加加速度连续的S型加减速规划算法
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摘要
传统S型加减速算法的加加速度不连续,起止端存在突变导致机床进给过程中产生柔性冲击和振动,为改善机床动力学性能,提出一种加加速度无突变且起止端连续的加减速曲线,其加速度曲线由三角函数与直线连接组成,与纯三角函数加减速曲线相比可控性更强,可充分发挥机床的最大加速度性能。根据该加减速曲线特征,分别提出位移适配法和区间判别法对加减速模式进行规划分析和探讨。区间判别法只需简单少量计算,便可快速寻找出速度取值区间,规划出曲线构型,通过一次方程求解即可获得完整加减速曲线参数,具有高效的求解效率。对规划方法给出了详细的数学描述,并对曲线算法进行仿真和实验,得到平滑连续的加速度与速度曲线。仿真和实验结果证明了研究内容的正确性和方法的可行性。
The traditional S type acceleration/deceleration algorithm in CNC system is not suitable for high-speed motion due to the mutation of jerk. A flexible acceleration/deceleration algorithm suitable for high-speed motion system was introduced, in which the velocity, acceleration, jerk and displacement were all consecutive and the values of jerk at the beginning and end point were zero. Compared with traditional trigonometric function algorithms, the proposed algorithm was more flexible and could give full play to the maximum acceleration performance of CNC machine tool. Displacement adaptation method and interval discrimination method were proposed to plan the acceleration and deceleration mode. The interval discrimination method could quickly find the interval of velocity value by a few simple calculations. The acceleration and deceleration curve parameters could be obtained by solving quadratic equation only once, which ensured the high efficiency. This algorithm was analyzed and discussed with MATLAB. Through experiment, the smooth continuous acceleration and velocity curve were obtained, which proved the accuracy and the feasibility of the proposed algorithm.
The traditional S type acceleration/deceleration algorithm in CNC system is not suitable for high-speed motion due to the mutation of jerk. A flexible acceleration/deceleration algorithm suitable for high-speed motion system was introduced, in which the velocity, acceleration, jerk and displacement were all consecutive and the values of jerk at the beginning and end point were zero. Compared with traditional trigonometric function algorithms, the proposed algorithm was more flexible and could give full play to the maximum acceleration performance of CNC machine tool. Displacement adaptation method and interval discrimination method were proposed to plan the acceleration and deceleration mode. The interval discrimination method could quickly find the interval of velocity value by a few simple calculations. The acceleration and deceleration curve parameters could be obtained by solving quadratic equation only once, which ensured the high efficiency. This algorithm was analyzed and discussed with MATLAB. Through experiment, the smooth continuous acceleration and velocity curve were obtained, which proved the accuracy and the feasibility of the proposed algorithm.
引文
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[9] CHEN J H,YEH S S,SUN J T.An S-curve acceleration /deceleration design for CNC machine tools using quintic feedrate functions[J].Computer-Aided Design and Applications,2011,8(4):583-592.
[10] LIU Zhifeng,ZHANG Sen,CAI Ligang,et al.Five-phases-curve control method based on particle swarm optimization [J].Journal of Beijing University of Technology,2015,41(5):641-648(in Chinese).[刘志峰,张森,蔡力钢,等.基于粒子群优化五阶段S曲线加减速控制算法[J].北京工业大学学报,2015,41(5):641-648.]
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[12] LENG Hongbin,WU Yijie,PAN Xiaohong.New single segment ACC/DEC control method based on cubic polynomial model[J].Journal of Zhejiang University,2008,42(8):1440-1444(in Chinese).[冷洪滨,邬义杰,潘晓弘.三次多项式型段内加减速控制新方法[J].浙江大学学报,2008,42(8):1440-1444.]
[13] WANG F C,WRIGHT P K.Open architecture controllers for machine tools Part 2:a real time quintic spline interpolator[J].Journal of Manufacturing Science and Engineering,1998,120(2):425-432.
[14] ZHAO Guoyong,ZHAO Yugang,ZHAO Qingzhi,Acceleration & deceleration approach based on continuous jerk in CNC motion[J].Computer Integrated Manufacturing Systems,2011,17(2):316-320(in Chinese).[赵国勇,赵玉刚,赵庆志.数控运动中加加速度连续的加减速方法[J].计算机集成制造系统,2011,17(2):316-320.]
[15] GUO Xingui,LI Congxin.A new flexible acceleration and deceleration algorithm [J].Journal of Shanghai Jiaotong University,2003,37(2):205-207(in Chinese).[郭新贵,李从心.一种新型柔性加减速算法算法[J].上海交通大学学报,2003,37(2):205-207.]
[16] SONG Qingyu,GUO Baofeng,LI Jian,et al.Flexible acceleration and deceleration control algorithm for servo press[J].Transaction of the Chinese Society for Agriculture Machines,2013,44(6):269-273(in Chinese).[宋清玉,郭宝峰,李建,等.伺服压力机柔性加减速控制算法[J].农业机械学报,2013,44(6):269-273.]
[17] YANG Liangliang,XU Shoujin,SHI Weimin,et al.Research on S type acceleration and deceleration time planning algorithm with beginning and end speed non-zero[J].Journal of Mechanical Engineering,2016,52(23):199-206(in Chinese).[杨亮亮,许守金,史伟民,等.始末速度不为零的S型加减速时间规划算法研究[J].机械工程学报,2016,52(23):199-206.]
[18] LI Zhijie,WANG Huaiming.Design and analysis of conjugate cam beating-up motion law[J].Kew Engineering Materials,2016,693:53-57.
[2] BI Cheng’en,DING Naijian.Modern CNC machine tools[M].Beijing:China Machine Press,1993(in Chinese).[毕承恩,丁乃建,现代数控机床[M].北京:机械工业出版社,1993.]
[3] HUANG Yan,LI Jiaqi,YU Dong,et al.Design and implementation of s-shape acceleration and deceleration algorithm on CNC system[J].Manufacturing Technology and Machine Tool,2005(3):55-59(in Chinese).[黄艳,李家霁,于东,等.CNC系统S型曲线加减速算法的设计与实现[J].制造技术与机床,2005(3):55-59.]
[4] HAO Qi,GUAN Liwen,WANG Liping.Intelligent acceleration/deceleration control algorithm for drive force for a heavy duty hybrid machine tool[J].Journal of Tsinghua University,2009,49(11):1770-1773(in Chinese).[郝齐,关立文,王立平.重载混联机床智能加减速控制算法对驱动力的影响[J].清华大学学报,2009,49(11):1770-1773.]
[5] HU Jianhua,LIAO Wenhe,ZHOU Rurong.Research and comparison for several acceleration and deceleration curves in CNC system[J].Journal of Nanjing University of Aeronautics and Astronautics,1999,31(6):706-711(in Chinese).[胡建华,廖文和,周儒荣.CNC系统中几种升降速控制曲线的研究与比较[J].南京航空航天大学学报,1999,31(6):706-711.]
[6] KAAN E Y A.High speed CNC system design.Part Ⅰ:jerk limited trajectory generation and quintic spline interpolation[J].International Journal of Machine Tools & Manufacture,2001,41(9):1323-1345.
[7] SHI Chuan,ZHAO Tong,YE Peiqing,et al.Study on S-shape curve ACC/DEC control on NC system [ J ].China Mechanical Engineering,2007,18(12):1421-1425(in Chinese).[石川,赵彤,叶佩青,等.数控系统S曲线加减速规划研究[J].中国机械工程,2007,18(12):1421-1425.]
[8] TIAN Junfeng,LIN Hu,YAO Zhuang,et al.Study on S-shape curve acceleration and deceleration control fast planning on CNC system[J].Journal of Chinese Computer Systems,2013,34(1):168-172(in Chinese).[田军锋,林浒,姚壮,等.数控系统S型曲线加减速快速规划研究[J].小型微型计算机系统,2013,34(1):168-172.]
[9] CHEN J H,YEH S S,SUN J T.An S-curve acceleration /deceleration design for CNC machine tools using quintic feedrate functions[J].Computer-Aided Design and Applications,2011,8(4):583-592.
[10] LIU Zhifeng,ZHANG Sen,CAI Ligang,et al.Five-phases-curve control method based on particle swarm optimization [J].Journal of Beijing University of Technology,2015,41(5):641-648(in Chinese).[刘志峰,张森,蔡力钢,等.基于粒子群优化五阶段S曲线加减速控制算法[J].北京工业大学学报,2015,41(5):641-648.]
[11] REW K H,KIM K S.Using asymmetric S-curve profile for fast and vibration less motion[C] //Proceedings of2007 International Conference on Control,Automation and Systems.Washington,D.C.,USA:IEEE,2007.
[12] LENG Hongbin,WU Yijie,PAN Xiaohong.New single segment ACC/DEC control method based on cubic polynomial model[J].Journal of Zhejiang University,2008,42(8):1440-1444(in Chinese).[冷洪滨,邬义杰,潘晓弘.三次多项式型段内加减速控制新方法[J].浙江大学学报,2008,42(8):1440-1444.]
[13] WANG F C,WRIGHT P K.Open architecture controllers for machine tools Part 2:a real time quintic spline interpolator[J].Journal of Manufacturing Science and Engineering,1998,120(2):425-432.
[14] ZHAO Guoyong,ZHAO Yugang,ZHAO Qingzhi,Acceleration & deceleration approach based on continuous jerk in CNC motion[J].Computer Integrated Manufacturing Systems,2011,17(2):316-320(in Chinese).[赵国勇,赵玉刚,赵庆志.数控运动中加加速度连续的加减速方法[J].计算机集成制造系统,2011,17(2):316-320.]
[15] GUO Xingui,LI Congxin.A new flexible acceleration and deceleration algorithm [J].Journal of Shanghai Jiaotong University,2003,37(2):205-207(in Chinese).[郭新贵,李从心.一种新型柔性加减速算法算法[J].上海交通大学学报,2003,37(2):205-207.]
[16] SONG Qingyu,GUO Baofeng,LI Jian,et al.Flexible acceleration and deceleration control algorithm for servo press[J].Transaction of the Chinese Society for Agriculture Machines,2013,44(6):269-273(in Chinese).[宋清玉,郭宝峰,李建,等.伺服压力机柔性加减速控制算法[J].农业机械学报,2013,44(6):269-273.]
[17] YANG Liangliang,XU Shoujin,SHI Weimin,et al.Research on S type acceleration and deceleration time planning algorithm with beginning and end speed non-zero[J].Journal of Mechanical Engineering,2016,52(23):199-206(in Chinese).[杨亮亮,许守金,史伟民,等.始末速度不为零的S型加减速时间规划算法研究[J].机械工程学报,2016,52(23):199-206.]
[18] LI Zhijie,WANG Huaiming.Design and analysis of conjugate cam beating-up motion law[J].Kew Engineering Materials,2016,693:53-57.