The accurate modeling of lead crowning in gear systems is crucial due to its significant impact on dynamic behavior. This type of modification profoundly shapes gear dynamics by reducing mean mesh stiffness, changing mesh harmonics, and potentially eliciting nonlinear softening and jump phenomena. This study presents a versatile dynamic torsional model for spur and helical gears that embeds crowning effects through a slice-based formulation. A load-dependent stiffness field is first obtained for unmodified spur gears via an iterative tooth-load-sharing algorithm; for helical gears the stiffness of an equivalent spur gear is integrated efficiently into the helical slice model. Implemented in MATLAB/Simscape language, the framework automatically generates multi-slice gear pairs, each endowed with position- and load-dependent stiffness and backlash. Crowning is introduced by locally tailoring slice backlash, allowing any mathematically defined flank modification. The required slice resolution is then established, followed by calculation of static transmission error and the decomposition of average and fluctuating mesh stiffness components. The former supports drivetrain modal analysis, while the latter drives the nonlinear model to predict dynamic transmission error and emergent non-linear phenomena. The approach further recovers the dynamic load distribution along the face width, pinpointing potential overstressing. Computationally efficient and readily extendable to include shaft-hub interaction and surface defects, the methodology provides a comprehensive platform for gear design optimization, performance evaluation, and fault diagnosis.

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Dynamic modeling of spur and helical gears with lead crowning through a slice-based approach

  • Giovanni Paoli,
  • Matteo Autiero,
  • Marco Cirelli,
  • Luca D’Angelo,
  • Pier Paolo Valentini

摘要

The accurate modeling of lead crowning in gear systems is crucial due to its significant impact on dynamic behavior. This type of modification profoundly shapes gear dynamics by reducing mean mesh stiffness, changing mesh harmonics, and potentially eliciting nonlinear softening and jump phenomena. This study presents a versatile dynamic torsional model for spur and helical gears that embeds crowning effects through a slice-based formulation. A load-dependent stiffness field is first obtained for unmodified spur gears via an iterative tooth-load-sharing algorithm; for helical gears the stiffness of an equivalent spur gear is integrated efficiently into the helical slice model. Implemented in MATLAB/Simscape language, the framework automatically generates multi-slice gear pairs, each endowed with position- and load-dependent stiffness and backlash. Crowning is introduced by locally tailoring slice backlash, allowing any mathematically defined flank modification. The required slice resolution is then established, followed by calculation of static transmission error and the decomposition of average and fluctuating mesh stiffness components. The former supports drivetrain modal analysis, while the latter drives the nonlinear model to predict dynamic transmission error and emergent non-linear phenomena. The approach further recovers the dynamic load distribution along the face width, pinpointing potential overstressing. Computationally efficient and readily extendable to include shaft-hub interaction and surface defects, the methodology provides a comprehensive platform for gear design optimization, performance evaluation, and fault diagnosis.