distributions of the effective tool angles is also developed considering effects of the tool corner radius and the change of feed direction. By using the yield shear stress of the work material, the friction angle between the work and the tool material, the chip load distribution and the effective tool angles for each tool edge segment, the distributions of the cutting forces and force intensity along the tool edge was predicted. Turning cases of straight turning, contour turning, taper turning and facing are tested. The distributions of the effective tool angles and chip load, and the predicted force and force intensity distributions are analyzed. The distributions of force intensity on tool edge provide useful information for prediction of turning forces/power, optimization of cutting parameters and potential prediction of tool wear/life. 2 Turning Model Development The primary purpose of modeling cutting process is to predict cutting forces. With the knowledge of cutting forces, the power consumption, cutting tool properties and metal part quality can be estimated. The cutting process parameters can also be optimized based the prediction of cutting forces. The measured cutting forces should include both the forces due to metal shearing and a tertiary deformation process “ploughing” or “rubbing” at the flank of the cutting edge. It is convenient to express the cutting forces as two parts: metal shear force part and edge force part (Altintas, 2012). Ft K tc bh  K te b ½ ° (1) F f K fc bh  K fe b ¾ ° Fr K rc bh  K re b ¿ where ‫ܨ‬௧ ǡ ‫ܨ‬௙ ǡ ‫ܨ‬௥ are the tangential, feed and radial forces respectively and ‫ܭ‬௧௖ ǡ ‫ܭ‬௙௖ ǡ‫ܭ‬௥௖ are the cutting force coefficients in the three corresponding directions, ‫ܭ‬௧௘ǡ ‫ܭ‬௙௘ ǡ ‫ܭ‬௥௘ are the edge force coefficients in 455 Modeling of Cutting Force Distribution on Tool Edge in Turning Process Zhang and Guo the three directions respectively, and ܾ is the width of cut (edge length) and ݄ is the uncut chip thickness. As the edge force coefficients are purely determined by cutting experiments, the most important part of the cutting process modeling is to model the metal shear force. And the shear force modeling includes two aspects: chip load modeling and the cutting force coefficients modeling. The chip load is determined by the uncut chip thickness and the width of cut (or the feed rate and the depth of cut), the geometry and the orientation of the tool and the workpiece. The modeling the cutting force coefficients is determined by the material properties of the workpiece and the cutting tool, tool geometry, and the cutting speed. The modeling of the chip load and the cutting force coefficients will be discussed in the following sections. 2.1 Chip Load Model The chip load model computes the instantaneous cutting area. The nominal cutting area is determined by the uncut chip thickness and the width of cut (or the feed rate and the depth of cut). The accurate computation of the cutting area is also affected by other factors such as the geometry of the tool and the profile of the workpiece, the varying instantaneous feed direction, etc. The uncut chip thickness is not constant along the tool edge considering the curved tool edge around the tool corner and nonlinear tool path (e.g., contour turning). In order to accurately compute the cutting areas and the chip load distribution along the working tool edge, the tool edge is discretized. Figure 1 shows the approach of the edge discretization. After discretizing the working tool edge, the chip load is divided into a series of subareas with the same dimension in radial direction (݀‫ )ݔ‬of the turning except the last one in the tool corner part (D), while the axial dimensions of the subareas are the same (݀‫ )ݕ‬for the straight edge part (AB) and vary for the tool corner part (BCDE). In this work, the discretization length ݀‫ ݔ‬is 0.001 inch and ݀‫ ݕ‬is related to the feed rate and it changes with the location of the subareas (݀‫ ݕ‬is equal to the feed per revolution for the straight turning). With this discretization level, the simulation time is usually several seconds for one turning step in a regular laptop PC (e.g., DELL Latitude E6430). Edge position 1 Edge position 1 Edge position 2 Edge position 2 (a) Straight (b) General Figure 1: Discretization of the working tool edge The tool approach angle ߰௥ (or the side cutting edge angle ߢ௥ ሻmay change with the location on the tool edge (due to the corner radius) and the changing of the feed direction. In the straight turning shown in Figure 1(a), ߰௥஺ ൏ Ͳat point A and ߰௥஼ ൐ Ͳat point C, while ߰௥஽ ൌ ͻͲιሺߢ௥஽ ൌ Ͳιሻat point D. Figure 1(b) shows a more general case in which the instantaneous feed direction does not parallel to the axial direction of the workpiece. In Figure 1(b) the tool approach angle ߰௥ and the side cutting 456 Modeling of Cutting Force Distribution on Tool Edge in Turning Process Zhang and Guo edge angle ߢ௥ deviate from the nominal values even in the straight edge part (e.g., ߢ௥ீ ). The variation of the tool approach angle, ߰௥, will result in variation of other tool angles such as the edge inclination angle and the normal rake angle, thus result in the change of the cutting forces. 2.2 Shear Force Model For a given chip load, the shearing components of the cutting forces are determined by the cutting force coefficients. The cutting force coefficients for oblique cutting are shown in Equation 2 (Armarego & Uthaichaya, 1977) (Altintas, 2012). They are transformed from orthogonal cutting equations by using the angles transformation shown from Equation 3 to Equation 7. ½ Ws cos( E n  D n )  tan O s ˜ tan K ˜ sin E n ° K tc ˜ sin I n ° cos 2 (I n  E n  D n )  tan 2 K ˜ sin 2 E n ° Ws sin( E n  D n ) (2) ° K fc ˜ ¾ 2 2 2 sin I n ˜ cos O s cos (I n  E n  D n )  tan K ˜ sin E n ° ° cos( E n  D n ) ˜ tan O s  tan K ˜ sin E n Ws ° K rc ˜ sin I n ° cos 2 (I n  E n  D n )  tan 2 K ˜ sin 2 E n ¿ tan Os  tan D p cos\ r  tan D f sin \ r (3) tan D o  tan D p sin \ r  tan D f cos\ r (4) tan D n tan D o cos O s (5) tan E n tan E a cos O s (6) tan K § cos D n · tan Os ¨¨  sin D n ¸¸  I E tan( ) n n © ¹ (7) where ߰௥ is the tool approach angle, ߙ௙ is the side rake angle, ߙ௣ is the back rake angle, ߙ௢ is the orthogonal rake angle,ߙ௡ is the normal rake angle,ߚ௔is the friction angle from material test,ߚ௡ is the normal friction angle,߶௡ is the normal shear angle,ߣ௦ is the inclination angle, ߟ is the chip flow angle and ߬௦ is the yield shear stress of work material. The definitions of the major turning tool angles are shown in Figure 2. Figure 2: Geometry of turning tool 457 Modeling of Cutting Force Distribution on Tool Edge in Turning Process Zhang and Guo 3 Turning Force Model By applying the above chip load model and shear force model to each discretized edge segment, the distributions of the oblique forces are obtained. For different area elements, the directions of the feed force and normal force may be different. They need to be converted to the XYZ directions in turning operations. For the ݅ ௧௛ discretized edge segment we have the following equations (Equation 8). dFxi dFtci dF yi dF fci ˜ sin \ ri  dFrci cos\ ri dFzi dF fci ˜ cos\ ri  dFrci sin \ ri (8) where ݀‫ܨ‬௫௜ ǡ ݀‫ܨ‬௬௜ ǡ ݀‫ܨ‬௭௜ are the force elements in the tangential, radial and axial (feed) directions in the lathe respectively, and ݀‫ܨ‬௧௖௜ ǡ ݀‫ܨ‬௙௖௜ ǡ ݀‫ܨ‬௥௖௜ are the tangential, feed and normal force elements in the oblique cutting respectively, ߰௥௜ is the tool approach angle corresponding to the ݅ ௧௛ edge segment. The total tangential force, radial force and axial force can be obtained by summing the force elements in the same direction. 4 Case Studies and Results Analysis A comprehensive turning case including straight turning, contour turning, taper turning and facing operations are tested using the developed model. The tested case includes seven turning steps: 1) straight turning; 2) contour turning; 3) straight turning; 4) facing; 5) taper turning; 6) straight turning; 7) facing. A diamond tool inset with a corner radius of 1.524 mm (0.06 inch) is used. The tool tip angle is ͸Ͳι and the nominal approach angle is െͳͷι. The workpiece material is AISI-1045 steel with shearing stress of 693.4 MPa and the friction angle is 31.6° (Altintas, 2012). The tool insert and the workpiece before and after the seven turning steps are shown in Figure 3. The engagement profiles between the tool and the workpiece for all the seven steps are shown in Figure 4. For the entire turning process, the model identifies the instantaneous cutting area first using the information of the adjacent tool positions in each work revolution first, then computes and outputs the distributions of the effective tool angles, the cutting parameters, the chip load and the cutting force coefficients (i.e., the specific cutting forces) along the tool edge. In the following sections, the results for the two representative steps (straight turning and contour turning) will be analyzed to illustrate the model capability. (a) Before (b) After Figure 3: Orientation between the tool and the workpiece before and after turning 458 Figure 4: Tool-workpiece engagement profiles for all the seven steps Modeling of Cutting Force Distribution on Tool Edge in Turning Process Zhang and Guo 4.1 Case 1: Straight Turning Figure 5 shows the distributions of the tool approach angle, inclination angle, chip flow angle, normal rake angle, normal friction angle and the normal shear angle for the straight turning step (Step 1). In the figure, line segments AB and BC correspond to the straight edge and the tool corner part respectively. The turning point B is the tangential point between the straight edge and the tool corner. It is shown that for the straight turning operation, these angles are constant in the straight edge part, while they vary within the tool corner area. The normal friction angle and the normal shear angle have a similar trend as the normal rake angle. For the straight turning, the distributions of the tool angles for all workpiece revolutions are coincident. C B A C B A (a) Approach angle B (b) Inclination angle A B A C C (c) Chip flow angle B (d) Normal rake angle B A C A C (e) Normal friction angle (f) Normal shear angle Figure 5: Tool angle distributions for straight turning Figure 6 shows the distributions of the uncut chip thickness for all the revolutions in the first step (straight turning with sixty revolutions in total). The engaging length of the tool edge increases with 459 Modeling of Cutting Force Distribution on Tool Edge in Turning Process Zhang and Guo time for the first ten revolutions, such that the distributions of the uncut chip thickness are also changing correspondingly. From the tenth to the fifty-ninth revolution the thickness distributions are coincident. While the chip thickness for the last revolution (the sixtieth) is significantly smaller than that of the other revolutions as the feed amount is smaller than the nominal values when the tool reaches the end of the tool path. Figure 7 shows the distributions of the cutting areas for all the revolutions in the first step. From the tenth revolution (Rev 10-59), the area distributions become constant (even). For the revolutions 1059, the trends of the area distributions are different from that of the distributions of uncut chip thickness shown in Figure 6 as the area distribution is constant while the thickness is varying in the tool corner part. Again, the area distribution for the last revolution (Rev 60) is smaller than that of the other revolutions. Rev 10-59 Rev 10-59 Rev 9 Rev 9 Rev 8 Rev 8 Rev 60 Rev 2 Rev 1 Figure 6: The distributions of the uncut chip thickness for the first step (straight turning) Rev 60 Rev 2 Rev 1 Figure 7: The distributions of the cutting areas (Step 1) As the values of the area distribution depend on the interval of the edge discretization, it makes more sense to normalize the area distribution by using the lengths of the discretized edge segments. The normalized area distributions are shown in Figure 8. And the corresponding length distributions of the discretized edge segments of selected revolutions (Rev 5, 7, 9 and 11) are shown in Figure 9. It is seen that the lengths of the discretized edge segments are not constant along the tool edge, as the edge discretization is not in the tangential direction of the edge (it is perpendicular to the feed direction). From the Section 2, the cutting forces contributed by the metal shear action are determined by the chip load and the cutting coefficients (Equation 1). Figure 10 shows distributions of the tangential cutting force coefficients of the first step (straight turning). It is seen that for straight turning operation, the tangential cutting coefficients for all the revolutions are coincided. It is also seen that for the majority of the tool corner part, the tangential cutting coefficients are smaller than that of the straight edge part. This is due to that the effective normal rake angle at the most part of the corner is larger than that of the straight edge part. Figure 11 shows the distributions of the tangential cutting force for all the revolutions in Step 1. The trend of the tangential force is similar to that of the tangential cutting coefficients after the tenth revolution (Rev 10 – Rev 60). Also, as the discretized cutting force distributions depend on the interval of the discretization, it is necessary to normalize it with discretized edge length to obtain the force intensity similar to the normalization of the cutting areas. Force intensity reflects the load on unit edge length of the cutting tool. Figure 12 shows the distributions of the tangential force intensity. The trends of the force intensity distributions are similar to that of the distributions of the normalized cutting areas shown in Figure 8. 460 Modeling of Cutting Force Distribution on Tool Edge in Turning Process Zhang and Guo Rev 10-59 Rev 9 Rev 8 Rev 60 Rev 2 Rev 1 Figure 8: The distributions of the normalized cutting areas (Step 1) Figure 9: The distribution of the discretized edge length (Step 1) Figure 10: The distributions of the tangential cutting coefficients (Step 1) Rev 10-59 Rev 10-59 Rev 9 Rev 9 Rev 8 Rev 8 Rev 60 Rev 60 Rev 2 Rev 1 Figure 11: The distribution of tangential cutting force (Step 1) Rev 2 Rev 1 Figure 12: The distribution of the tangential force intensity (Step 1) 4.2 Case 2: Contour Turning In contour turning, the effective tool angles are affected by not only the tool edge profile but also the changing of the feed direction. Figure 13 shows the distributions of the major tool angles for the contour turning (Step 2). There are thirteen revolutions in total for the whole second step. In order to depict the curves clearer, only data for odd revolutions are shown in the figures. It is shown that for the contour turning operation, these angles are constant in the straight edge part at a time instance but they change with time due to the nonlinear direction of the feed motion. For the tool corner part, the 461 Modeling of Cutting Force Distribution on Tool Edge in Turning Process Zhang and Guo effective tool angles change with both the feed direction and the positions on the tool corner (due to the change of the side cutting edge angle). The length of the engaging tool edge changes (decreases for this specific case) with time during the whole contour turning step due to the change of the feed direction, as shown in Figure 14. (a) Approach angle (b) Inclination angle (c) Chip flow angle (d) Normal rake angle (e) Normal friction angle (f) Normal shear angle Figure 13: Tool angle distributions for contour turning (Step 2) Figure 15 shows the distributions of the uncut chip thickness for the odd revolutions in the second step (contour turning). It is seen that the distributions of the uncut chip thickness are different f or different revolutions due to the changing of the feed direction. Similar to that of the straight turning case, the thickness of the last revolution (Rev 13) is significantly smaller than that of other revolutions as the tool reaches the end of the tool path in this step. Similar trend will be seen in the plots for cutting 462 Modeling of Cutting Force Distribution on Tool Edge in Turning Process Zhang and Guo areas and forces shown in the following paragraphs. As some lines are too close to be distinguished, zoomed-in plots are added in some of the following figures. Figure 16 shows the distributions of the cutting areas for the odd revolutions in the Step 2. As the engaging length of the tool edge is changing from revolution to revolution for the whole contour turning step, the area distributions are also changing along the tool path. The normalized area distributions are shown in Figure 17. It is seen that the uncut chip thickness and cutting areas for the last revolution of the step are significantly smaller than that of other revolutions. Figure 18 shows the length distributions of the discretized edge segments used for normalizing the cutting areas (only a few selected revolutions, namely Rev 1, 5, 9, 13, are shown). L as t revolution F irs t revolution Figure 14: The working part of the tool edge changes with time in contour turning Figure 15: The distributions of the uncut chip thickness (Step 2) Figure 16: The distributions of the cutting areas (Step 2) Figure 17: The distributions of the normalized cutting areas (Step 2) Figure 18: The normalized distributions the discretized edge length (Step 2) 463 Modeling of Cutting Force Distribution on Tool Edge in Turning Process Zhang and Guo Figure 19 shows the distributions of the tangential cutting coefficients of the odd revolutions in the second step. It is seen that the trend of the tangential coefficients is changing from the first to the last revolution. The varying trend is due to the changing of the feed direction. The trend of the cutting coefficients for the last revolution is close to that of the straight turning shown in Figure 10, as the feed direction of the last revolution in contour turning is close to that of the straight turning. Figure 20 and Figure 21 show the distributions of the tangential cutting force and the force intensity for Step 2. Again only the odd revolutions are shown for simplicity. The trend of the tangential force for the last revolution (Rev 13) is similar to that of the straight turning shown in Figure 11. And the trends of the force intensity are similar to that of the normalized cutting areas. Figure 19: The distributions of the tangential cutting force coefficients (Step 2) Figure 20: The distributions of the tangential cutting force (Step 2) Figure 21: The distributions of the tangential force intensity (Step 2) In this section, modeling results for two typical turning operations (straight turning and contour turning) are analyzed to demonstrate the model capability. The shear forces are determined by the chip load and cutting coefficients. And the cutting force coefficients are determined by the tool angles and the material properties. As the major outputs, the distributions of the tool angles, uncut chip thickness, chip load, and the cutting coefficients are analyzed. The distributions of the tangential force and force intensity along the tool edge will be useful for tool wear/life evaluation and analysis. 5 Conclusions In this work, a mechanistic cutting force model for turning processes is developed. The model identifies the cutting area distribution, and computes the instantaneous effective tool angles, cutting 464 Modeling of Cutting Force Distribution on Tool Edge in Turning Process Zhang and Guo parameters, cutting forces, force intensity and their distributions. The distribution of the force intensity along the tool edge is a very important parameter as it reflects the force load variation and load time history on the tool edge. 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