Tool Orientation Optimization Based on Spatial Tractrix Method for Five-Axis CNC Machining with Ball End Cutters

Abstract

When milling part surfaces with a ball-end tool in 5-axis CNC machining, maintaining a constant cutting speed by keeping a fixed inclination angle between the tool axis and surface normal is crucial to ensure safe operation and achieve high quality of the machined surface. Under this constraint, the variation of tool orientation is expected to be “smoothest possible” to reduce the angular speed of the rotary axes for the efficient and robust machining. To address this issue, the spatial tractrix which is the extension of classic tractrix is presented to establish the geometry model of the tool orientation kinematics in the part coordinate system. The proposed model describes the relations between the tilt angle and the variation of ball-end tool orientation. Two spatial tractrix-based methods, synchronizing tractrix-based method and equilibrating tractrix-based method, are developed to minimize the variation of tool orientation by controlling the variation of tilt angle. These methods are used to plan the tool orientation on a part surface modeled by a bicubic spline surface. The performance evaluation carried by intense simulations demonstrates the equilibrating tractrix-based method provide the best results in most cases compared with the existing differential geometry-based methods such as the tractrix-based method and parallel transport method. The synchronizing tractrix-based method works well in some special cases.

Keywords

Five-axis machining / Ball-end tool orientation / Spatial tractrix / Tool orientation optimization

References

[1] Bi QZ, Wang YH, Ding H. A GPU-based algorithm for generating collision-free and orientation smooth five-axis finishing tool paths of a ball-end cutter. Int. J. Prod. Res.. 2010, 48 4 1105-1124

[2] Can A, Ali N. A novel iso-scallop tool-path generation for efficient five-axis machining of free-form surfaces. Int. J. Adv. Manuf. Tech.. 2010, 51 9 1083-1098

[3] Farouki RT, Li SQ. Optimal tool orientation control for 5-axis CNC milling with ball-end cutters. Comput. Aided Geom. Des.. 2013, 30 2 226-239

[4] Farouki RT, Han CY, Li SQ. Inverse kinematics for optimal tool orientation control in 5-axis CNC machining. Comput. Aided Geom. Des.. 2014, 31 1 13-26

[5] Gao S, Zhou H, Hu P . A general framework of workpiece setup optimization for the five-axis machining. Int. J. Mach. Tool. Manu.. 2020, 149 103508

[6] Han CY. Tractrix-based tool orientation control for 5-axis CNC machining. Appl. Math. Comput.. 2016, 272 P1 92-99

[7] Hu PC, Tang K. Improving the dynamics of five-axis machining through optimization of workpiece setup and tool orientations. Comput. Aided. Des.. 2011, 43 1693-1706

[8] Huang KT, Zhang ZY, Gong H . Constructing smooth tool orientation field based on radial basis function for 5-axis machining. Int. J. Adv. Manuf. Technol.. 2017, 91 1369-1379

[9] Huang T, Zhang XM, Leopold J . Tool orientation planning in milling with process dynamic constraints: a minimax optimization approach. J. Manuf. Sci. E-T Asme.. 2018, 140 22 111002

[10] Kang H, Li X. A new method to design cubic pythagorean-hodograph spline curves with control polygon. Commun. Math. Stat.. 2019, 7 363-381

[11] Lagarias JC, Reeds JA, Wright MH . Convergence properties of the nelder-mead simplex method in low dimensions. SIAM J. Optim.. 1998, 9 1 112-147

[12] Li M, Dong S, Li D. Tool orientation planning method based on divided surface. Mach. Des. Manuf.. 2017, 174 878-884

[13] Liang F, Kang C, Fang F. A smooth tool path planning method on NURBS surface based on the shortest boundary geodesic map. J. Manuf. Process. 2020, 58 646-658

[14] Lu YA, Wang CY, Sui JB . Smoothing rotary axes movements for ball-end milling based on the gradient-based differential evolution method. J. Manuf. Sci. E-T Asme.. 2018, 140 1-10

[15] Mi ZP, Yuan CM, Ma XH . Tool orientation optimization for 5-axis machining with C-space method. Int. J. Adv. Manuf. Technol.. 2017, 88 5–8 1243-1255

[16] Morishige K, Kase K, Takeuchi Y. Collision-free tool path generation using 2-dimensional C-space for five-axis control machining. Int. J. Adv. Manuf. Tech.. 1997, 13 6 393-400

[17] Plakhotnik D, Lauwers B. Graph-Based optimization of five-axis machine tool movements by varying tool orientation. Int. J. Adv. Manuf. Technol.. 2014, 74 1–4 307-318

[18] Sang Y, Yao C, Lv Y . An improved feedrate scheduling method for NURBS interpolation in five-axis machining. Precis. Eng.. 2020, 64 70-90

[19] She CH, Chang CC. Design of a generic five-axis postprocessor based on generalized kinematics model of machine tool. Int. J. Mach. Tool. Manu.. 2007, 47 3–4 537-545

[20] Tang DT. Algorithms for collision detection and avoidance for five-axis NC machining: a state of the art review. Comput. Aided. Des.. 2014, 51 1-17

[21] Tunc LT. Smart tool path generation for 5-axis ball-end milling of sculptured surfaces using process models. Robot. Cim-Int Manuf.. 2019, 56 212-221

[22] Uwitije R, Wang X, Aqrariyah A, Deng J. Nonlinear weighted average and blossoming. Commun. Math. Stat.. 2020, 8 361-378

[23] Wang Y, Xu J, Sun Y. Tool orientation adjustment for improving the kinematics performance of 5-axis ball-end machining via CPM method. Robot. Cim-Int Manuf.. 2021, 68 4 1105-1124

[24] Wan M, Liu Y, Xing WJ . Singularity avoidance for five-axis machine tools through introducing geometrical constraints. Int. J. Mach. Tool. Manu.. 2018, 127 1-13

[25] Xian Y, Duan FY, Zhu KP . Tool orientation optimization considering cutter deflection error caused by cutting force for multi-axis sculptured surface milling. Int. J. Adv. Manuf. Tech.. 2019, 103 5–8 1925-1934

[26] Xu RF, Cheng X, Zheng GM . A tool orientation smoothing method based on machine rotary axes for five-axis machining with ball end cutters. Int. J. Adv. Manuf. Technol.. 2017, 92 3615-3625

[27] Xu JT, Zhang DY, Sun YW. Kinematics performance oriented smoothing method to plan tool orientations for 5-axis ball-end CNC machining. Int. J. Mech. Sci.. 2019, 157–158 293-303

[28] Zhang X, Zhang J, Zheng X . Tool orientation optimization of 5-axis ball-end milling based on an accurate cutter/work-piece engagement model. CIRP J. Manuf. Sci. Technol.. 2017, 19 106-116

[29] Zou X, Tam HY, Xu HY . Flat-end tool orientation based on rotation-minimizing frame. Adv. Manuf.. 2019, 7 3 257-269

Funding

National Natural Science Foundation of China(51975231)