Camshaft Design System is a computing programme for the design of different types of valvetrains. Starting from the related acceleration curve of the valve, which is mapped as a spline,the cam profile is calculated using the valve train geometry.

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Valve Train Design and Calculationfor High-Performance Engines

The purpose of the system is thedevelopment of high-qualityvalve acceleration curves thatcomply with the hydrodynamicfringe conditions of the chargecycle while providing an oscilla-tion-attenuated valve train that issubjected to as little dynamicstress as possible. The cam pro-files obtained with this approachare also especially suitable forsubsequent dynamic simulationcalculations, e.g. using the multi-body simulation programme Re-curDyn from FunctionBay, be-cause, due to the particular splineapproach, they do not display nu-merical noise in the calculated ac-celeration curve.

Camshaft Design System(CDS) is applied in almost all ar-eas of engine development: carseries development, large dieselengines and all areas of motorracing, as well as by system sup-pliers, in research and teaching.As conventional design sooncomes up against limiting factors,special design tools have been de-veloped for valve trains in high-speed engines.

System ArchitectureThe flexibility and adaptability ofCDS is due to the modular struc-ture of the programme, which ismade possible by programmingwith the Borland C++ builder forthe Windows operating system.New requirements can be inte-grated without problems and cus-tom adaptations can be performedwithout loss of time. A specialmodule, for example a new typeof valve train, can be integrated

or the navigator. In this way, theacceleration curve can bechanged quickly without loss ofaccuracy. The dynamic openingand closing behaviour of a valvetrain is decisively influenced bythe ramp in the accelerationcurve. For this reason, the lengthand height of the ramp can bespecified. Which shape of ramp isused depends on the type of valvetrain and the conditions of serv-ice. To take care of this, the rampshape can be freely defined by theuser. During the computation, thespline nodes characterising theramps are automatically scaled tothe required height to obtain theramp lift. If the valve lift needs tobe changed, a central spline node(green) is defined. If this splinenode is enabled, the valve liftwidth can be set with the slider

without requiring the new instal-lation of the system.

The Design of the Accel-eration CurveThe Hertzian stresses of a valvetrain depend mainly on the forcesof inertia and therefore directlyon the acceleration of the partsinvolved. Therefore, the design ofthe valve train in the CDS systemstarts with the layout of the relat-ed valve acceleration curve, Fig-ure 2.

By generating the accelerationfunction with any number ofspline nodes, any required char-acteristic can be obtained. Thisacceleration curve can simply beoptimised and adapted by shiftingthe nodes with the mouse pointer

Figure 1: Camshaft Design System is applied in almost all areas of engine development.

The cam profilesare especially

suitable for subsequent dy-

namic simulationcalculations

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teristics can be viewed in summa-ry in the development history andrestored if necessary. This sup-ports the systematic optimisationwith automatic documentation.

A description of the completefunctionality of the system is notpossible within the scope of thisarticle. However, it should be not-ed that other interfaces with CADsystems, for quality control andtesting, which ensure the homo-geneous nature of the subsequentprocesses are available.

Manufacture and QualityManagementThe interface to manufacturingand quality control generates datafor the grinding and measuringmachines in the required format.The following grinding machinesare supported: Kopp, Schaudt,Fortuna, and Landis, and themeasuring machines: Adcole andHommel.

Influencing the DynamicBehaviour The dynamic behaviour of a valvetrain depends very much on thestiffness and attenuation of theparts of the valve train and the

that is visible in the lower leftpart of the screen. The curve ex-tends or shrinks accordingly. Theacceleration curve and the rampshape do not change.

A pointer tool that directlyshows the area conditions in thefirst integral of the curve is visiblein the lower right of the screen.Correct surface compensation isimportant to avoid partial liftingor exceedingly large deformationduring cam rotation.

From the valve law of motiongenerated in this way, the camprofile is calculated by linking itwith the valve train geometry. Thevalve train geometry can be gen-erated with a few parameters inan input screen. This makes thegeometry easy to vary and opti-mise.

The generated cam profile fea-tures high numerical quality,which is very important when us-ing it for dynamic simulation. Onthe other hand, a profile of thiskind can only be obtained from avalve law of motion that complieswith the same numerical require-ments. The spline method bywhich the valve lifting curve iscalculated offers, by the way of2nd derivative of the valve law ofmotion (acceleration), all possibil-ities to obtain the required nu-merical quality.

For a direct assessment of theeffects of modifying the valve ac-celeration and valve train geome-try, the CDS system provides a

large number of standard valuesfor valve train analysis and as-sessment of the producibility ofthe cam. For example, the dis-tance inertia spring force (if avail-able), the negative curvature radii,Hertzian pressure and the lubri-cating film thickness at the camcontact surface are calculated asparameters of the dynamic behav-iour and displayed in a window.All steps of the optimisationprocess with the typical charac-

Figure 2: Graphical user interface for the modification of the acceleration curve.

Figure 3: Multi-resolution analysis.

The interface tomanufacturingand quality con-trol generates da-ta for the grindingand measuringmachines in therequired format

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points of contact and joint. Be-cause the valve spring is the partwith the least hardness and thelowest natural frequency, its effectis especially high. For example,the shape of the valve accelerationcurve can excite frequencies in therange of the natural frequencies ofthe valve springs. The orders ex-cited by the valve acceleration aredisplayed by means of so-calledmulti-resolution analysis (MRA),Figure 3.

MRA coefficientsMRA establishes a correlation be-tween the Fourier orders with theirglobal action and the local effectsof the MRA coefficients. This isvery important because the natu-ral frequencies of the valve springchange significantly with thevalve lift. This makes it possible toassign frequencies from the spec-trum of natural frequencies to lo-cal areas.

The lower diagram shows theFourier coefficients that can be as-signed to a frequency with refer-ence to the speed of a camshaft.After selecting the Fourier coeffi-cients that are to be modified, theMRA coefficients that effect theselected Fourier order are dis-played in tabular format. The rele-vance shown in the table is ameasure of the influence of theMRA coefficients on the selectedFourier order.

The third column of the tableindicates the local range in whichthe MRA coefficient influences theacceleration function. The curve inthe top diagram shows the localeffect of the modified MRA coeffi-cients on the acceleration curve.The MRA coefficients are selectedin such a way that there is no ef-fect on the ramp. The deviationsof the Fourier orders from theoriginal curve are shown in thelower diagram. After the end ofthe MRA, a reference curve is gen-erated from the modified curve.The reference curve (red colour) isdisplayed in the development sys-tem. The acceleration curve is ad-justed to the reference curve byshifting the spline nodes. Next, thecalculation is performed again andthe MRA is displayed. It may benecessary to repeat this procedureseveral times before the requiredresult after the dynamic simula-

tion is obtained. At this time, thecalculations are exclusively madeon the valve lift curve.

Finger Follower with Vari-able Follower ContoursThe speeds of the engines used inFormula1 racing cars cannot beobtained with wire springs. Thesevery high speeds produce ex-tremely high forces of inertia. Thecompressive forces at the camprofile and the cam follower aswell as the deformation forcesacting on the valve are corre-spondingly high. Consequently, itwas necessary to develop a valve

train concept that allowed min-imisation of the compressiveforces at the cam and the trans-versal forces at the valve, Figure 4.

Follower contour at the camend: Generally, the contour of thecam follower is characterised by acircular arc, which is sufficient forthe conventional valve train. If thecircular arc is substituted by aspline, it is possible to assign dif-ferent curvatures to the follower.The calculation of a cam profilewith such a follower contour can-not be accomplished with conven-tional methods. Therefore, a newmethod of calculation for a vari-able follower contour had to bedeveloped. If the follower contour

Figure 4: Valve train: finger follower with variable follower contours.

Figure 5: Graphical user interface for the manipulation of the follower contour spline.

The shape of thevalve acceleration

curve can excitefrequencies in the

range of the natural frequen-cies of the valve

springs

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with a spline is characterised, thecontour can be modified exactlyat those points at which the curva-ture radii of the cam profile, theHertzian pressure or the entrain-ment velocity are influenced. Fig-ure 5 illustrates the programme

with which the spline of the fol-lower can be modified. The char-acteristic points — positions ofminimum concave radii at the camprofile and of maximum Hertzianpressure between the cam and fol-lower — have been highlighted.

The follower contour at thevalve: In order to reduce the trans-verse forces at the valve, a suitablefollower contour at the valve endof the lever has to be developed.Here, the circular involute is agood solution. The circular invo-lute can be derived directly fromthe valve train geometry. What ismore, the circular involute has aroll motion characteristic in themovement with the valve. This al-lows a significant reduction in thetransverse forces acting on the topretainer, and the stress on thepneumatic seals is relieved. Final-ly, the reduction in the frictionloss means that the reliability ofthe valve train can be improvedsubstantially.

The Interface to the Simulation SystemThe interface in the valve traincalculation transfers the cam pro-file, valve train geometry and thevalve spring to the simulation sys-tem. Stiffness values of the valve

Figure 6: Finger follower with a wire spring in the RecurDyn simulation system.

The circular involute can bederived directlyfrom the valvetrain geometry

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train, forces of inertia and thecontact characteristics can be setin a wide-range tool. The simula-tion calculation runs as a back-ground process and comprises thepredefined speed range with thespecified speed steps.

The target of the simulationwith RecurDyn is the subsequentdynamic evaluation of the valvetrain kinematics developed inCDS, especially under the actionof the calculated cam profile. Onefocus of study is the excited natu-ral frequencies of the valve springin the range of the lift and basecircle phases, because the reso-nant ranges of the spring, as thelowest frequencies in the system,are critical to the dynamic behav-iour of the valve train, especiallyat high speed. A so-called multi-mass spring and a diagram as agenuine finite element structureare available for the detailed im-aging of the valve spring. This fi-

nite element structure is alsoavailable for the valve and lever,Figure 6.

In order to enable the assess-ment of CDS-designed ramps forthe opening and closing of thevalve under dynamic aspects, Re-curDyn has a series of hydraulicclearance compensation elements.Whereas the hydraulic behaviourof this backup element is almostrigid in the phase of highest ac-celeration, it is critical to thecharacteristics of the valve set-down behaviour, in particular, forexample, in connection with theclosing ramp of the cam. Depend-ing on the frequency range or de-tail of a problem under study, cer-tain parts, in most cases the levers(finger follower, rocker arm, etc.)or the valve, can also be substi-tuted by flexible components andcan be studied in RecurDyn. Inthis way, the dynamic actioncaused by the flexural elasticityof levers and valves can also beconsidered, Figure 7 and Figure 8.

To avoid having to generate anew valve train every time in thestandard range, a library of valvetrains with preset parameters hasbeen developed and included inthe RecurDyn/Valve module.Their data can either be inputmanually or – preferably – can beimported automatically in CDSvia the interface. Thus, when usedin combination, CDS and Recur-Dyn provide a simulation envi-

ronment that constitutes a closeddevelopment loop from the designof the fundamental valve trainkinematics to the detailed simula-tion of dynamic behaviour.

The post-processing providesviews of the result of the simula-tion in 3D or 2D images, Figure 9.

Concluding RemarksThe use of CDS for developmenttasks in motor racing and espe-cially Formula 1 proves the highcapability of this developmenttool. The close cooperation withthe users and partners and theirvaluable input have made CDS auniversal tool for valve train de-velopment.

by Dipl.-Math. Dieter Zuck,Ingenieurbüro Zuck, and Dipl.-Ing. Thomas Kelichhaus,FunctionBay

Figure 9: Simulation post-processing: force at cam with increasing speed.

Figure 7: Finger and valve in a finite element structure.

Figure 8: Finger in a finite element structure.