Doctoral thesis, 2001
Brake judder is a braking induced, forced vibration occurring in different types of vehicles. The frequency can be as high as 500 Hz, but usually remains below 100 Hz and often as low as 10-20 Hz. The driver experiences judder as vibrations in the steering wheel, brake pedal and floor. In the higher frequency range, the structural vibrations are accompanied by a sound. Note that a phenomenological definition (i.e forced vibration) of brake judder is used. Hence, the low frequency brake vibrations, creep groan (related to stick-slip) and dynamic groan (an instability phenomenon), are not studied in this work.
The vibration starts with medium to heavy braking from high speed and remains until low speed, if the brakes are continuously applied. There is a considerable amplification of the judder vibration near certain critical vehicle speeds. This behavior has been successfully simulated by the amplitude function technique, which was developed within the project. The method is specially designed for theoretical analysis of forced vibrations like brake judder. The use of amplitude functions was also found to be valuable when analyzing measured vibrations in a braking vehicle.
Brake torque variation (BTV) and brake pressure variation (BPV) are the primary excitation mechanisms for judder vibrations. While BPV causes vibrations mostly in the hydraulic system, BTV is believed to be responsible for vibrations in the vehicle structure. This work concentrates on the vibrations caused by BPV; direct effects of BPV like pedal vibrations are not studied. BTV arises mostly as a result of permanent or reversible, geometrical defects, e.g. DTV (Disc Thickness Variation) of disc brakes and shape deviations of drum brakes. DTV in turn is affected by manufacturing tolerances, disc runout, thermal coning and buckling of the disc, uneven disc wear, uneven friction film generation, uneven heating and Thermo-Elastic Instabilities (TEI).
Verifying measurements were made on a street-going vehicle with strong first order DTV on one of its front brakes. The measured vibration variation during braking was predicted almost exactly by a rotor-stator model, exposed to a sinusoidal BTV with a sweeping frequency due to the finite deceleration. However, the maximal measured vibration level was seen to vary considerably compared to the predicted value. A full vehicle model, including the aerodynamic drag etc., combined with a more accurate signal analysis, was found to improve the absolute vibration level prediction, especially at low decelerations. Most of the remaining differences at low deceleration levels are believed to be caused by the fact that the relative BTV of the calculations was approximated by the measured relative BPV level. At high brake pressure levels, the relative BPV level becomes too low (less than 5%) to admit a reliable estimation. Besides, the estimation of the correction terms due to aerodynamic drag etc. affects the theoretical vibration level. To avoid all this, one should try to measure the brake torque directly.
However, measuring the BPV level is useful if one wishes to estimate the instantaneous DTV level in a braking vehicle. This is possible if a relevant pad compression model is available. It was found that a pad stiffness that increases with the brake pressure was able to explain the measured BPV level dependence on the absolute brake level. For such a pad stiffness characteristic, an increase of the DTV level (whatever reason) by 50% might result in more than a 100% 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.