Study On Dynamic Problems Of Gear Transmission System With Cracked Dedendum And Axial Contact Ratio

One of the main failure modes of the involute spur gear is the bending fatigue due to the cracked dedendum.However the cracked dedendum cannot be found easily for the gear transmission system is often in the sealed gearbox.Because the gears with cracked dedendum still have remaining life,it is important to study the dynamic problems of the gear transmission system with cracked dedendum to the prediction of the remaining life and the malfunction diagnose of gear transmission system.For a long time,improving the bearing capacity and dynamic performance of involute spur gear transmission systems has been a hot issue for engineers.As is known to all,an effective way is to improving the contact ratio of the gear transmission system.For the above reasons,the spur gear transmission system with axial contact ratio and cracked dedendum is studied in this paper.After the meshing process of the system is analyzed,the total time-varying mesh stiffness of the gear transmission system is calculated.The dynamic model of torsional vibration with single degree of freedom is established,and Runge-Kutta method is applied to solve the equation in order to obtain the response of the normal vibration displacement,velocity and the normal force of the system.The key problem is to calculate the time-varying mesh stiffness of the gear with the cracked dedendum.A novel energy method is proposed.The relationship between the stress intensity factors and the energy release rate can be used to obtain the energy release rate of the cracked dedendum,thereby the free energy of the crack surface is solved.Then the time-varying mesh stiffness of the gear with cracked dedendum can be calculated by the principle of energy conservation.The weight function method is applied to solve the stress intensity factors of the cracked dedendum.The finite width plate with an edged crack is selected to calculate the analytical expression of the stress intensity factor at the reference load.The stress at the virtual crack position of the dedendum is solved by the material mechanics method.The stress intensity factors of the cracked dedendum is obtained by the weight function method on the whole gear meshing process from beginning to end.The calculation results are reasonable to compared with the results obtained by the finite element method.The calculation accuracy of the weight function is evaluated by the green function method.The calculation results show that the solution efficiency of weight function method is high,the stress intensity factors of the cracked dedendum increase nonlinearly with the dedendum crack length and are closely related to the magnitude and position of the normal force during the whole gear meshing process.The crack length of dedendum has a great influence on the gear mesh stiffness,the gear mesh stiffness decreases as the crack length increases.The bearing capacity and dynamic performance of the gear transmission system with axial contact ratio and different crack lengths have a significant improvement,the varying amplitude of the gear mesh stiffness is reduced by nearly one time compared with the standard involute spur gear.Meanwhile the amplitudes of the normal vibration displacement,velocity and the normal force peaks decrease remarkably.The gear transmission system with axial contact ratio studied in this paper has a significant improvement in damping effect and bearing capacity,and almost all the advantages for the standard spur gear is retained,its application prospect is attractive in mechanical engineering.