Analysis of vibration characteristics of spur gear pair considering the randomness of error and tooth surface friction

With the development of spur gear transmission system towards high speed and high power density, how to solve vibration and noise reduction has become the primary problem of spur gear transmission with high efficiency, low noise and high durability. The changes of gear processing, assembly form and operating environment will lead to the random characteristics of the comprehensive transmission error and the micro morphology of the tooth surface of the spur cylindrical gear, resulting in the complex dynamic behavior of the spur cylindrical gear system. In engineering practice, the transmission error uncertainty of spur gear transmission in the process of machining and assembly leads to a certain randomness of tooth surface morphology. The tooth surface morphology affects the tooth surface friction, and the tooth surface friction increases with the increase of tooth surface roughness. The transmission error and tooth friction parameters of spur gear affect each other. The transmission dynamic characteristics of spur gear under the comprehensive consideration of random error and tooth friction parameters are not clear. Therefore, the research on the dynamics of Spur Gear Considering the random comprehensive transmission error and tooth surface friction parameters of spur gear provides important theoretical support for the subsequent reliability analysis and dynamic optimization of spur gear transmission.

Scholars at home and abroad have done a lot of theoretical and Experimental Research on the vibration characteristics of spur gear system under different forms of excitation. Some scholars consider the influence of random error on the dynamics of spur gear system, but the friction factor is not considered in the above research. Some scholars have studied the spur gear system in the field of tooth surface friction, but in order to better discuss the relationship between friction and dynamics, scholars began to conduct in-depth discussion on the random parameters that interfere with the friction characteristics of gears.

In recent years, scholars at home and abroad have explored the random dynamic characteristics of spur gears by comprehensively comparing the action mechanism of random error and tooth surface friction. Among them, Huang Kang and others established the mathematical model of tooth surface roughness profile based on fractal theory, and established the dynamic model of spur gears affected by static error under the action of tooth surface random roughness, The influence of tooth surface roughness on the dynamic behavior of spur gear system is studied. Mo w et al. Combined the vibration equivalent displacement of the active and passive gears with the gear error, and proposed a simple and general method to calculate the length of the contact line, friction force and friction torque according to the geometric relationship of the helical gear system.

To sum up, the current research characteristics are as follows: ① synthesize the comprehensive gear tooth error based on the deterministic theory method, ignoring the time-varying of gear surface friction; ② The existing models do not consider the comprehensive influence of error and tooth surface friction randomness on the dynamic characteristics of spur gears. Therefore, combining probability statistics and lumped mass method, the error and tooth surface friction parameters are mathematically characterized in the form of random variables, and a 3-DOF bending torsional coupling vibration model of spur cylindrical gear pair considering the randomness of tooth surface friction parameters under random error is established to analyze the influence of random parameters on the dynamic response of the system, It provides a theoretical basis for the subsequent dynamic optimization of spur gear transmission system.

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