偏心渐开线齿轮传动的不等分模型及其数值解法

Inequality Model and Numerical Solution of Eccentric Involute Gear Transmission

针对等分模型下配对齿工作齿廓出现实际啮合不会发生的齿廓交叉或者分离现象,根据渐开线齿廓啮合几何关系,提出一种不存在假设误差的偏心渐开线齿轮传动不等分模型,以奇数齿偏心齿轮传动为例,给出不等分模型数值求解的完整算法。根据内公切线与两轮配对齿工作齿廓的交点数不同,啮合点搜索算法能处理任意转角关系下连续转动的4种情形,能正确产生7种不同的配对结果。计算结果表明,几何中心连线与内公切线段的交点不相互等分两线段,啮合点不总是在内公切线上,和轴心距大小无关。当基准齿工作齿廓坐标点数为5 000点时,啮合点搜索的坐标控制精度可达到0.001 mm,转角误差精度可达到0.001°,计算方法可以得到非常精确的转角关系,可以为偏心齿轮传动的准确分析和优化设计提供依据。

Aiming at the phenomena that working contours of matching teeth can intercross or separate each other under equality model of eccentric involute gear transmission and it should not take place in real gear transmission,a kind of inequality model of eccentric involute gear transmission without assumption error is presented according to the geometric meshing relationship between involute teeth contours of driving gear and driven gear.A complete numerical solution of inequality model is given by taking odd teeth gear transmission as an example.According to the numbers of different intersection generated between inner common tangent line and working contours of matching teeth of two gears,a searching algorithm of meshing points can process four kinds of situations when the driving gear drives the driven gear continuously at a random rotation angle,and produces correctly seven kinds of different meshing results of matching teeth.Computational results show that the intersection between the geometric center line and the inner common tangent line of two gears do not divide evenly the two lines,and the meshing points of the eccentric involute gear transmission are not always on the inner common tangent line,which has nothing to do with distance between shafts.When 5 000 coordinate points of involute working contours of benchmark tooth are determined to compute the inequality model,the coordinate control precision of searching meshing points can reach 0.001 millimetre and the angle error can reach 0.001 degree.Numerical solution may get precise rotation angle relationship between the driving gear and the driven gear,and may provide a reference for accurate analysis and optimization design of eccentric involute gear transmission.