Source: Applus IDIADA
Article by Juan Jesús García, PhD, Product Manager, Braking Systems in Applus IDIADA
Introduction
ADELANTO, Calif. – During brake judder excitation, the hard points of suspension systems apply tri-dimensional forces into the sub-frame and vehicle body. Due to the nature of judder excitation, these forces are basically periodic and can normally be broken down as wheel rotation orders that are determined by the circumferential distribution of the disk thickness variation (DTV).
If DTV overcomes acceptable targets, during braking application, DTV can generate a fluctuating brake torque that will induce a variable longitudinal force on the vehicle. This fluctuating force can produce a longitudinal oscillation of the suspension and if its intensity is high or the vehicle is particularly sensitive, this oscillation can also be perceived by the driver as vibrations on the vehicle body, steering wheel and brake pedal.
The sensitivity of a given vehicle to judder excitation can be assessed using a calibrated DTV profile values previously generated on the surface of the brake disc. In general, the generation of this circumferential DTV can follow any harmonic form and can be carried out using abrasive paper material. Since the braking force changes as determined by the DTV variation, so will the fluctuating longitudinal braking force. It can then be shown that the forcing action on the vehicle can be approximated by a longitudinal force of the form
where ω is the angular wheel speed, n denotes the wheel order and θn is the phase for the order n. During a braking application, the order amplitude An will vary depending on the coupling between the pads and the disk. In general, the evolution of order amplitudes is plotted versus wheel rotation frequency.
In-vehicle Operational Brake Judder Tests
The work reported in this article is based on a comparative analysis of cold brake judder behavior on a SUV with two different chassis layouts and design exhibiting unequal dynamic stiffness. Herein, we will call the two configurations of a test vehicle with the corresponding chassis design as V-Chassis 1 and V-Chassis 2 versions. The judder of the test vehicle with its default chassis configuration (V-Chassis 1) was initially compared with reference data from a database available in IDIADA. These two versions of the chassis have the same layout as shown in Figure 1, but V-Chassis 1 is assembled to the vehicle with four rubber bushings, while V-Chassis 2 uses four rigid (steel) bushings in the same locations.
The vehicle under study was a state-of-the-art SUV with an engine providing about 100 kW. The vehicle incorporated front and rear disk brakes with ventilated discs and floating calipers, single piston cylinders with diameters 60, 38 mm respectively. The dimensions of the front rotor were:
- Ext. diameter: 305 mm
- Thickness: 25 mm
- Effective radius: 125 mm
A representative braking application for judder generation, taken from a matrix of braking parameters, was chosen to perform the vibration analysis. In order to find a severe judder condition for the test vehicle, a cold judder matrix developed by IDIADA was applied. This matrix defines a sequence of initial and final speeds, initial brake temperature (IBT) and vehicle deceleration that boosts the generation of judder in disc brakes for commercial vehicles. The braking parameters defined here correspond to the braking events selected as the ones that produced maximum discomfort for the driver due to judder. The braking parameters found for the worst judder occurrence were as follows:
- Initial speed: medium high speed
- Final speed: medium – low
- IBT (C°) = 50 to 100
- Vehicle deceleration: low
In the analysis reported here, this procedure was used with a harmonic disc thickness variation of 20 µm of amplitude with a first wheel order distribution. This disc was installed on the left front wheel only, for both vehicle-chassis configurations.
About Applus IDIADA
With more than 25 years’ experience and 2,450 engineers specializing in vehicle development, Applus IDIADA is a leading engineering company providing design, testing, engineering, and homologation services to the automotive industry worldwide.
Applus IDIADA is located in California and Michigan, with further presence in 25 other countries, mainly in Europe and Asia.
