Effects of random interval parameters on spur gear vibration

Abstract

Gear driving devices are commonly used in mechanical transmission systems. Due to the inevitable random errors in manufacturing, installation, and operation, the dynamics of a gear transmission system will fluctuate randomly. To reveal the dynamic characteristics, an interval parameters dynamic model of a single-stage spur gear pair is established, in which the uncertainties of displacement excitation, load excitation, and stiffness excitation are included, and their formulations are derived in detail by using interval mathematics. The established interval parameters dynamic model is solved by combining the Chebyshev inclusion function method and the Runge–Kutta method. Finally, the influence of the random interval parameters of meshing stiffness, input torque, and transmission error as well as backlash on the vibration velocity interval and transmission reliability of the gear transmission system are studied. The analysis results show that the three types of excitations have different effects on the dynamic characteristics. To be specific, the effects of uncertain parameters on the dynamic characteristics can be ordered as meshing stiffness, input torque, backlash, and transmission error in sequence from the strongest to the weakest. The present study may serve as a sound theoretical basis and can provide references for the design and vibration control of spur gear transmission systems.