research article bond graph modeling and validation of an ...bond graph would be a preferable method...

Research ArticleBond Graph Modeling and Validation ofan Energy Regenerative System for Emulsion Pump Tests

Yilei Li, Zhencai Zhu, and Guoan Chen

School of Mechanical and Electrical Engineering, China University of Mining and Technology, Xuzhou 221116, China

Correspondence should be addressed to Zhencai Zhu; [email protected]

Received 3 April 2014; Accepted 24 April 2014; Published 22 May 2014

Academic Editor: Guojie Zhang

Copyright © 2014 Yilei Li et al. This is an open access article distributed under the Creative Commons Attribution License, whichpermits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

The test system for emulsion pump is facing serious challenges due to its huge energy consumption and waste nowadays. To settlethis energy issue, a novel energy regenerative system (ERS) for emulsion pump tests is briefly introduced at first. Modeling such anERS of multienergy domains needs a unified and systematic approach. Bond graph modeling is well suited for this task. The bondgraph model of this ERS is developed by first considering the separate components before assembling them together and so is thestate-space equation. Both numerical simulation and experiments are carried out to validate the bond graph model of this ERS.Moreover the simulation and experiments results show that this ERS not only satisfies the test requirements, but also could save atleast 25% of energy consumption as compared to the original test system, demonstrating that it is a promising method of energyregeneration for emulsion pump tests.

1. Introduction

The emulsion pump, one of hydraulic applications, has beenwidely applied in industry because it has the advantages ofcommon hydraulic oil pump. As a result, the emulsion pumphas gradually become the necessary equipment in manyindustries.

In coal mine industry, for instance, the emulsion pumpis necessarily employed on the fully mechanized coal miningface as a hydraulic source of the hydraulic support whichis used to support the working space underground andtherefore to keep mine workers’ lives safe. Consequently,the emulsion pump should be strictly tested before its fieldusages according to the coal industry standard MT/T 188.2–2000 of China. The original test system used in the teststandard is simple but energy-demanding, which uses aninductionmotor as the direct driver of test pumpand employsa throttle valve to set the required load pressure of the testemulsion pump, wasting all the energy during the test. Thereare several kinds of tests in the standard, such as zero-loadtest, half-load test, and full-load test. Among all these tests,the durable test costs and wastes the most energy becauseit requires that the pump be tested continuously under

full-load pressure for 500 hours, take, for example, the mostcommonly used emulsion pump in coal mine of which thenominal pressure and flow rate are 31.5MPa and 400 L/min.One durable test of such an emulsion pump would cost105 000 kW⋅Ch. Moreover, the heat energy converted by thethrottle valve and then contained in the emulsion fluid mayneed a particular radiating system to be dissipated, costingmore energy again. As a result, from the environmental pointof view, especially energy saving, the original test system isfacing serious challenges due to its large energy consumptionand low energy efficiency.TheERS has great potential to solvethis problem.

Researches on ERS to date have generally been diverse,focusing on variable systems of hydraulic oil, such ashydraulic elevators [1, 2] and hydraulic excavators [3–6],as well as hydraulic forklifts and cranes [7, 8]. These ERSsfor hydraulic oil system, however, are not suitable to theemulsion pump tests because of the working fluid difference,not hydraulic oil but emulsion, resulting in no industry pro-ductions available inmarket, like emulsionmotor. ERSs [4, 9–11] employing accumulators as the energy-saving unit arenot available options because they are not fit for continuousoperation systems without working condition changes.

Hindawi Publishing Corporatione Scientific World JournalVolume 2014, Article ID 289839, 12 pageshttp://dx.doi.org/10.1155/2014/289839

2 The Scientific World Journal

Motor

Variable displacement

pump

Variable displacement

hydraulic motor

Emulsion pump

Speed sensor

Pressure sensor

Relief valve

Accumulator

Directionvalve

Emulsion cylinderOil cylinder

Rectifier valve

Check valve

Flow-rate sensor

Cooler

M

Figure 1: Schematic diagram of the novel energy regenerative system.

Aiming at the decrease of energy consumption, a novelERS for emulsion pump tests has been proposed in [12].Bond graph would be a preferable method for investigatingthis ERS, since it contains some energy conversions amongmechanical translational, rotational, and hydraulic domains.

Bond graph modeling, a graphical methodology par-ticularly suited for modeling multidisciplinary dynamicengineering systems in which components from differentdisciplines dynamically interact by exchanging energy andin which different forms of energy are involved, was firstconceptualized by Paynter [13] in 1959 and then elaboratedby Karnopp et al. [14] into a unified modeling methodologythat is popular in variable research areas of many physicaldomains [15–19]. Apart from being a graphical, port-basedmodeling approach, one advantage of bond graph for ERSslies in the fact that it is domain-independent, using unifiednotations for elements and variables across various energydomains; hence, it is capable of representing a complexsystem involving diverse energy domains. Bond graph hasbeen applied in modeling various complex mechanical sys-tems, such as railway trucks [20], automobiles [21, 22], andaircrafts [23]. Bond graph methodology has also been usedfor modeling and investigating different kinds of hydraulicsystems [24–28]. Borutzky et al. [29] developed bond graphmodels of some hydraulic components in Modelica software.Renewable energy systems, such as wave and wind energyconversion system, have been modeled based on bond graphin [30, 31].

The main objectives of this paper are the modeling ofthis ERS for emulsion pump tests using bond graph approachand validation. The remainder of this paper is organized asfollows. In the second section, the overall structure of theERS is briefly described at first. Then bond graph modelof this ERS is established by first considering the separate

components before assembling them together, and the state-space equations are derived accordingly. In the third section,simulations of the bond graph model are performed withinMATLAB/Simulink software.The ERSmodel and simulationare then validated in the fourth section using experimentaldata. Conclusions are summarized in the final section.

2. Bond Graph Modeling

2.1. ERS Description. The novel ERS for emulsion pumptests, as shown in Figure 1, consists of induction motor,variable displacement pump (VDP), variable displacementhydraulic motor (VDHM), direction control valve, a coupleof symmetrical cylinders, rectifier valve, and several kinds ofsensors.

The induction motor and its connected VDP serve asthe energy source of the whole system, converting electricenergy into hydraulic energy. The VDHM which is actuatedby the output oil of both VDP and the rectifier valve drivesthe test emulsion pump, converting the hydraulic energy ofoil first into mechanical rotational energy and then back intohydraulic energy of emulsion fluid.The output emulsion fluidfrom emulsion pump, through the direction valve, flows intothe left chamber of emulsion cylinder and pulls the piston ofoil cylinder rightward via the common piston rod.Therefore,the oil in the right chamber of oil cylinder is extrudedout through the rectifier valve and back into VDHM. Bythe two cylinders, the output hydraulic energy of emulsionfluid is converted first into mechanical energy of pistonand then back into hydraulic energy of oil, implementingthe energy regeneration function of this system. As crucialcomponents of this system, the two cylinders not only convertand save energy from emulsion fluid to hydraulic oil, but alsosimultaneously isolate these two kinds of fluid strictly from

The Scientific World Journal 3

1

2

3 4

5

8

6 7

Sf MTF

R

R R

C

Pump friction Pump outlet cap

p relief valvePump leakage

Motor speed Pump disp01

Figure 2: Bond graph model of the variable displacement pump.

each other to avoid mutual contamination. From the energyconversion point of view, the left oil cylinder functions morelike a pump with linear motion. The fully detailed workingprinciple of this ERS could be referred to as in the previouspaper [32].

2.2. ComponentsModeling. Since the system consists ofmanyhydraulic components and energy conversion processes, itwould be much easier to model each single component ofthe system at first and then assemble them together accord-ingly. Therefore the decomposition of the whole system intosubsystemmodels exchanging energy is performed before themodeling of the whole system.

2.2.1. Variable Displacement Pump. The VDP converts theenergy from mechanical rotational domain into hydraulicdomain and generally serves as a hydraulic power source tothe whole system. A detailed model of VDP is establishedin order to obtain a better dynamic behavior of the pumpin which the rotational friction and internal leakage of thepump as well as the fluid compressibility inside the pump areall well considered, as depicted in Figure 2. To simply andclearly denote the power bonds and elements, all the bondsare numbered consecutively and the element attached to thebond is numbered accordingly. Also as preference, both theeffort (𝑒) and flow (𝑓) pointing into the 0-junction and 1-junction are signed as positive while those pointing awayfrom the 0-junction and 1-junction as negative.

The induction motor is simply represented by a velocitysource element of 𝑆𝑓

1, assuming that it rotates continuously

and steadily at a constant angular speed. In addition, due tothe steady input angular speed of pump, the inertia momenteffect of the pump is reasonably neglected. The transformratio of MTF, which is the pump displacement, can bemodulated by an input control signal, and the constitutiverelation of MTF could be expressed as follows:

𝑓

4= 𝑓

3× 𝑉

𝑝(𝛼) ,

𝑒

3= 𝑒

4× 𝑉

𝑝(𝛼) ,

(1)

where 𝑒4and 𝑓

4are the pressure and flow rate of the pump,

respectively; 𝑒3and 𝑓

3are the torque and angular velocity

of induction motor, respectively; 𝑉𝑝(𝛼) is the geometric

displacement of the pump; and𝛼 is the control signal of pumpdisplacement.

Clearly, in a realistic model, energy losses inside thecomponent have to be accounted for. In a hydraulic system orcomponent, these losses are mainly pressure drops, leakages,and frictions and can be represented by the resistive element𝑅 in bond graph modeling. The rotational friction loss andleakage loss, in other words, the mechanical and volumetriccoefficients, are implemented with simple resistive elements𝑅

2and 𝑅

6, respectively, while the capacitance effect which

occurs both inside the pump and at the outlet due to fluidcompressibility is symbolized by an energy store element of𝐶

5. The compressed fluid volume represented by the element

𝐶

5consists of both the pump displacement and the internal

space of the pipe connected to the pump outlet.Additionally, the relief valve employed at the pump outlet

for safety is generally represented by a resistive element𝑅

7with nonlinear resistance. In most cases the internal

dynamics of the relief valve could be neglected because itsresponse speed is much faster than any other componentsof the hydraulic system. The constitutive relation of the 𝑅

7

is described as

𝑓

7=

{

{

{

{

{

0 if 𝑒7≤ 𝑝set

(𝑒

7− 𝑝set)

𝑅

7

if 𝑒7> 𝑝set,

(2)

where 𝑓7and 𝑒7are the flow rate and pressure of the relief

valve, respectively, and 𝑅7and 𝑝set are the resistance and

predefined pressure of the relief valve, respectively.In bond graph methodology, the time integral of effort

of the 𝐼 element (known as generalized momentum 𝑃) andthe time integral of flow of 𝐶 element (known as generalizeddisplacement𝑄) are usually chosen for system state variables.After the completion of causality assignment, the state-spaceequation of the VDP is derived as follows:

̇

𝑄

5= −

1

𝐶

5

(

1

𝑅

6

+

1

𝑅

7

)𝑄

5+ 𝑉

𝑝𝑓

1− 𝑓

8, (3)

where 𝑄5is the oil volume; ̇𝑄

5is the flow rate (the time

differential of 𝑄5); and 𝑓

1and 𝑓

8are the induction motor

velocity and pump output flow rate, respectively.

2.2.2. Variable Displacement HydraulicMotor. In this system,theVDHM, functioned as the actuator of the emulsion pump,converts the hydraulic energy of oil into mechanical rota-tional domain. As shown in Figure 3, the bond graph modelof VDHM consists of three power interchange ports with theenvironment: the first two ports are the hydraulic inflow andoutflow ports of motor, while the third port represents themechanical connection to the next components, the emulsionpump. Like the VDP model, the internal leakage and rota-tional friction effects are taken into consideration. Besides,the inertia moment of the motor is also modeled due to thepossible fluctuations of rotation velocity and is represented byan energy store element of 𝐼

10. The constitutive relations of

MTF element symbolizing the variable displacement motorcan be expressed as

𝑒

9= 𝑒

8× 𝑉

𝑚(𝛽) ,

𝑓

8= 𝑓

9× 𝑉

𝑚(𝛽) ,

(4)


1Port 1

23

4

5

6

7

8 9

10

11

12Port3

Port 2

Motor leakage

Motor disp

Motor friction

Moment of inertia

0

0

1

11 MTF

R R

I

Figure 3: Bond graph model of the variable displacement motor.

1Port 1 2 6

3

105

9

87

Port 2

4

01

R

RR

TFTF

C

Gearbox ratio

Moment of inertiaI

E pump friction E pump C

E pump leakageE pump R valve

E pump disp

Figure 4: Bond graph model of the emulsion pump.

where 𝑒8and 𝑓

8are the input pressure and flow rate of

VDHM, respectively; 𝑒9and 𝑓

9are the output torque and

angular velocity of VDHM, respectively; and𝑉𝑚(𝛽) and 𝛽 are

the motor geometric displacement and displacement controlsignal, respectively.

The state-space equation of VDHMderived from its bondgraph model can be expressed as

̇

𝑃

10= −

𝑅

11

𝐼

10

𝑃

10+ 𝑉

𝑚𝑒

1− 𝑉

𝑚𝑒

5− 𝑒

12, (5)

where 𝑃10

is the angular momentum; ̇𝑃10

is the torque (thetime differential of 𝑃

10); and 𝑒

12is the output torque of

hydraulic motor.

2.2.3. Emulsion Pump. By the emulsion pump, the inputmechanical rotational energy is converted into hydraulicenergy of emulsion fluid. As illustrated in Figure 4, themodelof emulsion pump is similar to that of VDP except that theemulsion pump is a fixed displacement pump represented bya TF element instead of an MTF and that the emulsion pumpcontains an internal gearbox. The gearbox can be modeledby another TF element of which the constitutive equation isexpressed as

𝑓

2= 𝑓

1× 𝑖,

𝑒

1= 𝑒

2× 𝑖,

(6)

where 𝑓1and 𝑓

2are the input and output angular velocity of

the gearbox, respectively; 𝑒1and 𝑒2are the input and output

Port P1

Port A

2 3

4 56

7 8

9

1011

12 1314

1516

Port T

Port B

Positionsensors

R PA R AT

R PB R BTMR MR

MRMR

0 0

0

01 1

11

Figure 5: Bond graph model of the direction valve.

torque of the gearbox, respectively; and 𝑖 is the transmissionratio of the gearbox.

Similar to the VDHM model, the inertia moment ofemulsion pump is added to the model for the considerationthat the rotation velocity may fluctuate during operation.

After causality assignment, the state-space equations ofthe emulsion pump are obtained as follows:

̇

𝑃

4= −

𝑅

3

𝐼

4

𝑃

4−

𝑉ep

𝐶

9

𝑄

9+ 𝑖𝑒

1,

̇

𝑄

9=

𝑉ep

𝐼

4

𝑃

4− (

1

𝑅

7

+

1

𝑅

8

)

1

𝐶

9

𝑄

9− 𝑓

10,

(7)

where 𝑃4and ̇𝑃

4are the angular momentum and torque,

respectively; 𝑄9and ̇𝑄

9are the fluid volume and flow rate,

respectively; and 𝑒1and 𝑒10

are the input torque and outputpressure of emulsion pump, respectively.

2.2.4. Direction Control Valve. To cycle the operation of thissystem, the 4/3 way direction control valve is used to reversethe flow direction of cylinder chambers when the cylinderpiston reaches its end of stroke. The valve contains fourports: ports P and T are linked to pressurized oil and thetank, respectively, while ports A and B are connected to thetwo chambers of cylinder. The valve has only two workingpositions (left and right positions) and is controlled to changeposition by the position sensors installed on the cylinder rod.When the valve works at its left position, the flow paths insidethe valve from port P to port A and from port B to port T areopen, whereas the flow paths from port P to port B and fromport A to port T are sealed. When the valve is triggered tochange to its right working position, the flow paths patternchanges reversely. This kind of working principle can beimplemented employing four position-modulated dissipativeelements of MR between the ports of PA, AT, PB, and BT,the resistance of which is modulated by the control signalfrom the position sensors, as shown in Figure 5. When theMR resistance between ports P and A, for example, is set toa sufficiently large value, the flow path from ports P to A isclosed and hence no fluid passes. A relatively much smallerresistance of MR between port P and port A means that


the flow path from port P to port A is open. The constitutiveequation of MR can be expressed as follows:

𝑓 =

{

{

{

{

{

𝐶

𝑑𝐴√

2Δ𝑝

𝜌

if flow path is open

0 if flow path is closed,(8)

where 𝑓 is the flow rate; 𝐶𝑑is the discharge coefficient of

valve;𝐴 is the flow area;Δ𝑝 is the pressure difference betweentwo ports; and 𝜌 is the fluid density.

According to the bond graph methodology, the outputflow rate of the four ports can be derived and expressed as

𝑓

1= (

1

𝑀𝑅

3

+

1

𝑀𝑅

15

) 𝑒

1−

1

𝑀𝑅

3

𝑒

5−

1

𝑀𝑅

15

𝑒

13,

𝑓

5=

1

𝑀𝑅

3

𝑒

1− (

1

𝑀𝑅

3

+

1

𝑀𝑅

7

) 𝑒

5+

1

𝑀𝑅

7

𝑒

9,

𝑓

9= −

1

𝑀𝑅

7

𝑒

5+ (

1

𝑀𝑅

7

+

1

𝑀𝑅

11

) 𝑒

9−

1

𝑀𝑅

11

𝑒

13,

𝑓

13=

1

𝑀𝑅

15

𝑒

1+

1

𝑀𝑅

11

𝑒

9− (

1

𝑀𝑅

15

+

1

𝑀𝑅

11

) 𝑒

13,

(9)

where 𝑓1, 𝑓5, 𝑓9, and 𝑓

13are the flow rate of ports P, A, T, and

B, respectively and 𝑒1, 𝑒5, 𝑒9, and 𝑒

13are the pressure of ports

P, A, T, and B, respectively.

2.2.5. Symmetrical Cylinders. A hydraulic cylinder is essen-tially a power transformer which converts the hydraulicpower into mechanical translational domain and could besimply symbolized by a TF element in bond graph modelingwith the following constitutive equations:

𝐹 = 𝑝 × 𝐴,

𝑞 = V × 𝐴,(10)

where 𝐹 and V are the output force and velocity of cylinder,respectively; 𝑝 and 𝑞 are the input pressure and flow rate ofcylinder, respectively; and 𝐴 is the piston area.

In this particular system, the two hydraulic cylindersare the energy regenerative components, recovering andconverting the hydraulic energy of emulsion fluid outputfrom emulsion pump first into mechanical energy and thenback into hydraulic energy of oil. A couple of symmetricalcylinders are employed to make sure that the output forceand velocity of cylinder remain the same no matter whichchamber of the cylinder is filled with pressurized fluid. Asillustrated in Figure 6, a sophisticated model of the sym-metrical cylinder is established. This model contains threeinteract ports with the environment: port A and port B arethe inflow and outflow ports of hydraulic domain, while portC is the velocity output port of mechanical domain. Lossesassociated with the internal leakage and friction at the pistonare implemented using the resistive elements 𝑅

5and 𝑅

13,

respectively. The two capacitive elements 𝐶2and 𝐶

8are used

to represent the compressibility of fluid in the two chambersof cylinders, the capacitance of which keeps changing during

12

34

5

6

78

9

1011

12

13

14

Port B

Port C

Port A

0

0

MassC

C

I

1 11TFPiston area

Cylinder friction

Chamber A

Chamber B

Leakage

R

R

Figure 6: Bond graph model of the cylinder.

operation due to the change of chamber volume caused by thepiston movement.

The state-space equations of cylinder derived from itsbond graph could be expressed as

̇

𝑄

2= −

1

𝐶

2𝑅

5

𝑄

2+

1

𝐶

8𝑅

5

𝑄

8−

𝐴pi

𝐼

12

𝑃

12+ 𝑓

1,

̇

𝑄

8=

1

𝐶

2𝑅

5

𝑄

2−

1

𝐶

8𝑅

5

𝑄

8+

𝐴pi

𝐼

12

𝑃

12− 𝑓

7,

̇

𝑃

12= −

𝐴pi

𝐶

2

𝑄

2+

𝐴pi

𝐶

8

𝑄

8−

𝑅

13

𝐼

12

𝑃

12+ 𝑒

14.

(11)

In the above, 𝑄2, ̇𝑄2and 𝑄

8, ̇𝑄8are the volume and flow rate

of the two chambers of cylinder, respectively; 𝑃12and ̇𝑃

12are

the outputmomentumand force of cylinder, respectively; and𝑓

1, 𝑓7, and 𝑒

14are the input flow rate, output flow rate, and

output force of cylinder, respectively.

2.2.6. Rectifier Valve. The rectifier valve, which resemblesa full-wave rectifier circuit in electrical system, consists offour check valves connected in a certain pattern. As known,the check valve allows flow in only one direction, like adiode in electrical systems. Such behavior can be modeled inbond graph using a MR element with conditional equationswhich determine the flow through the valve depending on thepressure difference between the two ports. The equation ofone check valve is given as follows:

𝑞

𝑐=

{

{

{

{

{

{

{

{

{

{

{

{

{

{

{

{

{

{

{

Δ𝑝

𝑝cl𝑞cl if Δ𝑝 < 𝑝cl

𝑞cl +Δ𝑝 − 𝑝cl𝑝op − 𝑝cl

(𝑞op − 𝑞cl) if 𝑝cl ≤ Δ𝑝 ≤ 𝑝op

𝐶

𝑑𝐴

𝑐√

2Δ𝑝

𝜌

if Δ𝑝 > 𝑝op,

(12)

where 𝑞𝑐and Δ𝑝 are the flow-rate and pressure difference of

check valve, respectively; 𝑝cl and 𝑝op are reference pressuresfor the closing and opening of the valve; 𝑞cl and 𝑞op are thecorresponding flow rate; 𝐶

𝑑is the discharge coefficient of

valve; 𝐴𝑐is the cross-section area of valve; and 𝜌 is the fluid

density.As shown in Figure 7, the bond graph model of the

rectifier valve contains three ports: port 1 and port 2 are linked


Port 2

15

Port 1

Port 3

1

23

4

56

78

9

1413

12

11 10

16

chk valve2 chk valve1

chk valve4chk valve3

MR MR

MRMR

Se

0

00

0

1 1

11

Backpressure

Figure 7: Bond graph model of the rectifier valve.

to the two chambers of the recovery cylinder, whereas port3 is connected to VDHM, transferring the recovered energyback into the system again.

The flow rate of the rectifier valve could be expressed as

𝑓

1= (

1

𝑀𝑅

3

+

1

𝑀𝑅

6

) 𝑒

1−

1

𝑀𝑅

6

𝑒

8−

1

𝑀𝑅

3

𝑒

16,

𝑓

8= −

1

𝑀𝑅

6

𝑒

1+ (

1

𝑀𝑅

10

+

1

𝑀𝑅

6

) 𝑒

8−

1

𝑀𝑅

10

𝑒

12,

𝑓

12=

1

𝑀𝑅

10

𝑒

8− (

1

𝑀𝑅

10

+

1

𝑀𝑅

14

) 𝑒

12+

1

𝑀𝑅

14

𝑒

16,

𝑓

16=

1

𝑀𝑅

3

𝑒

1+

1

𝑀𝑅

14

𝑒

12− (

1

𝑀𝑅

3

+

1

𝑀𝑅

14

) 𝑒

16,

(13)

where𝑓1, 𝑒1,𝑓12, and 𝑒

12are the flow rate and pressure of port

1 and port 2, respectively; 𝑓8and 𝑒8are flow rate and pressure

of oil supply, respectively; and 𝑓16

and 𝑒16

are the flow rateand pressure of port 3, respectively.

2.2.7. Accumulator. The accumulator, like a capacitor inelectrical systems, could smooth the pressure and flowfluctuations in the system as well as store hydraulic energy.The accumulator employed in this system is a common gas-charged one which uses a gas-filled bladder in its chamber. Inpractical applications, the gas chamber of the accumulator isprecharged to a certain pressure before installation and there-fore the accumulator only functions when the fluid pressuresurpasses the gas pressure. When the accumulator is beingcharged (or discharged), the compression (or expansion) ofthe gas follows the following relation:

𝑝

2= 𝑝

1(

𝑉

1

𝑉

1− Δ𝑉

)

𝑘

,(14)

where 𝑝1and 𝑉

1are the initial gas pressure and volume,

respectively; Δ𝑉 is the fluid volume that flowed into theaccumulator; and 𝑝

2is the charged pressure of accumulator.

1

2

43

5Port 2Port 1 0

1

acc inlet R

C

Oil accumulator C

MR

Figure 8: Bond graph model of the accumulator.

3Port 2Port 1

1

2 4

5

Pipe R Pipe CR C

1 0

Figure 9: Bond graph model of the pipeline.

The value of the specific heat ratio 𝑘 depends on whether theexpansion and compression occur rapidly or slowly.

The bond graph model of an accumulator is illustratedin Figure 8. The MR element used here not only representsthe flow resistance at the inlet port of accumulator when theaccumulator interacts with the whole system, being chargedor discharged, but also functions like a switch which couldisolate the accumulator from the system if the fluid pressuredoes not surpass the precharged gas pressure. The resistanceof MR is modulated by the control signal of inlet pressuresymbolized by a triangle arrow in Figure 8.

The state-space equation of accumulator derived fromFigure 8 could be expressed as follows:

̇

𝑄

4= −

1

𝐶

4𝑀𝑅

3

𝑄

4+

1

𝑀𝑅

3

𝑒

1, (15)

where 𝑄4and ̇𝑄

4are the volume and flow rate of fluid in the

accumulator, respectively, and 𝑒1is the input fluid pressure of

accumulator.

2.2.8. Pipelines. Pipelines, similar to transmission lines inelectrical systems, transfer hydraulic fluid from one point toanother. The bond graph model of pipelines is illustrated inFigure 9. There are two significant characteristics of pipeswhich should be considered in modeling this system. One isthe energy loss which happens by means of pressure dropsas the fluid flows through the pipelines. This pressure dropalong the pipes can be symbolized by a resistive element andexpressed as

𝑅 =

128𝜌𝜐𝐿

𝜋𝐷

4,

(16)


1

2

3 4

5

6 7

89

17

10

11

12

13

14

15

16

18

1920

2122

25

24

26

27

29

28

30

31

32 33

23

34

35 36

3738

40

39

41

727345

42

56

46 44

43

55

48

54

58

57

47

5051

49

52

53

6465

63

62

61

60

59

66

67

78

84 74

75

85

6869

70

71

77

86

8382

768081

799291

90

89

87

88 Position sensor

Pump

Accumulator

Pipe

Pipe

Hydraulic motor Emulsion pump

Accumulator

Direction valveEmulsion cylinder

Recovery cylinderRectifier valve

R

R

R

R

RR

R

RR

R C

C

C C

C

C

1 1 1 1 1

1

1

1

1

0 0

0

0 00Sf MTFMTF

MRMR

TF TF

I

I

R R

R

C

C

C

C

1

1 11 1 1

1 1

1 1

1

11

0

0

0

0 0 0

0

0

0

0

0 0

Vp Vm

MRMR

MR MR

Se TF TF

MR

MR MR

MR

Se

Se

Figure 10: Bond graph model of the overall system.

where 𝜌 is the fluid density; 𝜐 is the kinematic viscosity of thefluid; 𝐿 is the pipe length; and𝐷 is the pipe diameter.

The other one is the capacitance effect of the fluid insidethe pipes represented by a 𝐶 element, like the chamber of acylinder. However, the inertia effect of fluid in pipelines isreasonably neglected because flow-rate fluctuations of highfrequency do not exist in this system during operation.

The state-space equation of the pipeline is derived asfollows:

̇

𝑄

4= −

1

𝐶

4𝑅

2

𝑄

4+

1

𝑅

2

𝑒

1− 𝑓

5, (17)

where𝑄4and ̇𝑄

4are the volume and flow-rate of fluid inside

the pipelines, respectively, and 𝑒1and𝑓5are the input pressure

and output flow rate of the pipelines, respectively.

2.3. System Modeling. The bond graph model of the overallsystem, as shown in Figure 10, is established by assemblingall the components models according to the hydraulic sys-tem in Figure 1. In Figure 10, the bonds and elements inmagenta represent the power transferring and distributionsin mechanical domain, while the bonds and elements in redand blue symbolize the power transferring and distributionsin hydraulic domain of oil and emulsion fluid, respectively.

Some simplifications and approximations are made inthe overall model to avoid the causality conflicts of energystore elements (𝐶 and 𝐼) and hence the differential algebraicequations. Further information about causal conflicts andsolutions could be referred to in [32, 33]. The 𝐼

66element,

for instance, represents the combined mass of pistons androds of both cylinders. Similarly, the 𝐼

27element represents

the combined moment of inertia of both hydraulic motorand emulsion pump. The overall bond graph model of thissystem contains 12 energy store elements (𝐶 and 𝐼 elements)and hence the state-space equations derived from this modelconsist of 12 state variables and 12 equations. The state-spaceequation of the overall system in matrix can be expressed as

[ẋ (𝑡)]12×1 = [A]12×12 ∙ [x (𝑡)]12×1 + [B]12×4 ∙ [u (𝑡)]4×1,(18)

where [x(𝑡)]12×1

= [𝑄

5𝑄

11𝑄

15𝑄

21𝑃

27𝑄

34𝑄

40𝑄

57

𝑄

61𝑃

66𝑄

72𝑄

77]

𝑇; [ẋ(𝑡)]12×1

is the time differential of[x(𝑡)]12×1

; and [u(𝑡)]4×1

= [𝑓

1𝑒

24𝑒

49𝑒

82]

𝑇. The detailed[A]12×12

and [B]12×4

are presented in Appendix.

3. Simulation of ERS

The simulation of the bond graphmodel of the overall systemwas carried out within the MATLAB/Simulink software. Thedurable test in the test standard, for instance, was chosenfor simulation which required the test emulsion pump to berunning continuously and constantly at its nominal pressureand speed for 500 hours. The nominal pressure and speedof the test emulsion pump used in simulation are 20MPaand 1470 rev/min, and themajor parameters of simulation areshown in Table 1.

During the simulation the geometric displacements ofboth VDP and VDHM were kept constant to ensure that


Table 1: Simulation parameters.

Parameter Value UnitMotor rotation speed 1470 rev/minPump displacement 23.9 mL/revHydraulic motor displacement 42.0 mL/revMechanical efficiency of pump andhydraulic motor 0.95 —

Volumetric efficiency of pump andhydraulic motor 0.91 —

Emulsion pump displacement 73.1 mL/revNominal input rotation speed ofemulsion pump 1470 rev/min

Internal reduction ratio 1470/547 —Crankshaft speed of emulsion pump 547 rev/minMechanical efficiency of emulsion pump 0.9 —Volumetric efficiency of emulsion pump 0.9 —Cylinder piston area 10725 mm2

Cylinder stroke 0.75 mBack pressure 1.4 MPaPrecharged gas pressure of accumulator 10.5 MPaAccumulator volume 10 L

0 20 40 60 80 100 120 140 1600

4

8

12

16

20

24

28

32

PressureRotation speed

Time (s)

Pres

sure

(MPa

)

0

210

420

630

840

1050

1260

1470

1680

Rota

tion

spee

d (r

ev/m

in)

Figure 11: Simulation results of the test emulsion pump.

the emulsion pump will be running at the nominal conditionas the test standard required. The simulation was carried outfor 160 s with a maximum step of 0.15 s, simulating the ERSstarting from static stage to final steady dynamic stage. Thesimulation results are depicted in Figures 11–13.

As illustrated in Figure 11, it takes nearly 80 s for the ERSto establish its final steady state due to the two accumulatorsof which the precharged gas pressures are much lower thanthe steady ones. In the steady stage, the rotation speed isaround 1470 rev/min and the pressure is 20MPa, satisfyingthe requirements of durable test.

More importantly the power consumptions of majorcomponents should be investigated in depth, as depicted inFigure 12. On one hand, it is the output power of emulsion

0 20 40 60 80 100 120 140 160

0

3

6

9

12

15

18

Pow

er (k

W)

Time (s)

Hydraulic motor outputEmulsion pump inputEmulsion pump output

Motor outputRecovery

Figure 12: Power consumption ofmajor components by simulation.

0 20 40 60 80 100 120 140 160

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

Pump lossRectifier valve Backpressure valve

Pow

er lo

ss (k

W)

Time (s)

Emulsion pumpHydraulic motorCylinders

Figure 13: Power loss comparison of major components by simula-tion.

pump that can be recovered and reutilized from the durabletest by this ERS but wasted by the original system in the teststandard. This total recoverable power is around 11.93 kW,while the regenerative power saved by this ERS is about9.74 kW.Therefore, the regenerative coefficient of this system(the ratio of the recovered power to output power of emulsionpump) reaches as high as 81.6%. The remaining 18.4% of11.93 kW is cost by means of frictions and pressure losses incylinders and rectifier valve.

On the other hand, the overall energy efficiency ofthe whole system is also of great significance for ERS.From the global energy point of view, the actual powerconsumption of this ERS for durable test, that is, the outputpower of induction motor, is about 10.36 kW, whereas theinput power of emulsion pump, that is, the power cost andwasted by the original test system, is 14.83 kW. In other


Motor

Oil tank

Pump

Cooler

Controlsystem

Accumulator

Hydraulicmotor

Emulsionpump

Emulsiontank

Cylinders

Rectifier valve

Pressuresensor Flow-rate

sensor

Figure 14: Test bench.

words, when doing durable tests, this novel ERS costs only10.36 kW instead of the original 14.83 kW, saving 4.47 kW.Consequently the energy-saving coefficient of this system(the ratio of decreased power consumption to original powerconsumption) is as high as 30.1%.

Figure 13 illustrates the comparison of power lossesbetween major components. As seen in Figure 13, emulsionpump costs the most power loss (2.90 kW) due to its volu-metric and mechanical coefficient and accounts for 28.0% ofthe total power loss (10.36 kW). The power losses of VDHMandVDP are 2.12 kW and 1.34 kW and account for 20.5% and12.9% of the total loss, respectively. The two cylinders cost1.67 kW (16.1%), while the rectifier valve costs 1.15 kW (11.1%).The power loss of backpressure valve is 0.88 kW and accountsfor 8.5% of the total power loss.

These losses caused by the internal friction and leakageof hydraulic components, however, could be reduced byemploying hydraulic components with higher machiningaccuracy quality and hence higher efficiency, achieving abetter energy efficiency of the overall system and savingmoreenergy.

4. Experimental Validation

Experiments were carried out to validate the bond graphmodeling and simulation results of the novel ERS. This testbench, as shown in Figure 14, was built according to theschematic diagram in Figure 1. For validation conveniences,major parameters of the test bench are the same as those of thesimulation shown in Table 1. Like the simulation, the wholesystem was driven by the electric motor from the state of rest,and during experimental tests the geometric displacements ofboth VDP and VDHM were kept constant to ensure that theemulsion pump will be running at the nominal condition asthe test standard required. The experiment was also carriedout for 160 s with a sample time of 0.15 s. The experimentresults are depicted in Figures 15–17.

In Figure 15, the speed and pressure curves illustrate thatthe test emulsion pump is running at its nominal speed(1470 r/min) and pressure (20MPa), satisfying the durabletest requirements and verifying that both the bond graphmodeling and simulation of this novel ERS are accurate.

0 20 40 60 80 100 120 140 1600

4

8

12

16

20

24

28

32

PressureRotation speed

Time (s)

Pres

sure

(MPa

)

0

210

420

630

840

1050

1260

1470

1680

Rota

tion

spee

d (r

ev/m

in)

Figure 15: Experiment results of the test emulsion pump.

0 20 40 60 80 100 120 140 160

0

4

8

12

16

20

Pow

er (k

W)

Time (s)

Hydraulic motor outputEmulsion pump inputEmulsion pump output

Motor outputRecovery

Figure 16: Power consumption of major components by experi-ment.

Due to the buffering of two accumulators, the systemgradually establishes its final steady state in around 65seconds.The periodic fluctuations in speed curves are causedby the motion direction changes of the cylinders. Whencylinders come to the stroke end, position sensors trigger thedirection control valve to change from one working positionto the other one, changing the flow paths. These transientflow paths changes result in the flow-rate loss of cylindersand rectifier valve, and hence the input flow-rate of VDHMdecreases, so does the output speed of VDHM (also the speedof emulsion pump). After comparison and analysis, we findthat these periodic fluctuations could be better buffered byaccumulators of larger volume.

The experiment results of power consumptions aredepicted in Figure 16. The output power of emulsion pumpis around 11.80 kW, while the regenerative power saved bythis ERS is about 10.18 kW. Therefore, the experimental


0

1

2

Pump

Pow

er lo

ss

(kW

)

(a)

0123

Hydraulic motor

Pow

er lo

ss

(kW

)

(b)

024

Emulsion pump

Pow

er lo

ss

(kW

)

(c)

0

1

2

Cylinders

Pow

er lo

ss

(kW

)

(d)

0

1

2

Rectifier valve

Pow

er lo

ss

(kW

)

(e)

0

1

Backpressure valve

Pow

er lo

ss

(kW

)

(f)

0 20 40 60 80 100 120 140 1600123

Time (s)

Others

Pow

er lo

ss

(kW

)

(g)

Figure 17: Power loss comparison of major components by experiment.

regenerative coefficient of this system (the ratio of the recov-ered power to output power of emulsion pump) is as highas 86.3%. The output power of induction motor is 11.43 kW,whereas the input power of emulsion pump is 15.02 kW. So thepower saved by experimental tests is 3.59 kW and the energy-saving coefficient by experiment is 23.9%.

Figure 17 illustrates the detailed power losses of majorcomponents. As shown in Figure 17, emulsion pump costs themost power loss (3.22 kW) due to its efficiency and accountsfor 28.2% of the total power loss (11.43 kW). The averagepower losses of VDHM and VDP are 2.51 kW and 1.44 kWand account for 22.0% and 12.6% of the total loss, respectively.The two cylinders cost 1.41 kW (12.3%), while the rectifiervalve costs 1.24 kW (10.8%). The power loss of backpressurevalve is 0.77 kW and accounts for 6.7% of the total power loss.

These experimental results in both power consumptionand loss reasonably match those of simulation with littleerrors and consequently validate the accuracy of bond graphmodeling and simulation of the novel system.

5. Concluding Remarks

This paper demonstrates the virtue of bond graph methodol-ogy in modeling the energy regenerative system for emulsionpump tests, a system involving several energy domainsand energy conversion processes, by first considering thecomponents separately and then assembling them together

accordingly. Bond graph models of each component aredeveloped and the state-space equations of each componentare also derived, so are the bond graph model and the state-space equations of the whole system.

Illustrative simulation results of the novel ERS for thedurable test have been represented. The simulation resultsof the model validate that this ERS not only fulfills therequirements of the test but also recovers and reutilizes 81.6%of the output energy of the test emulsion pump which iswasted by the original test system. Moreover, this novel ERScould reduce 30.1% energy consumption as compared to theoriginal test system. Experiments are also carried out and theresults primely validate the accuracy of both the bond graphmodeling and simulation of this novel ERS.

Although it has periodic fluctuations of speed and itsenergy efficiency is not perfectly high enough, this ERS, webelieve, does provide a promising method of energy savingfor emulsion pump tests. In future, we would like to usethe described bond graph model to develop online controlalgorithms for this ERS.

Appendix

The nonzero item of [A]12×12

and [B]12×4

is as follows:

𝑎

1,1= −

1

𝐶

5

(

1

𝑅

6

+

1

𝑅

7

+

1

𝑀𝑅

10

+

1

𝑅

13

+

1

𝑀𝑅

87

+

1

𝑀𝑅

91

) ,


𝑎

1,2=

1

𝑀𝑅

10𝐶

11

, 𝑎

1,3=

1

𝑅

13𝐶

15

,

𝑎

1,11=

1

𝐶

72𝑀𝑅

87

, 𝑎

1,12=

1

𝐶

77𝑀𝑅

91

;

𝑎

2,1=

1

𝐶

5𝑀𝑅

10

, 𝑎

2,2= −

1

𝑀𝑅

10𝐶

11

;

𝑎

3,1=

1

𝐶

5𝑅

13

, 𝑎

3,3= −

1

𝐶

15

(

1

𝑅

13

+

1

𝑅

18

) ,

𝑎

3,4=

1

𝑅

18𝐶

21

, 𝑎

3,5= −

𝑉

𝑚

𝐼

27

;

𝑎

4,3= −

1

𝐶

15𝑅

18

, 𝑎

4,4= −(

1

𝑅

18

+

1

𝑅

23

) ,

𝑎

4,5= −

𝑉

𝑚

𝐼

27

;

𝑎

5,3=

𝑉

𝑚

𝐶

15

, 𝑎

5,4= −

𝑉

𝑚

𝐶

21

,

𝑎

5,5= (−𝑅

28+ 𝑖𝑅

31)

1

𝐼

27

, 𝑎

5,6= −

𝑖𝑉ep

𝐶

34

;

𝑎

6,5=

𝑖𝑉ep

𝐼

27

,

𝑎

6,6=

1

𝐶

34

(−

1

𝑅

35

−

1

𝑅

36

−

1

𝑅

39

+

1

𝑀𝑅

43

+

1

𝑀𝑅

55

) ,

𝑎

6,7=

1

𝑅

39𝐶

40

, 𝑎

6,8= −

1

𝑀𝑅

43𝐶

57

,

𝑎

6,9= −

1

𝑀𝑅

55𝐶

61

;

𝑎

7,6=

1

𝐶

34𝑅

39

, 𝑎

7,7= −

1

𝑅

39𝐶

40

;

𝑎

8,6=

1

𝐶

34𝑀𝑅

43

,

𝑎

8,8=

1

𝐶

57

(−

1

𝑀𝑅

43

+

1

𝑀𝑅

47

−

1

𝑅

59

) ,

𝑎

8,9=

1

𝑅

59𝐶

61

, 𝑎

8,10=

𝐴

𝐼

66

;

𝑎

9,6= −

1

𝐶

34𝑀𝑅

55

, 𝑎

9,8=

1

𝐶

57𝑅

59

,

𝑎

9,9=

1

𝐶

61

(−

1

𝑀𝑅

51

+

1

𝑀𝑅

55

+

1

𝑅

59

) ,

𝑎

9,10=

𝐴

𝐼

66

;

𝑎

10,8=

𝐴

𝐶

57

, 𝑎

10,9= −

𝐴

𝐶

61

,

𝑎

10,10= −

𝑅

67

𝐼

66

, 𝑎

10,11= −

𝐴

𝐶

72

,

𝑎

10,12=

𝐴

𝐶

77

;

𝑎

11,1=

1

𝐶

5𝑀𝑅

87

, 𝑎

11,10=

𝐴

𝐼

66

,

𝑎

11,11= −

1

𝐶

72

(

1

𝑅

75

+

1

𝑀𝑅

84

+

1

𝑀𝑅

87

) ,

𝑎

11,12=

1

𝑅

75𝐶

77

;

𝑎

12,1=

1

𝐶

5𝑀𝑅

91

, 𝑎

12,10= −

𝐴

𝐼

66

,

𝑎

12,11=

1

𝐶

72𝑅

75

,

𝑎

12,12= −

1

𝐶

77

(

1

𝑅

75

+

1

𝑀𝑅

80

+

1

𝑀𝑅

91

) ;

𝑏

1,1= 𝑉

𝑝, 𝑏

4,2=

1

𝑅

23

,

𝑏

8,3= −

1

𝑀𝑅

47

, 𝑏

9,3=

1

𝑀𝑅

51

,

𝑏

11,4=

1

𝑀𝑅

84

, 𝑏

12,4=

1

𝑀𝑅

80

.

(A.1)

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper.

Acknowledgments

This work was financially supported by the Program spon-sored for Scientific Innovation Research of College Graduatein Jiangsu Province (Grant no. CXZZ11 0288), the programsupported by the special fund of Jiangsu Province for theIndustrialization of Scientific and Technological Achieve-ments (Grant no. JHB2012-29), and the project funded by thePriority Academic Program Development of Jiangsu HigherEducation Institutions (PAPD). The authors’ heartfelt thanksshould also go to the reviewers for their valuable remarks.

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research article bond graph modeling and validation of an ...bond graph would be a preferable method...

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