Nonlinear dynamic and finite element analysis of gear teeth meshing

This research work describes the theoretical formulation and development of a two-dimensional nonlinear finite element computer program for dynamic analysis of two mating involute spur gear teeth. The program is able to handle geometry nonlinearity, structural interactive and sliding interface problems with both linear and nonlinear material properties. Gear meshing issues are solved using special local coordinate systems in the finite element formulation to eliminate the geometrically nonlinear part of motion in the gear system. A sliding interface is incorporated into FE formulation to handle the variations of constraint equations and friction between the mating gear teeth. The governing equations are solved using an explicit time integration method with a direct nodal-force computational scheme for the internal nodal forces. In the program, the dynamic response factors of gear teeth, such as stresses, strains, displacements in global coordinate system can be calculated and output at any moment as requested. Energy balance checks are used to check the fidelity of computations and to detect or arrest any incipient instabilities. The kinetic energy and internal energies of any group elements can be output which can be used to assess the distribution of damage and energy absorption in simulation. A conservative stability limitation is imposed on the time step. A subprogram is also developed to generate the finite element data for any arbitrary pair of involute gears, and its output is designed to be a part of the input file of the main FE code. Several cases are investigated in this work, and the analysis results are checked against the ones from: (1) the conventional technique in design of gears, (2) the existing FE package in SDRC Master Series and (3) the experiment of NASA Lewis Research Center, respectively.