A MATHEMATICAL MODEL FOR ANALYZING THE INFLUENCE OF SHAPE DEVIATIONS AND MOUNTING ERRORS ON GEAR DYNAMIC BEHAVIOUR

• Published in: Journal of sound and vibration Vol. 191; no. 5; pp. 629 - 660
• Main Authors: Velex, P., Maatar, M.
• Format: Journal Article
• Language: English
• Published: London Elsevier Ltd 18.04.1996; Elsevier
• Subjects: Applied sciences; Drives; Engineering Sciences; Exact sciences and technology; Gears; Mechanical engineering. Machine design; Line contact; Geometrical shape; Gear drive; Three dimensional model; Equation of motion; Dynamics; Lumped parameter system; Defect; Numerical method; Non linear effect; Transmission error; Contact line
• ISSN: 0022-460X; 1095-8568
• DOI: 10.1006/jsvi.1996.0148

A comprehensive mathematical model is introduced for analyzing the influence of shape deviations and mounting errors on gear dynamics. Contact conditions for both rigid and deformable solids are used for characterizing the gear set excitation sources. The deformed state is modeled by a lumped parameter non-linear system with six degrees-of-freedom on pinion and gear. Each potential contact line on the base plane is discretized in independent elementary cells of constant stiffness and an original procedure is proposed for simultaneously solving the normal contact problem between active flanks and the equations of motion. Comparisons with several results from the literature prove the versatility of the model as static and dynamic load distributions, transmission errors and mesh stiffnesses can be evaluated from a unified approach. Finally, the interest of the methodology is illustrated by some practical problems in gear dynamics: i.e., the influence of some geometrical errors and the role of linear profile modifications on spur and helical gears.