曲轴磨床切点跟踪运动三次样条逼近研究

摘要

According to the characteristics of the crankshaft grinder tangential point tracking movement,this paper explained the process of making the mathematical model,and proposed the method based on the cubic spline curve to approach the track points which are generated to track the movement of the crankshaft grinder cut-off point.At the same time,the process of deriving the cubic spline curve that track the movement of the crankshaft grinder cut point is illustrated in the paper.Cubic spline function has the continuous features of the first and second derivative,so the fitting effect is good and the cutting surface is smooth,which con-forms the profile requirements of the crankshaft parts.The results in the simulation show that the approxima-tion algorithm of the cubic spline enables the curve smooth overall,and the approximation error is small.%根据曲轴磨床切点跟踪运动的特点,文章阐述了建立切点跟踪数学模型的整个过程,并且提出用三次样条曲线对曲轴磨床切点跟踪运动过程中的轨迹点进行逼近的方法,演绎了曲轴磨床切点跟踪运动的三次样条曲线方程的推导过程.三次样条曲线函数具有一阶导数和二阶导数连续的特点,所以轨迹逼近拟合效果好,加工曲面整体光滑,符合曲轴零件型线轮廓要求.通过对比仿真实验结果证明,三次样条逼近算法能使磨削曲线整体平滑,并且逼近误差小.