ABSTRACTThermo-elastic and thermo-plastic behaviour takes place witha disc brake during heavy braking and it is this aspect ofbraking that this paper considers. The work is concerned withworking towards developing design advice that providesuniform heating of the disc, and equally important, evendissipation of heat from the disc blade.

The material presented emanates from a combination ofmodeling, on-vehicle testing but mainly laboratoryobservations and subsequent investigations. The experimentalwork makes use of a purpose built high speed brakedynamometer which incorporates the full vehicle suspensionfor controlled simulation of the brake and vehicle operatingconditions. Advanced instrumentation allows dynamicmeasurement of brake pressure fluctuations, disc surfacetemperature and discrete vibration measurements. Disc run-out measurements using non-contacting displacementtransducers show the disc taking up varying orders ofdeformation ranging from first to third order during highspeed testing. This surface interrogation during brakingidentifies disc deformation including disc warping, “ripple”and the effects of “hot spotting”. The mechanicalmeasurements are complemented by thermal imaging of thebrake, these images showing the vane and vent patterns onthe surface of the disc. The results also include static surfacescanning, or topographical analysis, of the disc which iscarried out at appropriate stages during testing. The workincludes stress relieving of finished discs and subsequentdynamometer testing. This identifies that in-service stress

relieving, due to high heat input during braking, is a strongpossibility for the cause of disc “warping”. It is also seen thatan elastic wave is established during a braking event, the discreturning to its original form on release of the brake.

INTRODUCTIONWhole vehicle NVH refinement has been extremelysuccessful over the past few years and as a result the re-emergence of effort towards finding a solution forproblematic brake instabilities has again become the focus ofincreasing attention. Research towards understanding brakenoise has never really remained static and so the advancedanalytical techniques developed over the last 20 years,combined with the improved practical investigative skills andthe sophisticated test facilities, have all enabled themechanisms involved to be better understood. As such thetechnical competence in controlling dynamically inducedvibrations, such as brake noise, has grown considerably soallowing this area to enjoy similar successes as generalvehicle NVH improvements. As a result of the continuousefforts in the areas of brake noise there are some improveddesign guidelines available that allow new brake designs tobe created with a reduced propensity to generate noise and sothe effort is stabilising a little.

This success in one area of braking NVH, noise, is notreflected in the mechanically induced vibrations of brakejudder and as such this has not advanced at the same rate.Judder in one form or another is now often seen to be moreproblematic than noise as shown in Figure 1 where judderissues absorb 73% of new brake NVH research effort. Some

Hot Judder - An Investigation of the Thermo-Elasticand Thermo-Plastic Effects during Braking

2011-01-1575Published

05/17/2011

John David FieldhouseUniv. of Huddersfield

David Bryant

Chris John TalbotUniv. of Huddersfield

Copyright © 2011 SAE International

doi:10.4271/2011-01-1575

of the fundamental mechanisms are well understood and thepractical investigation methodologies are well established,but these remain primarily vehicle based. This is anexpensive approach as much equipment must be dedicatedand carried on-board the vehicle as indicated in Figure 2 andeven then the data that may be collected is restricted becauseof accessibility and the prevailing environment. In additionthe available design guidelines remain restricted withmanufacturing accuracy and brake materials forming part ofthe equation.

The proportion of noise to judder issues is not a constant andvaries considerable from vehicle supplier to supplier. Theheavier, high performance, vehicle manufacturers appear tosuffer most from judder issues with the ratio being about 30%noise to 70% judder. Judder in this regard being as indicatedin Figure 1 - Pad deposition, corrosion, thermal and off brakewear. On the other hand the proportion may change for thelighter “town cars” to become 70% noise 30% judder. In thelatter case the types of judder will be the same but theproportions will differ from that in Figure 1. It is the demandsfor high speeds and braking performance on the edge of tyrefriction limits that leads to such proportions and proportionalchanges. Off-brake wear and thermal judder will becomemore evident as speed increases and thus more prevalent withthe higher performance cars. Clearly the speeds and energiesinvolved are less for lighter cars and indeed the requiredbraking forces are less. Brake judder, hot or cold, results fromthe degree of rotor distortion and the braking force applied.This combination results in a variable force being transmittedto the vehicle chassis and body - the heavier vehicle with theheavier braking being in a better position to generate theseforces, hence judder.

Figure 2. Typical equipment needed for on-board brakeinstability evaluation.

Judder is not a brake problem it is a vehicle problem and thefront corner assembly design can significantly influence thedegree of judder experienced by the driver. Figure 3 [1]shows a typical front corner assembly where it is seen theknuckle holds the disc, calliper, suspension system andsteering track rods; these therefore being mechanically linkedto the vehicle, and through the tyre to the road. Under normalbraking the knuckle will provide an appropriate reaction bytransmitting the braking force to the vehicle body and roadthrough any member attached to it and the vehicle. Thebraking torque would normally be steady so the reactionwould be even. If there is any variation in braking torque thereaction force provided by the knuckle assembly will alsovary and so the forces seen by the calliper, suspension,steering and tyre will also vary. The driver is also connectedto the front corner assembly through the brake hydraulicsystem (foot pedal), the steering wheel (steering gear) and thecabin structure interface with the chassis. It is the interfacesthat allows the driver to experience judder; through vibrationof the foot pedal, vibration of the steering wheel and anaudible noise. The frequency is not resonant but wheel speedrelated, similar to wheel imbalance, and in the region ofaround 100Hz. The effect of judder is not only an audible

Figure 1. Distribution of dynamic instabilities. (Courtesy Bentley Motors Ltd)

experience; it is felt throughout the vehicle as whole bodyvibrations. This dynamic and often dramatic effect of vehiclevibration demands the focus to be moved from brake relatednoise problems towards brake judder - both hot and cold. It isthe consideration of these two conditions that explain whybrake torque may vary.

Cold judder is generally accepted to be all mechanicallydriven instabilities that are not thermally induced. Theseinclude off-brake wear, corrosion and uneven surface filmtransfer.

Off-brake wear is most obvious with discs having high discrunout or swash (when disc faces are not machinedperpendicular to axis of shaft). A typical acceptable axialrunout on a newly fitted disc may be in the region of 0.08 mm(80 micron). If the disc is fitted with a spec of rust or dirt inthe region of 0.05mm (50 micron) then it is possible that theallowable runout will be exceeded. This swash allows thedisc to make contact with the pads during normal running so

leading to uneven off-braking rotor wear or disc thicknessvariation (DTV). On braking this DTV leads to a braketorque variation (BTV) with consequential brake calliper,steering and body vibrations. Figure 4 shows typical wearpattern of a disc with runout [2].

There may also be inherent DTV as a result of machininginaccuracies. Clearly this may be resolved through improvedquality control and effective calliper seal roll-back. Theformer solution may result in higher base costs whilst thelatter will result in enhanced pad retraction and willinevitably affect pedal feel.

Corrosion judder results from disc corrosion because ofextended vehicle parking in a mild corrosive environment(dockside storage) and is generally temporary and willeventually reduce during normal vehicle use. The exposedarea of the disc experiences rust whereas the area under thepad does not. Removal of the rust during initial brakingresults in DTV. With DTV the disc experiences uneven

Figure 3. Typical front corner suspension showing knuckle fitted with caliper, disc, suspension and steering [1].

Figure 4. Disc showing runout wear which leads to disc thickness variation. The disc has been rotated about the horizontal axisto show wear diametrically opposite and on the reverse face of the disc.

heating, the thicker area exhibiting the higher temperatureand expands more than the thinner area -a self servingcondition is created.

Surface film transfer, or pad deposition, may also causejudder if the film is not evenly distributed. This unevendistribution of surface film causes a variable disc/pad frictionvalue and thus brake torque variation (BTV). The transfer ofmaterial from pad to disc and disc to pad is a fact of life andany instability investigation should only be undertakenfollowing a degree of brake bedding or conditioning. Thisperiod of conditioning allows an even surface film transfer tobe established and so a more stable system regarding the disc/pad friction coefficient. If this transfer is uneven then theinterface friction characteristics will also vary and as suchBTV will result, hence judder. Control of surface filmtransfer is difficult and related to pad formulation which hasadditional demands such as a predictable compressibility,good wear characteristics, stable friction level, good clean-upcharacteristics and yet not be excessively aggressive. It is anarea that requires a careful study of compatible materialcharacteristics and is not the purpose of this paper.

Hot (thermal) judder is probably the least understood of alljudder experiences because it involves both low and highfrequency judder (drone). It occurs during heavy braking andthe resulting deformations and service data may reduce andeven disappear once the brake cools. The demand for highperformance cars will always exist but the high speeds,combined with high deceleration, means the need for thedissipation of high levels of energy. That energy is absorbedand rejected by the brake and as a result thermal effectsbecome the focus of concern. If the brake absorbs energysignificantly faster than it can dissipate it then the discexperiences high temperatures and as such thermaldeformation. This deformation may be recoverable and assuch judder may only be temporary. The issue becomes moreserious if the deformation does not recover and so the discwill hold a permanent wavelike shape resulting in classicaljudder.

It will be shown later that during a heavy braking stop thedisc can experience a high temperature rise, in the region of270°C. Clearly if the driver brakes again before the disc coolsthen the disc temperature will rise until the “soaking”temperature is reached - when the disc loses heat as fast as itis generated due to braking and a steady state temperature isachieved. With the uneven temperature caused by DTV thereis a possibility that the temperature can reach values in theregion of 650-700°C. At these temperatures the cast ironchanges structure and Cementite is formed. This Cementite isharder than the base cast iron and so wears less and the DTVbecomes worse. In addition the Cementite will run hotter as itis not a good “heat sink” and so penetration into the discsurface increases. If the discs are relatively new then theCementite may be removed by re-machining the discs but if

the penetration is too deep then the problem will quickly re-occur on refitting the discs.

It is common for high performance cars to use vented discs asthese allow the heat to be dissipated more readily, but theoverall purpose and effect is sometimes confused. Venteddiscs bring with them another form of thermal deformation inthe form of “hot spotting” or “blue spotting” [3]. Suchheating effects are localised and distributed about the disc inan apparent random manner but if left to multiply then thesurface of the disc becomes covered in these “hot spots” asshown in Figure 5. The hot spots may be localised regions ofCementite and as such the problems described above areequally relevant with these “hot spots”. The overall effect ishigh frequency judder leading to a droning sound caused bythe multiple localised thermal deformations about the discsurface. It is tentatively believed that high frequency judder(drone) is caused by uneven temperature distribution on thedisc surface, or within the brake rotor, causing both thermoelastic deformation and thermo elastic instabilities. Discripple also gives such effects. All these definitions and causeshave been detailed in previous literature [4], [5], and [6] andtherefore it is sufficient to only briefly mention them.

Figure 5. Extreme case of “hot spotting”. Often appearsto be random but may be a function of rotor speed.

This paper reviews earlier work on the topic of thermaljudder and focuses on establishing a disc design that avoids“heat sinks”, moving towards a more even heating andcooling of the disc surface and body. Such a design considersthe geometry of the disc/pad interface and on the ribprofiling. The purpose is not necessarily to increase thecooling capacity of the brake disc but to encourage a moretemperature stable brake disc by adequate consideration ofthe heat distribution across, around and through the disc, inaddition to overall even cooling of the disc body.

THERMAL ANALYSISTo evaluate the thermal impact on a braking system it ispossible to estimate the heat generated by a typical ABS stopfor a typical vehicle. Consider values for the vehicle asindicated in Table 1:

Table 1. Characteristics of a typical high performancevehicle.

Where “mass equivalent” (meq) represents the rotationalinertia of all the rotating parts within the transmission andalso the non-driven wheels. These rotational inertias arereferred to the wheels and represented as a mass that isadded to the vehicle mass (meq=Ieq/r2).

Ignoring drag and rolling resistance.

This is transposed to give t = u/d resulting in t = 50/(0.8 ×9.81) = 6.37 s

Power = Energy/ time = 4.79 × 106/6.37 = 752 kW

This power/energy is absorbed by the discs and is seen asheat.

Assuming proportion to front brakes during the stop 85% (notunreasonable).

From

For front brakes this gives

for a single ABS stop.

This assumes all the disc has time to absorb the heat whichwill not be the case and the disc will experience high thermal

gradients across its thickness with the surface temperaturebeing well in excess of the 270°C. If the disc does “hold” allthe heat uniformly then it will experience a thermal shock andwill try to expand circumferentially. The time is insufficientand high mechanical stresses will be imposed on the disc.Consider the blade disc as a beam of section 97.5mm ×40mm thick. Let the disc be represented as a straight beam ofa length equal to its effective circumference and constrainedat its ends as shown in Figure 6.

The disc material characteristics are listed in Table 2.

Figure 6. Disc blade represented as a beam constrainedat its ends.

Table 2. Characteristics of beam (disc):

The temperature rises over a very short space of time.

Thermal expansion

Giving Strain

and induced thermal stress = Eε = 86300×106 × 3036×10−6

=262 MN/m2

Axial mechanical load within disc to such cause stress =Stress × Area = 262 × 106 × 0.0975 × 0.040 = 1.022 MN

But buckling load of beam is given by Euler equation

THE FORMATION OF A WAVELIKESHAPE DURING BRAKING.With such loading considerations as shown by the thermalanalysis it is concluded that the beam, or in this case of thedisc blade, will buckle as the internal constrained/inducedload is more than twice the allowable critical buckling load.This may be one reason for the disc to exhibit a wavelikeshape. If the induced stress exceeds yield of the material thenthe deformation will remain to some degree. Such a discshape may be seen in Figure 7 which shows runout (0.06mm)as supplied and the permanent wave after bedding and severalbraking events. It is seen that the disc has developed apermanent wavelike shape as predicted. It is seen that thewave will reach a limited maximum distortion of about0.2mm and then stop to deform any further. If the disc isreground and retested it will once again continue to deformfurther. It is suspected that the continuing deformation is apurely mechanical (inbuilt stress) limitation, the regrindingremoving that constraint. Runout measurements of the frontand reverse side of the disc shown a thickness variation to beforming. This is seen on Figure 7 where the leading flank ofthe wave shown two distinct profiles.

Figure 7. Disc before running showing runout and discafter running showing permanent wavelike shape. Solid

line is front of disc and dotted rear.

This feature may be seen on most runout measurements. It isfelt that this is due to the pad “ploughing” into the faceresulting in high pressures at the interface and thus increasedwear. The trailing flank does not exhibit the wear as thepressures are less. This type of contact also results in a braketorque and pressure variation. Such a typical recording ofBPV is as shown in Figure 9 where the pressure fluctuation isaround 0.1 MPa peak to peak with a mean pressure of about0.44 MPa. The disc temperature during the recording was150°C. This pressure fluctuation (measured on a test rigduring earlier work) [7] may be compared to on-vehiclepressure measurements of an entirely different brake - Figure10.

Figure 8. Shows pad negotiating the disc wave. Theleading face causes an increase in pressure but also

results in increased wear of this face.

The similarities are clear and may infer that there may berepeatability in the mechanism regardless of disc type.

Figure 9. Resulting brake pressure fluctuation resultingfrom the permanent set wavelike shape.

Figure 10. Pressure reading from on-vehicle testing.Note similarity of smoothed curve to pressure readings

shown in Figure 9.

MANUFACTURINGCONSIDERATIONSCASTING CONCERNS

Figure 11. Graph showing percentage change in weightabout the disc.

Casting is not an exact science and during dynamometertesting there was evidence of asymmetric heating of a discduring braking. Such thermal gradients may causeasymmetric thermal expansion of the disc, hence differencesin deformation, and may contribute to the formation of thewavelike shape. The temperature variation tended to berelated to the balance groove and a simple test wasundertaken to investigate the density of the disc about itsdiameter. The discs were cast vertically which may result inchange in density across the diameter due to carbonmigration. To test whether this was the case 8 sections werecut from a disc, machined individually to a common size andweighed [8]. The normalised result is shown in Figure 11.The change would not appear significant, it being only 4%overall, but the introduction of any temperature gradient mayinduce small changes that are exacerbated during the brakingprocess. A secondary issue is the asymmetric stressesremaining after machining due to the density variation. It wasthis aspect of manufacturing that was investigated further.

STRESS RELIEVING EFFECTSThe formation of a wavelike shape in the disc may be due tothermal “buckling” as indicated earlier. Other factors have tobe considered and as such the stress relieving process duringbraking was investigated. It was felt that the repeated heatingand cooling of the brake disc during testing was relieving theunstable stress field which remained after the casting andmachining processes, the uneven density adding to this issue.

Stress Relieving Measurement and ExperimentalProcedureEarlier brake dynamometer testing had indicated a possiblestress relieving process was occurring during hot running ofthe brake disc. To identify whether this was the case testingwas conducted consecutively on both standard un-used brakediscs and also on brake discs which had been manually stressrelieved after machining. The process would be in stages,namely; to measure the flatness of the brake discs, to stressrelieve, re-measure, test and finally to measure again.

Bare metal brake discs were delivered for measurementwithout a protective zinc flake coating applied; it wastherefore possible to get the discs stress relieved, minimisingany scaling or oxidisation on the disc surface. The stressrelieving process involved heating the discs to 550°C in avacuum followed by a controlled cool-down. Following thisthe discs were measured again to identify any deformation asa result of the stress relieving process.

The absence of the protective coating increased the accuracyof the measured results. All surface measurements wereperformed using a CMM with a probing error of 0.7µm, ascanning error of 1.3µm and a volumetric accuracy betterthan +/−3 microns.

Subsequent measurements of the installed run-out (cold) onthe dynamometer were recorded using digital DTI with aresolution of 1µm and an accuracy of <3µm, whilst thedynamic hot disc shape was recorded using non-contactingcapacitive displacement transducers with a capture frequencyof 10 kHz. Each dynamometer test comprised a sequence ofeight, eight second braking events each separated by fourseconds. The dynamometer speed was a constant 1200r/min,whilst brake pressure was 16bar, equivalent to a brake torqueof approximately 600Nm.

Stress Relieving Results and DiscussionFigure 12 shows the measurements of a disc that has followedonly the manual stress relieving process. The images clearlyshow that following stress relieving the disc has deformedsignificantly with the right hand edge deflecting upwards byapproximately 40 microns. The graph shown in Figure 13shows a scan at the mean rubbing radius of the brake disc preand post stress relieving. It is evident that the disc has

changed from low (15 microns) first order run-out to a large(65 microns) predominantly first order wave, with asecondary peak as shown.

The reverse (outboard) side of the disc was also measuredand as expected this reflected the same tendency to deform.In this case the friction ring transformed from 18 microns to57 microns of run-out with again a secondary peak beingevident after stress relieving.

Surface CMM scans from a second disc showed a similarsecond order mode of deformation present within the discfollowing the stress relieving process. This basic test showsthat during the manufacturing process troublesome stressesare retained within the disc material as a result of unevenremoval of material or variable density of the basic castingwhich will also disrupt the distribution of the inboundstresses following casting and cooling.

Figure 13. Disc 3 aligned inboard surface scan at aradius of 167mm. Note formation of secondary peak in

addition to increased deformation.

It is believed that this stress relieving process is occurringduring braking as a result of the elevated disc temperaturesfollowed by cooling. It is unclear as to why the disc takes upsecond order deformation following stress relieving and theorientation of the deformation was different for the two discstested. The differences may be due to density variationsuperimposed on the casting/core tolerances. Regardless thishas clearly identified that the stress relieving process isoccurring during the braking process.

Dynamometer Testing of a Stress Relieved DiscA further test was undertaken to evaluate the deformation of adisc that had been stress relieved and then tested on adynamometer. The dynamometer test was carried out using astress relieved disc to identify if there was any further changein the distortion, or evidence of further thermo-plasticdeformation during braking. It would be expected that therewould be little or no change in the post stress relieveddeformation during dynamometer testing if the stressrelieving theory was valid. It was felt that the stress relievingprocess would remove any tendency for the brake to deformif all the manufacturing stresses had already been removed.The result of such a test is shown in Figure 14. This graphshows that there is little change between the pre and postdynamometer test run-out of the brake disc in both magnitudeand shape. The minor changes that do take place may beargued to being the result of residual stresses still being heldin the disc, the stress relieving process being out of thecontrol of the authors. It would be expected that if the thermaldeformation was as a result of the braking then thedeformation would occur regardless of stress relieving. Ingeneral it may be concluded that deformation of a disc doesoccur when the disc is stress relieved, either prior tomachining or during braking.

In summary, if this stress relieving takes place during brakingthe disc will exhibit a second or higher made shape and hencejudder. If the stress relieving takes place during the manualstress relieving process the disc deforms as expected and

Figure 12. Disc 3 (inboard friction ring) pre stress relieving (left) and post stress relieving (right) - Same scale.

before testing and during testing it does not changesignificantly. If this is the case then thorough stress relievingbefore machining could help reduce in-braking stressrelieving and subsequent thermal distortion.

Confirmation of the test may be seen by comparing Figure 14and the two shapes in Figure 15. These show a standard discfront set (as supplied) which was brake tested in the samemanner as the disc in Figure 14 (a sequence of eight, eightsecond braking events each separated by four seconds). Themarked amplitude changes are more obvious which shows theeffect of in-braking stress relieving.

Summary and CommentOn-vehicle and dynamometer testing show the disc toestablish a wavelike shape during braking. A similarwavelike shape occurs if the disc is simply stress relieved. Itis felt that this is not a coincidence and that the continuouswavelike shapes are due primarily to in-braking stressrelieving. It is believed that this has the effect of changing thedisc distortion from first order ‘cold’ deformation to secondorder deformation during brake testing. Stress relieving a pairof un-used discs has supported this speculation, identifyingthat there are significant stresses retained in the discfollowing casting and machining, and that the removal of

these stresses allows the disc to deform significantly. In bothcases the mode of disc deformation was second order. It isproposed that repeat testing is carried out to fully substantiatethis “de-stressing” process. It is also necessary to absolutelyconfirm this element of distortion by testing a disc which hasbeen thoroughly stress relieved prior to machining. It hasbeen shown that stress relieving a disc after machining allowsthe disc to deform in a manner according to the degree ofstress remaining after processing. The resulting run-out of thedisc becomes quite large leaving the disc susceptible to coldlow frequency judder in addition to off brake wear, whichwill eventually lead to drone. It must be mentioned that stressrelieving after machining imposes a necessary degree of carethat may prevent full stress relieving to be realized. Stressrelieving prior to machining would remove this problem andalso give a very good base disc to further analyse the“elastic” deformation of the brake disc during braking,without any other influencing factors.

DYNAMOMETER TESTING ANDTEST EQUIPMENTElastic Behaviour: Some of the results of dynamometertesting have been shown earlier but these were thermo-plasticbehaviour, typically Figures 13 and 14. Dynamometer testing

Figure 14. Graph showing the similarities between the pre and post test installed run-out of a stress relieved brake disc.

Figure 15. Graphs showing pre and post test run-out for a standard brake disc mounted on-vehicle. Left graph left hand front.Right graph right hand front.

here is to show the “elastic” behaviour that may occur duringbraking. The brake dynamometer used for the purpose of thistesting is a bespoke design created especially forinvestigation of brake judder. The dynamometer comprises abrake rig and motor as shown in Figure 16. Briefly the designencompasses the following aspects:

A full quarter car suspension is identical to that used on thevehicle and is rigidly mounted to a substantial steel backplatewhere it would be mounted to the vehicle hard-points. Thesuspension geometry is aligned so that the driveshaft is in anoptimal horizontal position as would be seen on the vehicle.Loading of the suspension is applied through the base of theupright using a rubber mount to simulate the tyre stiffness.The quarter car suspension allows investigations of brakejudder into the transmission path from the brake assembly,through the suspension, to the vehicle structure.

It also allows excitation frequencies of the variouscomponents to be analysed. The brake disc is directly coupledto a 110kW motor using the original driveshaft and CVjoints. This allows unconstrained movement of thesuspension system and brake head. The motor can drive thediscs at speeds of up to 2400rpm with a maximum braketorque of 700Nm. This brake torque is sufficient to replicatethe typical high speed low deceleration braking which cancause brake judder. The brake is actuated via a pneumaticproportioning valve which controls hydraulic pressure in thebrake master cylinder and allows for repeatable brakeactuation. The brake assembly used for the purposes of brakejudder investigations comprises of a single piece cast ironvented brake disc and two piston sliding fist type calipers.The disc is designed with 40 straight vanes and is 405 mmdiameter. The brake disc itself is mounted to the hub bearingusing the centre section of the vehicle wheel. This allowsidentical mounting conditions, including clamping area, stressand torque, to be replicated. The mating faces of both the discand hub are cleaned prior to mounting, and equal torque isapplied to each of the mounting bolts. In doing this theinstalled run-out of the disc, and therefore the possibility ofcold judder due to off brake wear, is minimised. It has beenargued [4] that a full suspension dynamometer presents themost realistic results when carrying out high speed juddertests, allowing excitation frequencies of various suspensioncomponents to be investigated.

Figure 13. General view of the dynamometer assemblyshowing motor, backplate, suspension assembly and

brake disc.

Figure 14. Mounting arrangement of the displacementtransducers. Run-out measured at 167 mm radius.

Measurement of the dynamic disc thickness variation andsurface run-out is made possible by the use of non-contactingcapacitive displacement transducers connected to a highspeed data acquisition device. The transducers are rigidlymounted to a thick steel plate to eliminate any unwantedvibrations, as shown in Figure 14, and are positioned at themean rubbing radius of 167 mm. The steel plate forms an arcaround the disc allowing measurements to be taken atdifferent positions. Rubbing thermocouples are mounted onthe disc surface to give reference temperature measurementsfor both displacement and pressure measurements. Thethermocouples also allow for accurate calibration of thethermal camera to take place by allowing for emissivitychanges of the disc surface. Brake line pressure is measuredat the caliper using a pressure transducer.

ELASTIC & THERMO-ELASTICEFFECTS

Figure 15. Graph showing typical brake pressureapplication

Dynamometer testing shows the distortion of the brake discto be highly dynamic in nature, with quite dramatic changesduring and after braking. The mode order of brake discdistortion can change rapidly during the duration of a singlebraking event. The disc may be seen to revert back to lowerorders of distortion immediately upon release of the brakedisc, generally 1st order. A typical dynamometer testsequence is shown in Figure 15, which highlights theapplication of the brake pressure. Each dynamometer testinvolves eight second braking applications at 16 bar and 1200rpm.

From cold the brake disc being used for this example exhibits1st order run-out as shown in Figure 16.

When the brake is applied during the first braking applicationthe disc shape is still predominantly 1st order, however asuperimposed higher order of displacement is also moreapparent as shown in Figure 17. This may be caused byexpansion of the raised regions, seen in Figure 16, due to nonuniform contact and subsequent heating of the brake discsurface. The run-out of the disc at the initiation of brakingalso appears to be reduced due to the clamping action of thebrake pads.

Figure 16. Graph showing normal first order run-out ofthe brake disc shape when cold.

Figure 17. Graph of disc distortion when brake is firstapplied.

As braking progresses the order of deformation is seen tochange from 1st order to 3rd order approximately mid waythrough the braking event. The data shown in Figure 18 istaken at t = 7.5 seconds into the braking event.

Figure 18. Graph showing disc deformation towards theend of the first braking application.

It highlights the change in disc deformation during braking,where three peaks are clearly seen per disc revolution. Therelative magnitude of deformation of the disc has nowdoubled from the initiation of braking and is now the samemagnitude as the cold disc.

Figure 19. Graph showing disc deformation immediatelyafter the brake is released

Immediately following the release of the braking force thedisc reverts back to dominant 1st order deformation shown inFigure 19. It is interesting to note that the waveform now hasa slight “plateau” possibly due to wear at the peak of thewaveform. There is evidence of secondary peaks on each“plateau” which would also indicate plastic deformation andthe move towards higher mode orders. It must be noted thatthe sequence of events shown is a repeatable event on thisbrake system which is observed during every test on thebrake dynamometer. These results indicate both plastic and

elastic deformation occurs during a braking operation - bothcontributing to the occurrence of judder. The displacementtraces shown in Figure 20 show the results of a subsequenttest with the following sequence; no braking, start of braking,end of braking, brakes released. Again the “off braking” atthe start and finish are the same indicating a degree of discelastic deformation is taking place during braking. Theimages of elastic recovery are (Figure 20) not unusual buthave only been able to be detected on the test rig because ofthe difficulties of on-vehicle testing. These elastic effectsmay have been recorded by the test engineers as some otherform of judder as the deformation cannot be readily detectedon the stationary vehicle.

Figure 20. Graphs of outboard side of disc displacementfor the 1st braking event.

The results shown are for the first stop of the test and ithighlights that the disc distortion is occurring from cold andalmost instantaneously. Also of note is the apparent similarityof the waveform between both off-brake periods, this beingan indication of elastic behaviour. As the braking sequenceprogresses and the temperature rises the “on-braking”deformation tends to become “set” and as such the disc doesnot fully recover back to its original shape - a permanentplastic deformation takes place. The above is a demonstrationof the elastic/plastic behaviour of the disc during braking, theelastic possibly providing misleading information to thebrake test engineers.

FE THERMAL MODELLINGFor the purpose of this paper a simplified transient thermalmodel of a stationary brake disc with heat flux being appliedto each friction ring was modeled. This was constructed usinga mesh of tetrahedral elements and represented a single brakedisc as used by the research vehicle. Transient simulations ofthree braking events from a vehicle test were chosen becausethe purpose of the investigation was to identify temperaturedistribution over time; with a steady state analysis only

constant heat flux loads could be applied, this was notrepresentative of the actual system where the heat flux loadswere nonlinear due to the aerodynamic drag force on thevehicle which was proportional to the square of the vehiclespeed and aided vehicle deceleration. With a transient modelthe heat flux loads were non linear and therefore morerepresentative of the actual system.

Figure 21. Graph showing simulated temperatureagainst measured on-vehicle data.

This allowed for investigation of heat flow through the brakedisc due to the transient heat flux loads, whilst identifyingany areas of concern. Whilst this was not a like for likesimulation, the results presented demonstrate that this methodhas good correlation with measured data.

The thermal FEA simulations were validated againstmeasured data from on-vehicle testing with a materialproperty sensitivity analysis to improve the correlation of theresults with the measured data. This validation is shown inFigure 21. Simulations were then performed to identify theheat distribution through the brake disc and a new design wascreated to reduce the brake disc operating temperature and toimprove the heat distribution through the brake disc to reducethe propensity towards hot spotting and thermal distortion.

The FEA models used blanket convective coolingcoefficients. It can be seen that the simulated disctemperatures in the final cooling phase fell quicker than themeasured data (Figure 21). This indicated that the linearcooling curve used for the simulation did not fully representthe actual vehicle conditions in the final cooling phase.However the FE study was mainly focused upon the heatingphase and the simulated data showed good correlation for thethree braking events therefore no modification to theconvective heat transfer coefficients was required.

The FE analysis showed that vent geometry influences thesurface temperature profile causing a rippling effect on thedisc surface - Figure 22. A small section of the analysis isshown in Figure 23 where the thermal ripple is more evident.This ripple will be the same as the disc “wavelike” shape butat a lower level of amplitude. The effect though would be the

same, high thermal areas, the formation of hot areas leadingto possible “hot spotting”, the formation of Cementite and soon. This is a demonstration for the need to provide a uniformheating and cooling design.

Figure 22. FE model of brake disc with temperature riseof 300°C imposed. Note disc thermal ripple.

Figure 23. Section of disc showing higher temperaturesbetween the disc pillars before redesign.

FE MODELING OF DISC REVISEDDESIGNCurrent work is concerned with developing a vane geometryto reduce disc maximum temperature and at the same timeprovide uniform heating and cooling. The predicted thermalresult from such a preliminary vent design is shown in Figure24 where evidence of the vane thermal profile is minimal.The prototype design centered on modifications to the ventprofile of the standard brake disc to achieve an improvedtemperature profile and reduced disc temperature. The FEAprototype design incorporated two wavy profiles, bothsymmetrical about their own mid planes. The aim of this wasto add mass midway between the vanes to try and draw heatmore evenly from the surface of the disc and to avoid build-up of the hot regions on the surface and vent ceiling.

Figure 24. Principle of adding mass to inner vent facebut “thinning” blade thickness to maintain overall mass.

The redesign was created with improved sculpting of the ventcross section to distribute the thermal, mass allowing forimproved heat conduction path (Figure 24). The design of thevent is as shown in Figure 25. The general profile of the discwould then be as shown in Figure 26 which promotes moreeven heating of the disc surface, reduces the thermal gradientand improves heat distribution.

Several profiles were investigated as indicated in Table 3. Itmust be noted that N1, N2 and N3 refers to the geometry ofthe dimple protruding into the disc vent with N3 protrudingthe furthest. For the FEA simulations all discs (apart from thestandard design) had the friction rings thinned so that themass of the disc was identical to the standard design. Thisremoved the effect that the added mass would have on thedisc temperature. It can therefore be claimed that thetemperature reduction is due to the redistribution of the massin the vent and not an increased in disc bulk mass.

Such a modification reduces the thermal stress gradients andthe potential for uneven thermal deformation. The designshowed a 46°C improvement in maximum surfacetemperature following a 3 stop simulation for an equal discmass. This reduction is equivalent to an 8% reduction in adisc temperature at 550°C.

Figure 25. Preliminary aerodynamic design of disc vent.The CFD analysis shows reduced separation and

improved air flow [9].

Figure 26. Scrap view of predicted (FE) thermal patternwith the modified vents as shown in Figure 25. Profile

replicates that in Figure 24.

Concurrent work continues with the improved aerodynamicdesign of the disc pillars and vents [9]. The objective in thiscase would be to avoid airflow separation from the disc wallsand pillars. It is anticipated that combining the re-sculpturedpillar with the improved aerodynamic geometry will furtherimprove disc temperatures and cooling.

SUMMARY/CONCLUSIONS• Thermal judder is associated with high performance carsand in particular heavy high performance cars. As such the

Table 3. Disc design parameters and thermal predictions.

brakes have to absorb, and dissipate, a considerable amountof heat. If the heat absorbed exceeds that which is dissipatedthen the disc will reach temperatures such that the discmaterial with undergo a phase change with the formation oflocalized Cementite and a plastic deformation will beimposed on the disc. There is no issue with understanding theenergy that has to be absorbed - that is a scientific fact andthe brake engineer can do little about that. The biggestproblem of the brake engineer therefore reduces to heatmanagement and better distribution of that heat.

• Judder is complex and may result from a combination ofelastic and plastic disc deformation.

• The properties of the disc material may change due toexcessive heating, Cementite being formed.

• The disc can relax back to differing orders of deformationupon cooling, usually first or second order. A disc which haspreviously taken up second order deformation upon coolingcan relax back to first order deformation in follow-up testing.

• The pressure response leading to brake judder has shown tohave a component at the same frequency as the discdeformation. These higher frequencies may be related tolocalized heating of vane “clusters”.

• For a sharp rise of only 300°C it would be expected that thedisc would buckle and form a wavelike shape.

MANUFACTURING SUGGESTIONS• Within this manufacturing process the design andproduction issues need to be addressed. At the outset thecasting process priority must be to improve mass distribution.This may include improved core position control througheffective tolerancing, casting orientation and stress relievingbefore machining.

• The first process in disc design phase is to reducetemperature variation during the braking process, that is toensure overall even heating of the disc, acknowledge there isa difference between the inboard and outboard braking forcesand arrange the design to account for that. The principalreason is to minimise inboard to outboard, radial, thickness orcircumferential temperature gradients. The existence of largegradients will lead to localised deformation.

• The second challenge is to ensure even cooling of the disc -again the avoidance of large thermal gradients to moreacceptable levels. The cooling needs to be lost as quickly as itis gained but under extreme braking that is difficult so theprimary concern should be towards even cooling. The processis therefore air management around and through the disc byway of optimized vent design, care regarding cast surfacefinishes and well placed turbulence generators. Thegeneration of heat generation radially needs to be recognizedand the mass distributed accordingly to account for that. Suchdesign considerations will maximise heat transfer through thebody of the disc, with even cooling being paramount.

• The third challenge is to accept that temperature gradientswill always exist - they will be unavoidable over the myriadrange of braking situations possible. It was mentioned veryearly that judder is not a braking issue - it is a vehicle issue.As a result pressure fluctuations will be inevitable and theassociated brake torque variations will always be present. Thechoice then is to collaborate with the suspension engineers inan attempt to desensitize the vehicles from the likelyfrequencies.

• If the forgoing proves unacceptable then the brake engineerneeds to accept that the root causes of thermal judder anddrone will always exist and accommodate for the brakepressure fluctuations at source.The elastic deformation, as measured and observed during thebraking event, needs further investigation.

REFERENCES1. http://media.photobucket.com/image/wheel%20knuckle/superex91/100 0538.jpg

2. http://www.powerbrake.co.za/sitemap.htm, PowerbrakeBrake Tech “The final word on brake judder and ‘warped’discs”.

3. Steffen, T., “Hot Spot Simulation”, IMechE, Braking 2006- Advances in Vehicle Braking Technology, pp199-207, 2006

4. Jacobsson, H., “Aspects of disc brake judder”,Proceedings of the Institution of Mechanical Engineers Vol.217 Part D: Journal of Automobile Engineering, 2003

5. De Vries, A. and Wagner, M., “The Brake JudderPhenomenon,” SAE Technical Paper 920554, 1992, doi:10.4271/920554.

6. Jacobsson, H., “Modeling of disc-brake judder inpassenger cars”, IMechE, Brakes 2000, pp68-69.

7. Fieldhouse, J. and Beveridge, C., “An ExperimentalInvestigation of Hot Judder,” SAE Technical Paper2001-01-3135, 2001, doi:10.4271/2001-01-3135.

8. Fieldhouse, J., Bryant, D., Palmer, E., and Mishra, R. “AStudy of the Thermo-elastic Effects of Braking on HighPerformance Cars”, 21st JUMV International AutomotiveConference Science and Motor Vehicles, Belgrade 2007

9. Palmer, Edward, Mishra, Rakesh and Fieldhouse, John D.(2008) A computational fluid dynamic analysis on the effectof front row pin geometry on the aerothermodynamicproperties of a pin-vented brake disc. Proceedings of theInstitution of Mechanical Engineers Part D Journal ofAutomobile Engineering, 222 (7). pp. 1231-1245. ISSN0954-4070

BIBLIOGRAPHYAfferrante, L., Ciavarella, M., “Thermo-elastic dynamicinstability (TEDI) - how frictional heating excites the

thermoelasto-dynamic modes in a simple 1D model” IMechE,Braking 2006 - Advances in Vehicle Braking Technology,pp189-198, 2006

Kubota, M., Suenaga, T., and Kazuhiro, D., “A Study on theMechanism Causing High Speed Brake Judder,” SAETechnical Paper 980594, 1998, doi: 10.4271/980594.

Link Engineering, “Link Engineering Newsletter”, LinkEngineering, Issue No. 8 - Vol. 1, 2003

Little, E., Kao, T., Ferdani, P., and Hodges, T., “ADynamometer Investigation of Thermal Judder,” SAETechnical Paper 982252, 1998, doi: 10.4271/982252.

Angus, H. T., “Cast Iron: Physical and EngineeringProperties”, Butterworths, Second Edition, pp295, 1978

Litos, P., “The Measuring System for the ExperimentalResearch of Thermo-mechanical Instabilities of DiscBrakes”, IMechE, Braking 2006 - Advances in VehicleBraking Technology, pp189-198, 2006

CONTACT INFORMATIONProfessor John D FieldhouseThe University of HuddersfieldQueensgateHudderesfield HD1 3DH UKTel + 44 (0) 1484 472698j.d.fieldhouse@hud.ac.uk

ACKNOWLEDGMENTSThe Authors would like to thank Bentley Motors for theirsupport of this project and their ongoing support.

TERMINOLOGYNVH

Noise Vibration & Harshness.

DTVDisc Thickness Variation.

BPVBrake Pressure Variation.

BTVBrake Torque Variation.

BPFBrake Pressure Fluctuation.

CMMCoordinate Measuring Machine.

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