Gear meshing algorithm for spur gears

[tches-co]

Gear Meshing Stiffness Implementation

Commit hash: 8925a74

This project is currently under development, and we welcome feedback for further improvement. Below is a detailed explanation of the implementation, current progress, and areas for enhancement.

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Overview

The implementation of gear meshing stiffness is based on the methodologies proposed by:

• Sainsot et al. (2004): Focused on bidimensional analytical formulas considering gear body contributions.
• Ma et al. (2014): Developed time-varying mesh stiffness calculations for cracked spur gears.

The gear tooth is modeled as a cantilever beam, and meshing stiffness is calculated at each contact position using the energy method. This approach enables precise modeling of the gear’s dynamic behavior.

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Current Progress

Meshing Algorithm

The algorithm can evaluate a half-tooth profile to extract geometric parameters necessary for stiffness calculation. Below is an example of a half-tooth profile:

Stiffness Calculation

Examples of stiffness plots demonstrate the relationship between the angular displacement of the pinion (x-axis) and the stiffness of the meshing coupling (y-axis). These plots provide insights into the stiffness variations during gear rotation:

Precision Comparisons

Comparisons between the implemented algorithm and the results from both authors' methodologies indicate areas for refinement. Notably, errors tend to increase with gear tooth rotation. Addressing this issue is a current focus of our development efforts.

Examples of comparative error plots:

Integration with ROSS

Integration with other gear implementations in ROSS is not yet complete but is a key milestone we aim to achieve soon.

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Challenges and Next Steps

• Error Reduction: Refining the algorithm to minimize errors in calculating the contact point position between meshing teeth.
• Integration: Seamlessly combining the stiffness calculation module with other ROSS functionalities.
• Validation: Further benchmarking against established methodologies to ensure accuracy.

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References

• Ma, H., Song, R., Pang, X., & Wen, B. (2014)
  Time-varying mesh stiffness calculation of cracked spur gears.
  Engineering Failure Analysis, 44, 179–194.
  https://doi.org/10.1016/j.engfailanal.2014.05.018

• Sainsot, P., Velex, P., & Duverger, O. (2004)
  Contribution of gear body to tooth deflections - A new bidimensional analytical formula.
  Journal of Mechanical Design, 126(4), 748–752.
  https://doi.org/10.1115/1.1758252