backBack to 1/2016
Technical Issues
1/2016 pp. 90-95

pdf Get full text pdf

Abstract

The aim of this study was to investigate the influence of the time of pressure increase during single braking on the temperature in a brake disc. The case of linear pressure increase from zero to nominal value in the initial stage of braking and maintaining this value to standstill was considered. The time distribution of the sliding velocity of frictional elements was determined from the differential equation of motion with the initial condition. Based on the time distributions of pressure and sliding velocity, the intensity of the frictional heat flux, which affects on the disc surface, was determined. Spatio-temporal distribution of the temperature in a brake disc was found from analytical solution of the heat conduction boundary–value problem for semi–space heated on the outer surface heat flux with known a priori intensity. The numerical analysis conducted allowed to determine engineering equation, which describes relation between maximum temperature and the time of pressure increase.

Key words

braking, frictional heating, temperature, brake disc

References

1. Abramowitz, M., Stegun, I.A., Handbook of Mathematical Functions with Formulas, Graphs, and Tables, National Bureau of Standards, Washington, 1972.

2. Carlslaw, H.S., Jaeger, J.C., 1959. Conduction of Heat in Solids, 2nd ed.Clarendon Press, Oxford, 1959.

3. Chichinadze, A.V., Braun, E.D., Ginsburg, A.G., Ignat’eva, Z.V., Calculation, Test and Selection of Frictional Couples, Nauka, Moscow, 1979, (in Russian).

4. Jewtuszenko, O., (red) Analityczne i numeryczne modelowanie procesu nieustalonej generacji ciepła w elementach tarciowych układów hamulcowych, Oficyna Wydawnicza Politechniki Białostockiej, Białystok, 2014.

5. Kuciej, M., Zagadnienia cieplne tarcia dla układu warstwa-podłoże, Rozprawa doktorska, Politechnika Białostocka, Białystok, 2007.

6. Kuciej, M., Analityczne modele nieustalonego nagrzewania tarciowego, Oficyna Wydawnicza Politechniki Białostockiej, Białystok, 2012.

7. Ling, F.F., Surface Mechanics. Wiley: New York, 1973.

8. Ozisik, M.N., Heat conduction, 2nd Ed. Wiley: New York, 1993.

9. Prudnikov, A.P., Brychkov, Yu.A., Marichev, О.I., Integrals and Series. Vol. 1: Elementary Functions, Gordon and Breach: New York, 1986.

10. Topczewska, K., Influence of the protective strip properties on the distribution of the temperature in brake disc. II – Braking with constant deceleration. Zagadnienia aktualne poruszane przez młodych naukowców 3, Creativetime, Kraków, 2015.

11. Topczewska, K., The temperature of a brake disc during frictional heating with linear distribution of the contact pressure, Creativetime, Kraków, 2016, Forthcoming.

12. Wrzesiński, T., Hamowanie pojazdów samochodowych. WKŁ, Warszawa, 1978.