Mesh Stiffness Calculation And Dynamic Characteristic Study Of Gear Pair With Body Crack

Gearboxes are the most commonly used transmission system to provide speed and torque from one rotating power source to another device.However,due to the harsh operating environment of gearboxes,various failures may occur,such as tooth root cracking,tooth surface wear,tooth surface pitting,etc.Gearbox failure can cause great damage to the entire system,and tooth root cracking accounts for a large proportion of gearbox failure.Therefore,it is of great engineering significance to master the formation mechanism,preventive measures and expansion path of tooth root crack and to understand the impact of crack on the dynamic characteristics of gear subsets for early fault detection,identification and diagnosis of gearboxes.The time-varying meshing stiffness of a gear pair is one of the main internal excitations of a gear transmission.Accurate calculation of the time-varying meshing stiffness of a gear pair and the establishment of a dynamic model that is more consistent with the actual operating conditions are the keys to accurate analysis of the dynamic characteristics,and are the prerequisites for vibration and noise reduction and fault diagnosis of gear transmission systems.This paper is devoted to the study of the timevarying mesh stiffness and dynamic characteristics of cracked gear pairs.The main research contents are as follows:(1)Based on the principle of potential energy method,the calculation formula of the meshing stiffness of standard straight cylindrical gear pair with accurate tooth profile is derived;the change law of the five stiffnesses of the master and driven wheels during the gear meshing process and the relationship between the meshing stiffness of the gear pair when single and double teeth are meshed are analyzed respectively;the comparative analysis of the local contact stiffness,single tooth and comprehensive meshing stiffness under different load torques is given.(2)Considering the influence of crack defects on gear stiffness,firstly,the base body stiffness and gear tooth stiffness of gears with root crack defects are calculated and analyzed using the principle of potential energy method;secondly,an analytical-finite element framework for calculating the mesh stiffness of gear pairs with base body crack defects is constructed based on the principle of potential energy method and finite element theory for the case of crack extension to the gear base.Finally,a standard cylindrical spur gear model with accurate tooth profile curves is established by using APDL of ANSYS,and the finite element results are compared with the method in the paper to prove the feasibility of the method in the paper.(3)Firstly,according to the actual application scenario of the gearbox,a five-degreeof-freedom dynamics model with fluctuating speed as the external excitation source and the coupling stiffness of the shaft and bearing as the support stiffness is established,taking into account the characteristic that the engine output speed varies periodically;secondly,the numerical solution of the nonlinear differential equations corresponding to the model is given;finally,the key parameters in the dynamics model are calculated.(4)The time-varying meshing stiffness of the healthy gear pair and the gear pair with cracked matrix are introduced into the above dynamics model,and the dynamic transmission error characteristics caused by the coupling support stiffness and the dynamic transmission error characteristics caused by the matrix crack,the dynamic meshing force characteristics and the tooth surface friction characteristics are analyzed.When cracked gear teeth are involved in meshing,the dynamic transmission error characteristics and dynamic meshing force characteristics will have a shock every one rotation cycle,and the shock increases with the increase of crack length;the matrix crack will cause the dynamic transmission error to have a side band at its meshing frequency and its harmonics,and the side band will become obvious with the increase of crack length;the residual signal of dynamic transmission error is more favorable for crack fault diagnosis;when the active wheel When there are fluctuations in the rotational speed and the rotational speed is too high,it is easier to perform logarithmic processing on the frequency domain signal of the dynamic transmission error for fault diagnosis.The results of this paper have some guiding significance for the strength design of gears and the fault diagnosis of gearboxes.