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Difficulties During Testing

Because there were different braking areas along the track, the conditions for each braking test were slightly different. Therefore, the adhesion coefficient and consequently the rate of braking changed over each braking event. If more time had been available the brake events would have been performed in just one braking zone to increase accuracy of results.

Weather conditions at MIRA at the moment of the test:

• 6ºC
• Damp and dry depending on the area of the track
• Wind: variable 0-5m/s

The test track stayed with the same conditions during the whole test.

The test driver estimated the effort needed to reach the desired Brake Line Pressure for each break event and did seldom meet the target pressure exactly. The actual values were used for the analysis.

Analysis of the Data

All the tests were conducted with the vehicle transmission in neutral position. Therefore, only the braking effect of the brakes (and aerodynamic drag) was considered. For a more realistic result, involving the engine brake effect, the car would have needed to be left in gear during the brake events.

Tests 1, 3 and 4 plots involving Rate of Braking vs Brake Line Pressure should project back through the origin (0,0). They should behave like that because when there is no brake line pressure there should be no braking force on the brakes. With no braking force the rate of braking should equal zero, hence the trend line should pass through the origin. However, in the test there were forces acting against the vehicle which made it come to a stop. These forces include: internal friction forces, rolling resistance in the tyres and aerodynamic drag coefficient. All these forces would eventually bring the vehicle to a halt. These forces can be seen in the trend line of rate of braking as very small values just before the braking event begins.

When comparing the results of the Case Study with the Test Data it can be seen that there are not dramatic differences.  In terms of rate of braking it can be seen that both the Case Study and the Test Data plots follow the same trend. This close relation can be explained by the fact that the track conditions were almost optimum and that the vehicle had been equipped with new brake pads and discs recently. Therefore the efficiency of the system was very close to 100%. If the track was in a poorer condition, such as wet, the results for the braking rate for the Test Data would have been drastically worse.

If the car had been loaded to its maximum permissible weight the rate of braking would have decreased. This is because the momentum in the vehicle would have increased and therefore, with the same braking force the car would have needed a longer distance to stop.

When the braking distribution achieved in the Case Study is compared to the Test Data (1 and 2) it can be seen that both behave very similarly. This is, again, due to the good conditions encountered during the test. The braking distribution from tests 3 and 4 was very different from the one in tests 1 and 2. This is because tests 3 and 4 only used one axle braking, whereas tests 1 and 2 used both axles braking. Therefore the braking distribution between 1 and 2 differs from the braking distributions from 3 and 4.

The calculated values of adhesion were consistent throughout the test. The overall adhesion values were reasonable for the slightly damp track conditions. The European Braking Directive states that the ABS Adhesion Utilization should meet the value of 1.2, however the Adhesion coefficient calculated was of 1.05 which is under the legislation. This can be explained because of the damp track.

The mean adhesion coefficient was calculated to be 0.788. It can be seen that this adhesion coefficient corresponds to a rate of braking of 0.72. In other words, this means that the rear wheels would lock first. However, it can be seen that the actual rate of braking achieved was much higher (0.92) until the rear wheels locked. This can be explained by the fact that this braking event took place in an area were the tarmac was very rough, so it provided higher adhesion coefficient that the mean value.

If the test 1 was carried with the booster disabled and the vehicle loaded to its maximum permissible weight (18394N) the vehicle would have passed the Braking Directive R13H requiring 2.44m/s² (0.248g) rate of braking with a maximum pedal force of 500N.

The legislation requires a minimum of 0.248g, therefore the vehicle passes the Braking directive.

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A vehicle which ABS and EBS could be disconnected and selective front/rear/all axles braking was used. The vehicle has a front axle weight of 9352.9N and the rear axle weight of 7506.5N

Four braking points were selected in the MIRA test track to perform the braking tests. Not all the points had the same track conditions; therefore they are shown and explained:

The following tests were performed until full locking of one axle was achieved.

Test 1 – All brakes, ABS and EBD disabled

9 Stops from 40mph. Table of results:

Test 3 – Front brakes only, ABS and EBD disabled

9 Stops from 40mph. Table of results:

Test 4 – Rear brakes only, ABS and EBD disabled

9 Stops from 30mph. Table of results:

A sample deceleration and pressure trace from test D1 is shown to illustrate how the mean values were determined. The target pressure for this test was 400psi (2.758Mpa), however the driver averaged 1.905MPa.

Following figure shows test 1 and test 2 comparison

Following figure shows test 3 and test 4 comparison.

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A static test was conducted with and without the booster function to determine the increase of brake line pressure with the assistance of a booster.

Normal Booster function

Test is conducted with the engine idling and at normal running temperature. Driver’s seat was positioned to suit stature of driver so that force was applied perpendicularly to the brake pedal. Brake line pressure [MPa] and pedal force [N] were recorded for 50N increments of pedal force from 50N to 500N. For each reading, the pedal force was slowly increased until the intended value was reached. Pedal force was never reduced, even if the target pedal force was exceeded. Between each reading the pedal was released and the engine was allowed to idle for a few moments to rebuild vacuum in the booster.

The results of the Normal Booster Function can be seen in the following figure:

Failed Booster

The engine was stopped and the pedal was pressed a few times until the vacuum was exhausted. Then the procedure was repeated for the same range of pedal forces (this time, the line pressures were lower because there was no assistance).

The results of the Failed Booster can be seen in the following figure:

For the normal booster it can be seen that an increase in the Brake Pedal Force produces a considerable increase in the Brake Line Pressure up to 250N of Pedal Force. From that point onwards the increase is more subtle. The maximum Brake Line Pressure achieved for Normal Booster Function was 9.8MPa, however for the Failed Booster  the maximum pressure only reached 1.8MPa.

The following figure shows the relationship between the increase of Brake Line Pressure to the increase of Pedal Force. The knee point can be found for the Normal Booster Function plot. The knee point starts where the gradient of the trend line of the Normal Booster Function starts to become parallel to the gradient of the Failed Booster trend line. This occurs around 7.5MPa of Brake Line Pressure.

The Boost ratio was found dividing the change in gradient of the two cases:

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Rearranging this equation is possible to find Master Cylinder Pressure (P_(m)) :

The modified Braking distribution ratio is:

The following plot shows the Braking Distribution Ratio against the Master Cylinder Pressure. The EBD effect is shown by the double red line. The EDB reduced the pressure in the rear brakes when these were about to lock. When a vehicle locks the rear wheels loses stability. The modified braking ratios (X_1var/X_2var) and the the rate of braking (X₁/X₂)  against Master Cylinder Pressure figure.

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The braking ratio is defined as:

And can be calculated using equation:

Where T_f [N] is the braking force front and  T_r [N] is the braking force rear. More information on calculating these can be found here.

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The adhesion utilizations, f, can be calculated using the equations:

 The loads applied (static load +/- transfer load) on the front (N₁) and rear (N₂) axles can be calculated using the following equations:

Where:

P = Weight of car

Z = Rate of braking

h = Height of CG.

P₁ = Front axle weight

P₂ = Rear axle weight

E = Wheelbase

N₁ = Front down force

N₂ = Rear down force

Please see following figure. Rate of Braking, Z, is the level of deceleration in g. Adhesion Utilization is equivalent to the Coefficient of Friction. All wheels lock together at 0.821g.  Front  wheels lock first at a rate of braking smaller than 0.821g. Rear wheels lock for rates of braking higher than 0.821g.

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