弧齿锥齿轮齿面拓扑修形及加工参数计算

为了能够实现对齿面啮合性能的灵活控制,针对弧齿锥齿轮小轮提出一种齿面拓扑修形方法,即借助二阶曲面对齿面偏差拓扑的近似表达,将齿面拓扑修形分解为5个方向:螺旋角修正、压力角修正、齿长曲率修正、齿廓曲率修正及齿面挠率修正,通过改变5个方向的修形系数对小轮齿面拓扑结构进行自由控制。在此基础上,建立齿面偏差与机床加工参数之间的修正数学模型,通过构建敏感性矩阵并采用最小二乘法求解,反求出获得修形齿面的小轮加工参数,以便指导加工。以一对弧齿锥齿轮副为例进行修形啮合分析,仿真结果表明:选取齿长曲率修形系数为0.0001,齿廓曲率修形系数为0.0005,齿面挠率修形系数为0.0003,对齿面进行拓扑修形后传动误差幅值为-25.60″,接触迹线倾斜角度变为54.7°,相比原始结果啮合性能得到改善。滚检接触区与理论仿真结果一致,验证了修形方法的有效性。 

Tooth surface topology modification and processing parameters calculation for spiral bevel gears

In order to control tooth meshing performance freely,a kind of tooth surface topology modification method for pinion was proposed.By means of second-order surface approximation for tooth surface deviations,the tooth surface topology modification can be divided into five parts:spiral angle correction,pressure angle correction,lengthwise curvature correction,profile curvature correction and longitudinal twist correction,by changing five modification factors the pinion tooth surface topology can be controlled freely.On this basis,the modified model between tooth surface deviations and processing parameters correction was established,and the pinion processing parameters allowing to acquire modified tooth surface can be calculated by constructing sensitivity matrix and least squares method.The meshing analysis for a pair of spiral bevel gears was carried out.The results demonstrate that by selecting lengthwise curvature modification factor 0.0001,profile curvature modification factor 0.0005,longitudinal twist modification factor 0.000 3,the transmission error magnitude is changed to-25.60",and the contact path orientation is changed to 54.7° after tooth surface topology modification,and the meshing performance is improved compared with initial result.The rolling test result agrees well with simulation result,verifying the effectiveness of modification method.