Abstract
The transient temperature field and corresponding quasi-static thermal stresses are analysed in a system consisting of a semi-space and a strip. The strip is heated on its outer surface by a heat flux with the intensity equal to the specific power of friction during braking with a uniform retardation. The evolution and distribution in depth from a surface of friction for temperatures and thermal stresses were investigated for the metal-ceramic FMK-11 material of the strip.
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Abbreviations
- A a1 :
-
Nominal friction surface of a pad, m2
- A a2 :
-
Nominal friction surface of a disc, m2
- A ov = Aa1 /Aa2:
-
Overlap coefficient, dimensionless
- d :
-
Strip thickness, m
- E :
-
Young’s modulus, Pa
- f :
-
Coefficient of friction, dimensionless
- H():
-
Heaviside’s step function
- K :
-
Heat conductivity, W/(mK)
- k :
-
Thermal diffusivity, m2/s
- p 0 :
-
Pressure, Pa
- q0 = γfp0V0:
-
Intensity of the frictional heat flux, W/m2
- T :
-
Temperature, °C
- T max :
-
Maximal temperature, °C
- T0 = q0d/K p :
-
Temperature scaling factor, °C
- T a :
-
Surrounding ambient temperature, °C
- t :
-
Time, s
- t s :
-
Braking time, s
- t c :
-
Time of the sign change of lateral stress, s
- t max :
-
Time, when maximal temperature is reached, s
- \({u=2\sqrt{\tau }}\) :
-
Dimensionless
- \({u_s =2\sqrt{\tau _s }}\) :
-
Dimensionless
- V :
-
velocity sliding, m/s
- V 0 :
-
initial velocity sliding, m/s
- x, y, z:
-
Spatial coordinates, m
- α :
-
Linear thermal expansion coefficient, K−1
- γ:
-
Heat participation factor, dimensionless
- ν :
-
Poisson’s ratio
- σ0 = αET0/(1 − ν):
-
Stress scaling factor, Pa
- σ x , σ y :
-
Normal stresses, Pa
- \({\sigma _{x,y}^{\ast} =\sigma _{x,y} /\sigma _0}\) :
-
Dimensionless
- c :
-
Calliper (foundation)
- d :
-
Disc
- p :
-
Pad (strip)
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Yevtushenko, A., Kuciej, M. & Yevtushenko, O. Temperature and thermal stresses in material of a pad during braking. Arch Appl Mech 81, 715–726 (2011). https://doi.org/10.1007/s00419-010-0445-4
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DOI: https://doi.org/10.1007/s00419-010-0445-4