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Centrifugal stiffening analysis of gear pair with generalized component mode synthesis and semi-analytic contact technique

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Abstract

Cantilever beam assumption is widely used to estimate gear flexibility for analytical calculation of transmission error of gear pair. Similar to the rotating beam, it is supposed that centrifugal stiffening will also affect dynamic transmission error of gear pair. This work presents an efficient computational procedure for centrifugal stiffening analysis of gear pair. As inertia centrifugal force is distributively applied on gear body, the finite element grid model of gear pair is firstly established. Then, in order to reduce large number of degrees of freedom in finite element grid, the generalized component mode synthesis is employed to establish dynamic equation of flexible gear with constant mass matrix and co-rotated constant stiffness matrix. In order to avoid highly refined grid near contact zone, the semi-analytic contact technique which incorporates advantage of penalty method and Lagrange multiplier method is employed to calculate contact force between non-matching sparse tooth face meshes. After transforming system dynamic differential algebraic equation into ordinary differential equation, dynamic contact analysis of a helical gear pair is carried out, and dynamic transmission error at different rotational speeds are compared. Inflation deformation of gear under inertia centrifugal force is shown as explanation for influence of centrifugal stiffening on dynamic transmission error.

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References

  1. Rajasekaran S (2013) Differential transformation and differential quadrature methods for centrifugally stiffened axially functionally graded tapered beams. Int J Mech Sci 74:15–31

    Article  Google Scholar 

  2. Cirelli M, Valentini PP, Pennestrì E (2019) A study of the non-linear dynamic response of spur gear using a multibody contact based model with flexible teeth. J Sound Vib 445:148–167

    Article  ADS  Google Scholar 

  3. Cappellini N, Tamarozzi T, Blockmans B, Fiszer J, Cosco F, Desmet W (2018) Semi-analytic contact technique in a non-linear parametric model order reduction method for gear simulations. Meccanica 53(1–2):49–75

    Article  MathSciNet  Google Scholar 

  4. Tamarozzi T, Ziegler P, Eberhard P, Desmet W (2013) On the applicability of static modes switching in gear contact applications. Multibody Syst Dyn 30(2):209–219

    Article  Google Scholar 

  5. Schurr D, Holzwarth P, Eberhard P (2018) Investigation of dynamic stress recovery in elastic gear simulations using different reduction techniques. Comput Mech 62(3):439–456

    Article  MathSciNet  Google Scholar 

  6. Gerstmayr J, Schöberl J (2006) A 3D finite element method for flexible multibody systems. Multibody Syst Dyn 15(4):309–324

    Article  MathSciNet  Google Scholar 

  7. Zwölfer A, Gerstmayr J (2019) Preconditioning strategies for linear dependent generalized component modes in 3D flexible multibody dynamics. Multibody Syst Dyn 47(1):65–93

    Article  MathSciNet  Google Scholar 

  8. Fernández DRA, Viadero F, Iglesias M, García P, de-Juan A, Sancibrian R (2013) A model for the study of meshing stiffness in spur gear transmissions. Mech Mach Theory 61:30–58

    Article  Google Scholar 

  9. Lin TJ, Ou H, Li RF (2007) A finite element method for 3D static and dynamic contact/impact analysis of gear drives. Comput Methods Appl Mech Eng 196:1716–1728

    Article  ADS  Google Scholar 

  10. Wriggers P (2006) Computational contact mechanics, 2nd edn. Springer, Berlin, pp 157–224

    Book  Google Scholar 

  11. Shabana AA (2005) Dynamics of multibody systems, 3rd edn. Cambridge University Press, New York, pp 267–308

    Book  Google Scholar 

  12. Pechstein A, Reischl D, Gerstmayr J (2013) A generalized component mode synthesis approach for flexible multibody systems with a constant mass matrix. J Comput Nonlinear Dyn 8(1):011019

    Article  Google Scholar 

  13. Nikravesh PE (1988) Computer-aided analysis of mechanical systems. Prentice-Hall, New Jersey, pp 313–338

    Google Scholar 

  14. Fu SH, Wang Q (2006) Numerical method of Lyapunov exponents of multibody systems with constraints. J Beijing Univ Aeronaut Astronaut 32(6):742–746

    Google Scholar 

  15. Timoshenko SP, Goodier JN (2004) Theory of elasticity, 3rd edn. Tsinghua University Press, Beijing, pp 80–104

    Google Scholar 

  16. Fakher C, Tahar F, Mohamed H (2009) Analytical modelling of spur gear tooth crack and influence on gearmesh stiffness. Eur J Mech A/Solids 28(3):461–468

    Article  Google Scholar 

  17. Stachowiak GW, Batchelor AW (2014) Engineering tribology, 4th edn. Butterworth-Heinemann, Oxford, pp 293–370

    Google Scholar 

  18. Liu JP, Shu XB, Kanazawa H, Imaoka K, Mikkola A, Ren GX (2018) A model order reduction method for the simulation of gear contacts based on Arbitrary Lagrangian Eulerian formulation. Comput Methods Appl Mech Eng 338:68–96

    Article  ADS  MathSciNet  Google Scholar 

  19. Neto DM, Oliveira MC, Menezes LF, Alves JL (2016) A contact smoothing method for arbitrary surface meshes using Nagata patches. Comput Methods Appl Mech Eng 299:283–315

    Article  ADS  MathSciNet  Google Scholar 

  20. LSTC (2014) LS-DYNA theory manual (package insert). LSTC, California, pp 32-1–32-6

    Google Scholar 

  21. Li ST (2013) Effects of centrifugal load on tooth contact stresses and bending stresses of thin-rimmed spur gears with inclined webs. Mech Mach Theory 59:34–47

    Article  Google Scholar 

  22. Shweiki S, Rezayat A, Tamarozzi T, Mundo D (2019) Transmission error and strain analysis of lightweight gears by using a hybrid FE-analytical gear contact model. Mech Syst Signal Process 123:573–590

    Article  ADS  Google Scholar 

Download references

Funding

This study was funded by National Natural Science Foundation of China (Grant No. 51875057) and National Key Research and Development Program of China (Grant No.  2018YFB2001502).

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Authors and Affiliations

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

    Tengjiao Lin, Quancheng Peng, Wen Liu & Bingkui Chen

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  1. Tengjiao Lin
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  2. Quancheng Peng
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  3. Wen Liu
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  4. Bingkui Chen
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Correspondence to Tengjiao Lin.

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Lin, T., Peng, Q., Liu, W. et al. Centrifugal stiffening analysis of gear pair with generalized component mode synthesis and semi-analytic contact technique. Meccanica 55, 567–579 (2020). https://doi.org/10.1007/s11012-020-01126-0

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  • DOI: https://doi.org/10.1007/s11012-020-01126-0

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