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.
The influence of the change with time of friction power on thermal stresses in a friction element of a brake system is investigated. For this purpose, a list of ten different temporal profiles of specific friction power is used, which has been experimentally established for a single braking process. The corresponding profiles of transient temperature fields in the considered element are applied as input parameters to find quasi-static thermal stresses. Numerical analysis concerned with spatio-temporal distributions of the stresses and their evolutions on the heated surface is presented.
In this paper influence of temporal profile of the specific friction power (i.e. the product of the coefficient of friction, sliding velocity and contact pressure) on thermal stresses in a friction element during braking was investigated. Spatio-temporal distributions of thermal stresses were analytically determined for a subsurface layer of the friction element, based on the model of thermal bending of a thick plate with unfixed edges (Timoshenko and Goodier, 1970). To conduct calculations, the fields of dimensionless temperature were used. These fields were received in the article (Topczewska, 2017) as solutions to a one-dimensional boundary-value problem of heat conduction for a semi-space heated on its outer surface by fictional heat flux with three, different time profiles of the friction power.
In this paper analytical solutions of the thermal problems of friction were received. The appropriate boundary-value problems of heat conduction were formulated and solved for a homogeneous semi–space (a brake disc) heated on its free surface by frictional heat fluxes with different and time-dependent intensities. Solutions were obtained in dimensionless form using Duhamel's theorem. Based on received solutions, evolution and spatial distribution of the dimensionless temperature were analyzed using numerical methods. The numerical results allowed to determine influence of the time distribution of friction power on the spatio-temporal temperature distribution in brake disc.
In this paper the analytical solution of the boundary–value heat conduction problem for a brake rotor was developed. A solid brake disc is heated by frictional heat flux during braking with constant deceleration. Intensity of the heat flux affecting friction surface of the disc is proportional to the specific power of friction. It was assumed that contact pressure between the pad and the disc increases linearly, from zero in the initial moment of the braking process to the maximum value in standstill. Calculations were carried out on variables and parameters in the dimensionless form. The obtained results were compared with adequate resultsduring braking with constant deceleration, with an assumption of pressure constant in time.
Artykuł zawiera opis udarowo-obrotowej metody wiercenia. Wykorzystuje się ją z coraz większym powodzeniem przy różnego rodzaju wierceniach. Jednym z ważnych zastosowań jest wykonywanie otworowych wymienników ciepła.
EN
The article contains a description of rotary percussion drilling method. It is gaining ground in different drilling applications. One of the key applications of this method is drilling borehole heat exchangers. Rotary percussion drilling method achieves higher rate of penetration than the rotary method. This is especially the case for hard and very hard rocks. These rocks have usually high thermal conductivity factors and therefore are more favourable for extracting Earth's internal heat. Rotary drilling method in these rocks is costly and time consuming. Borehole heat exchangers require no reservoir fluid exploitation, hence the only criterion of drilling them is the rate of penetration.
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