A Generalized Dynamic Model For Parallel Shaft Gear Transmissions And The Influences Of Dynamic Excitations

Gear transmission is a complex mechanical system which consists of elastic gear pairs,shafts, bearings and housing. Due to the advantages of compact structure, high efficiency andlong life, gear transmission is widely used in most areas of national industries. The contactcharacteristics and dynamic performance are greatly affected by elastic deformation,manufacturing error and meshing impact during the meshing process. With the requirement toimprove the performance of mechanical systems, gear transmission tends to be high-speed,heavy-duty and low-noise. Therefore, it is very helpful to acquire the essences of geardynamics if the influence of various dynamic excitations and working conditions on thedynamic response of gear system is well studied, and it will be of great significance for thedesign improvement of low-noise gear system.In this study, a loaded tooth contact model is built to calculate the transmission error andmesh stiffness, and a universal dynamic model for different types of parallel shaft gearsystems is proposed. The influences of different internal excitations on dynamic responses arestudied systematically. The main research works and achievements are as follows:1. Combined with the finite element method (FEM) and analytical contact mechanics, amodified loaded tooth contact model is built to calculate the transmission error and meshstiffness. The nonlinear contact problem can be well considered in the modified model.Compared with the conventional FEM, the proposed method has higher computationalefficiency, better convergence and consistency. The method for determining the integratedmeshing error is given and the relation between tooth deformation, tooth error andtransmission error is accordingly clarified. It is found that the mesh stiffness is increasingnonlinearly with the increase of transmitted torque. The structure parameters will change thestiffness of gear body, thereby changing the mesh stiffness. When a single basic parameterchanges, the mesh stiffness can be approximated by the total length of contact lines. The meshstiffness will have smaller fluctuation when the transverse contact ratio or overlap ratio isclose to an integer, while it will have larger fluctuation when total contact ratio is close to aninteger.2. A universal dynamic model, which has fully coupled the vibrations of gear, shaft,bearing and housing, is proposed based on the generalized finite element method. Thedynamic model with12degrees of freedom for a gear pair is built to simulate the flexural,torsional, axial and pendular vibrations when the gears have different hands or rotationaldirections. The interactions between elastic shafts, gears and housing are considered in thismodel. The assembly procedure of the overall equations of motion, the method to solve the differential equations and the post processing are presented in details. The proposed method isapplicable to the rapid dynamic modeling and analyses for different configurations and geartypes of parallel shaft gear systems using a standardized computer program. The model isvalidated by comparing the simulation results with experimental data.3. Considering the internal excitations of time-varying mesh stiffness, gear error andmeshing impact, the influences of different forms of profile deviation, pitch deviation andhelix deviation on dynamic mesh force are investigated. The results show that the profiledeviation and pitch deviation both have great influence on vibrations of spur gears and helicalgears. The helix deviation has a significant effect on helical gears but littile effect on spurgears. The concave forms of profile deviation and helix deviation will produce larger dynamicfoctor, while the convex forms will produce smaller dynamic factor. The negative pitchdeviation on the wheel will cause larger vibration than positive pitch deviation. Comparedwith the meshing impact, the transmission error is the main excitation that causes unwantedvibrations.4. The effects of gear errors on the mesh stiffness, transmission error and dynamicresponse of the system are studied. It is found that the tendencies of actual total length ofcontact lines and actual mesh stiffness are similar to each other. The tooth error is thedominating factor in the transmission error and system vibration under light load condition,while the tooth deformation is crutial factor under heavy load condition. The vibration of thesystem will be decreased when the gears have higher accuracy, and greater improvement canbe expected to achieve under light load condition. The critical torque when the tooth surfacejust realizes full contact is found. The actual contact ratio is smaller than the theoretical onewhen the applied torque is lower than the critical torque, and the system will produce greaterdynamic foacors. When the applied torque is greater than the critical torque, the acturalcontact ratio is equal to the theoretical one, and the dynamic factor will not change.5. The patial contact loss due to gear error and dynamic displacement is introduced. Thedefinition of dynamic mesh stiffness and its calculation method is presented. The results showthat the dynamic and static mesh stiffnesses differ significantly when the system has largedynamic displacement. In addition, it is observed that even in heavy load condition, the partialcontact loss will turn to total contact loss near resonance.Finally, some conclusions and comments are given and the further research works arepointed out.