# Study of the temperature distribution in disc brakes by the method of order-of-magnitude analysis

Mohd Amin, Azriszul and Mohd. Seri, Suzairin and Vijay, R. Raghavan (2007) Study of the temperature distribution in disc brakes by the method of order-of-magnitude analysis. In: Regional Conference on Engineering Mathematics, Mechanics, Manufacturing & Architecture (EM3arc) 2007, 2007.

## Abstract

Disc brakes have been used for many years in automobiles and are still undergoing further development in terms of the temperatures that they can reach and operate safely at. Many methods have been introduced in the past to simulate and predict the temperature history of the disc brake, such as lumped analysis, one-dimensional analytical method and numerical method for analysis in 2-D or 3-D. These numerical simulations range from finite differences to finite elements, each with a variety of assumptions. In this paper, we show that the method of order-of-magnitude analysis, originally proposed by Ludwig Prandtl in his analysis of fluid flow and boundary layers, could be advantageously applied to the study of temperature distribution in disc brakes. The governing equations are formulated in their entirety sans simplifying assumptions, as a 3-D transient problem, in the axial, radial and peripheral directions, also accounting for enthalpy flow and fin effect. The equations are then normalized with respect to variables of physical significance in the problem. The normalized equations are then examined for the order of magnitude of the coefficients of the terms in order to determine their relative importance. This approach has been applied with success in fluid flow, convective heat transfer and transient conduction. The results of the analysis of a disc brake based on the order-of-magnitude approach are compared with previously obtained solutions in the literature and found to have very good agreement. The value of the method is that, even without a physical understanding of the underlying phenomena, it is possible to make appropriate problem simplifications and get efficient solutions. Further, the analysis has the potential to be extended to include thermal cracking, warping and thermal stress in the disc brake.

Item Type: Conference or Workshop Item (Paper) disc brake; thermal analysis; order-of-magnitude approach T Technology > TJ Mechanical engineering and machinery > TJ1040-1119 Machinery exclusive of prime movers Faculty of Mechanical and Manufacturing Engineering > Department of Manufacturing and Industrial Engineering Normajihan Abd. Rahman 09 Sep 2013 09:18 21 Jan 2015 07:38 http://eprints.uthm.edu.my/id/eprint/4124 View Download Statistic