Coupled Analysis Of Dynamics And Fracture Mechanics Of Cracked Gear Transmission System

Gear transmission system is one of the most popular transmission systems and widely used in mechanical transmission. Mechanical motion and high power are transferred when gearing transmission system works and periodic varying force is applied on the meshing gear teeth. Fatigue crack or fractures often occur in the root of teeth. Hence it is necessary to study the problems of dynamics and fracture mechanics for the gear transmission system. A spur gear transmission system is studied in this thesis. The program to solve the motion differential equation of the systems is developed in MATLAB language. Periodic varying force on the teeth surface in one mesh cycle is calculated by the program. The two-dimensional fracture models for the cracked tooth are established in ANSYS, and the dynamic stress intensive factors of the cracked tooth are calculated by dynamically applying the periodic varying force on the surface of the tooth. The calculating result is useful to predicting residual life for the cracked gear.The cracked beam theory is applied on solving the time-varying stiffness of cracked gear transmission system. And the gear with the tooth root crack is studied as the research object. The dynamics model is established by considering the gear teeth as a cantilever beam. The numerical method is used to solve the differential equations of the crack-free vibration of gear system, so a displacement response of a gear vibration cycle is got. In the above calculation process, time-varying stiffness which are changed along with the meshing line and fixing damping coefficient are considered. Then the computer simulation of dynamic properties of the cracked gear is made. The change rules are got though above two ways and a good foundation for recognition system of the crack is provided, which have a good value to diagnose the damage of the gear transmission system.Fracture mechanics analysis of the gear teeth is based on the calculation results of dynamics analysis. The variation rules along with gear meshing line of periodic varying force on the teeth surface and the gear load angle are obtained using the dynamic analysis of gear transmission system. Then the program to finite element analytical calculation is developed by the software ANSYS, and the dynamic crack intensity factors of the cracked tooth are calculated by APDL language.Within solving the problem of the coupled analysis of dynamics and fracture mechanics of the gear, according to the proposed studying with coupling method, the different crack depth of dynamic response in a gear system should be calculated firstly. And using the same crack depth of dynamic result to calculate the crack-tip stress intensity factor of corresponding crack depth, so the results of changes from different results of dynamic fracture mechanics are to be acquired. At last, according to Paris formula and the results which is calculated, further analysis and calculation of the crack residual life is made.Fracture characteristics of the crack were calculated by applying dynamic load, which had been calculated from the dynamic simulation model on the meshing line of the gear tooth surface. The calculation results were more accurate and have certain significance engineering value for cracking gear fault diagnosis and maintenance of the gear transmission system.