The ultimate goal in this study is to investigate the effects of tooth profile modifications (TPMs) on PGTs by performing parametric studies. For this purpose, firstly a nonlinear planetary gear dynamics model with time-varying stiffness is introduced. A time-varying stiffness function is included into the analysis by using loaded static transmission error (LSTE) for sun-planet and ring-planet gear meshes. In this analysis the computationally calculated values of LSTE are used; however, if an experimentally measured LSTE can be used, it will include all gear errors that exist in the gear pair, as well as time-varying mesh stiffness. Therefore, when this method is used with experimentally measured LSTE for dynamic modeling of planetary gear trains, one does not require any additional computational tool to estimate the time-varying mesh stiffness parameter. A drive-train simulation tool (Transmission3D), which combines analytical contact mechanics solutions with FE effectively, is used for verification purposes. The validity of the proposed model is shown by comparisons of the dynamic response of the proposed model with the response obtained through Transmission3D on an example PGT. A wide frequency range is selected to cover superharmonics of the natural frequencies in order to verify the accuracy of the dynamic model for speed ranges lower than the natural frequencies of the system, which are often encountered in practical applications. Harmonic balance method (HBM) is used to obtain the nonlinear algebraic equations of motion in frequency domain, which are solved by using Newton's method with arc length continuation. Parametric studies are performed by employing the mathematical model suggested important outcomes for application of TPMs in PGTs. The relationships between the distinct modal characteristics of PGTs and effectivity of TPMs are investigated in detail, leading to interesting outcomes. Moreover, different sensitivity characteristics are observed for linear and parabolic modification schemes. These outcomes; along with further evaluations on other aspects of design such as load intervals during operation, manufacturing tolerances, wear on gears, etc.; can be used in design guidelines for PGTs.

这项研究的最终目标是通过进行参数研究来研究牙齿轮廓修改（TPM）对PGT的影响。为此，首先引入具有时变刚度的非线性行星齿轮动力学模型。通过对太阳行星齿轮和环形行星齿轮啮合使用静态载荷传递误差（LSTE），将时变刚度函数包括在分析中。在此分析中，使用LSTE的计算值；但是，如果可以使用实验测量的LSTE，它将包括齿轮对中存在的所有齿轮误差以及随时间变化的啮合刚度。因此，当将此方法与实验测量的LSTE一起用于行星齿轮系的动态建模时，不需要任何其他计算工具即可估算随时间变化的网格刚度参数。结合了有效的有限元分析接触力学解决方案的传动系统仿真工具（Transmission3D）用于验证。通过将示例模型的动态响应与通过示例3的PGT上通过Transmission3D获得的响应进行比较，表明了所提出模型的有效性。选择一个宽的频率范围以覆盖自然频率的超谐波，以验证速度模型低于系统自然频率的动态模型的准确性，这在实际应用中经常会遇到。使用谐波平衡法（HBM）来获得频域中的非线性运动代数方程，并使用牛顿算法求解 弧长连续的s方法。通过使用数学模型进行参数研究，该数学模型建议将TPM应用于PGT中的重要结果。详细研究了PGT独特的模态特征与TPM有效性之间的关系，得出了有趣的结果。此外，对于线性和抛物线修改方案，观察到了不同的灵敏度特性。这些结果；以及对设计其他方面的进一步评估，例如操作期间的负载间隔，制造公差，齿轮磨损等；可用于PGT的设计指南。详细研究了PGT独特的模态特征与TPM有效性之间的关系，得出了有趣的结果。此外，对于线性和抛物线修改方案，观察到了不同的灵敏度特性。这些结果；以及对设计其他方面的进一步评估，例如操作期间的负载间隔，制造公差，齿轮磨损等；可用于PGT的设计指南。详细研究了PGT独特的模态特征与TPM有效性之间的关系，得出了有趣的结果。此外，对于线性和抛物线修改方案，观察到了不同的灵敏度特性。这些结果；以及对设计其他方面的进一步评估，例如操作期间的负载间隔，制造公差，齿轮磨损等；可用于PGT的设计指南。