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Meshing analysis and optimization for plane-generated enveloping toroid hourglass worm drive

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Abstract

Optimal design parameter combination and transmission optimization for plane-generated enveloping toroid hourglass worm drive are proposed. The modeling frame and mathematical model of the worm were constructed first to provide a perfect transmission. Then, the mathematical representations of transmission performance, including lubrication angle, induced normal curvature, and length of meshing line for worm drive, were derived according to differential geometry and coordinate transformation approach. In addition, the influence of various design parameters on transmission performance was associated with main parameters, and the influence of the main parameters on transmission was evaluated. Next, a multivariate transmission optimization considering lubrication effect, bearing capacity and contact strength was conducted in view of the whole meshing cycle. The optimal global solution of the multivariate optimization model was also evaluated using a genetic algorithm. Calculation and experimental results indicated the optimization study was in good agreement with experimental results. Finally, the comprehensive transmission performance of the worm drive has an increase of 9.2 %.

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Abbreviations

Rot z (-π/2) :

Coordinate transformation matrix rotates around z-axis

α σ :

Lubrication angle

σ H :

Hertzian stress

B ca :

Contact load per unit meshing line

Z E :

Coefficient of elastic influence

k σ :

Induced normal curvature of worm drive

Ψ :

Bound function that avoids interference and undercut

L j :

Length of meshing lines of worm

k 1 :

Coefficient of base circle of tool rest (reference circle of worm wheel)

k 2 :

Coefficient of reference circle of worm

Mα σ :

Average lubrication angle of all meshing points

Mk σ :

Average induced normal curvature

ML :

Average length of all meshing lines

B b :

Bearing capacity before optimization

B a :

Bearing capacity after optimization

L Tb :

Average lubrication performance before optimization

L Ta :

Average lubrication performance after optimization

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Acknowledgments

The authors would like to acknowledge the support of the National Natural Science Foundation of China (No. 51675393), Hubei Province Key Science Foundation of China (No. D20192903, 2021BGE023) and Huanggang Science Foundation of China (No. XQYF2020000031). The authors would also like to express their acknowledgment to the reviewers and editors for their insightful comments and suggestions.

Author information

Authors and Affiliations

  1. School of Electromechanical and Automobile Engineering, Huanggang Normal University, Huanggang, China

    Zhi Liu, Qingmeng Wang & Qianju Cheng

  2. School of Mechanical and Electronic Engineering, Wuhan University of Technology, Wuhan, China

    Hong Lu & Zhangjie Li

Authors
  1. Zhi Liu
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  2. Hong Lu
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  3. Qingmeng Wang
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  4. Zhangjie Li
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  5. Qianju Cheng
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Corresponding author

Correspondence to Zhi Liu.

Additional information

Zhi Liu works as a Professor at Huang-gang Normal University. He received his Ph.D. at Wuhan University of Technology in China. His research interests include digital design and manufacture of complicated transmission mechanisms and systems.

Hong Lu works as a Professor at Wuhan University of Technology. She received her Ph.D. at Wuhan University of Technology in China. Her research interests include CAD, CAM, and control of mechanical component and equipment.

Qingmeng Wang is a Lecturer of Huanggang Normal University. He received his Ph.D. in Materials Science and Engineering at Wuhan University of Technology. His research interests include new energy devices, solar thermal power generation, and alloy materials.

Zhangjie Li is a Ph.D. candidate at the School of Mechanical and Electrical Engineering, Wuhan University of Technology. He received his Master’s degree in Wuhan University of Technology, China. His research interests include mechanical dynamics and systems monitoring and control.

Qianju Cheng is a Lecturer of Huang-gang Normal University. He received his Ph.D. in Mechanical Engineering from Harbin Engineering University. His research interests include nonlinear vibration, energy harvesting, and intelligent manufacturing.

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Liu, Z., Lu, H., Wang, Q. et al. Meshing analysis and optimization for plane-generated enveloping toroid hourglass worm drive. J Mech Sci Technol 35, 3069–3080 (2021). https://doi.org/10.1007/s12206-021-0629-6

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  • DOI: https://doi.org/10.1007/s12206-021-0629-6

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