Advertisement

Optimization of the one stage cycloidal gearbox as a non-linear least squares problem

  • Roman KrólEmail author
  • Marcin Wikło
  • Krzysztof Olejarczyk
  • Krzysztof Kołodziejczyk
  • Albert Zieja
Conference paper
Part of the Mechanisms and Machine Science book series (Mechan. Machine Science, volume 73)

Abstract

Cycloidal gearboxes are mechanisms which can work under higher loading conditions than other sprockets with comparable dimensions. Cycloidal gears can be smaller than other gears because in these complex mechanisms many lobes work at the same time. In this article, Levenberg-Marquardt algorithm for solving non-linear least squares problems is used for optimization of the one stage cycloidal gearbox. The results are compared with the Steepest Descent Method applied for the same theoretical model of the optimized gear. Application of gradient based optimization method for cycloidal gears is innovative. In other works, a genetical algorithm approach is used, but there are many simplifications in an objective function and constraints concerning the shape of the cycloidal gear. In this paper, the function for the accurate calculation of the cycloidal gear volume is presented. Optimization method was implemented in MATLAB software. In the presented method: the volume of the cycloidal gear, the contact stress in the internal sleeves, the contact stress at the lobes and the contact stress at the pits of the cycloidal gear are minimized with the box constraints implemented using the Penalty Function Method.

Keywords

Cycloidal gearbox Levenberg-Marquardt algorithm Steepest Descent Method Optimization Penalty Function Method 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    X. Li, C. Li, Y. Wang, B. Chen, and T. C. Lim, “Analysis of a Cycloid Speed Reducer Considering Tooth Profile Modification and Clearance-Fit Output Mechanism,” J. Mech. Des., vol. 139, no. 3, p. 033303, 2017.CrossRefGoogle Scholar
  2. [2]
    C. F. Hsieh, “Traditional versus improved designs for cycloidal speed reducers with a small tooth difference: The effect on dynamics,” Mech. Mach. Theory, vol. 86, pp. 15–35, 2015.CrossRefGoogle Scholar
  3. [3]
    Y. W. Hwang and C. F. Hsieh, “Geometric Design Using Hypotrochoid and Nonundercutting Conditions for an Internal Cycloidal Gear,” J. Mech. Des., vol. 129, no. 4, pp. 413–420, 2006.CrossRefGoogle Scholar
  4. [4]
    Z. Y. Ren, S. M. Mao, W. C. Guo, and Z. Guo, “Tooth modification and dynamic performance of the cycloidal drive,” Mech. Syst. Signal Process., vol. 85, no. September 2016, pp. 857–866, 2017.CrossRefGoogle Scholar
  5. [5]
    M. Blagojevic, N. Marjanovic, Z. Djordjevic, B. Stojanovic, and A. Disic, “A New Design of a Two-Stage Cycloidal Speed Reducer,” J. Mech. Des., vol. 133, no. 8, p. 085001, 2011.CrossRefGoogle Scholar
  6. [6]
    J. W. Sensinger, “Unified Approach to Cycloid Drive Profile, Stress, and Efficiency Optimization,” J. Mech. Des., vol. 132, no. 2, p. 024503, 2010.CrossRefGoogle Scholar
  7. [7]
    J. Wang, S. Luo, and D. Su, “Multi-objective optimal design of cycloid speed reducer based on genetic algorithm,” Mech. Mach. Theory, vol. 102, no. 600, pp. 135–148, 2016.CrossRefGoogle Scholar
  8. [8]
    N. Kostić, M. Blagojević, N. Petrović, M. Matejić, and N. Marjanović, “Determination of real clearances between cycloidal speed reducer elements by the application of heuristic optimization,” Trans. Famena, vol. 42, no. 1, 2018.CrossRefGoogle Scholar
  9. [9]
    Król R., Software for the one stage cycloidal gearbox optimization using the Steepest Descent Method and Levenberg-Marquardt algorithm (MATLAB scripts), DOI:  https://doi.org/10.5281/zenodo.2166718

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Faculty of Mechanical EngineeringUniversity of Technology and Humanities in RadomRadomPoland

Personalised recommendations