Maximum Contact Temperature Rise in a Sphere-on-Flat Contact

Results

Temperature rise is shown for the operating point. The chart compares sensitivity to each body’s sweep endpoint.

Equation and assumptions

The calculator evaluates the Bos fit for maximum temperature rise in an elliptical sliding contact:

DeltaT = Q / (sqrt(ax ay) * (K1/theta1 + K2/theta2))

Heat generation is Q = mu * 2/3 * pH * (u1 - u2) * pi * ax * ay. Peclet-number calculations use a fixed density of 7880 kg/m3 for both bodies.

Maximum Flash Temperature According to Bos

Bos considered numerical solutions for heat generation in tribological contacts and proposed a function fit for the maximum temperature rise in sliding elliptical contacts. The calculator above keeps that practical fit and exposes the intermediate values that control the prediction.

The maximum temperature rise is calculated as:

Tmax = Q / (sqrt(ax ay) * (K1/theta1 + K2/theta2))

Here Q is the total frictional heat generation, K1 and K2 are the thermal conductivities of the two bodies, and ax and ay are the Hertzian contact semi-axes in and perpendicular to the sliding direction. The dimensionless temperatures theta1 and theta2 are calculated from the Bos fit using the contact ellipticity, shape factor, Peclet numbers, and heat partition term.

The heat generation term is:

Q = mu * 2/3 * pH * (u1 - u2) * pi * ax * ay

where mu is the coefficient of friction, pH is maximum Hertzian pressure, and u1 and u2 are the signed surface speeds. Peclet-number calculations use a fixed density of 7880 kg/m3 for both bodies.

Maximum Flash Temperature According to Tian and Kennedy

Tian and Kennedy studied maximum and average flash temperatures for several heat-source shapes. For ball-on-flat or ball-on-ball contacts, their moving circular heat-source result is another common way to estimate flash temperature risk. The calculator currently evaluates the Bos elliptical-contact method; this section keeps the Tian and Kennedy reference visible as related formula background.

These temperature-rise calculations are useful for screening adhesive wear, scuffing, and other high-temperature contact risks. They are engineering estimates: inputs such as friction coefficient, pressure, speed, contact size, and thermal properties should be representative of the real operating condition.

References

PhD Thesis of J. Bos: https://ris.utwente.nl/ws/portalfiles/portal/6080060/thesis_J_Bos.pdf

Tian, X., and Kennedy, F. E. (1994). Maximum and Average Flash Temperatures in Sliding Contacts. Journal of Tribology, 116(1), 167. doi:10.1115/1.2927035