1. Mech 324
Lab 9: Cam Testing
Lab 06 Group 01
Sam McCreery, Abdullah, Alex Larson, Marco Martinez
Due December 5th, 2014

2. 1. Executive Summary
Thislab wasprimarilyfocusedonutilizingaseriesof polynomialexpansionfunctionsanddifferential
equationsinwhichacam lobe wasinitiallydesignedvirtually.Thereafter,the camwas physically
manufacturedusingaComputerNumerical Controlledmachine.Thismodel wasbuiltoutof an acrylic
compound.Withthe physical model,iterative datapointscouldbe successfullymeasuredwiththe cam
runningat a specifiedconstantRPM.The cam wastestedupona follower,whichtestedhow well the
Rise-Fall andDwelldurationswere executed.Additionally,specialcare wastakeninensuringthatthe
cam didnot encounterdiracdeltafunctionsorsevere discontinuities.
2. Background
DesignConsiderations
In designingcams,there mustbe amultitude of mathematical considerationsmade. When
choosinganycalculusor differentialequationbased functions,whichmaybe thoughtof as piecewise
functionsinsectorsof rise,fall,anddwell,inanygiven displacementmodel,one mustchoose afunction
whichwill not"runout" of derivatives.Initializingfromdisplacementinwhichds/dtyields velocity,in
whichdv/dtisacceleration,andda/dt resultsin jerk.Itisthen sometimes necessarytoselecta
sinusoidal orcosine type functionwhichderivesandintegratesbetweencosineandsine,andtherefore
doesnotencountera "Dirac deltafunction",whichresultsin somethingreferred toas“infinityspikes”
startingat accelerationandpassingonto jerk.This theoreticallystatesthatthe camlobe isexperiencing
zerostressand force.Thisisthe opposite of the truth, however, asthiswouldresultinasharplypointed
cam lobe,whichwouldexperiencemassivestressconcentrationatitstip. Thistipwould resultantly rub
off intoa blunternormal shapedcam overtime,as a resultof the incredible stress buildupatthissharp
tip.In calculus,these "Infinityspikes"are the design resultsof vertical linesinthe velocitydiagram
whichcreatesdiscontinuities.
A dwell isalocation where acam lobe haszerovelocityandacceleration.Non-dwell piecewise
functionsatnon-zerovelocityandaccelerationmustbe linkedcontinuouslytodwellswithzerovelocity
and accelerationaccordingtothe fundamentalsof camdesign.
Cam lobe designreliesprimarilyonsolvinganumberof unknownswithgivenboundary
conditionsasinputs.Withthese,one canspecifyandcustomtailorthe polynomial expansionforcam
designtothe properfinal exponential,whichisone integerlowerthanthe number of givenboundary
conditions.The polynomialexpansionrepresentsaninitial functionfordisplacement,inwhich
derivativesmaybe takentoderive polynomial expansionequationsforvelocity,acceleration,andjerk,if
needed.The followingmaybe solved byhand,thoughwouldbe veryintensive,andisratherideally
solvedcomputationally byamatrix setup. The angularterm “Beta” representsthe sumof the rotational
angle of the rise and fall phase of the cam lobe,andmay be relatedtothe term“theta”, whichis
dimensionallyhomogeneouswithbeta.Thetarepresentsthe angle of interestorthe angle specified.

3. Flat Faced Followersvs.RollerFollowers
From a designstandpoint,rollerfollowersare often preferred foranease of replacementandavast
availabilityfromamultitude of suppliers,whichmakesreplacementcosteffective andrelativelyeasy.
Additionally,groovedandtrackedcamsrequire the use of rollerfollowers.However,flat-facedfollowers
are largelyfavoredinthe automotiveindustry,whereenoughmass-productionvolumeallowsadequate
quantityandmarketfor easyreplacement.Additionally,there isalimitationof free space inside the
valve cover,andflat-facedfollowersallow betterandmore efficientpackagingatopthe engine head.
Lastly,rollerfollowershave the advantage of acceptingnegativeradii of curvature. Rollerfollowersare
oftenutilizedinmassproductionmachinerywhichallowsveryrapidreplacementof wornfollowers.

4. Figure 1 Flat FacedFollower

5. Real Life Example
Figure 2 Flat faced followers are often used in automotive engines, such as this Toyota 5sFE I-4
Figure 2 representsaninline four-cylinderengine cutaway,witha“DOHC” or “Dual OverheadCam”
layout.Thisallowsthe removal of aneedforrocker armsor pushrods,andallowsadirectcam lobe to
valve contactvia flatfacedfollowers.Thisiswidelyusedinmodernautomotivepowertrains.
Additionally,the oil sumpof the engine above holdstwobalance shafts,whichequilibrates the inherent
imbalancesof inline4-cylinderengines.

6. Figure 3 Roller follower
Optimizingandtherefore minimizingcamlobe size hasa numberof advantages.Specifically,there is
usuallyadesire forspace efficiencyinmachinerydesign,andaminimallyoptimizedcamsize canmake
efficientuse of valuablespace ina machine.Additionally,machinerysuchasautomotive enginesmust
fitina certain environment,suchasan engine bay.Nowadays,thereisapushfor maintainingcompact
dimensionsof vehicleswhilemaximizinginteriorvolume whileengine baypackagingbecomesmore and
more packedwithincreasinglyadvancingspecifications.
3. Results
Figure 4
-2
-1.5
-1
-0.5
0
0.5
1
0 5 10 15 20 25 30 35
Acceleration
Acceleration

7. Figure 5
Figure 6
4. Appendix
HelloSethDavies!
Toyota5sFE enginediagram http://nlp.ilsp.gr/soaplab2-results/93dbfb32-d55f-4619-8454-
5f45fe923856/xml/11577.html
Flat Faced Follower diagram
http://www.engr.colostate.edu/~dga/mech324/Labs/Lab%207/MECH324%20-%20Lab%207.htm
Stansloski,Mitchell, Laboratory7,CamDesign, Online,ColoradoState University
http://www.engr.colostate.edu/~dga/mech324/Labs/Lab%207/MECH324%20-%20Lab%207.htm
-5.00E-02
0.00E+00
5.00E-02
0 5 10 15 20 25 30 35
Velocity
Velocity
-2.00E-03
-1.00E-03
0.00E+00
1.00E-03
2.00E-03
0 5 10 15 20 25 30 35
Displacement
Displacement