This study demonstrates the transient and steady state dynamic loading on teeth within a two-stage gear transmission arising from backlash and geometric manufacturing errors by utilizing a nonlinear multibody dynamics software model. Backlash between gear teeth which is essential to provide better lubrication on tooth surfaces and to eliminate interference is included as a defect and a necessary part of transmission design. Torsional vibration is shown to cause teeth separation and double-sided impacts in unloaded and lightly loaded gearing drives. Vibration and impact force distinctions between backlash and combinations of transmission errors are demonstrated under different initial velocities and load conditions. The backlash and manufacturing errors in the first stage of the gear train are distinct from those of the second stage. By analyzing the signal at a location between the two stages, the mutually affected impact forces are observed from different gear pairs, a phenomenon not observed from single pair of gears. Frequency analysis shows the appearance of side band modulations as well as harmonics of the gear mesh frequency. A joint time-frequency response analysis during startup illustrates the manner in which contact forces increase during acceleration.

Planetary gear trains can be more compact and efficient as power transmissions than fixed axis gear trains but are also more complicated and less understood in terms of vibration health monitoring. A practical differential planetary gear train, which combines two inputs and one output, is studied using multi-body dynamics software. Backlash between the sun gear and planet gears are precisely specified to avoid teeth interference and undercut. In order to calculate accurate impact forces, an impact model is chosen. Tooth geometry errors are created on the sun gear. Constraints and contact forces to the model are applied as close as possible to real operating conditions. Torsional vibration induced by backlash and tooth geometry errors is shown to cause teeth separation and doublesided impacts in unloaded and lightly loaded gearing drives. Planetary gears with only backlash errors are compared to those containing both backlash and tooth defects under different kinematic and loading conditions. Time domain results show that the dynamic responses due to the combination of backlash and tooth defects depend on the interaction of many components of the differential planetary system.

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The objective of this thesis is to develop vibration-based fault detection strategies for on-line condition monitoring of gear transmission systems. The study divides the thesis into three sections. First of all, the local stresses created by a root fatigue crack on a pinion spur gear are analyzed using a quasi-static finite element model and non-linear contact mechanics simulation. Backlash between gear teeth which is essential to provide better lubrication on tooth surfaces and to eliminate interference is included as a defect and a necessary part of transmission design. The second section is dedicated to fixed axis power trains. Torsional vibration is shown to cause teeth separation and double-sided impacts in unloaded and lightly loaded gearing drives. The transient and steady-state dynamic loading on teeth within a two stage crank-slider mechanism arising from backlash and geometric manufacturing errors is investigated by utilizing a non-linear multi-body dynamics software model. The multi-body model drastically reduces the computation time required by finite element methods to simulate realistic operation. The gears are considered rigid with elastic contact surfaces defined by a penalty based non-linear contact formulation. The third section examines a practical differential planetary transmission which combines two inputs and one output. Planetary gears with only backlash errors are compared to those containing both backlash and tooth defects under different kinematic and loading conditions. Fast Fourier Transform (FFT) analysis shows the appearance of side band modulations and harmonics of the gear mesh frequency. A joint time-frequency analysis (JTFA) during start-up reveals the unique vibration patterns for fixed axis gear train and differential planetary gear, respectively, when the contact forces increase during acceleration.

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