*TROY, Mich. — This is the second of two articles by Juan Jesús García, PhD, Product Manager, Braking Systems at Applus IDIADA, on the impact of brake judder on body bending and torsion.*

BRAKE JUDDER LOAD ON BENDING AND TORSION OF A VEHICLE BODY (PART 1 OUT OF 2)

This work presents an experimental methodology to measure in-service vehicle body bending and torsion based on the use of six tri-axial accelerometers located on the body. The simultaneous acquisition of the relative acceleration of these location points when the vehicle is excited with operational brake judder loads makes it possible to calculate the global bending and torsion deformation experienced by the vehicle.

The first part of this article introduced the problem and described the methodology, while this second part will focus on the measurements and results from a case study.

**Measurements: Case study**

In order to assess the sensitivity of the proposed method to detect changes in vehicle body bending and torsion due to a brake DTV variation, an in-service test with a passenger car (B segment) was carried out installing two different sets of discs installed in the front wheels. The first set of discs had a nominal DTV of 2 µm, and the second, 10 µm. The later was artificially generated using abrasive paper. Both DTVs produced a dominant first wheel order excitation. Figure 3 depicts the measured DTV for the nominal and the modified brake discs used in the tests. Note that the nominal DTV was approximately 2 µm and the modified one 10 µm.

The braking testing conditions used with both sets of the front brake discs are as follows:

- Initial Brake Temperature (IBT): 100 ºC
- Deceleration: 0.2 g
- Speed 160 to 30 km/h

The subjective response of the vehicle to judder excitation was assessed with the two disc sets and the corresponding acceleration data from the accelerometer array whown in figure 1 was recorded for later processing.

**2. Results**

The study of the overall evolution of the bending and torsion angles during judder can be better analysed by calculating the impulsive root mean square (r.m.s) value of these magnitudes. The impulsive r.m.s. value of a signal *x(t)* is defined as,

where *Δt* is the size of the analysis window in seconds. In our case *x(t)* is used to denote both, the bending and the torsion angles versus time. In the calculations reported herein, the value of Δt has been taken as 2 seconds.

Figures 4 to 8 show the measured body bending and torsion angles obtained with the discs with a nominal DTV of 2 µm, and figures 9 to 13, those corresponding to the discs with DTV of 10 µm. The results show that the overall level of both the body bending and the torsion angles change considerably as the braking progresses from high speed (160 km/h) to low speed (30 km/h). As expected, the maximum levels of bending and torsion are achieved with the highest DTV.

Figures 8 and 13 compare the 2D graphs of the bending and torsion for both DTVs. We observe that the amplitude of the torsion angle is about four to five times higher than the one for the bending. Figure 14 shows the locus of the bending-torsion pairs for both DTV values during one second of the total braking application. The locus lines have been calculated with equation (7) and, thus, represent impulsive r.m.s values (Δt=2s). Regardless of the DTV value, the graph shows a high variability in the instantaneous bending-torsion pairs during judder. Also, as the DTV increases the figure exhibits a clear shifting of the bending-torsion locus towards higher values. This trend is particularly clear in figure 15, where one can see the time evolution of the impulsive r.m.s (equation (7)) for the bending and the torsion angles of the test vehicle for the nominal, 2 µm, and the 10 µm DTVs. From these results we can infer that vehicle body torsion is the dominant deformation response during judder with an energy amplitude of about five times that of the bending.

From a brake engineering point of view, this bending and torsion deformation during braking application can be correlated with other braking parameters, such as brake pressure fluctuation or the DTV. This allows the definition of transfer functions that relate the body deformation with other relevant braking parameters.

**Conclusions**

This work presents a simple and robust experimental method to measure the in-service overall vehicle body bending and torsion under fluctuating braking loads. This body bending and torsion stiffness information during braking can be correlated with, for example, the associated operational Disc Thickness Variation (DTV) that produces brake torque fluctuation. Thus, a correlation can be established between DTV, judder induced vibration and vehicle body deformation. This information is very important for understanding and optimising vehicle body stiffness for vehicle judder performance and for correlating simulation models of chassis dynamics.

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