dynamic virtual prototyping modeling and simulation of

Appl. Math. Inf. Sci.9, No. 2L, 627-636 (2015) 627

Applied Mathematics & Information SciencesAn International Journal

http://dx.doi.org/10.12785/amis/092L38

Dynamic Virtual Prototyping Modeling and Simulation ofSpecial Vehicle

Guang Liu1,2,∗, Bin Xu1,2, Jidong Yang2 and Tiesheng Zheng1

1 Department of Mechanics and Engineering Science, Fudan University, 200433 Shanghai, China2 Shanghai Electro-Mechanical Engineering Institute, 200233 Shanghai, China

Received: 6 Aug. 2014, Revised: 7 Nov. 2014, Accepted: 8 Nov.2014Published online: 1 Apr. 2015

Abstract: Taking Special Vehicle as an example, the research is made ondynamic virtual prototyping modeling and simulationof complex mechanical, electrical and hydraulic integrated system. Based on hydro-pneumatic spring model, ”magic formula” tiremodel, road spectrum model, flexible body model of key components, and vehicle control-hydraulic model, a mechanical, electricaland hydraulic coupling dynamic virtual prototyping model of Special Vehicle is built capitalizing on dynamic simulation analyticalsoftware ADAMS and control system simulation analytical software MATLAB/Simulink, and the virtual prototyping modelis validatedand verified by the physical test data. On the basis of the built prototyping model, the virtual tests are carried out in various typicalworking conditions, which include vehicle driving stability, vehicle unfolding and folding stability, etc. The complete data are obtainedfrom virtual tests and the performance indexes achievability and adaptability to the environment of Special Vehicle are evaluated.The correlation of the main design parameters and the performance indexes is established, which provides basic technical supportfor optimizing its overall design parameters. The researchresults have important significance for the simulation and optimization ofcomplicated mechanical, electrical and hydraulic integrated system.

Keywords: Special Vehicle, Dynamic Virtual Prototyping, Modeling, Co-simulation

1 Introduction

Special Vehicle is one of the most importantequipment in the weapon system, the main function ofwhich is to transport, erect and launch another importantequipment to ensure its stable work.

Special Vehicle, a kind of typical complicatedmechanical, electrical and hydraulic system, integrates amechanical subsystem, a control subsystem and ahydraulic subsystem, etc. The research and developmentof each subsystem and the integration and test of theentire system have a decisive impact on realization ofperformance indexes of Special Vehicle. The traditionaldesign of Special Vehicle is a process of iterative designwhich can be described as follows: each subsystem isdesigned independently and integrated into the wholesystem which is evaluated, and then subsystems areredesigned and reintegrated based on the evaluationresults. Because the coupling relationship between thevarious subsystems is not considered in the process of theindependent design, it is difficult to quickly find a fully

coordinated overall design concept between the varioussubsystems, and may even lead to the unbalance of thedevelopment risk between the various subsystems, whichwill affect the development process of Special Vehicle.The application of virtual prototyping technologyprovides an effective way to solve the above technicalproblems. Virtual prototyping technology is a high-techsolution to the traditional design defects from the angle ofanalyzing and solving the product’s overall performanceand related problems, which enables designers to simulatereal working state of the product in a variety of virtualenvironments, and even can conduct those tests which aredifficult or impossible for physical prototype [1].

In order to solve the technical problems in the SpecialVehicle’s development process, this paper presents theapplication of virtual prototyping technology to SpecialVehicle for system-level and multi-domain couplingmodeling and simulation. Based on hydro-pneumaticspring model, ”magic formula” tire model, road spectrummodel, flexible body model of key components andvehicle control-hydraulic model, the mechanical,

∗ Corresponding author e-mail:[email protected]

c© 2015 NSPNatural Sciences Publishing Cor.

http://dx.doi.org/10.12785/amis/092L38

628 G. Liu et. al. : Dynamic Virtual Prototyping Modeling...

electrical and hydraulic coupling dynamic virtualprototyping model of Special Vehicle is built usingADAMS—–a mechanical system dynamic simulationanalytical software and MATLAB/Simulink—–a controlsystem simulation analytical software. Through thevirtual simulation tests under all kinds of typical workingconditions, more complete virtual test data are obtainedand the evaluation on Special Vehicle’s capability toachieve the performance indexes and ability to adapt tothe environment is made. The correlation establishedbetween the main design parameters and the performanceindexes provides basic technical support for optimizationof the overall design parameters of Special Vehicle.

2 Dynamic Virtual Prototyping Platform ofSpecial Vehicle

With the application of existing commercialsoftware, the dynamic virtual prototyping platform ofSpecial Vehicle is built, which integrates a number ofCAE simulation software and can achieve theco-simulation between multi-domains such as themechanical system, the control system, the hydraulicsystem, etc[2,3,4,5,6]. Its block diagram of framework isshown in Figure 1.

Fig. 1: Dynamic virtual prototyping platform of Special Vehicle

The dynamic virtual prototyping platform of SpecialVehicle is quite systematic because it fully considers theinteraction between multi-domains such as mechanical,control and hydraulic systems to achieve their concurrentdesign and integrated simulation analysis; this platform isalso technically advanced because it capitalizes onhigh-quality common commercial software integrationthrough its own interface or secondary development, withfull consideration of current advanced and sustainabledeveloping technology in related domains.

3 Virtual Prototyping Modeling of SpecialVehicle

The virtual prototyping model of Special Vehiclecontains two main parts: the mechanical subsystem andthe vehicle control-hydraulic subsystem. The mechanicalstructure, as the framework support, is an important visualpart of the virtual prototyping model; the vehicle controlsystem as the controller and the hydraulic system as theexecutor are interdependent and inseparable, so they aregenerally called vehicle control-hydraulic system.

3.1 Mechanical dynamic modeling

The 3D solid model of Special Vehicle is built usingPro/E software with powerful 3D modelling function, andthen is imported into ADAMS simulation platform bymeans of the seamless interface program Mechanism/Pro,and finally the mechanical dynamic model of SpecialVehicle is built by defining a variety of constraints andapplied force in ADAMS.

All the data of the components’ mass, center-of-massand moment of inertia in the mechanical dynamic modelof Special Vehicle can be calculated automatically byPro/E software according to the 3D geometry modeloffered by the designer. The built multi-rigid bodydynamic virtual prototyping model of Special Vehicle has28 Degrees of Freedom (DOF). The mechanical dynamicmodel of Special Vehicle includes the following relativelyimportant models-hydro-pneumatic spring model, tiremodel, road spectrum model and flexible body model ofkey components.

3.1.1 Hydro-pneumatic spring modeling

The suspension of Special Vehicle is that ofhydro-pneumatic spring. The model of hydro-pneumaticspring is a kind of nonlinear spring-damping model andits schematic diagram is shown in figure 2. With theseveral assumptions of the hydro-pneumatic springtheoretical model [7], the relational expressions betweenpressures can be obtained based on thin-walled pinholemodel, pipe flow model and local pressure loss model dueto variable diameter of pipelines. Meanwhile, with the gasstate equation of the energy accumulator, the


Appl. Math. Inf. Sci.9, No. 2L, 627-636 (2015) /www.naturalspublishing.com/Journals.asp 629

mathematical model of hydro-pneumatic spring can beexpressed as:

p2− p1 =12ρ2

{

A2x[Cd1S1+Cd2S2(1−sign(x))/2]

}2sign(x)

p3− p1 =12(ρ1ζ1+2ρ1ζ21)

{

ρ1A1−ρ2A2ρ1S4

x}2

sign(x)

p4− p3 = (λ ld + ζ22)× (ρ3+ρ4)[

(ρ1A1−ρ2A2)(ρ3+ρ4)S3

x]2sign(x)

p5− p4 =12ρ5ζ3

{

ρ1A1−ρ2A2ρ5S3

x}2

sign(x)

p5[Vg0+(Vh0−ρ0Vh0−(ρ1A1−ρ2A2)x

ρ5)]

r= pg0Vr

g0(1)

Wherepi(i = 1, · · · ,5) is pressure;ρi(i = 1, · · · ,5) isdensity;A1 is inner cavity area of hydraulic cylinder;A2is ring cavity area of hydraulic cylinder;S1 is orifice area;S2 is check valve area;S3 is pipeline area;S4 iscross-sectional area of the junction between hydraulicpipeline and hydro-pneumatic spring cavity;l is thelength of pipeline;d is the diameter of pipeline;Vg0 is gasvolume in the energy accumulator;pg0 is gas pressure inthe energy accumulator;ρ0 is the density of hydraulic oil;Vk0 is oil volume in the energy accumulator;Cd1 andCd2are flux coefficient of thin-walled pinhole;ζ1,ζ21, ζ22 andζ3 are local resistance coefficient;λ is frictional resistantcoefficient; r is gas exponent;x and x are position andvelocity of piston of hydro-pneumatic spring hydrauliccylinder respectively.

Fig. 2: Schematic diagram of hydro-pneumatic spring

Under the Integrated Development EnvironmentVC++, capitalizing on the above built hydro-pneumaticspring mathematical model and the user-defined interfaceprogram SFOSUB [8] provided by ADAMS/solver, theuser subroutine of the hydro-pneumatic spring can bebuilt, compiled and linked to generate Dynamic LinkLibrary (DLL) which can be used in ADAMS to define

the 12 hydro-pneumatic springs of the independentsuspension in Special Vehicle.

3.1.2 Tire modeling

The tire model of dynamic virtual prototyping ofSpecial Vehicle is built based on the ”magic formula” tiremodel[9] which is in the form of sine-arctangentcombination to fit tire test data and obtain a set of tiremodels which can simultaneously express thelongitudinal force, the lateral force and the aligningtorque. The mathematical expression of ”magic formula”tire model is shown as follows:

Y(x) = Dsin{Carctg[Bx−E(Bx−arctgBx)]} (2)

WhereY is the longitudinal force, the lateral force orthe aligning torque;x is independent variable, which canbe used to express lateral angle or longitudinal slip rate oftire in different conditions;D is called the peak factor,which determines the peak of the tire’s characteristiccurve;C is called the shape factor, which determines theused part of the sine and, therefore, mainly influences theshape of the tire curve;B is called stiffness factor, whichstretches the tire curve;E is called curvature factor, whichcan modify the characteristic around the peak of the tirecurve.

The 6 tire models of Special Vehicle are establishedmaking use of PAC2002 tire template in the ADAMS/Tiretemplate library in the modeling process. Tire coefficientB, C, D and E are obtained from the fitting results of testdata via the tool provided by ADAMS.

3.1.3 Road spectrum modeling

Road model is an important part of the driving statesimulation study, and the road roughness is mainlyexpressed via road power spectrum density. In 1984International Standard Organization (ISO) issued thestandard draft of road roughness representation in the fileTC108/SC2N67, and in 1986 China also issued a nationalstandard (GB7031-86)—–”vehicle vibration input—–thestandard of road roughness representation”. For the roadpower spectrum density , both documents have suggestedthe fitting expression as [10]:

Gq(n) = Gq(n0)

(

nn0

)−ω(3)

Wheren is spatial frequency, which is the reciprocalof the wavelength, its unit ism−1; n0 is spatial referencefrequencyn0=0.1m−1; Gq(n0) is called road roughnesscoefficient, which is power spectrum density under thespatial reference frequencyn0, its unit is m3; ω is calledfrequency exponent, which is oblique line slope under thedouble logarithmic coordinates and determines frequencystructure of road power spectrum density.


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According to the standards or tests, differentcorresponding level values can be chosen forGq(n). Theroad roughness is divided into eight classes in the nationalstandard GB7031-86 according to road power spectraldensity. This paper selects the road roughness of class 2as per the design requirements for Special Vehicle andadopts software MATLAB to generate the requiredrandom road spectrum model file based on the whitenoise method [11].

3.1.4 Flexible body modeling

In order to build a more accurate virtual prototypingmodel and simulate the performance of Special Vehiclemore realistically, it is required to build the flexible bodymodel for the key components like the vehicle frame,erecting arm, and rack container etc.

The building process of the flexible body model is:through components grid discretization and a series ofrelevant definitions in the finite element modelingsoftware Patran, the finite element model input files(*.bdf) are generated, which are submitted to the finiteelement solver Nastran for mode calculation toautomatically generate the required MNF modal neutralfile which is finally read to define the flexible body modelvia ADAMS/Flex interface in ADAMS.

The expression method of flexile body in ADAMS isthe modal synthesis method, which is a particularlyeffective method to reduce DOF. The linear elasticstructure’s vibration deformation can be approximated asa linear combination of mode shapes whenever in free orforced vibration, that is:

u= Φq (4)

Where the column matrixu is the vector of linearphysical nodal deformation; the modal shape matrixΦ isthe transformation from the smaller set of modalcoordinates to the larger set of physical coordinates; thecolumn matrixq is the vector of modal coordinates.

The modal synthesis method has a variety of theoriesand calculation methods. ADAMS takes theCraig-Bampton method [12] which builds the structureRitz-basis from kinematics views. The structure is dividedinto several substructures of which any interior node’sdisplacement can be expressed as follows:

u=

[

uBuI

]

=

[

I 0ΦIC ΦIN

][

qCqN

]

= Φq (5)

Where uB is the boundary DOF;uI is the interiorDOF; I and 0 are identity and zero matrices respectively;ΦIC is the physical displacements of the interior DOF inthe constraint modes;ΦIN is the physical displacementsof the interior DOF in the normal modes;qC is the modalcoordinates of the constraint modes;qN is the modalcoordinates of the fixed-boundary normal modes.

The generalized mass and stiffness matricescorresponding to the Craig-Bampton basis are obtainedvia a modal transformation. The two matrices are shownin the following expression:

M = ΦTMΦ = ΦT[

MBB MBIMIB MII

]

Φ =

[

MCC MNC

MCN MNN

]

(6)

K = ΦTKΦ = ΦT[

KBB KBIKIB KII

]

Φ =

[

KCC 00 KNN

]

(7)

where M and K are generalized mass matrices andgeneralized stiffness matrices respectively;M and K aremass matrices and stiffness matrices of finite element forthe flexible component; the subscriptsI , B , N , andCdenote internal DOF, boundary DOF, normal mode andconstraint mode respectively.

The equation of motion of flexible body, in terms ofthe mode coordinates is:

Mq+Kq =

[

MCC MNC

MCN MNN

][

qBqI

]

+

[

KCC 00 KNN

][

qBqI

]

=

[

FB

F I

]

= f (8)

where f is the mode load vector, which is theprojection of the nodal force vector on the modelcoordinates. Its expression is shown as:

f = ΦTF (9)

whereF is the force vector in the physical coordinates.According to Craig-Bampton methodology, the built

vehicle frame and erecting arm flexible body models inADAMS are shown in figure 3.

Fig. 3: Flexible body of the vehicle frame and erecting arm

3.2 Vehicle control-hydraulic system modeling

The vehicle control system of Special Vehicleappears ”independent” relative to the hydraulic system., Itidentifies the working progress status of the hydrauliccircuit by reading the feedback signals on the pre-sensor



of Special Vehicle, obtains output control parametervalues by solving pre-set control strategies, and achievescontrol of the hydraulic system by adjusting the spoolposition of electromagnetic hydraulic valves. Thehydraulic system completes Special Vehicle body levelingand rack container erecting under the command of vehiclecontrol system. In the virtual prototyping model ofSpecial Vehicle, the integrated modeling of vehiclecontrol-hydraulic system utilizes the two systems’ highlyinterdependent relationship.

Fig. 4: The hydraulic schematic diagram of erecting circuit

Vehicle control-hydraulic system simulation adopts”co-simulation”, in which the vehicle control systemmodel is built by MATLAB/Simulink, the hydraulicsystem model is built by ADAMS/Hydraulics, and theirsoftware interface is realized by ADAMS/Controls.According to the schematic diagram of hydraulic systemof Special Vehicle, hydraulic system circuit model ofSpecial Vehicle is established by revising the hydrauliccomponent parameters in the block diagram modelerprovided by ADAMS/Hydraulics. Per the control circuitflow chart of Special Vehicle, the vehicle control systemmodel can be built in MATLAB/Simulink throughdesigning control block diagram and correspondingcontrol programs. The hydraulic schematic diagram andthe control flow chart of erecting circuit are shown infigure 4 and figure 5 respectively.

Fig. 5: The control flow chat of erecting circuit

3.3 Mechanical, electrical and hydraulicintegrated virtual prototyping model of SpecialVehicle

Based on the mechanical system modeling andvehicle control-hydraulic system modeling, themechanical electrical and hydraulic integrated virtualprototyping model of Special Vehicle is built inMATLAB/Simulink, importing the nonlinear mechanicalsystem model and hydraulic model Adamssub intoMATLAB via seamless interface programADAMS/Controls and combining the vehicle controlmodel. The mechanical dynamic virtual prototypingmodel built in ADMAS is shown in figure 6. The blockdiagram of the mechanical, electrical and hydraulicintegrated virtual prototyping model is shown in figure 7.The relationship between input and output interface ofAdamssub model is shown figure 8.

Fig. 6: Mechanical dynamic virtual prototyping model of SpecialVehicle




Fig. 7: Diagram of integrated mechanical, electrical and hydraulic virtual prototyping model of Special Vehicle

Fig. 8: Relationship between input and output interface of Adamssub model



4 Model Verification of Special Vehicle

To accurately predict the performance of SpecialVehicle under various typical working conditions, thebuilt virtual prototyping model of Special Vehicle isrequired to validate and verify. The verification method isthat parameters of the dynamic virtual prototyping modelof Special Vehicle are repeatedly adjusted to enable themulti-group performance indexes of virtual test results toconform to the physical test results.

4.1 Static verification of the model

Under static conditions, the axle-load distribution ofSpecial Vehicle is one of the most important designspecifications. The simulation result of dynamic virtualprototyping model of Special Vehicle indicates thatSpecial Vehicle’s axle-load ratio is 29:71, which meetsthe design requirements.

4.2 Dynamic verification of the model

At the speed of 40km/h and under the class-2 roadroughness condition, both time domain and frequencydomain methods are taken to compare the virtual testresults with the physical ones. . Figure 9 is the contrastcurves of acceleration time history of virtual tests andphysical tests measured in the mass center of importantequipment. Figure 10 is the contrast curves ofacceleration frequency spectrum density. From figure 9and figure 10 it can be concluded: whatever the timedomain or frequency domain, the data consistency ofvirtual test results and physical test results is good enoughto effectively prove the modeling accuracy of the virtualprototyping model of Special Vehicle.

Fig. 9: Contrast of time history curves of virtual test and physicaltest

Fig. 10: Contrast of frequency spectrum density of virtual andphysical test

5 Virtual Tests of Special Vehicle

5.1 Virtual tests of driving stability

The virtual tests of driving stability include thestability of quick start-up, high-speed driving and brakingand the stability of low-speed across trench and low-speedover obstacle, and so on. Virtual tests of driving stabilitycan be easily achieved by defining different drivingmotions on the driving shaft of Special Vehicle.

5.1.1 Virtual tests of quick start-up, high-speed drivingand braking stability

Special Vehicle frequently accelerates anddecelerates in the driving state. Under the extremeconditions, it assumes that the Special Vehicle acceleratesat 0.4 m/s2 from rest to start, 6 seconds later, andaccelerates at 2m/s2 until velocity of Special Vehiclereaches 22.4m/s (about 80km/h), and drives at a steadyspeed of 22.4m/s for 30 seconds, and then decelerates to8.4 m/s (about 30km/h) at -1.6m/s2 in 10 seconds, andfinally comes to brake test at acceleration of -2.9m/s2

until a complete stop.Figure 11 shows the response curve of vertical

vibration acceleration in the mass center of importantequipment at a period of time, which indicates: whenSpecial Vehicle is at the state of start-up, acceleration,high-speed driving and braking, the vertical accelerationof the mass center of important equipment is less than5m/s2 in the whole process, therefore, Special Vehiclemeets the corresponding dynamic environmentrequirements under the class-2 road roughness drivingconditions.




Fig. 11: Response curve of vertical vibration acceleration in themass center of important equipment

5.1.2 Virtual tests of low speed across trench and overobstacle

Special Vehicle is driven at 15km/h on the flat road.When the vehicle comes to a certain position, it crossesover a 0.7m-wide and 1m-deep trench, after that, it returnsto flat road. Figure 12 shows the virtual test results of lowspeed across trench.

Fig. 12: Virtual test of low speed across trench

Special Vehicle is driven at 3km/h on the flat road.When the vehicle comes to a certain position, it climbsover a 0.6m-high vertical obstacle, after that, it returns toflat road. Figure 13 shows the virtual test results of lowspeed over obstacle.

Both virtual test results indicate that the verticalacceleration of the mass center of important equipment isless than 15m/s2 when Special Vehicle is driven at lowspeed across the trench or over the vertical obstacle.Therefore, excessive impact acceleration is not generatedon the important equipment which meets thecorresponding dynamic environment requirements.

Fig. 13: Virtual test of low speed over obstacle

5.2 Virtual tests of vehicle unfolding and folding

The hydraulic executive system of Special Vehiclecarries out vehicle unfolding and folding under thecommand of vehicle control system. In this vehicleunfolding and folding process, the dynamic topology ofSpecial Vehicle has significant changes; ending state ofvehicle unfolding as the beginning state of the importantequipment working state undoubtedly has a significantimpact on normal operation of vehicle equipment. Thevirtual tests of vehicle unfolding and folding areimportant tools to verify the design quality of the controland hydraulic system and the operation platform ofdesign improving. The total time of vehicle unfolding andfolding is about 300 seconds. Figure 14 shows the virtualtest results of vehicle unfolding and folding. From figure14 it can be concluded that the change of the support legforce is stable in the whole process.

Fig. 14: Virtual test of unfolding and folding vehicle

The virtual tests of unfolding and folding processesindicate that at each process, the vehicle body is very



stable and has no instability phenomenon, and thehydraulic system has no excessive jitter, seizure oroscillation phenomenon. Therefore, Special Vehiclemeets the corresponding dynamic environmentrequirements.

6 Conclusion

Taking Special Vehicle as the prototype, this papercarries out research on dynamic virtual prototypingmodeling and virtual tests of the complex mechanical,electrical and hydraulic system. In the modeling process,the visible mechanical system and the vehiclecontrol-hydraulic system are elaborated, and themechanical, electrical and hydraulic integrated virtualprototyping model of Special Vehicle is built. Based onthe model, the dynamic characteristics of the largedynamic system composed of Special Vehicle and relativedynamic environment is studied. The correlationestablished between the main design parameters and theperformance indexes lays the foundation for optimizingits overall design parameters. The comprehensive virtualsimulation tests of Special Vehicle are carried out. Theresults of virtual tests quantitatively evaluate the ability toachieve performance indexes and ability to adapt to thedynamic environment of the important equipment invarious typical conditions, meanwhile estimate the overalldesign of Special Vehicle fully and systematically. Theresearch results have important significance for thesimulation and optimization of complicated mechanicalelectrical, and hydraulic integrated system.

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Guang Liu is a Ph.D.student at the Department ofMechanical and EngineeringScience, Fudan University,and a senior engineer atShanghai Electro-MechanicalEngineering Institute,China. In April 2003, Mr.Liu Guang obtained M.Sc.major in Aeronautical and

Aeronautical Manufacturing Engineering at NorthwesternPolytechnical University, China. His research interests arein the areas of mechanical system dynamics and aircraftdesign.

Bin Xu is a Ph.D.student at the Departmentof Mechanical andEngineering Science, FudanUniversity, and an engineer atShanghai Electro-MechanicalEngineering Institute,China. In June 2006, Mr.Xu Bin obtained M.Sc. majorin Solid Mechanics at Fudan

University, China. His research interests are in the areasof nonlinear dynamics and aircraft design.




Jidong Yang receivedthe Ph.D. degree fromNortheast University,major in MechanicalDesign in 2002. He iscurrently a senior engineer atShanghai Electro-MechanicalEngineering Institute, China.His research interests arein the areas of aircraft overall

design and mechanical system dynamics.

Tiesheng Zhengis a professor anddoctoral supervisorat the Department ofMechanical and EngineeringScience, Fudan University,China. His research fieldsare mechanical systemdynamics, fluid-structurecoupling vibration, nonlinear

dynamics, rotor dynamics and computational mechanics.He has published over 30 papers in international peerreviewed journals.


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