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.
","abstract_html":"<p>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.</p>","abstract_has_math":false,"creators":["Sommer, Andrew Patrick"],"institution":null,"degree_name":"MS in Mechanical Engineering","degree_level":null,"degree_discipline":"Mechanical Engineering","degree_department":null,"school":null,"contributors":["Xi Wu"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2011,"date_issued":"2011-09-01T07:00:00Z","date_published":"2011-09-01T07:00:00Z","updated_at":"2026-07-24T01:32:42Z","subjects":["vibration health monitoring","malfunction diagnostics","multi-body kinematic model","epicyclic transmission","backlash","joint time-frequency analysis","Acoustics, Dynamics, and Controls","Applied Mechanics","Computer-Aided Engineering and Design","Dynamics and Dynamical Systems","Electro-Mechanical Systems","Engineering Mechanics","Mechanics of Materials","Propulsion and Power","Signal Processing"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["10.15368/theses.2011.186"],"render_values":[{"text":"10.15368/theses.2011.186","href":"https://doi.org/10.15368/theses.2011.186","code":true}]}]},"links":{"outbound_url":"https://digitalcommons.calpoly.edu/theses/631","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Xi Wu"]},{"key":"dc:creator","label":"Author","values":["Sommer, Andrew Patrick"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2011-09-25T07:00:00Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mechanical Engineering"]},{"key":"thesis:degree_name","label":"Degree Name","values":["MS in Mechanical Engineering"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["vibration health monitoring","malfunction diagnostics","multi-body kinematic model","epicyclic transmission","backlash","joint time-frequency analysis","Acoustics, Dynamics, and Controls","Applied Mechanics","Computer-Aided Engineering and Design","Dynamics and Dynamical Systems","Electro-Mechanical Systems","Engineering Mechanics","Mechanics of Materials","Propulsion and Power","Signal Processing"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://digitalcommons.calpoly.edu/theses/631","10.15368/theses.2011.186"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["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.
"]},{"key":"dc:title","label":"Title","values":["Vibration-Based Health Monitoring of Multiple-Stage Gear Train and Differential Planetary Transmission Involving Teeth Damage and Backlash Nonlinearity"]}]}],"canonical_facts":{"dc:contributor":["Xi Wu"],"dc:creator":["Sommer, Andrew Patrick"],"dc:date.available":["2011-09-25T07:00:00Z"],"dc:description.abstract":["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.
"],"dc:identifier":["https://digitalcommons.calpoly.edu/theses/631","10.15368/theses.2011.186"],"dc:subject":["vibration health monitoring","malfunction diagnostics","multi-body kinematic model","epicyclic transmission","backlash","joint time-frequency analysis","Acoustics, Dynamics, and Controls","Applied Mechanics","Computer-Aided Engineering and Design","Dynamics and Dynamical Systems","Electro-Mechanical Systems","Engineering Mechanics","Mechanics of Materials","Propulsion and Power","Signal Processing"],"dc:title":["Vibration-Based Health Monitoring of Multiple-Stage Gear Train and Differential Planetary Transmission Involving Teeth Damage and Backlash Nonlinearity"],"thesis:degree_discipline":["Mechanical Engineering"],"thesis:degree_name":["MS in Mechanical Engineering"]},"updated_at":"2026-07-24T01:32:42Z"}