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

  • Jihua ChangEmail author
  • Shaojun Liu
  • Xiaozhou HuEmail author
  • Yu Dai
Technical Paper


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.


Flash temperature history Bulk temperature field Thermal steady state Scuffing failure 

List of symbols


Half contact width (mm)


Tooth width (mm)

c1, c2

Specific heat (J/kg °C)

d1, d2

Reference diameter (mm)

E1, E2

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)


Thermal conductivity (W/(m °C))


Surface outward normal

n1, n2

Gear rotation speed (r/min)




Normalized cooling capacity


Boundary heating flux (W/m2)


Radius of contact point (mm)


Reynolds numbers

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

Radius of curvature (mm)

R1, R2

Pitch radius (mm)


Ambient temperature (°C)


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








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


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Copyright information

© The Brazilian Society of Mechanical Sciences and Engineering 2019

Authors and Affiliations

  1. 1.School of Mechanical and Electrical EngineeringCentral South UniversityChangshaChina
  2. 2.State Key Laboratory for High Performance Complex ManufacturingCentral South UniversityChangshaChina

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