Loaded tooth contact analysis (LTCA) is an important tool for analyzing the meshing of spiral bevel gears. This paper presents a semi-analytical LTCA method, where the analytical formulas are used to calculate the tooth deformation and contact force, with partial coefficients corrected by finite element analysis (FEA) results. Based on Tredgold's Approximation, the tooth is sliced, of which the flank is determined by simulating the manufacturing process. In order to calculated the potential contact curves of a real gear pair, an optimization model is established to find the points more likely to be in contact within the range of contact curves obtained by the help of roll angle surfaces. The compliance of tooth is modeled as a combination of two contributions, where the deformation of cantilever beam under load is used to determine the global deformation, and the local contact deformation is obtained by Hertz line contact assumption. A contact judgement strategy is proposed to detect the contact of the slices at ends of contact curves, and the correction coefficients are introduced in the tooth deformation to consider the coupling effect among slices. In the end, a numerical instance of LTCA under different load torques is provided, which demonstrates the accuracy and efficiency of the presented LTCA method by comparisons with results of FEA. This method can be easily modified to analyze other gear pairs and has the ability to be extended to simulate the gears with local defects or cracks.

载荷齿面接触分析 (LTCA) 是分析螺旋锥齿轮啮合的重要工具。本文提出了一种半解析 LTCA 方法，其中解析公式用于计算牙齿变形和接触力，部分系数由有限元分析 (FEA) 结果校正。基于Tredgold's Approximation，对齿进行切片，通过模拟制造过程确定齿面。为了计算真实齿轮副的潜在接触曲线，建立了优化模型，在滚动角面获得的接触曲线范围内找到更可能接触的点。牙齿的顺应性被建模为两个贡献的组合，其中采用悬臂梁受载变形确定整体变形，局部接触变形由赫兹线接触假设得到。提出了一种接触判断策略来检测接触曲线端部切片的接触，并在牙齿变形中引入校正系数以考虑切片之间的耦合效应。最后，提供了不同负载扭矩下 LTCA 的数值实例，通过与 FEA 结果的比较证明了所提出的 LTCA 方法的准确性和效率。该方法可以很容易地修改以分析其他齿轮副，并且可以扩展以模拟具有局部缺陷或裂纹的齿轮。提出了一种接触判断策略来检测接触曲线端部切片的接触，并在牙齿变形中引入校正系数以考虑切片之间的耦合效应。最后，提供了不同负载扭矩下 LTCA 的数值实例，通过与 FEA 结果的比较证明了所提出的 LTCA 方法的准确性和效率。该方法可以很容易地修改以分析其他齿轮副，并且可以扩展以模拟具有局部缺陷或裂纹的齿轮。提出了一种接触判断策略来检测接触曲线端部切片的接触，并在牙齿变形中引入校正系数以考虑切片之间的耦合效应。最后，提供了不同负载扭矩下 LTCA 的数值实例，通过与 FEA 结果的比较证明了所提出的 LTCA 方法的准确性和效率。该方法可以很容易地修改以分析其他齿轮副，并且可以扩展以模拟具有局部缺陷或裂纹的齿轮。通过与 FEA 结果的比较，证明了所提出的 LTCA 方法的准确性和效率。该方法可以很容易地修改以分析其他齿轮副，并且可以扩展以模拟具有局部缺陷或裂纹的齿轮。通过与 FEA 结果的比较，证明了所提出的 LTCA 方法的准确性和效率。该方法可以很容易地修改以分析其他齿轮副，并且可以扩展以模拟具有局部缺陷或裂纹的齿轮。