Investigation of PolyMethyl Methacrylate for Speedometer Application

International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056

Volume: 09 Issue: 09 | Sep 2022 www.irjet.net p-ISSN: 2395-0072

Investigation of PolyMethyl Methacrylate for Speedometer Application

Sajal Anand1 , S.S Ohol2 , Subhajit Basu3

1Student, College Of Engineering Pune, Maharashtra

2Associate Professor, Department Of Mechanical Engineering, College Of Engineering Pune, Maharashtra 3Lead COC, Varroc Engineering Limited,Pune,Maharashtra ***

Abstract - This paper presents investigationof PMMA grade material for use in a Two-wheeler speedometer lens application. Of all the various components that make up the speedometer the lens is directly visible to the rider and hence correct and clear display of information is important as it directly affects their decision making. Mold flow analysis is carried out to establish the molding parameters and defects if any. From the risk assessment derived from the DFMEA and customer specific test standards CAEanalysis has beencarried at loading conditions of tightening torque of two different cases, modal analysis and harmonic response are simulated to check for any adverse stresses and deformations for any fouling and cracking at lens withinfrequencyrange of interest.

Key Words: Polymethyl Methacrylate, Speedometer, Mold Flow, CAE, Modal Analysis.

1. INTRODUCTION

A speedometer or speed meter is a gauge meter that measures and displays the instantaneous speed of the vehicles. A traditional speedometer is of mechanical type alsocalledaseddy-currenttype;aflexiblecabledrivenby the gear linked at transmission. When the vehicle is in motion, a gear assembly turns the speedometer cable. A smallpermanentmagnetaffixedtothecableinteractswitha small aluminum cup (called a speed cup) attached to the shaftofthepointerontheanalogspeedometerinstrument. Asthemagnetrotatesnearthecup,thechangingmagnetic field produces eddy current in the cup, which themselves produceanothermagneticfield.Withtheadvancementsin the field of mechatronics and development of sensor technology traditional mechanical speedometers were replacedbydigitalspeedometers.Smallmagnetattachedto the car's rotating drive shaft sweep past tiny magnetic sensors (either reed switches or Hall-effect Sensors) positionednearby.Eachtimethemagnetspassthesensors, theygenerateabriefpulseofelectriccurrent.Anelectronic circuit counts how quickly the pulses arrive and converts thisintoaspeed,displayedelectronicallyonanLCDDisplay. Aspeedometerunderstudyisanassemblyofthefollowing componentstransparentcoverlens,CRspongeSealingring, Printed dial, Reflector with tell tale symbols, PCB with electronicsandsteppedmotor,housing/casingandwiring harness.

1.1 LENS AND MATERIAL

TheLensformsthetransparentcoveratthevisiblesideofthe cluster and its primary function is to provide clear and transparent display of the data to the rider under all environment circumstances while taking in the vehicle operationalvibrationandloads.

The concerned lens has 4 vehicle mounting locations with ribsdesignedtocontrolwarpageduringmanufacturingand also serve as load bearing geometries with its design thickness and height as per guidelines mentioned in the standardsmentionedbefore.TheLens-Housingsubassembly isachievedthroughself-tappingscrewsat5locationsalong with locators. The concerned lens also has the trip button interference fitted onto the class A surface with class B surfacehavingacoatingofAntifog

Figure 1: Lens with 4 vehicle mounting locations and 5 self-taping screw sub assembly mountings

BynatureoftheapplicationthePMMAwillbesubjectedto various requirements in the form of its transparency, degradationretardingpropertiesmainlyUVresistanceand waterabsorption,andsincethecomponentwillbesubjected to various loads and vibration mechanical properties will playacrucialrole.

Based on the general material requirements of a lens, various amorphous polymers were studied for their propertiesandPMMAwaschosenasmaterialofchoice.

International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056

Volume: 09 Issue: 09 | Sep 2022 www.irjet.net p-ISSN: 2395-0072

Figure 2: Parameters for material selection

2. MOLD FLOW ANALYSIS OF LENS WITH PMMA

The objective of the analysis is to carry out FILL+PACK+WARP analysis for the component using an industry grade PMMA. Initial molding parameters will be established and any aesthetic defects can be addressed. AUTODESKMoldflow2021hasbeenusedforthisanalysis. DualDomainmeshhasbeencarriedoutfollowedbyadding 10layersof3Dtetras.Theaspectratioistobemaintained within 100, the total 779642 tetrahedral have been generated.Therecommendedmoldingconditionsfromthe softwareareasfollows,

Figure 5: Injection Pressure

Themaximumpressureobservedduringthefillingphaseis 101.2MPawhichwellbelowthemachinelimitof120MPa.

Figure 6: Shear Rate

The shear rate is a measure of the rate of slip between different layer so polymer material, shear rate generates temperature which is desirable for viscous material like PMMAtoenablebetterflowhowevertoolargeshearrates cancausematerialdegradation.Theshearrateobservedis 32290.3(1/s)whichisbelow4000(1/s).

Figure 3: Recommended processing conditions

A cold sprue edge gate has been used with width and thicknessas16mmand1.4mmrespectively.Packingprofile hasbeensetas80%oftheinjectionpressurefor10seconds.

Ittakes2.66secondstofillthecavitywithnoobservedshort shots.Areascoloredredaretheonesfilledtowardstheend aresubjecttomoreshrinkageduetolackofpacking.

Figure 7: Air traps

Airtraps(endfilllocations)andunavoidableweldlinesare observedatareasfurthestfromthegateasexpectedasthese regionsarefilledlastandflowfrontsmeet.Airtrapscanbe avoidedbyprovidingventingatthesepoints,althoughthe weldlinesareunavoidabletheyareattemperaturesabove themelttemperatureasshown

Figure.4 Fill time plot

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Volume: 09 Issue: 09 | Sep 2022 www.irjet.net p-ISSN: 2395-0072

Figure 7: Temperature plot

The shear along the mold walls and the shear rate cause temperaturestorisewithinthemeltdecreasingitsviscosity, the melt temperature was set at 235℃ and maximum temperatures observed are 10℃ above, no drop of temperatureisobservedhenceweldlinesarestrong.

Figure 10: Y direction deflection

Figure 8: Volumetric shrinkage

The volumetric shrinkage plot shows variable shrinkages which are due to variable thickness geometry. The thicker sectionsundergomoreshrinkageasthecoolingtimewithin themoldisnotsufficient,moreovertheportionsofgeometry furtherawayfromthegatewitnessmoreshrinkagesdueto the lack of packing. Multiple gates and more packing time/pressurecanbeprovidedtoreducethevalues.

Deflection plots due to differential shrinkage alone are plottedinX,Y&Zdirectionsindividuallyasshown.

Figure 11: Z direction deflection

The deflections in X(figure 9) direction are +0.6mm and0.59mm which are symmetric as desirable, moreover maximumdeflectionsareobservedinareasfurtherfromgate duetolackofpacking.Howeverthesedeflectionsarewithin thelimitsofallowableshrinkagesderivedfromDFMEA. The maximumdeflectionsinYdirection(figure10)are+0.35mm and-0.38mmwhicharebothsymmetricandwithinlimits. Deflections in Z direction (figure 11) are more in thicker regionswhichareexplainedaslackinpropercoolingtime, also the flappy parts are therefore designed with ribs to minimize warpage in Z direction, maximum values of deflectionsobservedare+0.23mmand-0.14mmwhichare withinlimit.

3. STRUCTURAL ANALYSIS OF COMPONENT WITH PMMA

Materialsusuallyexhibitafixedmeltingtemperaturesfor polymersthetemperatureatwhichhardglassystateofan amorphousmaterialchangestorubberystateiscalledasthe glasstransitiontemperatureTg.Asthetemperatureofthe materialreachedTgitsbehaviorchangesfromviscoelasticto viscoplastic. The Tg value of our chosen PMMA grade is 117℃butsinceourcomponentisexposedtotemperatures muchbelowtheTgmaterialnonlinearityisunaccountedfor andlinearstaticanalysisiscarriedout.Moreover,sincethe rise in temperature induces softness and hence a drop in yieldstressaFOSof2isareasonableparametertoaccount forinouranalysis.

Figure 9: X direction deflection

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Loadingandboundaryconditionsareasfollows,

From the customer specifications and DFMEA done the tightening torque values at the Speedometer assemblyvehiclemountinglocationshavebeentakenas1.3 Nm.The poission’s ratio of 0.35, yield stress and Young’s modulus havebeenderivedfromthematerialdatasheet. BETA CAR ANSA hasbeenusedforPre-processingandmeshingwitha globaledgelengthof2mm, MSC FEA 2020 hasbeenusedas solverandpostprocessor.

Tocalculatetheequivalentclampingforceasaconsequence ofthetighteningtorqueiscalculatedas

Where,

T=Tighteningtorque

K=Constantbasedonboltmaterial

d=Nominaldiameterofthebolt

I=Lubricationfactor.

Onenteringtherelevantvaluesweget F= 1300 N

TheVonmisesstressinducedasaconsequenceoftightening areshowninthefigure14.

Figure 12: Loading at 4 vehicle mounting location

Thefigure12showsthe4mountinglocationsatwhichthe 1300N equivalent clamping force has been applied using NASTRANbasedRBE2Stiffeningelementswithsalvenodes takenatwasher.Theboundaryconditionsareusedtoarrest the6DegreesoffreedomontheclassBsurfaceofthelensas showninfigure13.

Figure 14: Von Mises Stress

Themaximumstressvaluesobservedare11.4MPawhich arebelowthepermissiblelimitby70%calculatedusinga factorofsafetyof2.

At the 5 self-tapping screw locations a similar static structural analysis is carried with the same meshing conditions, the equivalent clamping force however is calculatedusing, Where, p-Pitch

µ1-Frictioncoefficientatscrew-lenssurface µ2-Frictioncoefficientatscrew-casingsurface

����-nominaldiameterofscrew

��ℎ-Diameterofcasingsurface

����-Diameteroflenssurface

����ℎ-Diameterofscrewheadbottom.

Puttinginthevaluesforatighteningtorquevalueof0.45Nm andfrictioncoefficientof0.7theequivalentclampingforce F= 250N

TheloadingconditionsusingtheRBE2elementsareshown in figure 15 while the arrested degree of freedom class B surfaceisshowninfigure16.

Figure 13: Arresting Degree of Freedom

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Figure 16: Self tapping screw boundary conditons

The Von mises stress generated as a consequence of this tighteningtorqueisshowninfigure17,

Figure 17: RBE 3 elements to connect equivalent mass

Figure 16: Von Mises Stress Values

ThemaximVonmisesstressvalueis5.37MPawhichiswell belowthepermissiblelimitby86%

4. MODAL ANALYSIS OF SPEEDOMETER WITH EQUIVALENT MASS

For the modal analysis materials are assigned to the different components of the speedometer assembly in the CATIAV5software.Anequivalentmassof173gramsofthe internal subassemblies is placed on the center of gravity. Using the BETA CAE ANSA meshing is carried out for the LensandthehousingwithNASTRANbasedRBE3elements connectingtheequivalentmassestothehousingmounting locationsasshown,

The4vehicle-speedometerassemblymountinglocationsare connectedusingRBE2elements.Carryingoutthefree-free modalanalysisallthe6degreesoffreedomarearrestedat thepointtoavoidthefirst3rigidbodymotionaccountingas modalfrequenciestobe0.Thefree–freemodalanalysiswas carried out using BETA CAE EPILYSIS as solver and BETA CAE META as post processor. The resulting modal frequenciesareobservedandfrequencieswithin50-500Hz are of further investigation based on the test standards employedbythecustomer.Thetablebelowgivesthemodal frequencyoutput, Mode Frequency(Hz) 1 382.03 2 517.46 3 710.50 4 767.20 5 785.77 6 857.45 7 922.67 8 1070.51 9 1132.33 10 1223.40

Table 1: Modal Frequencies

Modalfrequencyofinterestwithintherangeof50-500Hzis 382.03Hz.

5. HARMONIC RESPONSE

Theharmonicresponseofthespeedometerislens-housing andequivalentmasssubassemblyiscarriedoutwith10gof acceleration in X,Y,Z directions individually at frequency ranges of 50-500Hz and first modal frequency using dampingratioof5%.

International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056

Volume: 09 Issue: 09 | Sep 2022 www.irjet.net p-ISSN: 2395-0072

TheallowabledeformationsintheX&Ydirectionare0.5mm whileintheZdirectionis5mmasmentionedintheDFMEA. Moreover,thestressinducediscomparedagainstthefatigue limit value of σy /4 for our chosen PMMA grade. The softwaredisplaysthefrequencyatwhichthedeformationis maximum.FortheXdirectiontheresponseofthesystemis maximum at 382.03 Hz and the stresses generated are shownbelow,

Figure 19: Displacements in Y direction

Figure 17: Displacements in X direction

Figure 20: Stresses on Lens in Y direction

Similarly, the response of the system is maximum in Z directionatafrequencyof385.86Hz.Thevalueofmaximum displacementsobservedatthisfrequencyare0.13mmwhich is below the permissible limit of 5mm moreover the resulting stresses at this frequency on the lens amount to 2.16MPawhichisbelowthefatiguelimitby88.75%.The aboveisshowninfigures21and22respectively.

Figure 18: Stresses on Lens in X direction

ThemaximumvalueofdisplacementobservedinXdirection is 0.32 mm which is below the limit of 0.5mm while the stressesgeneratedasshowninfigure18are5.65MPawhich isbelowthematerialfatiguelimitby70.57%.

TheMaximumdisplacementsoccurringinYdirectiontake place at frequency of 500Hz while the maximum stresses generated on the lens amount to 0.61 MPa only both of which are under the permissible limit. They have been showninfigures19and20respectively.

Figure 21: Displacements in Z direction

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Based on risk assessment derived from DFMEA static structuralanalysiswascarriedoutfortighteningtorqueat2 locationsnamelyvehicle-speedometerassemblymounting locationsandlens-housingsubassemblyself-tappingscrew locations.Afactorofsafetyof2waschosenforthesame.The resultsofbotharerepresentedinatabularformatbelow.

Figure 22: Stresses on Lens in Z direction

RESULTS AND DISCUSSIONS

A thorough understanding of the general material requirements for the Lens was established and different amorphous polymers were studied for their thermo mechanicalproperties,safetyratings,opticalpropertiesand environmental degradation retarding properties etc. An AMECAlistengradeofPMMAwaschosenasourmaterialof choice. With the chosen material Mold Flow analysis was carriedouttoestablishmoldingparametersandtocheckfor any mold defects that could hamper the aesthetic region, followingresultswereobtainedfromthemoldflow. 

The single cavity old is filled with PMMA in 2.62 secondswithnoshortshot. 

Themaximumpressureduringinjectionisfoundto be101.2MPawhichiswithinmachinelimit. 

Temperatureatflowfrontrisesby10.6℃withno drop observed below the melt temperature of 235℃ 

Requiredclampingforceis138tonnes. 

Shearratesarewithinmateriallimitandprominent atthegatearea. 

Airtrapsarefoundattheendfill locationsandat theweldlinelocations. 

Weldlinesareunavoidableandvisiblebutstrongas temperature at front doesn’t fall below melt temperature. 

Volumetric shrinkage is found varying due to variablepartthickness. 

Deflectionobserved(InXdirectionis+0.60mm&0.59mm); (In Y direction is +0.35mm and0.38mm); (In Z’ direction is +0.23mm and0.14mm).

Figure 23: Result Summary for tightening torque

Afree-freemodalanalysiswascarriedoutwithmeshedlens andhousingwithanequivalentmassplacedatCglocation, thefirst10modalfrequencieswerecalledfortheresults.By thecustomerprovidedteststandardonlyfrequencieswithin 50-500Hzrangewereofinterest.Thefirstmodalfrequency of 382.05 Hz fell within this range. Further harmonic response wascarried outwitha 10gaccelerationvalue in X,Y,Z directions within the frequency range of interest including the first modal frequency. The results of the harmonicresponseareshownintabularformatinthefigure below.

Figure 24:

Figure 25:

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