Abstract
An algorithm to determine the maximum temperature of brake systems during repetitive short-term (RST) braking mode has been proposed. For this purpose, the intermittent mode of braking was given in the form of a few cyclic stages consisting of subsequent braking and acceleration processes. Based on the Chichinadze’s hypothesis of temperature summation, the evolutions of the maximum temperature during each cycle were calculated as the sum of the mean temperature on the nominal contact surface of the friction pair elements and temperature attained on the real contact areas (flash temperature). In order to find the first component, the analytical solution to the one-dimensional thermal problem of friction for two semi-spaces taking into account frictional heat generation was adapted. To find the flash temperature, the solution to the problem for the semi-infinite rod sliding with variable velocity against a smooth surface was used. In both solutions, the temperature-dependent coefficient of friction and thermal sensitivity of materials were taken into account. Numerical calculations were carried out for disc and drum brake systems. The obtained temporal variations of sliding velocity, friction power and temperature were investigated on each stage of braking. It was found that the obtained results agree well with the corresponding data established by finite element and finite-difference methods.
Highlights
Repetitive short-term mode of braking (RST) is a sequential performance of a certain number of cycles consisting of two stages: braking and acceleration [1]
Initiated by frictional heating during kth braking, we found transient temperature field T(k)(z, t) in this system from the solution to the following boundary-value problem of heat conduction, Equations (16)–(20):
In the drum brake the maximum temperatures Tm(ka)x determined by means of the proposed model, are equal to 353 ◦C, 387 ◦C, 416 ◦C and 443 ◦C (Table 3), and corresponding results presented in monograph [9] are 295 ◦C, 330 ◦C, 400 ◦C and 440 ◦C
Summary
Repetitive short-term mode of braking (RST) is a sequential performance of a certain number of cycles consisting of two stages: braking (heating) and acceleration (cooling) [1]. The equality of the specific friction power and the sum of heat flux intensities, directed inside each element of the friction pair perpendicular to the contact surface, is required in this condition The disadvantage of such an approach is that, when obtaining solutions, a constant, usually averaged with the braking time, the value of the friction coefficient is used. The implementation of the coupled calculation scheme allows to take into account the interdependence of sliding velocity and temperature during each stage of the RST braking mode Since both of the above-mentioned problems in the coupled models are non-linear, their solutions were obtained numerically, using FEM [15] or the finite differences method (FDM) [16]. Where Tm(k)—mean temperature of the nominal contact surface and Tf(k)—average temperature of the real contact area (flash temperature)
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