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Vibration characteristic analysis of gearbox based on dynamic excitation with eccentricity error

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Abstract

In this study, the vibration characteristics of gearbox considering the eccentricity error and the friction excitation of helical gear pair were evaluated theoretically and experimentally. A geometric model of a single-stage helical gear pair with eccentricity error was established to obtain the calculation formula of the length of the dynamic contact line and the friction excitation. The multi-degree-of-freedom dynamic model of the transmission system was established considering the influences of tooth friction, support stiffness and damping, meshing stiffness and damping, static error, and dynamic tooth backlash. Then, the dynamic meshing forces of the system were obtained and applied to the gearbox for vibration response analysis using mode superposition method. A correlation test rig was developed to measure vibration under different operating conditions for verifying the correctness of the simulation models. Comparison between simulation and test was performed to demonstrate the accuracy of the proposed model in predicting vibrations. Results showed that eccentricity greatly influenced the overall vibration characteristics. The relative error between measurement and prediction can be significantly reduced by considering the eccentricity error in the dynamic model of transmission system.

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Abbreviations

e1, e2 :

Eccentricity error of pinion and gear

r1, r2 :

Pitch circle radius of pinion and gear

ra1, ra2 :

Addendum circle radius of pinion and gear

rb1, rb2 :

Basic circle radius of pinion and gear

φ1, φ2 :

Eccentricity initial position angle of pinion and gear

z1, z2 :

Teeth number of pinion and gear

ω1, ω2 :

Rotational speed of pinion and gear

H :

Installation center distance between pinion and gear

l :

Actual geometrical center distance between pinion and gear

Y :

Azimuth angle of the gear pair

ψ :

Complementary angle of the angle between geometric center line and the meshing line

a :

Theoretical center distance

α t :

Transverse pressure angle

α′ t :

Dynamic meshing angle

i :

Instantaneous transmission ratio

v(t):

Linear velocity of the gear in the direction of the meshing line at any time t

ε α :

Transverse contact ratio

ε β :

Axial contact ratio

p t :

Normal transverse circular pitch

β b :

Helix angle of base circle

L(t):

Length of total contact line at any moment of the gear pair

F ij :

Normal forces on the contact line of each segment

L ij :

Instantaneous length of the ith contact line and the jth segment

F :

Total normal force

F fi :

Friction force of the contact line in each segment

μ :

Average friction coefficient of the tooth surface

T f :

Total friction torque

δ ni :

Relative displacement in the direction of meshing line for each gear pair

k x k y k z :

Support stiffness of each bearing

c x c y c z :

Support damping of each bearing

T in :

Input torque

T out :

Output torque

k mi C mi :

Meshing stiffness and meshing damping of each gear pair kmi Cmi

k ij C ij :

Torsional stiffness and torsional damping of each shaft

m i :

Mass of each gear

I i :

Moment of inertia of each gear

b t :

Backlash

f (δni):

Function of backlash

e(t):

Static transmission error

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Acknowledgments

This work is financially supported by the National Key R&D Program of China (No. 2018YFB2001502) and National Natural Science Foundation of China (No. 51875057).

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Authors and Affiliations

  1. State Key Laboratory of Mechanical Transmission, Chongqing University, Chongqing, 400044, China

    Wen Liu, Hang Zhao, Tengjiao Lin, Biao Gao & Yun Yang

Authors
  1. Wen Liu
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  2. Hang Zhao
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  3. Tengjiao Lin
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  4. Biao Gao
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  5. Yun Yang
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Corresponding author

Correspondence to Wen Liu.

Additional information

Wen Liu is the Associate Professor of the State Key Laboratory of Mechanical Transmissions, Chongqing University. He received his Ph.D. in Mechanical Engineering from Chongqing University. His research interests involve dynamics of mechanical system and analysis and control of vibration and noise.

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Liu, W., Zhao, H., Lin, T. et al. Vibration characteristic analysis of gearbox based on dynamic excitation with eccentricity error. J Mech Sci Technol 34, 4545–4562 (2020). https://doi.org/10.1007/s12206-020-1014-6

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  • DOI: https://doi.org/10.1007/s12206-020-1014-6

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