Part 1 of 3. Read Part 2 here.
By Fabio Squadrani, Ing., Senior Manager, Braking Systems in Applus IDIADA
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. It is normally caused by disc thickness variation (DTV) —refer to this article (link) to find out about a practical way of measuring operational in-service DTV under judder excitation.
Judder can be differentiated between cold and hot judder depending on the origin of the mentioned DTV. Cold judder can appear when there is DTV at ambient temperature. DTV generation can occur, for example, when driving for long distances on motorways without braking. When performing a DTV sensitivity test, discs with different DTV are artificially created and subjective judder tests are performed. An array of accelerometers is located on the steering wheel, seat rail and brake pedal in order to objectively analyze the judder perceived by the driver. The DTV sensitivity test allows testing the same vehicle with different levels of judder, from good to low ratings.
Judder is subjectively rated in three different categories: steering wheel, brake pedal and body. The driver gives a rating from 1 to 10 for each category and snub. Score 10 means that the driver does not feel any judder at all; rate 1 is the lowest.
Human sensitivity to vibration depends on the frequency of the excitation and the part of the body feeling it. ISO2631-1 and ISO5349-1 describe the filters that are used in this study to weight the measured acceleration so that the human sensitivity of the affected body part is taken into account in this analysis. The impulsive root mean square (IRMS) of the filtered signal is then calculated. The IRMS gives the energy of the vibration felt during a short time window. Different window sizes are explored in order to find the best correlation between objective and subjective results. The window sizes used are based on the experience of drivers that subjectively evaluate the judder. The acceleration is then calculated using different methods and compared with the subjective rating.
Experimental Application of the Methodology
The IRMS calculates the root mean square of a window that is displaced one value in each step, as shown in the equation below:
- ∆t is the size of the analysis window in seconds
- a(t) is the measured acceleration
Window size affects the IRMS curve and various sizes have been studied. Normally a driver takes between half a second to a full second in order to evaluate judder vibration. The window sizes studied in this work are: 0.35s, 0.5s, 0.75s, 1s and 1.25s.
The accelerometers used for the correlation are divided into three categories:
- Hand: triaxial accelerometer on top of the steering wheel.
- Body: triaxial accelerometer on the seat rail.
- Brake pedal: monoaxial accelerometer behind the brake pedal.
Different filters are used for each part of the body. For the hand induced vibration on the steering wheel, the filter used is described in ISO5349-1:
The total amplitude of the vibration felt by the hand is described in the equation below. This is calculated using the three IRMS curves for each direction, generating a new IRMS curve for the hand.
Foot–transmitted vibration is described in ISO2063‑1; the filter used is:
The total amplitude for the body vibration is:
Where the coefficients affecting the corresponding mean square value accelerations have been taken from ISO2631-1 for comfort of seated persons.
Having introduced the study and explained part of the methodology, the correlation between subjective judder ratings and objective accelerations results, together with the main conclusions, will be presented in the next section.
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.
Applus IDIADA is located in California and Michigan, with further presence in 25 other countries, mainly in Europe and Asia.
Source: Applus Idiada
Editor’s note: Applus IDIADA is providing The Brake Report with technical content written by the company’s in-house engineers and technical experts.