Review Article A Review on Mechanical and Hydraulic System ...downloads.hindawi.com/archive/2016/9409370.pdf · hydraulic systems: mathematical modeling and simulation modeling using

Review ArticleA Review on Mechanical and Hydraulic System Modelingof Excavator Manipulator System

Jiaqi Xu and Hwan-Sik Yoon

Department of Mechanical Engineering University of Alabama Box 870276 Tuscaloosa AL 35487-0276 USA

Correspondence should be addressed to Hwan-Sik Yoon hyoonenguaedu

Received 26 January 2016 Accepted 29 August 2016

Academic Editor Eric Lui

Copyright copy 2016 J Xu and H-S YoonThis is an open access article distributed under the Creative CommonsAttribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

A recent trend in the development of off-highway construction equipment such as excavators is to use a systemmodel for model-based system design in a virtual environment Also control system design for advanced excavation systems such as automaticexcavators and hybrid excavators requires systemmodels in order to design and simulate the control systemsTherefore modelingof an excavator is an important first step toward the development of advanced excavators This paper reviews results of recentstudies on the modeling of mechanical and hydraulic subsystems for the simulation design and control development of excavatorsystems Kinematic and dynamic modeling efforts are reviewed first Then various approaches in the hydraulic system modelingare presented

1 Introduction

The model-based system design approach allows for an effi-cient way of designing and developing complex engineeringsystems in a virtual environment [1 2] In model-basedcontrol system design four steps are typically employed (1)modeling a plant (2) synthesizing a controller for the plant(3) simulating the plant and controller together and (4)integrating the overall system Therefore system modelingis an important first step in model-based system designExamples of the systems that can benefit from model-based design include off-highway construction and miningequipment as well as automotive and aerospace systems Byemploying themodel-based systemdesign approach productdevelopment cost and time can be significantly reduced

Hydraulic excavators are from the most widely usedearthmoving equipment in construction and mining indus-try and they will continue to play an important role amongoff-highway vehicles in years to come [3ndash5] Typical opera-tions of hydraulic excavators include grading digging andloading which all require coordinated manipulation of theboom arm and bucket cylinders Due to the high level of skillrequired for the coordinated operation of the manipulator

system operating an excavator efficiently is not an easy taskAn automated excavation system can assist less experiencedoperators to complete given tasks in a time-efficient mannerwith acceptable work quality For example an autonomous25-ton hydraulic excavator can fully load a truck in aboutsix passes with a typical loading time of 15ndash20 seconds perpass This rate is very close to what an expert operator canperform to manually load a truck using an excavator of thesame size [6] In addition automatic excavators have thepotential to facilitate various excavation and exploration tasksin hazardous environments or remote areas such as radiationzones [7 8]

The model-based system design approach can be appliedto the design and development of advanced excavators suchas automatic excavators and hybrid excavators Like anymodel-based system design the usual practice in controllerdevelopment for an advanced excavator system is to derivethe system model first and then develop a controller basedon the model Therefore deriving a systemmodel is a criticalcomponent in the development of an excavator Amongmanysubsystems and components in an excavator this paper isaimed at providing an overview on the recent developmentof system models for excavator manipulators

Hindawi Publishing CorporationJournal of Construction EngineeringVolume 2016 Article ID 9409370 11 pageshttpdxdoiorg10115520169409370

2 Journal of Construction Engineering

1205791

Z0 Y1

X1O1

X0O0

1205793

1205792

1205823

Y2

Y4

X2

X4

X3

1205824

1205822 Y3O3

O2

1205794

O4

Figure 1 Excavator coordinate systems in Denavit-Hartenbergconvention

An excavator manipulator is comprised of kinematicallyoperating mechanical links and a hydraulic system Thereexist two main approaches in modeling the mechanical andhydraulic systems mathematical modeling and simulationmodeling using commercially available software tools Thispaper starts with a review on kinematic and dynamic mod-eling of the mechanical linkage and then various modelingapproaches on hydraulic systems will be presented In eachsystem modeling review mathematical models will be pre-sented first and then simulation models will follow

2 Kinematic and Dynamic Modelsof Excavator Manipulator

Kinematic and dynamic models are used for simulation andcontroller development for an excavator manipulator system[9]

21 Kinematic Models Kinematic equations describe themotion of an excavator manipulator without considerationof the driving forces and torques [10] In the conventionalapproaches for kinematic analysis geometrical dimensionsof system components are defined first Although the actualboom arm and bucket in a manipulator are irregularlyshaped for the sake of simplicity of the analysis theyare assumed to be straight joint links whose lengths aredefined by the distance between two joints Each link hasits own Cartesian coordinate system that moves with thelink In order to handle coordinate transformation betweentwo Cartesian coordinate systems the Denavit-Hartenberg(D-H) convention is employed in most research The D-Hconvention was first adopted by Vaha and Skibniewski [11]to analyze the kinematics of an excavator model and thenfurther developed by Koivo et al [12 13] According to the D-H convention 119911-axis of the local coordinate system for eachlink is chosen to be in the direction of rotation of a revolutejoint and 119909-axis is set to point the other joint in the samelink [10] Then the direction of 119910-axis is defined accordingto the right-hand rule Finally a fixed Cartesian coordinatesystem is assigned to the excavator cab to be used as the globalcoordinate system as shown in Figure 1

s

r

B = (fa fr F)

997888a

997888l

997888e

997888u

Figure 2 Basic behavior module of integrated behavior-basedcontrol framework

Forward kinematic equations were derived to calculatethe positions and orientations of the manipulator linkswhen the joint angles and lengths of the links are given[10 13] By applying the Denavit-Hartenberg conventiona transformation matrix between two adjacent coordinatesystems (from 119894th to (119894 + 1)th) on a link can be written as

119894119879119894+1

= [[[[[[

cos 120579119894+1 minus cos120572119894+1 sin 120579119894+1 sin120572119894+1 sin 120579119894+1 119886119894+1 cos 120579119894+1sin 120579119894+1 cos120572119894+1 cos 120579119894+1 minus sin120572119894+1 sin 120579119894+1 119886119894+1 sin 120579119894+10 sin120572119894+1 cos120572119894+1 119889119894+10 0 0 1

]]]]]] (1)

where 120579119894+1 is the rotation angle about 119911119894 axis 120572119894+1 is therotation angle of 119911119894 axis about 119909119894+1 axis 119889119894+1 is the offsetalong the 119911119894 axis and 119886119894+1 is the length of the link Usingthe coordinate transformation matrix an arbitrary point inany local coordinate system can be represented in the globalcoordinate system as

0119875 = 0119879119899119899119875 = 011987911119879221198793 sdot sdot sdot 119899minus1119879119899119899119875 (2)

where 119899119875 is the position vector in the 119899th coordinate system0119875 is the position vector in the global coordinate system and0119879119899 is the transformation matrix from the 119899th to the globalcoordinate systems

Conversely inverse kinematic relations can be employedto determine the joint angles and cylinder lengths when thepositions and orientations of the links are known [12] Byapplying inverse kinematics sequentially all joint angles andhydraulic cylinder lengths can be obtained In the researchconducted by Pluzhnikov et al a behavior-based inversekinematic solver was proposed as shown in Figure 2 [21]Thebehavior-based module is characterized by triples such as

119861 = (119891119886 119891119903 119865) (3)

where 119891119886 represents the activity function 119891119903 is the targetrating function and 119865 is the transfer function of the jointbehavior In Figure 2 119904 is the stimulation

997888119897 is the inhibitionand997888119890 is the input vectorThese functions calculate the outputsignals activity 997888119886 target rating 119903 and the output vector 997888119906 According to the authors this method does not require highcomputation power but may not find solutions in some caseseven if the desired position is reachable

Journal of Construction Engineering 3z

(mm

)

3500

3000

2500

2000

1500

1000

500

0

minus500

minus1000

x (mm)3000 4000 5000 6000 7000 8000

Boom tip

Arm tip

Bucket tip

ExcavationLifting

(a) Experiment case 1 far operator 2 5th trial 1 cycle

z(m

m)

3500

3000

4000

2500

2000

1500

1000

500

0

minus500

x (mm)3000 4000 5000 6000 7000

Boom tip

Arm tip

Bucket tip

ExcavationLifting

(b) Experiment case 3 medium operator 23rd trial 1 cycle

z(m

m)

3500

3000

2500

2000

1500

1000

500

0

minus500

minus1000

x (mm)3000 4000 5000 6000 7000 8000

Boom tip

Arm tip

Bucket tip

ExcavationLifting

(c) Experiment case 2 near operator 2 5th trial 1cycle

Figure 3 Tracks of the tips of the boom arm and bucket [14]

In the kinematic design of an automatic excavator pathplanning is of primary concern where the desired globalcoordinates of the bucket tip and the associated motionof the other links need to be determined As an analyticalmethod the Cartesian-Space trajectory planning methodhas been extensively applied in the literature [18 22ndash25]More specifically 3rd- or 5th-order polynomials have beenemployed in the path planning of a manipulator occasionallyThe most common practice to design the trajectory is tospecify a desired starting point and end point correspondingto operation time as well as the working area and apply the3rd-order polynomialmethod as shown in the following [24]

119902 (119905) = 1198880 + 1198881119905 + 11988821199052 + 11988831199053 (119905) = 1198881 + 21198882119905 + 311988831199052 (4)

where 119888119895rsquos are coefficients of the polynomials 119905 representstime 119902 is the displacement and is the velocity

Although the 3rd-order method is simple to use themajor disadvantage of this approach is that the acceleration ofthe manipulator links is not continuous The discontinuitiesin the acceleration profile may cause sudden and large forcevariations which lead to jerk on the manipulator [18 24]For this reason a jerk-free trajectory planning method wasdeveloped using 5th-order polynomials where the motiontrajectories can be described by

119902 (119905) = 1198880 + 1198881119905 + 11988821199052 + 11988831199053 + 11988841199054 + 11988851199055 (119905) = 1198881 + 21198882119905 + 311988831199052 + 411988841199053 + 511988851199054 (119905) = 21198882 + 61198883119905 + 1211988841199052 + 2011988851199053

(5)

where is the acceleration of a link on the given trajectory [1026] With the position velocity and acceleration constraintsthe unknown coefficients of the 5th-order polynomials canbe obtained In this manner the position velocity andacceleration of each joint and link can be determined at agiven time instance

Table 1 Example of rule script for truck loading [6]

Situation Command

Joint 1 swing

(1) When digging finishes wait 1205791 = 5∘(2) If 1205792 gt 14∘ swing to truck 1205791 = 101∘(3) If 1205794 gt 10∘ swing to dig 1205791 = 0∘(4) If 1205791 = 0∘ stop and execute dig NA

Joint 2 boom (1) When digging finishes raise 1205792 = 18∘(2) If 1205791 lt 60∘ lower to dig 1205792 = 6∘

Joint 3 stick

(1) When digging finishes wait 1205793 = minus100∘(2) If 1205791 gt 31∘ move to spill point 1205793 = minus76∘(3) If 1205794 gt minus30∘ move to dump point 1205793 = minus92∘(4) If 1205791 lt 65∘ move to dig 1205793 = minus75∘

Joint 4 bucket(1) When digging finishes curl 1205794 = minus90∘(2) If 1205791 gt 60∘ and 1205793 gt minus89∘ open 1205794 = 30∘(3) If 1205791 lt 60∘ move to dig 1205794 = 7∘

In addition to the analytical methods there exist theso-called rule-based path planning methods Yamamoto etal and Yoshida et al conducted a series of experiments tomeasure trajectories of a manipulator controlled by differentoperators [14 27ndash29] In their research trajectories of thelinks the corresponding cylinder lengths and joint anglesduring excavation and loading processes were measured Inthis manner kinematic features of the motion trajectoriescould be experimentally extracted for typical excavationoperations conducted by skilled operators Usually the rule-based paths are designed based on actual manipulator oper-ations and thus are dependent on human operators [6 1429ndash32] Laser rangefinders have been applied to scan thetarget area to recognize the topography to determine themanipulator motion that should be followed An example setof control rules for a truck loading operation is shown inTable 1

The human dependency of the produced trajectorieswill introduce variations inevitably Figure 3 shows recorded

4 Journal of Construction Engineeringy

car p

os (

m)

10

5

0

minus5

minus10

x car pos (m)0 10 20 30 40 50

Figure 4 Example trajectory obtained by using random treemethod for a path searching problem to avoid obstacles [15]

tracks of tips of the boom arm and bucket links during dif-ferent operations by an expert operator conducting complexmaneuvers

To enhance the tracking capability for a valid path forthe manipulator a rapidly exploring random tree methodwas developed byMaeda et al which improved the responsesto the environment disturbances [15] An example trajectoryobtained by the random tree method is shown in Figure 4 fora path searching problem to avoid collisions with obstacles(shown as gray rectangles in the figure)

Another method to generate a working path was devel-oped by Makkonen et al by combining manipulator positiondata with a working zone terrain CADmodel which employstriangular elements defined by vertices [33 34] In theresearch by Lee and Kim [16] the excavating trajectory of anautonomous excavator was created by using a method calledvirtual motion camouflage (VMC) which was enlightenedby a predator tracking its prey The researchers conductedtwo types of simulations and created trajectories accordinglyone is the obstacle avoidance which is shown in Figure 5(a)and the other is the digging motion which is shown inFigure 5(b) The red trajectory shown in Figure 5 is the preypath which is formed without considering obstacles in thepath The green trajectory is the predator trajectory whichis created by considering the physical constraint The bluepoints are reference points which are used to determinethe relative position of the points on the prey and predatortrajectories

Recently artificial neural networks were applied in thetrajectory planning In the research by Atmeh and Subbarao[35] a dynamic neural network consisting of a recurrentneural network and two feedforward neural networks wasused to solve the trajectory generation problems adaptively

Additionally a trajectory compensationmethod based onpath prediction was developed Using this method a trajec-tory can be predicted and compensated based on real-timesimulation of a simplified system model to improve controlaccuracy [36] In order to optimize an energy consumptionrate Kim et al applied a gradient descent method Usingthemethod theminimum torque or minimumworking timetrajectorywas obtained and the energy consumption ratewasreduced as a resultThe geometric and dynamic restrictions ofthe excavator were taken into account as well in this method[37ndash39]

22 DynamicModels In a conventional study ofmanipulatordynamics mathematical models are derived by applyingNewton-Eulerrsquos or Euler-Lagrangersquos method These two dif-ferent approaches are equivalent and lead to the same setof dynamic equations [11 13 37 40ndash43] In Euler-Lagrangersquosapproach dynamic equations can be derived from a Lagrangeenergy function by treating a manipulator system as awhole [10 26] Dynamic equations can also be derived byapplying Newton-Eulerrsquos method successively to each link byconsidering each link as a free body [11 13 23 41 42] Ingeneral the resulting equation takes the following form

120591 = M (119906) + h (119906 ) + g (119906) (6)

where 120591 is the torque vector at all joints 119906 representsan angular displacement of the corresponding joint M(119906)represents the mass matrix h(119906 ) is the Coriolis force termand g(119906) is the gravity term

In addition to the conventional mathematical modelingmodeling methods based on transfer functions have beendeveloped In the research by Gu et al [17] a dynamicresponse model based on a transfer function was establishedby using the Simplified Refined Instrumental Variable (SRIV)method For example a dynamic equation of a manipulatorlink can be written as

119910 (119896) = 119887 (119911minus1)1 minus (119911minus1)119906 (119896) (7)

where 119911 is a differential operator 119910(119896) is the output angleof the corresponding link 119906(119896) is the input voltage and 119887is a time-invariant numerator parameter estimated for eachmanipulator operation In an experiment for the acquisitionof a manipulator input-output relation input voltage 119906(119896)is specified first Then parameter 119887 is estimated by theSRIV algorithm and the system transfer function can bedetermined as a result [17] An example plot of an excavatorarm displacement for a constant input drive is shown inFigure 6 Also Filla developed a rule-based dynamic modelwhere the model is simulated based on human operatorrsquosinputs [44]

In research by Tafazoli et al [45] a method for gravi-tational parameter estimation was proposed The estimatedgravitational parameters were torques produced by gravita-tional forces The estimated parameters can be used in grav-itational compensation control to obtain improved dynamicperformances For example for the linkage system shown inFigure 7 joint torque equations can be set up as follows

1205914 = 119872bu1198921199034 sdot cos (120579234 + 1205724) 1205913 = 1205914 +119872bu1198921198863 sdot cos (12057923) + 119872st1198921199033 sdot cos (12057923 + 1205723) 1205912 = 1205913 + (119872bu +119872st) 1198921198862 sdot cos (1205792) + 119872bo1198921199032

sdot cos (1205792 + 1205722) (8)

The parameters in the equations above are shown in Figure 7

Journal of Construction Engineering 5

z(m

)

7

6

5

4

3

2

1

0

x (m)0 1 2 3 4 5 6

Prey motionInitial guessReference point

(a) Obstacle avoidance motion

z(m

)

x (m)


4

3

2

1

0

minus1

minus2

0 1 2 3 4 5 6 7 8 9

(b) Digging motion

Figure 5 Example trajectories created by using VMCmethod [16]

Dip

per a

ngle

(∘)

minus20

minus40

minus60

minus80

minus100

minus120

minus140

Time (s)0 10 20 30 40 50 60 70 80

Figure 6 Comparison of estimated transfer functionmodel outputswith experimentally measured data [17]

In their research load pins were used to measure loadtorques on the links indirectly Then a series of staticexperiments without load on the bucket were carried out Inthis manner the parameters could be estimated with a 5error [45]

For accurate simulation and visual presentation of exca-vator manipulators various commercial software tools havebeen utilized Among many choices three software tools arewidely used for excavator simulation MATLABSimulinkAmesim and Adams [18 19 46ndash48] For example an excava-tor manipulator dynamic model developed in SimMechanics

1205722 r2

1205912

1205913

1205792

a2

r3

r4

12057923

120579234

1205723

1205724

a3

a4

1205914

120587 + 1205793

120587 + 1205794cg2

cg4Mstg

Mbug

cg3

Mbog

Figure 7 Configuration for joint torque equations

is shown in Figure 8 and an excavator model developed inAdams is shown in Figure 9

Dynamic system simulation software typically has thefunctionality to produce dynamic properties of amanipulatorwhen a CAD model for the manipulator is available [18 46]This process expedites the dynamic modeling of an excavatorsystem with relatively high accuracies

3 Hydraulic System Modeling

For excavator manipulators the drive forces or torques areproduced by hydraulic systems including pumps valves andcylinders [18 25 49] Therefore modeling and simulation ofhydraulic systems comprise an important component for thedesign and analysis of an excavator manipulator system Asshown in the general hydraulic system modeling process in


Env

Machineenvironment Ground Joint O0

B F

B F

Ground 1 Joint O4

O0

O1

O2

O3

O2

O1

A1

A2

A2

A3 A3A6

A6B1

B1

B2

B2

C2

C2

O4

Port A

Port A

Port A

A1R

Port B

Port B

Port B

Cylinder 1A Cylinder 1 pair Cylinder 1B

Cylinder 2A Cylinder 2

1 2

3 4

5 6

ArmBoom

Bucket

Cylinder 3A

Cylinder 2B

Cylinder 3 Cylinder 3B

Bucket linkage

Figure 8 Excavator manipulator model developed in SimMechanics [18]

Figure 9 Excavator model in Adams [19]

Original hydraulic system model

Simplification

Simplified hydraulic system model

Governing equations

Simulation result

Modeling software

and so forthAmesimSimHydraulics

Figure 10 Hydraulic system modeling and simulation process

Figure 10 a model simplification procedure is important dueto the complexity of the system

The conventional modeling approach for a hydraulicsystem is to apply Newtonrsquos law For example the following

Ap

P1

XpP2

Q1Q2

X

Ps Pr

U

Figure 11 Schematic of a hydraulic cylinder and control valve

state variable vector can be defined for a simplified hydraulicsystem shown in Figure 11

119909 = [1199091 1199092 1199093]119879 = [119909119901 V119901 119886119901]119879 (9)

where 119909119901 V119901 and 119886119901 are the displacement velocity andacceleration of the piston respectively Then dynamic


equations for the hydraulic system can be derived as followsby neglecting the valve dynamics

1 = 1199092 = V1199012 = 1199093 = 1198861199013 = 1119898119903 (119860119901119897 minus Re 119904) = 119901

(10)

where119860119901 is the cross-sectional area of the hydraulic cylinder119901119897 is the cylinder differential pressure and Re 119904 is thederivative of the resistance force on the piston [20 40 45 50ndash55]

Mathematical modeling of hydraulic pipes used inmanipulators has been well studied and can be found intextbooks [56] Thus it is not included in this review paperIn the research conducted by Casoli and Anthony a variabledisplacement hydraulic pump was modeled [55] As a criticalcomponent of the pump a flow compensator wasmodeled bygoverning equations which described interaction of the fluiddynamics model and mechanical-geometrical model Thefluid dynamics model calculates the internal pressure of thechamber and the flow rate between the adjacent chambersand themechanical-geometrical model determines the forcesacting on the spool which affects the dynamics and flowarea In the fluid dynamics model time rate of change of thepressure can be described by the following equation

119889119901119894119889119905 = 120573120588119894 sdot1119881119894 (120594) (sum minus 120588119894 119889119881119894 (120594)119889119905 ) (11)

where 119901 is the fluid absolute pressure 120573 is bulk modulus ismass flow rate 120588 is fluid density 119881(120594) is control volume and119894 identifies the control volume consideredThemass flow rateis calculated as

= 120588119862119889119860 (120594) sdot radic 2 1003816100381610038161003816Δ1199011003816100381610038161003816120588 (12)

where119862119889 is the discharge coefficient and119860(120594) is the flow areaIn addition to mathematical modeling excavator

hydraulic systems have beenmodeled by using software toolssuch as SimHydraulics and Amesim In recent publicationsvarious hydraulic system modeling software tools havebeen applied to model hydraulic systems [18 46 51ndash53 57]These modeling software tools feature graphical modelingcapabilities so that a user can easily construct a systemmodelby arranging components in a physically representativemanner For example an excavator hydraulic systemmodeled in SimHydraulics in MATLABSimulink is shownin Figure 12

Lee and Chang proposed a bond-graph based hydraulicsystem modeling approach as shown in Figure 13 [20] Bondgraph which interprets the relation between components onthe basis of energy transmission is applied to conceptuallymodel a simplified hydraulic system first Then a nonlinearmathematical model of the target system can be generated byusing modeling software

It was found that friction in an excavator hydraulic systemis significant and cannot be neglected [45] Due to thedifficulties in estimating the loads in the system preciselyhowever a gray-box hydraulic system modeling method wasdeveloped with an associated machine learning method Inthe research conducted by Casoli and Anthony a variabledisplacement hydraulic pump was modeled as a gray box asshown in Figure 14 [55] As shown in the figure the flow andpressure compensators are modeled as white boxes and flowcharacteristics as a black box Together they are called graybox

There have also been efforts to develop empirical modelsPossible losses in hydraulic systems were also accounted ininput-output relations in the gray-box approach [49 54 5558 59]

In most hydraulic system modeling approaches govern-ing equations are derived first Then a graphical diagram isformed to construct a system model with hydraulic systemmodeling software Additionally the system uncertainties areestimated and bounded and then added to the systemmodelIn this manner a relatively accurate hydraulic system modelcan be developed

Finally some of the key features of widely used modelingand simulation software are summarized in Table 2

4 Conclusion and Outlook

Model-based system design practice can be applied to thedesign and development of advanced excavators Since thefirst important step in the model-based system design is thesystem model development significant amount of researchhas been conducted on the modeling of excavator systemsespecially manipulators

The Denavit-Hartenberg process has been extensivelyapplied in the kinematic analyses of excavator manipulatorsand both experimental and analytical trajectory planningmethods have been used to generate desired trajectoriesof excavator manipulators Dynamic system models havebeen derived by applying Newton-Eulerrsquos method or byusing software tools such as SimScape Amesim and AdamsHydraulic system models are usually simplified greatly dueto the complexity of the real hydraulic systems For hydraulicsystems modeling of the hydraulic loss is essential forsimulation accuracy Since it is difficult to accurately modelhydraulic systems especially when the system is complexhowever designers rely mostly on commercial software toolsfor that purpose

Advancement in excavator systems design can occurin many different ways Two notable directions includeelectrification and hybridization for energy efficiency andautomation of excavator operations Due to the increas-ing complexity in the system architecture development ofthese advanced excavator systems inevitably requires model-based system design approach Therefore accurate modeldevelopment will be increasingly important and high-fidelitymultiphysics software tools will be required to design andsimulate both mechanical and hydraulic subsystems simul-taneously


1

23

4

5

6

Boom cylinder ABoom cylinder B

Arm cylinder AArm cylinder B

Bucket cylinder A

Bucketcylinder B

AAAAA

A

ABBBBB

B

B

HP1 HP2 HP3 HP4 HP5HP6S P T

A B

S P T

A B

S P T

Boom valve Arm valveBucket valve

Boom disp

Arm disp

Bucket disp

S PS

S PS

S PS

S PS

Simulink-PSconverter

Simulink-PSconverter 1



09

Engine speed

Engine

T

B

P

FC

F

R CMRR

1

2

3f(x) = 0

Solverconfiguration

Hydraulic fluid

S

AB

P

T

Pressure relief valve

Rotational friction PumpHydraulic reference

Figure 12 Hydraulic system model developed in SimHydraulics [18]

The current state-of-the-art simulation software allowshigh-fidelity simulation of hydraulic systems in connectionwith mechanical multibody dynamics They allow forma-tion of complex hydraulic systems using numerous built-incomponentmodels including pipes valves and pumpsUsingthus-formed system models various dynamic and hydraulicperformances can be simulated and studied The simulationresults are accurate enough to replace numerous physical pro-totyping and testing required for new system development

While the current simulation models and software arefocused mainly on the mechanical and hydraulic perfor-mances the future research needs to be directed towarddevelopment of more energy-efficient systems by incorpo-rating power sources and transmission Thus a high-fidelityinternal combustion engine or hybrid electric system modelneeds to be employed and drive-cycle simulations need tobe conducted to improve the system design for better energyefficiency


Table 2 Key features of the different modeling software

Software Key features

Amesim bySimens PLM

(i) Open libraries available based on physics and applications(ii) Graphical user interface(iii) The solver can automatically select an appropriate one among various different algorithms based on the dynamicsof the system(iv) Provides a multidomain simulation including linear analysis

Adams by MSCSoftware

(i) Creation or import of component geometry in wireframe or 3D solids(ii) Definition of internal and external forces on the assembly to define the productrsquos operating environment(iii) Model refinement with part flexibility automatic control systems joint friction and slip hydraulic and pneumaticactuators and parametric design relationships(iv) Automatic generation of linear models and complex loads for export to structural analyses

Simscape byMathWorks

(i) Single environment for simulating multidomain physical systems with control algorithms in Simulink(ii) Physical modeling blocks cover more than 10 physical domains such as mechanical electrical hydraulic andtwo-phase fluid(iii) Ability to conduct real-time simulation and hardware-in-the-loop (HIL) testing(iv) Support for C-code generation (with Simulink Coder)

p1

p2

ip3

ip4

ip5

op5

op1

op2 op1

op4

op3op2op3

op3op2

op1 op4

op4

Boom hyd Bucket hyd

Arm hyd

Figure 13 Bond-graph model for hydraulic circuit in excavatormanipulator [20]

Pressurecompensator

Flowcompensator

Pumpmodel

PLS

PS

Flow

Figure 14 Gray-boxmodel of an integrated hydraulic pump system

Competing Interests

The authors declare that they have no competing interests

References

[1] J Reedy and S Lunzman ldquoModel based design acceleratesthe development of mechanical locomotive controlsrdquo SAETechnical Paper 2010-01-1999 SAE International WarrendalePa USA 2010

[2] G Barbieri C Fantuzzi and R Borsari ldquoA model-based designmethodology for the development of mechatronic systemsrdquoMechatronics vol 24 no 7 pp 833ndash843 2014

[3] W E N Hao ldquoAnalysis report of 2010 excavator market inChinardquo Construction Machinery Technology amp Managementvol 2 article 23 2011

[4] T Ni H Zhang C Yu D Zhao and S Liu ldquoDesign ofhighly realistic virtual environment for excavator simulatorrdquoComputers and Electrical Engineering vol 39 no 7 pp 2112ndash2123 2013

[5] ldquoGlobal excavator market report 2014 editionrdquo 2014[6] A Stentz J Bares S Singh and P Rowe ldquoA robotic excavator

for autonomous truck loadingrdquo Autonomous Robots vol 7 no2 pp 175ndash186 1999

[7] S Singh ldquoState of the art in automation of earthmovingrdquo Journalof Aerospace Engineering vol 10 no 4 pp 179ndash188 1997

[8] H Yu Y Liu andM SHasan ldquoReviewofmodelling and remotecontrol for excavatorsrdquo International Journal of AdvancedMechatronic Systems vol 2 no 1-2 pp 68ndash80 2010

[9] B P Patel and J M Prajapati ldquoA review on kinematics ofhydraulic excavatorrsquos backhoe attachmentrdquo International Jour-nal of Engineering Science and Technology vol 3 no 3 pp 1990ndash1997 2011

[10] M W Spong S Hutchinson and M Vidyasagar Robot Model-ing and Control vol 3 Wiley New York NY USA 2006

[11] P KVaha andM J Skibniewski ldquoDynamicmodel of excavatorrdquoJournal of Aerospace Engineering vol 6 no 2 pp 148ndash158 1993

[12] A J Koivo ldquoKinematics of excavators (backhoes) for transfer-ring surface materialrdquo Journal of Aerospace Engineering vol 7no 1 pp 17ndash32 1994

[13] A J Koivo M Thoma E Kocaoglan and J Andrade-CettoldquoModeling and control of excavator dynamics during diggingoperationrdquo Journal of Aerospace Engineering vol 9 no 1 pp10ndash18 1996


[14] T Yamaguchi and H Yamamoto ldquoMotion analysis of hydraulicexcavator in excavating and loading work for autonomouscontrolrdquo in Proceedings of the 23rd International Symposium onRobotics and Automation in Construction (ISARC rsquo06) pp 602ndash607 Tokyo Japan October 2006

[15] G J Maeda S P N Singh and H Durrant-Whyte ldquoA tunedapproach to feedback motion planning with RRTs under modeluncertaintyrdquo inProceedings of the IEEE International Conferenceon Robotics and Automation (ICRA rsquo11) pp 2288ndash2294 May2011

[16] B Lee and H J Kim ldquoTrajectory generation for an automatedexcavatorrdquo in Proceedings of the 2014 14th International Confer-ence on Control Automation and Systems (ICCAS rsquo14) pp 716ndash719 Seoul Republic of Korea October 2014

[17] J Gu J Taylor and D Seward ldquoModelling of an hydraulicexcavator using simplified refined instrumental variable (SRIV)algorithmrdquo Journal of Control Theory and Applications vol 5no 4 pp 391ndash396 2007

[18] J Xu B Thompson and H-S Yoon ldquoAutomated gradingoperation for hydraulic excavatorsrdquo SAE Technical Paper 2014

[19] C-G Park and K LimA Simulation Environment for ExcavatorDynamics 2004

[20] S-J Lee and P-H Chang ldquoModeling of a hydraulic excavatorbased on bond graph method and its parameter estimationrdquoJournal of Mechanical Science and Technology vol 26 no 1 pp195ndash204 2012

[21] S Pluzhnikov D Schmidt J Hirth and K Berns ldquoBehavior-based arm control for an autonomous bucket excavatorrdquo Com-mercial Vehicle Technology pp 251ndash261 2012

[22] J Gu X Ma J Ni and L Sun ldquoLinear and nonlinear control ofa robotic excavatorrdquo Journal of Central South University vol 19no 7 pp 1823ndash1831 2012

[23] Q Ha M Santos Q Nguyen D Rye and H Durrant-WhyteldquoRobotic excavation in construction automationrdquo IEEERoboticsand Automation Magazine vol 9 no 1 pp 20ndash28 2002

[24] G Jun andD Seward ldquoImproved control of intelligent excavatorusing proportional-integral-plus gain schedulingrdquo Journal ofCentral South University of Technology vol 19 no 2 pp 384ndash392 2012

[25] Q He D Zhang Z Huang and X Zhang ldquoAdaptive control ofhydraulic excavator manipulatorrdquo Journal of Tongji Universityvol 35 no 9 pp 1259ndash1288 2007

[26] S Niku Introduction to Robotics John Wiley amp Sons 2010[27] T Yoshida T Koizumi N Tsujiuchi K Chen andYNakamoto

ldquoEstablishment of optimized digging trajectory for hydraulicexcavatorrdquo in Topics in Dynamics of Civil Structures Volume 4F N Catbas S Pakzad V Racic A Pavic and P ReynoldsEds Conference Proceedings of the Society for ExperimentalMechanics Series chapter 58 pp 543ndash554 Springer BerlinGermany 2013

[28] H Yamamoto M Moteki H Shao et al ldquoDevelopment of theautonomous hydraulic excavator prototype using 3-D informa-tion for motion planning and controlrdquo in Proceedings of theIEEESICE International Symposium on System Integration (SIIrsquo10) pp 49ndash54 IEEE Sendai Japan December 2010

[29] Y Sakaida D Chugo H Yamamoto and H Asama ldquoTheanalysis of excavator operation by skillful operatormdashextractionof common skillsrdquo in Proceedings of the SICE Annual Interna-tional Conference on Instrumentation Control and InformationTechnology pp 538ndash542 August 2008

[30] D Schmidt M Proetzsch and K Berns ldquoSimulation andcontrol of an autonomous bucket excavator for landscapingtasksrdquo in Proceedings of the IEEE International Conference onRobotics and Automation (ICRA rsquo10) pp 5108ndash5113 AnchorageAlaska USA May 2010

[31] H N Cannon Extended Earthmoving with an AutonomousExcavator Carnegie Mellon University Pittsburgh Pa USA1999

[32] J Seo S Lee J Kim and S-K Kim ldquoTask planner design foran automated excavation systemrdquo Automation in Constructionvol 20 no 7 pp 954ndash966 2011

[33] T Makkonen K Nevala and R Heikkila ldquoA 3D model basedcontrol of an excavatorrdquoAutomation in Construction vol 15 no5 pp 571ndash577 2006

[34] T Makkonen K Nevala and R Heikkila ldquoAutomation of anexcavator based on a 3DCADmodel andGPSmeasurementrdquo inProceedings of the 21st International Symposium on Automationand Robotics in Construction (ISARC rsquo04) 2004

[35] G Atmeh and K Subbarao ldquoA dynamic neural network withfeedback for trajectory generationrdquo IFAC-Pap vol 49 no 1 pp367ndash372 2016

[36] G J Maeda S P N Singh and D C Rye ldquoImproving oper-ational space control of heavy manipulators via open-loopcompensationrdquo in Proceedings of the IEEERSJ InternationalConference on Intelligent Robots and Systems Celebrating 50Years of Robotics (IROS rsquo11) pp 725ndash731 September 2011

[37] Y B Kim J Ha H Kang P Y Kim J Park and F C ParkldquoDynamically optimal trajectories for earthmoving excavatorsrdquoAutomation in Construction vol 35 pp 568ndash578 2013

[38] S-H Lee J Kim F C Park M Kim and J E BobrowldquoNewton-type algorithms for dynamics-based robot movementoptimizationrdquo IEEE Transactions on Robotics vol 21 no 4 pp657ndash667 2005

[39] F C Park J E Bobrow and S R Ploen ldquoA Lie groupformulation of robot dynamicsrdquo The International Journal ofRobotics Research vol 14 no 6 pp 609ndash618 1995

[40] D Zhang A Research on the Motion Control of the HydraulicExcavator Manipulator Central South University 2006

[41] T Yoshida T Koizumi N Tsujiuchi Z Jiang and Y NakamotoldquoDynamic analysis of an excavator during digging operationrdquoSAE Technical Paper 2013

[42] Y H Zweiri L D Seneviratne and K Althoefer ldquoModel-basedautomation for heavy duty mobile excavatorrdquo in Proceedings ofthe IEEERSJ International Conference on Intelligent Robots andSystems vol 3 pp 2967ndash2972 October 2002

[43] S Tafazoli P D Lawrence and S E Salcudean ldquoIdentificationof inertial and friction parameters for excavator armsrdquo IEEETransactions on Robotics andAutomation vol 15 no 5 pp 966ndash971 1999

[44] R Filla ldquoOperator andmachinemodels for dynamic simulationof construction machineryrdquo 2005

[45] S Tafazoli P D Lawrence S E Salcudean D Chan SBachmann and C W De Silva ldquoParameter estimation andactuator friction analysis for a mini excavatorrdquo in Proceedings ofthe IEEE International Conference on Robotics and Automationvol 1 pp 329ndash334 1996

[46] Q H Le Y M Jeong C T Nguyen and S Y YangldquoDevelopment of a virtual excavator using simmechanics andSimHydraulicrdquo Journal of The Korean Society for Fluid Power ampConstruction Equipments vol 10 no 1 pp 29ndash36 2013


[47] E Assenov E Bosilkov R Dimitrov and T Damianov ldquoKine-matics and dynamics of working mechanism of hydraulicexcavatorrdquo University of Mining and Geology ldquoSt Ivan RilskirdquoAnnual vol 46 pp 47ndash49 2003

[48] S M Prabhu ldquoModel-based design for off-highway machinesystems developmentrdquo SAE Technical Paper 2007

[49] M Krishna and J E Bares ldquoHydraulic system model-ing through memory-based learningrdquo in Proceedings of theIEEERSJ International Conference on Intelligent Robots andSystems vol 3 pp 1733ndash1738 October 1998

[50] M Cobo R Ingram and S Cetinkunt ldquoModeling identifica-tion and real-time control of bucket hydraulic system for awheel type loader earth moving equipmentrdquoMechatronics vol8 no 8 pp 863ndash885 1998

[51] Q He D Zhang P Hao and X Zhang ldquoStudy on motionsimulation of hydraulic excavatorrsquos manipulatorrdquo Journal ofSystem Simulation vol 3 article 51 2006

[52] S Vechet and J Krejsa ldquoHydraulic arm modeling via Matlabsimhydraulicsrdquo Engineering MECHANICS vol 16 no 4 pp287ndash296 2009

[53] S Johnny Fu M Liffring and I S Mehdi ldquoIntegrated electro-hydraulic system modeling and analysisrdquo IEEE Aerospace andElectronic Systems Magazine vol 17 no 7 pp 4ndash8 2002

[54] M Krishna and J Bares ldquoConstructing hydraulic robot modelsusing memory-based learningrdquo Journal of Aerospace Engineer-ing vol 12 no 2 pp 34ndash42 1999

[55] P Casoli and A Anthony ldquoGray box modeling of an excavatorrsquosvariable displacement hydraulic pump for fast simulation ofexcavation cyclesrdquo Control Engineering Practice vol 21 no 4pp 483ndash494 2013

[56] E Doebelin System Dynamics Modeling Analysis SimulationDesign CRC Press 1998

[57] S H Park K Alam Y M Jeong C D Lee and S YYang ldquoModeling and simulation of hydraulic system for awheel loader using AMESimrdquo in Proceedings of the ICROS-SICE International Joint Conference (ICCAS-SICE rsquo09) pp 2991ndash2996 August 2009

[58] P Casoli A Anthony andM Rigosi ldquoModeling of an excavatorsystemmdashsemi empirical hydraulic pump modelrdquo SAE Interna-tional Journal of Commercial Vehicles vol 4 no 1 pp 242ndash2552011

[59] M Krishna and J Bares Constructing Fast Hydraulic RobotModels for Optimal Motion Planning The Robotics Institute1999

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



1205791

Z0 Y1

X1O1

X0O0

1205793

1205792

1205823

Y2

Y4

X2

X4

X3

1205824

1205822 Y3O3

O2

1205794

O4

Figure 1 Excavator coordinate systems in Denavit-Hartenbergconvention

An excavator manipulator is comprised of kinematicallyoperating mechanical links and a hydraulic system Thereexist two main approaches in modeling the mechanical andhydraulic systems mathematical modeling and simulationmodeling using commercially available software tools Thispaper starts with a review on kinematic and dynamic mod-eling of the mechanical linkage and then various modelingapproaches on hydraulic systems will be presented In eachsystem modeling review mathematical models will be pre-sented first and then simulation models will follow

2 Kinematic and Dynamic Modelsof Excavator Manipulator

Kinematic and dynamic models are used for simulation andcontroller development for an excavator manipulator system[9]

21 Kinematic Models Kinematic equations describe themotion of an excavator manipulator without considerationof the driving forces and torques [10] In the conventionalapproaches for kinematic analysis geometrical dimensionsof system components are defined first Although the actualboom arm and bucket in a manipulator are irregularlyshaped for the sake of simplicity of the analysis theyare assumed to be straight joint links whose lengths aredefined by the distance between two joints Each link hasits own Cartesian coordinate system that moves with thelink In order to handle coordinate transformation betweentwo Cartesian coordinate systems the Denavit-Hartenberg(D-H) convention is employed in most research The D-Hconvention was first adopted by Vaha and Skibniewski [11]to analyze the kinematics of an excavator model and thenfurther developed by Koivo et al [12 13] According to the D-H convention 119911-axis of the local coordinate system for eachlink is chosen to be in the direction of rotation of a revolutejoint and 119909-axis is set to point the other joint in the samelink [10] Then the direction of 119910-axis is defined accordingto the right-hand rule Finally a fixed Cartesian coordinatesystem is assigned to the excavator cab to be used as the globalcoordinate system as shown in Figure 1

s

r

B = (fa fr F)

997888a

997888l

997888e

997888u

Figure 2 Basic behavior module of integrated behavior-basedcontrol framework

Forward kinematic equations were derived to calculatethe positions and orientations of the manipulator linkswhen the joint angles and lengths of the links are given[10 13] By applying the Denavit-Hartenberg conventiona transformation matrix between two adjacent coordinatesystems (from 119894th to (119894 + 1)th) on a link can be written as

119894119879119894+1

= [[[[[[

cos 120579119894+1 minus cos120572119894+1 sin 120579119894+1 sin120572119894+1 sin 120579119894+1 119886119894+1 cos 120579119894+1sin 120579119894+1 cos120572119894+1 cos 120579119894+1 minus sin120572119894+1 sin 120579119894+1 119886119894+1 sin 120579119894+10 sin120572119894+1 cos120572119894+1 119889119894+10 0 0 1

]]]]]] (1)

where 120579119894+1 is the rotation angle about 119911119894 axis 120572119894+1 is therotation angle of 119911119894 axis about 119909119894+1 axis 119889119894+1 is the offsetalong the 119911119894 axis and 119886119894+1 is the length of the link Usingthe coordinate transformation matrix an arbitrary point inany local coordinate system can be represented in the globalcoordinate system as

0119875 = 0119879119899119899119875 = 011987911119879221198793 sdot sdot sdot 119899minus1119879119899119899119875 (2)

where 119899119875 is the position vector in the 119899th coordinate system0119875 is the position vector in the global coordinate system and0119879119899 is the transformation matrix from the 119899th to the globalcoordinate systems

Conversely inverse kinematic relations can be employedto determine the joint angles and cylinder lengths when thepositions and orientations of the links are known [12] Byapplying inverse kinematics sequentially all joint angles andhydraulic cylinder lengths can be obtained In the researchconducted by Pluzhnikov et al a behavior-based inversekinematic solver was proposed as shown in Figure 2 [21]Thebehavior-based module is characterized by triples such as

119861 = (119891119886 119891119903 119865) (3)

where 119891119886 represents the activity function 119891119903 is the targetrating function and 119865 is the transfer function of the jointbehavior In Figure 2 119904 is the stimulation

997888119897 is the inhibitionand997888119890 is the input vectorThese functions calculate the outputsignals activity 997888119886 target rating 119903 and the output vector 997888119906 According to the authors this method does not require highcomputation power but may not find solutions in some caseseven if the desired position is reachable


(mm

)

3500

3000

2500

2000

1500

1000

500

0

minus500

minus1000

x (mm)3000 4000 5000 6000 7000 8000

Boom tip

Arm tip

Bucket tip

ExcavationLifting


z(m

m)

3500

3000

4000

2500

2000

1500

1000

500

0

minus500

x (mm)3000 4000 5000 6000 7000

Boom tip

Arm tip

Bucket tip

ExcavationLifting


z(m

m)

3500

3000

2500

2000

1500

1000

500

0

minus500

minus1000

x (mm)3000 4000 5000 6000 7000 8000

Boom tip

Arm tip

Bucket tip

ExcavationLifting




119902 (119905) = 1198880 + 1198881119905 + 11988821199052 + 11988831199053 (119905) = 1198881 + 21198882119905 + 311988831199052 (4)



119902 (119905) = 1198880 + 1198881119905 + 11988821199052 + 11988831199053 + 11988841199054 + 11988851199055 (119905) = 1198881 + 21198882119905 + 311988831199052 + 411988841199053 + 511988851199054 (119905) = 21198882 + 61198883119905 + 1211988841199052 + 2011988851199053

(5)



Situation Command

Joint 1 swing



Joint 3 stick






car p

os (

m)

10

5

0

minus5

minus10

x car pos (m)0 10 20 30 40 50








120591 = M (119906) + h (119906 ) + g (119906) (6)







sdot cos (1205792 + 1205722) (8)



z(m

)

7

6

5

4

3

2

1

0

x (m)0 1 2 3 4 5 6



z(m

)

x (m)


4

3

2

1

0

minus1

minus2

0 1 2 3 4 5 6 7 8 9

(b) Digging motion


Dip

per a

ngle

(∘)

minus20

minus40

minus60

minus80

minus100

minus120

minus140

Time (s)0 10 20 30 40 50 60 70 80




1205722 r2

1205912

1205913

1205792

a2

r3

r4

12057923

120579234

1205723

1205724

a3

a4

1205914

120587 + 1205793

120587 + 1205794cg2

cg4Mstg

Mbug

cg3

Mbog







Env


B F

B F

Ground 1 Joint O4

O0

O1

O2

O3

O2

O1

A1

A2

A2

A3 A3A6

A6B1

B1

B2

B2

C2

C2

O4

Port A

Port A

Port A

A1R

Port B

Port B

Port B



1 2

3 4

5 6

ArmBoom

Bucket

Cylinder 3A

Cylinder 2B


Bucket linkage




Simplification


Governing equations

Simulation result

Modeling software





Ap

P1

XpP2

Q1Q2

X

Ps Pr

U



119909 = [1199091 1199092 1199093]119879 = [119909119901 V119901 119886119901]119879 (9)




1 = 1199092 = V1199012 = 1199093 = 1198861199013 = 1119898119903 (119860119901119897 minus Re 119904) = 119901

(10)



119889119901119894119889119905 = 120573120588119894 sdot1119881119894 (120594) (sum minus 120588119894 119889119881119894 (120594)119889119905 ) (11)


= 120588119862119889119860 (120594) sdot radic 2 1003816100381610038161003816Δ1199011003816100381610038161003816120588 (12)













1

23

4

5

6



Bucket cylinder A

Bucketcylinder B

AAAAA

A

ABBBBB

B

B


A B

S P T

A B

S P T


Boom disp

Arm disp

Bucket disp

S PS

S PS

S PS

S PS





09

Engine speed

Engine

T

B

P

FC

F

R CMRR

1

2

3f(x) = 0

Solverconfiguration

Hydraulic fluid

S

AB

P

T









Amesim bySimens PLM






p1

p2

ip3

ip4

ip5

op5

op1

op2 op1

op4

op3op2op3

op3op2

op1 op4

op4

Boom hyd Bucket hyd

Arm hyd


Pressurecompensator

Flowcompensator

Pumpmodel

PLS

PS

Flow


Competing Interests


References
































































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










(mm

)

3500

3000

2500

2000

1500

1000

500

0

minus500

minus1000

x (mm)3000 4000 5000 6000 7000 8000

Boom tip

Arm tip

Bucket tip

ExcavationLifting


z(m

m)

3500

3000

4000

2500

2000

1500

1000

500

0

minus500

x (mm)3000 4000 5000 6000 7000

Boom tip

Arm tip

Bucket tip

ExcavationLifting


z(m

m)

3500

3000

2500

2000

1500

1000

500

0

minus500

minus1000

x (mm)3000 4000 5000 6000 7000 8000

Boom tip

Arm tip

Bucket tip

ExcavationLifting




119902 (119905) = 1198880 + 1198881119905 + 11988821199052 + 11988831199053 (119905) = 1198881 + 21198882119905 + 311988831199052 (4)



119902 (119905) = 1198880 + 1198881119905 + 11988821199052 + 11988831199053 + 11988841199054 + 11988851199055 (119905) = 1198881 + 21198882119905 + 311988831199052 + 411988841199053 + 511988851199054 (119905) = 21198882 + 61198883119905 + 1211988841199052 + 2011988851199053

(5)



Situation Command

Joint 1 swing



Joint 3 stick






car p

os (

m)

10

5

0

minus5

minus10

x car pos (m)0 10 20 30 40 50








120591 = M (119906) + h (119906 ) + g (119906) (6)







sdot cos (1205792 + 1205722) (8)



z(m

)

7

6

5

4

3

2

1

0

x (m)0 1 2 3 4 5 6



z(m

)

x (m)


4

3

2

1

0

minus1

minus2

0 1 2 3 4 5 6 7 8 9

(b) Digging motion


Dip

per a

ngle

(∘)

minus20

minus40

minus60

minus80

minus100

minus120

minus140

Time (s)0 10 20 30 40 50 60 70 80




1205722 r2

1205912

1205913

1205792

a2

r3

r4

12057923

120579234

1205723

1205724

a3

a4

1205914

120587 + 1205793

120587 + 1205794cg2

cg4Mstg

Mbug

cg3

Mbog







Env


B F

B F

Ground 1 Joint O4

O0

O1

O2

O3

O2

O1

A1

A2

A2

A3 A3A6

A6B1

B1

B2

B2

C2

C2

O4

Port A

Port A

Port A

A1R

Port B

Port B

Port B



1 2

3 4

5 6

ArmBoom

Bucket

Cylinder 3A

Cylinder 2B


Bucket linkage




Simplification


Governing equations

Simulation result

Modeling software





Ap

P1

XpP2

Q1Q2

X

Ps Pr

U



119909 = [1199091 1199092 1199093]119879 = [119909119901 V119901 119886119901]119879 (9)




1 = 1199092 = V1199012 = 1199093 = 1198861199013 = 1119898119903 (119860119901119897 minus Re 119904) = 119901

(10)



119889119901119894119889119905 = 120573120588119894 sdot1119881119894 (120594) (sum minus 120588119894 119889119881119894 (120594)119889119905 ) (11)


= 120588119862119889119860 (120594) sdot radic 2 1003816100381610038161003816Δ1199011003816100381610038161003816120588 (12)













1

23

4

5

6



Bucket cylinder A

Bucketcylinder B

AAAAA

A

ABBBBB

B

B


A B

S P T

A B

S P T


Boom disp

Arm disp

Bucket disp

S PS

S PS

S PS

S PS





09

Engine speed

Engine

T

B

P

FC

F

R CMRR

1

2

3f(x) = 0

Solverconfiguration

Hydraulic fluid

S

AB

P

T









Amesim bySimens PLM






p1

p2

ip3

ip4

ip5

op5

op1

op2 op1

op4

op3op2op3

op3op2

op1 op4

op4

Boom hyd Bucket hyd

Arm hyd


Pressurecompensator

Flowcompensator

Pumpmodel

PLS

PS

Flow


Competing Interests


References
































































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










car p

os (

m)

10

5

0

minus5

minus10

x car pos (m)0 10 20 30 40 50








120591 = M (119906) + h (119906 ) + g (119906) (6)







sdot cos (1205792 + 1205722) (8)



z(m

)

7

6

5

4

3

2

1

0

x (m)0 1 2 3 4 5 6



z(m

)

x (m)


4

3

2

1

0

minus1

minus2

0 1 2 3 4 5 6 7 8 9

(b) Digging motion


Dip

per a

ngle

(∘)

minus20

minus40

minus60

minus80

minus100

minus120

minus140

Time (s)0 10 20 30 40 50 60 70 80




1205722 r2

1205912

1205913

1205792

a2

r3

r4

12057923

120579234

1205723

1205724

a3

a4

1205914

120587 + 1205793

120587 + 1205794cg2

cg4Mstg

Mbug

cg3

Mbog







Env


B F

B F

Ground 1 Joint O4

O0

O1

O2

O3

O2

O1

A1

A2

A2

A3 A3A6

A6B1

B1

B2

B2

C2

C2

O4

Port A

Port A

Port A

A1R

Port B

Port B

Port B



1 2

3 4

5 6

ArmBoom

Bucket

Cylinder 3A

Cylinder 2B


Bucket linkage




Simplification


Governing equations

Simulation result

Modeling software





Ap

P1

XpP2

Q1Q2

X

Ps Pr

U



119909 = [1199091 1199092 1199093]119879 = [119909119901 V119901 119886119901]119879 (9)




1 = 1199092 = V1199012 = 1199093 = 1198861199013 = 1119898119903 (119860119901119897 minus Re 119904) = 119901

(10)



119889119901119894119889119905 = 120573120588119894 sdot1119881119894 (120594) (sum minus 120588119894 119889119881119894 (120594)119889119905 ) (11)


= 120588119862119889119860 (120594) sdot radic 2 1003816100381610038161003816Δ1199011003816100381610038161003816120588 (12)













1

23

4

5

6



Bucket cylinder A

Bucketcylinder B

AAAAA

A

ABBBBB

B

B


A B

S P T

A B

S P T


Boom disp

Arm disp

Bucket disp

S PS

S PS

S PS

S PS





09

Engine speed

Engine

T

B

P

FC

F

R CMRR

1

2

3f(x) = 0

Solverconfiguration

Hydraulic fluid

S

AB

P

T









Amesim bySimens PLM






p1

p2

ip3

ip4

ip5

op5

op1

op2 op1

op4

op3op2op3

op3op2

op1 op4

op4

Boom hyd Bucket hyd

Arm hyd


Pressurecompensator

Flowcompensator

Pumpmodel

PLS

PS

Flow


Competing Interests


References
































































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










z(m

)

7

6

5

4

3

2

1

0

x (m)0 1 2 3 4 5 6



z(m

)

x (m)


4

3

2

1

0

minus1

minus2

0 1 2 3 4 5 6 7 8 9

(b) Digging motion


Dip

per a

ngle

(∘)

minus20

minus40

minus60

minus80

minus100

minus120

minus140

Time (s)0 10 20 30 40 50 60 70 80




1205722 r2

1205912

1205913

1205792

a2

r3

r4

12057923

120579234

1205723

1205724

a3

a4

1205914

120587 + 1205793

120587 + 1205794cg2

cg4Mstg

Mbug

cg3

Mbog







Env


B F

B F

Ground 1 Joint O4

O0

O1

O2

O3

O2

O1

A1

A2

A2

A3 A3A6

A6B1

B1

B2

B2

C2

C2

O4

Port A

Port A

Port A

A1R

Port B

Port B

Port B



1 2

3 4

5 6

ArmBoom

Bucket

Cylinder 3A

Cylinder 2B


Bucket linkage




Simplification


Governing equations

Simulation result

Modeling software





Ap

P1

XpP2

Q1Q2

X

Ps Pr

U



119909 = [1199091 1199092 1199093]119879 = [119909119901 V119901 119886119901]119879 (9)




1 = 1199092 = V1199012 = 1199093 = 1198861199013 = 1119898119903 (119860119901119897 minus Re 119904) = 119901

(10)



119889119901119894119889119905 = 120573120588119894 sdot1119881119894 (120594) (sum minus 120588119894 119889119881119894 (120594)119889119905 ) (11)


= 120588119862119889119860 (120594) sdot radic 2 1003816100381610038161003816Δ1199011003816100381610038161003816120588 (12)













1

23

4

5

6



Bucket cylinder A

Bucketcylinder B

AAAAA

A

ABBBBB

B

B


A B

S P T

A B

S P T


Boom disp

Arm disp

Bucket disp

S PS

S PS

S PS

S PS





09

Engine speed

Engine

T

B

P

FC

F

R CMRR

1

2

3f(x) = 0

Solverconfiguration

Hydraulic fluid

S

AB

P

T









Amesim bySimens PLM






p1

p2

ip3

ip4

ip5

op5

op1

op2 op1

op4

op3op2op3

op3op2

op1 op4

op4

Boom hyd Bucket hyd

Arm hyd


Pressurecompensator

Flowcompensator

Pumpmodel

PLS

PS

Flow


Competing Interests


References
































































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Env


B F

B F

Ground 1 Joint O4

O0

O1

O2

O3

O2

O1

A1

A2

A2

A3 A3A6

A6B1

B1

B2

B2

C2

C2

O4

Port A

Port A

Port A

A1R

Port B

Port B

Port B



1 2

3 4

5 6

ArmBoom

Bucket

Cylinder 3A

Cylinder 2B


Bucket linkage




Simplification


Governing equations

Simulation result

Modeling software





Ap

P1

XpP2

Q1Q2

X

Ps Pr

U



119909 = [1199091 1199092 1199093]119879 = [119909119901 V119901 119886119901]119879 (9)




1 = 1199092 = V1199012 = 1199093 = 1198861199013 = 1119898119903 (119860119901119897 minus Re 119904) = 119901

(10)



119889119901119894119889119905 = 120573120588119894 sdot1119881119894 (120594) (sum minus 120588119894 119889119881119894 (120594)119889119905 ) (11)


= 120588119862119889119860 (120594) sdot radic 2 1003816100381610038161003816Δ1199011003816100381610038161003816120588 (12)













1

23

4

5

6



Bucket cylinder A

Bucketcylinder B

AAAAA

A

ABBBBB

B

B


A B

S P T

A B

S P T


Boom disp

Arm disp

Bucket disp

S PS

S PS

S PS

S PS





09

Engine speed

Engine

T

B

P

FC

F

R CMRR

1

2

3f(x) = 0

Solverconfiguration

Hydraulic fluid

S

AB

P

T









Amesim bySimens PLM






p1

p2

ip3

ip4

ip5

op5

op1

op2 op1

op4

op3op2op3

op3op2

op1 op4

op4

Boom hyd Bucket hyd

Arm hyd


Pressurecompensator

Flowcompensator

Pumpmodel

PLS

PS

Flow


Competing Interests


References
































































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











1 = 1199092 = V1199012 = 1199093 = 1198861199013 = 1119898119903 (119860119901119897 minus Re 119904) = 119901

(10)



119889119901119894119889119905 = 120573120588119894 sdot1119881119894 (120594) (sum minus 120588119894 119889119881119894 (120594)119889119905 ) (11)


= 120588119862119889119860 (120594) sdot radic 2 1003816100381610038161003816Δ1199011003816100381610038161003816120588 (12)













1

23

4

5

6



Bucket cylinder A

Bucketcylinder B

AAAAA

A

ABBBBB

B

B


A B

S P T

A B

S P T


Boom disp

Arm disp

Bucket disp

S PS

S PS

S PS

S PS





09

Engine speed

Engine

T

B

P

FC

F

R CMRR

1

2

3f(x) = 0

Solverconfiguration

Hydraulic fluid

S

AB

P

T









Amesim bySimens PLM






p1

p2

ip3

ip4

ip5

op5

op1

op2 op1

op4

op3op2op3

op3op2

op1 op4

op4

Boom hyd Bucket hyd

Arm hyd


Pressurecompensator

Flowcompensator

Pumpmodel

PLS

PS

Flow


Competing Interests


References
































































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










1

23

4

5

6



Bucket cylinder A

Bucketcylinder B

AAAAA

A

ABBBBB

B

B


A B

S P T

A B

S P T


Boom disp

Arm disp

Bucket disp

S PS

S PS

S PS

S PS





09

Engine speed

Engine

T

B

P

FC

F

R CMRR

1

2

3f(x) = 0

Solverconfiguration

Hydraulic fluid

S

AB

P

T









Amesim bySimens PLM






p1

p2

ip3

ip4

ip5

op5

op1

op2 op1

op4

op3op2op3

op3op2

op1 op4

op4

Boom hyd Bucket hyd

Arm hyd


Pressurecompensator

Flowcompensator

Pumpmodel

PLS

PS

Flow


Competing Interests


References
































































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












Amesim bySimens PLM






p1

p2

ip3

ip4

ip5

op5

op1

op2 op1

op4

op3op2op3

op3op2

op1 op4

op4

Boom hyd Bucket hyd

Arm hyd


Pressurecompensator

Flowcompensator

Pumpmodel

PLS

PS

Flow


Competing Interests


References
































































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation



























































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation

























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









Documents

Review Article A Review on Mechanical and Hydraulic System ...downloads.hindawi.com/archive/2016/9409370.pdf · hydraulic systems: mathematical modeling and simulation modeling using