[1] 孙玉文, 徐金亭, 任斐,等. 复杂曲面高性能多轴精密加工技术与方法[M]. 北京:科学出版社, 2014:1-7. SUN Y W, XU J T, REN F, et al. Technologies and methods for high-performance multi-axis precision machining of complex surfaces[M]. Beijing:Science Press, 2014:1-7(in Chinese).
[2] 郭东明, 孙玉文, 贾振元. 高性能精密制造方法及其研究进展[J]. 机械工程学报, 2014, 50(11):119-134. GUO D M, SUN Y W, JIA Z Y. Methods and research progress of high performance manufacturing[J]. Journal of Mechanical Engineering, 2014, 50(11):119-134(in Chinese).
[3] LASEMI A, XUE D Y, GU P H. Recent development in CNC machining of freeform surfaces:A state-of-the-art review[J]. Computer-Aided Design, 2010, 42(7):641-654.
[4] MAKHANOV S S. Adaptable geometric patterns for five-axis machining:A survey[J]. The International Journal of Advanced Manufacturing Technology, 2010, 47(9-12):1167-1208.
[5] TUNC L T. Smart tool path generation for 5-axis ball-end milling of sculptured surfaces using process models[J]. Robotics and Computer-Integrated Manufacturing, 2019, 56:212-221.
[6] 吴宝海, 罗明, 张莹, 等. 自由曲面五轴加工刀具轨迹规划技术的研究进展[J]. 机械工程学报, 2008, 44(10):9-18. WU B H, LUO M, ZHANG Y, et al. Advances in tool path planning techniques for 5-axis machining of sculptured surfaces[J]. Chinese Journal of Mechanical Engineering, 2008, 44(10):9-18(in Chinese).
[7] 樊文刚, 叶佩青. 复杂曲面五轴端铣加工刀具轨迹规划研究进展[J]. 机械工程学报, 2015, 51(15):168-182. FAN W G, YE P Q. Research progress in tool path planning for five-axis end milling machining of sculptured surfaces[J]. Journal of Mechanical Engineering, 2015, 51(15):168-182(in Chinese).
[8] 徐金亭, 刘伟军, 邱晓杰, 等. 自由曲面加工中的等参数螺旋轨迹生成方法[J]. 机械工程学报, 2010, 46(3):148-151, 157. XU J T, LIU W J, QIU X J, et al. Isoparametric and spiral toolpath for free-form surfaces machining[J]. Journal of Mechanical Engineering, 2010, 46(3):148-151, 157(in Chinese).
[9] LONEY G C, OZSOY T M. NC machining of free form surfaces[J]. Computer-Aided Design, 1987, 19(2):85-90.
[10] HE W, LEI M, BIN H Z. Iso-parametric CNC tool path optimization based on adaptive grid generation[J]. The International Journal of Advanced Manufacturing Technology, 2009, 41(5-6):538-548.
[11] ZOU Q, ZHAO J B. Iso-parametric tool-path planning for point clouds[J]. Computer-Aided Design, 2013, 45(11):1459-1468.
[12] SURESH K, YANG D C H. Constant scallop-height machining of free-form surfaces[J]. Journal of Engineering for Industry, 1994, 116(2):253-259.
[13] 徐金亭, 刘伟军, 卞宏友, 等. 基于网格曲面模型的等残留刀位轨迹生成方法[J]. 机械工程学报, 2010, 46(11):193-198. XU J T, LIU W J, BIAN H Y, et al. Constant scallop tool path for triangular surface machining[J]. Journal of Mechanical Engineering, 2010, 46(11):193-198(in Chinese).
[14] BALABOKHIN A, TARBUTTON J. Iso-scallop tool path building algorithm "based on tool performance metric" for generalized cutter and arbitrary milling zones in 3-axis CNC milling of free-form triangular meshed surfaces[J]. Journal of Manufacturing Processes, 2017, 28:565-572.
[15] LIU W, ZHU S M, HUANG T, et al. An efficient iso-scallop tool path generation method for three-axis scattered point cloud machining[J]. The International Journal of Advanced Manufacturing Technology, 2020, 107(7-8):3471-3483.
[16] 孙玉文, 刘伟军, 王越超. 基于三角网格曲面模型的刀位轨迹计算方法[J]. 机械工程学报, 2002, 38(10):50-53. SUN Y W, LIU W J, WANG Y C. Research on the algorithm of nc tool path calculation for triangular surface machining[J]. Chinese Journal of Mechanical Engineering, 2002, 38(10):50-53(in Chinese).
[17] DING S, MANNAN M A, POO A N, et al. Adaptive iso-planar tool path generation for machining of free-form surfaces[J]. Computer-Aided Design, 2003, 35(2):141-153.
[18] SUN Y W, GUO D M, JIA Z Y, et al. B-spline surface reconstruction and direct slicing from point clouds[J]. The International Journal of Advanced Manufacturing Technology, 2006, 27(9-10):918-924.
[19] YANG D C H, CHUANG J J, OULEE T H. Boundary-conformed toolpath generation for trimmed free-form surfaces[J]. Computer-Aided Design, 2003, 35(2):127-139.
[20] ZHANG R, HU P C, TANG K. Five-axis finishing tool path generation for a mesh blade based on linear morphing cone[J]. Journal of Computational Design and Engineering, 2015, 2(4):268-275.
[21] SARKAR S, DEY P P. Tool path generation for algebraically parameterized surface[J]. Journal of Intelligent Manufacturing, 2015, 26(2):415-421.
[22] TAKASUGI K, ASAKAWA N. Parameter-based spiral tool path generation for free-form surface machining[J]. Precision Engineering, 2018, 52:370-379.
[23] AGRAWAL R K, PRATIHAR D K, CHOUDHURY A R. Optimization of CNC isoscallop free form surface machining using a genetic algorithm[J]. International Journal of Machine Tools and Manufacture, 2006, 46(7-8):811-819.
[24] SU C, JIANG X, HUO G Y, et al. Initial tool path selection of the iso-scallop method based on offset similarity analysis for global preferred feed directions matching[J]. The International Journal of Advanced Manufacturing Technology, 2020, 106(7-8):2675-2687.
[25] QUINSAT Y, SABOURIN L. Optimal selection of machining direction for three-axis milling of sculptured parts[J]. The International Journal of Advanced Manufacturing Technology, 2007, 33(7-8):684-692.
[26] SUN Y W, GUO D M, JIA Z Y, et al. Iso-parametric tool path generation from triangular meshes for free-form surface machining[J]. The International Journal of Advanced Manufacturing Technology, 2006, 28(7-8):721-726.
[27] XU J T, JIN C N. Boundary-conformed machining for trimmed free-form surfaces based on mesh mapping[J]. International Journal of Computer Integrated Manufacturing, 2013, 26(8):720-730.
[28] SUN Y W, GUO D M, JIA Z Y. Spiral cutting operation strategy for machining of sculptured surfaces by conformal map approach[J]. Journal of Materials Processing Technology, 2006, 180(1-3):74-82.
[29] REN F, SUN Y W, GUO D M. Combined reparameterization-based spiral toolpath generation for five-axis sculptured surface machining[J]. The International Journal of Advanced Manufacturing Technology, 2009, 40(7-8):760-768.
[30] SUN Y W, XU J T, JIN C N, et al. Smooth tool path generation for 5-axis machining of triangular mesh surface with nonzero genus[J]. Computer-Aided Design, 2016, 79:60-74.
[31] XU J T, JI Y K, SUN Y W, et al. Spiral tool path generation method on mesh surfaces guided by radial curves[J]. Journal of Manufacturing Science and Engineering, 2018, 140(7):071016.
[32] XU J T, XU L K, SUN Y W, et al. A method of generating spiral tool path for direct three-axis computer numerical control machining of measured cloud of point[J]. Journal of Computing and Information Science in Engineering, 2019, 19(4):1-19.
[33] XU J T, SUN Y W, ZHANG L. A mapping-based approach to eliminating self-intersection of offset paths on mesh surfaces for CNC machining[J]. Computer-Aided Design, 2015, 62:131-142.
[34] XU J T, SUN Y W, WANG S K. Tool path generation by offsetting curves on polyhedral surfaces based on mesh flattening[J]. The International Journal of Advanced Manufacturing Technology, 2013, 64(9-12):1201-1212.
[35] SUN Y W, REN F, ZHU X H, et al. Contour-parallel offset machining for trimmed surfaces based on conformal mapping with free boundary[J]. The International Journal of Advanced Manufacturing Technology, 2012, 60(1-4):261-271.
[36] XU J T, WANG Y J, ZHANG X K, et al. Contour-parallel tool path generation for three-axis mesh surface machining based on one-step inverse forming[J]. Proceedings of the Institution of Mechanical Engineers, Part B:Journal of Engineering Manufacture, 2013, 227(12):1800-1807.
[37] LI W, YIN Z, HUANG Y, et al. Tool-path generation based on angle-based flattening[J]. Proceedings of the Institution of Mechanical Engineers, Part B:Journal of Engineering Manufacture, 2010, 224(10):1503-1509.
[38] CHIOU C J, LEE Y S. A machining potential field approach to tool path generation for multi-axis sculptured surface machining[J]. Computer-Aided Design, 2002, 34(5):357-371.
[39] KIM T, SARMA S E. Toolpath generation along directions of maximum kinematic performance; a first cut at machine-optimal paths[J]. Computer-Aided Design, 2002, 34(6):453-468.
[40] 孙玉文, 束长林, 刘健. 基于矢量分析的数控加工轨迹设计方法研究[J]. 机械工程学报, 2005, 41(3):160-164, 170. SUN Y W, SHU C L, LIU J. Vector analysis based tool path generation for precision surface machining[J]. Chinese Journal of Mechanical Engineering, 2005, 41(3):160-164, 170(in Chinese).
[41] BARAKCHI FARD M J, FENG H Y. Effective determination of feed direction and tool orientation in five-axis flat-end milling[J]. Journal of Manufacturing Science and Engineering, 2010, 132(6):061011.
[42] MY C A, BOHEZ E L J, MAKHANOV S S, et al. On 5-axis freeform surface machining optimization:Vector field clustering approach[J]. International Journal of CAD/CAM, 2009, 5(1):1-14.
[43] KUMAZAWA G H, FENG H Y, BARAKCHI FARD M J. Preferred feed direction field:A new tool path generation method for efficient sculptured surface machining[J]. Computer-Aided Design, 2015, 67-68:1-12.
[44] LIU X, LI Y G, MA S B, et al. A tool path generation method for freeform surface machining by introducing the tensor property of machining strip width[J]. Computer-Aided Design, 2015, 66:1-13.
[45] ZHANG K, TANG K. An efficient greedy strategy for five-axis tool path generation on dense triangular mesh[J]. The International Journal of Advanced Manufacturing Technology, 2014, 74(9-12):1539-1550.
[46] YE T, XIONG C H, XIONG Y L, et al. Kinematics constrained five-axis tool path planning for high material removal rate[J]. Science China Technological Sciences, 2011, 54(12):3155-3165.
[47] MOODLEAH S, MAKHANOV S S. 5-axis machining using a curvilinear tool path aligned with the direction of the maximum removal rate[J]. The International Journal of Advanced Manufacturing Technology, 2015, 80(1-4):65-90.
[48] LAMIKIZ A, DE LACALLE L N L, SÁNCHEZ J A, et al. Cutting force integration at the CAM stage in the high-speed milling of complex surfaces[J]. International Journal of Computer Integrated Manufacturing, 2005, 18(7):586-600.
[49] MANAV C, BANK H S, LAZOGLU I. Intelligent toolpath selection via multi-criteria optimization in complex sculptured surface milling[J]. Journal of Intelligent Manufacturing, 2013, 24(2):349-355.
[50] HUO G Y, JIANG X, SU C, et al. CNC tool path generation for freeform surface machining based on preferred feed direction field[J]. International Journal of Precision Engineering and Manufacturing, 2019, 20(5):777-790.
[51] XU K, LUO M, TANG K. Machine based energy-saving tool path generation for five-axis end milling of freeform surfaces[J]. Journal of Cleaner Production, 2016, 139:1207-1223.
[52] SUN S X, SUN Y W, XU J T, et al. Iso-planar feed vector-fields-based streamline tool path generation for five-axis compound surface machining with torus-end cutters[J]. Journal of Manufacturing Science and Engineering, 2018, 140(7):071013.
[53] SUN Y W, SUN S X, XU J T, et al. A unified method of generating tool path based on multiple vector fields for CNC machining of compound NURBS surfaces[J]. Computer-Aided Design, 2017, 91:14-26.
[54] TANG T D. Algorithms for collision detection and avoidance for five-axis NC machining:A state of the art review[J]. Computer-Aided Design, 2014, 51:1-17.
[55] LIANG F S, KANG C W, FANG F Z. A review on tool orientation planning in multi-axis machining[J]. International Journal of Production Research, (2020-07-09)[2020-11-26]. https://doi.org/10.1080/00207543.2020.1786187.
[56] RAO A, SARMA R. On local gouging in five-axis sculptured surface machining using flat-end tools[J]. Computer-Aided Design, 2000, 32(7):409-420.
[57] YOON J H, POTTMANN H, LEE Y S. Locally optimal cutting positions for 5-axis sculptured surface machining[J]. Computer-Aided Design, 2003, 35(1):69-81.
[58] WARKENTIN A, ISMAIL F, BEDI S. Multi-point tool positioning strategy for 5-axis mashining of sculptured surfaces[J]. Computer Aided Geometric Design, 2000, 17(1):83-100.
[59] GRAY P J, BEDI S, ISMAIL F. Arc-intersect method for 5-axis tool positioning[J]. Computer-Aided Design, 2005, 37(7):663-674.
[60] GRAY P, BEDI S, ISMAIL F. Rolling ball method for 5-axis surface machining[J]. Computer-Aided Design, 2003, 35(4):347-357.
[61] KIM S J, YANG M Y. Triangular mesh offset for generalized cutter[J]. Computer-Aided Design, 2005, 37(10):999-1014.
[62] CHOI B K, KIM D H, JERARD R B. C-space approach to tool-path generation for Die and mould machining[J]. Computer-Aided Design, 1997, 29(9):657-669.
[63] BALASUBRAMANIAM M, LAXMIPRASAD P, SARMA S, et al. Generating 5-axis NC roughing paths directly from a tessellated representation[J]. Computer-Aided Design, 2000, 32(4):261-277.
[64] LACHARNAY V, LAVERNHE S, TOURNIER C, et al. A physically-based model for global collision avoidance in 5-axis point milling[J]. Computer-Aided Design, 2015, 64:1-8.
[65] BEDI S, GRAVELLE S, CHEN Y H. Principal curvature alignment technique for machining complex surfaces[J]. Journal of Manufacturing Science and Engineering, 1997, 119(4B):756-765.
[66] CHIOU J C J, LEE Y S. Optimal tool orientation for five-axis tool-end machining by swept envelope approach[J]. Journal of Manufacturing Science and Engineering, 2005, 127(4):810-818.
[67] GONG H, CAO L X, LIU J. Improved positioning of cylindrical cutter for flank milling ruled surfaces[J]. Computer-Aided Design, 2005, 37(12):1205-1213.
[68] GONG H, CAO L X, LIU J. Second order approximation of tool envelope surface for 5-axis machining with single point contact[J]. Computer-Aided Design, 2008, 40(5):604-615.
[69] ZHU L M, ZHANG X M, ZHENG G, et al. Analytical expression of the swept surface of a rotary cutter using the envelope theory of sphere congruence[J]. Journal of Manufacturing Science and Engineering, 2009, 131(4):041017.
[70] ZHU L M, ZHENG G, DING H, et al. Global optimization of tool path for five-axis flank milling with a conical cutter[J]. Computer-Aided Design, 2010, 42(10):903-910.
[71] JUN C S, CHA K, LEE Y S. Optimizing tool orientations for 5-axis machining by configuration-space search method[J]. Computer-Aided Design, 2003, 35(6):549-566.
[72] LAUWERS B, DEJONGHE P, KRUTH J P. Optimal and collision free tool posture in five-axis machining through the tight integration of tool path generation and machine simulation[J]. Computer-Aided Design, 2003, 35(5):421-432.
[73] HO M C, HWANG Y R, HU C H. Five-axis tool orientation smoothing using quaternion interpolation algorithm[J]. International Journal of Machine Tools and Manufacture, 2003, 43(12):1259-1267.
[74] WANG N, TANG K. Automatic generation of gouge-free and angular-velocity-compliant five-axis toolpath[J]. Computer-Aided Design, 2007, 39(10):841-852.
[75] SUN Y W, BAO Y R, KANG K X, et al. A cutter orientation modification method for five-axis ball-end machining with kinematic constraints[J]. The International Journal of Advanced Manufacturing Technology, 2013, 67(9-12):2863-2874.
[76] HUANG K T, ZHANG Z Y, GONG H, et al. Constructing smooth tool orientation field based on radial basis function for 5-axis machining[J]. The International Journal of Advanced Manufacturing Technology, 2017, 91(1-4):1369-1379.
[77] LAVERNHE S, TOURNIER C, LARTIGUE C. Optimization of 5-axis high-speed machining using a surface based approach[J]. Computer-Aided Design, 2008, 40(10-11):1015-1023.
[78] WANG N, TANG K. Five-axis tool path generation for a flat-end tool based on iso-conic partitioning[J]. Computer-Aided Design, 2008, 40(12):1067-1079.
[79] BI Q Z, WANG Y H, ZHU L M, et al. Wholly smoothing cutter orientations for five-axis NC machining based on cutter contact point mesh[J]. Science China Technological Sciences, 2010, 53(5):1294-1303.
[80] CASTAGNETTI C, DUC E, RAY P. The Domain of Admissible Orientation concept:A new method for five-axis tool path optimisation[J]. Computer-Aided Design, 2008, 40(9):938-950.
[81] HU P C, TANG K. Improving the dynamics of five-axis machining through optimization of workpiece setup and tool orientations[J]. Computer-Aided Design, 2011, 43(12):1693-1706.
[82] PLAKHOTNIK D, LAUWERS B. Graph-based optimization of five-axis machine tool movements by varying tool orientation[J]. The International Journal of Advanced Manufacturing Technology, 2014, 74(1-4):307-318.
[83] MI Z P, YUAN C M, MA X H, et al. Tool orientation optimization for 5-axis machining with C-space method[J]. The International Journal of Advanced Manufacturing Technology, 2017, 88(5-8):1243-1255.
[84] WANG Q R, FENG Y X, ZHANG Z X, et al. Tool orientation sequence smoothing method based on the discrete domain of feasible orientations[J]. The International Journal of Advanced Manufacturing Technology, 2017, 92(9-12):4501-4510.
[85] XU R F, CHENG X, ZHENG G M, et al. A tool orientation smoothing method based on machine rotary axes for five-axis machining with ball end cutters[J]. The International Journal of Advanced Manufacturing Technology, 2017, 92(9-12):3615-3625.
[86] XU J T, ZHANG D Y, SUN Y W. Kinematics performance oriented smoothing method to plan tool orientations for 5-axis ball-end CNC machining[J]. International Journal of Mechanical Sciences, 2019, 157-158:293-303.
[87] SUN S X, SUN Y W, LEE Y S. A gouge-free tool axis reorientation method for kinematics compliant avoidance of singularity in 5-axis machining[J]. Journal of Manufacturing Science and Engineering, 2019, 141(5):051010.
[88] ZHAO Z Y, WANG S B, WANG Z H, et al. Interference-and chatter-free cutter posture optimization towards minimal surface roughness in five-axis machining[J]. International Journal of Mechanical Sciences, 2020, 171:105395.
[89] LAYEGH K S E, YIGIT I E, LAZOGLU I. Analysis of tool orientation for 5-axis ball-end milling of flexible parts[J]. CIRP Annals, 2015, 64(1):97-100.
[90] SUN C, ALTINTAS Y. Chatter free tool orientations in 5-axis ball-end milling[J]. International Journal of Machine Tools and Manufacture, 2016, 106:89-97.
[91] HUANG T, ZHANG X M, LEOPOLD J, et al. Tool orientation planning in milling with process dynamic constraints:a minimax optimization approach[J]. Journal of Manufacturing Science and Engineering, 2018, 140(11):111002.
[92] WANG Y P, XU J T, SUN Y W. Tool orientation adjustment for improving the kinematics performance of 5-axis ball-end machining via CPM method[J]. Robotics and Computer-Integrated Manufacturing, 2021, 68:102070.
[93] CRIPPS R J, CROSS B, HUNT M, et al. Singularities in five-axis machining:Cause, effect and avoidance[J]. International Journal of Machine Tools and Manufacture, 2017, 116:40-51.
[94] MUNLIN M, MAKHANOV S S, BOHEZ E L J. Optimization of rotations of a five-axis milling machine near stationary points[J]. Computer-Aided Design, 2004, 36(12):1117-1128.
[95] SØRBY K. Inverse kinematics of five-axis machines near singular configurations[J]. International Journal of Machine Tools and Manufacture, 2007, 47(2):299-306.
[96] BOZ Y, LAZOGLU I. A postprocessor for table-tilting type five-axis machine tool based on generalized kinematics with variable feedrate implementation[J]. The International Journal of Advanced Manufacturing Technology, 2013, 66(9-12):1285-1293.
[97] PESSOLES X, LANDON Y, SEGONDS S, et al. Optimisation of workpiece setup for continuous five-axis milling:application to a five-axis BC type machining centre[J]. The International Journal of Advanced Manufacturing Technology, 2013, 65(1-4):67-79.
[98] LIN Z W, FU J Z, SHEN H Y, et al. Non-singular tool path planning by translating tool orientations in C-space[J]. The International Journal of Advanced Manufacturing Technology, 2014, 71(9-12):1835-1848.
[99] LIN Z W, FU J Z, SHEN H Y, et al. Improving machined surface texture in avoiding five-axis singularity with the acceptable-texture orientation region concept[J]. International Journal of Machine Tools and Manufacture, 2016, 108:1-12.
[100] AFFOUARD A, DUC E, LARTIGUE C, et al. Avoiding 5-axis singularities using tool path deformation[J]. International Journal of Machine Tools and Manufacture, 2004, 44(4):415-425.
[101] YANG J X, ALTINTAS Y. Generalized kinematics of five-axis serial machines with non-singular tool path generation[J]. International Journal of Machine Tools and Manufacture, 2013, 75:119-132.
[102] WAN M, LIU Y, XING W J, et al. Singularity avoidance for five-axis machine tools through introducing geometrical constraints[J]. International Journal of Machine Tools and Manufacture, 2018, 127:1-13.
[103] GRANDGUILLAUME L, LAVERNHE S, TOURNIER C. A tool path patching strategy around singular point in 5-axis ball-end milling[J]. International Journal of Production Research, 2016, 54(24):7480-7490.
[104] ERKORKMAZ K. Efficient fitting of the feed correction polynomial for real-time spline interpolation[J]. Journal of Manufacturing Science and Engineering, 2015, 137(4):044501.
[105] TAJIMA S, SENCER B. Global tool-path smoothing for CNC machine tools with uninterrupted acceleration[J]. International Journal of Machine Tools and Manufacture, 2017, 121:81-95.
[106] TULSYAN S, ALTINTAS Y. Local toolpath smoothing for five-axis machine tools[J]. International Journal of Machine Tools and Manufacture, 2015, 96:15-26.
[107] YANG J X, YUEN A. An analytical local corner smoothing algorithm for five-axis CNC machining[J]. International Journal of Machine Tools and Manufacture, 2017, 123:22-35.
[108] HUANG J, DU X, ZHU L M. Real-time local smoothing for five-axis linear toolpath considering smoothing error constraints[J]. International Journal of Machine Tools and Manufacture, 2018, 124:67-79.
[109] TAJIMA S, SENCER B. Accurate real-time interpolation of 5-axis tool-paths with local corner smoothing[J]. International Journal of Machine Tools and Manufacture, 2019, 142:1-15.
[110] HENG M, ERKORKMAZ K. Design of a NURBS interpolator with minimal feed fluctuation and continuous feed modulation capability[J]. International Journal of Machine Tools and Manufacture, 2010, 50(3):281-293.
[111] DUAN M L, OKWUDIRE C. Minimum-time cornering for CNC machines using an optimal control method with NURBS parameterization[J]. The International Journal of Advanced Manufacturing Technology, 2016, 85(5-8):1405-1418.
[112] LU Y A, DING Y, ZHU L M. Smooth tool path optimization for flank milling based on the gradient-based differential evolution method[J]. Journal of Manufacturing Science and Engineering, 2016, 138(8):081009.
[113] YUEN A, ZHANG K, ALTINTAS Y. Smooth trajectory generation for five-axis machine tools[J]. International Journal of Machine Tools and Manufacture, 2013, 71:11-19.
[114] PATELOUP V, DUC E, RAY P. Bspline approximation of circle arc and straight line for pocket machining[J]. Computer-Aided Design, 2010, 42(9):817-827.
[115] FAN W, LEE C H, CHEN J H. A realtime curvature-smooth interpolation scheme and motion planning for CNC machining of short line segments[J]. International Journal of Machine Tools and Manufacture, 2015, 96:27-46.
[116] BI Q Z, SHI J, WANG Y H, et al. Analytical curvature-continuous dual-Bézier corner transition for five-axis linear tool path[J]. International Journal of Machine Tools and Manufacture, 2015, 91:96-108.
[117] SENCER B, ISHIZAKI K, SHAMOTO E. A curvature optimal sharp corner smoothing algorithm for high-speed feed motion generation of NC systems along linear tool paths[J]. The International Journal of Advanced Manufacturing Technology, 2015, 76(9-12):1977-1992.
[118] SHI J, BI Q Z, ZHU L M, et al. Corner rounding of linear five-axis tool path by dual PH curves blending[J]. International Journal of Machine Tools and Manufacture, 2015, 88:223-236.
[119] HU Q, CHEN Y P, JIN X L, et al. A real-time C3 continuous tool path smoothing and interpolation algorithm for five-axis machine tools[J]. Journal of Manufacturing Science and Engineering, 2020, 142(4):041002.
[120] SHI J, BI Q Z, WANG Y H, et al. Development of real-time look-ahead methodology based on quintic PH curve with G2 continuity for high-speed machining[J]. Applied Mechanics and Materials, 2013, 464:258-264.
[121] ZHANG L B, YOU Y P, HE J, et al. The transition algorithm based on parametric spline curve for high-speed machining of continuous short line segments[J]. The International Journal of Advanced Manufacturing Technology, 2011, 52(1-4):245-254.
[122] ZHAO H, ZHU L M, DING H. A real-time look-ahead interpolation methodology with curvature-continuous B-spline transition scheme for CNC machining of short line segments[J]. International Journal of Machine Tools and Manufacture, 2013, 65:88-98.
[123] ZHANG Y, YE P Q, WU J Q, et al. An optimal curvature-smooth transition algorithm with axis jerk limitations along linear segments[J]. The International Journal of Advanced Manufacturing Technology, 2018, 95(1-4):875-888.
[124] FAN W, JI J W, WU P Y, et al. Modeling and simulation of trajectory smoothing and feedrate scheduling for vibration-damping CNC machining[J]. Simulation Modelling Practice and Theory, 2020, 99:102028.
[125] BEUDAERT X, LAVERNHE S, TOURNIER C. 5-axis local corner rounding of linear tool path discontinuities[J]. International Journal of Machine Tools and Manufacture, 2013, 73:9-16.
[126] ERKORKMAZ K, ALTINTAS Y. High speed CNC system design. Part I:jerk limited trajectory generation and quintic spline interpolation[J]. International Journal of Machine Tools and Manufacture, 2001, 41(9):1323-1345.
[127] DU X, HUANG J, ZHU L M. A complete S-shape feed rate scheduling approach for NURBS interpolator[J]. Journal of Computational Design and Engineering, 2015, 2(4):206-217.
[128] HU J, XIAO L J, WANG Y H, et al. An optimal feedrate model and solution algorithm for a high-speed machine of small line blocks with look-ahead[J]. The International Journal of Advanced Manufacturing Technology, 2006, 28(9-10):930-935.
[129] ZHANG Z L, GUO S J, WANG H D, et al. A new acceleration and deceleration algorithm and applications[C]//2012 Second International Conference on Intelligent System Design and Engineering Application. Piscataway:IEEE Press, 2012:121-124.
[130] HUANG J, ZHU L M. Feedrate scheduling for interpolation of parametric tool path using the sine series representation of jerk profile[J]. Proceedings of the Institution of Mechanical Engineers, Part B:Journal of Engineering Manufacture, 2017, 231(13):2359-2371.
[131] WANG Y S, YANG D S, GAI R L, et al. Design of trigonometric velocity scheduling algorithm based on pre-interpolation and look-ahead interpolation[J]. International Journal of Machine Tools and Manufacture, 2015, 96:94-105.
[132] SENCER B, ALTINTAS Y, CROFT E. Feed optimization for five-axis CNC machine tools with drive constraints[J]. International Journal of Machine Tools and Manufacture, 2008, 48(7-8):733-745.
[133] ZHANG K, YUAN C M, GAO X S, et al. A greedy algorithm for feedrate planning of CNC machines along curved tool paths with confined jerk[J]. Robotics and Computer-Integrated Manufacturing, 2012, 28(4):472-483.
[134] BEUDAERT X, LAVERNHE S, TOURNIER C. Feedrate interpolation with axis jerk constraints on 5-axis NURBS and G1 tool path[J]. International Journal of Machine Tools and Manufacture, 2012, 57:73-82.
[135] SUN Y W, ZHAO Y, BAO Y R, et al. A smooth curve evolution approach to the feedrate planning on five-axis toolpath with geometric and kinematic constraints[J]. International Journal of Machine Tools and Manufacture, 2015, 97:86-97.
[136] DONG J, STORI J A. A generalized time-optimal bidirectional scan algorithm for constrained feed-rate optimization[J]. Journal of Dynamic Systems, Measurement, and Control, 2006, 128(2):379-390.
[137] LIU Y, WAN M, QIN X B, et al. FIR filter-based continuous interpolation of G01 commands with bounded axial and tangential kinematics in industrial five-axis machine tools[J]. International Journal of Mechanical Sciences, 2020, 169:105325.
[138] ERKORKMAZ K, HENG M. A heuristic feedrate optimization strategy for NURBS toolpaths[J]. CIRP Annals, 2008, 57(1):407-410.
[139] CHEN M S, SUN Y W. A moving knot sequence-based feedrate scheduling method of parametric interpolator for CNC machining with contour error and drive constraints[J]. The International Journal of Advanced Manufacturing Technology, 2018, 98(1-4):487-504.
[140] FAN W, GAO X S, LEE C H, et al. Time-optimal interpolation for five-axis CNC machining along parametric tool path based on linear programming[J]. The International Journal of Advanced Manufacturing Technology, 2013, 69(5-8):1373-1388.
[141] GUO J X, ZHANG K, ZHANG Q, et al. Efficient time-optimal feedrate planning under dynamic constraints for a high-order CNC servo system[J]. Computer-Aided Design, 2013, 45(12):1538-1546.
[142] ERKORKMAZ K, CHEN Q G, ZHAO M Y, et al. Linear programming and windowing based feedrate optimization for spline toolpaths[J]. CIRP Annals, 2017, 66(1):393-396.
[143] SUN Y W, CHEN M S, JIA J J, et al. Jerk-limited feedrate scheduling and optimization for five-axis machining using new piecewise linear programming approach[J]. Science China Technological Sciences, 2019, 62(7):1067-1081.
[144] YEH S S, HSU P L. Adaptive-feedrate interpolation for parametric curves with a confined chord error[J]. Computer-Aided Design, 2002, 34(3):229-237.
[145] DU X, HUANG J, ZHU L M, et al. Third-order chord error estimation for freeform contour in computer-aided manufacturing and computer numerical control systems[J]. Proceedings of the Institution of Mechanical Engineers, Part B:Journal of Engineering Manufacture, 2019, 233(3):863-874.
[146] LIN M T, TSAI M S, YAU H T. Development of a dynamics-based NURBS interpolator with real-time look-ahead algorithm[J]. International Journal of Machine Tools and Manufacture, 2007, 47(15):2246-2262.
[147] JIA Z Y, SONG D N, MA J W, et al. A NURBS interpolator with constant speed at feedrate-sensitive regions under drive and contour-error constraints[J]. International Journal of Machine Tools and Manufacture, 2017, 116:1-17.
[148] WANG J, SUI Z, TIAN Y T, et al. A speed optimization algorithm based on the contour error model of lag synchronization for CNC cam grinding[J]. The International Journal of Advanced Manufacturing Technology, 2015, 80(5-8):1421-1432.
[149] DONG J, STORI J A. Optimal feed-rate scheduling for high-speed contouring[J]. Journal of Manufacturing Science and Engineering, 2007, 129(1):63-76.
[150] CHEN M S, SUN Y W. Contour error-bounded parametric interpolator with minimum feedrate fluctuation for five-axis CNC machine tools[J]. The International Journal of Advanced Manufacturing Technology, 2019, 103(1-4):567-584.
[151] YANG J X, ASLAN D, ALTINTAS Y. A feedrate scheduling algorithm to constrain tool tip position and tool orientation errors of five-axis CNC machining under cutting load disturbances[J]. CIRP Journal of Manufacturing Science and Technology, 2018, 23:78-90.
[152] DUONG T Q, RODRIGUEZ-AYERBE P, LAVERNHE S, et al. Contour error pre-compensation for five-axis high speed machining:offline gain adjustment approach[J]. The International Journal of Advanced Manufacturing Technology, 2019, 100(9-12):3113-3125.
[153] KHOSHDARREGI M R, TAPPE S, ALTINTAS Y. Integrated five-axis trajectory shaping and contour error compensation for high-speed CNC machine tools[J]. IEEE/ASME Transactions on Mechatronics, 2014, 19(6):1859-1871.
[154] CHEN M S, SUN Y W, XU J T. A new analytical path-reshaping model and solution algorithm for contour error pre-compensation in multi-axis computer numerical control machining[J]. Journal of Manufacturing Science and Engineering, 2020, 142(6):061006.
[155] ERKORKMAZ K, LAYEGH S E, LAZOGLU I, et al. Feedrate optimization for freeform milling considering constraints from the feed drive system and process mechanics[J]. CIRP Annals, 2013, 62(1):395-398.
[156] GUZEL B U, LAZOGLU I. Increasing productivity in sculpture surface machining via off-line piecewise variable feedrate scheduling based on the force system model[J]. International Journal of Machine Tools and Manufacture, 2004, 44(1):21-28.
[157] ERDIM H, LAZOGLU I, OZTURK B. Feedrate scheduling strategies for free-form surfaces[J]. International Journal of Machine Tools and Manufacture, 2006, 46(7-8):747-757.
CJA