Effect of backlash on vibration spectrum in gear boxes

An ideal gear box would produce no vibration at all because all energy would be channeled into the work to be done; but a well-designed gear box will produce low levels of inherent vibration. As the gear teeth wear, however, backlash between meshing teeth increases and this is reflected in an increase in the vibration energy. As the vibration energy is dissipated through the gear box, it excites resonances and exerts extra dynamic loads on gear teeth. It is of great interest to the maintenance engineers to predict the occurrence of backlash between gear teeth. The fact that vibration signals carry much information relating to running conditions of gear boxes can be used to solve this problem. In this study, a mathematical model was formulated to simulate the effect of backlash between gear teeth on the vibration spectrum of gear boxes. A single stage helical gear box was used to demonstrate this model. In this simulation, the transmission shafts were treated as lumped parameter systems. The elasticity of shafts, bearings, and gear teeth were also included. The grounded-chair representation was used to obtain the equations of motion that were solved using the Runge-Kutta method. The vibration spectra of the gear box system were obtained using fast Fourier transform (FFT). These spectra can be used to construct a vibration chart which, in turn, can be used to determine the proper times for maintenance of gear boxes to avoid failure of such units.