Article by: Juan Jesús García, PhD, Product Manager, Braking Systems in Applus IDIADA
This is the 4th and latest part of the study aimed at developing a tool for judder optimization through advanced NVH measurements. The 1st article introduced the problem and the actual vehicle under investigation; the 2nd part focused on the experimental
Mechanical integrity of attachment points at the sub-chassis rear points
The mechanical integrity of the attachment points of the sub-frame reinforcement to the body was investigated to explore if the stiffness of the chassis and the chassis reinforcement matched the dynamic stiffness of the body at the attachment points. By mechanical integrity it is understood that the relative vibration movement at the evaluation point is negligible. This aspect is important since big differences in body and chassis dynamic stiffness induce vibrations and relative displacements between parts. As an example, for the problem analyzed here, the analysis of the mechanical integrity of the point called as Sub-frame-Rear RL has been compared for Vehicle 1 and Vehicle 2:
The results show that in Vehicle 1, the active and passive part of the attachment points had very similar vibration and spectrum level in the X direction. This is associated with a correct behaviour of the joint. However, the equivalent point in Vehicle 2 showed important differences in both level and frequency. This suggests that the stiffness of the aluminium reinforcement and the vehicle body did not have homogenous behaviour. This could be caused by the fact that the reinforcement in Vehicle 2 had low stiffness in the X and Y direction. This idea is presented below:
We note that the chassis reinforcement design in combination with the steering layout seems to boost the steering wheel vibrations during judder due to the low stiffness along the red line shown in the figure above. This was not the case for Vehicle 1 variant, where the steel tube sub-frame reinforcement seemed to be stiffer:
Very possibly, during judder bending waves can propagate in the plane of the sub-frame reinforcement. Bending waves in thin panes, as the name implies, take the form of waves of flexure propagating parallel to the surface, resulting in normal displacement of the surface. The relative stiffness of the aluminium reinforcement versus the steel pipe sub-frame can be expressed as
Where Es and EA denote the Young’s modulus of the steel and the aluminium respectively. Isub_muleto and Isub_VP are the cross-sectional second moments of area of the part along the transversal line shown Vehicle 1. It is estimated that the bending stiffness of the aluminium sub-frame reinforcement in Vehicle 2 is about 7 times lower than the one for the steel pipe reinforcement in Vehicle 1. This seems to be consistent with the higher levels of the FRFs for the aluminium reinforcement.
Average vibration energy distribution during braking
In order to arrange the vehicle points that exhibit higher vibration levels, we compared Vehicles 1 and 2 average mean square acceleration levels in all the measured points during the braking event. This calculation allowed an approximate assessment of the points at which the vibration energy was injected or transmitted in the vehicle. The global values of the mean square acceleration have been calculated taking into account a spatial average value of the mean square acceleration at the points under study during braking. The X, Y and Z directions have been averaged so that a single value can be associated with each point:
The right-hand side column in the table presents the ratio between the average mean square values for both vehicles. Values higher than three have been marked so that critical transmission or input points can be identified. Note that the ratio values depend on the braking induced vibration and the vehicle transmissibility. In our case, we noted that the braking induced vibration and transmissibility of Vehicle 1 and Vehicle 2 were quite different. Thus the values on the left column take into account the overall effect.
The results showed that the points that need attention to explain the different judder performance of the two vehicles were:
- Understand the higher vibration sensitivity of the front suspension in Vehicle 2 with respect to Vehicle 1. This is based on the fact that the point inertance (acceleration/force) for the knuckle of vehicle 2 was higher than the one for vehicle 1 (graphs not reported in the paper).
- Lower and upper strut attachment points
- Sub-frame rear & sub-frame rear body
Operational deflection shapes of chassis under judder excitation
A running mode analysis (RMA) of the brake and chassis assembly for both vehicles was carried out in order to find out the main differences of the global vibration of this subsystem under judder conditions.
Vehicle 1, Order 2 – 1183 rpm (40 Hz) – Global upper view. The green point denotes the steering wheel. Colours: blue, sub-frame; orange, body; purple, control arms + knuckle; red, caliper:
Vehicle 2, Order 4 – 1377 rpm (90 Hz) – Global upper view. The green point denotes the steering wheel. Colours: blue, sub-frame; orange, body; purple, control arms + knuckle; red, caliper:
The interpretation inferred from the observation of the animations is summarized as:
Therefore, we observe that the high mobility of the chassis and its deformation at judder frequencies in Vehicle 2 explains the higher judder vibration response.
The main conclusions that can be inferred from the analysis presented here are:
- The results found in this work suggest that the generation of judder by the brake system used, as assembled to the vehicles suspension, responds to the block diagram feedback coupling between the brake performance under judder conditions and the suspension and chassis response. This concept should be compared against the more common approach, which assumes a feedforward effect of brake torque and vehicle vibration.
- The longitudinal resonance of the front suspension of Vehicle 2 and Vehicle 1 occur at different frequencies. Also the sensitivity of the suspension of Vehicle 2 to absorb vibration energy was higher. Since the design of the front suspensions of the vehicles (not the chassis) was the same, the difference in its longitudinal resonance was due to the lower longitudinal and lateral stiffness of the sub-frame of Vehicle 2.
- The operational vibration for the steering wheel and seat rail found in Vehicle 2 was considerably higher than the one for Vehicle 1 with an important 4th order contribution. The results suggested that the aluminium sub-frame reinforcement stiffness used in this vehicle could have an important effect on the transmission of the 4th order vibration into the body and the steering rack. Y and Z direction stiffness seemed to be lower than required.
- The vibration transmissibility (based on FRF measurements exciting the vehicle with a force applied at the centre of the wheel knuckle) of Vehicle 2 was higher in the X and Y directions. The results suggested that this might be caused by a lower dynamic stiffness of the aluminium sub-frame reinforcement vs. the steel pipe solution adopted for Vehicle 1.
- The lower longitudinal resonance of the front suspension for Vehicle 2 seemed to be affected by the lower lateral stiffness of the lower control arm hard points, which was caused by the lower dynamic stiffness of the sub-frame reinforcement. During judder, the Vehicle 2 suspension did not preserve its nominal geometry exhibiting a highly distorted movement as shown in the 3D animation, compared with the suspension of Vehicle 1. This was revealed in a running mode analysis reported next.
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