磨齿五轴运动多项式系数敏感性分析

Sensitivity Analysis of Polynomial Coefficients in Five Axis Grinding

成形磨齿时,优化五轴(X,Y,Z,C,A)附加运动的高次多项式系数可以修正齿面误差,但迭代计算量大,优化结果不稳定,很难应用于实际加工。为简化附加运动模型,并为后续设计高效高精度的齿面误差修正策略提供理论依据,对磨齿五轴运动多项式系数进行了敏感性分析。首先,建立了五轴磨齿系统的数学模型;将各轴运动表示为6次多项式曲线,并推导出五轴磨削运动时砂轮与工件的动态接触条件;其次,根据砂轮基本信息与动态接触条件,得出实际加工包络面,进而获得齿面偏差信息,并给出齿面精度评价方法;最后,采用SOBOL全局敏感性分析法进行了五轴运动多项式各项系数对齿面误差影响的敏感性分析。实例中绘制了一阶敏感性系数S i和总体敏感性系数S Ti的柱状图,并根据各系数对各精度指标的影响大小进行了排序。结果表明,对齿面误差影响的主要系数为二次及以下项系数;对于齿形倾斜误差fhα和齿向倾斜误差fhβ,各系数的影响相互独立,利于修正;修正fhα和fhβ的关键运动轴分别为Y、C、X轴和Y、C、Z轴。

In the process of gear forming grinding,the tooth surface error can be corrected by optimizing the coefficients of the high-order polynomials of the five axis(X,Y,Z,C,A)additional motion.However,the amount of iterative calculation is large and the optimization results are unstable,which makes it difficult to apply to actual machining.In order to simplify the additional motion model and provide a theoretical basis for the subsequent design of highly efficient and high-precision tooth surface error correction strategy,the sensitivity analysis of the five axis motion polynomial coefficients of gear grinding is carried out.Firstly,the mathematical model of five axis gear grinding system is established;The motion of each axis is expressed as a polynomial curve of degree 6,and the dynamic contact conditions between the grinding wheel and the workpiece during five axis grinding are derived;Secondly,according to the basic information and dynamic contact conditions of the grinding wheel,the actual machining envelope surface is obtained,and then the tooth surface deviation information is obtained,and the tooth surface accuracy evaluation method is given;Finally,SOBOL global sensitivity analysis method is used to analyze the sensitivity of five axis motion polynomial coefficients to tooth surface error.In the example,the histogram of S i and S Ti is drawn,and the order is made according to the influence of each coefficient on each precision index.It is concluded that the main coefficients affecting the tooth surface error are quadratic and lower coefficients;For fhαand fhβ,the influence of each coefficient is independent,which is conducive to correction;The key motion axes for correcting fhαand fhβare Y,C,X and Y,C,Z respectively.