Low Speed Plate Brake Tester

Reprinted with permission from the SAE Technical Paper Series
901701

Paul G. Marting and Nick J. Colarelli
Hunter Engineering Company
Bridgeton, Missouri

ABSTRACT

A low speed plate brake tester has been designed to measure brake forces applied to the road simultaneously at all four wheels. The dynamic data is displayed in the form of four force vs. time graph. Computations of dynamic brake balance between the front and rear axles and between individual wheels on each axle are displayed. The objective measurements can be automatically compared to specifications for the purpose of auditing vehicles. The static weight distribution of the vehicle is also measured for the purpose of determining the maximum deceleration achieved by the vehicle during the test.

INTRODUCTION

At present, vehicle brake balance is measured using torque wheels, roller dynamometers, high speed road transducers or the SAE single­axle test procedure. This paper presents an alternative method for rapidly inspecting vehicle braking systems.

The modular construction of the low speed plate tester allows for many different configurations in either a two­plate or a four­plate system for various customer requirements. The individual components of the brake tester are discussed in detail and a step by step description of an actual test is given.

Results of research is provided to validate the accuracy and correlation of the low speed plate brake tester. Brake balance data is calculated from the torque wheels of an instrumented vehicle and compared to test results from a high speed road transducer and the low speed brake tester. Results are provided for both front biased and rear biased cases and for low and high speed tests. In addition, design and calibration information is presented to explain the construction and operation of the equipment.

Some actual display results are used to demonstrate that the plate brake tester also has some diagnostic capability in the event of a brake system failure.

BRAKING PRINCIPLES

When the brakes on a vehicle are applied, friction between the brake shoes and drum or between the pads and rotor slow the rotation of the wheels. This in turn increases the friction between the tire and the road surface, decelerating the vehicle. Under normal operating conditions, as the driver increases the force on the brake pedal, the braking forces at the wheels increases proportionally. Thus, increase in braking force continues until the limit of tire­to­road surface traction is exceeded and one or more of the wheels will lock and skid. At each wheel the brake force divided by the normal force cannot be larger than the peak tire/road coefficient of friction.

When brake torque is applied to a wheel, a braking force or retarding force is generated at the interface between the tire and the road surface.

See Figure 1. As braking torque is increased, the braking force at the wheel is increased until slippage will occur between the tire and the road.

To generate slippage between a tire and road surface, the rotational speed of the tire must be less than the speed of the vehicle. Thus slippage between tire and road surface is known as “wheel slip.”, Wheel slip is measured in percent as described below:

%slip= V-Vw/v x 100

where V= vehicle speed

Vw= rotational wheel speed

(1)

If the rotational speed of the wheel is identical to the speed of the vehicle (V = Vw), the wheel has 0% slip. In normal driving, wheel slip rarely exceeds 1 or 2%. At the opposite extreme, if a vehicle is skidding and the wheels are locked, the rotational speed of the wheels is zero (Vw = 0) and the wheels are operating at 100% slip.

The amount of braking force that can be generated by a wheel is dependent on the load on the wheel, the construction of the tire and the condition of the road surface (friction between the tire and road). At the start of a brake application, brake pressure is increased and wheel slip increases (1)* (Numbers in parentheses designate references at end of paper) and at a maximum point on the adhesion/slip curve (Figure 2) reaches the limit between the stable and unstable ranges. At this point, there is no further increase in braking force for a further increase in brake pressure or braking torque.

In addition to braking forces, tires must also generate lateral or cornering forces to direct the vehicle in accordance with steering inputs. Lateral forces are also dependent upon the amount of wheel slip.

As shown in Figure 2, the lateral force at the wheel decreases substantially as wheel slip increases. This is an important consideration when designing a brake system. Not only is it important to prevent premature wheel lock­up from a standpoint of achieving the best brake performance, but it becomes important for vehicle handling. Since the lateral forces decrease with wheel slip, the ability to steer and maintain directional control of a vehicle decreases substantially with increasing wheel slip. Since the lateral forces decrease with wheel slip, the ability to steer and maintain directional control of a vehicle decreases substantially with increasing wheel slip.

SIGNIFICANCE OF VEHICLE BRAKE BALANCE

The distribution of braking forces between the front and rear axles (2) that results from the application of force at the service brake pedal is defined as brake balance. Vehicle brake balance is an important factor in determining the theoretic limits of a vehicle deceleration under braking. By knowing the brake force at each axle, it is possible to calculate the vehicle deceleration by simply summing these forces to obtain the total retarding force acting on the vehicle and relating it to the weight of the vehicle. During actual braking on the road, other variables such as grade, road camber and power train characteristics all influence the distribution of forces parallel and normal to the tire/road interface, thereby affecting overall deceleration.

The ideal vehicle would have the brake force distribution and normal force distribution coincide under all rates of vehicle deceleration. A vehicle with these characteristics is said to have neutral balance and will achieve the shortest stopping distance. Another way of showing neutral balance would be the % rear braking equals the % rear normal force under all rates of vehicle deceleration.

An example to show very poor brake force distribution would be a two axle truck having a weight distribution of 20% front / 80% rear but having brake forces distributed 80% front / 20% rear. As braking forces are increased from zero, the front axle will develop lock­up at very low pressure. In addition, the majority of the vehicle weight is not being utilized to its fullest extent in providing the normal force where it can be translated to a retarding force.

As stated above, a neutral brake balanced vehicle is the ideal situation. This is difficult to achieve, however, under all rates of deceleration, vehicle loading and road friction. Since locked wheels lose their ability to control the vehicle's direction of motion, a vehicle with locked rear wheels will, even if the front wheels are rolling freely, invariably spin whereas a vehicle with locked front wheels and free­rolling rear wheels will follow a straight path in whatever direction the rear wheels point. The locked rear wheels, resulting in vehicle spinning, is considered to be more hazardous, therefore vehicle designers today will tend to let the front wheels lock first when the point of maximum braking efficiency is achieved. The vehicle would be intentionally front bias.

From a vehicle control standpoint and for optimum stopping distance, brake balance determination is very important. A fast test to determine if a road vehicle still is operating at its proper brake balance is imperative. The measurement of brake force on each wheel to determine brake balance also provides a measure of side­to­side variation on both the front and rear axle. Imbalance side­to­side can spot a potential handling problem in a panic brake application. Although all vehicles are designed to have equal side­to­side brake forces on each axle, aging brake systems can show large differences in side­to­side brake force on the same axle. Stuck wheel cylinder pistons, frozen calipers, brake fluid or grease on linings are all potential causes of unequal braking side­to­side on the same axle.

METHODS TO MEASURE BRAKE BALANCE

TORQUE WHEELS ­ Torque wheels are typically strain gage transducers that bolt onto the brake drum or rotor via the wheel studs. The wheel and tire is then bolted to the transducer with a separate set of studs. Since the torque transducer rotates with the wheel, a rotary transformer or slip ring must be used for the output signals. On board vehicle instrumentation is used to measure and record brake torque for each wheel. Brake torque measurements can be made at various decelerations and analyzed to give brake balance over the complete range of tire to road coefficients. To obtain the actual brake force at each wheel, the measured torque is divided by the dynamic rolling radius of the tire. The dynamic rolling radius is usually determined experimentally but does not appear to introduce any significant error into the calculation. The conversion of brake torque to brake force is necessary when comparing torque wheel data to other accepted methods of measuring vehicle brake balance.

Torque wheels yield very accurate results; however, this method of determining brake balance is very impractical for measuring a large number of vehicles due to mounting requirements of the torque transducers and associated vehicle modifications required. The cost of a torque wheel installation and on­board instrumentation is very expensive, with a minimum of $40,000 per vehicle.

LOW­SPEED ROLLER DYNAMOMETER - The low speed roller tester consists of roller sets mounted in pits that cradle one axle of a vehicle at a time and drive the wheels independently with electric motors at a speed of 3 mph. The rollers have a high coefficient coating to prevent slippage. The motors drive the wheel against the applied brakes and are mounted so that their reaction torque is transmitted through transducers that are calibrated to read the brake force. Since only one axle can be tested at a time, it is necessary to add a pedal force transducer so that the front and rear brake forces can be compared with the same input.

The low speed roller tester produces accurate results of brake balance (3) when the tested vehicle does not have a load or deceleration­sensing proportioning valve. The reason for this is that the vehicle is stationary on the rollers and there is no weight transfer when the brakes are applied. Many passenger cars with a high percentage of front braking will lock the front wheels at relatively low deceleration as compared with their actual performance on the road. The sustained measurements that can be made contribute to accuracy and repeatability. This test takes time to run because the vehicle has to be repositioned on the rollers for each axle. The low speed roller dynamometer is inexpensive (about $10,000). This type of tester is common in inspection stations and garages in Europe.

ROAD TRANSDUCER ­ General Motors (GM) developed (4) a system for measuring brake force distribution at normal driving speeds that utilizes plates installed in the test track and require essentially no instrumentation on board the vehicle being tested. The system is called the Road Transducer Plate (RTP). In its current configuration, the RTP uses 4 plates installed at the level of the road, each plate being 7' long. Brake forces at each wheel are measured simultaneously as the vehicle crosses the plates while being decelerated. The target crossing speed is 40 mph. The RTP measures brake force as well as vertical (normal) force and lateral (side) force at each wheel. The computer­based data acquisition and analysis system provides immediate graphical display of brake balance over the vehicle's entire deceleration range. Usually six to seven runs across the RTP at different levels of constant deceleration are required to give enough data points to predict neutral balance for all tire­road friction levels, the axle lock sequence and the brake efficiency.

SINGLE­AXLE TEST ­ SAE recommended practice, “Brake System Torque Balance Test Code ­ Commercial Vehicles ­ SAE J225” is the basis of this method of determining brake balance. Brake applications are first made with all brakes operational. Using the same input pressure from the all­brake test, applications are made with brakes operational on only one axle at a time. Brake balance is achieved by comparing the sum of deceleration on each individual axle with the deceleration achieved with all axles being braked. Some vehicle instrumentation is required and the vehicle's hydraulic system has to be disturbed to install shut­off valves to run the individual axle tests. This is an indirect method for measuring brake balance and is more susceptible to error than the above “direct reading” methods.

LOW SPEED PLATE BRAKE TESTER ­ A system very popular in Europe is now available in the U.S. It uses plates installed in the shop floor to measure the brake force at each wheel. No special vehicle instrumentation is required, the test is run very quickly, and the equipment is relatively inexpensive. This tester is similar to the RTP except that vehicle test speeds are usually 4 to 8 mph. The type of data taken from the low speed plate tester is also similar to that obtained from the RTP. The following sections discuss the equipment and operation of the low speed plate brake tester in detail.

LOW SPEED PLATE TESTER EQUIPMENT AND OPERATION

The System B400 Low Speed Brake Tester is a modular system which can be configured in many different ways to satisfy individual customer requirements. In its basic forms, it uses two or four braking plates installed on the shop floor with a display console along side. Four plates allow all four wheels of a vehicle to be tested simultaneously. If the two­plate tester is used, only one axle at a time is tested. A typical shop installation is shown in Figure 3.

Each brake plate consists of a fixed chassis bolted to the floor, a top plate assembly which is moveable in the longitudinal direction, and a sensor assembly with a force transducer. The transducer connects the fixed chassis to the moveable top plate and is electrically connected to a circuit board. The electronics provide a digital indication of the brake force which is exerted on the top plate. The top plate rolls on linear bearings to minimize the friction between the top plate and the chassis. The top of the brake plate is covered with expanded metal which provides a very high coefficient of friction between it and the tires of the vehicle being tested.

Figure 4 shows a partial cut­away of one of the brake plate assemblies.

Another major component of the low speed plate tester is the weigh scale. In order to determine the deceleration rate that the vehicle brakes can produce, it is necessary to know the weight of the vehicle. Deceleration is then derived from the measured brake force received from the brake plate and the weight of the vehicle. Weighing a vehicle is done automatically by slowly driving over the scales which are mounted on either the front end (drive­on end) or at the opposite end of the tester installation. If weigh scales are not used, the maximum vehicle weight will be displayed for the given brake forces in order to achieve the minimum required deceleration. It is then up to the operator to verify that the vehicle weighs less than this maximum weight.

The weigh scale consists of a chassis which is bolted to the floor, a sensor assembly with two symmetrical force transducers, and a U­shaped weigh bar which connects the two transducers (Figure 5). The wheel can be driven over any portion of the U­shaped weigh bar and the weight will be measured accurately since the output of each force transducer is electronically summed. The force/weight measurements will be discussed in detail in a later section.

All system installations have four ramps, one at each end of both runways. The ramps minimize any bump that occurs when a vehicle is driven over the equipment. Connecting plates are used to mechanically link two components together such as between the weigh scale and a brake plate. Spacer plates are used between brake plates (four­plate system) to give proper separation between the front and rear brake plates on each runway. Wiring thresholds are used to route the sensor cables along the floor between the runways and to the console. In Figure 6 a typical four­plate system is shown with the components labeled.

Additional system layouts are also shown in Figure 7.

Load cell transducers are used in the brake plates to measure brake force and in the weigh scales to measure weight. The type of load cell used is either a bending bar or a shear beam. Figure 8 shows how these types of load cells are applied. For a weight scale, the force is applied to the top of the beam as shown. For a brake plate, the transducer is mounted on its side. The force is applied through a threaded rod attached between the top plate and the transducer. In the case of a weigh scale, two transducers are required. The actual weight is the sum of both transducers.

In both cases, when the force is applied, there is a small deflection in the cavity where the bridge of strain gauges is glued. This deflection causes some of the strain gauges to elongate and some to compress. The net result is a change in electrical resistance in the strain gauge bridge. This change in resistance is proportional to the applied force and can be detected by the sensor electronics.

FORCE/WEIGHT SENSOR ASSEMBLY ­ Figure 9 shows how the force transducers are installed in the sensor assembly. Strain gauge load cells can be damaged by humidity. For this reason, and because of the harsh environment they are exposed to, the sensor assemblies are sealed at every opening.

The sensors communicate on the sensor bus, allowing sensors to be 'daisy­chained,' from the front to the rear of the test lane. This reduces cabling and allows for easy installation and maintenance.

PERFORMING A TEST ON THE LOW SPEED PLATE TESTER ­ Depending on the installation (two plate or four plate), the service brakes on the front and rear axles are tested in one or two runs. The testing of the parking brake is a separate test. The actual test consists of driving the vehicle up the ramps onto the brake plates. When the wheels are on the beginning of the plates, the brakes are applied and held until the vehicle is stopped. The actual measurement takes less than two seconds. The best results are obtained when using as much of the brake plate length as possible. The vehicle speed when approaching the ramps is 4 to 8 mph.

After the test, the brake forces measured by the brake plates are graphed on the left side of the screen. See Figure 10. The measurement time (x­axis) is approximately one second for a service brake test and two seconds for a parking brake test. Indices on the x­axis note the time at which the brake forces were a maximum. The maximum brake forces are shown next to the vehicle outline in the upper left hand of the CRT. These maximum forces are color coded as are the brake force graphs. For example, the blue brake force graph corresponds to the left front wheel on the vehicle outline which is also displayed as blue.

The right side of the CRT displays the vehicle brake balance in the form of bar graphs. The first bar graph is the front axle left­to­right balance. An ideal vehicle would have equal braking on both wheels, therefore, the left­to­right ratio would be zero. In this case, the left wheel was 5.2% stronger than the right wheel. This is well inside the limits which are shown graphically as green slices. In all cases, if the bar graph ends inside of the green limits, the bar will be white and the vehicle will pass. If the bar graph ends outside of the green limit, the bar will turn red and the vehicle will fail.

For the left­to­right ratios, the bar will always start in the middle and point to the weaker wheel. By convention, a negative left­to­right ratio indicates that the left wheel is weaker than the right wheel. A vehicle which fails a left­to­right ratio can have handling problems during braking.

The second bar graph is the rear axle left­to­right balance. The ideal vehicle would again have a rear axle left­to­right ratio of zero. In this case the right wheel was 7.4% weaker than the left wheel. Note that the rear axle limits are normally set to a wider tolerance than the front axle. This is because rear axle forces are normally smaller than front axle forces, and drum brakes are, in general, less repeatable than disk brakes.

The third bar graph is the front­to­rear balance. The number shown for this ratio indicates what percent of the total braking was done by the front axle ­ in this case, 66.8%. The limits in this example require that the front axle generate from 50% to 95% of the total brake force. This vehicle was well within this specification. In other words, these limits require that the front axle generate more brake force than the rear axle; however, the rear axle needs to generate at least 5% of the total brake force.

For a two plate configuration, two stops have to be made. The front axle service brake test will display two force graphs, one for each wheel on the front axle, and one bar graph ­ the front axle left­to­right ratio. After the rear axle service brake test is completed, the other two force graphs will be drawn and the rear axle left­to­right ratio and front­to­rear bar graphs will appear. The front­to­rear ratio calculation assumes that the same brake pedal force was used for each of the two stops.

During a service brake test, the deceleration is computed as the sum of all four brake forces divided by the weight of the vehicle. At the end of the test, the maximum brake forces are displayed in the upper left hand corner of the CRT. These are the forces used in the deceleration calculation. If the weight of the vehicle is known, the deceleration will be computed. If the installed system does not include the optional weight scales, the computer will display the maximum vehicle weight that will pass the minimum required deceleration specification.

As an example, Figure 11 shows the same service brake results discussed above, but with the weight of the vehicle known, the results now include the deceleration and the static weight distribution bar graphs.

The total of these four brake forces divided by the weight of the car in this case is 0.535. Depending on the selected units, this deceleration would be displayed as:

0.535 x 32.2 = 17.2 fV52
0.535 x 9.8 = 5.2 m/s2
0.535 x 100% = 53.5%

If the installed system did not include weight scales, and if the minimum required deceleration were 45%, the computer would calculate the maximum weight of the vehicle in order to achieve a 45% deceleration:

In this case, the technician must verify that this vehicle indeed weighs less than 4011 Lbs.

Most vehicles can achieve the required deceleration. Normally, if a vehicle fails the minimum required deceleration limit, the test should be repeated with a higher pedal force applied. A pedal force meter is also available which will measure the applied pedal force and compare it against the maximum allowable pedal force limit.

If the brake pedal is pressed too hard, at least one wheel will lock. During lockup, the brake graphs will look very irregular and the brake balance ratios will not be as accurate. For this reason a maximum limit on deceleration is available. This limit will reject any test where the deceleration is above the maximum deceleration limit. If this feature is not desired, the limit can be set to 100%.

With modern tire compounds and the expanded metal surface on the brake plates, it is possible to achieve decelerations in excess of 100%. For clarity, the brake tester will truncate any decelerations greater than 100% to 100%.

The deceleration is displayed with the fourth bar graph. The bar must end up between the two green limits to pass. The lower limit is necessary to insure that the vehicle was stopped hard enough. The brake balance ratios are most accurate for tests above 50% decelerations. The upper limit can be used to reject uncontrolled and dangerous stops.

The weight of the vehicle is displayed by the fifth bar graph. Note that there are no green limits in this case. A blue slice is shown to separate the front axle weight from the rear axle. The front axle weight is always shown first ­ as long as the vehicle was driven over the scales in the anticipated direction.

The time at which the brake forces are at a maximum are indicated at the bottom of the force graph area. One index for each graph is displayed in the appropriate color at the point in time where the forces were a maximum. The maximum forces are taken at the point where the sum of the brake forces on an axle are a maximum. Therefore, the indices for the front wheels will always be next to each other. Likewise, the indices for the rear wheels will be side by side. Note that the front axle and rear axle maximums do not necessarily have to be taken at the same point in time. The forces that appear next to the vehicle outline are the brake forces measured at these points. The forces can be displayed in the following units:

One use for these indices might be in the case of a lockup. The technician can reject a test if the maximums were taken while the wheel was bouncing due to the lockup condition.

Rebound peaks will often be visible in the lower right corner of the force graph area. These occur after the vehicle has come to a stop, rocked backward and then rocked forward. They are not important and will never be taken as the maximums.

The bar graph displays have been designed so that the technician can get a feel for the condition of the vehicle quickly and from a long distance away.

The bar graph horizontal axis is divided into ten sections. These sections are marked by the three dimensional indices at the bottom of the bar graph area.

The extreme magnitudes of each bar graph are shown to the left and the right of the bar graph area. These numbers are always in the same units as the value being graphed. Each three dimensional block in the bar graph represents one tenth of the total range. In the previous example, the front­to­rear ratio has a range of 0­100%. Each block would represent 10% in this case. The measurement was equal to 66.8%; therefore, the bar graph has six complete blocks and one partial block which represents the remaining 6.8%.

The front­to­rear ratio is always a positive number. When a number can be both positive or negative, the bar graph will start from the center instead of from the extreme left side. The left­to­right ratios and the sideslip measurement are examples of signed measurements. For example, the range on the front axle left­to­right in the previous example is ­50% to +50%. This still has a total range of 100 percentage points; therefore in this case, each block also represents 10%. The measurement was 5.2%, therefore, a partial block is shown starting from the center and ending 5.2% to the right.

In the weight bar graph shown in the example, the total range is 5000 Lbs. Each block in this case would represent 500 Lbs.

The extreme magnitudes of the bar graphs which are shown to the left and right of the bar graph area are computed after the measurement is made. The computer will select the appropriate range. For example, if a left­to­right measurement was greater than 50%, the computer would set the range from ­100% to 100%. In this case, each block would represent 20%.

DISPLAY OF VEHICLE BRAKE BALANCE TESTING

After a service brake test is performed on the B400 tester, the results are displayed on the CRT screen. Information displayed includes a graph of brake force versus time for each wheel, the difference between left and right brake force on the front axle expressed as a percent, the difference between left and right brake force on the rear expressed as a percent, the brake force distribution front/rear expressed in percent front braking, the vehicle deceleration based as a percent of (9), and the weight of the vehicle. The graphs and measured values can then be printed. See Figure 12 showing typical results screen.

With measurements of deceleration and percent front/rear brake distribution taken simultaneously, it is possible to make predictions of braking efficiency for a vehicle. Braking efficiency is defined as the ratio of maximum vehicle deceleration without wheel lockup divided by the coefficient of friction between the tire and the road. Another way of stating this is the percentage of available surface friction that can be utilized without wheel lockup. For example, if on a slippery surface the coefficient of friction between the tire and road is only 0.2 and the vehicle is capable of decelerating at a rate of 0.2 (% of 9), the braking efficiency is 100% or the vehicle is doing the very best it can possibly do on that surface. This could only happen with a vehicle having neutral.brake balance. By using a surface with a high coefficient of friction, brake force distribution and braking efficiency can be determined over a large range of vehicle deceleration. It is not necessary to know the exact value of the coefficient for these tests, only that it is high. By going through a series of calculations, it is then possible to predict efficiency on lower coefficient surface.

A typical display of vehicle brake balance and braking efficiency is shown by the two graphs in Figure 13. Since a continuous (4) relationship exists between the brake force distribution required for 100% efficiency and the dynamic normal force distribution, this can be shown as a straight line. This line is calculated from various vehicle parameters and the instantaneous vehicle deceleration.

With the vehicle's center of gravity above the road surface, normal force from the rear axle will be transferred to the front axle in proportion to the instantaneous vehicle deceleration. At zero deceleration, the normal force distribution is equal to the static weight distribution.

The brake balance curve (the series of plotted points) is obtained by making stops at various decelerations and recording deceleration and percent rear braking. Depending on which side of the dynamic normal force line this curve falls determines if the vehicle is front bias or rear bias. That is, the front wheels w.ill be first to lock when the brake force is increased to the tire traction limit or the rear wheels will be the first to lock at the tire traction limit. The series of "curved" lines both above and below the dynamic normal force line are constant coefficient of friction lines and are calculated from the various vehicle parameters.

The efficiency curve (lower curve on Figure 13) is then plotted by taking each value of measured deceleration and dividing it by the coefficient of friction where that point falls on the “fish bone'” curve. Besides giving the efficiency over the range of tire/road coefficients, it will show which axle will lock first.

Figure 13 shows a typical rear bias vehicle. A similar set of curves in Figure 14 shows efficiency and brake balance for a front bias vehicle with data taken from the low speed plate tester.

A vehicle is considered to have a good braking system if the efficiency is 80% or greater for a rear bias condition or as low as 70% for a front bias condition. The lower efficiency is accepted for a front bias case as the vehicle with the front wheels locking first will still follow a straight path.

Changing a vehicle's brake balance by means of an adjustable proportioning valve can be shown on the “fishbone” plot. In Figure 15, deceleration vs. brake balance is plotted for the same vehicle when tested on the low speed plate tester with four different settings of the proportioning valve. The brake balance is observed to change from front bias to near neutral and then to a rear bias condition. Approximately four or five stops are required at each setting of the valve to generate each curve.

Brake balance data from the low speed plate tester can also be graphed as Adhesion Utilization curves. The ratio of the brake force to the calculated normal force at the axle is defined as the adhesion utilization.

For a given measured deceleration and corresponding measured brake forces on the low speed brake tester, the equivalent normal force on each axle can be calculated from the vehicle parameters (center of gravity., wheelbase, etc.). Dividing the brake force by the normal force gives the adhesion utilization or F/N = AU = mu . This is plotted against deceleration. The data from the vehicle test used in Figure 13 is shown as an

Since the rear axle has the highest adhesion utilization, it will be the first to lock. This will be consistent for the total range of deceleration and the total range of tire to road coefficients in this particular case since the rear axle adhesion utilization is always higher than the ideal line. Brake efficiency can be calculated from deceleration and adhesion utilization (AU) by taking the AU of the axle that will lock first and dividing this value into the deceleration and multiplying the ratio by 100.

A similar adhesion utilization curve can be plotted for a vehicle that is front bias. The vehicle described in Figure 14 is also shown plotted in this form with a series of brake force and equivalent deceleration measurements taken off of the low speed plate brake tester.

Since the front axle has the higher AU, it will be the first to lock. The braking efficiency can be calculated for any point on AU curve. For example, in Figure 17 at an AU of .75 (circled) the equivalent deceleration is .659. The braking efficiency is .65/.75 or 86%. Another way of stating this is that with a tire to road coefficient of .75 the vehicle will be able to use 86 percent of the available friction.

PARKING BRAKE ­ A typical parking brake test run on the plate brake tester will display two curves showing the brake force vs. time for each rear wheel, the numerical value for the maximum brake force at each wheel, the vehicle weight and the deceleration due to the application of the parking brake. See Figure 18 showing the parking brake test results screen.

Since the function of the parking brake is to hold a parked vehicle rather than making a dynamic stop, this test is not nearly as important as the full service brake test. This test does, however, point out the high variation from one side to the other on many vehicles. Due to the cable­operated system and “crude” cable guides and the collection of road dirt and undercoating, many older vehicles exhibit poor balance side to side on this test. In general, the “low” side can usually be improved by cable adjustment or by reducing friction at various points in the system and provide much better hill holding.

The total parking brake force as measured on the plate brake tester can also be used to predict the hill­holding capability of the vehicle. Parking brake performance is dependent on many variables such as the brake force available at the rear wheels, the coefficient of friction between tires and the slope, the direction the vehicle is parked (uphill or downhill), how the parking brake is set (service brake being applied while parking brake is applied) and the percent of vehicle weight that is on the axle with parking brakes.

In general, the deceleration obtained from the parking brake test can be equated to the sine of the angle of the slope

DECEL= 9 sin a or

% DECEl. = sin a (~)

The vehicle test results shown in Figure 18 shows a deceleration of 32.2% due to the application of the parking brake.

0.322 = sin a
or
a= 18.78°

The equivalent grade that the vehicle would hold on would be approximately 34%. This is the theoretical grade and assumes the coefficient of friction between the braked wheels and the slope to be 1.0. When actually parking on a slope, the brakes have to provide enough power to keep the vehicle from rolling down and the normal force on the parked wheels and the coefficient of friction between the tire and slope have to be high enough to prevent the vehicle from sliding down the slope.

On an actual road with a tire­to­road coefficient of friction of .75, the calculation would be:

.75 (% decel) = sin a
.75 (.322) = sin a
.2415 = sin a
a= 13.97°

(5)

The equivalent grade the vehicle will hold on would be approximately 24%. In this case, the vehicle had enough rear normal force to hold on the 24% grade. If the normal force had not been adequate, the vehicle would slide down the grade. Federal Motor Vehicle Safety Standard FMVSS­105 requires a vehicle to remain stationary with the parking brake applied on a 20% grade. This vehicle would comply with this standard.

Sometimes a parking brake test can be used as a tool to diagnose a service brake failure. A vehicle with a “frozen” right rear wheel cylinder will show low or no braking force on the service brake test whereas the parking brake test will show good side­to­side braking. This indicates the friction material to be good, but something in the hydraulic system is not functioning.

FRONT­TO­REAR ESTIMATION ALGORITHM

It is common in plate brake testers to measure the front axle brake force and compare it to the total vehicle brake force. This number has been described previously as the front­to­rear ratio and is generally displayed in units of percent front braking. For example, if a vehicle generates a maximum of 4000 N of brake force on the front axle and 2300 N of brake force on the rear axle, the front­to­rear ratio can be calculated as:

4000/4000 + 2300 x 100 = 63.5% front braking (6)

It is also common to compare this measured value with stored specifications and make a judgment on the brake balance of the vehicle. Plate brake testers have been implemented which compare the measured value to a minimum percent front braking specification, typically around 50% front braking. This specification basically requires that a vehicle generate more brake force on the front axle than on the rear axle. Some plate brake testers have also been implemented which compare the measured value to a maximum percent front braking specification, typically around 95% front braking. This specification requires that the rear axle provide at least 5% of the total vehicle brake force.

Unfortunately, the nominal front­to­rear ratio is dependent on some design parameters of the vehicle as well as some test conditions. The comparison of this vehicle dependent measurement with absolute limits for the purpose of auditing vehicle braking performance has been known to cause problems. Vehicles designed to carry cargo for example, often will have considerably higher rear weight percentages when loaded than when unloaded. In the loaded condition, it is entirely likely that the nominal front­to­rear ratio for a vehicle be very close to the minimum percent front braking specification. Traditionally, the front­to­rear ratio specifications have been set artificially wide to allow for these conditions.

For a vehicle to be able to stop in the shortest possible distance, the nominal front­to­rear braking ratio should equal the vehicle front­to­rear dynamic weight ratio at all decelerations. At low decelerations, the nominal front­to­rear braking ratio approaches the static weight distribution of the vehicle. As the rate of deceleration increases, the weight on the rear axle decreases and the weight on the front axle increases. This weight transfer depends on the wheelbase and center of gravity (c.g.) height of the vehicle as well as the instantaneous deceleration. The dynamic rear axle weight percentage can be written as:

%DRW = %SRW­ (%d) x (c.g. height) / wb

%DRW = dynamic rear weight percentage
%SRW = static rear weight percentage
%d = deceleration as a percentage of gravity
c.g. height = center of gravity height
wb= wheelbase

Figure 19 shows a plot of percent rear brake vs. deceleration for various vehicle design parameters. The nominal front­to­rear braking ratio in units of percent front braking can be written as:

%Fnom = 100 ­ %DRW (8)
or
%Fnom = 100 ­ %SWR + (%d) x (c g.height)/wb (9)

A plate brake tester can be equipped with weigh scales, and in this case, the static weight distribution of the vehicle can be measured directly. Deceleration is a function of the measured brake force and the measured vehicle weight which are known, therefore the deceleration can be computed. The maximum deceleration, in units of percent of gravity, can be defined as:

%d max = Max[LF(t) + RF(t)] + Maxt[LR(t) + RR(t)] / W

O<t<T

%d max = maximum deceleration achieved as a percentage of gravity.

LF(t) = measured brake force of left front wheel at time t.

RF(t) = measured brake force of right front wheel at time t.

LR(t) = measured brake force of left rear wheel at time t.

RR(t) = measured brake force of right rear wheel at time t.

T = brake test duration

W =  vehicle weighs

(10)

It is not normally required in plate brake testing systems that the maximum of the front axle brake forces and the maximum of the rear axle brake forces occur at the same time, however the maximum brake force of one axle is normally defined as the point in time where the sum of both brake forces on that axle are a maximum.

The wheelbase can be estimated using the following algorithm:

wb = W + 4222.01 lbs / 69.2125 Lbs/in; 1661 less than or equal to W < 5122 lbs

wb= 85 in
wb= 135 in
O<W<1661 Lbs
5122 Lbs < = W

(11)

Figure 20 shows a plot of curb weight vs. wheelbase for various 1989 vehicles. The wheelbase estimate function is also shown. Appendix B shows the errors induced in the nominal front­to­rear braking ratio due to the estimated wheelbase for various decelerations. The maximum error occurs for the Chevrolet Corvette. At a 70% deceleration, for example, the error is 1.66%.

The c.g. height is estimated using the rule of thumb value of 21.6 inches. Appendix C shows the errors induced in the nominal front­to­rear braking ratio due to the estimated c.g. height for various decelerations at three different wheelbases. Consideration was given to a c.g. height estimate based on weight, however the largest errors are in the short wheelbase, high c.g. height vehicles which do not necessarily weigh more than the average passenger car.

Appendix D shows the errors induced in the nominal front­to­rear braking ratio due to both the estimated wheelbase and c.g. height for a 70% deceleration for various passenger cars and light trucks. The largest passenger car estimate error was 2.1% for a Pontiac LeMans. Light truck and van estimates are within 8%, with the largest errors being the short wheelbase trucks and vans. The majority of the light truck and van estimates were accurate within 4%.

It should be noted that the exact wheelbase and c.g. height values for an individual vehicle can be entered into the computer by hand if preferred. In this case, the estimated values will be overridden and the nominal front to­rear braking ratio will be recomputed and redisplayed. A second and more accurate rule of thumb for estimating c.g. height is 40% of the roof height, which can be easily measured.

Specifications can be added based on the estimated nominal front­to­rear braking ratio. These new specifications can be used in conjunction with absolute percent front braking specifications, replace the absolute specifications, or can be omitted.

There are four specifications which can be used to determine the pass/fail status of the front­to­rear ratio of a vehicle. The absolute minimum and maximum specifications are independent of the estimated nominal front­to­rear ratio. In this example, the minimum allowable front braking is 40% front and the maximum allowable front braking is 95% front. The front bias and rear bias specifications are dependent on the the estimated nominal front­to­rear ratio (shown in Figure 21 as a triangular cursor).

The front biased specification of nominal + 20% means that the maximum allowable front braking is the estimated nominal front­to­rear ratio + 20%. If a vehicle has more front braking than expected it is considered front biased. In an emergency stop, the front axle of a front biased vehicle would lock first. The rear biased specification of nominal ­ 15% means that the minimal allowable front braking is the estimated nominal front­to­rear ratio­ 15%. If a vehicle has less front braking than expected it is considered rear biased. In an emergency stop, the rear axle of a rear biased vehicle would lock first. Since a locked rear axle significantly decreases directional stability, a tighter tolerance can be used for the rear biased case than for the front biased case.

When a service brake test is performed, the lower limit that is used will be the maximum of the absolute minimum and rear biased specification. The upper limit that is used will be the minimum of the absolute maximum and front biased specification. If the absolute minimum or the rear biased specifications are not desired, they can be set to zero or (nominal ­100%) respectively and will not be used. If the absolute maximum or the front biased specifications are not desired, they can be set to 100% or (nominal + 100%) respectively and will not be used. In the case where the upper limit is less than the lower limit, the upper limit is set equal to the lower limit. In the case where the lower limit is greater than the upper limit, the lower limit is set equal to the upper limit.

The specifications shown in Figure 21 can be applied for a number of estimated nominal front­to­rear braking ratios as in table 1.

Figure 22 shows the pass/fail envelope using the specifications in Figure 21. Figure 23 shows the pass/fail envelope using only absolute specifications. This is the case for most plate brake testers prior to the front­to­rear estimation algorithm. In this case, the upper and lower limits do not depend on the estimation. Figure 24 shows the pass/fail envelope if the absolute limits were not used.

Figure 25 shows simulated results from a plate brake tester application. The triangular cursor points to the estimated nominal front­to­rear braking ratio on the front­to­rear bar graph. The exact values of the upper and lower limits, the estimated nominal front­to­rear braking ratio, and the wheelbase and c.g. height estimates would appear in a printout. In this example, the nominal front­to­rear braking ratio was calculated to be 73.0% front braking. The measured front­to­rear ratio was 74.2% making this vehicle slightly front biased. The minimum limit used was 58.0% (73.0% ­ 15.0%) since this limit was greater than the absolute limit of 40.0%. The maximum limit used was 93.0% (73.0% + 20%) since this limit was less than the absolute limit of 95%. The measurement was well between the two limits, therefore the vehicle would pass and the bar graph would be shown in white.

ACCURACY AND CORRELATION OF LOW SPEED PLATE TESTER

In order to verify the accuracy of the low speed plate tester, an instrumented vehicle with torque wheels was used to gather simultaneous brake torque data while brake forces were recorded on the brake plates. The instrumented vehicle, a 1985 General Motors “C,” body four­door sedan (Figure 26), was equipped as follows:

4 torque wheels

4 speed sensors

4 brake pressure sensors and LCD display

1 pedal force sensor and LCD display

1 decelerometer and LCD display

2 Adjustable proportioning valves (diagonal split system)

4 manual shut­off valves (to simulate brake failure)

1 Compaq AT computer with Analog Device RTI­860 high speed data acquisition board

1 optical trigger

The torque wheels used on the instrumented car consist of a torque transducer mounted between the axles and wheels. Since the torque transducers are rotating, a rotary transformer is used to couple the instrumented wheels to the data acquisition equipment on board the vehicle. Since wheel torques rather than actual road forces are measured, it is necessary to determine the dynamic tire radius and convert torques to brake forces when making brake balance comparisons between the low speed plate tester and the instrumented vehicle.

With torque wheels and the GM Road Transducer Plate (RTP) as two additional measuring tools, the following comparisons can be made of brake balance to deceleration:

Low Speed Plate Tester to torque wheels

RTP to torque wheels

The instrumented car with torque wheels was the base line for determining the overall accuracy of the Low Speed Brake Plate Tester. The torque wheels were calibrated from the manufacturer; however, for our own satisfaction a static calibration test was run on each wheel by applying known weights at a known lever arm length. A lever and basket was designed and manufactured so that eight dead weights of 10kg each could be used. The lever arm was 48.25 inches long. With the wheels raised and brake pedal applied, the output of each torque wheel was measured on the computer simultaneously while a static torque was applied. Table 2 shows values for each wheel vs. static applied torque.

The results show that the torque wheels are well within their accuracy specifications of 0.1% of full scale (20,000 LB­IN.)

To further verify the accuracy of the instrumented car's torque wheels, tests were run comparing brake balance results with the N.H.T.S.A. Road Transducer Pad (RTP). This equipment was designed by General Motors and installed at N.H.T.S.A'.s Transportation Research Center in East Liberty, Ohio. The RTP is an instrumented section of roadway which measures the braking forces developed at each wheel as a vehicle is driven across with brakes applied. Only snubs from 40 m.p.h. are made rather than complete stops as on the low speed plate tester.

Braking forces developed at the road surface are dynamically measured at each wheel by four instrumented platforms or transducers. The instrumented car was repeatedly driven across the platforms with brakes applied to achieve various levels of constant deceleration. Usually six to eight passes are made to obtain a spread of deceleration up to the traction limit. Brake forces are measured and deceleration and percent rear brakes are calculated for each pass of the vehicle over the RTP.

With a high level of confidence that the torque wheels were recording accurately, a series of tests were run over the N.H.T.S.A. RTP in East Liberty, Ohio. A series of constant deceleration snubs were made by their experienced test drivers while the torque wheels simultaneously recorded wheel torques. A dynamic rolling radius was used to convert torque wheel data to brake force at the road. The brake balance as determined from the torque wheels and the RTP is plotted below for various speed and proportioning valve settings.

Over a range of deceleration, speed and with different proportioning valve settings, there is good correlation between the instrumented vehicle (torque wheels) and the RTP (Figures 30 and 31).

Similar tests were run comparing the instrumented vehicle to the B400 Brake Tester.

The actual torque trace for each wheel converted to force by dividing by the dynamic rolling radius, and the brake force traces as measured b; the B400 over the complete stop, are also compared. Figure 32 shows this correlation for a typical stop. At all times the shape of the two curves showed extremely good agreement.

CALIBRATION OF THE LOW SPEED PLATE TESTER

FACTORY CALIBRATION ­ The force transducers that are common to both the brake plate and weigh scales are purchased from the manufacturers having a total combined error of less than 1% of full scale. Before the transducers are installed in any brake test component, they are calibrated using a ten point piecewise linear approximation over their entire working range. The calibration is performed at the factory using a fixture which applies an increasing load from 0 to 10000 Newtons (2248 Lbs.). A photograph of the factory calibration fixture is shown in Figure 33. The load applied to the force transducer is applied to a master transducer which is in series with the force transducer that is under calibration.

The brake test sensors employ a 1 0­bit analog to digital converter (ADC). The output of the ADC at no load is very close to 0 counts and the output at full load is very close to 1024 counts (2 to the 10th power).

Calibration constants are computed for the tested transducer at every multiple of 100 counts. As the load applied by the calibration fixture increases, the computer in the fixture queries the transducer under test. When the number of counts being measured by the ADC reaches some multiple of 100, a new calibration constant is calculated. For example, if the applied load is enough to cause the transducer under test to measure 100 ADC counts, then the load measured by the master transducer at that time is stored in the calibration memory as K1. K1 is the force which generates a count of 100. This is repeated for the remaining constants K2, K3, … K10. Each brake test sensor assembly has a non­volatile memory for storage of these calibration constants. The constants will be used by the brake tester until that sensor is recalibrated.The ten point piecewise linear calibration is used to minimize any error due to nonlinearities in the transducer. If a transducer was perfectly linear, then a two point calibration would be just as accurate as a ten point. If, however, the transducer had a non­linear characteristic over any part of its operating range, then the ten point piecewise approximation could more precisely correct for it. Force calculations in the brake tester employ a linear interpolation algorithm using the two calibration constants closest to the load being measured.

A six­inch diameter air cylinder is used to generate the applied force to the transducer. Air is metered through a needle valve to allow a gradual buildup of force from 0 to 10000 Newtons in approximately 45 seconds while load samples are taken for the tested transducer and the master transducer.

The master transducer used in the factory calibration fixture has been calibrated in accordance with ASTM specification E74­83, “Standard Practice of Calibration of Force­Measuring Instruments for Verifying the Load Induction of Testing Machines.” The calibration was performed using dead weights standardized by the National Institute of Standards and Technology (NBS). The calibration was performed by National Standards Testing Laboratory, a private testing laboratory in Rockville, Maryland. The maximum error of the master transducer is .016% of its full scale reading.

To assure that the master transducer stays in calibration, a weight hood was constructed and nine (9) laboratory grade cast iron test weights of 100 kg each were obtained. Periodic checks can be made by comparing the cast iron test weights against the mastertransducer. One to nine weights can be attached to the hood so that a ten point check can be made. The weight hood by itself, with all attaching hardware, is equal to 100 kg. The setup for checking the master transducer is shown in Figure 34.

UNIT SELF­CALIBRATION ­ When the brake tester is powered up, each sensor assembly performs an internal offset compensation. This is used to eliminate any residual forces due to friction, electrical drift, or mechanical stresses. The brake tester will also perform an automatic self test periodically. This self test is used to perform additional offset compensations and to guarantee the general integrity of the system.

In addition to the ten range calibration constants and the offset compensations, the brake tester also supports an electrical calibration (ECAL). This check is made also during self test. An electrical stimulus is applied to the strain gauge bridge by an internal digital to analog convertor. The analog to digital converter is used to measure this stimulus. The measurement is checked against the ECAL constant stored in memory and must be within the required limits. The ECAL test is used to check any electrical drifts.

FIELD CALIBRATION ­ Provisions have been made in both the brake plates and the weigh scales for attaching calibration equipment after the units are installed in the field. Actual field calibration is seldom needed, however, if a problem is suspected either due to the unit being mechanically overloaded, excessive dirt or regular flooding, it is possible to connect the field calibration fixture and apply known loads to the device while reading the indicated load. Recalibration of a component can be performed similar to that done in the factory; however, if excessive friction is found to be the cause of a low reading, the cause should be corrected by replacing bearings, damaged mechanical parts, etc., to eliminate the source of friction.

A common loading device is used for the brake plates and weigh scales, the method of attachment and hardware is the only difference The actual loading device is made up of a force transducer attached to an arm in the shape of a “U.” The legs of the “U” deflect as a load is applied by a screw thread. The signal from the loading device transducer is processed by the electronics board and sent to the console by a cable which attaches to a special service connection. Both the load generated by the calibration device and the load of the component being tested will appear on the CRT screen. Figures 35 and 36 show installation of the field calibration device on a brake plate and weigh scale, respectively.

ADVANTAGES AND LIMITATIONS OF THE LOW­SPEED PLATE TESTER

The major advantage of a plate tester is that it measures true front and rear brake forces because it takes into account the rear to front weight shift during braking just as it would on the road. By measuring the brake force at each wheel simultaneously, the brake balance for a vehicle is determined. The plate tester is basically a brake balance tester. With a little experience by the operator, many items that can be learned about vehicle brake systems by looking at the brake force vs. time curves that the vehicle generates. Below are the items that can be checked with example brake force curves showing each items.

1. Curve of brake force vs. time for each wheel
2. Front to rear balance, %
3. Front, left to right balance, %
4. Rear, left to right balance, %
5. Total vehicle weight ­ if equipped with optional weight scale
6. Static weight distribution ­ if equipped with optional weight scale
7. Deceleration of the vehicle ­ if equipped with optional weight scale
8. Actual peak brake force in pounds for each wheel.
9. Pedal force for the stop ­ if equipped with optional pedal force meter.
   Figure 37 shows these items observed on a service brake screen.
10. Actual peak brake force in pounds for the parking brakes.
11. Deceleration due to parking brake application.
12. Left to right balance for parking brakes.

13. Proportioning valve operation. By making several stops on the brake tester at varied decelerations, a plot of percent rear brake vs. deceleration can be made. As deceleration increases, the rear brake percent should decrease due to the action of the valve. The plot in Figure 39 shows this reduction in rear braking as deceleration is increased.

Proportioning valve operation can also be observed on the service brake force graphs. In general, if the applied pedal pressure is above the kneepoint of the proportioning valve, the slopes of the rear brakes will be less.

14. Inoperative brake due to seized wheel cylinder or caliper piston or due to a blocked hydraulic line. This will show up as a missing brake force curve and no peak (numerical) value. Side to side balance will also reflect this problem. Note bar graph shows 100% braking on one side of the front axle.

15. A dragging brake will be displayed as a brake force curve that has some initial magnitude before the remaining brakes on the vehicle have started to apply. As the vehicle comes to a stop on the brake plates, all four brake forces will go to zero including the dragging

16.Contaminated friction material such as grease or brake fluid on the lining can cause a large percentage difference in left/right balance on a particular axle. The brake force vs. time curve, the numerical value and the bar graph for that axle show this result.

17. Out of round drums or out of parallel rotors are shown by a brake force that varies over the circumference of the wheel. When the graphs of the left and right brake force vary substantially and cross over, it is a sign of out­of­roundness.

18. The functioning of anti­lock brake systems may be detected by observing severe dips in the brake­force curves. The number of “dips” will give an indication of the frequency the system actuates in cycles/second. The brake tester, however, should not be used as a tool to test an anti­lock system and give the customer a pass­or­fail verdict. Anti­lock brake systems of various manufacturers all function at different minimum speeds and under different conditions. The speeds obtainable on a particular brake tester installation may not be high enough to get into the operating range for the vehicle being tested. If the brakes are close to a neutral balance, it may be difficult to obtain a wheel lock condition on the expanded metal top of the brake plate.

19. A stuck parking brake cable will show up as a large differential in the brake force curves and in the numerical value for each rear brake when the parking brake test is performed. The bar graphs will show results out of specification for left to right balance and deceleration.

20. A failed front to rear ratio is shown with the rear wheels having a greater brake force than the front wheels. This could be due to a proportioning valve failure or due to improper lining on one axle. The bar graph for the fronT/rear ratio is shown as failed. The peak brake force values and the color­coded curves show this failure.

LIMITATIONS ­ The plate tester will not tell the thickness of the friction material (lining) that remains on a shoe or disc pad. This determination can only be made by an inspection procedure. It is very possible that a vehicle can pass all the specific tests on the plate tester and within a week's time a “metal to metal” condition can develop.

One disadvantage of the plate tester is its short test duration. A typical 15” tire has an 88­inch circumference that will not make one full rotation on the 72” long brake plate. Problems caused by prolonged brake application are usually not detectable on the plate tester. Heat­related problems such as brake fade or a sharp increase in friction due to heating of the friction material are not observable on a one­stop test.

A low brake fluid level in the brake master cylinder may not be found. A vehicle may perform well on the plate tester with a very low fluid reserve in the reservoir. After repeated brake applications on the road and corresponding expansion of drums, the fluid level can drop below the vent port, causing increased pedal travel or failure of a portion of the hydraulic system. The pressure differential switch or fluid level indicator should detect this.

Because the plate tester is operated at low speed, the front to rear balance as seen on the plate tester may be slightly different than the front to rear balance at highway speeds. This can occur, for example, due to speed sensitivity of a rear drum brake. At low speeds the plate tester would show slightly more rear bias.

Repeatability of a test is hard to control due to the short time the operator is on the brake pedal. If the operator could apply exactly 100 Lbs. of pedal  force twice in succession, the brake force output would be extremely close; however, making exactly a 100 lb. application twice in succession is the difficulty.

Four­wheel drive vehicles can be tested on the plate tester but a constant engaging four wheel drive system can only be tested on a four­plate system.

REFERENCES

1. Robert Bosch, Adhesions/Slip Curve, Bosch Automotive Handbook, 1st English Edition, 1976.

Flavin, T.A. and Smith, J.S. “Objective Testing for Vehicle Brake Balance.” April, 1987. General Motors Current Product Engineering.

Radlinski, R.W. “Assessment of Experimental Methods for Determining Braking Efficiency.” Presented at the 12th International Technical Conference on Experimental Safety Vehicles in Gothenburg, Sweden, May, 1989.

Wolanin, Michael J. and Baptist, Thomas A. “Road Transducer-Objective Brake Balance Measurement Without Vehicle Instrumentation.” SAE Paper No. 870266, February, 1987.

5. Garrott, W. Riley and Monk, Michael W. and Chrstos, Jeffrey P. “Vehicle Inertial Parameters ­ Measured Values and Approximations.” SAE Paper No, 881767, November, 1988.