TBR Technical Corner: Optimized Braking System Sizing by Means of a Parametric 1D Brake Model (Part 2 out of 3)

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This article presents a methodology that incorporates a 1D (non-geometric) brake model, together with conventional vehicle tests, into the solution of problems associated with the sizing of a braking system.

The first part introduced the problem and presented some results. As already explained, the methodology is divided into three phases:

• Phase 1: vehicle and brake specifications are gathered in order to model the problem by means of the 1D tool. Once the simulation is completed, prediction results are correlated using the previously-measured vehicle test data.
• Phase 2: it consists of modelling the available replacement off-the-shelf components, thus reducing associated costs and getting shorter lead times; the outcome is a gap analysis, i.e. exploring the relative impact that each modified component has on the critical attributes.
• Phase 3: the new components are tested on the vehicle; newly-obtained evidence is compared against the baseline experimental results in order to check whether the targeted improvements are successfully met.

Results

Phase 1 (continuation)

The 1D brake model recreates a parametric braking system. The user is requested to fill the specifications —input parameters—, which contain information about:

‘Stability control’ includes data about the devices used to control the brake forces distribution (mainly the EBD) and to prevent the wheels from locking (ABS).

Figure 2 shows a flow diagram detailing the intermediate parameters —from the brake pressure to the pedal effort and travel— that need to be considered in order to estimate the brake pedal feeling, whilst Figure 3 presents the method that is employed to simulate the legislative tests. Note that it is an iterative process and, therefore, most variables at brake level (pressure, effort and travel) and vehicle level (deceleration, speed, distance) need to be updated at every time step until the car is brought to a complete halt.

Table 7 compares the experimental data with the results extracted from the 1D (non-geometric) model. The percentage gaps, in brackets, take the vehicle test values as reference.

Note that the level of correlation of the service braking test is not as good as those found for the emergency braking stops. The correlated model mainly focuses on the most critical tests, i.e. the booster and the primary circuit failures —specially the latter, which does not reach the minimum MFDD of 2.2 m/s2.

The 1D calculation identifies the tire-road adhesion as the limiting factor for the neutral and secondary circuit failure stops. The unboosted test is inherently restricted by the booster’s own non-vacuum performance. The primary circuit failure stop, for its part, reaches the total stroke of the MC secondary chamber, what prevents the pressure from growing further. Figure 4 shows the estimated pedal feeling for the baseline configuration. As previously indicated, no experimental data are available and, as a consequence, this prediction cannot be initially correlated. Notice that the feeling is dependent on the vehicle weight state and, therefore, is expressed in terms of the extreme conditions: DOW (dotted) and GVW (solid).

Each sub-plot reveals valuable information about the different components that form the braking system. From left to right, and top to bottom, this can be summarized as:

• Pedal effort vs. vehicle deceleration: feeling of effectiveness.
• Pedal travel vs. vehicle deceleration: feeling of control.
• Pedal effort vs. pedal travel: pedal box stiffness.
• Pedal travel vs. MC pressure: MC performance.
• Pedal effort vs. MC pressure: booster performance.
• Vehicle deceleration vs. MC pressure: brake lining effectiveness.

Phase 2

As the baseline configuration is set, different specifications can be easily modified in order to assess its impact on the overall vehicle performance —primarily the emergency braking tests and the pedal feeling, as long as none of the other attributes is worsened. After evaluating several configurations, the following specifications are revised:

All other parameters remain unchanged. Note that the selected figures correspond to existing off-the-shelf components available from the suppliers, thus getting shorter lead times.

The stroke of the MC’s secondary chamber is increased given that, during the primary circuit failure test, the piston reaches the end of the chamber —what prevents the brake pressure from increasing further. On the other hand, the reduction in pedal ratio allows shortening the pedal travel, while the enlargement of the piston area in the front caliper (and the consequent sizing of the disc) guarantees that the system pressure is lowered over the complete working range.

Table 9 shows a direct comparison between the predicted legislative results for both baseline and new configurations.

The 1D tool estimates that the MFDD obtained for the primary circuit failure test can increase up to 2.46 m/s2, thus meeting the 2.2 m/s2 criterion laid down in UNECE Regulation No. 13. Note that the introduction of the new specifications does improve all predicted results except for the booster failure test, whose performance is slightly diminished —but deemed as acceptable given that there is still margin with respect to the minimum requirements.

Figure 5 shows the predicted pedal feeling for both baseline and new configurations. The enlargement of the pistons is the only modification that has an effect upon the absorptions. At this stage, the new caliper is not available and, thus, front brake absorptions are approximated.

Note that the brake pressure —and the consequent vehicle deceleration— that is achieved, for a similar force level, has been slightly diminished because of the reduced pedal ratio. But most importantly, the pedal is significantly shortened: the initial dead stroke is attenuated and the stiffness (travel / deceleration ratio), enhanced.