Article by Juan Jesús García, PhD, Product Manager, Braking Systems in Applus IDIADA
Part 2 of 4. Read Part 1 here.
In the first part of the article, the study aimed at developing a tool for judder optimization through advanced NVH measurements has been introduced, and the actual problem under investigation has been presented: vehicle(s) and brake(s) specifications, braking conditions and the frequency content of the consequent judder excitation.
Methodology
Measurement points
The figure and table below define the measurement points selected for the vibration analysis. Note that the points are characterized by their tri-dimensional movement using tri-axial accelerometers. A total of 105 channels were used.
Note that the driver’s side contains more sensors than the passenger side. This asymmetric arrangement was selected to optimize the number of channels and their location on the most critical points in the vehicles for the judder investigation, i.e., suspension points, hard points, chassis crane and chassis reinforcement.
The measurement locations allow estimating the input forces into the vehicle body and visualizing (harmonic motion) the movement of the suspension systems, as well as the chassis deformation associated with judder.
The accelerometers layout was defined in order to determine the main flow of vibration from the wheel-caliper to the body through the knuckle and the sub-frame. Note that sensors at the active and passive side of the sub-frame also allow the calculation of the transmissibility though the hard points between the sub-frame and the body. The left side contains additional accelerometers to measure the vibration in the upper control arm and its connection to the body. The remaining part of the matrix layout is symmetrical. We note that the selected points emphasised the expected importance of the suspension resonance and the sub-frame behaviour under judder loads.
The importance of suspension resonance is that it will control the frequency and level of excitation and its input energy is proportional to the suspension mass and the level of the acceleration squared (for a given frequency). Sub-frame to body transmission controls the percentage of this energy that propagates to the seat rail and steering wheel. In this respect, we note that both vehicle variants combined the structural stiffness of the body and the sub-frame to provide a robust structure for handling and vibration excitation (braking or road input). Since the X direction of excitation is important during braking, the coupling of the sub-frame components (main sub-frame + rear reinforcement) and the body is of paramount importance. Experimental evidence showed that the transmissibility behaviour of the rear-sub-frame reinforcement in Vehicle 1 and Vehicle 2 were quite different. This is explained in more detail later.
Vehicle response
Vehicle response to judder is a function of the suspension forces generated by the brake and applied to the vehicle and the response of the receiving structure, which is determined by the sensitivity of the system made up by the suspension, the chassis and the vehicle body itself. Thus, in general, one can state that the response of the control points (comfort assessment points) can be expressed by
where [Ac] is a vector of the operational accelerations on the vehicle control points, [Hv] is the matrix of vibration transfer functions relating the input forces, or the forces on the wheel axis of the wheel generating judder, and the response at the control points on the vehicle. [FJ] denotes the vector of operational forces on the wheel axis. This equation represents the general equation of a transfer analysis problem, as shown here:
Since the brake system used in both vehicle variants was the same, one could assume that the vector of operational forces [FJ] is also the same for both vehicles. However, the answer to this question depends on whether the judder phenomenon responds with feedforward or feedback characteristic. This brake performance is shown below, for a simplified feedforward model:
The figure above suggests that the brake torque variation during judder only depends on the piston force and the DTV, regardless of the level of vibration perceived by the brake system due to the judder effect. The figure below, however, assumes that during judder the piston force is affected by the level of vibration experienced by the suspension due to the induced judder; it is a more realistic feedback model:
We note that the piston force on the pads is affected by the caliper vibration. This suggests that any given brake design can vary its performance if it is exposed to a vibration load. The values of the experimental average square acceleration suggest that the feedback loop produced by judder is of the form
where Pp is the piston force during judder, k is a constant (that can be estimated to the order 7 x 103 bar/(m/s2), and Δ(<aJ>2) is the increment in the average mean square pressure of the acceleration of the caliper during judder. This equation suggests that when the acceleration of the caliper increases due to judder, the required cylinder pressure required to generate similar judder phenomenon must be increased by a factor of the order of
This suggests that during judder, the brake pads tend to reduce the level of interaction with the disc surface and, thus, additional piston force is needed to re-establish the interaction between the pads and the brake disc to generate judder. In this case, the summing point would appear as:
The difference in the operational accelerations found between the Vehicle 1 and Vehicle 2 variants during judder can be expressed as:
where Sp denotes the pad’s area (m2) which, in our case, has been found to take a value of about two. Since Δ[Ac] was found to be of the order of 10 to 25 dB, this means that the observed change in the magnitude of the terms of the matrix [HV] should be of the order of 3 to 15. Therefore, we can conclude that the term [Ac] is dominated by [HV], which suggests that the judder investigation should focus on the dynamic response of the chassis and vehicle body.
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