Study of the temperature distribution in disc brakes by the method of order-ofmagnitude analysis
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 lumpe...
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| Main Authors: | , , |
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| Format: | Conference or Workshop Item |
| Published: |
2007
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| Subjects: | |
| Online Access: | http://eprints.uthm.edu.my/1938/ http://eprints.uthm.edu.my/1938/1/STUDY_OF_THE_TEMPERATURE_AZRISZUL_MOHD_AMIN.pdf |
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| Summary: | 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. |
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