变传动比齿条共轭曲面的数值计算方法

NUMERICAL METHOD ON VARIABLE-RATIO RACK CONTOUR COMPUTATION

提出了一种不使用啮合方程求解与齿轮啮合的齿条共轭齿面的数值计算方法,只要确定了齿轮参数与具体的运动要求,就可以由该方法直接计算出离散化齿条共轭曲面,在剖分点上的共轭曲面计算没有原理误差,精度取决于计算方法。为了提高共轭曲面的计算精度,可以设置更高的剖分精度。给出了变传动比齿条的共轭曲面数值计算具体实现方法和具体算例。分析表明该方法简洁明了,易于实现,尤其适合于求解变传动比共轭曲面。

In a variable-ratio rack and pinion steering, both thepressure and skew angles of each rack tooth vary along its length within the variable-ratio region of the rack. As a result, the teeth are both curved along their length and changing in cross-section across the width of the rack, and analytical solution of rack geometry becomes almost impossible. A numerical method is proposed for direct numerical solution of the rack geometry. With a given helical pinion and the required variable-ratio transmission, geometry of the mating rack can be computed, where solution of meshing equations is not needed. Numerical results are 3D data of a large number of selected points on the contour of the rack, being highly compatible with CNC machining. A computation example is worked out, along which the proposed method is shown to work well and the computational complexity is shown to be reasonable.