In this study, the stochastic dynamic response of a spur gear pair model under the excitation of filtered noise is investigated. The spur gear pair is modeled as a single degree of freedom (SDOF) system in which nonlinear and non-smooth backlash and time-varying mesh stiffness as well as stochastic excitation are concurrently considered. Four cases are addressed, based on how the noise is incorporated in the loading terms. A first order filter is employed to generate various filtered noises with the same energy but different power spectrum. The combination of the SDOF gear model and the shaping filter leads to a (3D) Markov model. The numerical path integration (PI) technique is adopted to obtain the probabilistic response of the gear model using an adaptive time-stepping method in order to increase the accuracy of the time integration. A 4D system is also considered by applying a second order filter to model a narrow-band noise. The results are verified by comparing with Monte Carlo simulations. The effect of the noise spectrum on the probabilistic response is evaluated for different loading cases. The response PDF is of key importance in relation to reliability assessment of gear systems.

在这项研究中，研究了正齿轮副模型在滤波噪声激励下的随机动态响应。正齿轮副建模为单自由度（SDOF）系统，在该系统中同时考虑了非线性和非平滑齿隙以及时变啮合刚度以及随机激励。根据负载项中如何包含噪声，解决了四种情况。一阶滤波器用于产生具有相同能量但具有不同功率谱的各种滤波噪声。SDOF齿轮模型和整形滤波器的组合导致了（3D）马尔可夫模型。为了提高时间积分的准确性，采用数值路径积分（PI）技术使用自适应时间步长方法获得齿轮模型的概率响应。还可以通过应用二阶滤波器对窄带噪声建模来考虑4D系统。通过与蒙特卡洛模拟进行比较来验证结果。对于不同的载荷情况，评估了噪声谱对概率响应的影响。响应PDF对于齿轮系统的可靠性评估至关重要。