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ABSTRACT
A system of equations of heat dynamics of friction and wear (HDFW) for a pad–disc tribosystem during a single braking has been formulated. It takes into account the coefficient of friction dependent on the maximum temperature, which is the sum of the mean temperature of the nominal contact region (the macro contact) and the flash temperature on the real contact area (the micro contact), temperature-dependent properties of materials and wear. Numerical solution of the initial problem of motion and the nonlinear boundary-value heat conduction problem was obtained. Computations were performed using the axisymmetric FE contact model for the metal ceramic pad and the cast-iron disc.
Nomenclature
| Aa | = | area of the nominal contact region (m2) |
| Ac | = | area of the contour contact region (m2) |
| Ar | = | total area of the real contact regions (m2) |
| b0 | = | characteristic of the curve of the rough bearing surface |
| c | = | temperature-dependent specific heat capacity (J/(kg°C)) |
| = | specific heat capacity at the initial temperature (J/(kg°C)) | |
| dr | = | current mean diameter of the real contact region (m) |
| f | = | coefficient of friction |
| f(0) | = | coefficient of friction at initial temperature |
| h | = | heat transfer coefficient (W/(m2°C)) |
| hmax | = | maximum height of the asperities (m) |
| I0 | = | moment of inertia of the friction couple (kg m2) |
| Iw | = | temperature-dependent coefficient of wear rate (µg/(N m)) |
| = | temperature-dependent coefficient of wear at the initial temperature (µg/(N m)) | |
| I | = | wear (kg) |
| HB | = | temperature-dependent Brinell hardness (MPa) |
| = | Brinell hardness at the initial temperature (MPa) | |
| K | = | temperature-dependent thermal conductivity (W/(m°C)) |
| = | thermal conductivity at the initial temperature (W/(m°C)) | |
| M | = | current moment of braking force from Aa (N m)) |
| M0 | = | initial moment of braking force from Aa (N m)) |
| p | = | current contact pressure (MPa) |
| p0 | = | nominal value of the contact pressure (MPa) |
| q | = | current specific power of friction (W/m2) |
| Q | = | current power of friction (W) |
| r | = | radial coordinate |
| rav | = | mean rounded radius of the asperities (m) |
| req | = | equivalent radius of the contact region (m) |
| T | = | temperature (°C) |
| T0 | = | initial/ambient temperature (°C) |
| Tf | = | flash temperature on the friction surface (°C) |
| Tm | = | mean temperature on the friction surface (°C) |
| Tmax | = | maximum temperature on the friction surface (°C) |
| t | = | time (s) |
| tm | = | time of increase in the contact pressure to nominal value (s) |
| ts | = | braking time (s) |
| = | braking time at constant retardation (s) | |
| V | = | current velocity at the equivalent radius req (m/s) |
| W0 | = | kinetic energy per one braking system (J) |
| z | = | axial coordinate |
| Γ | = | contact region |
| δ | = | thickness of the analyzed region (m) |
| θ | = | circumferential coordinate |
| ν | = | characteristic of the curve of the rough bearing surface |
| ρ | = | density (kg/m3) |
| ω | = | angular velocity (rad/s) |
| ω0 | = | initial angular velocity (rad/s) |
| Ω | = | computational region |
| Subscripts | = | |
| d | = | indicates disc |
| p | = | indicates pad |
Nomenclature
| Aa | = | area of the nominal contact region (m2) |
| Ac | = | area of the contour contact region (m2) |
| Ar | = | total area of the real contact regions (m2) |
| b0 | = | characteristic of the curve of the rough bearing surface |
| c | = | temperature-dependent specific heat capacity (J/(kg°C)) |
| = | specific heat capacity at the initial temperature (J/(kg°C)) | |
| dr | = | current mean diameter of the real contact region (m) |
| f | = | coefficient of friction |
| f(0) | = | coefficient of friction at initial temperature |
| h | = | heat transfer coefficient (W/(m2°C)) |
| hmax | = | maximum height of the asperities (m) |
| I0 | = | moment of inertia of the friction couple (kg m2) |
| Iw | = | temperature-dependent coefficient of wear rate (µg/(N m)) |
| = | temperature-dependent coefficient of wear at the initial temperature (µg/(N m)) | |
| I | = | wear (kg) |
| HB | = | temperature-dependent Brinell hardness (MPa) |
| = | Brinell hardness at the initial temperature (MPa) | |
| K | = | temperature-dependent thermal conductivity (W/(m°C)) |
| = | thermal conductivity at the initial temperature (W/(m°C)) | |
| M | = | current moment of braking force from Aa (N m)) |
| M0 | = | initial moment of braking force from Aa (N m)) |
| p | = | current contact pressure (MPa) |
| p0 | = | nominal value of the contact pressure (MPa) |
| q | = | current specific power of friction (W/m2) |
| Q | = | current power of friction (W) |
| r | = | radial coordinate |
| rav | = | mean rounded radius of the asperities (m) |
| req | = | equivalent radius of the contact region (m) |
| T | = | temperature (°C) |
| T0 | = | initial/ambient temperature (°C) |
| Tf | = | flash temperature on the friction surface (°C) |
| Tm | = | mean temperature on the friction surface (°C) |
| Tmax | = | maximum temperature on the friction surface (°C) |
| t | = | time (s) |
| tm | = | time of increase in the contact pressure to nominal value (s) |
| ts | = | braking time (s) |
| = | braking time at constant retardation (s) | |
| V | = | current velocity at the equivalent radius req (m/s) |
| W0 | = | kinetic energy per one braking system (J) |
| z | = | axial coordinate |
| Γ | = | contact region |
| δ | = | thickness of the analyzed region (m) |
| θ | = | circumferential coordinate |
| ν | = | characteristic of the curve of the rough bearing surface |
| ρ | = | density (kg/m3) |
| ω | = | angular velocity (rad/s) |
| ω0 | = | initial angular velocity (rad/s) |
| Ω | = | computational region |
| Subscripts | = | |
| d | = | indicates disc |
| p | = | indicates pad |