数控系统的插补算法及加减速控制方法研究
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摘要
插补及加减速控制的精度和速度是CNC系统的重要指标,决定了数控系统的性能优劣。本文针对这两方面的问题做了深入的理论和应用研究。
针对研制自主知识产权的经济型数控系统,本文主要研究插补精度高、换向较少、有利于轴连续运动的最小偏差插补算法及直接加减速控制方法。在改进原算法的基础上处理了非过原点线形的插补问题,证明了特殊情况下的插补精度,推导出最小偏差法三维直线插补算法,并首次采用解析法证明了三维直线插补精度,详细讨论了终点判别条件,解决了圆弧插补时因终点错误而导致飞车的问题,首次将计算机图形学的Bresenham算法与最小偏差法有机结合,建立了图形学与电机控制系统的关系。本文还提出了基于最小偏差算法的加减速控制方法,采用实时速度计算法,通过减少静态变量、减少参数传递、减少程序的长转移、简化乘除法运算,以解决实时计算浪费机时的问题,使进给速度达到2500 mm /min。该速度控制方法使操作者可以根据负载的情况,灵活改变最高运行频率、加速度等速度控制参数,而无需重新制表,可方便实现数控系统与机床的配套。上述的研究展现了一个从理论推导到实际应用的完整的最小偏差插补算法和速度控制方法,满足经济型数控系统的精度、速度的要求,并已应用于本实验室自主开发的数控系统中,为其产业化铺平了道路。
针对目前大多数中高档CNC系统只具有直线圆弧插补指令的现状,本文研究了Step标准中的Nurbs曲线插补算法、多坐标参数曲面插补算法及自适应速度控制方法。插补过程中,为提高插补计算的精度和速度,提出了改进的试探修正法,以代替复杂的求导过程。速度控制过程中,采用插补前S型加减速曲线进行速度控制,将插补的弓高误差、机床许用加速度均考虑在内,并提出时间顺延法,加减速对称法,实现了在线实时自适应的加减速控制。本文提出的方法不仅充分发挥了插补前加减速控制的位置精确的优势,还解决了减速点预测困难的问题,具有位置精度高、无冲击、自适应等优点。其中的弧长求解算法的精度高于CAD/CAM的计算精度。该速度控制方法也可以用于加工前的仿真,帮助编程人员选择合理的进给速度、加速度、跃变度等参数,从而提高加工的精度和效率。上述的研究使CNC系统具备了Nurbs曲线、五坐标参数曲面插补功能,避免了加工过程中直线圆弧逼近曲线曲面的种种弊端,可有力支持高速、高精加工,将对提高我国CNC系统水平起到积极的推动作用。
It is important for CNC system to control the precision and speed of interpolatorand Acceleration and deceleration, which decide the character of CNC system. Theresearch to this two aspects is done deeply in this paper.
In order to research and develop economic-type CNC system, Minimumdeviation interpolator and feed-control method are studied, which possesses higherprecision and benefit for motor. On the basis of improved original interpolator, onesof line and circle not to go through the initial point are solved, interpolation precisionin special cases is proved, three-dimensional line one is deduced. Analysis is takenstep firstly to prove the precision of three-dimensional line interpolator. The endpoint criterion is discussed in detail so that no-stop caused by error end is solved. It iscombined between Bresenham algorithm in computer graphic area and Minimumdeviation interpolator to establish the bridge between them. The real-timeAcceleration-Deceleration control algorithm to stepper motor is put forward, whichbreaks away form traditional look-up table and uses real-time calculating way. Butthis method has its disadvantage that calculating speed is slower. For this reason,multiform means, for example, decreasing static variables, decreasing parametertransfer, decreasing long jump and simplified multiplication-division operation, areused to deal with its disadvantage in practice and take effective. The fastest feedreaches 2500 mm /min. The engineer may change flexibly highest frequency,acceleration and so on according to loading, without renewing chart.
Above all, a complete minimum deviation interpolator and feed-control method isshowed, which meet the need of economic-type CNC system and benefit forindustrialization
In order to improve present level of CNC system, the Nurbs curve,multi-coordinates parameter surface interpolator and adaptive-feed control methodare discussed. In order to improve the precision and rate of interpolator, advancedtrial-amendment method is adopted. S shape Acceleration-Deceleration methodforehand Nurbs interpolator is adopted, taking chord error and jerk into consideration,
proposing time-progressive-last and Acce-Dece-symmetry method, which not onlymake good use of higher position in Acce-Dece control of forehand interpolator, butalso solving rationally difficulty in the predetermination Deceleration-point. In which,the accuracy of the calculation of arc is better than the one in CAD/CAM software.This method is a higher position, no impact and adaptive one. It also may become theassistant to the programmer, helping them to select optimizing parameter, forexample, feed, acceleration and jerk as well through the simulation so as to improveprecision and efficiency of machining. Above all, the Nurbs curve interpolator andparametrical surface interpolators are realized, which can support strongly the higheraccuracy and higher speed machining, avoid the disadvantage of transfer curve andsurface into line or circle and will promote the level of Chinese CNC system.
针对研制自主知识产权的经济型数控系统,本文主要研究插补精度高、换向较少、有利于轴连续运动的最小偏差插补算法及直接加减速控制方法。在改进原算法的基础上处理了非过原点线形的插补问题,证明了特殊情况下的插补精度,推导出最小偏差法三维直线插补算法,并首次采用解析法证明了三维直线插补精度,详细讨论了终点判别条件,解决了圆弧插补时因终点错误而导致飞车的问题,首次将计算机图形学的Bresenham算法与最小偏差法有机结合,建立了图形学与电机控制系统的关系。本文还提出了基于最小偏差算法的加减速控制方法,采用实时速度计算法,通过减少静态变量、减少参数传递、减少程序的长转移、简化乘除法运算,以解决实时计算浪费机时的问题,使进给速度达到2500 mm /min。该速度控制方法使操作者可以根据负载的情况,灵活改变最高运行频率、加速度等速度控制参数,而无需重新制表,可方便实现数控系统与机床的配套。上述的研究展现了一个从理论推导到实际应用的完整的最小偏差插补算法和速度控制方法,满足经济型数控系统的精度、速度的要求,并已应用于本实验室自主开发的数控系统中,为其产业化铺平了道路。
针对目前大多数中高档CNC系统只具有直线圆弧插补指令的现状,本文研究了Step标准中的Nurbs曲线插补算法、多坐标参数曲面插补算法及自适应速度控制方法。插补过程中,为提高插补计算的精度和速度,提出了改进的试探修正法,以代替复杂的求导过程。速度控制过程中,采用插补前S型加减速曲线进行速度控制,将插补的弓高误差、机床许用加速度均考虑在内,并提出时间顺延法,加减速对称法,实现了在线实时自适应的加减速控制。本文提出的方法不仅充分发挥了插补前加减速控制的位置精确的优势,还解决了减速点预测困难的问题,具有位置精度高、无冲击、自适应等优点。其中的弧长求解算法的精度高于CAD/CAM的计算精度。该速度控制方法也可以用于加工前的仿真,帮助编程人员选择合理的进给速度、加速度、跃变度等参数,从而提高加工的精度和效率。上述的研究使CNC系统具备了Nurbs曲线、五坐标参数曲面插补功能,避免了加工过程中直线圆弧逼近曲线曲面的种种弊端,可有力支持高速、高精加工,将对提高我国CNC系统水平起到积极的推动作用。
It is important for CNC system to control the precision and speed of interpolatorand Acceleration and deceleration, which decide the character of CNC system. Theresearch to this two aspects is done deeply in this paper.
In order to research and develop economic-type CNC system, Minimumdeviation interpolator and feed-control method are studied, which possesses higherprecision and benefit for motor. On the basis of improved original interpolator, onesof line and circle not to go through the initial point are solved, interpolation precisionin special cases is proved, three-dimensional line one is deduced. Analysis is takenstep firstly to prove the precision of three-dimensional line interpolator. The endpoint criterion is discussed in detail so that no-stop caused by error end is solved. It iscombined between Bresenham algorithm in computer graphic area and Minimumdeviation interpolator to establish the bridge between them. The real-timeAcceleration-Deceleration control algorithm to stepper motor is put forward, whichbreaks away form traditional look-up table and uses real-time calculating way. Butthis method has its disadvantage that calculating speed is slower. For this reason,multiform means, for example, decreasing static variables, decreasing parametertransfer, decreasing long jump and simplified multiplication-division operation, areused to deal with its disadvantage in practice and take effective. The fastest feedreaches 2500 mm /min. The engineer may change flexibly highest frequency,acceleration and so on according to loading, without renewing chart.
Above all, a complete minimum deviation interpolator and feed-control method isshowed, which meet the need of economic-type CNC system and benefit forindustrialization
In order to improve present level of CNC system, the Nurbs curve,multi-coordinates parameter surface interpolator and adaptive-feed control methodare discussed. In order to improve the precision and rate of interpolator, advancedtrial-amendment method is adopted. S shape Acceleration-Deceleration methodforehand Nurbs interpolator is adopted, taking chord error and jerk into consideration,
proposing time-progressive-last and Acce-Dece-symmetry method, which not onlymake good use of higher position in Acce-Dece control of forehand interpolator, butalso solving rationally difficulty in the predetermination Deceleration-point. In which,the accuracy of the calculation of arc is better than the one in CAD/CAM software.This method is a higher position, no impact and adaptive one. It also may become theassistant to the programmer, helping them to select optimizing parameter, forexample, feed, acceleration and jerk as well through the simulation so as to improveprecision and efficiency of machining. Above all, the Nurbs curve interpolator andparametrical surface interpolators are realized, which can support strongly the higheraccuracy and higher speed machining, avoid the disadvantage of transfer curve andsurface into line or circle and will promote the level of Chinese CNC system.
引文
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