Article by Juan Jesús García, PhD, Product Manager, Braking Systems in Applus IDIADA
Part 1 of 4. Read previous TBR Technical Corner articles here.
Introduction
Brake judder is a phenomenon that normally occurs when braking at high speeds with low decelerations. It is felt by drivers as a vibration on the body, brake pedal and steering wheel and as a low-frequency noise.
Previous articles of the TBR Technical Corner have presented a practical way of measuring operational in-service DTV under hot/cold judder excitation (link), as well as a study of correlation between subjective and objective results in a cold judder DTV sensitivity test (link). In this work, a deep characterization of a judder problem is analyzed, and a development tool for judder optimization through advanced NVH measurements is consequently proposed.
During brake judder excitation, hard points of suspension systems apply tri-dimensional forces into the 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 disc 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 to judder excitation can be considered in terms of the vibration transfer function values between a longitudinal input force applied on the front axle and its consequent response in any point of interest located on the vehicle chassis or body. This simple measurement is very useful from an engineering point of view since it is simple, repetitive and cost-effective, while revealing very useful information about the response of the vehicle and chassis assembly against longitudinal excitation associated with judder.
As observed in the following figure, the fluctuating braking moment generates a fluctuating longitudinal force (FB) that induces vehicle vibrations. The figure also depicts the system of coordinates used in the measurements.
The relationship between the fluctuating braking torque and the associated longitudinal braking force is given by the relationship shown in Figure 1. We note that this relationship shows that the spectral content of the brake torque time signal is the same as the one of the longitudinal braking force. Thus, if the braking torque changes as determined by the DTV variation, so will the fluctuating longitudinal braking force. This is shown by the relationship between the Fourier Transform of the braking force, FB, and the fluctuating moment, MB, i.e.
where R is the wheel radius and FT{} denotes de Fourier Transform. Therefore, from this equation we can conclude 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 disc. In general, the evolution of order amplitudes is plotted versus wheel rotation frequency.
The problem under investigation
The work reported in this article is based on a comparative analysis of hot brake judder behaviour on a sport vehicle with two different chassis layouts that exhibit unequal longitudinal dynamic stiffness. Herein, we will call the vehicles Vehicle 1 and Vehicle 2. The vehicle under study was a high-performance car with a V6 petrol engine providing 425 HP. The vehicle’s front axle incorporated ventilated dual cast discs and six-cylinder calipers with diameters of 30, 34 and 38 mm respectively. The front rotor had an external diameter of 380 mm, a thickness of 34 mm and an effective radius of 158 mm.
Two representative braking applications (one for each vehicle variant) were chosen to perform the vibration analysis – these are the snubs that produced the worst judder occurrence. However, despite being the brake stops with the highest judder-induced excitation, the subjective ratings were unalike.
| Vehicle 1 | Vehicle 2 | |
| Stop No | 26 | 23 |
| Subj. Evaluation | High rating | Low rating |
| Target Pressure | 3 bar | 5 bar |
| Initial Speed | 178 km/h | 216 km/h |
| Final Speed | 79 km/h | 87 km/h |
| Deceleration (Avg) | 0.817 m/s2 | 1.38 m/s2 |
| FL Pressure (Avg) | 2.93 bar | 5.74 bar |
| FR Pressure (Avg) | 2.87 bar | 5.76 bar |
| FL Disc Initial Temp. | 250.9º C | 236.7º C |
| FR Disc Initial Temp. | 181.3º C | 227.8º C |
| RL Disc Initial Temp. | 159.6º C | 205.9º C |
| RR Disc Initial Temp. | 202.2º C | 222.1º C |
The frequency content of the braking applications carried out during this exercise is defined in the figures below for both Vehicle 1 and Vehicle 2 variants. The information obtained from the front knuckles during hot judder shows that the excitation in Vehicle 2 can be up to 25 dB higher than the one in Vehicle 1. This is especially true in the X and Z directions and for the 4th order contribution (900 rpm), which tends to dominate during the judder event.
Vehicle 1, knuckle excitation under judder conditions:
Vehicle 2, knuckle excitation under judder conditions:
The subjective ratings of the judder event showed that Vehicle 2 exhibited higher braking induced vibration, which affected the subjective perception associated with the steering wheel, seat and pedal performance. The vibration evolution during judder for the Vehicle 1 and Vehicle 2 variants in the seat rail and steering wheel confirmed that the vibration levels in the seat rail and the steering wheel for Vehicle 2 variant in the X, Y and Z were higher than those for Vehicle 1. The most important directions and rpm were:
Therefore, we can conclude that the two vehicle variants performed differently in terms of braking. In this work, we have assumed that the braking events under study, for Vehicle 2 and Vehicle 1, belong to the same statistical population of braking events (the brakes were the same). Therefore, the difference found should be associated to the coupling effect between the natural modes of the front suspension and the pad-disc interaction during braking with low cylinder pressures. This idea will be covered in more detail later.
Provided exclusively to The BRAKE Report Technical Corner by Applus IDIADA.
About Applus IDIADA
With over 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.
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