Disc brake judder considering instantaneous disc thickness and spatial friction variation

Abstract

Brake judder is a braking-induced vibration. The character of judder is typical of forced vibrations passing through a critical speed. No specific friction characteristic is needed for judder to occur. In two previous models, i.e. a rotor-stator model and a whole vehicle model, the vibration during a brake application was simulated. The vibrations were assumed to be driven by a brake torque variation (BTV) during a wheel revolution. The BTV was assumed to be proportional to the brake pressure variation (BPV) which was measured. Moreover, the proportionality constant was assumed to be independent of the braking conditions. Verifying measurements were made on a street going vehicle with strong disc thickness variation (DTV) on one of its front wheels. The measured vibration variation during braking was predicted almost exactly by the models. However, the maximum measured vibration level could only be approximated. In the present paper a more accurate analysis of the measurements was found to improve strongly the agreement between predicted and measured vibrations. Hence, the deviation in slope between measured and experimentally generated curves was markedly reduced by replacing the overall mean values of brake pressure level, etc. by slowly varying time functions. The new extended model of the present paper takes into account that the BTV may be generated by variations in normal force (i.e. BPV) and other synchronous variations (called BXV), e.g. spatial friction variation and variation of the equivalent brake radius. The result indicates that BXV may be induced by high BPV levels. Even at judder vibrations primarily caused by heavy DTV (20 μm or more in the cold state), there may be considerable contributions to the vibration level from other synchronous disturbances, i.e. BXV. Further, it was found that the pad stiffness increases with the brake pressure. For such a pad stiffness characteristic, an increase of the DTV level (for whatever reason) by 50 per cent might result in more than a 100 per cent increase in the corresponding BPV and BTV levels. Hence, a progressive pad is more sensitive to increases of the DTV level than a linear pad would be.