hydraulic pump model published 09/13/2011

17 January 2022

Modeling of an Excavator System – Semi empirical hydraulic pump model / P. Casoli; A. Anthony; M. Rigosi. - In: SAEINTERNATIONAL JOURNAL OF COMMERCIAL VEHICLES. - ISSN 1946-391X. - 4(2011), pp. 242-255. [10.4271/2011-01-2278]

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ABSTRACTThis paper describes the preliminary results of a studyfocused on the semi empirical modeling of an excavator'shydraulic pump. From the viewpoint of designing and tuningan efficient control system, the excavator is a very complexnonlinear plant. To design and tune such a complex controlsystem an extremely good nonlinear model of the plant isnecessary. The problem of modeling an excavator isconsidered in this paper; a nonlinear mathematical model ofan excavator has been developed using the bond graphmethodology realized in the AMESim® simulation softwareto replicate actual operating conditions. The excavator modelis described by two models: a hydraulic model and akinematic model. At this stage of research the hydraulicmodel deals solely with the model of the main hydraulicpump, which has been conceived as a semi empirical model.The pump model has been conceived as a grey box model;where the flow compensator and pressure compensator havebeen modeled as white box models while the actual flowcharacteristics of the pump as a black box model. The otherexcavator hydraulic system components comprising of valveblock and actuators have been created using genericmathematical models. This approach has been followed toenable the study of the pump's dynamic behavior andinteraction with a completely developed kinematic model ofthe excavator. Dynamic loading of the system has beenrealized through a 2D kinematic model of the excavator'sbody elements. The kinematic model comprises of the boom,arm and bucket whilst their respective motions have beendefined for a cycle of operation. The dynamic parameters ofeach element are continuously calculated during anexcavation cycle, thereby providing a platform to study thepump's behavior. At this phase of model development the

semi empirical model of the variable displacement pump hasbeen validated on the basis of a set of experimental datacollected on a test rig at particular experimental operatingconditions. The final objective of this study would be todevelop a complete mathematical model of the ExcavatorHydraulic Control System and in turn facilitate the study ofalternate control strategies towards energy efficient systems.This paper presents the results of this study.

KEY WORDSHydraulic Excavator, Semi Empirical Modeling, VariableDisplacement Pump

INTRODUCTIONThe development of control systems for complex mechanicalsystems such as large manipulators, mobile cranes andexcavators requires the use of powerful softwaredevelopment tools. This is particularly true, where a shortcommissioning period is desired. Here, the complete control-system must be developed and tested by simulation methods.This requires a comprehensive software package formechatronic systems, consisting of a modeling andsimulation part and a control development part. Thesimulation of the kinematics and dynamics of multi-bodysystems is a topic of increasing importance in many industrialbranches, due to its potential for reducing costs and that itprovides insight into inherent effects governing the systemsbehavior. At a more detailed level, simulation offersenhanced product assessment, the potential of early stageconceptual testing, and a virtually unlimited spectrum of“what if” analysis [7]. Towards realizing this objective amodel comprising of a hydraulic and kinematic systems havebeen developed. The need to model these systems is

Modeling of an Excavator System - Semi EmpiricalHydraulic Pump Model

2011-01-2278Published

09/13/2011

Paolo Casoli and Alvin AnthonyUniversita di Parma

Manuel Rigosi

Copyright © 2011 SAE International

doi:10.4271/2011-01-2278

SAE Int. J. Commer. Veh. | Volume 4 | Issue 1 (October 2011)242

http://dx.doi.org/10.4271/2011-01-2278

attributed to the inherently nonlinear hydraulic drive, used toachieve precise motion and power control. This choice ofdrive is imputed to the superior power density of hydraulicsystems in comparison to electrical or mechanical drives;regrettably the indigent energy efficiency of these systems isa major drawback. The need for energy efficient systemsdemands that this potent drive be self adjusting to meet actualload requirements [12]. A method of adjusting these systemsto meet load requirements is by controlling the flow of apump. In this context, variabledisplacement axial pistonpumps are often used, whereby the displacement of the pumpcan be varied by tilting a swash plate. This can be achievedfast enough to meet the dynamic demands affected bymultiple loads. In this research, a nonlinear pump model hasbeen developed, which takes into account the essentialnonlinearities of the system and can be easily adjusted topumps of different displacement sizes in the same modelrange. A practical pump model must enable one to examinethe dominant characteristics influencing the behavior of thepump. In a load sensing pump this would include theresponse of the pressure and flow compensators in addition tothe sensitivity of swash plate motion which defines thepump's displacement. This model can be conceived in anumber of ways either as purely mathematical, empirical or amix of the two as a semi empirical model. The approach ofsemi empirical modeling of the pump has been adopted inthis paper, thereby providing a basis to rapidly examinedifferent pump sizes to vary the flow gain of a completeexcavator with the objective of achieving desired designcharacteristics. The pump displacement is controlled by thehighest pressure feedback generated from the excavator'sactuators, in an operating cycle. To subject the pump to thesevarying forces a detailed model of the kinematics has beenrealized. Due to the complexity of the whole system, dynamicforces are required for computing the load on the systemwhich is achieved by the kinematic model of the excavator.Previously published research comparisons describe thedifferences between these static and dynamic forces [7]. Thenonlinear effects occurring during the excavation cycle suchas the bucket-soil interaction and the nonlinearities of thehydraulic system complicate the control of the pump. Thesefactors have to be taken into account in hydraulic modelingand control. The above details provide a glimpse into thecomplexity of variable forces that a system would experienceduring an operating cycle for which the variable pumpcompensates its displacement. Thus far, having described theobjective of this research, the following sections will detailthe modeling of the pump, the excavator kinematics andvalidated results of the pump model.

PHYSICAL MODELINGPUMP MODELThe pump model described in this paper is that of a loadsensing variable displacement axial piston pump. This is astandard line production pump developed by Casappa SpAand belongs to the MVP series. The study of optimaldisplacement control of variable displacement pumps hasbeen a topic of interest for fluid power researchers' worldover and continues to provide scope for development withelectro hydraulics and recent advances in robust controlstrategies. To set the pace of study, this paper describes thecurrent stage of model development and will detail the actualpump being produced, i.e. with classical hydraulic feedback.As depicted in Fig.1, the pump model comprises of three sub-models a flow compensator, pressure compensator and theflow characteristics. The pump model has been conceived asa grey box model, i.e. a model based on both insight into thesystem and experimental data as can be seen in Fig.2. Theflow and pressure compensators have been modeled as whitebox models and that of the flow characteristics as a black boxmodel. The grey box model of the pump correlates thecontrol piston pressure and the system pressure to provide theequilibrium of forces that defines the swash plate angle. Thismodel approach has been adopted to provide themanufacturer with the flexibility of selecting pumps withdiscrete maximum displacements to vary the completesystem's gain.

Fig. 1. Model breakup of the MVP series, Load SensingVariable Displacement Pump

Fig. 2. Grey Box modeling methodology

SAE Int. J. Commer. Veh. | Volume 4 | Issue 1 (October 2011) 243

The mathematical models of the flow compensator, pressurecompensator and flow characteristics have been developedusing the bond graph methodology realized through theAMESim® simulation software. This methodology uses thetransfer of power between elements to describe the dynamicsof the system. The basic idea being - the direction of powerflow at any moment in a system is invariant. Power may beexpressed as a multiplication of two factors - generalizedeffort and generalized flow. Bond graphs are far morepowerful in modeling complex systems which involve theinteraction of several energy domains [2].

Flow Compensator ModelThe flow compensator (FC) has the most important functionof offsetting the pump displacement for a set preload byregulating the swash plate angle. This component has beenmodeled and verified in great detail [10].

The logic integrated in the FC is to compare the dominantload pressure (PLS) with the pump's output pressure (PS) tomodulate the flow through the FC, hence regulating thepump's displacement. The objective of the FC is to maintain afixed differential pressure across the control orificeaccomplished by modulating the pump's flow. The FC'sspring comprises of two springs one being a snubber spring.This arrangement has been adopted to provide a snubbingfunction - thereby resiliently biasing the spool from the firstoperating position to the second operating position, when thefluid pressure in the LS chamber is increased from a firstpressure level to a second pressure level. This feature has anattribute of controlling pressure spikes more carefully due tothe precise metering characteristics of the valve, thusreducing the oscillations on the swash plate.

The functioning of the FC as depicted in Fig.3 and Fig.4 issuch that the pump pressure enters the FC valve through thechamber A. The pressure entering this chamber acts on thearea of spool 1 to create a force. This is realized in the modelby means of a transformer element, in the form of spool 1,where the modulus of the transformer is the ratio between thespool - piston and rod area. The force created by the pumppressure on spool 1 is countered by the force created by thesprings 5 and the LS pressure which is sensed in chamber D.The sum of these two forces i.e. spring 5 and the LS pressureacting on the area of piston 4 is the force value used tomaintain the force balance of the spool. When the pumppressure is greater than the force on piston 4, the spool isdisplaced to the left creating a flow path between chamber Aand chamber B, referred to as the intermediate chamber. Theflow through this chamber has the function of varying thepump's swash plate angle, and in this way the pumpdisplacement is regulated. Chamber C is connected to tankand its function is to drain the oil from the intermediatechamber. Spool 2, has been modeled as a transformer elementwith the modulus being the area ratio between the spool -

piston and rod. Leakage models have been included asdepicted in 3 (Fig.4) to describe internal leakage betweenchambers and to increase the system damping.

Fig. 3. CAD model of the Flow Compensator

Fig. 4. AMESim® model of the Flow Compensator

The governing equations are described by the interactionbetween a fluid-dynamic model (FDM) and a mechanical-geometrical model (MGM). The FDM calculates thepressures inside the chambers and the flow rate betweenadjacent chambers, while the MGM calculates the forcesacting on the spool and determines its dynamics and the flowareas.

The FDM is based on a lumped parameter framework. Thepressure inside each control volume is assumed uniform andtime dependent, and is determined by the pressure-rise rateequation:

(1)

The model assumes a constant value of fluid temperature.The fluid density is evaluated as a function of pressure asdescribed in [8]. The summation term represents the net massflow rate entering or leaving the volume. This is obtained byconsidering the contribution of all orifices connected with theconsidered volume. The mass exchange occurring through theorifices is calculated using the generalized Bernoulli'sequation under quasi-steady conditions, Eq. (2):


(2)

The user sets an appropriate saturated value for thecoefficient of discharge of each connection, on the basis ofexperimental data or using values reported in literature, suchas [8, 9]; thereafter the instantaneous coefficient of dischargevalue is evaluated as a function of Reynolds number, toaccount for partially developed or fully turbulent conditions.Annular leakages past spool bodies have been evaluatedusing Eq. (3) as reported in [8, 9]:

(3)

The mechanical model calculates the instantaneous positionand velocity of the spool using Newton's second law:

(4)

The forces acting on the spool, Fig.4, are: hydrostatic forces;spring force; friction forces; hydrodynamic forces. Static anddynamic friction forces are evaluated by use of the Karnoppfriction model and considering the Stribeck effect; static anddynamic friction coefficients are assumed constant; thehydrodynamic forces are proportional to the orifice flowsectional area and pressure drop across the orifice, the modelimplements the equation:

(5)

where the jet or flow angle θ is affected by chambergeometry, orifice clearance and sharpness; for spool valveswith a sharp edged orifice and no clearance between spooland sleeve, θ can be assumed equal to 69° [3]. The otherassumptions are that fluid inertia is neglected; springs areassumed linear.

Pressure Compensator ModelThe function of the pressure compensator (PC) is that of arelief valve and its function is to limit the maximum pressureof the system, Fig.5. The relief valve provides an alternateflow path to tank while keeping the system pressure at therelief valve setting. The relief valve realized in the PC is thatof the direct operated type, it operates with a spring to pre-load the valve spool. Since a small flow rate is passedthrough the spool, the set pressure can be maintained withnearly no effect on the pressure flow characteristics of the

valve. The functioning of the PC is such that the systempressure enters the PC through chamber E (Fig.6) and thepressure acts on the area of spool 6 to create a force, whichresists the force created by the spring 8 and spool 9, creatinga relief setting pressure. When the system pressure is greaterthan the relief setting pressure, the spool 6 is displaced andcreates a flow path to the swash plate actuating piston and totank through an orifice S1 (Fig.6), which is housed in the PCvalve. The governing equations describing the physicalbehavior of the PC are the same as those described in thesection on the modeling of the flow compensator.

Fig. 5. CAD model of the Pressure Compensator

Fig. 6. AMESim® model of the Pressure Compensator

Flow Characteristics ModelA model of the pump's flow characteristics must permit theexamination of dominant characteristics influencing thepump's behavior. In a load sensing pump this would includethe response of the pressure and flow compensators inaddition to the sensitivity of swash plate motion whichdefines the pump's displacement. Due to intricaciesencountered in the control, design and implementation of thistype of pump, it is advantageous to have a comprehensivemodel of the pump. Such a model would include determiningthe motion of the pump's swash plate based on theinstantaneous operating conditions. To achieve this, themodel must include the effects of friction acting on internalcomponents, accurate determination of pressure in thepumping pistons and the effects of the swash plate motion onthe control actuator. The model must reflect both the supplyflow characteristics of the pump as well as the dynamicbehavior associated with the internal components in the pumpitself.


In practice the accurate prediction of swash plate motion isthe exclusive parameter required to represent an axial pistonpump, as all pump components interact with the swash plateto determine its motion. The angle of the swash platedetermines the stroke of the pumping pistons, the length ofwhich dictates the flow characteristics. The prediction of theswash plate motion is made difficult due to the excitingforces imparted on the swash plate by the pumping pistons aswell as the compressibility of the fluid in the control piston.The bond graph model of the pump Fig.7, describes that thenet torque acting on the swash plate comprises of the torquecontributed by the swash plate inertia, pumping pistonstorque, return spring torque, control piston torque anddamping effects. These torque values define the swash plateangle to the transformer that modulates the pump'sdisplacement. Regrettably the white box model approach isquite elaborate and does not afford the flexibility required toexamine pumps of different sizes as all the constants (pistonmass, lengths and diameters, swash plate mass, damping,valve plate geometry etc.) would have to be modified toadopt a different pump.

Fig. 7. Bond graph representation of the Pump

The objective of this research has been to adopt a techniquefor identifying the dominant characteristics of a pump and tofacilitate the study of different pump sizes in a feasiblemanner. This flexibility has been integrated into the model tostudy the flow gain offered by different pumps to the system.The black box system identification was identified as the bestmodel methodology to integrate this flexibility. This choiceof modeling methodology was also attributed to theavailability of an instrumented test facility and a large sampleof experimental data. The black box model was realized bytaking into account that the position of the swash plate couldbe determined by solely balancing the parameters of thecontrol piston pressure and the system pressure. The controlpiston pressure is the pressure in the actuator that is used todisplace the swash plate. The control piston receives its inputfrom the flow/pressure compensator, depending on the stateof the system. The system pressure is the pressure that acts on

the swash plate to determine the forces on it. The forcesacting on the swash plate affected by the system pressurecomprises of the forces exerted by the pumping pistonsexposed to the load and the internal friction forces.

Fig. 8. Correlation between control pressure and systempressure for swash angle position at 1000 r/min

The authors have experimentally obtained a linear relationbetween the control piston pressure and the system pressure.It was found that the functioning of the pump in differentswash angle positions can be defined by two equations. Thefirst equation (6), as depicted in Fig. 8 curve I, describes thecontrol piston pressure (PC) versus the system pressure (PS)that would be needed to initially displace the pump from itsmaximum swash angle position.

(6)

The second equation (7) is the pressure balance relation forthe intermediate positions. Experiments were carried out bymaintaining the swash plate at different positions and varyingthe load. From these tests it was observed that for the variousintermediate swash angle positions, the pressure relationshipswere found to overlap. Equation (7) was derived byinterpolating the family of curves depicted in Fig.8 curve J.

(7)

The flow characteristics model has been realized by the useof two pistons - the control piston, 10, and the barrel forcespiston, 11 (Figure.10), defined by the system pressure. Therelation between these two equations has been realized by aconstant value in the simulation model which has been usedto switch between the two equations when the swash plate isdisplaced from its initial position. After the swash plate angleshifts from maximum swash position, the model utilizes acorrection factor of 0.644 and a different constant force tomodify the pressure relationship described by equation (6)into equation (7). A transformer element in the form of alever is used to balance the forces from the two pistons. The


linear displacement of the control piston actuator is measuredand converted into the swash plate angle. An orifice 13, (Fig.10) with a fixed area has been used to realize the function ofinternal leakages of the pump and to simulate the pump'sdrain characteristics.

Fig. 9. Cross section view of the swash plate and controlpiston

Fig. 10. AMESim® representation of Fig. 9

Although it is known that the leakage flow is a complex termand is best represented experimentally, it was found that theuse of a specific flow area provided fairly reliable flowcharacteristics.

The pump's end stop has been simulated by the use ofelement 12. The model of the pump's flow characteristics hasbeen created by use of an ideal pump element 14 (Fig.10).The use of the fixed orifice to replicate the draincharacteristics provides for fairly reliable flow characteristics.Future work would include maps of the mechanical andvolumetric efficiency to replace the drain orifice 13 and todrive the pump's flow characteristics model.

EXCAVATOR DYNAMICSThis section describes the modeling of the excavatorkinematics which has been used to create the realistic forceson the hydraulic actuators. Considering the benefits of havingthe kinematic model integral with the hydraulic model, thelinkage parameters were coupled to the hydraulic modelusing the Planar Mechanics library of AMESim® [4, 6]. Thisfacilitates the understanding of dynamic loads on thehydraulic cylinder. The driving joint torques of the boom,arm and bucket are generated by the forces of the hydraulicram actuators. The translational and rotational motions ofthese links are described by the dynamic model of theexcavator system. The kinematic model has beenincorporated as a lumped parameter model, which accountsfor angular position, relative coordinates, distances betweenlinks, relative velocity, relative acceleration and the outputforces. Joint forces of contact and stiffness, are alsoconsidered in the model. The equations of motion can bederived by applying the Euler-Lagrange equations to aLagrangian energy function. The revolute pairs have beenmodeled as Lagrange multipliers and are calculated from theBaumgarte stabilization method applied to the constraintequations [11].

To further enhance the force simulation of the model, thevisco-elastic properties of the material being handled havebeen recreated as a force during the excavation process. Animpulse force which acts on the bucket during soilpenetration has been included as described in [5]. The motionof the excavator implements would be to follow a pre-planned digging trajectory. During digging, three maintangential resistance forces arise: the resistance to soilcutting, the frictional force acting on the bucket surface incontact with the soil and the resistance to movement of thesoil ahead of and in the bucket. The magnitude of the diggingresistance forces depends on many factors such as the diggingangle, volume of the soil, volume of material ripped into thebucket, and the specific resistance to cutting. These factorsare generally variable and unavailable. Moreover, due to soilplasticity, spatial variation in soil properties, and potentiallysevere heterogeneity of material under excavation, it isimpossible to exactly define the force needed for certaindigging conditions. Accounting for these variable forceconditions of the soil by including the parameters from [5]and the study of its effect on the system during the digging


cycle have led to a well developed model of the kinematicsystem of the excavator.

OVERVIEW OF THE COMPLETEMODELFigure12 depicts the complete model as it is in the presentstage of model development. The model is represented inthree sections, the first section comprising of the pumpmodel, the second section of the valve blocks and pressurefeedback logic and the third section representing the rigidbody linkage. As part of the present stage of modeldevelopment, the pump and kinematics model have beenlinked together, using valve blocks and pressure compensatedflow control valves with ideal characteristics. The pressuresacross all actuator ports have been compared to provide themaximum load at any instant of time to provide the LSpressure to the FC. The actuators in this model are linearactuators and have been modeled as components whichinclude pressure dynamics in the volumes on either side ofthe piston, viscous friction, and leakage past the piston. Infuture work, detailed models of the valve block withcompensators and actuators will be included to recreate thecomplete functioning of the system.

Fig. 11. AMESim® model of the Excavator Kinematics

EXPERIMENTAL TEST SETUPPUMP EXPERIMENTAL TEST SETUPThe main components of this test stand are the variabledisplacement axial piston pump P, flow compensator FC,pressure compensator PC, ball valve and the prime moverwhich is a DC motor. The LS signal is tapped from the outputof the ball valve and is measured using sensor P3. Theactuator for controlling the swash plate is controlled by theFC/PC valve and the swash plate position is measured usingan LVDT. The use of an LVDT to derive an angular value isjustified by the fact that in this case, the curvature of the arcrepresenting the swash plate rotation is extremely large andcan be represented as a straight line. The system load isgenerated by a proportional relief valve, rated for 315 barmaximum pressure with a capacity to control the pressure foran inputted constant or mathematical function. The schematicdiagram of the hydraulic circuit of the test facility is as

depicted in Fig. 13 and the instrumentation used on thesystem is summarized in Table.1. Figure 14 is a photographof the pump mounted on the test facility. The test rig is alsoequipped with an off line circuit (not represented in Fig.13)for oil temperature control, constituted by a system of heatexchangers, electronically regulated over a specified workingtemperature.

COMPARISON BETWEENEXPERIMENTAL AND SIMULATIONRESULTSLOAD SENSING PUMPComparison of Results - Preliminary TestsThe complete model of the pump was verified byexperimental results. The load pressure values (Fig.15),which comprised of a cyclic pressure loading was obtainedfrom experimental test and were used to drive the simulationpump model's load characteristics. The other controlledparameter was that of the ball valve used to control the orificeopening (Fig.16). A random input was used to study thesimulation models ability to reproduce intermediate swashplate positions. In effect the model was subjected to twovarying inputs to verify the reproducibility of the pumpparameters. The parameters that were verified to developconfidence in the reproducibility of the pump dynamics werethat of the swash plate displacement and the pressurecharacteristics of the control piston. This was verified inexperimental results, by use of a LVDT which was mounteddirectly on the swash plate. The rotation of the swash platewas approximated as linear, as the angle of rotation is small.Figure 17 represents the swash plate position of the pump;Fig.18 describes the output flow of the pump. Figure 19represents the control piston pressure. The actual controlpressure plots are noisy, this is attributed to the pumpingfrequency and have been fitted in Fig.19 to represent thecorrelation. Fig 20, describes the spool displacement of theFC valve. The FC valve provides a flow path when thedisplacement value exceeds 3.90mm. Figures 17,18,19present the verification of simulation results against the actualtest data. It is evident that there is a good relation between thesimulation and experimental results.


Fig. 12. Overview of the Complete Model


Fig. 15. Load pressure cycle Fig. 16. Orifice opening

Fig. 13. Test setup for Load Sensing Variable Displacement pump testing

Fig. 14. Photograph of the pump with compensators mounted on the test bench


Fig. 17. Comparison between experimental andsimulation swash angle

Fig. 18. Comparison between experimental andsimulation flow rate

Fig. 19. Comparison between experimental andsimulation actuator pressure

Fig. 20. Flow compensator simulated displacement

Table. 1. Features of sensors and main elements of the apparatus used in the present research


EXCAVATOR MODELExcavator Model Executing a Digging Cycle withBoom, Arm and BucketOn analysis of results presented in the previous section, it isevident that the pump model is capable of reproducing actualconditions. Thus the model was extended to include the valveblocks and the kinematics as depicted in Fig.12 and describedin section 2.3. The complete system was subjected to a dutycycle as described in Table.2. The values from Table.2 wereused to control the valve opening for respective implements.The pump's maximum displacement used for this simulationwas 84 cm3/rev and the engine speed was set at 1000 rev/min.Figure 21 describes the initial condition of the excavator inthe simulation model. Figure 22 describes the forces on theimplements and the effects of these forces can be seen inFigs. 23, 24 and 25 in pressure terms on the boom, arm andbucket actuators. Figure 26 describes the pressures across theFC, as it can be seen the LS pressure is the instantaneousmaximum pressure of the system derived from the actuatorsand the pump pressure is the instantaneous system pressure.Figure 27 describes the differential pressure across the FC,that is equal to the pump margin set to about 17 bar. Figures28 and 29 describe the spool displacements of the PC and FCrespectively: the FC provides a flow path through the spoolwhen the displacement is greater than 3.90 mm and the PCwhen the displacement is greater than 2.10mm. Figure 30describes the pump swash angle controlled by the flow acrossthe FC and PC spools.

Fig. 21. Initial position of the Excavator

Fig. 22. Actuator Forces

Table. 2. Duty cycle - Control Signals to Valve Block for Boom, Arm, Bucket Motion


Fig. 23. Pressure in Boom Actuator

Fig. 24. Pressure in Arm Actuator

Fig. 25. Pressure in Bucket Actuator

Fig. 26. Pressure Across the FC

Fig. 27. Differential pressure across the FC

Fig. 28. Displacement of the FC


Fig. 29. Displacement of the PC

Fig. 30. Swash Angle

SUMMARY/CONCLUSIONSThe paper has presented the analysis of an excavator controlsystem. A nonlinear mathematical model of an excavator hasbeen developed using the AMESim® modeling environmentto replicate actual operating conditions. The model isdescribed by two models: hydraulic grey box model and a 2Dkinematic model to simulate the excavator's body elements.This approach has enabled the study of the dynamic behaviorand interaction of the pump with a completely developedkinematic model of the excavator. The detailed hydraulicmodel described is that of the main hydraulic pump, whichhas been conceived as a grey box model; where the flow andpressure compensators have been modeled as white boxmodels and the actual flow characteristics of the pump as ablack box model. The black box model to obtain the swashplate positions has been developed using a relation betweenthe control piston pressure and the net torque acting on theswash plate through the system pressure. A linear relationbetween these pressure characteristics were derived fromexperimental results and was used to simulate the functioningof the pump. This methodology has the advantage of beingeasily applicable to pumps of different types and sizes. Themodel of the variable displacement pump has been validatedon the basis of a set of experimental data collected at

particular operating conditions. It has permitted the necessaryverification of the pump's behavior and provides confidencein the expected interaction between the hydraulic andkinematic model. Therefore the authors are confident to bringthe study forward and assess a set of strategies aimed toimproving the control of the system and the overall systemefficiency.

REFERENCES1. Anthony, Alvin Casoli, Paolo Vacca, Andrea. (2010).Analysis of a tractor rear hitch control system. Proc. Of 6th

FPNI-PhD Symposium West Lafayette, 15-19 June 2010, pp.589-602. FPNI Fluid Power Net Publications, 2010

2. Mukherjee, Amalendu Karmakar, Ranjit Samatry, A.K.(2006) Bond Graph in Modeling Simulation and FaultIdentification, I.K International Publishing House

3. Blakburn, J. F., Reethof, G. & Shearer, J. L. (1966) FluidPower Control. USA: MIT Press, 1966. ISBN 0262520044.

4. Casoli, P., Vacca, A., Anthony, A., Berta, G.L. (2010).Numerical and Experimental Analysis of the HydraulicCircuit for the Rear Hitch Control in Agricultural Tractors.7th International Fluid Power Conference, (pp. 51-63, vol. 1)Aachen, 22-24/03 2010, ISBN 978-3-940565-90-7

5. Grzesikiewicz, W. (1998). Dynamics of a ground diggingtool. XI scientific Conference Problems of Work Machines,konferencja Naukova Problem Maszyn Roboczych) Polska:Zakopane, 1998

6. LMS Imagine - AMESim® Reference manual 2009

7. Hiller, Manfred. (1996). Modeling, simulation and controldesign for large and heavy manipulators, Journal of Roboticsand Autonomous Systems 19 (1996) 167-177

8. McCloy, D., Martin, H. M. (1973). The control of FluidPower, Longman, London, 1973

9. Merrit, H.E. (1967) Hydraulic Control Systems, Wiley,New York.

10. Casoli, Paolo Anthony, Alvin Modeling of an Excavator- Pump Nonlinear Model and Structural Linkage/MechanicalModel, Proc. Of 12th Scandinavian International Conferenceon Fluid Power, May 18-20, 2011, Tampere, Finland

11. Lin, Shih-Tin. (2002) Stabilization of Baumgarte'sMethod Using the Runge-Kutta Approach, ASME Journal ofMechanical Design, December 2002

12. Wu, D., Burton, R., Schoenau, G., Bitner, D. (2007),Analysis of a Pressure -Compensated Flow Control Valve,ASME Journal of Dynamic Systems, Measurement andControl, March 2007


CONTACT INFORMATIONPaolo [email protected]

Alvin [email protected]

ACKNOWLEDGMENTSThe authors would like to acknowledge the active support ofthis research by Casappa SpA., Parma, ITALY.

DEFINITIONS/ABBREVIATIONSA

flow area

aacceleration

Cddischarge coefficient

Fforce

hgap height

ivolume index

mmass

ṁmass flow rate

PPressure

PcControl Piston Pressure

PsSystem Pressure

QlLeakage Flow

QsLoad Flow

RRadius

Llength of the leakage

VVolume

tTime

Greek Lettersβ

bulk modulus

μdynamic viscosity

ρdensity

AcronymsFC

Flow compensator

PCPressure compensator

PSSystem Pressure

PLSLoad Sensed Pressure


mailto:[email protected]

mailto:[email protected]

hydraulic pump model published 09/13/2011

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