Bryant, David (2010) Thermo-elastic Deformation of a Vented Brake Disc. Doctoral thesis, University of Huddersfield.

The subject of retarding a moving vehicle or object in a controlled manner has been investigated over hundreds of years with many different solutions being developed over the years. As time has progressed a common overall design has almost uniformly been agreed upon for vehicle use; a brake disc and caliper or brake drum arrangement. As vehicle refinement has improved there has been increasing focus on the refinement of such designs with regards to their noise, vibration and harshness (NVH)characteristics. Whilst brake noise has had significant research analysing its cause, effect and solutions, brake judder has had less research
focussed upon it. The principal reason for past research priorities and the recent interest in judder is because of the increased demands being placed on brakes – higher power absorption with lighter structures. The subject of this thesis was to address the least known phenomena of brake judder, that of the thermo-elastic deformation of vented brake discs. The research utilised experimental, analytical and empirical methods to give a broader understanding of the transient deformation process, both thermo-plastic and thermo-elastic, of a high performance vehicle disc

Initial characterisation of thermal judder was carried out on-vehicle where it was identified that brake pressure could be used as a reliable indicator to show the developing nature of this phenomenon. The brake pressure pulsation was shown to change from low order (first or second order) to high order (up to eighth order) over
the duration of a high speed vehicle brake test which involved up to thirty braking events. The pressure pulsation indicated a link to brake disc deformation with the magnitude and order of brake pressure variation increasing with increasing disc
temperature. The highly dynamic, transient, nature of brake disc distortion was also investigated on a bespoke quarter car suspension brake dynamometer. Thermoelastic wave-like deformation was shown to occur during the process of a single braking event with the order of deformation corresponding to the brake pressure
variation. The order of this wave-like deformation was shown to be linked to the amount of energy transferred into the braking system with higher energy braking events resulting in higher order deformation. Thermal images of the brake disc have shown an equispaced formation of hot-spots on the inboard and outboard friction ring surfaces which was linked to the disc waveform. The wave-like deformation was attributed to circumferential buckling of the brake disc as suggested by Lang [1].
This resulted from rapid thermal expansion of the friction rings due to the sudden - 4 - influx of heat during braking. Thermal gradients between the hot and cold regions of the brake disc constrained the radial thermal expansion of the friction ring and caused compressive stresses to build up. When the tangential load causing the
stress was in excess of the critical buckling load, buckling of the brake disc occurred with the mode order of the buckled disc related to the temperature of the friction ring.
Stress relieving of the brake disc was shown to occur during brake testing on the brake dynamometer causing a thermo-plastic effect. This “in service” stress relieving effect removed the retained stresses resulting from the casting and machining processes and allowed the disc to adopt a second order mode of deformation. Data
from the on-vehicle and dynamometer testing was used to generate and validate finite element analysis simulations which were used to investigate thermal inputs and heat dissipation from the brake disc. These findings were then combined with that of an associated aerodynamic study [2] to generate a modified brake disc vent profile which reduced the surface temperature variation, thermal gradients and maximum disc temperature. On-vehicle testing of the prototype design showed an average 14% reduction in maximum disc temperature and it was proposed that this would reduce the propensity for the disc to generate judder by reducing the thermal deformation of the brake disc.

dbryantfinalthesis.pdf - Accepted Version
Available under License Creative Commons Attribution Non-commercial No Derivatives.

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