Computational Studies on Mesh Stiffness of Paralleled Helical Beveloid Gear Pair
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International Journal of Precision Engineering and Manufacturing https://doi.org/10.1007/s12541-020-00452-3
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Computational Studies on Mesh Stiffness of Paralleled Helical Beveloid Gear Pair Ruihua Sun1 · Chaosheng Song1 · Caichao Zhu1 · Yawen Wang2 · Xingyu Yang1 Received: 15 September 2019 / Revised: 9 November 2020 / Accepted: 27 November 2020 © Korean Society for Precision Engineering 2020
Abstract Considering the asymmetrical left and right tooth profiles including the transient curve at the tooth root region and the varying thickness along the axial direction due to the cone angle, we build the accurate profile curve model including the transient curve at the tooth root of helical beveloid gear with machining parameters to solve the problem of non-applicability of real digital model. According to the feature of gear shape varying along tooth width direction, we introduced the slicing method and derived its grouping formula. Finally, the efficient and accurate slicing-based mesh stiffness calculation model of paralleled helical beveloid gears was proposed using potential energy theory. Then, mesh stiffness was calculated using finite element contact model for comparison and verification. Finally, the impacts of macro geometry parameters including cone angle, normal pressure angle, helix angle, tooth width and addendum coefficient on single and total mesh stiffness were analyzed. The calculated mesh stiffness correlates well with the results from FEM with the maximum peak error is 4.8%. Results show that the tooth width shows an obvious incremental impact on average total mesh stiffness. When the pressure angle, helix angle, cone angle and addendum coefficient increase, the average total mesh stiffness increases first and then decreases. For the fluctuating value, it increases as the tooth width, helix angle and cone angle increase. However, the pressure angle and addendum coefficient show an opposite impact on the fluctuating value. Keywords Helical beveloid gear · Parallel axis · Mesh stiffness · Slicing model · Asymmetrical profile
1 Introduction The helical beveloid gear transmission, whose backlash can be adjusted by the axial shifting without changing the center distance, is suitable for the precision transmission because of the linear profile shift coefficient along tooth width direction. Expect for the geometry characteristics, the dynamic characteristics are also directly related to its transmission performance. Computational method of mesh stiffness, which is a key parameter for the dynamic characteristic, naturally drew lots of attention of researchers. Methods of calculating mesh stiffness can be concluded as two kinds, finite element method and analytical method.
* Chaosheng Song [email protected] 1
The State Key Laboratory of Mechanical Transmissions, Chongqing University, Chongqing 400030, China
Department of Mechanical and Aerospace Engineering, University of Texas at Arlington, Arlington, TX 76019, USA
2
Studies about finite element method focus on the esta
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