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The Prediction of Frictional Temperature Increases in Dry, Sliding Contacts Between Different Materials

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The work done in overcoming frictional resistance between sliding surfaces is transformed into heat at the separate, very small, and very highly loaded asperity contacts that make up the real area of contact. The temperature increases at these initial asperity contacts (the “flash temperatures”) are superimposed on the bulk temperature and give maximum temperatures at the asperity contacts which, although of very short duration, can cause important local changes at and near the surfaces. In an earlier paper (Smith and Arnell in Tribol Lett 53(3):407–414, 2013), the authors presented a new approach to calculating these maximum temperatures that relies on the solution, by finite-element analysis, of the three-dimensional equation for transient heat flow in a hemispherical asperity. Also, a design of experiments exercise produced predictions for the temperature that agreed extremely well with the FE calculations, and response surfaces were presented that facilitated the determination of maximum temperatures without resorting to FE analysis. The preliminary analysis described in Smith and Arnell (Tribol Lett 53(3):407–414, 2013) treated the simplest case of the interaction between two identical asperities of the same material. In this paper, the analysis is extended to the interaction of asperities of different materials with widely different thermal and mechanical properties, and it is shown that it can be applied successfully to such situations. Many earlier models of frictional heating have been designed to calculate the flash temperature rises, under the assumption that the total maximum temperature rise could then be predicted by adding the bulk temperature to the flash temperature rise. However, there is a generic problem with this approach as the bulk temperature varies rapidly immediately below the contacting asperities and monotonically to the heat sinks, so it is not clear what temperature should be chosen for the bulk temperature to add to the flash temperature. This is a significant problem as it is the maximum temperature that governs the rates of any thermally activated changes in the sliding materials. In contrast, the FE model used here predicts the maximum transient temperature for each asperity interaction directly and has the potential to model the cumulative rises in maximum temperature as successive interactions occur until a steady state is reached. Therefore, the need to specify the bulk temperature does not arise. In addition, it is shown that the same FE analysis can be extended to calculate the partition between the two materials of the heat generated at the sliding surface and this, with their known physical properties, can be used to predict their bulk temperature profiles. The results can act as a benchmark against which other theoretical approaches can be measured. The authors believe they have developed a method for predicting maximum contact temperatures between rubbing asperities of different materials which is a significant improvement on existing techniques.

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a :

Radius of flattened area (m)

A i :

Coefficients in the regression equation for the response surface of maximum flash temperature

A ap :

Apparent contact area (m2)

b :

Depth of material (m)

B i :

Coefficients in the regression equation for the response surface of heat partition

C :

Specific heat (Jkg−1 m−3)

d :

Depth of flattening (m)

f i :

Proportion of generated heat that flows into an asperity (W)

f 2 :

Proportion of generated heat that flows into body 2 (W)

H :

Hardness (Pa)

h :

Heat transfer coefficient (Wm−2 K−1)

k :

Thermal conductivity (Wm−1 K−1)

K i :

Time-averaged value of contact area over a single traverse

p i :

Parameters in the regression equations

P :

Mean pressure due to applied load

q :

Total heat flow rate into a body (W)

Q :

Total heat flux generated in the contact (Wm−2)

q 2 :

Heat flow rate entering body 2 (W)

R :

Radius of asperity (m)

t :

Time (s)

T 1 , T 2 :

Temperatures in bodies 1 and 2 (C)

T amb :

Ambient temperature (C)

T bulk :

Bulk temperature in the hemispherical asperity (C)

T flash :

Maximum surface temperature rise above bulk temperature (C)

T max :

Maximum surface temperature during a traverse (C)

V :

Sliding velocity (ms−1)

Δ :

Transient contact area (m2)

δW :

Normal load on an asperity (N)

ρ :

Density (kgm−3)

Pe :

Péclet number, (ρC)1 aV/k 1

\(\overline{k}\) :

Thermal conductivity ratio, k 2/k 1

\(\overline{d}\) :

Flattening ratio, d/R

\(\overline{\rho C}\) :

Thermal capacitance ratio, (ρC)2/(ρC)1

\(\overline{T}_{max}\) :

Non-dimensional maximum flash temperature in a traverse, T max k 1/(μHVa)

µ :

Coefficient of friction


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Correspondence to E. H. Smith.



See tables 4, 5, 6 and 7.

Table 4 Design variables employed to produce the low Péclet response surface
Table 5 Values of variables for the “off-design” points for the low Péclet model
Table 6 Design variables employed to produce the high Péclet response surface
Table 7 Values of variables for the “off-design” points for the high Péclet model

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Smith, E.H., Arnell, R.D. The Prediction of Frictional Temperature Increases in Dry, Sliding Contacts Between Different Materials. Tribol Lett 55, 315–328 (2014). https://doi.org/10.1007/s11249-014-0359-3

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  • Flash temperature
  • Friction
  • Bulk temperature
  • Sliding contact