What is a braking force

1 What is braking. Brake primer. 1.1 The braking force F B: 1.2 The unit of measurement for the braking force F B


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3 1 What is braking 1.1 The braking force F B: F B The braking force F B (F as a sign from English force: the force) is required to brake vehicles from higher to lower speeds; it always counteracts the direction of movement. 1.2 The unit of measurement of braking force Forces are measured in the unit N (pronounced: njuten, named after the English physicist Isaac Newton). F W 1 kn ¾ F = 1000 N = 1 kn roughly corresponds to the weight F W of 100 kg, which is exactly 0.981 kn. 1

4 1.3 Different braking options There are many ways to brake vehicles; the following figures outline some of them. I painful and ruinous II poor braking effect 2

5 III Rabid road treatment IV V Cases IV and V point the right way: braking the wheels. 3

6 2 How do you brake? 2.1 Physics Some basic physical observations: I The static (-friction) force FH (sticking) speed v = 0 II The frictional force FR (slipping) It takes more force to set an object at rest than to slide it uniformly into it Keep moving. Adhesive and frictional forces are proportional to the weight of the body and depend on the nature of the material surfaces that stick or slide on each other (including unevenness). ¾ F H = µ H F W> F R = µ R F W (µ H, µ R: coefficient of adhesion or friction) 4

7 2.2 Adhesive and frictional forces occurring in the vehicle The sketch applies to an unbraked forward drive, F WH is the rear axle and F WV is the front axle load. The adhesive and frictional forces for each wheel depend on the one hand on the respective proportion of the weight of the vehicle acting on this wheel (in the simplest case this is the axle weight divided by the number of wheels on the relevant axle) and on the other hand on the respective coefficients of adhesion or friction between wheel and base. Different axle loads and different wheel-base ratios cause different adhesive and frictional forces. 5

8 2.3 Driving and braking The vehicle is driven and braked well when the drive and braking forces generated in the vehicle are optimally transferred to the surface - mostly the road. This is ideally the case when the wheel rolls firmly on the surface and does not slip on the surface. (Slip). Slipping or slipping of a wheel always occurs when the drive or braking force acting on this wheel is greater than the adhesive force. In the event of a drive, the wheels spin - the cavalier start; When braking, the wheel begins to slip more or less on the surface - it turns less than what corresponds to the braking distance covered. Even blocks the wheel. So now only the smaller frictional force acts and the more forceful grip of the vehicle brakes in the wheel has no effect; in addition, the driving behavior becomes uncontrollable. I drive (drive force F A) rollers: 6

9 Slip (partially slipping): ¾ n 1 smaller than n 2 and v 1 larger than V 2. II Braking (wheel braking force FB, R) Rolling: Slipping (partially slipping): Note: The braking force FB, R on a wheel can never become greater than the adhesive force between the wheel and the base. 7th

10 2.4 Applying the braking force The braking force FB, R on the wheel contact surface is triggered by the pedal force FP generated on the brake pedal, which III is amplified by levers and hydraulics as pressure forces FP on the brake disks (or brake drums), where a frictional force FR (at this point there must be no sticking, otherwise the wheel will block). The resulting torque with respect to the wheel axis (M = F R h) is equal to the torque M = F B, R r (r = radius of the wheel) for the rolling, non-slipping wheel. The following applies: ¾ F h = = with f = transfer factor. r B, R FR f FP 8

11 3 How are braking forces measured? It is important that the braking forces of the wheels on the same axle are the same in order to avoid skidding. Therefore, each wheel is measured individually on a brake test bench. A static and a dynamic method are available for this. 3.1 Static test method With the static method, with the brake applied, the force is determined which is necessary to turn the wheel standing on a plate. 9

12 3.2 Dynamic test method rotatably mounted drive motor with bending beam support of the housing With the dynamic method - more practical - the wheel is brought to a predefinable speed by motor-driven rollers and then braked. A feeler roller measures the wheel speed directly. The size of the slip can be determined by comparing the drive speed with the feeler roller speed. From a slip of around 30%, the braking force measurements no longer make sense. In addition, the tire wear would then be too great. The braking attempt is then aborted. 10

13 3.3 The measuring principle The measuring principle is the same for both test methods. The drive motor is rotatably mounted. Without further storage, the drive shaft and the housing would rotate in opposite directions when the load is applied, depending on the distribution of forces. This further storage consists of a beam on which the housing is supported. The steel bar now bends according to the torque to be applied by the motor, which the bar has to withstand. At the beginning of the brake test, the torque is zero for the static method and just as large as necessary for the dynamic method to move the drive rollers and wheel when the brakes are released. 11

14 3.4 The measuring probe A strain gauge is attached to the bending beam. Its electrical resistance, which is strongly dependent on length, is measured. This is a very sensitive measure for the bending of the beam and thus also for the torque applied in every phase of the braking attempt, which can easily be converted electronically into the braking force between the wheel and the surface and displayed. 12th

15 4 Measurement results and evaluations of a brake tester 4.1 Deceleration in general The deceleration is a measure of how quickly the speed of a vehicle is reduced, i.e. in what time the speed is reduced and how much. This can be formulated in formula symbols as follows: v ¾ a = in m / s² t where v represents the change in speed and t represents the time consumed. Example: A vehicle is brought to a standstill in 5 seconds at 20 m / s (= 72 km / h). There is a delay of 4 m / s². 4.2 Determination of deceleration on roller brake test stands In many countries, depending on the category, vehicles must achieve a minimum amount of deceleration. Since a deceleration measurement on the road is too complex, roller brake test stands are mostly used for this. If this minimum deceleration is not achieved, the vehicle may no longer be used in traffic. The braking force and (if there is a weighing facility) the weight of the wheels / axles can be measured on the roller brake tester. 13th

16 If you take the maximum braking force achieved in relation to the weight, you also get the deceleration of the vehicle. The formula for this is as follows: FB ¾ a = in m / s² G Example: The four wheels of a car achieve a total braking force of 8000 Newtons during the brake test, the vehicle weight is 1600 kg. There is a delay of 5 m / s². Often the deceleration is also shown as a percentage of the acceleration due to gravity of 9.81 m / s². For the example above, this results in a 50.97% delay. 4.3 Coefficient of friction The maximum achievable braking force depends directly on the coefficient of friction µ between the tire and the ground and the force with which the wheel is pressed onto the ground (normal force). The following formula applies: ¾ FB = µ FN In nature, e.g. the following coefficients of friction for average tire rubber compounds: ¾ dry concrete: ~ 0.7 ¾ dry asphalt: ~ 0.6 ¾ snow: ~ 0.2 ¾ wet black ice: ~ 0.01-0.1 roller brake testers usually have Surface structures that simulate concrete or asphalt coefficients of friction, i.e. around 0.7. 14th

17 4.4 Brake force difference If one of the two brakes on an axle has less effect than the other, a one-sided braking effect occurs, which is referred to as brake force difference or inequality. If the difference becomes too great, the vehicle will tend to break away in the direction of the harder braking side. Therefore, a vehicle becomes unsafe for traffic as soon as a limit value is exceeded. In many countries the difference is shown as a percentage of the measured braking force difference in relation to the higher of the two braking forces. This is usually calculated as follows: ¾ Difference (%) = FB (higher) - FB (lower) FB (higher) Example: The left wheel has a braking force of 2 kn. At the same moment, 3 kn are measured on the right wheel. The difference is 33%. Since the difference is always determined from the currently applicable braking forces, there can be strong fluctuations in the value if, for example, the brake drums (discs) are very out of round (ovality). Fluctuates e.g. the measured braking force of one wheel with a constant brake pedal position due to an out-of-roundness between 2 kn and 3 kn while the other wheel achieves a constant braking force of 2 kn, the difference fluctuates between 0% and 33%. This influence must be taken into account when measuring braking force differences, as it may can lead to different results with repeated measurements. 15th

18 4.5 Out of roundness (ovality) As described under 4.4, brakes can act out of round. To measure the out-of-roundness, the pedal is held steady at the desired measuring point. Actually, the display values ​​of the test stand should then also show a constant braking value. However, when the brakes are not round, the display fluctuates. The ovality can now be determined from the difference between the highest braking value that has occurred and the lowest braking value that has occurred during the ovality determination. Example: The measured value of a wheel brake fluctuates between 1.9 kn and 2.2 kn when the brake pedal position is constant. The ovality is 0.3 kn. To determine a percentage ovality value, the ovality is often related to the maximum braking force value. Example: The above brake achieves a maximum braking force value of 3 kn. The percentage ovality in this case is 10%. Depending on the legislation, vehicles are often no longer permitted to drive above a certain ovality value. 16


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