modelling a variable displacement axial piston...

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Alessandro Roccatelloe-mail: [email protected]

Salvatore Mancòe-mail: [email protected]

Nicola Nervegnae-mail: [email protected]

Politecnico di Torino,The Fluid Power Research Laboratory (FPRL),

Corso Duca degli Abruzzi 24,Torino, 10129, Italy

Modelling a VariableDisplacement Axial Piston Pumpin a Multibody SimulationEnvironmentAnalysis of a variable displacement axial piston pump, as in other complex fluid powerand mechanical systems, requires appropriate insight into three multidisciplinary do-mains, i.e., hydraulics, mechanics and tribology. In recent years, at FPRL, modelling ofaxial piston pumps has evolved in AMESim (one-dimensional code) where a three-dimensional mechanical approach has required generation of proprietary libraries lead-ing to the evaluation of internal forces/reactions in all pump subsystems. Tribologicaspects in axial piston pumps modelling are also being investigated but AMESim, in thisrespect, does not appear as the appropriate computational environment. Consequently, anew approach has been initiated grounded on MSC.ADAMS. In this perspective, thepaper details how the model has been developed through proprietary macros that auto-matically originate all pump subsystems parametrically and further apply required con-straints and forces (springs, contacts and pressure forces). The ADAMS environment hasalso been selected due to co-simulation capabilities with AMESim. Accordingly, the paperelucidates how the entire modelling has been construed where hydraulics is managed inAMESim while ADAMS takes care of mechanics. A comparison between simulated andexperimental steady-state characteristics of the axial pump is also presented. As such thispaper indicates an innovative methodology for the analysis of complex fluid power sys-tems in the hope that, eventually, tribology will also fit into the scene.�DOI: 10.1115/1.2745851�

ntroduction

During the 1980s, a pervasive diffusion of digital computersriggered a continuously growing impetus for “simulation” in sci-ntific research. At that time and within the fluid power commu-ity simulation essentially implied hydraulic simulation developedhrough in-house written software almost exclusively coded in theortran language. Those codes granted great flexibility but lackedser friendliness while becoming quite rapidly obsolete. In the990s, commercial codes for hydraulic simulation started to bevailable featuring user friendly interfaces and steady updatesrom the development team. Two emblematic examples may suf-ce: Easy5 and AMESim.At FPRL after a brief experience with Easy5 �1� the decision

as taken to elect AMESim as the environment for hydraulicimulation. In that context it was indeed possible to continueodel development studies through writing Fortran pieces of

ode. Thus, once the hydraulic simulation of an axial piston pumpas perfected and validated experimentally, the need emerged of

ooking into the modelling of the mechanical parts within theump. This was done generating new submodels embodying mo-ion and constraints equations. In those same years a fundamentalrowth of 3D Cad software was evolving. In fact nowadays, fromhe original aim of providing three-dimensional representations ofomponents and systems, the 3D software is progressively andteadily advanced towards multidomain simulation models featur-

Contributed by the Dynamic Systems, Measurement, and Control Division ofSME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CON-

ROL. Manuscript received July 14, 2006; final manuscript received December 11,006. Review conducted by Kim Stelson. Paper presented at the 8th Biennial ASMEonference on Engineering Systems Design and Analysis �ESDA2006�, July 4–7,
006, Torino, Italy.
56 / Vol. 129, JULY 2007 Copyright © 20

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ing functional realism in designed virtual prototypes. Conse-quently, new and powerful research tools are being made avail-able.

Today the aim is to endorse a fully functional virtual prototyperather than a physical mock-up exacting continuous remakes. Thisto remedy quandaries of a design phase missing accurate percep-tion of all relevant aspects. In fluid power these encompass hy-draulics, structural analysis, computational fluid dynamics, gearprofiles generation, tribology, controls, etc. Accordingly, develop-ment of a homemade software spanning outspread multidomaintopics is out of reach for a limited group of researchers. It is thennecessary to make recourse to specialized software and focus at-tention on models development within FPRL competence. Thispaper illustrates the first steps into this path of virtual reality.

The multibody programming environment chosen is ADAMS.More precisely, an attempt is made to apply to axial piston pumpsa procedure similar to that followed in ADAMS/ENGINE �pow-ered by FEV� for individual powertrain components, completeengines and subsystems. The intention being that of generating acomplete pump model through use of templates and employingexternal libraries for the simulation of user-defined modelling el-ements �e.g., tribologic phenomena�.

From a mechanical point of view, a variable displacement axialpiston pump �for brevity pump� is a fairly complex multibodysystem. Analysis of such a system, beside hydraulics characteris-tics, involves a twofold objective: �1� assess a model to simulateforces acting on individual components; �2� account for tribologi-cal aspects within the pump. The first objective was reachedthrough development of a proprietary library, in AMESim �swash-plate, pistons, barrel, shaft, etc.; see Mancò et al., �2��. This led,through appropriate extensions of AMESim potentials, to theevaluation of system kinematic and dynamic properties in threedimensions. Initially, this paper shows how this purported effort
leads to the attainment of numerous and valuable information �in
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upport of design and dimensioning� but, at the same time, suffersrom many drawbacks: the analytic determining of system kine-atics, the writing of individual components equilibria and the

ack of a three-dimensional graphic interface. The ensuing me-hanical model �hereafter referred to as “traditional”� is thereforeumbersome and interpretation of results requires attentive analy-is for proper comprehension. Furthermore, this model is alsoampered by the fact that the relative positioning of componentshere tribologic investigations are of prime interest �i.e., gapsetween barrel and portplate, slippers and swashplate, piston andylinder� is an input parameter and as such stays constant during aimulation and independent of pump loading conditions. There-ore, aspects related to mechanics have been revisited in a differ-nt perspective and precisely looking at the pump as a multibodyystem.

Ivantysynova �3� stresses the need for considering the effects ofntervening phenomena within hydraulic pumps and motorshrough a synergic use of CFD, multibody and FEM methodolo-ies. The stated choice in favor of developing a specific in-houseode rather than using different dedicated commercial software isotivated by the wish of preventing and possibly avoiding nu-eric problems as well as by the opportunity of enacting use of a

ingle numerical solver engine.The prospect of developing an in-house designed multibody

imulation environment was evaluated; specific papers presentifferent formulations to generate and solve motion equations andnforce appropriate constraints �see Schiehlen �4��. However itas soon decided to use a commercial multibody software to cir-

umvent numerous difficulties associated with a proprietary codeevelopment �see remarks in Deeken �5��. MSC ADAMS waselected for essentially two reasons: its co-simulation capabilityith AMESim �this preserved the existing hydraulic model�; itsigh ranking in the analysis of fluid power systems according ton extended literature survey. In particular, Antoszkiewicz et al.6� simulated dynamic stresses on the gearing of a double bent-xis pump using ADAMS also for a simplified evaluation of pis-ons chambers pressures. This analysis also pinpointed that exclu-ive use of ADAMS in a multidomain project has definiteestrictions. Deeken �7� uses ADAMS and DSHplus in co-imulation to demonstrate the feasibility of simulating forces in anxial piston pump �those stemming from pistons� and assert therospect of using diverse software specific to given engineeringomains �e.g., hydraulic, mechanic� to study and analyze complex

Fig. 1 AMESim

uid power systems. Again, Deeken �8� uses the cited tools to

ournal of Dynamic Systems, Measurement, and Control


account for tribological aspects within the pump, comparingmodel vs experimental results relative to barrel tilt at differentloads and speeds. Kudav et al. �9�, using ADAMS, looked at dy-namic loads on a pump, whose geometry was imported fromCAD, for the purpose of assessing stress conditions on materials�FEA analysis�. More generally, Larsson et al. �10� analyzed pos-sible approaches for the simulation of multidomain systems. Theirstudy focused on an earth-moving machine. Simulink, ADAMSand Hopsan were exercised to simulate the engine-driveline, tires-chassis and steering systems, respectively.

The present paper introduces the “traditional” method for themechanical simulation of a pump to substantiate difficulties tiedwith the writing of all equilibrium equations and the implementa-tion of tribologic phenomena. Subsequently, it elucidates howADAMS and AMESim can co-simulate. Two methods are intro-duced that lead to the design of a variable displacement pump in amultibody approach, emphasizing the fact that it is definitely fea-sible to generate a fully parametric model automatically. One keypoint in model building is centred on an attentive selection ofconstraints; in this respect prevention of redundancies is stressedalong with the fact that the mere use of standard ADAMS con-straints may lead to totally unrealistic outcomes. To enlightenthese points a piston multibody model will be presented for com-parison with the “traditional.” Simulated and experimental steady-state characteristics of the pump unit will be addressed. Finally,benefits in using a multibody approach will be suggested in viewof developing proper libraries in support of tribologic studies andsimulations.

Present Standing of the Simulation ModelThe axial piston pump model, in its present standing, is shown

in Fig. 1 and it is entirely developed within the AMESim simula-tion environment. In the upper portion of Fig. 1 submodels areassembled that are dedicated to the hydraulic portion, while thosepertinent to mechanical items of the pump are shown at the bot-tom. In both cases submodels belong to proprietary libraries pur-posely developed for the simulation of this kind of pump units�see Mancò et al. �2��. Mechanical analysis determines unknownreaction forces on the basis of the “free body diagram” of eachcomponent: Figure 2 presents that relative to a piston, useful forunderstanding the approach and for subsequent comparison with

del of the pump
mo
the corresponding multibody model.

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Mechanical Model of a Piston. All forces acting on the pistonust be made explicit �for brevity, friction forces are not

ccounted�.Assuming the pump axis is horizontal, the weight of the piston

s written as

W = mg �1�

he inertia force, acting on the piston is equal to

Fi = m · az �2�

he piston rotates about an axis offset from its center of gravitynd therefore a centrifugal force exists that can be written as

Fc = m · �2 · Rm �3�

omponents of this force �see Fig. 2� are

Fcx = − m · �2 · Rm · sin � j

Fcy = m · �2 · Rm · cos � j �4�

luid pressure originates an axial force �along the z-axis�,

Fpr =� · D2

4· pj �5�

o evaluate the aforesaid forces, piston kinematics must also beesolved to establish position zp, velocity vz and axial accelerationz �see Appendix A for the attainment of the following equations�:

zPj = Rm · cos � j · tan � +ds − dO + e · tan � �6�

Fig. 2 Forces a

cos �

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vzj = �1 + tan2 �� · � · �e + �ds − dO� · sin � + Rm · cos � j� − ¯

+ Rm · sin � j · tan � · � �7�

azj = �1 + tan2 �� · �Rm · �− 2�̇� sin � j + cos � j · �2 tan � · �̇2 + �̈�� + ¯

��ds − do� · sin � · ��̈ − 2�2 tan �� + e�2 tan � · �̇2 + �̈�� + ¯

+ �ds − dO� ·�̇2

cos �− Rm · tan � · �sin � j · �̇ + cos � · �2� �8�

For the analysis of reaction forces it is deemed that the pistonpossesses only 2 DOF with respect to the cylinder: one relative totranslational motion along the z-axis �removed by the slipper re-action�, the other associated with rotation about the same z. As aresult, the barrel constrains the piston with respect to translationsand rotations along axes x and y, by means of four correspondingreactions.

However, in reality and due to clearances, the piston can tiltwithin the cylinder and it can be presumed that contacts are ide-ally located in two points as shown in Fig. 3. The position of suchpoints is bound to the piston location and thus on the shaft’sangular condition; their standing along the piston’s external pe-riphery is instead not known a priori since it depends on externalforces, that at any given time, act on the piston.

Reaction forces are supposed to be active at these two points:two radial resultants Fpit1 and Fpit2 will then exist, each possess-ing two components along the x and y axes that altogether repre-sent the four cited reactions.

Piston and slipper are coupled through a spherical joint that

g on the piston

constrains piston translation along the three reference axes. The

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eaction �Fpipa� has therefore three components. With referenceo Fig. 2 the following equilibrium equations can be written:

• translational equilibrium along the x-axis:

Fpipax + Fpit1x + Fpit2x − Fcx = 0 �9�• translational equilibrium along the y-axis:

Fpipay + Fpit1y + Fpit2y + Fcy − W = 0 �10�• translational equilibrium along the z-axis:

Fpipaz − Fi − Fpr = 0 �11�• rotational equilibrium along the x-axis with respect to point

P:

�− W + Fcy� · dG − Fpit1y · �bpit1 − zP� − Fpit2y · b1 = 0

�12�• rotational equilibrium along the y-axis with respect to point

P:

− Fcx · dG + Fpit1x · �bpit1 − zP� + Fpit2x · b1 = 0 �13�

ll written equations become part of the piston submodel andome reactions must be determined through equilibria involvingther components �e.g., the slipper�. It is then clear how the writ-ng of the mechanical model of the entire pump unit becomes aather heavy task and indeed also for the difficult management ofhe various intervening submodels. Moreover, aiming at the pos-ibility of enriching the model with a fundamental issue regardingribologic aspects it must be considered that piston motion is notully defined by solving dynamic equilibria of intervening forcesut is rather enforced by kinematic equations �e.g., Eqs. �6�–�8��.rom this follows that the model is not apt to calculate the posi-

ion that the piston will really occupy �e.g., indicated in Fig. 3� in

Fig. 3 Reaction forces on the piston „from barrel…

Fig. 5 Pump model in AMESim with ADA



the presence of a variable height gap within the cylinder. Thus it isonly possible to cope with a constant gap height that as an inputparameter will stay fixed during simulation. The same also hap-pens for other tribological pairs such as the barrel-portplate or theslipper-swashplate.

From the remarks made so far it can be easily understood thereason why a radical change was pursued and effected in definingthe pump mechanical model through a multibody rather than a“traditional” approach. This clear-cut choice yields in addition anopen pathway for further integrations bound with tribological as-pects.

ADAMS - AMESim CosimulationThe two software environments may fruitfully cooperate under

different co-simulation strategies �see Rahmfeld �11��; the one fol-lowed in the present paper is shown in Fig. 4: AMESim solvesstate equations pertinent to the hydraulic model and gathers fromADAMS, that processes mechanical state equations, results of themultibody model at fixed time intervals; much in the same wayADAMS receives from AMESim all information stemming fromthe hydraulic model. Data exchange evolves at each time interval,this being designated as the “Communication interval” �. Wheneither AMESim �or ADAMS� receives a value processed by thecompanion software, the specific information remains constantwithin the extent of the communication interval; thus, it is quiteimportant that this period be defined appropriately while consid-ering that its reduction increases simulation time. In this respectRahmfeld �11� pinpoints the fact that the mechanical modelshould be sampled at a frequency at least double with respect tothe maximum associated with the mechanical items to prevent the“aliasing” phenomena.

Figure 5 shows the evolution of the AMESim model once acosimulation approach is being effected. In fact, by direct com-parison with Fig. 1 none of the mechanical icons are shown, all ofthem being collectively and effectively replaced by the ADAMSinterface. This interface handles input-output data exchange and

Fig. 4 Co-simulation process between ADAMS and AMESim

MS co-simulation interface submodel

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lso writes specific files that can be accessed to examine attainedesults and perform a multibody model animation.

eneration of the Multibody ModelIn ADAMS, two approaches are possible for generating the

ump mechanical model. Each has advantages as well as disad-antages. The first path implies that model geometry is importedrom CAD into ADAMS �see Kudav et al. �9�� and manual inter-entions are required to impose constraints and forces. The secondnd most valuable approach is instead grounded on the build up ofacros to automatically perform and enact most ADAMS com-ands.

Manual Generation of the Model. Once a 3D Cad model ofhe pump is at hand it is possible to import it into ADAMShrough various protocols �e.g., Parasolid files�. In this case all

odel components are already present and their representationeatures a high accuracy. However, some significant difficultiesxist since some functions and geometric properties of solids �e.g.,xtrusions, axes, origins� are not mapped into ADAMS. Thiseavily impairs the subsequent multibody model assessment. Inhis respect it will suffice to notice that definitions of joints ashose existing between the piston-slipper pair must be assigned

anually. The reason being that, in lack of reference geometry,enters of spherical joints are not identified by appropriatearkers.1 This requires a patient search of coordinates that be-

omes soon overwhelming if one considers that such manual ac-ions must often be repeated several times! Moreover, even sup-osing that such a strenuous effort be brought to completion, stillfrustrating limitation will survive. By this it is meant that the

ttained model is, so to say, “frozen” in that specific state and eachntervention will require a complete and manual reprocessing.hese issues steered the decision about the approach being by noeans adequate to the scope.

Automatic-Model-Generation Through Macros. In ADAMS,s in other software environments, macros permit automatic codeeneration recording manual sequences of commands issued byhe user while pursuing a definite task. Use of this resource aimst two targets: �a� define a “parametric” model of the axial pistonump; �b� generate the entire multibody model automatically. Tochieve both targets the procedure shown in Fig. 6 is proposed.urthermore a GUI was developed to serve as a guide in theesign of parametric models similar to those offered by ADAMS/NGINE, ADAMS/CAR for valvetrains, cranktrains and vehicleubsystems.

With reference to Fig. 6, by loading the Master macro a specificenu is added to the ADAMS menu bar. This awakens a form

epicted in Fig. 7 and loads a text file where all parameterseeded for the definition of the solid geometry of pump compo-ents are collected. The form �through tag windows� allows acti-ation of five macros that ultimately lead to the automatic genera-ion of the pump multibody model. This is effected on the base ofnput parameters �.txt file� and other inputs that the user loads inppropriate list boxes �e.g., number of pistons, swashplate angle,pring geometry, etc.�.

The first macro �Geometry create� leads to the generation of apecific component. Subsequently, each is positioned in concertith known parameters and the geometry shown in Fig. 8 is fi-ally achieved and visible. The second macro �Joint create� gen-rates constraints: some are predefined �e.g., the piston-slipperpherical joint�, others may be selected by the user in a list boxsee Fig. 7� to permit evaluation of different choices. The thirdacro �Force create� applies all forces within the pump unit with

he exception of those stemming from fluid pressures: more spe-ifically beside those associated with springs, mechanical end-stopnd more generally with intervening contacts, others are also ac-

1
In ADAMS a marker defines a point integral with a given solid body.
60 / Vol. 129, JULY 2007


counted that are evaluated by external subroutines �an examplewill be addressed in subsequent paragraphs�. The fourth macro�Friction create� introduces friction forces among constitutivecomponents whereas the last �AMESim interface� generates allhydraulic forces. These are outcomes from the AMESim code thatare transferred to ADAMS and updated at each communicationinterval.

The parametric 3D pump model can also be useful in the designprocess since the effects of a change in parameters is immediatelyvisible for mindful evaluation much as the fact that overall dimen-sions and geometric congruency may all be kept in control andappropriately corrected should the need arise.

Constraints in the Axial Piston Pump. Enforcing appropriateconstraints is equivalent to writing the dynamic equation for thevarious components �as those previously written for the piston�: itis on this factual consideration that the multibody approach quali-fies as a more intuitive and fast methodology than the “traditional”that involves the error prone process of writing a multitude ofequilibrium equations.

ADAMS offers a number of different constraints that removeone to three translational/rotational DOF �see Table 1�. Takingadvantage of this, different constraints may be applied to the unitand their relative merits and pitfalls appreciated. One typical lay-out showing the complete constraints for the pump is depicted inFig. 9. Regardless of the chosen layout, redundant constraintsmust be carefully avoided since redundancy invariably entailssimulation failures or, at best, erroneous results.

By way of example, if one considers the pump shaft and aims atdeveloping models of the journal bearings, among other solutions,the following may be proposed:

1. A revolute joint with the pump case: this allows shaft rota-tion but reaction forces from supporting bearings cannot bedistinguished.

2. A spherical joint for one bearing and an “in line” joint for

Fig. 6 Macros for automatic generation of the multibodysystem

the other: the disadvantage in this case is that a reaction



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axial force would be manifest at one bearing whereas in theother the reaction would simply not exist. In addition a re-dundant constraint may result as a consequence of jointsselected in the shaft-barrel �e.g., translational� and barrel-portplate �e.g., planar� pairs.

The layout in Fig. 9 avoids cited problems and also accounts forhe fact that the shaft-bearing pair can exhibit a certain degree ofompliance. All this is achieved through use of Bushings that arept to giving rise to a force proportional to position and relativeelocity of two markers. Bushings do not belong to the family ofoints �constraints� and therefore do not eliminate DOF but ratherntroduce a force. If high stiffness is desired this corresponds to aontact force between the shaft-bearing pair lumped at a givenoint. In this respect, while still making reference to Fig. 9, somedditional remarks will possibly be expedient:

• the symbol AME �with an arrow� indicates that on the ref-erenced component a force of hydraulic origin is applied.This force is evaluated in AMESim; the shaft transfers in-stead the torque required to drive the pump.

• to transfer the elastic force of the spring housed within thebarrel on to the slipper retaining plate, for each of three pins,two “in-plane” joints are applied at their extremities capableof enacting an axial force equal to 1/3 of the spring force�see also Fig. 10�. The pins rotate with the shaft while atranslational joint allows them to move in the axial direc-tion.

Fig. 7 Dialog box „GUI… for the ax

• The slipper-swashplate and barrel-portplate joints are of the



planar-type and corresponding gaps are therefore of constantheights. In fact, the planar joint originates the force andtorque needed to prevent axial translation and tilt of twosolid bodies in relative motion. However, this simplistic ap-proximation is being removed since the load carrying capac-ity of the fluid film within gaps is now being progressivelyaccounted via numerical solution of the appropriate Rey-nolds equation. In models developed earlier in AMESimonly the hydrostatic force contribution was evaluated by as-suming an analytic pressure distribution profile; the hydro-dynamic portion was then estimated as being the differencebetween the resultant of axial forces acting on the compo-nent and the hydrostatic quota.

A Piston Model Within ADAMS. Discussing the piston modeldeveloped in ADAMS it will be possible to bring to evidence theadvantage of making use of a multibody environment as well as todemonstrate that in some situations use of standard constraintslisted in Table 1 is not the appropriate choice for modelling acorrect mating of two components.

Figure 11 shows three different possibilities in constraining apiston with respect to the barrel and its slipper. While a sphericaljoint binding the piston-slipper pair is common to all schemes, thepiston-barrel pair may involve the following:

1. A cylindrical joint �Fig. 11�a�� allowing translation as wellas rotation about the piston axis. Though this is the simplestpossible constraint, it doesn’t lead to information regarding

piston machines multibody library

reaction forces at the piston’s extremities �see Fig. 3�.

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Fig. 8 Pump model automatically generated through macros in ADAMS

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Table 1 Joints and degree of freedom

Rotational DOF removed

0 1 2 3

Translation DOFremoved

0 = Perpendicular Parallel Orientation

1 in-plane in-plane + perpendicular planar in-plane + orientation2 in-line in-line +

perpendicularcylindrical translational

3 spherical Hooke revolute fixed

Fig. 9 A feasible constraints layout

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2. Two in line joints �Fig. 11�b�� both prevent translatory mo-tion along axis x and y and therefore corresponding reactionsare evaluated. However also this layout is inadequate inmodelling the real system since a reaction force in ADAMSis always applied in a specific point �marker� that identifiesthe position of the point. Now this point may either belongto the piston or the barrel.2 In the first case, when the pistonmoves beyond the barrel’s rim the fact that the reaction forceis effectively acting at the rim would be overlooked �see Fig.3, left�. In the second case, when the piston is completelywithin the cylinder �see Fig. 3 right�, the fact that the pointwhere the reaction is effectively active is now moving withthe piston would not be taken into account �Fig. 11�b�, point2�.

It is worth noting that the two preceding schemes besides in-olving inappropriate modelling also appear inadequate if tribo-ogic aspects were to be embedded in the system simulation

odel. In fact constraints imply ideal mating of involved compo-ents, with no clearances that would allow relative tilting or trans-ational motion. This holds true not only in the piston-barrel caseut in general: joints �e.g., planar� between barrel and portplate orlipper-swashplate preclude the possibility of simulating varia-ions of the indicated gap height in dependence of pump operatingonditions.

To solve problems and limitations just discussed, joints willave to be replaced with properly defined “forces;”3 in the ab-ence of a tribologic model these will behave as contact forces,amely, vanish when clearances fall within a specified intervale.g., in Fig. 11�c� the radial clearance between the piston-cylinderair� and, subsequently increase to the extent of representing end-tops for contacting components. A feasible model for such forcesan be written as follows �see the qualitative plot of a GFORCE inig. 12�:

F =� 0 if �y� � h

k��y� − h�sign�y� + cv�1 − e−3��y�−h�

d � if �y� � h�14�

being a relative velocity along the y axis; when y=h and aonzero velocity subsists, the exponential term precludes the oc-urrence of a force discontinuity.

It must be observed that ADAMS already features a contactorce model library. However, the present situation, where a 3Dodel is under consideration, would require use of the “solid to

olid contact.” This model heavily impacts simulation time andhe integration process tends to become unstable.

Figure 11�c� shows three forces �GF1,GF2,GF3� modelled by

2Reaction forces are applied at the marker of the first item selected in the paironstrained by the joint. Accordingly, it is possible that these will be either acting onhe piston �in axial translatory motion� or on the center of the cylinder �in rotationalotion about the shaft’s axis�, this depending on how selections have been made in

he process leading to joint creation.3ADAMS allows definition of generic forces �GFORCE� through analytic rela-

Fig. 10 Pump details

ions or external subroutines.



equations similar to Eq. �14�. Only two of such forces are simul-taneously applied. This, at the left end of the piston, allows acorrect simulation of the reactions bearing in mind that the pointof application is not fixed but rather moves with the piston.

Figure 13 collects simulation results for the three different con-straints layouts addressed above �delivery pressure 200 bar,1500 rpm and maximum displacement�. With the first layout ofFig. 11�a� �results on Fig. 13�a�� the cylindrical joint originates avertical reaction �piston equilibrium along the y-axis� and atorque. The latter restrains piston rotation about the x-axis. This isthe least informative constraints layout because only a single ver-tical reaction exists and it is applied at the marker of the cylindri-cal joint �integral with the piston� therefore there is no possibilityof obtaining information about reaction forces at the piston’sextremities.

Making use of two in line joints �layout on Fig. 11�b�� the two

Fig. 11 Possible constraints for the piston

Fig. 12 Example of end-stop force between piston and barrel

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ertical reactions are evaluated, the positive being applied at theeft end of the piston �see Fig. 13�b��. However, since the distanceetween the two joints stays fixed regardless of piston positionelative to the cylinder, the reaction modulus does not increasehen the piston moves out of the cylinder rim. In fact, in this

onfiguration the arm between the two forces decreases and con-equently it is expected that vertical forces increase to grant pistonotation equilibrium about the x-axis. Therefore results stemmingrom this modelling approach are not faithful to the real situation.

Instead, the ADAMS model shown in Fig. 11�c� �results in Fig.3�d�� practically yields the same results obtained with AMESimFig. 13�c��; the reaction reported in the continuous line is the sumf GF2 and GF3 forces, respectively, active when the piston pro-rudes from the cylinder and when it is sliding inside it �see con-gurations in Fig. 3�. It is also possible to note that the distanceetween the two vertical forces decreases when the piston movesut of the cylinder rim and, consequently, reaction forces increase.n addition, the model also accounts for the clearance in theiston-cylinder pair: piston position is now calculated and notnforced by the user. The considerable agreement of results at-ained via the AMESim mechanical and ADAMS multibody mod-ls leads to the conclusion that the co-simulation procedure doesot introduce spurious and adverse effects that could possibly im-air the proposed approach. This holds true as long as the com-unication interval is kept at a reasonably low value. For simu-

ation results presented in this paper the communication interval is0−5 s while the ADAMS integration step size is 10−6 s.

imulation and Experimental ResultsHaving considered in detail the case of a piston, additional

imulations will now be presented to demonstrate that even at aider and more general perspective, the multibody model results

onform quite favorably with traditional outcomes. In fact, theimulation takes now into account the presence of various dis-lacement controls �see Gilardino et al. �12� and Mancò et al. �2��nd precisely an absolute pressure limiter �LPA�, a differentialressure limiter �LPD� and a torque limiter �LC�. All these hy-raulic controls were simulated in AMESim. The only interfaceith the mechanical model concerns two forces originating from

he contrasting and displacement actuators �see Fig. 8�.Figure 14 presents shaft torque and delivery pressure time his-

Fig. 13 Comparison between sim

ories, the latter being an input to the ADAMS model. Shaft

64 / Vol. 129, JULY 2007


torque obtained via the multibody model closely matches tradi-tional results: in both cases and up to t=0.35 s the torque in-creases with pressure and is thereafter held almost constant due tothe torque limiter control that causes swashplate tilt to decrease as

Fig. 14 AMESim vs ADAMS „cosimulation… results: pressureand shaft torque

Fig. 15 AMESim vs ADAMS „cosimulation… results: swash-

ion results: piston-barrel reaction
ulat
plate tilt



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hown in Fig. 15 �at t=0.35 s shaft torque is 100 N m, equal to theorque limiter setting�. When delivery pressure reaches the abso-ute pressure limiter setting �at t=0.8 s� torque is decreased fur-her.

Figure 15 further indicates swashplate tilt time history and onceore results match in a quite satisfactory manner. The torque

imiter �LC� and absolute pressure limiter �LPA� interventions arelearly identified. However a slight mismatch exists at pump’saximum displacement conditions. The traditional model shows

hat tilt stays constant at its maximum value bound to pump ge-metry while the multibody model evidences an increase in tilt ofbout 0.12° �delivery pressure 125 bar, see Fig. 16� followed by aecrease induced by displacement controls. Recent experimentalnvestigations at the Fluid Power Research Laboratory involving

easurements of swashplate tilt via an LVDT transducer locatedt the contrasting actuator axis �see Fig. 17, pump CasappaVP48�, seem to confirm that in real operation a slight increase ofhe maximum tilt angle is observed as delivery pressure is in-reased. The multibody model helps in understanding this finding.ome supporting devices and mechanical end-stop �specific is thease of the displacement actuator and of the swashplate� haveeen modelled with high stiffness springs that, while opposingpplied forces, undergo a compression. When the pump is oper-ted at maximum displacement, the contrasting actuator applies tohe swashplate a force proportional to delivery pressure;4 thisorce is transferred to the displacement actuator that is in contactmechanical end-stop� with the pump cover and therefore decidesn the maximum swashplate tilt �see Fig. 17�. Since these forcesre of the order of 103 N, involved materials may undergo localeformations that provide a possible reason for the cited increasen maximum tilt with delivery pressure.

Figure 18 details a comparison between experimental and simu-ated steady-state characteristics for swashplate tilt and shaftorque �@1500 rpm, LPA setting 280 bar, LC setting 100 N m�.xperimental data were sampled at 10 kHz and their averages

aken over a time window of 2 s. Upon setting the flow area of anrifice located downstream the pump delivery port, data acquisi-ion began when the pressurized system had reached steady-stateonditions. Simulated data have been obtained by use of AMESimnd also through co-simulation of the ADAMS-AMESim soft-are. In both instances, the characteristics are generated automati-

ally by a submodel developed at FPRL; this fixes the orifice flowrea and tracks some specific variables �e.g., delivery pressure,orque and tilt�. When all observed variables have reached ateady-state condition �defined through explicit criteria� one pointf the characteristic is gathered and stored. Subsequently the flowrea is changed and the procedure repeated until completion.rom the reported plots it is possible to observe a fair matching

4

Fig. 16 Experimental swashplate tilt

The actuator is permanently connected to pump deliver through a pilot line.



between experimental and simulated data using either AMESim orco-simulation �in this last case ADAMS evaluates shaft torque andswashplate tilt�.

Figure 18 demonstrates that the multibody model can correctlysimulate the mechanic behaviour of the pump as was already thecase with AMESim. As for the simulation time required by thetwo approaches in yielding data reported in Fig. 18, see AppendixB.

Figure 19 shows a snapshot relative to an animation frame ofthe rotating pump where almost all forces �associated with vec-tors� acting on the barrel are visible. A 3D graphic engine as thatbuilt into ADAMS is extremely useful for analyzing and investi-gating phenomena that occur in the unit while in operating condi-tions. Looking at reaction forces on the barrel originated by pis-tons, it can be perceived that these tend to tilt the barrel in thecounterclockwise direction. The effort is balanced by the reactionforce of the shaft. Therefore, the possibility of having a 3D visualcue of simulation results represents an invaluable advantage of themultibody model; however, this as well as other “merits” entail an

Fig. 17 Swashplate tilt measurement

Fig. 18 Screenshot during ADAMS animation

JULY 2007, Vol. 129 / 465


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ncrease in simulation time that in the specific co-simulation dealtith in this paper can be five times higher than in the traditionalodel.

ritical Analysis of Models and PerspectivesPrior to the beginning of the analysis of axial piston hydrostaticachines through a multibody approach a library developed in theMESim environment was available and apt in simulating theechanical and hydraulic behavior of axial piston pumps and mo-

ors inclusive of the dynamics of the swashplate and shaft �forrevity reference will generally be made to pumps�. The will ofmplementing also the analysis of tribologic phenomena led to thedoption of the MSC-ADAMS multibody software.

The principal advantages attained through this choice are asollows:

�1� It is possible to simulate the dynamics of all principal com-ponents of the pump, not only of the shaft and swashplate.In particular, the possibility exists of predicting the relativepositioning of the intervening bodies of tribologic interest�barrel-portplate, piston-cylinder and slipper-swashplate�.

�2� In an analogous fashion to the previously discussed pistoncase, it is no more necessary to write complex kinematicand equilibrium equations; it is indeed possible to concen-trate only on the proper assessment of constraints and act-ing forces,

�3� Models developed through AMESim libraries have beenvalidated experimentally as to the principal and measurablehydraulic and mechanical quantities �delivered and drainedflows, shaft torque, instantaneous delivery pressure, dy-namics of the swashplate�. The multibody model has alsoallowed to obtain a verification on forces and reactions ex-changed among principal components. Even if that was not

Fig. 19 Experimental and simu

an experimental verification �often impossible in specific

66 / Vol. 129, JULY 2007


cases�, the attainment of very similar results with two ratherdifferent approaches contributes proper ground in confirm-ing the inherent significance of developed simulation mod-els.

�4� The elected multibody software is open to external librariespurposely construed for the analysis of more complexforces, e.g., those stemming from pressure distributions ingaps of fundamental interest.

The main disadvantages bound to the adoption of a secondsimulation environment are not only confined to a sensible in-crease in computation time while in the co-simulation mode. Infact co-simulation has brought to evidence numerical instabilitieswhen the communication interval and integration time step ofboth software codes are improperly tuned. In recent developmentsof the multibody model and more specifically when the numericalanalysis of the barrel-portplate pressure field has been introduced,the decision was taken of using solely the MSC-ADAMS envi-ronment to circumvent such delicate tuning problems. In such asituation it is necessary to accept the assumption that the pumppossesses a constant displacement and assess a lookup table whereinstantaneous pressures within cylinders are collected as functionsof shaft angular position. By doing so, just the mechanical behav-ior is simulated �the hydraulic in fact becomes an input� this lead-ing to a much more stable and fast computation.

For what has been stated, the presented multibody model ispotentially apt for the investigation of tribologic phenomena; atpresent, research work is progressing aiming at putting these po-tentials into an effective fruition. In greater detail:

�a� At FPRL a method has been developed grounded on stud-ies by Wang et al. �13,14� to numerically solve the Rey-

ed steady-state characteristics

nolds equation. This has already been applied to the



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analysis of the slipper-swashplate and barrel-portplate lu-bricated gaps;

�b� The pressure field so evaluated is then integrated andmapped into a resultant force that replaces that utilizedpreviously while simulating in a rather simplistic fashionthe effects of hydrostatic and hydrodynamic forces �rela-tions similar to Eq. �14��;

�c� This resultant force is implemented in the multibodymodel through external libraries: MSC-ADAMS inte-grates solid bodies positions in space.

Points addressed above qualify the final aim of this study andighlight the importance of using a multibody code. Reaching inact just point a� useful information on tribologic forces wouldave been obtained but at the expense of being unable to simulatehe dynamics of bodies subject to forces that vary with positiongap height�, tilt and axial velocity �e.g., the barrel case�. From theoint of view of thermal effects at present the model is still lim-ted to isothermal conditions. In this respect it must be pointed outhat other researchers already consider nonisothermal models �seevantysynova et al. �15��.

onclusionsIn this paper reasons that led to radical changes in simulation

ools adopted in the mechanical modelling of axial piston pumpsave been elucidated: the most significant being associated withhe need of laying proper ground to model tribological aspectsegarding the barrel-portplate, piston-cylinder and slipper-washplate pairs. Along this research path a library was developed

Fig. 20 Geometric parameters for the pump

n ADAMS, hinged on macros that eventually lead to generate the



entire unit automatically and in full parametric description. Themodel interfaces with AMESim where hydraulic modelling is per-formed and evaluated.

Attained results have been contrasted with those proper to thetraditional model with the conclusion that the ADAMS mechani-cal approach can quite effectively replace the one originally de-veloped in AMESim with the additional and fundamental merit ofallowing investigations of phenomena that otherwise would havebeen forcibly left unattended.

Along this research frame the multibody model is being furtherdeveloped to also account for tribologic aspects. This will hope-fully lead in the near future to a modelling tool capable of accu-rate portrayal of the three basic domains to be considered in ahydrostatic unit and precisely the hydraulic, mechanical and tri-bologic.

NomenclatureD piston diameter

DAE differential algebraic equationsDOF degrees of freedom

Fi inertia forceFc centrifugal force

Fpr pressure force acting on the pistonFpit barrel reaction force on the piston

Fpipa slipper reaction force on the pistonG piston center of gravity

LC torque limiterLPA absolute pressure limiterLPD differential pressure limiter

N number of pistonsO projection of point O� on shaft axis

O� projection of point O� on swahsplate planeO� swashplate rotation center

ODE ordinary differential equationsP center of the piston-slipper ball-jointQ center of the slipper’s circular surface �swash-

plate side�Rm shaft axis-piston axis distance

W weight forceb1 piston length from the ball joint center

bpit1 Fpit1 arm along the z-axisc damping coefficient

dG distance of the piston’s ball joint center fromthe piston center of gravity �GP�

ds distance of the piston’s ball joint center fromthe slipper surface �PQ�

dO distance of the swash plate surface from theswash plate rotation center �O�O�, positive ifzO��zO��

e swashplate eccentricityg acceleration of gravityh radial clearance between piston and barrelk stiffness

m piston massp pressuret time

z, v, a position velocity and acceleration�, �̇, �̈ swashplate angular position, velocity and

acceleration� j angular position of the piston j� AMESim-ADAMS communication interval

�, �̇ shaft velocity and acceleration�� j jth piston or slipper

��x/y/z components along the x, y, z axis

Appendix A: Determination of Eqs. (6), (7), and (8)
The coordinate z of point P is given by �see Fig. 20�
JULY 2007, Vol. 129 / 467


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zP = L1 + L2 + L3 �A1�

eing lengths L1, L2, L3 functions of parameter values that definehe pump geometry ��, �, Rm, e, ds, dO�. In particular,

L1 = Rm · cos � · tan � �A2�

L2 = e · tan � �A3�

2 accounts for the fact that an eccentricity may exist for thewashplate, this meaning that the swashplate axis of rotation go-ng through O� and directed along x does not intersect the pistonsxis of revolution z. From a mechanical point of view, this eccen-ricity allows the torque generated by forces exchanged betweenlippers and swashplate in originate in a tilt of the swashplate thatay either increase or decrease pump displacement.5 As an ex-

mple, in the situation shown in Fig. 20 eccentricity induces aeduction in displacement. A proper of the contrasting actuatornd a suitable choice of the eccentricity value allow a relationetween discharge pressure and pump displacement to be estab-ished to enforce a power limit on the pump unit �see Mancò et al.16��. The last addend to Eq. �6� comes from

L3 =ds − dO

cos ��A4�

umming up all contributions �Eqs.�A2�, �A3�, and �A4�� Eq. �6�s demonstrated,

zPj = Rm · cos � j · tan � +ds − dO

cos �+ e · tan �

hence piston speed and acceleration along z can be obtained.

ppendix B: A Note on State Variables and SimulationimeWhile in the co-simulation mode, ODE and DAE state variables

eing integrated in AMESim amount to 34. Essentially these in-olve instantaneous pressures within cylinders, absolute, differen-ial and torque limiter, suction and delivery volumes as well asositions and velocities of spools in cited limiters. ADAMS in-tead, through its solver, integrates a set of 15 state variables forach of the 33 constituent solid bodies of the pump model �seeegrut et al. �17��.The following table collects information regarding the simula-

ion time for spawning the steady state characteristic shown inig. 19. Utilizing a communication interval of 10−4 s theDAMS-AMESim co-simulation involves a time span 2.5 times

onger than that required by AMESim. Smaller communicationntervals would permit higher precision but at the expense of a

5Hydrostatic forces pushing pistons onto the swashplate also depend on pressurealues in each cylinder that are in turn dependent on piston angular position � and

Table 2 Simulation time for steady-state characteristic

AMESim ADAMS-AMESim

imulation time to complete ateady-state char. �min�

109 240 ��=10−4 s�

ardware Processor: Pentium 4 HT 3.20 GHZMemory: 1.50 GB RAM; 1 MB L2 cache�50% CPU usage due to HT technology�

ltimately on portplate geometry.

68 / Vol. 129, JULY 2007


longer simulation time. However, results in Fig. 19 indicate that asatisfactory precision was achieved and no instabilities becameapparent while co-simulating.

Table 2 collects time information for producing the steady statecharacteristic shown in Fig. 19 by means of 21 simulated operat-ing points. These altogether indicate that a satisfactory matchingwas achieved. A preliminary analysis of transient pump perfor-mance can normally be acquired through one shaft turn. This canbe done in less than 3 min in AMESim and in slightly over 6while co-simulating.

Table 3 shows the time needed to run all macros originating thepump multibody model and to export data needed for co-simulation.

References�1� Caretto, R., Mancò, S., Nervegna, N., and Rundo, M., 1996, “Modelling,

Simulation and Experimental Studies on a Variable Displacement Radial Pis-ton Pump Prototype for Automotive Application,” FPST- vol. 3. Fluid PowerSystems and Technology, 1996 Collected Papers. The 1996 ASME Interna-tional Mechanical Engineering Congress and Exposition, Nov. 17–22, Atlanta,GA, pp. 1–9.

�2� Mancò, S., Nervegna, N., Lettini, A., and Gilardino, L., 2002, “Advances inthe Simulation of Axial Poiston Pumps,” 5th International Symposium onFluid Power JFPS, Vol. 1, pp. 251–258.

�3� Ivantysynova, M., 2003, “Prediction of Pump and Motor Performance byComputer Simulation.” 1st International, Conference on Computational Meth-ods in Fluid Power Technology, Melbourne.

�4� Schiehlen, W., 1997, “Multibody System Dynamics: Roots and Perspectives,”Multibody Syst. Dyn., 1�2�, pp. 149–188.

�5� Deeken, M., 2003, “Simulation of the Tribological Contacts in an Axial PistonMachine,” Ölhydraulik und Pneumatik, 11–12, pp. 235–242.

�6� Antoszkiewicz, P., and Piechnick, M., 2002, “Simulation of a Hydraulic Vari-able Axial Piston Double Pump of Bent Axis Design With Subsystems,” The1st MSC.ADAMS European User Conference, London.

�7� Deeken, M., 2002, “Simulation of the Reversing Effects of Axial Piston PumpsUsing Conventional CAE tools,” Ölhydraulik und Pneumatik, 6, pp. 315–322.

�8� Deeken, M., 2005, “Simulation Hydrostatischer Verdrängereinheiten Mit HilfeModerner CAE-Werkzeuge,” Ölhydraulik und Pneumatik, 11–12, pp. 600–603.

�9� Kudav, G., Kasper, L., Zhang, H., and Kimpel, R., 2005, “Development of aHeavy Duty Piston Pump Using Flexible Body Approach,” Proceedings of the50th National Conference on Fluid Power, pp. 349–359.

�10� Larsson, P., Krus, P., and Palmberg, J. O., 2001, “Modelling, Simulation andValidation of Complex Fluid and Mechanical Systems,” 5th International Con-ference on Fluid Power Transmission and Control, �ICFP2001�.

�11� Rahmfeld, R., 2003, “Modelling of Hydraulic-Mechanical Systems—Co-Simulation between ADAMS and Matlab/Simulink,” Lectures for Design ofMechatronic System I+II Using CAD.

�12� Gilardino, L., Mancò, S., Nervegna, N., and Viotto, F., 1999, “An Experiencein Simulation: The Case of a Variable Displacement Axial Piston Pump,” 4thJHPS International Symposium on Fluid Power, Tokyo, pp. 85–91.

�13� Wang, X., and Yamaguchi, A., 2002, “Characteristics of Hydraulic Bearing/Seal Parts for Water Hydraulic Pumps and Motors. Part I,” Tribol. Int., 35, pp.425–433.

�14� Wang, X., and Yamaguchi, A., 2002, “Characteristics of Hydraulic Bearing/Seal Parts for Water Hydraulic Pumps and Motors. Part 2: On Eccentric Load-ing and Power Losses,” Tribol. Int., 35, pp. 435–442.

�15� Ivantysynova, M., and Huang, C., 2005, “Thermal Analysis, in Axial PistonMachines Using CASPAR,” 6th International Conference on Fluid PowerTransmission and Control, Hangzhou, China.

�16� Mancò, S., Nervegna, N., Lettini, A., and Colella, L., 2003, “Simulation of aSplit Delivery Pump,” 18th International Conference on Hydraulics and Pneu-matics, Prague, pp. 448–461, ISBN 80-02-01567-3.

�17� Negrut, D., and Dyer, A., 2004, “ADAMS/Solver Primer,” MSC. Software

Table 3 Time for macros „ADAMS…

ADAMS macros

Time needed to generate the multibodymodel through macros �s�

12

Documentation, Ann Arbor.



modelling a variable displacement axial piston...

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