A transmission system is a complex structure consisting of a driver (motor), many shafts, gears, couplers and load. The shafts and gears may be held to the housing with the help of bearings. The primary objective of this work is to obtain the natural frequencies and mode shapes of this complex system and then, obtain the dynamic response of the system due to external excitations such as transmission error, friction force and shuttling moment.
A finite element formulation is chosen for the above purpose and it can be used to transmissions using parallel axis shafts with spur and/or helical gears. In the program developed, shafts are modeled as beam elements with six degrees of freedom per node. The effect of bearings modeled by the use of 6x6 bearing stiffness matrix. The driver and load are modeled as discrete inertias, couplers as discrete inertias with a diagonal coupler stiffness matrix. The nodes between meshing gears are appropriately coupled together using the corresponding mesh stiffness. The complete system, involving many simultaneous equations, is formulated as an eigenvalue problem and first few natural frequencies and corresponding mode shapes are determined and then external excitations are applied and the frequency response of various degrees of freedom is obtained and later, this solution is used to calculate the dynamic transmission error, mesh force and bearing forces at various excitation frequencies. Using the program developed, a single stage reduction system, and an idler gear system are analyzed and the results are compared with already in-use programs like GearVib, developed at OSU Gearlab.
A secondary objective of this thesis is to develop a user-friendly analytical computer program for thin-rimmed spur or helical gears. A windows based front end is added to the thin rim program developed at OSU Gearlab and boundary conditions such as adjacent teeth effects are modified and parameters such as the number of sectors to be modeled in the program are studied for spur and helical gears.