驱动桥主减速器中的螺旋锥齿轮是传动系统的重要零件，其性能的优劣对驱动桥性能有较大影响。为研究主减速器螺旋锥齿轮齿面设计分析与优化方法，本文进行了以下研究：首先，研究了螺旋锥齿轮齿面局部共轭原理、齿面加工参数计算方法和齿面数学模型建立方法：通过局部共轭原理计算获得了齿面机床加工参数；建立了齿面数学模型；同时，为考虑传动系统对齿轮的影响，建立了驱动桥传动系统的有限元模型，获得了系统变形产生的齿轮错位量。其次，利用齿面数学模型，研究了齿面空载接触分析方法和加载接触分析方法并进行了试验验证：利用空载接触分析方法，获得了齿面空载接触印迹和传动误差；利用加载接触分析方法，获得了齿面加载接触印迹、接触应力、传动误差和齿根弯曲应力，用于齿面性能评价；通过齿轮加工、空载和加载啮合印迹试验对空载和加载接触分析方法进行了验证。基于上述方法，开发了螺旋锥齿轮设计分析软件。再次，在局部共轭原理获得齿面初始设计的基础上，研究了基于修形面的螺旋锥齿轮齿面设计方法：首先建立了考虑错位量后完全共轭的小轮齿面；其次采用高次传动误差曲线上的特征点和投影面的接触印迹，建立了设计高次传动误差的齿面(下称：高次设计)时使用的修形面控制参数，实现了考虑错位量的齿面高次设计；同时，采用该方法进行了二次传动误差的齿面设计(下称：二次设计)；最后通过分析和试验，研究了齿面高次设计和二次设计方法分别适用的载荷工况。最后，在齿面设计方法的基础上，研究了齿面加载性能优化方法：首先针对现有优化方法中未考虑齿根弯曲应力的问题，建立了考虑齿根弯曲应力的齿面加载接触印迹优化模型，利用Kriging代理模型结合单目标遗传算法获得了优化的齿面接触印迹；其次针对现有优化方法中仅考虑单一载荷工况的问题，建立了以多载荷工况综合传动误差和满载最大接触应力为目标函数的多目标优化模型，采用Kriging代理模型和多目标遗传算法得到了优化齿面，其各载荷工况的加载传动误差峰峰值均处于较低水平，提高了齿面设计对载荷工况的稳健性。
The spiral bevel and hypoid gear is the core part of the main reducer in the drive axle, and its performance has a great influence on the performance of the drive axle. In order to study the design, analysis and optimization approaches of the spiral bevel and hypoid gear, the following researches are studied:First, the local conjugation principle of spiral bevel and hypoid gear, the calculation of machine settings and the mathematical model of the tooth flank are studied. Machine settings are obtained through the local conjugation principle. The mathematical model of the tooth flank is established. In addition, in order to consider the influence of the transmission system on the gears, a finite element model of the drive axle system is established to calculate the misalignment caused by system deformation. Second, based on the mathematical model of the tooth flank, the tooth contact analysis (TCA) method and loaded tooth contact analysis (LTCA) method are studied. The unloaded contact pattern and unloaded transmission error are obtained by TCA. The loaded contact pattern, contact pressure, loaded transmission error and tooth root bending stress are obtained by LTCA to evaluate the performance of the tooth flank. Through gear manufacturing, unload tooth contact experiment and loaded tooth contact experiment, TCA and LTCA methods are validated. A design and analysis software of spiral bevel and hypoid gear is developed based on the above research. Third, based on the initial design of tooth flank obtained by the local conjugation principle, an ease-off based approach to design tooth flank of spiral bevel and hypoid gear is studied. The conjugate pinion tooth flank considering misalignment is established first. Then feature points on the high-order transmission motion curve and contact pattern on the pinion projection plane are established as the control parameters of the ease-off surface for the high-order transmission error design (referred to as “high-order design”). The high-order design is achieved considering misalignment. Moreover, the tooth flank design with second-order transmission error (referred to as “second-order design”) is also achieved by this approach. Finally, the applicable load cases of the high-order design and second-order design are studied considering misalignments under different load cases through analysis and experiments. Finally, based on the design approach, the optimization methodology of the loaded performance of spiral bevel and hypoid gear is studied. Firstly, in order to solve the problem that root bending stress was not considered in the existing optimization methods, an optimization model to optimize the loaded contact pattern considering root bending stress is established. The Kriging based surrogate model together with the single-objective genetic algorithm is used to solve this optimization problem, and the optimized loaded contact pattern was achieved. Secondly, in order to solve the problem that only one single load case was considered in optimization, a multi-objective optimization model is established with the loaded transmission error under multi-load cases and the maximum contact pressure under full load as two objective functions. The Kriging based surrogate model together with the multi-objective genetic algorithm is used to solve this multi-objective problem, and the optimized designs are obtained. The optimized designs have low peak-to-peak loaded transmission error under multi-load cases, which improves the robustness to load conditions.
