Abstract: To solve variable ratio tooth profile design problem of Rack and pinion variable ratio steering gear,a novel digital modeling method was proposed.The helical gear of variable ratio gear pair was taken as a set of intersection lines obtained by using countless planes perpendicular to the axis to cut the helical gear.Assuming there was a line through a point on the variable ratio tooth profile and parallel to the variable ratio rack,it would generate a series of interactions between this line and the corresponding intersection lines,and the point that the length coordinate value was the minimum of all intersections was a variable ratio tooth profile point.The mathematical models to solve the variable ratio tooth profile points were established and the corresponding solution algorithm was developed.Tooth profile point cloud of a variable ratio rack was obtained based on this method,and relevant tests of transmission ratio and transmission stability on the sample were performed.The experimental results verified the correctness of the proposed method.

Key words: rack and pinion variable ratio steering gear, variable ratio tooth profile, variable ratio curve, digital modeling, transmission stability, digital modeling method

摘要： 为解决交错轴变比齿条变比齿廓建模问题,提出一种数字设计方法。该方法将变比齿轮齿条副中的渐开线斜齿轮,看作无数无限接近且垂直于其轴线的平面与其截交后截交线的集合;定义一条计算直线与变比齿廓固连且平行于变比齿条的长度方向,并在变比齿轮齿条副传动过程中,将该计算直线与遍历的截交线渐开线齿廓所有交点中长度值取得极值的点称为变比齿廓点;基于约束最优数学思想,建立了变比齿廓数字求解模型,开发了求解算法,生成了变比齿廓点云,拟合得到了齿廓实体模型。通过试制样件的传动比和传动稳定性测试,验证了该方法的正确性。

关键词: 交错轴变比, 变比齿廓, 变比曲线, 数字建模, 传动稳定性, 数字设计方法