含安装误差的鼓形齿轮承载接触分析

基于齿轮范成原理，建立修形后直齿的鼓形面数学模型，并根据齿轮接触分析（Tooth contact analysis，TCA）结果进行齿面接触线上接触点的离散。基于Weber能量法，求解齿间载荷分布，并利用线性规划法，求解齿向载荷分布。在得出齿面的实际载荷分布后，建立鼓形齿面的圆柱体模型。利用赫兹原理，对含安装误差的鼓形齿面进行齿面接触应力分布求解。分析结果发现垂直平面误差较轴平面误差对接触应力分布影响更大，起鼓修形后齿面载荷分布虽然得到明显改善，但接触应力值会有所增大。接触应力分布结果与有限元方法结果规律相一致，证明了该方法的合理性，为齿轮承载接触分析（Loaded tooth contact analysis，LTCA）提供了新的简便方法。

Loaded Tooth Contact Analysis of Spur Gears with Longitudinal Modification Considering Assembly Errors

Based on the principle of gear generation, the mathematical model of the crowned surface of the straight tooth after modification is established, and the contact points located in the contact lines on the tooth surface is discretized according to the results of gear contact analysis (Tooth contact analysis, TCA). Based on the Weber energy method, the load distribution between teeth is solved, and the linear programming method is used to solve the load distribution in the tooth direction. After the actual load distribution of the tooth surface is obtained, a cylindrical model of the crowned tooth surface is established. Then, the tooth surface contact stress distribution is solved for the crowned tooth surface with assembly error by using the Hertz principle. The analysis results show that the axial plane error has a greater impact on the contact stress distribution than the vertical plane error. Although the load distribution on the tooth surface is significantly improved after crowning, the contact stress value will increase. The results of the contact stress distribution are consistent with the results of the finite element method, which proves the rationality of the method, and provides a new and convenient method for gear load contact analysis (Loaded tooth contact analysis, LTCA).