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Graph A2. Circuits pressure, lateral and longitudinal vehicle acceleration (Test 2 — Table 3)

Table 3 Graph A2. Circuits pressure, lateral and longitudinal vehicle acceleration (Test 2 — Table 3)

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Figure 1. (a) Disc brake and caliper; (b) Brake bias; (c) Dial The brake system of this work has got a disc brake in all of four wheels, with hydraulic drive and without assistance. The brake pedal activates two independent master cylinders, one to act on the front wheels and the other one to act on the rear wheels (Fig. 1-a).
Figure 1. (a) Disc brake and caliper; (b) Brake bias; (c) Dial The brake system of this work has got a disc brake in all of four wheels, with hydraulic drive and without assistance. The brake pedal activates two independent master cylinders, one to act on the front wheels and the other one to act on the rear wheels (Fig. 1-a).
The optimum braking force distribution is achieved when all wheels reach the imminent locking simultaneously [5, 6, 10]. The model developed to calculate these forces take into account the following hypothesis: both the tire rolling resistance and the aerodynamic drag are neglected; the braking occurs only in straight line and with uncoupled transmission; the tires are on the imminence of locking during braking and the wheel moment of inertia is negligible. Although the vehicle analyzed in this work is a single seater race car, it is not equipped with wings and during competitions the velocity usually is lower than 75 km/h. Appling the Newton-Euler equations for the system of Fig. 2 one obtains:
The optimum braking force distribution is achieved when all wheels reach the imminent locking simultaneously [5, 6, 10]. The model developed to calculate these forces take into account the following hypothesis: both the tire rolling resistance and the aerodynamic drag are neglected; the braking occurs only in straight line and with uncoupled transmission; the tires are on the imminence of locking during braking and the wheel moment of inertia is negligible. Although the vehicle analyzed in this work is a single seater race car, it is not equipped with wings and during competitions the velocity usually is lower than 75 km/h. Appling the Newton-Euler equations for the system of Fig. 2 one obtains:
Considering a pedal force of 425 N, a brake bias ratio equal to 71.5% and applying Eq. (8), (9), (11) and (12), one obtains the actual braking force distribution, as shown in Fig. 5. The optimum braking force curve intersects the actual braking force line when the vehicle achieves a deceleration equal to 1.0g. If the maximum tire/road adhesion coefficient is achieved when the vehicle deceleration is equal to 1.0g, there will be a simultaneous locking of the four wheels. When decelerations are higher than 1.0g, the locking of rear axle will occur first. On the other hand, when decelerations are lower than 1.0g, the locking of front axle will occur first. Figure 6 represents the optimum and the actual braking force distribution referred to the operating range of the brake bias. This range is sufficient for the drivers to achieve the optimum brake balance during competition.
Considering a pedal force of 425 N, a brake bias ratio equal to 71.5% and applying Eq. (8), (9), (11) and (12), one obtains the actual braking force distribution, as shown in Fig. 5. The optimum braking force curve intersects the actual braking force line when the vehicle achieves a deceleration equal to 1.0g. If the maximum tire/road adhesion coefficient is achieved when the vehicle deceleration is equal to 1.0g, there will be a simultaneous locking of the four wheels. When decelerations are higher than 1.0g, the locking of rear axle will occur first. On the other hand, when decelerations are lower than 1.0g, the locking of front axle will occur first. Figure 6 represents the optimum and the actual braking force distribution referred to the operating range of the brake bias. This range is sufficient for the drivers to achieve the optimum brake balance during competition.
Figure 6. Normalized optimum and actual braking force distribution
Figure 6. Normalized optimum and actual braking force distribution
gure 7. Pedal Force Gain — according to NHTSA shaded area represents the optimum gain In order to evaluate the pedal force during braking, the pedal force gain was calculated, which is the relation between pedal force and vehicle deceleration [5]. According to the model prediction, the required pedal force to the vehicle achieves a deceleration of 1.0g is 425 N, considering a mass of the driver equal to 78 kg. For a driver mass of 60 kg, this force is 404 N and for 90 kg the force is 438 N. These values were compared to NHTSA research, which has identified an optimum range for pedal force gain, as seen in Fig. 7. As there is no specific reference for formula cars type, a NHTSA recommendation developed for passenger was used for the single seater race car of this study. The red points in Fig. 7 represent the pedal force gain for the three drivers.
gure 7. Pedal Force Gain — according to NHTSA shaded area represents the optimum gain In order to evaluate the pedal force during braking, the pedal force gain was calculated, which is the relation between pedal force and vehicle deceleration [5]. According to the model prediction, the required pedal force to the vehicle achieves a deceleration of 1.0g is 425 N, considering a mass of the driver equal to 78 kg. For a driver mass of 60 kg, this force is 404 N and for 90 kg the force is 438 N. These values were compared to NHTSA research, which has identified an optimum range for pedal force gain, as seen in Fig. 7. As there is no specific reference for formula cars type, a NHTSA recommendation developed for passenger was used for the single seater race car of this study. The red points in Fig. 7 represent the pedal force gain for the three drivers.
Two tests were performed to evaluate the brake system. In the first one, the results obtained with the mathematical model were compared to collected data during experimental tests to evaluate this model. The second test analyzed the performance of the braking system in a competition circuit. Both tests were monitored by sensors to measure the pressure on the front and rear lines of the brake system, the longitudinal and lateral acceleration and the velocity of the vehicle.
Two tests were performed to evaluate the brake system. In the first one, the results obtained with the mathematical model were compared to collected data during experimental tests to evaluate this model. The second test analyzed the performance of the braking system in a competition circuit. Both tests were monitored by sensors to measure the pressure on the front and rear lines of the brake system, the longitudinal and lateral acceleration and the velocity of the vehicle.
3.2. Performance test of brake system at a competition circuit
3.2. Performance test of brake system at a competition circuit
Table 3. Pressure lines and longitudinal vehicle deceleration Table 3 shows a comparison between the values of deceleration obtained from the model and the values measured during the tests. The experimental data collected during the tests were disregarded when the lateral accelerations were higher than 0.10g, the longitudinal decelerations were lower than 0.35g or higher than 1,50g.
Table 3. Pressure lines and longitudinal vehicle deceleration Table 3 shows a comparison between the values of deceleration obtained from the model and the values measured during the tests. The experimental data collected during the tests were disregarded when the lateral accelerations were higher than 0.10g, the longitudinal decelerations were lower than 0.35g or higher than 1,50g.
Table 4. Disc brake temperature (°C) The maximum temperature reached during the test was 157°C, which does not generate loss of braking efficiency due to fading effect. The recovering time of the system up to the initial temperature (about 40°C) measured after the vehicle has stopped was from 10 to 20 seconds. To avoid reading error due to rapid recovery of the system, the temperature measurements were performed immediately after vehicle has stopped.
Table 4. Disc brake temperature (°C) The maximum temperature reached during the test was 157°C, which does not generate loss of braking efficiency due to fading effect. The recovering time of the system up to the initial temperature (about 40°C) measured after the vehicle has stopped was from 10 to 20 seconds. To avoid reading error due to rapid recovery of the system, the temperature measurements were performed immediately after vehicle has stopped.
Figure 9. Braking points during the test
Figure 9. Braking points during the test
Figure 10. Pressure inside the front (red line) and rear (blue line) brake circuits
Figure 10. Pressure inside the front (red line) and rear (blue line) brake circuits
Table 5. Front and rear brake pressure Figure 11 shows the total brake pressure (obtained by adding the front and rear pressures), the vehicle longitudinal velocity and the longitudinal acceleration of the vehicle. The numbers correspond to the track section where the driver was acting on the brake pedal (see Figure 9).
Table 5. Front and rear brake pressure Figure 11 shows the total brake pressure (obtained by adding the front and rear pressures), the vehicle longitudinal velocity and the longitudinal acceleration of the vehicle. The numbers correspond to the track section where the driver was acting on the brake pedal (see Figure 9).
Figure 11. Vehicle Speed, Longitudinal Acceleration and Total Pressure inside the brake circuits When the car was in track section number 2, the pressure of brake circuit reached its peak value of 7.13 MPa (71.3 bar). Exactly when the brake pressure achieved that peak, the longitudinal acceleration was equal to 1.06 g and immediately arose to 1.21 g. Table 6 shows the values of velocity, longitudinal and lateral acceleration of the vehicle at the exact instant when the brake pressure achieved the peak in each track section shown in Figure 9. Note that the peak of longitudinal acceleration did not occur at the exact moment when the brake pressure achieved its maximum value, what can be observed in Figure 11.
Figure 11. Vehicle Speed, Longitudinal Acceleration and Total Pressure inside the brake circuits When the car was in track section number 2, the pressure of brake circuit reached its peak value of 7.13 MPa (71.3 bar). Exactly when the brake pressure achieved that peak, the longitudinal acceleration was equal to 1.06 g and immediately arose to 1.21 g. Table 6 shows the values of velocity, longitudinal and lateral acceleration of the vehicle at the exact instant when the brake pressure achieved the peak in each track section shown in Figure 9. Note that the peak of longitudinal acceleration did not occur at the exact moment when the brake pressure achieved its maximum value, what can be observed in Figure 11.
Table 6. Vehicle Velocity, Longitudinal and Lateral Acceleration
Table 6. Vehicle Velocity, Longitudinal and Lateral Acceleration
VEHICLE PARAMETERS EMPLOYED IN SIMULATIONS AND EXPERIMENTAL TESTS Appendix
VEHICLE PARAMETERS EMPLOYED IN SIMULATIONS AND EXPERIMENTAL TESTS Appendix
Graph A1. Circuits pressure, lateral and longitudinal vehicle acceleration (Test 1 — Table 3) The time unit employed in the graphs below is Minute : Second.
Graph A1. Circuits pressure, lateral and longitudinal vehicle acceleration (Test 1 — Table 3) The time unit employed in the graphs below is Minute : Second.
Graph A3. Circuits pressure and longitudinal vehicle acceleration (Test 3 — Table 3)
Graph A3. Circuits pressure and longitudinal vehicle acceleration (Test 3 — Table 3)
Graph A4. Circuits pressure and longitudinal vehicle acceleration (Test 4 — Table 3
Graph A4. Circuits pressure and longitudinal vehicle acceleration (Test 4 — Table 3
Graph A5. Circuits pressure, lateral and longitudinal vehicle acceleration (Test 5 — Table 3)
Graph A5. Circuits pressure, lateral and longitudinal vehicle acceleration (Test 5 — Table 3)
Graph A6. Circuits pressure and longitudinal vehicle acceleration (Test 6 — Table 3
Graph A6. Circuits pressure and longitudinal vehicle acceleration (Test 6 — Table 3
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