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Evolution of surface spur gear tooth temperature based on three-dimensional finite element model

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Abstract

In order to meet the special needs of helicopters with sufficient operating time for landing safely under loss-of-lubrication conditions, it is necessary to avoid the scuffing failure and predict the operating time. A spur gear is taken as the research object. Considering the change of moving source of heat on the gear, simplified models are adopted. Both the spatial distribution and the time history of the gear temperature are simulated by finite element method. The simulation results of bulk temperature are compared with the test measurement ones, while those of the flash temperature history are compared with the experimental and calculation results by Blok flash temperature formula, respectively. The comparison shows a good agreement. The results of simulation and comparison are discussed.

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Abbreviations

a :

Half contact width (mm)

b :

Tooth width (mm)

c 1, c 2 :

Specific heat (J/kg °C)

d 1, d 2 :

Reference diameter (mm)

E 1, E 2 :

Young’s modulus (N/mm2)

\( F_{\text{nc}} \) :

Normal force (N)

\( F_{\text{tc}} \) :

Tangential force (N)

\( h_{\text{c}} \) :

Convective heat transfer coefficient (W/m2 °C)

\( H_{\text{c}} \) :

Height of contact point on the tooth (mm)

k :

Thermal conductivity (W/(m °C))

n :

Surface outward normal

n 1, n 2 :

Gear rotation speed (r/min)

P r :

Prandtl

q tot :

Normalized cooling capacity

Q :

Boundary heating flux (W/m2)

r c :

Radius of contact point (mm)

R e :

Reynolds numbers

\( R_{\text{E1}} \), \( R_{\text{E2}} \) :

Radius of curvature (mm)

R 1, R 2 :

Pitch radius (mm)

T 0 :

Ambient temperature (°C)

T tor :

Torque (N m)

\( V_{\text{e}} \) :

Sliding velocity (m/s)

\( V_{ 1} \), \( V_{ 2} \) :

Velocity (m/s)

\( W_{\text{b}} \) :

Load (N/mm)

\( X_{\text{R}} \) :

Roughness factor (μm)

\( \alpha \) :

Pressure angle (rad)

\( \eta \) :

Dynamic viscosity (N s/m)

\( \lambda_{1} \), \( \lambda_{2} \) :

Thermal conductivity (W/m °C)

\( v_{\text{oil}} \) :

Kinematic viscosity (m2/s)

\( \rho_{1} \), \( \rho_{2} \) :

Density (kg/m3)

\( \nu_{1} \), \( \nu_{2} \) :

Poisson’s ratio

1:

Pinion

2:

Gear

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Acknowledgements

The paper is supported by National Defense Pre-study Fund of China Grant 8130208.

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Authors and Affiliations

  1. School of Mechanical and Electrical Engineering, Central South University, Changsha, 410083, China

    Jihua Chang, Shaojun Liu, Xiaozhou Hu & Yu Dai

  2. State Key Laboratory for High Performance Complex Manufacturing, Central South University, Changsha, 410083, China

    Jihua Chang, Shaojun Liu, Xiaozhou Hu & Yu Dai

Authors
  1. Jihua Chang
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  2. Shaojun Liu
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  3. Xiaozhou Hu
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  4. Yu Dai
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Correspondence to Jihua Chang or Xiaozhou Hu.

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Technical Editor: André Cavalieri.

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Chang, J., Liu, S., Hu, X. et al. Evolution of surface spur gear tooth temperature based on three-dimensional finite element model. J Braz. Soc. Mech. Sci. Eng. 41, 370 (2019). https://doi.org/10.1007/s40430-019-1870-0

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  • DOI: https://doi.org/10.1007/s40430-019-1870-0

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