循环球变比转向器螺母变比齿廓数值建模与加工方法

Digital Modeling and Manufacturing Method of Rack Variable Ratio Tooth Profile of Recirculating Ball Steering Gear

循环球变比转向器中具有变化传动比齿廓的螺母是实现变比转向的关键部件,螺母变比齿廓为与之啮合的齿轮渐开线齿廓按照变比传动关系包络运动后形成的包络面,因包络过程较为特殊,导致了其建模困难,由此阻碍了变比齿廓数控加工的实现。作者研究一种面向数控加工的变比齿廓数值建模方法,实现变比齿廓的数控端铣加工。该方法将转向器变比齿扇螺母副中的渐开线齿扇,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,与螺母齿条变比齿廓相交且平行于螺母齿条长度方向的计算直线,随螺母变比传动,与对应截交线渐开线齿廓的交点中,长度值取得极值的点为变比齿廓点。建立了变比齿廓求解数学模型,开发了求解算法,通过设置计算直线间距,生成了直接用于数控端铣等残留高度刀具路径规划的变比齿廓点云,规划了刀具路径;并且采用生成的齿廓点云,实现了刀头半径选择以及刀位点刀杆矢量的计算,实现了变比齿廓的数控端铣加工。从变比齿廓的关键设计参数"变比曲线"和"变速传动特性"入手,提出了变比齿廓设计的验证方法,通过试制样件的测试,验证了方法的正确性。该方法克服了采用啮合原理设计变比齿廓时,建立的啮合方程的解不唯一;无法获得变比齿廓齿顶、齿根边界点的精确值;有些出于解析需要选择的参数不直接对应数控加工,数据转换时会引入原理性误差等弊端,实现了循环球变比转向器变比齿廓的数字建模和数控端铣加工。

The variable ratio tooth profile is the key to realize ＂variable transmission ration＂ for recirculating ball variable ratio steering gear, and it is a kind of envelope surface formed by the envelope process of involute tooth profile in accordance with the variable ratio transmission relationship.This special envelope process leads to difficulties in modeling and Computer Numerical Control（CNC） machining of the variable ratio tooth profile. Focused on the digital design method and CNC machining method for variable ratio tooth profile of recirculating ball variable ratio steering gear, the gear sector of variable ratio gear pair was taken as a set of intersection lines obtained by using countless planes perpendicular to the axis of the gear sector to cut the gear sector. Assuming that there was a line through a point on the variable ratio tooth profile and parallel to the variable ratio rack would generate a series of interactions between this line and the corresponding intersection lines in gear transmission, and the point that the length coordinate value was the extremum of all intersections was a variable ratio tooth profile point. The mathematical models used 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. Using the tooth profile point cloud, planning of the tool path, size selection of the finishing tool and calculation of the cutter bar vector at cutter-contact point were completed, and CNC end milling of the variable ratio tooth profile was achieved. The relevant tests of transmission ratio and transmission stability on the sample were performed, and the experimental results verified the correctness of the proposed method. This method could overcome some disadvantages of designing variable ratio tooth profile with meshing principle, and realize the digital modeling and CNC end milling of variable ratio tooth profile.