Gray box in excavator

7/26/2019 Gray box in excavator

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Gray box modeling of an excavators variable displacement hydraulic pump

for fast simulation of excavation cycles

Paolo Casoli n, Alvin Anthony

Industrial Engineering Department, University of Parma Italy, Parco Area delle Scienze 181/A, 43124 Parma (PR), Italy

a r t i c l e i n f o

Article history:

Received 27 October 2011

Accepted 26 November 2012Available online 6 February 2013

Keywords:

Hydraulic excavator

Gray box modeling

Variable displacement pump

Load sensing

Excavator kinematics

a b s t r a c t

This paper describes the results of a study focused on the application of gray box modeling

methodology on an excavators hydraulic pump. This modeling approach has been adapted to

accelerate the control system development time for a complete excavator, while providing accuratesystem dynamics. This mathematical model has been developed using the bond graph methodology.

The excavator is described by two models: a hydraulic model and a kinematic model; dynamic

parameters are continuously calculated during an excavation cycle, providing a platform to study the

pumps behavior. The gray box model of the variable displacement pump has been validated on the

basis of a set of experimental data collected on a test rig and on the field using an excavator. Herewith

the results of this study are presented.

& 2012 Elsevier Ltd. All rights reserved.

1. Introduction

In todays world a lot of focus is placed on infrastructure

projects which require construction equipment to realize theseprojects. This requirement for construction equipment places an

increasing need on the manufacturers engineering teams to

enable them to tune these systems based on operators needs

hailing from different geographical locations. A major bottle neck

in tuning or adapting these systems is the simulation time

required to study the interaction between the different subsys-

tems of the machinery. Towards this end, this paper deals with a

simulation approach to accelerate the control system develop-

ment time. The development of control systems for complex

mechanical systems such as large manipulators, mobile cranes

and excavators requires the use of powerful software develop-

ment tools. This is particularly true when a short commissioning

period is desired. Here, the complete control-system must be

developed and tested by simulation methods. This requires acomprehensive software package for mechatronic systems, con-

sisting of a modeling and simulation part and a control develop-

ment part. The simulation of the kinematics and dynamics of

multi-body systems is a topic of increasing importance in many

industrial branches, due to its potential for reducing costs.

It further provides insight into inherent effects governing the

systems behavior. At a more detailed level, simulation offers

enhanced product assessment, the potential of early stage con-

ceptual testing, and a virtually unlimited spectrum of what if

analysis (Hiller, 1996). Towards realizing this objective a model of

hydraulic and kinematic systems has been developed. The need tomodel these systems is attributed to the inherently nonlinear

hydraulic drive, used to achieve precise motion and power

control. This choice of drive is imputed to the superior power

density of hydraulic systems in comparison to electrical or

mechanical drives; regrettably the indigent energy efficiency of

these systems is a major drawback. The need for energy efficient

systems demands that this potent drive be self-adjusting to meet

actual load requirements (Inderelst, Losse, Sigro, & Murrenhoff,

2011; Wu, Burton, Schoenau, & Bitner, 2007; Zimmerman &

Ivantysynova, 2011). A method of adjusting these systems to

meet load requirements is by controlling the flow of a pump. In

this context, variable-displacement axial piston pumps are often

used, whereby the displacement of the pump can be varied by

tilting a swash plate. This can be achieved fast enough to meet thedynamic demands affected by multiple loads. In this research, a

nonlinear pump model has been developed, which takes into

account the essential nonlinearities of the system and can be

easily adjusted to pumps of different displacement sizes in the

same model range. A practical pump model must enable one to

examine the dominant characteristics influencing the behavior of

the pump. In a load sensing pump, this would include the

response of the pressure and flow compensators in addition to

the sensitivity of swash plate motion which defines the pumps

displacement. This model can be conceived in a number of ways

either as purely mathematical (Borghi, Specchia,&Zardin, 2009;

Zecchi & Ivantysynova, 2012), empirical or a mix of the two as

Contents lists available at SciVerse ScienceDirect

journal homepage: www.elsevier.com/locate/conengprac

Control Engineering Practice

0967-0661/$ - see front matter & 2012 Elsevier Ltd. All rights reserved.

http://dx.doi.org/10.1016/j.conengprac.2012.11.011

n Corresponding author. Tel.: 39 0521 905868; fax: 39 0521 905705.

E-mail addresses: [email protected] (P. Casoli),

[email protected] (A. Anthony).

Control Engineering Practice 21 (2013) 483494
http://www.elsevier.com/locate/conengprachttp://www.elsevier.com/locate/conengprachttp://dx.doi.org/10.1016/j.conengprac.2012.11.011mailto:[email protected]:[email protected]://dx.doi.org/10.1016/j.conengprac.2012.11.011http://dx.doi.org/10.1016/j.conengprac.2012.11.011mailto:[email protected]:[email protected]://dx.doi.org/10.1016/j.conengprac.2012.11.011http://dx.doi.org/10.1016/j.conengprac.2012.11.011http://dx.doi.org/10.1016/j.conengprac.2012.11.011http://www.elsevier.com/locate/conengprachttp://www.elsevier.com/locate/conengprac


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a gray box model. The approach of gray box modeling using

existing methods has been adapted in this paper to develop a

model of the load sensing pump.

This would provide a platform to rapidly examine different

pump sizes to vary the flow gain of a complete excavator with the

objective of achieving desired design characteristics. The pump

displacement is controlled by the highest pressure feedback

generated from the excavators actuators, in an operating cycle.

To subject the pump to these varying forces a detailed model ofthe kinematics has been realized. Due to the complexity of the

whole system, dynamic forces are required for computing the

load on the system which is achieved by the kinematic model of

the excavator. Previously published research describes the differ-

ences between these static and dynamic forces (Hiller, 1996). The

nonlinear effects occurring during the excavation cycle such as

the bucketsoil interaction and the nonlinearities of the hydraulic

system complicate the control of the pump. These factors have to

be taken into account in hydraulic modeling and control. The

above details provide a glimpse into the complexity of variable

forces that a system would experience during an operating cycle

for which the variable pump compensates its displacement. The

following sections will detail the modeling of the pump, the

excavator kinematics and validated results of the pump model.

2. Physical modeling

2.1. Pump model

The pump model described in this paper is that of a load

sensing variable displacement axial piston pump. This is a

standard line production pump developed by Casappa S.p.A. and

belongs to the MVP series. The study of optimal displacement

control of variable displacement pumps has been a topic of

interest for fluid power researchers world over and provides

scope for further development with electro hydraulics and recent

advances in robust control strategies. To set the pace of study, thispaper first describes the current stage of model development and

will detail the actual pump 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 the flow characteristics. The pump model has

been conceived as a gray box model, i.e. a model based on both

insights into the system and experimental data as can be seen in

Fig. 2. The gray box model is based on known methods which

offers an interesting method to study the dynamic behavior of a

pump whilst reducing computational time. The flow and pressure

compensators have been modeled as white box models and that

of the flow characteristics as a black box model. The gray box

model of the pump correlates the control piston pressure and the

system pressure to provide the equilibrium of forces that defines

the swash plate angle. This model approach has been adopted to

provide the manufacturer with the flexibility of selecting pumps

with discrete maximum displacements to vary the complete

systems gain.

The mathematical models of the flow compensator, pressure

compensator and flow characteristics have been developed using

the bond graph methodology realized through the AMESims

simulation software. Bond graphs originated as an attempt to

write block diagrams for electro-hydraulic systems as a means of

controlling them automatically (Thoma & Mocellin, 2006). This

methodology uses the transfer of power between elements to

describe the dynamics of the system. The basic idea being the

direction of power flow at any moment in a system is invariant.

Power may be expressed as a multiplication of two factors

generalized effort and generalized flow. Bond graphs are far more

powerful in modeling complex systems which involve the inter-

action of several energy domains (Mukherjee, Karmakar, &

Samatry, 2006). Model accuracy is critical for understanding,

optimizing and controlling the dynamics of a given system

effectively. This can be achieved by studying the order of

importance of the energy elements in the model. This paper has

applied but does not describes the Model Order Reduction

Algorithm used to reduce the size of the model based on a user-

supplied threshold of the percent of the total activity to be

retained in the reduced model (Boruzky, 2011). This has been

achieved by sorting of the activity index needed to reduce the

full model based on the needs and requirements of the user.

A decision based on the essential dynamics of the pump critical to

controller development has been identified as the threshold for

the model reduction criterion. This threshold has been used to

trim the model to retain sufficiently accurate predictions of the

pumps behavior. This has been the basis for adopting the model-

ing methodology as illustrated inFig. 2.

2.1.1. Flow compensator modelThe flow compensator (FC) has the most important function of

offsetting the pump displacement for a set preload by regulating

the swash plate angle. This component has been modeled and

verified in great detail (Casoli, Anthony& Rigosi, 2011).

The logic integrated in the FC is to compare the dominant load

pressure (PLS) with the pumps output pressure (PS) to modulate

the flow through the FC, hence regulating the pumps displace-

ment. The objective of the FC is to maintain a fixed differential

pressure across the control orifice accomplished by modulating

the pumps flow. The FCs spring consists of two springs one being

a snubber spring. This arrangement has been adopted to provide a

snubbing functionthereby resiliently biasing the spool from the

first operating position to the second operating position, when

the fluid pressure in the LS chamber is increased from a first

Fig. 1. Model breakup of the MVP series, load sensing variable displacement

pump.

Fig. 2. Gray box modeling methodology.

P. Casoli, A. Anthony / Control Engineering Practice 21 (2013) 483494484


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The other assumptions are that fluid inertia is neglected; springs

are assumed linear.

2.1.2. Pressure compensator model

The function of the pressure compensator (PC) is that of a relief

valve and its function is to limit the maximum pressure of the

system,Fig. 5. The relief valve provides an alternate flow path to

tank while keeping the system pressure at the relief valve setting.

The relief valve realized in the PC is that of the direct operatedtype, it operates with a spring to pre-load the valve spool. Since a

small flow rate is passed through the spool, the set pressure can

be maintained with nearly no effect on the pressure flow

characteristics of the valve. The functioning of the PC is such that

the system pressure enters the PC through chamber E (Fig. 6) and

the pressure acts on the area of spool 6 to create a force, which

resists the force created by the spring 8 and spool 9, creating

a relief setting pressure. When the system pressure is greater

than the relief setting pressure, the spool 6 is displaced and

creates a flow path to the swash plate actuating piston and to

tank through an orifice S1 (Fig. 6), which is housed in the PC valve.

The governing equations describing the physical behavior of the

PC are the same as those described in the section on the modeling

of the flow compensator.

2.1.3. Flow characteristics model

A model of the pumps flow characteristics must permit the

examination of dominant characteristics influencing the pumps

behavior. In a load sensing pump this would include the response

of the pressure and flow compensators in addition to the

sensitivity of swash plate motion which defines the pumps

displacement. Due to intricacies encountered in the control,

design and implementation of this type of pump, it is advanta-

geous to have a comprehensive model of the pump. Such a model

would include determining the motion of the pumps swash plate

based on the instantaneous operating conditions. To achieve this,

the model must include the effects of friction acting on internal

components, accurate determination of pressure in the pumping

pistons and the effects of the swash plate motion on the control

actuator. The model must reflect both the supply flow character-

istics of the pump as well as the dynamic behavior associated

with the internal components in the pump itself.

In practice the accurate prediction of swash plate motion is theexclusive parameter required to represent an axial piston pump,

as all pump components interact with the swash plate to

determine its motion. The angle of the swash plate determines

the stroke of the pumping pistons, the length of which dictates

the flow characteristics. The prediction of the swash plate motion

is made difficult due to the exciting forces imparted on the swash

plate by the pumping pistons as well as the compressibility of the

fluid in the control piston. The bond graph model of the pump

(Fig. 7) describes that the net torque acting on the swash plate

consists of the torque contributed by the swash plate inertia,

pumping pistons torque, return spring torque, control piston

torque and damping effects. These torque values define the swash

plate angle to the transformer that modulates the pumps dis-

placement. Regrettably the white box model approach is quite

elaborate and does not afford the flexibility required to examine

pumps of different sizes as all the constants (piston mass, lengths

and diameters, swash plate mass, damping, valve plate geometry,

etc.) would have to be modified to adopt a different pump.

Fig. 5. CAD model of the pressure compensator.

Fig. 6. AMESims model of the pressure compensator.

Fig. 7. Bond graph representation of the pump.



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by applying the EulerLagrange equations to a Lagrangian energy

function. The revolute pairs have been modeled as Lagrange

multipliers and are calculated from the Baumgarte stabilization

method applied to the constraint equations (Lin& Huang, 2002).

To develop a dynamics model of the manipulator, forward

recursive equations similar to those applied in iterative Newton

Euler method were used to obtain kinematic relationships

between the time rates of joint variables and the generalized

Cartesian velocities for the centroid of the links. The obtained

kinematic relationships were represented in bond graph form,

while considering the link weights and moment as the elements

led to a detailed bond graph model of the manipulator. Forward

recursive equations for motion of manipulators similar to those

used in NewtonEuler method are used to derive the kinematic

relationships between the time rates of joint variables, and the

generalized Cartesian velocities (translational and angular velo-cities) of mass centers of the links. These kinematic relations are

further used for graphical representation of the system dynamics

using bond graphs (Mvengei & Kihiu, 2009). Inertial effects of

cylinders and their pistons are negligibly small compared to those

of manipulator links, the hydraulic cylinders transmit axial forces

only, the revolute joints have no friction, and all the links and

supports are rigid, a bond graph model representing the mechanical

dynamics of the excavating manipulator was developed.

One of the problems in studying the dynamics of an excavator

is the soil excavation process. It is quite complicated, partly

because the bucket cutting edge can move along an arbitrary

path and excavations often are carried out in non-homogeneous

material. Thus the forces acting on the bucket are difficult to

evaluate. They depend mainly on the type of soil, weight of the

excavated material as well as the velocity and position of the

bucket against the soil. The shape of the bucket itself is also

important. The type of the soil depends on many components: its

humidity, internal structure, porosity, as well as hardness. Usually

these values vary in the course of whole excavation process.

To further enhance the force simulation of the model, the visco-

elastic properties of the material being handled have been

recreated as a force during the excavation process. A model that

accounts for the material being retained in the bucket, which was

developed by Reeces fundamental earthmoving equation in soil

mechanics, was applied in this study to determine the force

exerted by the excavator bucket to the soil. An impulse force

which acts on the bucket during soil penetration has been

included as described in Grzesikiewicz (1998). The motion of

the excavator implements would be to follow a pre-planned

digging trajectory. Following industry best practices the quintictrajectory planning approach has been employed for the excava-

tion cycles. During digging, three main tangential resistance

forces arise: the resistance to soil cutting, the frictional force

acting on the bucket surface in contact with the soil and the

resistance to movement of the soil ahead of and in the bucket. The

magnitude of the digging resistance forces depends on many

factors such as the digging angle, volume of the soil, volume of

material ripped into the bucket, and the specific resistance to

cutting. These factors are generally variable and unavailable.

Moreover, due to soil plasticity, spatial variation in soil properties,

and potentially severe heterogeneity of material under excava-

tion, it is impossible to exactly define the force needed for

certain digging conditions. Taking into account the variable force

conditions of the soil while including the parameters from

Fig. 10. AMESims representation ofFig. 9.



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Grzesikiewicz (1998) and the study of its effect on the system

during the digging cycle have led to a well-developed model of

the kinematic system of the excavator.

2.3. Overview of the complete model

A model has been developed for the simulation of vehicle

behavior. Fig. 11depicts the complete model as it is in the present

stage of model development. As it can be seen the model thus far

represents and deals with the upper carriage system. The model isrepresented in three sections, the first section comprising of the

pump model, the second section of the valve blocks and pressure

feedback logic and the third section representing the rigid body

linkage. As part of the present stage of model development, the

pump and kinematics model have been linked together, using valve

blocks and pressure compensated flow control valves with ideal

characteristics. The pressures across all actuator ports have been

compared to provide the maximum load at any instant of time to

provide the LS pressure to the FC. The actuators in this model are

linear actuators and have been modeled as components which

include pressure dynamics in the volumes on either side of the

piston, viscous friction, and leakage past the piston. In future work,

detailed models of the valve block with compensators and actuators

will be included to recreate the complete functioning of the system.

3. Experimental setup

3.1. Pump experimental test setup

The main components of this test stand are the variable

displacement axial piston pump P, flow compensator FC, pressure

compensator PC, ball valve and the prime mover which is a DC

motor. The LS signal is tapped from the output of the ball valve

and is measured using sensor P3. The actuator for controlling the

swash plate is controlled by the FC/PC valve and the swash plateposition is measured using an LVDT. The use of an LVDT to derive

an angular value is justified by the fact that in this case, the

curvature of the arc representing the swash plate rotation is

extremely large and can be represented as a straight line. The

system load is generated by a proportional relief valve, rated for

315 bar maximum pressure with a capacity to control the

pressure for an inputted constant or mathematical function. The

schematic diagram of the hydraulic circuit of the test facility is

depicted inFig. 13and the instrumentation used on the system is

summarized in Table 1. Fig. 13 is a photograph of the pump

mounted on the test facility. The test rig is also equipped with an

off-line circuit (not represented in Fig. 12) for oil temperature

control, constituted by a system of heat exchangers, electronically

regulated over a specified working temperature.

Fig. 11. Overview of the complete model.

P. Casoli, A. Anthony / Control Engineering Practice 21 (2013) 483494 489


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4. Comparison between experimental and simulation results

for the pump model

4.1. Comparison of resultslaboratory testing of pump

characteristics

The complete model of the pump was verified by experimental

results as depicted in Fig. 13. The load pressure values Fig. 14,

which composed of a cyclic pressure loading, were obtained from

experimental test and were used to drive the simulation pump

models load characteristics. This cyclic pressure loading was used

to validate the models independent of pressure values to estimate

the pumps behavior. The other controlled parameter was that of

the ball valve used to control the orifice opening (Fig. 15).

A random input was used to study the simulation models ability

to reproduce intermediate swash plate positions. In effect themodel was subjected to two varying inputs to verify the reprodu-

cibility of the pump parameters. The parameters that were

verified to develop confidence in the reproducibility of the pump

dynamics were that of the swash plate displacement and the

pressure characteristics of the control piston. This was verified in

experimental results, by the use of a LVDT which was mounted

directly on the swash plate. The rotation of the swash plate was

approximated as linear, as the angle of rotation is small. Fig. 16

represents the swash plate position of the pump; Fig. 17describes

the output flow of the pump.Fig. 18represents the control piston

pressure. The actual control pressure plots are noisy; this is

attributed to the pumping frequency and has been fitted in

Fig. 18 to represent the correlation. Fig. 19 describes the spool

displacement of the FC valve. The FC valve provides a flow path

when the displacement value exceeds 3.90 mm. Figs. 1618

present the verification of simulation results against the actual

test data. It is evident that there is a good relation between the

simulation and experimental results.

4.2. Comparison of resultsfield tests on an excavator for pump

characteristics

The digging cycle tests on the excavator were carried out

to measure the pumps response to different excavation cycles.

Table 1

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

Sensor Type Main features

M Prime mover ABBs, 4-quadrant electric motor, 75 kW

P Pump CASAPPAs MVP60, 84 cm3/r

P1 Strain gage WIKAs, scale: 0..40 bar, 0.25% FS accuracy

P2P3P4 Strain gage WIKAs, scale 0..400 bar, 0.25% FS accuracy

Q1, Q2 Flow meter VSEs VS1, scale 0.05..80 l/min, 0.3% measured value accuracy

T Torque/speed meter HBMs T, scale: 0..500 Nm, 12,000 r/min limit velocity, 0.05 accuracy classy Incremental encoder HEIDENHAINs ERN120, 3600 imp./r, 4000 r/min limit velocity, 1/20 period accuracy

Fig. 12. Test setup for load sensing variable displacement pump testing.

Fig. 13. Photograph of the pump with compensators mounted on the test bench.



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The data from the excavation cycles were used to verify and

validate the functioning of the simulation model of the excavator.

Digging cycles were carried out at different engine speeds to

verify the functionality of the pump response at different operat-

ing conditions and load cycles.Fig. 20depicts the excavator that

Fig. 14. Load pressure cycle.

Fig. 15. Orifice opening.

Fig. 16. Comparison between experimental and simulation swash angle.

Fig. 17. Comparison between experimental and simulation flow rate.

Fig. 18. Comparison between experimental and simulation control piston actua-

tor pressure.

Fig. 19. Flow compensator simulated displacement.

Fig. 20. Photograph of the excavator used for the verification of the simulation

model.



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was used to carry out the experimental field tests and Table 2

describes the instrumentation used to measure the represented

data as well as verifying the mathematical model. The simulation

plots were verified at three different engine speeds: 1000 r/min,

1500 r/min and 1750 r/min as can be seen in Figs. 21, 23 and 24

respectively.Fig. 22describes the valve input signal that was used

to actuate the valve on the excavator; these data were measured

and used to drive the simulation model as an input signal.

The verification of the actual pumps response can be seen in

the following graphs as compared to the simulation model of the

pump. The comparison of the experimental and simulation data

shows that the simulation model has the capability of replicating

the actual characteristics of the real pump. The difference in the

plot results arrives from the actual excavator valve having non-

linear orifice opening characteristics, whilst the model of the

valve on the excavator has ideal orifice opening characteristics.

This issue will be dealt with in future work, where the generic

valve model will be replaced with a detailed mathematical model

of the valve capable of recreating the non-linear orifice character-

istics, thereby replicating the actual behavior of the pump.

5. Excavator model

5.1. Excavator model executing a digging cycle with boom, arm and

bucket

On analysis of results presented in the previous section, it is

evident that the pump model is capable of reproducing actual

conditions. Thus the model was extended to include the valve

blocks and the kinematics as depicted inFig. 11and described in

Section 2.3. The complete system was subjected to a duty cycle as

described inTable 3. The values fromTable 3were used to control

the valve opening for respective implements. The pumps max-imum displacement used for this simulation was 84 cm3/r and the

engine speed was set at 1000 r/min. Fig. 25 describes the initial

condition of the excavator in the simulation model. Fig. 26

describes the forces on the implements and the effects of these

forces can be seen inFigs. 2729in pressure terms on the boom,

arm and bucket actuators. Fig. 30 describes the pressures across

the FC, as it can be seen that the LS pressure is the instantaneous

maximum pressure of the system derived from the actuators and

the pump pressure is the instantaneous system pressure. Fig. 31

describes the differential pressure across the FC, which is equal to

the pump margin set to about 17 bar. Fig. 32 and 33describe the

spool displacements of the PC and FC respectively: the FC

provides a flow path through the spool when the displacement

is greater than 3.90 mm and the PC when the displacement is

Table 2

Features of sensors and main elements of the apparatus used on

the excavator.

Sensor Type

Pump output pressure Strain gauge

Swash angle sensor Inclination sensor

Load sensing pressure Strain gauge

Valve pilot pressure Strain gage

Actuator extension pressure Strain gaugeActuator retraction pressure Torque/speed meter

Output flow Flow meter

Fig. 21. Swash angle at 1000 r/min.

Fig. 22. Valve input signal for 1000 r/min.





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Fig. 25. Initial position of the excavator.

Fig. 26. Actuator forces.

Fig. 27. Pressure in boom actuator.

Table 3

Duty cyclecontrol signals to valve block for boom, arm, bucket motion.

Name Time (s) Valve opening (%) Actuator action

Boom

05 080 (ramp) Retraction

510 0

1015 080 (ramp) Extension

1520 0

Arm

05 0

510 10020 (ramp) Extension1015 080 (ramp) Retraction

1520 0

Bucket

05 0

510 100 Extension

1015 0

1520 020 Retraction

Fig. 28. Pressure in arm actuator.

Fig. 29. Pressure in bucket actuator.

Fig. 30. Pressure across the FC.

Fig. 31. Differential pressure across the FC.



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greater than 2.10 mm. Fig. 34 describes the pump swash angle

controlled by the flow across the FC and PC spools.

6. Conclusions

This paper has presented the analysis of an excavator control

system. A nonlinear mathematical model of an excavator has been

developed using the AMESims modeling environment to replicate

actual operating conditions. The model is described by two models:

hydraulic gray box model and a 2D kinematic model to simulate the

excavators body elements. This approach has enabled the study of

the dynamic behavior and interaction of the pump with a developed

upper carriage kinematic model of the excavator. The detailed

hydraulic model described is that of the main hydraulic pump,

which has been conceived as a gray box model; where the flow and

pressure compensators have been modeled as white box models

and the actual flow characteristics of the pump as a black box

model. The black box model to obtain the swash plate positions has

been developed using a relation between the control piston pressure

and the net torque acting on the swash plate through the system

pressure. A linear relationship between these pressure character-

istics was derived from experimental results and was used to

simulate the functioning of the pump. This methodology has the

advantage of being easily applicable to pumps of different types andsizes. The model of the variable displacement pump has been

validated on the basis of a set of experimental data collected at

particular operating conditions. It has permitted the necessary

verification of the pumps behavior and provides confidence in the

expected interaction between the hydraulic and kinematic model.

Therefore the authors are confident of bringing the study forward

and assessing a set of strategies aimed at improving the control of

the system and the overall system efficiency.

Acknowledgments

The authors would like to acknowledge the active support of

this research by Casappa S.p.A., Parma, Italy.

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Fig. 32. Displacement of the FC.

Fig. 33. Displacement of the PC.

Fig. 34. Swash angle.

http://dx.doi.org/10.1007/978-1-4419-9368-7http://dx.doi.org/10.4271/2011-01-2278http://dx.doi.org/10.1016/j.simpat.2006.09.006http://dx.doi.org/10.1016/j.simpat.2006.09.006http://dx.doi.org/10.1016/j.simpat.2006.09.006http://dx.doi.org/10.1016/j.simpat.2006.09.006http://dx.doi.org/10.4271/2011-01-2278http://dx.doi.org/10.4271/2011-01-2278http://dx.doi.org/10.4271/2011-01-2278http://dx.doi.org/10.1007/978-1-4419-9368-7http://dx.doi.org/10.1007/978-1-4419-9368-7http://dx.doi.org/10.1007/978-1-4419-9368-7

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Gray box in excavator

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