*TROY, Mich. — This is the first 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.*

Vehicle body bending and torsion due to fluctuating brake judder forces affect body vibration transmission at low frequencies. This dictates part of the vibration annoyance perceived by the driver when brake judder occurs. Other sources of vehicle judder sensitivity may also be related to chassis stiffness and chassis-to-body hard points impedance. The operational measurement of vehicle body bending and torsion stiffness reveals parameters of paramount importance to understanding brake judder performance as well as other vehicle dynamic behavior under transient loads.

**Introduction**

Vehicle bending and torsion during operational conditions is normally unknown due to a lack of suitable instrumentation to carry out these measurements. However, these in-service vehicle body characteristics are very important because, among other factors, they affect vibrational comfort and vehicle dynamic performance. At low frequencies vehicle global bending and torsion exhibit resonances that can be excited by road loads, vehicle dynamic maneuvers or brake torque variability. In the context of brake judder, which is a low frequency excitation source, the vibration response of the vehicle due to the Disc Thickness Variation (DTV) is fundamental to understanding the relative contribution of the body to the total perceived vibration. Thus, access to a simple and efficient method to measure vehicle body bending and torsion can be of high value to support experimental analysis of the interaction between brake judder and vehicle body stiffness and its vibration response.

**Methodology** – Definition of the measurement array

The experimental methodology proposed in this work to measure the operational vehicle body bending and torsion under judder loads is based on the use of tri-axial accelerometers located at six positions of the vehicle body. The simultaneous acquisition of the relative accelerations 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 body.

In this context, complementary accurate in-service DTV measurements are valuable because they can be related with subjective and objective response to judder excitation. In this case, the objective assessment of judder response is aimed at correlating the vibration levels perceived by the driver with his/her subjective perception. From the vehicle structure point of view, it is also possible to correlate the DTV levels with the bending and torsion exhibited by the vehicle body under judder excitation. This information is important if one wants to assess the relative contribution of body stiffness to overall judder response.

The measurement of dynamic bending and/or torsion of a vehicle body under judder conditions can be assessed using the approach presented in figure 1 below. As shown, in the application presented here, the six tri-axial accelerometers are in the suspension domes of the vehicle and the center of the body sills.

The accelerometer locations define a dihedral as the one shown in figure 1. The operational deformation of this dihedral allows us to calculate the global bending and torsion of the vehicle body under any operational load (such as, for example, road deterministic inputs, transient VD maneuvers and braking) and, in particular, for judder excitation. In the latter case, body stiffness under brake judder excitation reveals the part of the overall judder vibration sensitivity due to the dynamic body bending & torsion deformation

**Calculation of the vehicle body bending and torsion**

The main concept to calculate the bending and torsion of the vehicle body is using the accelerometer array shown in figure 1 to track down the deformations of this array based on the measured point accelerations during judder. Since point displacements can be calculated by double integration of the corresponding acceleration signals it is then possible to know, for each instant in time, the locations in space of the six measurement points. From this, one can calculate the associated bending and torsion induced in the array. This is shown in figure 2.

From this figure, we can infer that the vectors that define the dihedral deformation for any given value of time are given by the following equations:

where, for example, are the coordenates of the point at time *t*, , denote the nominal coordinates of the same point when the dihedral is undeformed, and is the change in the coordinates of point during the time interval , with equal to the inverse of the sampling frequency.

We note that the incremental part of the vectors defined in equations (1) to (6) is calculated by double integration of the acceleration data from the eighteen acceleration channels. These give the vibration displacement of all the points of the nominal dihedral, which, after the application of the corresponding geometric relationships yields the corresponding time histories for the torsion and the bending angles of a vehicle body modelled as shown in figure 2. As an application example, section 3 shows the measured time history of the vehicle body bending (in the vertical plane) and the torsion angle of a test vehicle under brake judder load. Hereinafter, the term bending will refer to the angular deformation of the dihedral in figure 2, measured in the vertical plane.

We note that the acceleration data provided by the accelerometers attached to the vehicle body must have a very high signal-to-noise ratio in order to be used for bending and torsion estimation. This requires the use of high-quality low noise acquisition systems and sensors. It is, thus, important to assess this aspect comparing, for each acceleration channel, the electric background noise of the accelerometers with the signals obtained during the measurements. The accelerometers used in this work were PCB 356A15 and the acquisition system, a LMS SCM09.

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