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Spur gear time-varying mesh stiffness considering meshing phase difference caused by angle misalignment error

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Abstract

Angle misalignment error is a common issue in gear transmission systems that can alter the contact state between gear pairs and change their internal excitation. This paper establishes a time-varying mesh stiffness (TVMS) iterative model considering the change of meshing phase difference caused by angle misalignment error. The model considers the effects of torsional deformation, nonlinear contact, and friction excitation of spur gears. The proposed model is verified by finite element method (FEM). This study presents a simulation and analysis of the impact of misalignment error and load on the TVMS of gear teeth. The results show that the proposed model agrees with FEM results, and as the misalignment angle increases, the percentage difference of TVMS also increases nonlinearly. In addition, with an increase in load, the TVMS in the vertical direction increases more significantly. These findings provide a theoretical basis for understanding the influence mechanism of angle misalignment error.

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Abbreviations

\(\alpha_{1i}\) :

Meshing angle of the i-th gear teeth

A x :

The area of the section

b i :

Distance from gear end face to shaft end face

d i :

The distance from the tooth force to the origin

f :

Gear tooth friction force

F a/ F b :

The theoretical axial compression and shear forces decomposed by meshing force F

\( F^{\prime}_{{ai}} \)/\(F^{\prime}_{{bi}}\) :

The actually axial compression and shear forces along the center line

h i :

The distance from the meshing point of section i to the center line of half tooth thickness

h x :

The distance between the point on the tooth curve corresponding to the section

I x :

The area moment of inertia of the section

G i/ P i :

The intersection of the gear and pinion profile and the meshing line of i-th slice gear

k bi/ k si/ k ai/ k hi/ k fi :

Stiffness of bending/shear/axial compression/contact/fillet foundation of gear slice

k ci :

Coupling stiffness between the i-th and (i + 1)-th slices

k ei :

Equivalent stiffness on the meshing line

k gn :

Slice stiffness of gear

k m :

Time-varying meshing stiffness

k ti :

Stiffness of torsion

T :

Applied torque on the driving gear

T rt :

Matrix of global coordinates into local coordinates

r p/ r g :

Radius of dividing circle of gear and pinion

W :

Tooth width

x :

The distance from the tooth root

\(\theta_{x}\)/\(\theta_{y}\)/\(\xi\) :

Angle misalignment error in x/ y/ comprehensive direction

\(\delta\) :

Actual deformation of slice gear

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Acknowledgements

This study was funded by State Key Program of National Natural Science Foundation of China (Grant No. 52035002), the Chongqing Natural Science Foundation (Grant No. CSTB2022NSCQ-MSX1243) and Anhui Natural Science Foundation (2108085QE224).

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Authors and Affiliations

  1. State Key Laboratory of Mechanical Transmission, Chongqing University, Chongqing, 400044, People’s Republic of China

    Desheng Zou, Liming Wang, Wennian Yu, Wenchao Pan & Yimin Shao

  2. College of Mechanical and Vehicle Engineering, Chongqing University, Chongqing, 400044, People’s Republic of China

    Desheng Zou, Liming Wang, Wennian Yu, Wenchao Pan & Yimin Shao

  3. Chongqing Gearbox Co., Ltd, Chongqing, 400044, People’s Republic of China

    Hui Ye

  4. Department of Mechanical and Materials Engineering, Queen’s University, Kingston, ON, K7L 3N6, Canada

    Mechefske Chris

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  1. Desheng Zou
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  2. Liming Wang
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Contributions

D.Z.: Conceptualization, Methodology, Writing—original draft. L.W.: Conceptualization, Writing-review & editing. H.Y.: Writing-review & editing. W.Y.: Writing-review & editing. W.P.: Writing-review & editing. Y.S.: Project administration. M.C.: Writing-review & editing.

Corresponding author

Correspondence to Liming Wang.

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The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: We declare that we do not have any commercial or associative interest that represents a conflict of interest in connection with the work submitted.

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Zou, D., Wang, L., Ye, H. et al. Spur gear time-varying mesh stiffness considering meshing phase difference caused by angle misalignment error. Meccanica 59, 475–490 (2024). https://doi.org/10.1007/s11012-024-01762-w

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