ABSTRACTThe advantages of Variable Valve Actuation (VVA) in theaspects of improved engine performance, fuel economy andreduced emissions are well known in the industry. However,the design and optimization of such systems is complex andcostly. The design process of VVA mechanisms can begreatly accelerated through the use of sophisticatedsimulation tools. Predictive numerical analysis of systems toaddress design issues and evaluate design changes can assurethe required performance and durability. One notablerequirement for the analysis and design of novelmechanically-actuated VVA systems is a general-purpose fastand easy-to-use planar mechanism kinematics analyzer withcam solution/design features, which can be applied to generalmechanisms.

This paper introduces a general simulation and design tool,which features general planar kinematics and multi-bodydynamics analysis capabilities, as well as integratedhydromechanics and hydraulics to model devices such as lashadjusters and cam phasers. Application of the methodology tovarious mechanically-driven variable valve actuation systemsis discussed, with focus on a specific system. The modelingprocess is broken down into multiple stages. First, theanalysis of kinematic motion of valvetrain components alongwith the procedure to calculate the cam shape profile requiredto produce the desired valve lift is described. Second, aconstrained-dynamics simulation of a rigid system is carriedout in search of nominal (quasi-dynamic), inter-componentforces, valve spring margin and cam-follower separationspeed. Third, a complete multi-body dynamics analysis,

which considers the elasticity of valvetrain components andinter-component contacts, is employed to produce a widearray of detailed dynamic predictions. Ways of rapidlyoptimizing the key design parameters through the use ofdedicated numerical analysis are briefly discussed.

INTRODUCTIONVariable Valve Actuation offers many opportunities toimprove the performance of an internal combustion engine inthe areas of fuel economy, power density and emissions.Evidence of this can be seen in the ever-increasing number ofproduction engines incorporating VVA systems to vary thetiming, duration and shape of the valve lift curve [1], [2], [3],[4]. In the last couple of decades, several kinds of VVAstrategies have been researched and implemented, rangingfrom mechanically-driven valvetrains to camless systems thatare actuated electrically, hydraulically and/or pneumatically.Whatever the method of variable valve control, the designand optimization of such systems remain difficult, time-consuming and expensive activities. The amount ofimprovement in engine performance that can be achieved isclearly limited by the actual capabilities of each specific typeof valvetrain and its actuation system and, often, requiresmultiple iterations and juggling of different design factorsbefore an optimal set of operating parameters is found.

The design process of VVA mechanisms can be greatlyaccelerated through the use of sophisticated numericalsimulation tools. This paper gives an overview of suchgeneral-purpose simulation tool, which features generalplanar kinematics, multi-body dynamics as well ashydromechanics and hydraulics analysis capabilities. The tool

Application of a General Planar Kinematics andMulti-Body Dynamics Simulation Tool to theAnalysis of Variable Valve Actuation Systems

2010-01-1193Published

04/12/2010

Marcin Marek Okarmus and Rifat KeribarGamma Technologies Inc.

Edward SuhDelphi Powertrain Systems

Copyright © 2010 SAE International

has been developed as part of the GT-SUITE simulationsoftware, which is specifically designed for applications inthe engine, powertrain and vehicle industries [5]. Thesolution methodologies implemented in the tool are presentedin the context of application to variable valve control systemsthat employ a mechanical actuating principle. In particular,the swing-cam type, variable valve actuation mechanismspresented in [6] and [7] (a schematic of the mechanismdescribed in [6] is shown in Figure 1 below) are discussedand multiple stages of a numerical modeling process of suchvalvetrains are described including:

• planar kinematics analysis of component motions combinedwith a specialized algorithm to compute the rotational camand/or swing cam shape profile required to produce thedesired valve lift

• constrained-dynamics simulations of the system, whichignores component elasticity, to obtain nominal (quasi-dynamic) predictions, i.e. inter-component forces, valvespring margin and cam-follower separation speed, etc.

• lumped-parameter model multi-body dynamics analysis,which considers the elasticity of valvetrain components andinter-component contacts.

The scope of the paper is further expanded to describe adedicated library of specialized valvetrain system analysiscomponents, which utilizes all capabilities of the previously-mentioned general-purpose simulation tool, but significantlysimplifies data input and model setup and, hence, speeds upthe design process. Finally, the discussion is extended toinclude an example of integrated hydro-mechanical analysis.Several results from the simulation that are of high interest toa valvetrain designer are presented and ways of rapidlyoptimizing the key design parameters are discussed.

Figure 1. Swing-cam type, mechanically-actuated VVAmechanism analyzed in the paper

GENERAL PLANAR KINEMATICSANALYSIS TOOLBOXHaving a tentative geometrical layout of the valvetrain alongwith the desired valve lift profile, the numerical modelingprocess typically begins with the kinematic analysis of thesystem. The aim of this simulation is to obtain idealizedmotions of all valvetrain components along with other usefulkinematic predictions, i.e. component velocities andaccelerations, motions of contact points, entrainment andscrub velocities at inter-component contacts, perfect rollingspeed of the cam-follower roller, etc., but, primarily, tooptimize the geometry and compute the cam shape profilerequired to realize the desired valve lift.

The general-purpose planar kinematics analysis toolboxavailable in the simulation software and presented here issuitable for simulating single-degree-of-freedom, planarmechanisms. The swing-cam type, variable valve actuationsystems mentioned above belong to the family of suchmechanisms. The toolbox is essentially a library of kinematicoperators (connections), which solve linear or non-linearrelationships between translational or rotational kinematicnodes (components) shown in Figure 2. The assemblies ofkinematic components and connections forming a mechanismare recognized by means of a recursive algorithm. Applyingan angular or linear displacement (typically as a function ofcrank or cam rotation angle) to any component in theassembly results in the solution of motions of all otherkinematic nodes in the cluster constituting the mechanism.Computational time required to complete the kinematicsimulation is very low, usually on the order of a few seconds,

which makes the use of this tool feasible for rapid design andoptimization studies.

Figure 2. Rotational and translational kinematic nodes

For instance, if we denote the angular displacement of therotating node as and the planar displacement of thetranslating node along the prescribed direction as , then theconnection linking these two nodes solves the followingrelationship to compute the motion of one (output)component as a function of known displacement of other(input) component and mechanism geometry:

(1)

Various types of kinematic operators are available in the toolincluding:

• binary links

• crank-sliders

• constant and variable gear ratios

• rack-pinion couplings

• planar contacts

Selected examples are illustrated below in Figures 3 and 4.

Solution to the non-linear function representing therelation between displacements of kinematic nodes isobtained either analytically, as is in the case of the planar fourbar linkage mechanisms shown in Figure 3 where the angular

displacement of the output link, , is computed as a

function of rotation angle of input link, , and mechanismgeometry, or using an iterative numerical procedure to solve,for example, the kinematics of a cam-to-translating circularfollower contact of Figure 4 and compute the displacement ofthe follower, , as a function of cam rotation angle, , andcontact geometry.

Figure 3. Four bar linkage mechanism defining akinematic relationship between two rotating nodes

Figure 4. Kinematics of the cam-to-translating circularfollower contact

Vectors and in Figure 4 are position vectors ofcandidate contact points on body k (cam) and body l(translating circular follower), respectively measured with

respect to inertial reference frame ( , ). Furthermore,

vectors and are tangent and normal vectors to thesurface of body k at common contact point. Similarly, vectors

and are tangent and normal vectors to the surface ofbody l. Eq. (2),3,(4) below describe the kinematics of thisplanar cam-to-follower contact (as well as any other planarcontact) and are solved simultaneously to obtain thedisplacement of output node as a function of displacement ofinput node and contact geometry. Multidimensional SecantMethod (Broyden's Method) [8] is an algorithm employed to

solve these non-linear equations. Notation indicates a

transpose of a vector. Note that Eq. (4) defines the gap (lash),, between the contacting surfaces.

(2)

(3)

(4)

An additional useful feature of the planar kinematics analyzeris an ability to account for lash at the contacting interfacesbetween kinematic components. Lash can be specified at anylocation in the system and its presence will influence theresulting motions of kinematic components. A sampleapplication where this type of feature proves to be very usefulis a study of loss of valve lift and change in area under valvelift curve as a function of valve-to-follower lash. Thealgorithm to account for lash is implemented as follows.First, Eq. (2) and (3) are solved simultaneously using themethod described above to obtain the position vectors and of candidate contact points. The value ofinstantaneous gap, , is then computed using Eq. (4). In case

, indicating separation (lash) between contactingsurfaces, the displacement of output node is set to zero.

Otherwise, if , indicating interference betweencontacting surfaces, Eq. (2),3,(4) are solved together againresulting in the displacement of the output kinematic node.

Another novel feature of the planar kinematics analysistoolbox is a specialized cam lobe profile solution algorithm.The idea behind this algorithm is presented graphically inFigure 5. Given a displacement (angular or linear) of anycomponent in the kinematic assembly as a function ofrotation angle, , of another component in the assembly andthe nodal location of cam lobe surface as input, the module

enables computation of the cam lobe surface profile (expressed in polar form as cam radius vs. local rotationangle ) rigidly attached to a rotational kinematic node andrequired to produce the desired input displacement function.

Figure 5. Graphical representation of the idea behind thecam lobe solution algorithm

For the VVA mechanisms such as that shown in Figure 1,there are two locations of cam lobe surface profile, that of therotational cam and that of the swing cam (see Figure 6) andthe cam lobe solution algorithm can be applied to each ofthese locations. This means that:

• given the valve lift profile as a function of rotation angle ofrotational cam and the surface profile of the swing cam asinput, the algorithm can solve for the shape of the rotationalcam

• given the valve lift profile as a function of rotation angle ofrotational cam and the surface profile of the rotational cam asinput, the algorithm can solve for the shape of the swing cam

Figure 6. Locations of the rotational cam and swing camfor the swing-cam type VVA mechanism

The basis for solution of the cam lobe shape profile is thetheory of envelopes from calculus [9]. The theory states thatthe cam shape (inner envelope) that will produce the desiredmotion of the follower is obtained by fitting a tangent curveto the family of curves defining all possible followerpositions. This procedure is presented graphically in Figure 7for a cam-to-circular follower contact (the same procedure isused to solve the problem of a cam-to-flat-faced followercontact) and effectively boils down to simultaneous solutionof the following equations for the X and Y coordinates of thecam shape profile:

(5)

(6)

Function represents a family of curves that describe theplanar positions of the follower. Components of vector

define the X and Y coordinates of the cam profile. Angle ,called the parameter of the family, distinguishes the member

curves from one another, i.e. for a particular value of , Eq.(5) defines one member of the family of curves.

Figure 7. A graphical basis for describing the camprofile by means of theory of envelopes

Application of the above cam lobe shape profile solutionalgorithm and other kinematic analysis capabilities to theactual swing-cam type VVA mechanisms will be presented inthe following sections.

GENERAL MULTI-BODY DYNAMICSANALYSIS TOOLBOXMulti-body dynamics simulation of the valvetrain at thesubsystem and system level has become necessary inreducing design cycle time. Using analytical models toperform this type of analysis at the concept design stage canidentify potential problems and further aid in optimizing thedesign [10]. The general-purpose, multi-body dynamicssimulation toolbox can be applied to model valvetrainsincluding VVA's as well as other types of mechanisms in one,two and three dimensions (i.e. 1D/2D/3D). The description ofthe broad range of dynamic analysis capabilities available inthe simulation tool and the underlying solutionmethodologies can be found in [5] and [11]. Here, thediscussion will be limited to planar (2D) applications.

Similar to the planar kinematics analyzer, the multi-bodydynamics analysis tool is an object-oriented library ofcomponents and connections. These represent the physics ofreal parts/links/joints and serve as fundamental buildingblocks for mechanical systems. The internal solverarchitecture is based on the Finite Element Method (FEM). Italso satisfies one of the distinguishing requirements of multi-body dynamic analysis (e.g. when compared to finite elementanalysis), which is the requirement to consider various typesof “joints” that impose constraints on the relative motions ofthe bodies in the system. The constraints are implementedusing the Lagrange Multiplier technique [12]. This type of

infrastructure, combined with Herting's modal reductiontechniques [20], a sparse matrix (“skyline”) storage andsolution scheme for non-symmetric matrices and an option touse several, different types of integration methods (bothexplicit and implicit), allow the user to create and efficientlyanalyze general mechanisms that may contain combinationsof rigid and flexible bodies, joints and external loads. Thesolution procedure amounts to solving (and integrating) thefollowing system of equations to obtain the states ofstructural components:

(7)

where is the configuration dependent, positive-definitemass matrix, is a vector that includes damping, elastic andexternally applied loads, is the displacement vector, isthe constraint Jacobian matrix, is a vector of Lagrangemultipliers associated with constraints, is the vectorcontaining terms associated with the differentiation of

constraint equations and represents the derivative withrespect to time.

The multi-body dynamics solution procedures describedabove can be employed in the planar analysis of variablevalve actuation mechanisms. In addition to the geometricallayout of the system, which by this time has been optimizedbased on results from the simulation of mechanismkinematics, the input required to the model also includes themass-elastic properties of the valvetrain parts along withstiffness, damping and frictional characteristics of inter-component contact, bearings, guides, etc.

The study of VVA system dynamics appropriate at theconcept design level can be carried out in multiple stepsstarting with a fast but simplified, rigid, constrained-dynamics simulation, which ignores component elasticity andonly considers inertial effects, friction and valve spring force,and proceeding to a full-blown dynamic model, which alsoaccounts for elastic compliance, component separation andimpact, valve spring surge, etc. The term “rigid constrained-dynamics” refers to a simulation mode, in which allcomponents are modeled as rigid bodies and all inter-component contacts and joints (i.e. guides, pivots) arehandled with constraints. The ability to eliminate highfrequency response associated with high stiffness ofcomponents and contacts from the dynamic solution enablesto obtain “clean”, nominal (quasi-dynamic) predictions forforces and moments acting on the valvetrain and, at the sametime, significantly decrease the computational time requiredto complete the analysis. Other results that are of high interestto valvetrain designer, which can be extracted by means of

the constrained-dynamics simulation, include componentseparation speeds, valve spring margin, nominal contactHertz deformation and stress, etc. Inclusion of componentcompliance and contact stiffness in the model leads toadditional important predictions including componentdeformations, strains and stresses, loss of lift due todeformation, component vibration and surge, valve seatingvelocity and bounce, detailed Hertz and elastohydrodynamic(EHD) results and many more. The wide array of availableoutputs permits a thorough understanding of the mechanism'soperation and provides means for fine-tuning the model.

Application of the multi-body dynamics simulation to theanalysis of the VVA systems will be described in thefollowing sections.

SPECIALIZED ANALYSIS OFVALVETRAIN SYSTEMSSpecialized, valvetrain system kinematics and multi-bodydynamics analysis capabilities of the GT-SUITE softwarehave been presented in numerous publications [13], [14],[15], [16]. This tool, which is specifically tailored to be usedby valvetrain engineers, offers all of the planar kinematicsand multi-body dynamics simulation features describedabove. It can be applied to various types of valve controlsystems including mechanically-driven VVA's. Furthermore,being part of an integrated simulation environment, itpresents other features that prove to be very useful in rapid,concept level design and optimization of valvetrains [5].These include a visual pre- and post-processor, an ability touse a direct optimizer and a DOE processor, distributedcomputing and, foremost, a formal integration of multi-bodydynamics with other numerical modeling libraries, i.e. 1Dflow simulation and hydraulics, electrical and magneticcomponents, control components.

Vast valvetrain designer “know-how” is incorporated into theanalysis tool making it easy and efficient to use. The input tothe tool (i.e. valvetrain mechanism specifications) is pre-processed to automatically generate the underlying planarkinematic and multi-body dynamics models. The results fromsimulations of the underlying models are fed back to thevalvetrain tool and further post-processed to create a widearray of specialized valvetrain outputs. Flow diagram infigure below illustrates the process.

Figure 8. Flow diagram illustrating valvetrain systemanalysis process

APPLICATION OF SIMULATIONTOOL TO THE ANALYSIS OF VVASYSTEMS AND VALIDATION OFSIMULATION RESULTSThe simulation tool was applied to the analysis of a swing-cam type, variable valve actuation mechanisms. Kinematicand dynamic predictions were validated by comparing resultsfrom other simulation programs. The first system selected foranalysis was the Continuously Variable Valve Lift (CVVL)valvetrain developed by Delphi Corporation [17].Geometrical layout of this mechanism is shown below inFigure 9. The system is composed of a rotational (input) cam,which actuates an oscillating/swing cam (also referred to as arocker or output cam). The swing cam, in turn, drives tworoller finger follower (RFF)-valve assemblies. Variable valvelift is realized by changing the position of the control shaftand effectively modifying the location of the swing cam pivotpoint. The pivot point moves along a section of a circularpath, which is centered at the RFF roller. More details on theprinciple of operation of this and similar mechanisms can befound in [1] and [6].

Figure 9. Continuously Variable Valve Lift (CVVL)valvetrain

A model of the CVVL mechanism was constructed from thelibrary of specialized valvetrain components based on theinformation provided by Delphi. Geometrical layout of thesystem along with mass-elastic properties of valvetrain partswere imported into the object-oriented interface of thesimulation tool. Figure 10 below illustrates the main buildingblocks of the simulation model.

<figure 10 here>

PLANAR KINEMATICS ANALYSISFirst, a planar kinematics simulation of the valvetrain wascarried out. In addition to geometrical specifications of thesystem, the input to this simulation included the rotationaland the swing cam shape profiles. The model was analyzed atseveral (total of 17) positions of the control shaft,corresponding to the angular displacement of the swing campivot point from 0 deg. (max. lift) to 16 deg. (min. lift) in theclockwise direction, to produce a family of valve lift curvesalong with many other kinematic predictions. Total timerequired to complete the simulation (all 17 cases) wasreported at about 15 seconds on a 2GHz, dual-core machine.Selected results from the simulation of planar kinematics arepresented below in Figures 11,12,13,14. Figures 11 and 12show the kinematic lift and acceleration of the valve,respectively, plotted vs. rotational cam angle. Furthermore,Figures 13 and 14 show the angular displacement of theswing and a finger follower roller pressure angle. All resultswere normalized through division by a maximum value in therange analyzed.

Figure 11. CVVL kinematic valve lift Figure 12. CVVL kinematic valve acceleration

Figure 10. Simulation model of the CVVL valvetrain

Figure 13. CVVL kinematic swing cam angulardisplacement

Figure 14. CVVL kinematic RFF roller pressure angle

Kinematic predictions presented above were validated bycomparing results from another simulation tools. Here, theUnigraphics motion analyzer, UG Motion, was used as areference program for comparison. Figures 15,16,17 belowshow comparisons of simulated kinematic valve lift, velocityand acceleration (referred to as “Simulation”) to the referenceresults (labeled as “Reference”). For clarity of presentation,three simulation scenarios, corresponding to three distinctlocations of the control shaft, i.e. 0 deg (max. lift), 8 deg(middle lift) and 16 deg (min. lift), were selected and used forcomparison. As seen below, the plots show very goodagreement between “Reference” and “Simulation” with amaximum percent difference of ∼1.2% (in the selectedregions of valve acceleration) and an average percentdifference of ∼0.1%. These small percent differences inhigher derivatives of lift can be associated with the differentnumerical algorithms used for computation of functionderivatives.

Figure 15. Validation of kinematic results - CVVL valvelift comparison

Figure 16. Validation of kinematic results - CVVL valvevelocity comparison

Figure 17. Validation of kinematic results - CVVL valveacceleration comparison

Once validated, the kinematic model of CVVL valvetrain wasfurther exercised in order to test the novel cam shape profiledesign features. This time, the input to the model included therotational cam shape profile as well as the maximum targetvalve lift defined as a function of rotational cam angle. Thegoal of this exercise was to compute the swing cam shaperequired to produce the desired valve lift. Figure 18 showsthe comparison between the “Reference” swing cam lobeexcess radius (excess radius is defined as the radius above thebase radius of the cam) and the one obtained using the“Calculation”. Results were again normalized throughdivision by the maximum value of the “Reference” signal.

Figure 18. Calculation of the CVVL swing cam lobeprofile - comparison

In a similar fashion, the rotational cam shape profile can beback-calculated by the same algorithm. In this case, the swingcam angular displacement corresponding to the maximumvalve lift scenario and defined versus rotational cam angle

was used as input to the calculation and the result was theshape (excess radius) of the rotational cam. Again, thecomparison between the “Reference” and “Calculation”rotational cam lobe profile is shown in the figure below.

Figure 19. Calculation of the CVVL rotational cam lobeprofile - comparison

The above mentioned cam shape profile solution algorithmcan be efficiently applied in rapid design of lobe profiles ofboth rotational and swing cams and, effectively, inoptimization of valve lift curves. Subject to a set of designcriteria, the fast planar kinematics solver can be integratedinto an optimization loop in order to compute the cam shapewhich produces the desired valve lift and, at the same time,meets all the required design specifications. The designcriteria mentioned here typically include parameters such as amaximum valve acceleration limit, an allowable range of camradius of curvature, cam-to-roller follower contact pressureangle limit, limit on the kinematic prediction of roller perfectrolling speed along with contact scrub and entrainmentvelocities, etc. For illustration purposes, a sample study wasset up where a “Reference” shape of the rotational cam wasused as input to the simulation and the magnitude of“Reference” target valve lift (also input to the analysis) wasvaried in 2 steps. The output from this simulation was theshape of the swing cam corresponding to each of the inputvalve lift profiles. Input valve lifts and resulting swing camshape profiles were compared to their “Reference” values andare shown below in Figures 20 and 21, respectively.

Figure 20. Study - calculation of the CVVL swing camlobe profile - input valve lifts

Figure 21. Study - calculation of the CVVL swing camlobe profile - computed lobe profile

As previously described, the kinematics solver is quitegeneral and can be applied to the analysis of various types ofplanar mechanisms. To illustrate this, the solutionmethodologies were applied to the study of another swing-cam type VVA mechanism, namely the continuouslyVariable Valve Lift and Duration (VVLD) valvetraindescribed in detail in [7] and pictured in Figure 22. Thisdesign concept, which realizes a relatively high lift with smallduration by virtue of its structure and can operate atconsiderably high engine speeds through its high rigidity [7],is somewhat similar to the CVVL mechanisms analyzedabove. The key difference is the presence of an additionaloscillating component, i.e. control arm, between the swingcam and the rocker arm. Variable valve lift is realized byturning the control shaft, which subsequently modifies thelocation of pivot point of the control arm.

Figure 22. Continuously Variable Valve Lift andDuration (VVLD) valvetrain

Since the main purpose of this exercise was to showcase thegenerality of the simulation tool and due to the lack of truegeometrical specifications of the valvetrain, the dimensionsof system's components were approximated to resemble theVVLD mechanism in question. Similarly, rotational andswing cam shape profiles were borrowed from a differentvalvetrain model. Planar kinematics simulation was carriedout at 11 different positions of the control shaft. The resultingfamily of valve lift curves is shown in Figure 23 below.

Figure 23. VVLD kinematic valve lift

It can be observed that the shape of valve lift profiles doesnot look realistic. As mentioned above, this is a result of thelack of detailed information about the geometry of this VVAmechanism. Nevertheless, this application supports the mainpremise, which was to emphasize the generality of thesimulation tool. The VVLD system described above was

analyzed in the “forward” mode with the rotational and swingcam profiles as input. However, the same cam lobe shapesolution procedures used in the case of CVVL valvetrain canalso be applied to this as well as other, mechanically-driven,conventional valvetrains and variable valve control systems.

PLANAR, MULTI-BODY DYNAMICSANALYSISThe focus of the following section is on the simulation ofdynamic behavior of the VVA systems. As explained above,this type of analysis can be broken down into multiple stagesaccording to the level of model complexity and resultingphysical phenomena captured by numerical simulation. Ittypically starts with a simplified study of “rigid” and“constrained” dynamics of the valvetrain and extends to amore detailed analysis of components' elastic response anddynamic vibrations.

RIGID AND CONSTRAINED MULTI-BODYDYNAMICSIn this analysis, the elasticity of all valvetrain components isignored. The components are modeled as lumped inertias thatare free to move in 2-D space. Further, planar motions ofthese inertias can be limited through the application ofconstraints, e.g. revolute joints, prismatic joints, slidingjoints, etc. The inter-component contacts can either beassumed to be very stiff but still allow separation oradditional contact constraints can be prescribed to preventlash and force valvetrain parts to follow kinematicallydetermined motions.

The simulation tool was applied to the study of a rigiddynamics model of CVVL valvetrain. Frictional effects wereignored in the analysis. Valve spring and the swing camtorsion spring were modeled as massless links. Effectivemoving mass of the valve spring was added to the mass of thevalve. Given the material properties and geometry of matingsurfaces, the contact stiffness was calculated based on theHertz model [19]. High contact damping coefficients wereused to attenuate the high frequency noise associated withcontact stiffness. Selected results from the simulation of thevalvetrain run at 6000 RPM were again compared to thereference results generated using another simulation program.The ADAMS multi-body dynamics simulation tool fromMSC Software [18] was used as a reference program forvalidation. Comparison of normalized valvetrain dynamicspredictions (“Simulation”) to the “Reference” results isshown below in Figures 24,25,26,27,28,29 for three distinctlocations of the control shaft, i.e. 0 deg (max. lift), 8 deg(middle lift) and 16 deg (min. lift). An average CPU timerequired to complete a single engine cycle was 3 seconds on a2GHz, dual-core machine. Again, a very good agreementbetween the “Reference” and “Simulation” results can beobserved with the highest percent difference of ∼4% and an

average way below this number. These small differences inthe results can be attributed to the uncertainty in the values ofcontact stiffness and damping parameters used.

Figure 24. Validation of rigid dynamics results - CVVLvalve acceleration comparison

Figure 25. Validation of rigid dynamics results - CVVLvalve pallet contact force comparison

Figure 26. Validation of rigid dynamics results - CVVLvalve pallet contact scrub velocity comparison

Figure 27. Validation of rigid dynamics results - CVVLswing cam contact force comparison

Figure 28. Validation of rigid dynamics results - CVVLrotational cam torque comparison

Figure 29. Validation of rigid dynamics results - CVVLrotational cam contact Hertz stress comparison

In addition to the results presented above, the rigid,constrained-dynamics analysis can be used to obtain otherpredictions that are of high value to valvetrain designers.Examples include the swing cam-roller and rotational cam-roller separation speed (i.e. speed at which the magnitude ofnormal contact force drops to 0 N) or the valve spring andswing cam torsion spring margin. The spring margin is a non-dimensional quantity that determines if the spring is capableof producing a force, which will be sufficient to keepvalvetrain components in contact and prevent separationduring the region of negative cam acceleration. It is computed

as where is an equivalent spring

force (measured at cam-follower contact) and is theeffective valvetrain inertia force. The spring margin results ofCVVL valvetrain springs (both valve and torsion) computed

at 6000 RPM for different locations of the control shaft areplotted in Figures 30 and 31. Both the valve spring and thetorsion spring margins were found to be adequate for theCVVL design at the engine speed analyzed.

Figure 30. Rigid, constrained-dynamics results - CVVLvalve spring margin

Figure 31. Rigid, constrained-dynamics results - CVVLswing cam torsion spring margin

FLEXIBLE MULTI-BODY DYNAMICSRigid, constrained-dynamics simulation presented in theprevious section is very useful in quickly investigating thebehavior of a valvetrain and obtaining a set of nominal(quasi-dynamic) predictions. However, a true dynamicresponse of the system can be closer analyzed by means of aflexible multi-body dynamics simulation. A lumped-parameter, linear-elastic model, although a bit morecomputationally expensive as compared to a rigid model, isstill feasible at a concept level of valvetrain design. Such amodel takes into account the compliance of valvetrain

components and the elasticity of inter-component contacts. Itcan also account for friction resulting from relative motionsof contacting surfaces. Valuable predictions from suchmodel, in addition to those obtained via rigid dynamics,include: component deformations, component vibrations andresonance, valvetrain tribology and frictional power loss, lossof valve lift (as compared to idealized, kinematic lift) due todeformations, contact forces, component separation andimpact, valve seating velocity and others.

For illustration, the dynamic model of Delphi's CVVL systemwas modified to account for elasticity of valvetrain parts. Ingeneral, mechanically-driven VVA mechanisms are designedfor high rigidity. The compliance of valvetrain parts can beobtained either experimentally via a strain gage measurementof component's deformation due to an applied load or bymeans of the static finite element (FE) analysis. In absence oftrue stiffness values, the compliance of the swing cam and theroller finger follower parts was approximated and modeled asa single torsional stiffness value. A massless valve springconnection was replaced by a more physical mass-elasticmodel of a helical spring in order to capture the inertialeffects associated with motion of spring coils as well as coilclash. Coulomb friction model was applied to account forfriction at contacting surfaces. The simulation was carried outat the engine speed of 6000 RPM. The use of implicitintegration scheme (3-stage Radau algorithm) to integrate thedynamic equations of motion ensured that the simulation timestep was not constrained by the presence of high frequencymodes (e.g. stiff spring vibration modes) and that the modelremained computationally efficient. An average simulationtime was found to be about 30 seconds per engine cycle on a2GHz, dual-core machine. Selected results from the dynamicsimulation of the valvetrain at 6000 RPM for control shaftpositions of 0 deg, 8 deg and 16 deg are shown below inFigures 32,33,34,35.

Figure 32. Flexible dynamics results - CVVL valve liftplotted together with kinematic lift

Figure 33. Flexible dynamics results - CVVL valve palletfrictional power loss

Figure 34. Flexible dynamics results - CVVL rollerfinger follower torsional deformation

Figure 35. Flexible dynamics results - CVVL swing camcontact force

INTEGRATED HYDRO-MECHANICAL SIMULATION OFVVA SYSTEMSThe multi-physics simulation environment of GT-SUITEsoftware enables direct integration between the multi-bodydynamics simulation tool and a 1-D fluid flow dynamics andhydraulics analysis. The ability to combine the dynamic andhydraulic models in a single simulation is essential inunderstanding the true physical phenomena that are takingplace in the system. This, in turn, allows for rapid predictiveanalysis of design issues and evaluation of design changes.Examples of application of integrated simulations to the studyof hydro-mechanical interactions in valvetrains can be foundin [15] and [16]. A possibility to couple with hydraulics

significantly expands the scope of application of thevalvetrain simulation tool, which now covers components andsub-systems such as hydraulic cylinders, cam phasers,hydraulic lash adjusters, etc.

To showcase the ability to combine multi-body dynamics andhydraulics models in a single, integrated simulation run, amodel of the hydraulic lash adjuster (HLA) was added to theflexible dynamics model of the CVVL valvetrain. In thissetup, the main function of the HLA was to support the pivotend of the RFF and automatically control the finger armposition in order to eliminate lash and keep the finger incontact with the swing cam and the valve. A hydro-mechanical model of the HLA assembly consisted of thefollowing components:

• high pressure chamber, which represents the outer shell/housing of the HLA

• plunger, which is hollow and contains an orifice throughwhich oil is pumped from the supply gallery into the mainchamber

• check valve assembly comprised of a ball-shaped valve,spring and spring retainer cage

• main HLA spring

More details regarding the hydraulic lash adjuster model,including the equation governing the evolution of pressure inthe high pressure chamber, can be found in [16]. A combinedhydro-mechanical analysis of the CVVL valvetrain was,again, executed at 6000 RPM at several positions of thecontrol shaft. It required 40 seconds of CPU time per enginecycle on a 2GHz, dual-core machine. Figures 36,37,38 showvarious interesting results extracted from the coupled model.

Figure 36. Integrated hydromechanics results - CVVLmotion of RRF pivot

Figure 37. Integrated hydromechanics results - CVVLHLA chamber pressure

Figure 38. Integrated hydromechanics results - CVVLHLA leakage flow rate

SUMMARY/CONCLUSIONSNovel features and solution methodologies of a general-purpose planar kinematics and multi-body dynamicssimulation tool were presented in the context of application tomechanically-driven, swing-cam type, variable valveactuation systems. In the same fashion, the tool can beapplied to the analysis of any planar mechanism. Multiplestages of the VVA valvetrain analysis process feasible at theconcept design level were described including:

• analysis of kinematic motions of valvetrain componentsalong with a procedure to calculate the rotational and swingcam shape profiles required to produce the desired valve lift

• rigid, constrained-dynamics simulation to extract nominal(quasi-dynamic) predictions• flexible, multi-body dynamics analysis to account forelasticity of valvetrain components and inter-componentcontacts, frictional effects, etc.

A specialized and dedicated valvetrain system analysis tool,which simplifies and accelerates the model building process,was described and used to construct VVA valvetrain models.Numerical simulation procedures were applied to analysis ofthe Continuously Variable Valve Lift mechanism. Resultsfrom planar kinematics and rigid dynamics simulations werevalidated through comparison to results from other simulationprograms. A very good agreement between simulation resultswas shown. Furthermore, various kinematic and dynamicpredictions that are of high interest to mechanical VVAsystem designers were presented. The generality of thesimulation tool was further demonstrated by applying it toanother, swing-cam type (VVLD) valvetrain. The tool'sability to include models of hydro-mechanical componentsand to perform integrated analysis of valvetrain dynamics andhydraulics was also demonstrated.

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CONTACT INFORMATIONM. Okarmusm.okarmus@gtisoft.com

ABBREVIATIONSVVA

variable valve actuation

1Done-dimensional

2Dtwo-dimensional

3Dthree-dimensional

FEMfinite element method

EHDelastohydrodynamic

CVVLcontinuously variable valve lift

RFFroller finger follower

RPMrevolutions per minute

VVLDvariable valve lift and duration

HLAhydraulic lash adjuster

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ISSN 0148-7191

doi:10.4271/2010-01-1193

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