Conversion of images of 3D friction maps to study the coupling between coefficient of friction, velocity and contact temperature of the disc brake

Abstract

• 3D friction maps were used for thermally coupled braking simulations. • The calculated velocity and coefficient of friction agree with the experimental data. • The accuracy of the solution depends on the temperature field determination. • The proposed approach allows for a comprehensive analysis of the given friction pair. The coefficient of friction during braking is not constant. Determining its variability requires measurements in real conditions. This paper presents a methodology of conversion of the measured time profiles of the sliding velocity V eq , contact temperature T , and coefficient of friction f , into analytical formulation of two variables z = f(x,y) . This was executed in the following steps: 1) creating a three-column table V eq , T , f from experimental measurements; 2) interpolation using Kriging; 3) creating a contour map of the coefficient of friction dependent on the sliding velocity and temperature, 4) import of a grey scale image of the friction map into the finite element (FE) software, and 5) definition of a function z = f(x,y) . The studies were carried out for five composite organic friction materials and cast-iron brake disc of a railway vehicle. The developed five friction maps for each friction pair were based the data from the full-scale bench tests during braking from the initial vehicle velocity of 80 km h −1 , 120 km h −1 , 140 km h −1 , 160 km h −1 , 200 km h −1 to a stop. In the second part of the study the initial-value problem for the equation of motion combined with the heat conduction problem were formulated and solved numerically using special functionalities of the FE software, e.g. Deformed Geometry, Mathematics. Changes in the vehicle velocity and time profiles of the coefficient of friction were determined from the solution of the coupled thermal problem. The computational FE model was verified by comparing the measured and calculated changes in the vehicle velocity, coefficient of friction and evolutions of the brake disc temperature during single braking. The maximum calculated temperature 1 mm under the contact surface of the brake disc, during braking from initial vehicle velocity of 80 km h −1 , was obtained for the base friction material and was equal to T 1 , 3 , 5 Num . = 72 °C. The corresponding experimental value was T 1 - 6 Exp . = 66.1 °C. When braking from 140 km h −1 , for the same material it was T 1 , 3 , 5 Num . = 129.7 °C and T 1 - 6 Exp . = 130.7 °C. The obtained differences in braking times calculated and measured did not exceed 1.7 %. The corresponding temperature differences of the disc at the stopping time were lower than 5.5 %.

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