基于曲面包络逼近原理的点啮合齿面整体设计方法

基于曲面活动标架理论,提出了点啮合齿面整体设计的曲面包络逼近方法:以第一齿面包络特征线为样条曲线,以第二齿面沿接触点迹线的齿面局部结构作为曲面插值条件,通过第一齿面运动不变量描述的运动变换,构造完全由第一齿面的运动不变量描述的第一齿面共轭运动空间作为第二齿面整体优化设计空间,确保齿面设计方法的可全局优化性和可加工性。根据点啮合齿面加载接触实验数据,以空载啮合时两齿面间隙作为预测和控制重载情况下的接触区形状和大小的设计目标参数,建立点啮合齿面整体优化设计的变分不等式模型。与以往点啮合齿面设计和齿面接触分析(TCA)方法相比,该齿面设计方法摆脱了以往齿面接触分析(TCA)中以特定机床加工参数作为齿面重构参数而给齿面优化设计带来的不必要的限制,能在满足预定的加载的啮合特性要求的同时,确保齿面能用盘铣刀通过多轴联动数控加工方法以展成法加工。仿真实例计算和分析表明:本齿面设计方法能形成完整的弧齿锥齿轮齿面,该齿面在满载啮合时,重合度达到2.122,传动误差幅值降低至0.063°,具有优良的加载啮合特性。 

Design method for global properties of point-contact tooth surfacebased on envelope-approximation theory

A method (envelope-approximation theory) based on the surface moving frame was presented to design the global properties of point-contact tooth surface. The presented method proposed a universal approach to reconstruct the second tooth surface with motion invariants of the first tooth surface. The proposal reconstruction approach was formulated for approximating the conjugate surface of the first tooth surface to the first tooth surface under the movement transformation described with motion invariants of the first tooth surface. The basis function of the previously mentioned approximation was taken as the characteristic curve on the first tooth surface, the interpolation condition was designated as the local structure of the second tooth surface along the contact curve. Based on the experiment data of tooth contact, a variational inequality model for the global optimal design of tooth surfaces was established to determine the loaded meshing characteristics of the second tooth surface according to the position, orientation and dimension of the contact area on the first tooth surface under load-deformation condition. Different from the previous studies about tooth contact analysis, the presented method, freeing the tooth surface optimization design from unnecessary restrictions of the specific machine tool processing parameters, can satisfy the predesigned loaded meshing characteristics and ensure that the tooth surface can be generated by multi-axis flank milling with a conical cutter. A numerical example was given to validate that above-mentioned design method can construct unbroken spiral bevel gear tooth surface with excellent loaded meshing characteristics, for exanple, the loaded contact ratio was increased to 2.122 and the loaded transmission errors amplitude was lowered to 0.063°.