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Modelling and analysis of a spur gear pair with the effect of bearing clearances

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Abstract

In the previous dynamic models of spur gear transmission systems, the effect of bearing clearance on gear backlash and mesh stiffness was ignored. In fact, bearing clearance has an effect on gear backlash and mesh stiffness, and the effect of which is related to vibration displacement. In this study, a nonlinear dynamic model of a spur gear pair with six degrees of freedom was developed, which took into account the surface friction, gear backlash, bearing clearance, transmission error and meshing stiffness. The variation of initial gear backlash and rotational speed was analyzed comprehensively according to the effect of bearing clearance on the meshing stiffness and dynamic gear backlash. After that, the dynamic characteristics under different excitation parameters were obtained. The results indicate that the vibration of the gear system is more violent when the effect of bearing clearance is taken into account. This study can provide a better understanding of the dynamic design of gears under practical conditions.

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Abbreviations

r ζ :

Pitch radii

z ζ :

Numbers of teeth

m n(ζ = 1, 2):

Modulus

r ζn :

Distance between the meshing point and gear center

a :

Standard central distance

α :

Standard pressure angle

r a1 :

Radius of the addendum circle of the driving gear

r b1 :

Radius of the basic circle of the driving gear

r a2 :

Radius of the addendum circle of the driven gear

r b2 :

Radius of the basic circle of the driven gear

cr :

Contact ratio

x :

Vibration displacement in x direction

y :

Vibration displacement in y direction

θ :

Vibration angular displacement

e(t):

Static transmission error

F mi (i = 1, 2):

Dynamic meshing force of the ith gear pair

k mi (i = 1, 2):

Time-varying meshing stiffness of the ith gear pair

c mi (i = 1, 2):

Meshing damping of the ith gear pair

f ms(Y):

Gear backlash function for the backlash

f md(Ẏ):

Gear backlash function for the relative speed

Δb :

Dynamic backlash

2b 0 :

Actual gear backlash

2b h :

Initial gear backlash

f bm(x):

Bearing clearance function for bearing clearances

f bd(ẋ):

Bearing clearance function for relative speed

λ i :

Directional coefficient

μ i :

Friction coefficient of the tooth surface

w :

Angular velocity

L 1i, L 2i :

Arms of the friction force between the ith tooth pair

c r :

Bearing support damping

k r :

Bearing support stiffness

T 1, T 2 :

Input and output torques

References

  1. Kahraman A (1994) Load sharing characteristics of planetary transmissions. Mech Mach Theory 29(8):1151–1165

    Article  MathSciNet  Google Scholar 

  2. Saada A, Velex P (1995) An extended model for the analysis of the dynamic behavior of planetary trains. J Mech Des 117(2A):241–247

    Article  Google Scholar 

  3. Lin J, Parker RG (1999) Analytical characterization of the unique properties of planetary gear free vibration. J Vib Acoust Trans ASME 15(3):316–321

    Article  Google Scholar 

  4. Yi G, Parker RG (2012) Dynamic analysis of planetary gears with bearing clearance. J Comput Nonlinear Dyn Trans ASME 7(4):041002

    Article  Google Scholar 

  5. Wang J, Wang H, Guo L (2015) Analysis of stochastic nonlinear dynamics in the gear transmission system with backlash. Int J Nonlinear Sci Numer Simul 16(2):111–121

    Article  MathSciNet  MATH  Google Scholar 

  6. Chowdhury S, Yedavalli RK (2017) Dynamics of low speed geared shaft systems mounted on rigid bearings. Mech Mach Theory 112:123–144

    Article  Google Scholar 

  7. Chowdhury S, Yedavalli RK (2018) Vibration of high speed helical geared shaft systems mounted on rigid bearings. Int J Mech Sci 142–143:176–190

    Article  Google Scholar 

  8. Hou L, Cao S (2019) Nonlinear dynamic analysis on planetary gears-rotor system in geared turbofan engines. Int J Bifurc Chaos 29(6):1950076

    Article  MathSciNet  Google Scholar 

  9. Wei J, Zhang A, Shi L, Qin D, Lim TC (2020) Modeling and dynamic characteristics of planetary gear transmission in non-inertial system of aerospace environment. J Mech Des Trans ASME 142(3):031103

    Article  Google Scholar 

  10. Sheng L, Sun Q, Li W, Ye G (2022) Research on gear crack fault diagnosis model based on permanent magnet motor current signal. ISA Trans 135:188–98

    Article  Google Scholar 

  11. Chen S, Tang J, Luo C, Wang Q (2011) Nonlinear dynamic characteristics of geared rotor bearing systems with dynamic backlash and friction. Mech Mach Theory 46(4):466–478

    Article  MATH  Google Scholar 

  12. Xiang L, Gao N (2017) Coupled torsion-bending dynamic analysis of gear-rotor-bearing system with eccentricity fluctuation. Appl Math Model 50:569–584

    Article  MathSciNet  MATH  Google Scholar 

  13. Yi Y, Huang K, Xiong Y, Sang M (2019) Nonlinear dynamic modelling and analysis for a spur gear system with time-varying pressure angle and gear backlash. Mech Syst Signal Process 132(Oct.1):18–34

    Article  Google Scholar 

  14. Margielewicz J, Ga˛ska D, Litak G (2019) Modelling of the gear backlash. Nonlinear Dyn 97:355–368

    Article  Google Scholar 

  15. Zhibo G, Ke X, Jiaxu W, Junyang L (2020) Nonlinear dynamic analysis of a rigid-flexible gear transmission considering geometric eccentricities. J Comput Nonlinear Dyn Trans ASME 15(8):084501

    Article  Google Scholar 

  16. Huang K, Cheng Z, Xiong Y, Han G, Li L (2020) Bifurcation and chaos analysis of a spur gear pair system with fractal gear backlash. Chaos, Solitons Fractals 142:110387

    Article  MathSciNet  Google Scholar 

  17. Geng Z, Xiao K, Wang J, Li J (2019) Investigation on nonlinear dynamic characteristics of a new rigid-flexible gear transmission with wear. J Vib Acoust Trans ASME 14:1–12

    Google Scholar 

  18. Geng Z, Xiao K, Wang J, Li J (2021) Bifurcation and chaos of a spur gear transmission with non-uniform wear. J Vib Acoust Trans ASME 143:031004

    Article  Google Scholar 

  19. Kuang JH, Yang Y (1992) An estimate of mesh stiffness and load sharing ratio of a spur gear pair. In: Proceedings of the 6th international power transmission and gearing conference, vol. 1, ASME DE-Vol, p 43–1

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Acknowledgements

This work was supported by Research Program supported by the National Natural Science Foundation of China (Grant No. 51975064), China

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Authors and Affiliations

  1. School of Aeronautics and Astronautics, University of Electronic Science and Technology of China, Chengdu, 611731, Sichuan, China

    Zhibo Geng & Min Chen

  2. Yangtze Delta Region Institute, University of Electronic Science and Technology of China, Huzhou, 313000, Zhejiang, China

    Min Chen

  3. College of Mechanical and Vehicle Engineering, Chongqing University, Chongqing, 40044, China

    Yanfeng Han & Cheng Wang

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  1. Zhibo Geng
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  2. Min Chen
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  4. Cheng Wang
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Correspondence to Min Chen.

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Geng, Z., Chen, M., Han, Y. et al. Modelling and analysis of a spur gear pair with the effect of bearing clearances. J Braz. Soc. Mech. Sci. Eng. 45, 392 (2023). https://doi.org/10.1007/s40430-023-04297-5

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