Wear Modeling And Dynamic Response Analysis Of Spur Gear

Gearbox is used more and more widely,and its role in mechanical equipment is becoming more and more important.During the operation of the gear,the amount of wear accumulates over time.Excessive wear will affect the normal meshing of the gear,and will also aggravate the vibration of the gear and cause other faults.Because the vibration response of the bearing will make the gear engage abnormally,and then affect the backlash and load,it is particularly important to consider the dynamic response of the wear gear with multi-clearance.In this paper,the involute spur gearbox is taken as the research object,and the following research is carried out:(1)Based on Hertz's contact theory and Archard's wear formula,the wear of standard installed spur gear pairs was simulated without considering bearing vibration and gear manufacturing error.Firstly,the load distribution of single-tooth and double-tooth meshing is averaged,the motion near the gear-tooth node is regarded as pure rolling,and the numerical simulation results are analyzed.Based on Weber-Banaschek method to calculate the time-varying meshing stiffness,considering the backlash,damping and time-varying stiffness,the meshing motion differential equation of single-degree-of-freedom gears is established,and the dynamic meshing force between gears is obtained.Then the numerical simulation of tooth surface wear is carried out and compared with the previous simulation based on static meshing force.The results show that the tooth profile wear based on static meshing force can not be continuously distributed,which is not correct in practice.When considering the wear of dynamic meshing force,the wear amount near the joint is almost zero,and the wear amount near the root and the top of the tooth is larger.Torque will increase the maximum wear amount of the gear teeth,and backlash has little effect on the wear amount.(2)The change of center distance of gear teeth caused by bearing clearance is deduced,and then the change of dynamic side clearance is deduced.Trigonometric function is used to simulate the wear fault of tooth surface.Torsional vibration model of a pair of meshing gear pairs is established considering the time-varying stiffness of gear teeth,bearing clearance,damping,elastic support of support system and wear.According to the comprehensive wear of tooth surface,the wear severity is divided into non-wear,slight wear and severe wear.The effects of tooth clearance,bearing clearance and comprehensive wear on the steady-state response of gear system are analyzed respectively.The results show that the bearing clearance has a great influence on the periodicity of the system vibration.The displacement response of the periodic state is larger than that of the chaotic state,and the step phenomenon appears.At low speed,the clearance has a smaller displacement response to the system.With the increase of backlash,the meshing impact between teeth increases,the amplitude increases,and a slight backlash occurs,the Continuous spectrum lines appear near the meshing frequency,and side frequency bands produced by amplitude modulation appear on both sides of bearing frequency.The wear of gear teeth makes the transmission error bigger,the side band of bearing vibration frequency disappears,and the modulated side band appears near the meshing frequency and its higher harmonic frequency.(3)Pro/E is used to build three-dimensional solid models of gears with different wear degrees.The inherent characteristics of gears without wear,slight wear and severe wear are analyzed by ANSYS Workbench.The wear makes the natural frequency of the gear increase and has little effect on the vibration mode.In the design of the gear box,the components should avoid the frequency band which may occur in the gear teeth,so as to avoid resonance.