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Research on vibration characteristics of multistage gears transmission system driven by internal and external excitation

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Abstract

In order to accurately describe the complex transmission systems and clarify the effects of internal and external excitation on the vibration characteristics for large complex transmission systems, a dynamics model considering gear meshing error and time-varying meshing stiffness is established at two-stage planetary gears systems. The coupling model is established by matrix set method for two-stage planetary gears and multistage spur gears transmission systems. The random load excitation verified by experiments is the external excitation in the system, and the excitation caused by the time-varying meshing stiffness and meshing error is the internal excitation. The research on the response of the vibration systems shows that the internal excitation caused by gear meshing stiffness and gear meshing error has important influence on the dynamic load behavior of spur gears transmission in complex systems. For the planetary system with heavy external load, the dynamic behavior mainly depends on the external load, and the influence of internal excitation on the dynamic meshing force is less than that of the external excitation for the planetary system. The external excitation mainly affects the low-frequency region of the dynamic meshing force for the system, and the internal excitation affects the high-frequency region of the dynamic force for the system. The frequency influence interval of the internal excitation is much larger than that of the external excitation.

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Abbreviations

t :

Time

ψ n :

The position angle of the nth planetary gear

α s, α r :

The meshing angle between the sun gear (the ring gear) and the planetary gear

ψ sn :

The difference between the position angle of the planetary gear and the meshing angle (αs)

ψ rn :

The sum between the position angle of the planetary gear and the meshing angle (αr)

m s, m c, m r, m n :

The mass of the sun gear, the planet carrier, the ring gear and the nth planetary gear

I s, I c, I r, I n :

Moment of inertia for the sun gear, the planet carrier, the ring gear and the nth planetary gear

r s, r c, r r, r n :

Base circle radius of the sun gear, the planet carrier, the ring gear and the nth planetary gear

k sp, k rp :

The meshing stiffness between the sun gear (the ring gear) and the planetary gear

e sp, e rp :

Gear meshing error between the sun gear (the ring gear) and the planetary gear

k s, k c, k r, k pn :

Support stiffness of the sun gear, the planet carrier, the ring gear and the nth planetary gear

k su, k cu, k ru :

Torsional stiffness of the sun gear, the planet carrier and the ring gear

Z av, A :

The mean value and amplitude fluctuation coefficients of the cutting force

Φ :

A random variable following the Gamma distribution

z s, z r, z n :

The teeth number of the sun gear, the ring gear and the planetary gear

k ai, e ri :

The amplitude coefficient of the gear meshing stiffness and the gear meshing error

k 0, e 0 :

The mean value of the gear meshing stiffness and the gear meshing error

ω i, φ i :

Gear meshing frequency and meshing phase angle, i is a harmonic series

P b :

Gear base pitch

F 12, F 23 :

The meshing force between gears g1 and g2 (g2 and g3)

F sp, F rp :

The meshing force between the sun gear (the ring gear) and the planetary gear

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Acknowledgements

The authors have been supported by Chinese National Natural Science Foundation (U1708254) and National Natural Science United Foundation of China (U1710119).

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Authors and Affiliations

  1. School of Mechanical Engineering and Automation, Northeastern University, Shenyang, 110819, China

    Wen-jia Lu, Hong-chuan Cheng & Zhou Yang

  2. School of Mechanical Engineering, Shenyang University of Chemical Technology, Shenyang, 110142, China

    Yi-min Zhang

Authors
  1. Wen-jia Lu
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  2. Yi-min Zhang
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  3. Hong-chuan Cheng
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  4. Zhou Yang
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Corresponding author

Correspondence to Wen-jia Lu.

Additional information

Technical Editor: Wallace Moreira Bessa, D.Sc..

The subscript “c” represents the planet carrier, the subscript “r” represents the inner ring gear and the subscript “s” represents the sun gear.

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Lu, Wj., Zhang, Ym., Cheng, Hc. et al. Research on vibration characteristics of multistage gears transmission system driven by internal and external excitation. J Braz. Soc. Mech. Sci. Eng. 40, 537 (2018). https://doi.org/10.1007/s40430-018-1452-6

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  • DOI: https://doi.org/10.1007/s40430-018-1452-6

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