Finite Element Analysis of Spur Gear Transmission Error

Abstract

The transmission error is the main source of vibration and noise in the gearbox between the mating gears. The term transmission error mainly describes the difference in the actual and theoretical positions of a driving and a driven gears. With knowledge of the proper running conditions of the gear members, it is possible to minimize vibration and noise level with proper design of gear members. There are two main reasons for transmission error to occur. First is due to the manufacturing defects and errors in mounting. Designers mainly tries to reduces transmission error by change of gear tooth geometry, and second mainly due to the elastic deflections under loading. This report mainly discusses the transmission error analysis of spur gears with involute profile using nonlinear Finite Element analysis. For obtaining a gear tooth geometry, a program for the profile of involute spur gear has been developed in Microsoft Excel using Macros module in Visual Basic language for any number of teeth, module and Pressure angles. Also for the simplification in compilation a form page is developed and linked with the program prepared in Visual Studio using C# language. For establishing the procedure of nonlinear contact problem using ANSYS work bench, initially problem has been solved with two cylinders. The results generated have been validated with the theoretical results. The results obtained for contact stress with FE analysis are in close agreement with the theoretical results. The results for the transmission error for 14.5 o, 20 o and 25 o pressure angle gears including various applied moments of 5Nm, 25Nm, 50Nm, 75Nm for the complete cycle of meshing of gear members have been obtained. It has been observed that the magnitude of the transmission error is directly proportional to the applied moment and transmission error also changes during the complete cycle. The effect of pressure angle on transmission error has also been studied. It can be seen that with 25o pressure angle deformation, the transmission errors are very less due to wider base of the gear tooth at the root, and with 14.5 pressure angle the transmission error is maximum.