Tribology International 34 (2001) 609615www.elsevier.com/locate/triboint

A reduced-scale brake dynamometer for friction characterizationP.G. Sanders *, T.M. Dalka, R.H. Basch

Ford Motor Company, Dearborn, MI 48121-2053, USA

Abstract

Friction behavior is a critical factor in brake system design and performance. For up-front design and system modeling it isdesirable to describe the frictional behavior of a brake lining as a function of the local conditions such as contact pressure, tempera-ture, and sliding speed. Typically, frictional performance is assessed using brake dynamometer testing of full-scale hardware, andthe average friction value is then used for the remaining brake system development. This traditional approach yields a hardware-dependent, average friction coefficient that is unavailable in advance of component testing, ruling out true up-front design andleading to redundant lining screening tests. To address this problem, a reduced-scale inertial brake dynamometer was developed todetermine the frictional characteristics of lining materials. Design of a reduced-scale dynamometer began with the choice of ascaling relation. In this case, the energy input per unit contact area was held constant between full-scale and reduced-scale hardware.All linear variables were thereby scaled by the square root of the scaling factor, while the pressure, temperature, sliding velocity,and deceleration were kept constant. Experimental validation of the scaling relations and the reduced-scale dynamometer focusedon comparisons with full-scale dynamometer data, particularly the friction coefficient. If similar trends are observed betweenreduced-scale and full-scale testing, the reduced-scale dynamometer will become an important tool in the up-front design andmodeling of brake systems. 2001 Published by Elsevier Science Ltd.

Keywords: Brake; Dynamometer; Reduced-scale; Coefficient of friction

1. Introduction

Reduced-scale or reduced-sample friction testing hasthe potential to decrease brake system development costand time. Historically, reduced-scale testing has beenused to compare friction materials for quality control,lining development, and material property assessments.For example, the friction assessment screening test(FAST) was developed to screen the friction stability ofdisk brake lining materials [1], while the Chase machinewas used to monitor drum brake lining materials [2].Other reduced-scale devices have been designed to mea-sure friction as a function of temperature, pressure, andtemperature by external control of these variables [3,4].Generally, reduced-scale testing has not been utilized toobtain quantitative data about friction material perform-ance relative to real-world usage primarily becausereduced-scale test machines historically did not repro-duce the operating conditions that the friction materialsexperienced on vehicles.

* Corresponding author. Fax: +1-313-248-5322.E-mail address: psande10@ford.com (P.G. Sanders).

0301-679X/01/$ - see front matter 2001 Published by Elsevier Science Ltd.PII: S0301- 67 9X( 01 )0 0053-6

The primary goal in the development of the currentreduced-scale brake dynamometer was to generateaccurate friction material data for use in brake systemdesign and lining screening. Brake system developmentwith computer-aided engineering (CAE) requires accur-ate friction coefficient (m) data; data that typically variesas a function of local conditions such as pressure (P),sliding velocity (vs), and temperature (T). Obtainingaccurate m (P, vs, T) data for modeling requires the elim-ination of effects related to the brake system hardware.

Many of the advantages of reduced-scale testing overfull-scale testing relate to hardware considerations.Reduced-scale friction testing can produce more accur-ate and reproducible results by eliminating full-scalehardware effects such as deflection of the caliper andanchor bracket and local pressure variations resultingfrom the piston/backing-plate interface. Friction coef-ficients generated by full-scale testing are an average ofthe friction coefficient over the entire pad. The use of astandard specimen size eliminates differences due to padgeometry that are commonly present in full-scale testing,while the small size ensures a more uniform pressuredistribution. Minimizing hardware variation generatesfriction coefficient data that are more readily modeledin terms of general, global variables such as P, vs, and T.

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Another advantage of reduced-scale testing is thatfriction materials can be tested easily without vehicle-specific fixtures and brake hardware. Such testing canlead to reduced development time because frictionmaterials can be screened before other components inthe brake system have been developed. Surrogate hard-ware has typically been used in the past, but this con-volves the friction data with additional hardware vari-ables. The elimination of full-scale hardware effectsallows friction data to be used across vehicle lines. Alarge database of friction material properties can bedeveloped and made available to all car lines to stream-line the lining selection process.

This paper describes the development of a reduced-scale dynamometer built by Link Engineering for theFord Research Laboratory. The dynamometer design andscaling relations will be discussed, followed by vali-dation of the friction material properties by comparingfull-scale and reduced-scale dynamometer resultsobtained from two different lining materials. This vali-dation process involved comparison of reduced-scale andfull-scale braking parameters such as pressure, tempera-ture, torque, and friction coefficients. The friction coef-ficients are expected to be similar, although hardwareeffects such as caliper deflection and uneven pad press-ure distribution may influence the full-scale results.

2. Scaling

One of the primary goals of reduced-scale testing isto measure the friction coefficient as a function of slidingvelocity, pad pressure, and temperature. For this reasonit is critical to maintain a one-to-one relationshipbetween full-scale and reduced-scale testing with respectto these parameters. Table 1 lists parameters that are thesame in full-scale and reduced-scale dynamometer test-ing.

Scaling the test parameters by the pad area is one wayto maintain the constant relationships, including constantenergy dissipation per unit area (energy density). TheGirling dynamometer [5] is a scaled version of a single-ended dynamometer designed to have equivalent energydissipation per unit area. This energy density approach

Table 1Constant parameters

Variable Units Symbol

Sliding velocity m/s vsDeceleration g gPad pressure Pa PEnergy density J/mm2 EaDisk temperature C TStop time s ts

has shown promising results when correlated withvehicle performance [6,7]. The scale factor (S) is definedas the ratio between the full-scale and reduced-scale padarea. If the full-scale pad area is denoted by A and thereduced-scale area by a, then

SAa

(1)

When distances are scaled, a factor of S1/2 is applied, asshown in Table 2. Scaling relations for derived quantitiessuch as torque and inertia are obtained by propagatingthese basic relationships through the calculation oftorque, inertia, and other test parameters. This processwill be illustrated for inertia, in which constant energydensity is explicitly included in the derivation. In allcases, the upper-case variable is the full-scale parameterand the lower-case variable is the reduced-scale variable.

The vehicle inertia (I) is defined asIMR2r (2)where M is the vehicle mass and Rr is the rolling radius.The energy per unit area (energy density) for one corneris given by

Ea1

2AMv2s (3)

where vs is the sliding velocity. Substituting M from Eq.(2) into Eq. (3) one obtains

Ea1

2AIvsRr2

(4)

Equating the full-scale energy density Ea with thereduced-scale energy density ea and simplifying yieldsthe following relation for the inertia ratio:

iI

a

ArrRr2

(5)

Inserting the scaling factor (Eq. (1)) into Eq. (5) yieldsI=iS 2, and this relation is included in Table 2.

Selecting a scaling factor is primarily dependent onvehicle size and available effective radii on the reduced-scale dynamometer. The scaling factor also impacts thesize of the reduced-scale pad, which is commonly cutfrom a full-scale brake pad. Generally, a scaling factor

Table 2Scaling relations

Variable Units Relation

Pad area mm2 A=aSEffective radius mm Re=reS 1/2Rolling radius mm Rr=rrS 1/2Linear velocity km/h Vl=vlS 1/2Torque N m T=tS3/2Inertia kg m2 I=iS 2

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of approximately 10 is appropriate for cars, while a fac-tor of 15 works well for light trucks.

By scaling the thermal mass it is possible to achieveagreement between the temperature rise observed inreduced-scale and full-scale braking events. For initialcorrelation exercises, where full-size hardware wasalready available, the thermal mass of the rotor wasdetermined by measuring the temperature rise duringtypical stops on the full-scale dynamometer. Determin-ing the thermal mass in this way includes heat dissi-pation by conduction into the mounting hardware. Toachieve the same temperature rise in the reduced-scalestop, the mass of the disk was adjusted so that the calcu-lated disk temperature rise (TfinalTinitial) matched that ofthe rotor. The reduced-scale disk mass was calculatedusing the predicted energy absorbed by the disk (e) fromthe scaled kinetic energy dissipated and the temperature-dependent specific heat of cast iron, Cp(T) (Eq. (6)).Conductive temperature losses in the reduced-scale testare minimized through the use of a ceramic insulatorbetween the disk and the mounting hardware. For proto-type testing, disk mass may be estimated by dividing theprototype rotor mass by the scaling factor.

me

Tfinal

Tinitial

Cp(t)+dT

(6)

Because the design of a reduced-scale friction machineis significantly different than that of a full-scale dyna-mometer, the cooling rates of the reduced-scale disk andthe full-scale rotor are not equivalent. Stop simulationsinitiated on the brake temperature are not affected bythis geometry change, but stops performed at fixed timeintervals can have dramatically different temperatures.For fixed intervals, the time between stops on thereduced-scale dynamometer must be adjusted to makethe initial brake temperature equivalent to the full-scaletest. The time between stops (t) for the reduced-scaletest machine can be calculated from the measuredexponential cooling coefficient (b) for the reduced-scalehardware (Eq. (7)) and compared to the full-scale initialand final temperatures. In Eq. (7), Tfinal1 refers to thefinal temperature at the end of the previous stop and Tini-tial denotes the initial temperature of the current stop. Agood estimate for prototype testing is that the reduced-scale cycle time is about two-thirds that of the full-scale time:

Tinitial(Tfinal1TRT) exp[bt]TRT (7)

The reduced-scale dynamometer built for Ford MotorCompany by Link Engineering (Fig. 1a) provides con-stant energy per unit pad area (energy density) as com-

Fig. 1. A full view of the reduced-scale dynamometer at FordResearch Laboratory (a). Also included are close-ups of the cast irondisk (b) and pad fixture (c) used for testing the semi-metallic liningmaterial. The thermocouple holes and wires are visible on the diskand pads.

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pared to the full-scale hardware. A scale factor of 1015yields a disk and pad of manageable size while keepingoperating costs low. The reduced-scale dynamometeruses a 90 mm diameter cast iron disk (Fig. 1b) with thesame composition and microstructure as that of the full-scale rotor. The fully-pearlitic cast iron disks havegraphite form VII, type A, and size 3 (longest flakes 2550 mm at 100) [8]. The two pads are spaced 180 apartand are applied on the same side of the disk (Fig. 1c).The pad dimensions are approximately (depending onscaling) 30 mm long by 15 mm wide with an effectiveradius of 34 mm.

3. Experimental

Brake dynamometer testing was used to evaluate thefriction behavior of two lining materials: (1) a non-asbestos inorganic (NAO) or Japanese-type lining usedon a full-size car, and (2) a semi-metallic lining used ona sport utility vehicle (SUV). Testing was first performedwith full-scale hardware on an inertial brake dyna-mometer. Next, parameters for the scaled tests were cal-culated from the vehicle and hardware parameters (Table3), and scaled disks and pads fabricated. The same fric-tion assessment test procedure was then run for eachlining on the reduced-scale dynamometer.A Ford Motor Company brake dynamometer frictionassessment test procedure was used that is similar tomany industry-standard screening tests. This procedureconsists of approximately 100 burnish stops and 100stops to assess pressure, temperature and speed sensi-tivity as well as fade performance and recovery. Burnishstops are performed from an initial brake temperature(IBT) of 80C at 0.25 and 0.15g decelerations. The tem-perature sensitivity stops, initiated at a range of IBTs,and the velocity sensitivity stops, initiated at a range ofspeeds, are all at a deceleration of 0.4g. The pressuresensitivity stops from 80 kph are performed at line press-ures from 10 to 80 bar. On the scaled dynamometer aload cell replaces the hydraulic pressure apply systemused on full-scale dynamometers; load control set points

Table 3Brake dynamometer experimental parameters

Vehicle parameter NAO Semi-metallic

Full-scale Reduced-scale Full-scale Reduced-scale

Corner weight (kg) 475 610Rolling radius (mm) 308 344Inertia (kg m2) 45 0.39 72 0.39Scaling factor 11 14Pad area (mm2) 9930 900 14,120 1016Effective radius (mm) 113 34 127 34

that achieve equivalent nominal contact pressure are pro-grammed into the scaled dynamometer.

4. Results and discussion

The results will be presented as a comparison betweenreduced-scale and full-scale dynamometer data. Therelations in Table 2 were used to convert the reducedscale data into full-scale values for comparison. For bothlining materials, the same pressure-controlled and decel-eration-controlled stops were chosen for analysis. Theconstant pressure stop was at a line pressure of 60 bar,an IBT of 80C, and an initial velocity of 80 kph, whilethe constant deceleration stop had a deceleration of 0.4g(3.9 m/s2), an IBT of 200C, and an initial velocity of100 kph.

Constant pressure stop parameters are shown in Fig.2 for the NAO and semi-metallic linings. For the NAOlining (Fig. 2a) the pad pressure, torque, and m all agreeextremely well, demonstrating that the reduced-scaledynamometer is capable of accurately reproducing theconditions of full-scale testing. As expected, the disktemperature is nearly the same in both tests (Fig. 2c).(This parameter was fit using Eq. (6).) The pad tempera-ture is consistently lower on the reduced-scale test, butthe effect on m was minor because m is not strongly tem-perature dependent in NAO materials.

The pressure-controlled stop with the semi-metalliclining is shown in Figs. 2(b) and (d). Once again, thepressure agrees well between the reduced-scale and full-scale dynamometers (Fig. 2b). However, m is lower inthe reduced-scale test and this leads to a lower torquelevel. The disk temperature agreement is acceptable, butthe pad temperature is significantly lower on thereduced-scale test (Fig. 2d). The lower lining tempera-ture is due in part to the greater thermal conductivity ofthe semi-metallic pad. Semi-metallic lining materialshave been observed to have greater batch-to-batch varia-bility in friction coefficients and this may be one reasonfor the discrepancy between the reduced-scale and full-scale stops. In addition, m generally rises with tempera-

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Fig. 2. Constant pressure dynamometer stops (60 bar, 80C IBT, 80 kph) for NAO (a, c) and semimetallic (b, d) lining materials. Torque, pressure,and friction coefficient are compared in (a, b) and velocity, disk temperature, and pad temperature are compared in (c, d). Curves depict full-scaledata and symbols show reduced-scale data.

ture for semi-metallics, so the lower pad temperatures inthe reduced-scale test may lead to a lower m.

The constant deceleration stops for the NAO andsemi-metallic lining materials are shown in Fig. 3. Linkdynamometers do not control the deceleration directly,but rather attempt to maintain a constant torque levelcalculated from the inertia and deceleration parameters.The feedback loop involves measuring the torque andadjusting the pressure to maintain the desired torque. Forthe NAO material (Fig. 3a) the torque levels are similarfor both tests, with the reduced-scale dynamometershowing more constant torque over time. The pad press-ure levels are also of similar magnitude, but the reduced-scale dynamometer varies the pressure more to maintainthe constant torque. Despite differences in torque controleffectiveness, the friction coefficients show good agree-ment. At 200C IBT, the disk and pad temperature pro-files show acceptable agreement (Fig. 3c).

The semi-metallic material also shows good torqueagreement (Fig. 3b). As in the pressure controlled stopabove, m was lower for the reduced-scale lining material.This led to higher pressures in deceleration control. Thedisk temperature agreement was acceptable, but the pad

temperature was significantly lower in the reduced-scaletest (Fig. 3d). Once again, lower semi-metallic pad tem-peratures can contribute to the lower m observed duringthis stop.

In Figs. 3(c) and (d) the NAO and semi-metalliclinings display shorter stop times for the reduced-scaletest. The reduced-scale dynamometer exhibits a highlevel of parasitic drag from the thrust bearings used tosupport the main shaft during braking. Without anybrake applied, the reduced-scale dynamometer coastsfrom 100 to 0 kph in 50 s. This is equivalent to a full-scale torque level of about 100 N m at 100 kph (a largefraction of the torque levels in Fig. 3). As mentionedabove, constant deceleration tests are controlled bymaintaining a constant torque calculated from the inertiaand the desired deceleration rate. Since parasitic drag isnot included in the calculation, its presence will lead toshorter stop times. The effect is more noticeable atslower deceleration rates (Fig. 3) than at higher deceler-ation rates (Fig. 2) in which the dynamometer drag is asmaller fraction of the total braking torque.

The fade section in the test procedure consists of 15stops from 100 to 0 kph at 0.4g deceleration. On the

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Fig. 3. Comparison of constant deceleration dynamometer stops (0.4g, 200C IBT, 100 kph) for NAO (a, c) and semimetallic (b, d) liningmaterials. Torque, pressure, and friction coefficient are compared in (a, b) and velocity, disk temperature, and pad temperature are compared in(c, d). Curves depict full-scale data and symbols show reduced-scale data.

full-scale dynamometer there is 60 s between each stop.For the reduced-scale dynamometer with semi-metalliclinings, a time of 37 s between each stop was calculatedusing Eq. (7). The fade section for the semi-metalliclining (Fig. 4) shows good agreement between thereduced-scale and full-scale temperature traces.

Fig. 4. Fade temperature for semi-metallic lining material. The cycletime was 60 s for the full-scale and 37 s for the reduced-yscale dyna-mometer.

Although the curves are not exactly the same shape, theminimum and maximum temperatures show good agree-ment.

The average friction coefficients (averaged over thewhole test procedure excluding burnishes) are shown inTable 4. There is good agreement for the NAO liningmaterial, although the variability is higher for thereduced-scale testing. For the semi-metallic material, mis always lower in reduced-scale tests, most likely as aresult of batch-to-batch lining variability and lowerpad temperatures.

To improve the reduced-scale tests, it is apparent thatmachine drag, lining variability, and pad temperatureissues should be addressed. Programming the drivemotor to provide a small amount of power to the dyna-mometer during the stop can minimize the effects ofparasitic dynamometer drag. This additional energy willcompensate for the bearing drag, which is roughly a lin-ear function of the rotational velocity. The lining varia-bility can be assessed by careful attention to the liningbatch and the location from which the reduced-scale padis cut from the full-scale pad. The lining temperatureduring reduced-scale testing was consistently low, parti-cularly for higher conductivity, semi-metallic linings.

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Table 4Average friction coefficient

NAO Semi-metallic

Hardware Repeat Full-scale Reduced-scale Full-scale Reduced-scale

A 1 0.39 0.38 0.37 0.28A 2 0.38 0.43 0.41 0.31B 1 0.36 0.31 0.39 0.31B 2 0.37 0.34 0.41 0.34Average 0.37 0.37 0.40 0.31Deviation 0.02 0.05 0.02 0.02

Improving the thermal insulation of the pad fixture canminimize this discrepancy. Since lining variability andpad temperature were found to be problems as a resultof this validation exercise, addressing these issues shouldimprove the agreement between reduced-scale and full-scale testing.

5. Summary

Reduced-scale dynamometer data based on constantenergy density scaling has been compared to full-scaledynamometer results. The agreement between dyna-mometer tests is excellent, especially for NAO materialswhich exhibit minimal batch-to-batch friction variability.Several areas for improvement were identified on thereduced-scale dynamometer, including corrections forparasitic drag and reducing the thermal conductivity ofthe pad fixture. Overall, the data generated by thereduced-scale dynamometer are highly correlated withthose from full-scale testing. The reduced-scale dyna-mometer promises to be an important lining screeningand design tool; friction coefficients can be determinedin advance of prototype hardware, enabling true up-frontCAE and friction behavior modeling.

Acknowledgements

J.W. Fash initiated the reduced-scale dynamometerwork at Ford. R. Hasson did some of the early validationexercises on the instrument and R. Mangan of LinkEngineering performed the reduced-scale measurementsreported in this paper.

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