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냕險꼊阩韥陹뼎쁁 2013 띍陹뼎ꯕ鲵쁁鬱ꓭ뎆 2013. 6. 21 KSFC Conference S1-1 - 1 - New Software Generation for Greener Energy Efficient Mechatronic System Design & Analysis V. Rémillard * , J. Sfeir, C. Quennouelle, D. Lenoble and S.-J. Lee Key Words : Virtual Machine, Knowledge Management System, Downstream Design, Mechatronic, Electrohydraulic, Dynamic, Hydraulic, Energy Consumption, Efficiency, Power Analysis, Hydrostatic Transmission. Abstract: In the world of simulation software, many different approaches are used to obtain accurate hydraulic circuit simulation. Most of these tools model components as a set of mathematical equations parameterized with mechanical and geometric data for each component. They are able to simulate in depth specific functions of a circuit, however it becomes progressively a more demanding task to simulate more complex and complete systems. One of the key elements of simulation software is its ability to model valve performance in terms of flow characteristics, pressure drop and flow force. This also holds true for pumps and motors where the knowledge of efficiencies is required to achieve realistic duty cycle behavior. In this paper, the chosen approach is to demonstrate the efficiency of modeling components using a software downstream design methodology by implementing readily available performance curves and other characteristics of hydraulic components and functions. This downstream method of modeling components ensures the reliability and accuracy of systems behavior based on manufacturer specific data and allows for fast simulation of complete virtual machines which is impractical to achieve by traditional upstream programming. The simulation of a complete hydraulic system delivers global validation and analysis capabilities that can also be exploited beyond the engineering design scope including maintenance diagnostics and training activities. This paper will demonstrate that using Automation Studio™ –a commercially available off-the-shelf drawing and simulation software tool that uses mainly downstream design– simulation data and OEM product information can be easily entered from a readily available hydraulic component vendor in order to create valves, pumps and motors for fast and accurate sizing and system simulation of a virtual machine. The ability to realistically simulate entire machines offers a unique capability to monitor, and study specific performance criteria such as: hysteresis, pressure drop, leakage, flow force, and other flow/pressure characteristics, power generation and transmission up to the full energy consumption at various operating conditions. Nomenclature e P : Electrical power consumed by motor, W e Q : Electric reactive power, VAR J P : Power loss due to Joule effect, W o i P P , : Mechanical power, W o i Z Z , : Shaft rotation speed, rad/s o i T T , : Torque, N.m o m v e K K K K , , , : Electrical, volumetric, mechanic, overall efficiency p ' : Differential pressure, Pa P : Hydraulic power, W Q : Hydraulic flow, m 3 /s l Q : Flow losses, m 3 /s l T : Torque due to friction, N.m P : Coefficient of viscosity, Pa.s m p D D , : Pump or motor displacement, m 3 /rad W : Forces (resp. Torques) applied on a body, N (resp. N.m) 1. Introduction With current economic pressures, system designers are increasingly constrained to provide more demanding technical designs in less time. Also, V. Rémillard (Speaker), J. Sfeir, C. Quennouelle, D. Lenoble: Famic Technologies inc. E-mail : [email protected], Tel : +1 514-748-8050 Sang-Jin Lee : Inroot Co., Ltd, Tel : 82-31-399-5711

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New Software Generation for Greener Energy Efficient Mechatronic System Design& Analysis

V. Rémillard*, J. Sfeir, C. Quennouelle, D. Lenoble and S.-J. Lee

Key Words: Virtual Machine, Knowledge Management System, Downstream Design, Mechatronic, Electrohydraulic,Dynamic, Hydraulic, Energy Consumption, Efficiency, Power Analysis, Hydrostatic Transmission.

Abstract: In the world of simulation software, many different approaches are used to obtain accurate hydrauliccircuit simulation. Most of these tools model components as a set of mathematical equations parameterized withmechanical and geometric data for each component. They are able to simulate in depth specific functions of acircuit, however it becomes progressively a more demanding task to simulate more complex and completesystems. One of the key elements of simulation software is its ability to model valve performance in terms of flowcharacteristics, pressure drop and flow force. This also holds true for pumps and motors where the knowledge ofefficiencies is required to achieve realistic duty cycle behavior. In this paper, the chosen approach is todemonstrate the efficiency of modeling components using a software downstream design methodology byimplementing readily available performance curves and other characteristics of hydraulic components andfunctions. This downstream method of modeling components ensures the reliability and accuracy of systemsbehavior based on manufacturer specific data and allows for fast simulation of complete virtual machines which isimpractical to achieve by traditional upstream programming. The simulation of a complete hydraulic systemdelivers global validation and analysis capabilities that can also be exploited beyond the engineering design scopeincluding maintenance diagnostics and training activities.

This paper will demonstrate that using Automation Studio™ –a commercially available off-the-shelf drawing andsimulation software tool that uses mainly downstream design– simulation data and OEM product information canbe easily entered from a readily available hydraulic component vendor in order to create valves, pumps andmotors for fast and accurate sizing and system simulation of a virtual machine. The ability to realistically simulateentire machines offers a unique capability to monitor, and study specific performance criteria such as: hysteresis,pressure drop, leakage, flow force, and other flow/pressure characteristics, power generation and transmission upto the full energy consumption at various operating conditions.

Nomenclature

eP : Electrical power consumed by motor, W

eQ : Electric reactive power, VAR

JP : Power loss due to Joule effect, W

oi PP , : Mechanical power, W

oi , : Shaft rotation speed, rad/s

oi TT , : Torque, N.m

omve ,,, : Electrical, volumetric, mechanic,

overall efficiencyp : Differential pressure, Pa

P : Hydraulic power, W

Q : Hydraulic flow, m3/s

lQ : Flow losses, m3/s

lT : Torque due to friction, N.m: Coefficient of viscosity, Pa.s

mp DD , : Pump or motor displacement, m3/rad

: Forces (resp. Torques) applied on a body, N (resp.N.m)

1. Introduction

With current economic pressures, system designersare increasingly constrained to provide moredemanding technical designs in less time. Also,

V. Rémillard (Speaker), J. Sfeir, C. Quennouelle, D. Lenoble:Famic Technologies inc. E-mail : [email protected],Tel : +1 514-748-8050Sang-Jin Lee : Inroot Co., Ltd, Tel : 82-31-399-5711

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rapidly increasing energy saving requirements addeven more constraints that force designers into makingdifficult compromises. This often results in neglectingcertain aspects of the product life cycle, either indesign, validation, documentation, training, sales ormaintenance.

In particular for the design and validation stages, avariety of tools exists on the market to help validatesystem design through simulation. Many simulationtools can be used to do upstream design byprogramming component internal attributes andphysical phenomena. Although these methodologiescan produce very accurate simulation results at theindividual level, they require the system designer tohave access to every component’s internal physicalparameter. This means that the designer must have agreat deal of expertise in the specifics of eachcomponent. Since a global system involves manydifferent elements, it would take a considerableamount of time and effort to calibrate and model acomplete system. This also significantly reducesreusability of upstream-designed systems, whichmakes them prohibitively costly and complex when itcomes to designing complete machines that involveseveral technologies.

Instead, a new trend of downstream design in theindustry has been developing. It consists of havingpre-modeled modules that are used as-is by the systemdesigner.

This paper details the characteristics of downstreamdesign as applied to a complete mechatronic system.Chapter 2 explains the concept of a virtual machinebuilt using preconfigured catalogue components.Chapter 3 explains certain concepts involved insystem design and shows some of the limitations ofupstream design. Chapter 4 gives specific examples ofdownstream design using Automation Studio™.Chapter 5 concludes with some final remarks on thecharacteristics of both upstream and downstreamapproaches and shows the advantages of usingmodular design software like Automation Studio™that allows combining technical design and simulationin one complete innovative tool.

2. Mechatronic Virtual Machine

Generally, speaking of Mechatronic VirtualMachine implies one of the two aforementionedapproaches. For example, a lot of virtual realitysoftware offer animated 3D models of a machine thatcan be realistically operated. However, most of thetime only a high-level global model of the machine issimulated and it does not take into accounts all therelated technologies that impact its behavior.

In this paper, “virtual machine”, means a completesimulation model, enhanced with a 3D visualizationmoving according to the real physical contributions ofall the involved technologies.

Fig. 1 illustrates perfectly this concept ofmechatronic virtual machine, where all the relatedtechnologies are simulated: electrical engineering,hydraulics, mechanics and control.

Fig. 1 Complete Mechatronic Virtual MachineThe presented machine is constructed using

hydraulic components exclusively selected fromcomponent manufacturer catalogs. Moreover, thevirtual machine is drafted using standard 2Drepresentation the related technologies.

Automation Studio™ offers the possibility to modelthese machines using two types of libraries: either byusing generic unit components that respect the ISO-1219 standard or by using a set of manufacturers’components, where symbols are exactly those used fortheir 2D drawing and where the technicalspecifications are already built in the components.Therefore the virtual machine is fully configured asand it is being built.

Moreover, this concept of virtual machine does notconsist of a set of recorded results produced by anoffline preconfigured simulation, but rather consists of

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an interactive live simulation where the evolution ofthe machine in time is monitored and acted upon liveby the user. This means that it is possible for a virtualmachine to be operated as the real machine would be.By modifying variable input generators, or by actingdirectly on some configurable components, it ispossible to dynamically modify parameters and toimmediately observe their impacts on the simulation.

This latter point offers the possibility to dointeractive tests, giving access to all possibleoperating conditions. Therefore it enables to performvery important analysis such as power analysis andenergetic functioning consumption of all components,as illustrated in Fig. 2.

Fig. 2 Energy Analysis of a Complete Virtual MachineTaken from [1], this graph shows, in the form of an

energy balance, the losses in each active component ofthe machine, where power is transmitted. A completesimulation model of the virtual machine enables torealistically model each of these functions andsubfunctions. And even if each of these analysis canbe done independently, i.e. technology by technologyusing different and specific modeling and simulationtools or approaches, it is essential to note that all theseanalyses are macroscopically linked in the virtualmachine, the output of a technology becoming theinput of another, and vice versa.

In order to illustrate this multi-technological aspectof virtual machines, the next section reviews generalmodels of the different technologies used in amechatronic system.

3. Simulation Models

3.1 Electrical System

In a motion transmission system involvingelectrical power components, several elements canimpact the overall efficiency of the electrical system.

In a classical electric system, the following effectsresult in power losses:

Switching element and conductor heating;Reactive Power transmission;Misc. effects.

Conductor heating is an inherent effect due to theresistive nature of conducting materials. As anillustration, the lost power can be quantified as

2iRPJ

Where JP represents the Joule resistive losses,

R represents the resistance of an element and irepresents the current flowing through it.

The minimization of Joule power losses is doneboth by designing low resistance elements (thick wires,low power consumption switching elements …) andby reducing the transited currents. In order to maintaintransit of the same power demanded by the hydraulicload, reducing currents implies raising the voltagelevels.

Reactive power is power that is transited in theelectric circuit without being transformed into work.This power transits unnecessary currents back andforth between the source and the load, thus creatingextra Joule losses in the conductors.

As an illustration, this extra current, called ReactiveCurrent can be quantified as

XQI e

r

Where eQ represents the reactive power and Xrepresents the circuit’s reactance.

The reactive power is related to the active power

eP (useable power) by

1cos

12ee PQ

Where cos represents the power factor.

So for a given active power, the minimization of thereactive current implies minimizing the reactive

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power which in turn implies maximizing the powerfactor by having it as close to 1 as possible.

Electric motors have an inherent reactive powerconsumption property, due to the magneticinteractions that are at the core of their function.Maximizing the power factor for a given motor isgenerally done by physically designing the motor tohave a high power factor under normal loadconditions or by using capacitors to locally providethe reactive power needed by the motor, which wouldreduce the reactive current transmission over thecomplete circuit.

Other effects that impact electrical power loss canalso be cited, like air gap, eddy current and harmonicpower losses. These effects are due to the electricalcomponents themselves rather than to theircombination in the electric circuit.

Practically, air gap losses are minimized bydesigning high-efficiency components motors. Theachievable efficiencies can reach upwards of 95% [6].

Eddy currents are due to varying magnetic fieldsthat generate currents in the metallic core of theelement. These are reduced by designing sheeted coresrather than solid cast cores.

Harmonics are generated by switching devices andby motors due to non-linear effects. These will tend tocreate high frequency current components thatincrease losses in the circuit. Those are usuallyreduced by adding low-pass filters in the circuit.

When validating the design of an electrical circuit,it is important to be able to render a realistic image ofthe energy balance of each stage in the transmissionsystem. This is due to the fact that the overallefficiency, being the product of all the individualefficiencies involved, will tend to be impacted by anysuboptimal element.

The efficiency of each element is difficult to modelwith a strictly parametric approach because thenumber of parameters and effect of each one on theoverall behavior is very difficult to keep track of bythe high-level designer. It is therefore more practicalto provide pre-modeled elements with customizablecurves that show the overall behavior of thecomponent, including its efficiency profile, rather thanproviding a list of low-level parameters that aredifficult to identify or quantify.

3.2 Hydraulic Components

When designing a hydraulic system, one of themain difficulties is having the full efficiency mapbased on various operating conditions. In this section,the main parameters that cause the losses in hydrauliccomponents will be introduced. Using the generalequations presented here, the efficiency relationshipscan be developed based on multidimensional curves,as explain in section 4.

3.2.1 Hydraulic Pumps

The hydraulic pump will receive mechanical powerfrom the source, either from a thermal engine or anelectrical motor, and will convert it into fluid power

Because there are losses, the output Power can bedescribed as follows:

pQP

Where is the output flow and is thedifferential pressure between the inlet and the outlet ofthe pump. When we compare this output flow and themaximum theoretical flow from the inputmechanical power, we realize that these componentsare not perfect. In a complete system analysis, weneed to consider them to be accurate.

For a pump, we can establish the Power lossesusing efficiency parameters, volumetric and mechanic.The volumetric efficiency, related with the flow losses

, can be expressed as follow:

thlthvp QQQ /)(

It is fairly easy to get the theoretical flow from theinput speed of the pump shaft and thedisplacement of the pump as follow:

ipth DQ

However, getting the flow losses is more difficult.The losses are caused by leakage, which can beinternal and external to the pump. Even if the leakagescan occur at many locations at the same time, sincethey are all of the same nature, we can generalizethem using different flow loss coefficientsand . This leads to a relationship that isproportional to the displacement and inversely

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proportional to the viscosity . This relationship canbe expressed as follows:

)()(int cippextcoppextp

jll

ppDCppDCpDC

QQj

This relationship can be simplified with somehypotheses on the outlet pressure , case pressure

and inlet pressure as written in [1].For the mechanical efficiency, we need to take into

account different friction types that will be added tothe input torque needed at a given pump pressure.

)/(/ lppipmp TTTTT

With,

pDT pp

The friction torque can be considered as the sum offour components:

jhcfll TTTTTT

j

Where T is the viscous friction,

ipj

jDCTT

is the mechanical friction,

)( ipoppfj

jff ppDCTT

is a constant friction caused by seals, and isthe hydrodynamic friction, which can be mostlyneglected.

This brings us finally to express the overallefficiency as follow:

mpvpop

If we refer to the equations established in thatsection, we can see that the efficiency of pump is afunction of many parameters, but the exactrelationships are difficult to obtain.

),,,( ipop pDf

Therefore, establishing a complete efficiencymapping in simulation is difficult using upstreamprogramming, and the model built will only beaccurate for specific pumps that have all therelationships created.

3.2.2 Hydraulic Valves, Lines & Others

The analysis of a fluid system based on completefluid dynamics analysis is a tremendous amount ofwork. Also, since some mathematical models aredifficult to establish and generalize for differentoperating conditions, energy losses in valves and linesin hydraulic design are often given by rules of thumbor empirical values. The goal of this section is not tocover advanced relationships such as in [7], but toestablish and easy way to realistically considerpressure drops in hydraulic valves and lines.

In order to do that, we can approximate the pressuredrop from two well-known relationships. If weconsider a hydraulic component as an orifice, thefollowing equation stands:

/pkQ v

Where is the flow coefficient. The previousrelationship considers a localized pressure drop. If theflow path is longer, then the following equation showsthe relationship between the pressure drop, thegeometry of the line, the fluid characteristic and thefluid velocity:

2)( 2

f

i

vdLfp

Regarding the head loss coefficient , its valuevaries based on the flow type - laminar, semi turbulentor turbulent - which can be determined based on thedimensionless Reynolds number and the Moody chartshown in Fig. 3.

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Fig. 3 Moody ChartFinally, as the flow is pumped in the system, it

generates pressure drops between inlet and outlet ofhydraulics components. Even if this is desired forcontrol and regulations applications, it produces alsoundesired energy losses that cannot be neglected in acomplete analysis. And if the system contains manyhydraulic components, equivalent and simplifiedrelationships can be used to accurately obtain globalpressure drop estimations in a system using localizedand distributed pressure drop models or othersimplifications based on other assumptions which canlead to even more simplified pressure drop relations asa function of the flow coefficient .

3.2.3 Hydraulic Motor

For hydraulic motors, the model is similar to thehydraulic pump. The main difference is that the motorreceives hydraulic power and converts it intomechanical power , as described in the followingequation.

ooo TP

Mainly, the theoretical torque calculated with theinput pressure and the motor displacement will behigher than the real torque output, since the outputspeed will be lower than the theoretical one from theinput flow. Similarly for motors, a general relationshipcan be established for the overall efficiency.

),,,( omom pDf

3.3 Mechanical System

Simulating a mechanical system actuated byhydraulics involves two additional aspects in theanalysis of the complete system efficiency: powertransfer among mechanically linked hydrauliccomponents, and losses in the mechanical systemproper.

3.3.1 Dynamic Model of a Mechanism

Because each mechanical system has its ownconfiguration and because there are no standardizedcharacteristics applicable to all configurations, thedynamic simulation is performed using general rigidmultibody equations [5]. In this case, thecharacteristics are the mechanism’s geometricparameters and the masses and inertias of the differentmoving parts. These parameters can be easily obtainedusing commonly used CAD software. The followingrelation between joint accelerations and forcesapplied on the bodies of the mechanical system is used:

),( qqCqM

Where is the generalized inertia matrix, isthe generalized bias force depending on - the jointcoordinates - and - the joint velocities. Thisequation can be efficiently computed usingFeatherstone’s algorithm [4].

Interaction with the hydraulic simulation is done intwo directions: forward dynamics, where thehydraulics simulation provides forces/torques and themechanical simulation computes linear/angularaccelerations, and inverse dynamics.

The mechanical system can also store energy in theform of kinetic energy when it is moving, gravitationpotential energy when the mass are lifted, and elasticpotential energy when the spring or other compliantparts are bent.

Power losses proper to the mechanical system aremainly due to friction in the joint motion that can besimplified using coefficients. Taking all thesecoefficients into account and multiplying them by thecorresponding joint velocity modifies the generalizedbias force ( , ), which becomes a non-conservativeforce. The actuator force used to fight this friction is

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not all used to accelerate the mechanism; therefore theoutput power is smaller than input power:

outoutoutininin qPqP

This approach makes power transfer and efficiencyanalysis considerably more practical, because theindividual parameters are easy to relate to by thedesigner, as opposed to when considering a genericapproach to the complete mechanical system.

3.3.2 Model of Rolling Machine

Another interesting mechanical model to consider isa rolling machine. This system is usually complex toanalyze in depth. If the analysis focuses on hydrostatictransmission, the machine can be simplified by arolling force relationship such as the one developed in[3]:

ar RWfWF cossin

Where is the load of the rolling machine, isthe grade of the road, is the rolling coefficient, and

is the aerodynamic resistive force.Once again, even if this is a simplified relationship,

it is important to take into account load characteristicsin order to enhance simulation analysis.

4. Examples using Automation Studio™

The following examples show that software likeAutomation Studio™ allow the configuration ofcomplete circuits or targeted functions usingcomponents from renowned manufacturers’ catalogs.Since product and application engineers have alreadytested these components and collected significantapplication information, this expertise and componentknowledge can be used to greatly benefit the systemdesigner by storing complete component knowledgein each element. It then becomes possible to interfacewith the virtual machine, always using realisticconditions, and to maintain optimal performance evenwhen changing the previously selected components orby modifying the initial circuit design.

This Machine Knowledge Management takes theanalysis beyond the hydraulic system. It allowsincluding all the related selected and optimized

technologies in the system analysis. This provides anenvironment where an operator can interface with allaspects of the system providing an educationalexperience with different operational machine modesand behaviors.

4.1 Open Loop Load Sensing Energy

Consumption Analysis

This first example shows a comparison betweentwo different systems based on the same duty cycle.The system represents a simplified version of a liftingand compacting mechanism of a refuse truck. Bothcircuits are shown in Fig. 4.

Fig. 4 Open-Loop ComparisonThe upper circuit is built using load sensing and

load independent valves of the CML60 Series fromEaton. It is compared with a traditional proportionalcircuit with a fixed displacement pump andproportional valves CM80 series of the samemanufacturer.

These proportional components are built inAutomation Studio™ using advanced but user-friendly directional valve models containing all thecharacteristics needed. In Fig. 5, the manufacturer’sflow curves are already inserted in the valves used ineach circuit.

Fig. 5 Valve Model – Flow Characteristics

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These curves are defined for a specific pressuredifferential and flow characteristics, to ensure propersimulation results as described in section 3.2.2.

With these readily available valve flow and pressuredrop characteristics, and with the realistic simulationof the pump efficiencies - variable displacement loadsensing in the first circuit and fixed displacement inthe second - we easily and efficiently highlight thedifferences in energy consumption in the twopreviously shown technologies.

If the pump is driven by a diesel motor, we can addan extra level of analysis based on a repetitive orrandom duty cycle. It becomes possible to annualizethe energy consumption of any hydraulic ormechatronic system, which allows us to clearly seewhen to prioritize the initial cost or the operating cost,and to quantify the environmental impact of thesystem.

4.2 Hydrostatic Transmission Design & Energy

Consumption Analysis

This example is patterned directly on the traditionalway of designing and analyzing hydrostatictransmissions. However, it is shown that with the useof Automation Studio™ and catalogs of preconfiguredcomponents, the analysis tasks are simplified, becausethe software performs advanced calculations withthese virtual hydrostatic transmissions and thenprovides a wide range of information useful in thestudy of energy conversion capabilities of the realpower transmission system. This includes conversionrange, operating limits, as well as other criteria from asizing point of view. It also allows performingefficiency analysis of individual components involvedin a complete power transmission chain, from theenergy source, thermal or electrical, through thehydraulic components, down to the moving load, asexplained in section 3.

Fig. 6 shows an example of component efficiencymapping using a 4 dimension curve

),,( ipop pDf typically used for an axial

piston pump that can be fully customized withAutomation Studio™. It gives precisely the energylosses, which would have been very difficult orimpossible to obtain by building a system of equationsas a function of the technology and the geometry of

the pump. Therefore, provided the known efficienciesare available, the pump model is accurately simulatedat all the desired operating points. Note that for thatanalysis the viscosity isn’t considered, since it ispossible to use a correction factor to take its effect intoaccount and improve the precision of the calculation.

Fig. 6 Overall Efficiency Mapping using 4D curvesSince such curves are available and configurable for

other components, it is possible to set the efficiency ofeach component and study its impact on the overallsystem efficiency.

As a case study, this example shows a hydrostatictransmission using Linde’s Series 02 axial pistoncomponents, including a variable displacement HPVpump and a fixed displacement HMF motor. Note thatthese components are taken directly from the LindeCatalogs, which offer standardized and modularsymbols, as well as all the relevant technical data forsimulation of a hydrostatic transmission system. Theyare easily interchangeable to test creativeconfigurations in order to find the best solutionaccording to predefined criteria, like studying theoperating limits and other considerations.

Fig. 7 shows the complete system’s power balanceby visualizing the amount of power transited at eachstage of the conversion process.

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Fig. 7 Closed-Loop System Design/Efficiency AnalysisIt is then possible to optimize component selection

and the operating modes according to the kind of loadthe transmission is moving and other application-specific test configurations. These kinds of analysesare particularly interesting with the usage of axialpiston products, which efficiency is drasticallyreduced when operating at small displacements.

5. Conclusions

Downstream design consisting of usingpreconfigured modules offers many advantages forefficiently developing fully integrated systems.Components can be packed with advanced behaviorsand manufacturer-specific data, which frees thesystem designer to focus on integrating the completemechatronic system. Also, this modular approachallows for easy reuse of components, which makessystem customization more efficient and less costly.

With this approach, it is possible to build completevirtual machines that simulate several technologiesand offer a realistic behaviour even in an interactivesimulation framework. This allows for improvingsystem analysis and offers new possibilities such asmaintenance technician and machine operator training.

Through extensive use of manufacturer catalogcomponents and integrated use of differenttechnological modules, Automation Studio™

empowers the user to design complex mechatronicvirtual machines and to accurately simulate them.

References

[1] Réjean Labonville, ing. “Conception des circuits

Hydrauliques; une approche énergétique”, Presses

internationales Polytechnique, Montréal, 1999.

[2] Jack L. Johnson, PE. “Designers’ Handbook for

Electrohydraulic Servo and Proportional Systems, 4th

Edition”, IDAS Engineering inc., 2008.

[3] J.Y Wong, “Theory of Ground Vehicles”, John Wiley

& Sons, 2008.

[4] R. Featherstone, “Rigid Body Dynamics Algorithms”,

Springer, 2007.

[5] A.A Shabana, “Dynamics of Multibody Systems”,

Cambridge, 2005.

[6] IEC Standard Rotating Electrical Machines – Part 1:

Rating and performance. IEC 60034-1, Edition 12.

[7] Frank M. White, “Fluid Mechanics”, McGraw-Hill,

2011.