插补前加减速运动时间周期化等效变换算法

中国机械工程 ›› 2014, Vol. 25 ›› Issue (24): 3320-3325.

插补前加减速运动时间周期化等效变换算法

尹涓1，2;罗福源2

1.南京航空航天大学金城学院,南京,211156
2.南京航空航天大学,南京,210016

出版日期:2014-12-25 发布日期:2014-12-30
基金资助:
国家自然科学基金资助项目(501205200);江苏省高校自然科学基金(14KJB460017);江苏省自然科学基金(BK2012388)

Equivalent Transformation Algorithm for Motion Time Periodization of Acceleration and Deceleration before Interpolation

Yin Juan1,2;Luo Fuyuan2

1.Nanhang Jincheng College,Nanjing,211156
2.Nanjing University of Aeronautics and Astronautics,Nanjing,210016

Online:2014-12-25 Published:2014-12-30
Supported by:
National Natural Science Foundation of China（No. 501205200）;Jiangsu Provincial Natural Science Foundation of Higher Education of China（No. 14KJB460017）;Jiangsu Provincial Natural Science Foundation of China（No. BK2012388）

摘要/Abstract

摘要：

针对数控系统插补前加减速控制计算得到的运动时间不是插补周期的整数倍的问题,提出了基于连续时间速度曲线与位移等效变换原理，生成满足插补周期整数倍特征的周期化离散速度曲线的方法，并以梯形加减速为例，详细推导了起止速度为任意正实数情况下不同加减速阶段的各个插补周期的进给速度计算公式。该方法无需改变插补周期，易于与传统伺服运动控制系统兼容。插补实例表明，提出的方法能够生成匀速运动速度严格等于指令速度的速度曲线，保证以指定的速度通过线段终点，且具有较高的运动效率与插补精度。

关键词: 加减速控制, 插补周期, 位移等效变换, 速度曲线

Abstract:

To solve the problem that the motion time calculated from acceleration and deceleration control before interpolation control in CNC system, on the basis of continuous time velocity profiles and the principles of displacement equivalent transformation, an algorithm for the generation of periodic discrete velocity profiles was proposed, whose motion time fited into an integral number of interpolation periods. The feedrate computational formulae for each interpolation period of different acceleration and deceleration phases were deduced in detail in cases where both start speed and end speed were any desired positive real number. The proposed method did not need variant interpolation periods and it was easy to apply in traditional servo motion control system. The interpolation instance shows it is able to generate such velocity profile that the constant speed is strictly equal to instruction speed and guarantees the velocity at the segment terminal to be the specified speed. In addition, it has high motion efficiency and interpolation accuracy.

Key words: acceleration and deceleration control, interpolation period, displacement equivalent transformation, velocity profile

中图分类号:

TP273

尹涓, 罗福源. 插补前加减速运动时间周期化等效变换算法[J]. 中国机械工程, 2014, 25(24): 3320-3325.

Yin Juan, Luo Fuyuan. Equivalent Transformation Algorithm for Motion Time Periodization of Acceleration and Deceleration before Interpolation[J]. China Mechanical Engineering, 2014, 25(24): 3320-3325.

参考文献

[1]陈友东,魏洪兴,王琦魁.数控系统的直线和S形加减速离散算法[J].中国机械工程,2010,21(5):567-570.
Chen Youdong,Wei Hongxing,Wang Qikui.An Algorithm of Sampled-data Linear and S Shape Acceleration and Deceleration for CNC Controller[J].China Mechanical Engineering,2010,21(5):567-570.
[2]许海峰,王宇晗,李宇昊,等.小线段高速加工的速度模型研究和实现[J].机械工程师,2005(4):9-13.
Xu Haifeng, Wang Yuhan,Li Yuhao,et al.Research on Feedrate Model of Look-ahead and Solution Algorithm of High-speed Machining of Small Line Segments[J]. Mechanical Engineer,2005(4):9-13.
[3]杨林,张承瑞.基于时间分割的前加减速快速插补算法[J].制造技术与机床,2008(9):93-96.
Yang Lin,Zhang Chengrui.Time Division Based Acceleration/Deceleration Interpolation Algorithm[J].Manufacturing Technology and Machine Tools,2008(9):93-96.
[4]何均,游有鹏,陈浩.步进运动控制系统最优插补周期研究[J].中国机械工程,2009,20(23):2811-2815.
He Jun,You Youpeng,Chen Hao.Optimal Interpolation Period for Stepping Motor Systems[J]. China Mechanical Engineering, 2009, 20(23):2811-2815.
[5]Shi Xuguang,Xu Bugong,Xie Wei,et al.Design and Implementation of S-shape Acceleration/Deceleration Algorithm Based on Rounding Error Compensation Tactic[C]//Proc. 7th World Congress on Intelligent Control and Automation. Chongqing: IEEE, 2008: 7912-7916.
[6]郑金兴,张铭钧.梯形速度控制变插补周期的实时插补算法研究[J].机床与液压,2007,35(1):77-80,133.
Zheng Jinxing,Zhang Mingjun.Study of Real-time Interpolation Algorithm with Varying Interpolation Period Based on Trapezoidal Velocity Profile[J].Machine Tool & Hydraulics,2007,35(1):77-80,133.
[7]王宇晗,肖凌剑,曾水生,等.小线段高速加工速度衔接数学模型[J].上海交通大学学报,2004,38(6):901-904.
Wang Yuhan,Xiao Lingjian,Zeng Shuisheng.An Optimal Feed Rate Model and Solution for High Speed Machining of Small Line Blocks with Look Ahead[J]. Journal of Shanghai Jiao Tong University,2004,38(6):901-904.

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