Article by: Juan Jesús García, Ph.D., Product Manager, Braking Systems in Applus IDIADA
Disc thickness variation (DTV) is the main cause of brake judder. Cold judder can be caused by a number of mechanisms such as uneven wear, which leads to disc thickness variation as the wheel rotates. The thickness variation leads again to torque variation that is sensed as vibrations by the driver. Hot judder, on the other hand, occurs due to heavy usage of the brake that results in uneven heating or hot spots that cause the distortion of the rotor of a disc brake, which also originate brake torque variations.
This article presents a practical way of measuring operational in-service DTV at constant speed and during braking applications, and how this information can be correlated with the real vehicle body deformation (bending & torsion) due to realistic brake torque fluctuations.
DTV can basically be measured in two fundamental conditions: quasi-static and dynamic (operational). In the quasi-static measurement, the brake disc is located on a test bench or with the vehicle on a hoist, which allows manual rotation of the measured wheel. In this situation, two high precision displacement sensors are located very close to both faces of the brake disc while it is rotated at very low speed (normally manually or using an electric motor). This type of static measurement is useful when it is necessary to characterize the nominal initial condition of a given disc as received from the manufacturer or during the artificial generation of a target DTV level required for a judder sensitivity analysis.
Dynamic DTV provides realistic information of the DTV as observed in running conditions. However, in-service measurements are less accurate than quasi-static ones; the main source of inaccuracy is the vibration induced by the road excitation on the displacement sensors, which affects their relative position with respect to the rotating disc. In general, this sensor vibration is uncontrolled and has a broadband frequency spectrum.
The conceptual practical sensor layout to measure DTV proposed herein is shown below:
The system includes a bracket that holds two displacement sensors in position facing a rotating brake disc. The displacement sensors measure the values of d1 and d2 versus time. This arrangement allows the measurement of the DTV versus time:
where T denotes the disc thickness and the sub-index ‘o’ denotes the initial condition when time equals to zero (which is an arbitrary reference point).
During operational measurements the fixture (bracket) holding the displacement sensors can exhibit unpredictable movements. These movements are complex but they are made up of simpler movements such as axial and radial displacements, and rotations:
Note that, if the bracket is assumed to be perfectly rigid, the previous equation holds for all these movements. This is due to the fact that any change of the distance measured by any sensor is counterbalanced by the same value, but with opposite sign, measured by the other displacement sensor.
However, in-service measurement of DTV can encounter situations in which the bracket cannot be assumed to be rigid (for instance, with road excitation). The error equals the differential relative deformation of the two holding arms of the bracket. This source of error can be minimized by taking the following actions:
a) Improving the dynamic stiffness of the bracket so that relevant natural modes are well above the frequency of road excitation.
b) Implementing a method to independently measure the dynamic displacements of the two displacement sensors. This requires the measurement of the three-dimensional vibration movement of the displacement sensors due to operational excitations.
This concept is shown in the figure below, which depicts an arrangement for DTV dynamic measurement with capability of measuring the tri-axial acceleration experienced by the displacement sensors during operational measurements.
The accelerations allow the vibrational displacement experienced by the displacement sensors due to, for example, road or engine excitations to be calculated. The vibration displacements exhibited by sensors S1 and S2 during in-service conditions are:
The vector information obtained from the double integration of the acceleration data can be used to correct the DTV time history values as:
where n12ut denotes the unitary vector connecting the centers of sensor S1 and S2 respectively and ‘·’ is the dot product.
Having introduced the study and explained the methodology, the actual experimental set-up and the main results, together with a correlation between DTV, judder-induced vibration and vehicle body deformation, will be presented in the next section.
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