Dynamic analysis of uncertain spur gear systems

Gear transmission systems are widely used in mechanical equipment. Due to manufacturing and processing errors, material defects, wear and external environments, there are uncertain parameters such as mass, mesh stiffness and support stiffness. Parametric uncertainty plays an important role in response predictions of the gear transmission systems. In order to evaluate reasonably the dynamic characteristics of the gear transmission systems, a dynamic model of an uncertain single-stage gear system is established. The dynamic responses of the bounded uncertain gear transmission system are investigated by an interval analysis method based on the Chebyshev inclusion function. A matrix form of the least square method is applied to improve the calculation efficiency of the interval approach. The investigation reveals the effects of different uncertain parameters on amplitude-frequency responses of the gear system. It is the first time to design and to implement a test rig of an uncertain single-stage spur gear transmission system. The experimental results verify the accuracy and the effectiveness of the theoretical analysis results. The results demonstrate that the parametric uncertainty may propagate in the gear transmission system and the propagation results in significant variations of the dynamic responses.