多畴模拟：挖掘机的机械学和液压学外文文献翻译、中英文翻译
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多畴模拟：挖掘机的机械学和液压学外文文献翻译、中英文翻译,模拟,挖掘机,机械学,液压,外文,文献,翻译,中英文
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Proceedings of the 3rd International Modelica Conference, Linkping, November 3-4, 2003, Peter Fritzson (editor) Paper presented at the 3rd International Modelica Conference, November 3-4, 2003, Linkpings Universitet, Linkping, Sweden, organized by The Modelica Association and Institutionen fr datavetenskap, Linkpings universitet All papers of this conference can be downloaded from http:/www.M/Conference2003/papers.shtml Program Committee ? Peter Fritzson, PELAB, Department of Computer and Information Science, Linkping University, Sweden (Chairman of the committee). ? Bernhard Bachmann, Fachhochschule Bielefeld, Bielefeld, Germany. ? Hilding Elmqvist, Dynasim AB, Sweden. ? Martin Otter, Institute of Robotics and Mechatronics at DLR Research Center, Oberpfaffenhofen, Germany. ? Michael Tiller, Ford Motor Company, Dearborn, USA. ? Hubertus Tummescheit, UTRC, Hartford, USA, and PELAB, Department of Computer and Information Science, Linkping University, Sweden. Local Organization: Vadim Engelson (Chairman of local organization), Bodil Mattsson-Kihlstrm, Peter Fritzson. Peter Beater and Martin Otter Fachhochschule Sdwestfalen in Soest; DLR, Germany: Multi-Domain Simulation: Mechanics and Hydraulics of an Excavator pp. 331-340 Multi-Domain Simulation:Mechanics and Hydraulics of an ExcavatorPeter Beater1, and Martin Otter21University of Applied Sciences Soest, Germany, pbbeater.de2DLR, Oberpfaffenhofen, Germany, Martin.Otterdlr.deAbstractIt is demonstrated how to model and simulate anexcavator with Modelica and Dymola by usingModelica libraries for multi-body and for hydrau-lic systems. The hydraulic system is controlled by a“load sensing” controller. Usually, models con-taining 3-dimensional mechanical and hydrauliccomponents are difficult to simulate. At hand of theexcavator it is shown that Modelica is well suitedfor such kinds of system simulations.1. IntroductionThe design of a new product requires a number ofdecisions in the initial phase that severely affectthe success of the finished machine. Today, digitalsimulation is therefore used in early stages to lookat different concepts. The view of this paper is thata new excavator is to be designed and several can-didates of hydraulic control systems have to beevaluated.Systems that consist of 3-dimensional me-chanical and of hydraulic components like exca-vators are difficult to simulate. Usually, two dif-ferent simulation environments have to be coupled.This is often inconvenient, leads to unnecessarynumerical problems and has fragile interfaces. Inthis article it is demonstrated at hand of the modelof an excavator that Modelica is well suited forthese types of systems.The 3-dimensional components of the exca-vator are modeled with the new, free ModelicaMultiBody library (Otter et. al. 2003). This allowsespecially to use an analytic solution of the kine-matic loop at the bucket and to take the masses ofthe hydraulic cylinders, i.e., the “force elements”,directly into account. The hydraulic part is mod-eled in a detailed way, utilizing pump, valves andcylinders from HyLib, a hydraulics library forModelica. For the control part a generic “loadsensing” control system is used, modeled by a setof simple equations. This approach gives the re-quired results and keeps the time needed for ana-lyzing the problem on a reasonable level.2. Modeling ChoicesThere are several approaches when simulating asystem. Depending on the task it may be necessaryto build a very precise model, containing everydetail of the system and needing a lot of informa-tion, e.g., model parameters. This kind of models isexpensive to build up but on the other hand veryuseful if parameters of a well defined system haveto be modified. A typical example is the optimiza-tion of parameters of a counterbalance valve in anexcavator (Kraft 1996).The other kind of model is needed for a firststudy of a system. In this case some properties ofthe pump, cylinders and loads are specified. Re-quired is information about the performance of thatsystem, e.g., the speed of the pistons or the neces-sary input power at the pump shaft, to make a deci-sion whether this design can be used in principlefor the task at hand. This model has therefore to be“cheap”, i.e., it must be possible to build it in ashort time without detailed knowledge of particularcomponents.The authors intended to build up a model ofthe second type, run it and have first results with aminimum amount of time spent. To achieve thisgoal the modeling language Modelica (Modelica2002), the Modelica simulation environment Dy-mola (Dymola 2003), the new Modelica library for3-dimensional mechanical systems “MultiBody”(Otter et al. 2003) and the Modelica library of hy-draulic components HyLib (Beater 2000) wasused. The model consists of the 3-dimensional me-chanical construction of the excavator, a detaileddescription of the power hydraulics and a generic“load sensing” controller. This model will beavailable as a demo in the next version of HyLib.3. Construction of ExcavatorsIn Figure 1 a schematic drawing of a typical exca-vator under consideration is shown. It consists of achain track and the hydraulic propel drive which isused to manoeuvre the machine but usually notduring a work cycle. On top of that is a carriage Peter Beater and Martin Otter Multi-Domain Simulation: Mechanics and Hydraulics of an Excavator The Modelica Association Modelica 2003, November 3-4, 2003Figure 1 Schematic drawing of excavatorwhere the operator is sitting. It can rotate around avertical axis with respect to the chain track. It alsoholds the Diesel engine, the hydraulic pumps andcontrol system. Furthermore, there is a boom, anarm and at the end a bucket which is attached via aplanar kinematic loop to the arm. Boom, arm andbucket can be rotated by the appropriate cylinders.Figure 2 shows that the required pressures inthe cylinders depend on the position. For the“stretched” situation the pressure in the boom cyl-inder is 60 % higher than in the retracted position.Not only the position but also the movements haveto be taken into account. Figure 3 shows a situationwhere the arm hangs down. If the carriage does notrotate there is a pulling force required in the cylin-der. When rotating excavators can typically ro-tate with up to 12 revolutions per minute theforce in the arm cylinder changes its sign and nowa pushing force is needed. This change is very sig-nificant because now the “active” chamber of thecylinder switches and that must be taken into ac-count by the control system. Both figures demon-strate that a simulation model must take into ac-count the couplings between the four degrees offreedom this excavator has. A simpler model thatuses a constant load for each cylinder and theswivel drive leads to erroneous results (Jansson etal. 1998).Figure 2 Different working situations Figure 3 Effect of centrifugal forces4. Load Sensing SystemExcavators have typically one Diesel engine, twohydraulic motors and three cylinders. There existdifferent hydraulic circuits to provide the consum-ers with the required hydraulic energy. A typicaldesign is a Load Sensing circuit that is energy effi-cient and user friendly. The idea is to have a flowrate control system for the pump such that it deliv-ers exactly the needed flow rate. As a sensor thepressure drop across an orifice is used. The refer-ence value is the resistance of the orifice. A sche-matic drawing is shown in figure 4, a good intro-duction to that topic is given in (anon. 1992).The pump control valve maintains a pressureat the pump port that is typically 15 bar higher thanthe pressure in the LS line (= Load Sensing line). Ifthe directional valve is closed the pump has there-fore a stand-by pressure of 15 bar. If it is open thepump delivers a flow rate that leads to a pressuredrop of 15 bar across that directional valve. Note:The directional valve is not used to throttle thepump flow but as a flow meter (pressure drop thatis fed back) and as a reference (resistance). Thecircuit is energy efficient because the pump deliv-ers only the needed flow rate, the throttling lossesare small compared to other circuits.If more than one cylinder is used the circuitbecomes more complicated, see figure 5. E.g. if theboom requires a pressure of 100 bar and the bucketa pressure of 300 bar the pump pressure must beabove 300 bar which would cause an unwantedFigure 4 Schematics of a simple LS system (Zhe) Peter Beater and Martin Otter Multi-Domain Simulation: Mechanics and Hydraulics of an Excavator The Modelica Association Modelica 2003, November 3-4, 2003movement of the boom cylinder. Therefore com-pensators are used that throttle the oil flow andthus achieve a pressure drop of 15 bar across theparticular directional valve. These compensatorscan be installed upstream or downstream of thedirectional valves. An additional valve reduces thenominal pressure differential if the maximumpump flow rate or the maximum pressure isreached (see e.g. Nikolaus 1994).Figure 5 Schematic drawing of a LS system5. Model of Mechanical PartIn Figure 6, a Modelica schematic of the mechani-cal part is shown. The chain track is not modeled,i.e., it is assumed that the chain track does notmove. Components “rev1”, ., “rev4” are the 4revolute joints to move the parts relative to eachother. The icons with the long black line are “vir-tual” rods that are used to mark specific points on apart, especially the mounting points of the hydrau-lic cylinders. The light blue spheres (b2, b3, b4,b5) are bodies that have mass and an inertia tensorand are used to model the corresponding propertiesof the excavator parts.The three components “cyl1f”, “cyl2f”,and “cyl3f” are line force components that describea force interaction along a line between two at-tachment points. The small green squares at thesecomponents represent 1-dimensional translationalconnectors from the Modelica.Mechanics.Trans-lational library. They are used to define the 1-dimensional force law acting between the two at-tachment points. Here, the hydraulic cylinders de-scribed in the next section are directly attached.The small two spheres in the icons of the “cyl1f,cyl2f, cyl3f” components indicate that optionallytwo point masses are taken into account that areattached at defined distances from the attachmentFigure 6 Modelica schematic of mechanical part of excavator Peter Beater and Martin Otter Multi-Domain Simulation: Mechanics and Hydraulics of an Excavator The Modelica Association Modelica 2003, November 3-4, 2003points along the connecting line. This allows toeasily model the essential mass properties (massand center of mass) of the hydraulic cylinders withonly a very small computational overhead.The jointRRR component (see right part ofFigure 6) is an assembly element consisting of 3revolute joints that form together a planar loopwhen connected to the arm. A picture of this partof an excavator, a zoom in the correspondingModelica schematic and the animation view isshown in Figure 7. When moving revolute joint“rev4” (= the large red cylinder in the lower part ofFigure 7; the small red cylinders characterize the 3revolute joints of the jointRRR assembly compo-nent) the position and orientation of the attachmentpoints of the “left” and “right” revolute joints ofthe jointRRR component are known. There is anon-linear algebraic loop in the jointRRR compo-nent to compute the angles of its three revolutejoints given the movement of these attachmentpoints. This non-linear system of equations issolved analytically in the jointRRR object, i.e., in arobust and efficient way. For details see (Otter et.al. 2003).Figure7 Foto, schematic and animation of jointRRRIn a first step, the mechanical part of the excavatoris simulated without the hydraulic system to testthis part separatly. This is performed by attachingtranslational springs with appropriate spring con-stants instead of the hydraulic cylinders. After theanimation looks fine and the forces and torques inthe joints have the expected size, the springs arereplaced by the hydraulic system described in thenext sections.All components of the new MultiBody li-brary have “built-in” animation definitions, i.e.,animation properties are mostly deduced by defaultfrom the given definition of the multi-body system.For example, a rod connecting two revolute jointsis by default visualized as cylinder where the di-ameter d is a fraction of the cylinder length L (d =L/40) which is in turn given by the distance of thetwo revolute joints. A revolute joint is by defaultvisualized by a red cylinder directed along the axisof rotation of the joint. The default animation (withonly a few minor adaptations) of the excavator isshown if Figure 8.Figure 8 Default animation of excavatorThe light blue spheres characterize the center ofmass of bodies. The line force elements that visu-alize the hydraulic cylinders are defined by twocylinders (yellow and grey color) that are movingin each other. As can be seen, the default anima-tion is useful to get, without extra work from theuser side, a rough picture of the model that allowsto check the most important properties visually,e.g., whether the center of masses or attachmentpoints are at the expected places.For every component the default animationcan be switched off via a Boolean flag. Removingappropriate default animations, such as the “center-of-mass spheres”, and adding some componentsthat have pure visual information (all visXXXcomponents in the schematic of Figure 6) givesquickly a nicer animation, as is demonstrated inFigure 9. Also CAD data could be utilized for theanimation, but this was not available for the ex-amination of this excavator. Peter Beater and Martin Otter Multi-Domain Simulation: Mechanics and Hydraulics of an Excavator The Modelica Association Modelica 2003, November 3-4, 2003Figure 9 Animation of excavator (start/end position)6. The Hydraulics Library HyLibThe (commercial) Modelica library HyLib (Beater2000, HyLib 2003) is used to model the pump,metering orifice, load compensator and cylinder ofthe hydraulic circuit. All these components arestandard components for hydraulic circuits and canbe obtained from many manufacturers. Models ofall of them are contained in HyLib. These mathe-matical models include both standard textbookmodels (e. g. Dransfield 1981, Merrit 1967,Viersma 1980) and the most advanced publishedmodels that take the behavior of real componentsinto account (Schulz 1979, Will 1968). An exam-ple is the general pump model where the outputflow is reduced if pressure at the inlet port fallsbelow atmospheric pressure. Numerical propertieswere also considered when selecting a model(Beater 1999). One point worth mentioning is thefact that all models can be viewed at source codelevel and are documented by approx. 100 refer-ences from easily available literature.After opening the library, the main win-dow is displayed (Figure 10). A double click on the“pumps” icon opens the selection for all compo-nents that are needed to originate or end an oil flow(Figure 11). For the problem at hand, a hydraulicflow source with internal leakage and externallycommanded flow rate is used. Similarly the neededmodels for the valves, cylinders and other compo-nents are chosen.All components are modeled hierarchi-cally. Starting with a definition of a connector aport were the oil enters or leaves the component Figure 10 Overview of hydraulics library HyLiba template for components with two ports is writ-ten. This can be inherited for ideal models, e.g., alaminar resistance or a pressure relief valve. Whileit usually makes sense to use textual input for thesebasic models most of the main library models wereprogrammed graphically, i.e., composed from ba-sic library models using the graphical user inter-face. Figure12 gives an example of graphical pro-gramming. All mentioned components were cho-sen from the library and then graphically con-nected.Figure 11 Pump models in HyLib7. Library Components in Hydraulics CircuitThe composition diagram in Figure 12 shows thegraphically composed hydraulics part of the exca-vator model. The sub models are chosen from theappropriate libraries, connected and the parametersinput. Note that the cylinders and the motor fromHyLib can be simply connected to the also showncomponents of the MultiBody library. The inputsignals, i.e., the reference signals of the driver ofthe excavator, are given by tables, specifying thediameter of the metering orifice, i.e. the referencevalue for the flow rate. From the mechanical part Peter Beater and Martin Otter Multi-Domain Simulation: Mechanics and Hydraulics of an Excavator The Modelica Association Modelica 2003, November 3-4, 2003of the excavator only the components are shown inFigure 12 that are directly coupled with hydraulicelements, such as line force elements to which thehydraulic cylinders are attached.8. Model of LS ControlFor this study the following approach is chosen:Model the mechanics of the excavator, the cylin-ders and to a certain extent the pump and meteringvalves in detail because only the parameters of thecomponents will be changed, the general structureis fixed. This means that the diameter of the bucketcylinder may be changed but there will be exactlyone cylinder working as shown in Figure 1. That isdifferent for the rest of the hydraulic system. Inthis paper a Load Sensing system, or LS system forshort, using one pump is shown but there are otherconcepts that have to be evaluated during an initialdesign phase. For instance the use of two pumps,or a separate pump for the swing.The hydraulic control system can be set upusing meshed control loops. As there is (almost) no way to implement phase shifting behavior inpurely hydraulic control systems the following ge-neric LS system uses only proportional controllers.A detailed model based on actual compo-nents would be much bigger and is usually notavailable at the begin of an initial design phase. Itcould be built with the components from the hy-draulics library but would require a considerableamount of time that is usually not available at thebeginning of a project.In Tables 1 and 2, the implementation of theLS control in form of equations is shown. Usually,it is recommended for Modelica models to eitheruse graphical model decomposition or to define themodel by equations, but not to mix both descrip-Table 1 Modelica code for definition for constants, parameters and variables for LS control system/ Definition of variables,/ parameters and constantsimport SI = Modelica.SIunits;SI.Pressure delta_p1;SI.Pressure delta_p2;SI.Pressure pump_ls;SI.Pressure pump_ls1;SI.Pressure pump_ls2;SI.Pressure dp_ref(start = 15e5,fixed = true);Boolean pump_q_max;Boolean pump_p_max(start = false,fixed = true);parameter Realk_LS=1e-5;parameter SI.Pressure p_max = 415e5Figure 12 Modelica schematic of hydraulic part of excavator Peter Beater and Martin Otter Multi-Domain Simulation: Mechanics and Hydraulics of an Excavator The Modelica Association Modelica 2003, November 3-4, 2003Table 2 Modelica code for LS Controller, see also Fig. 4 and 5function conductance Determine conductance of compensatorsinputSI.Pressure dp;output RealG;algorithmG := min(1e-8, max(1e-13, 1e-8 - dp*5e-14);end conductanceequation/ Set of equations to model the LS controller/ define pressure differential across the metering orifices/ for load compensator and documentation purposesdelta_p1 = if ref_boom.y1= 0 then pump.port_B.pelse metOri1.port_A.p - metOri1.port_B.p;delta_p2 = if ref_swing.y1= 0 then 0.0else metOri2.port_A.p - metOri2.port_B.p;delta_p3 = if ref_bucket.y1 = 0 then pump.port_B.pelse metOri3.port_A.p - metOri3.port_B.p;delta_p4 = if ref_arm.y1= 0 then pump.port_B.pelse metOri4.port_A.p - metOri4.port_B.p;/ calculate load pressure for pump controllerpump_ls1 = if ref_boom.y1= 0 then pump.port_B.pelse metOri1.port_A.p - comp1.port_B.p;pump_ls2 = if ref_swing.y1= 0 then pump.port_B.pelse metOri2.port_A.p - comp2.port_B.p;pump_ls3 = if ref_bucket.y1 = 0 then pump.port_B.pelse metOri3.port_A.p - comp3.port_B.p;pump_ls4 = if ref_arm.y1 8e-3;/ set Boolean state if max. pump pressure is reached (with hysteresis)pump_p_max = pump.port_B.p p_max orpre(pump_p_max) and pump.port_B.p 0.95*p_max;/ calculate command signal for pumppump.inPort.signal1 = if pump_p_max thenmin(7.5e-3, 7.5e-3 + k_LS*1e-2*(p_max - pump.port_B.p)else if pump_q_max then 7.5e-3 else (k_LS*(15e5 - pump_ls);/ modify reference signal if maximum pump flow rate is exceededdp_ref = if pump_q_max and not pump_p_max then pump_ls else 15e5;/ calculate conductances of pressure compensatorscomp1.inPort.signal1 = conductance(delta_p1 - dp_ref);comp2.inPort.signal1 = conductance(delta_p2 - dp_ref);comp3.inPort.signal1 = conductance(delta_p3 - dp_ref);comp4.inPort.signal1 = conductance(delta_p4 - dp_ref);tion forms on the same model level. For the LSsystem this is different because it has 17 input sig-nals and 5 output signals. One might built oneblock with 17 inputs and 5 outputs and connectthem to the hydraulic circuit. However, in this caseit seems more understandable to provide the equa-tions directly on the same level as the hydrauliccircuit above and access the input and output sig-nals directly. For example, ”metOri1.port_A.p”used in table 2 is the measured pressure at port_Aof the metering orifice metOri1. The calculatedvalues of the LS controller, e.g., the pump flowrate “pump.inPort.signal1 = .” is the signal at the Peter Beater and Martin Otter Multi-Domain Simulation: Mechanics and Hydraulics of an Excavator The Modelica Association Modelica 2003, November 3-4, 2003filled blue rectangle of the “pump” component, seeFigure 12).The strong point of Modelica is that aseamless integration of the 3-dimensional me-chanical library, the hydraulics library and the nonstandard, and therefore in no library available,model of the control system is easily done. Thelibrary components can be graphically connectedin the object diagram and the text based model canaccess all needed variables.9. Some Simulation ResultsThe complete model was built using the Modelicamodeling and simulation environment Dymola(Dymola 2003), translated, compiled and simulatedfor 5 s. The simulation time was 17 s using theDASSL integrator with a relative tolerance of 10-6on a 1.8 GHz notebook, i.e., about 3.4 times sloweras real-time. The animation feature in Dymolamakes it possible to view the movements in an al-most realistic way which helps to explain the re-sults also to non-experts, see Figure 9.Figure 13 gives the reference signals forthe three cylinders and the swing, the pump flowrate and pressure. From t = 1.1 s until 1.7 s andfrom t = 3.6 s until 4.0 s the pump delivers themaximum flow rate. From t = 3.1 s until 3.6 s themaximum allowed pressure is reached.Figure 13 Reference, pump flow rate and pressureFigure 14 gives the position of the boom and thebucket cylinders and the swing angle. It can beseen that there is no significant change in the pis-ton movement if another movement starts or ends.The control system reduces the couplings betweenthe consumers which are very severe for simplethrottling control.Figure 14 Boom and bucket piston position and swingangleFigure 15 shows the operation of the bucket cylin-der. The top figure shows the reference trajectory,i. e. the opening of the directional valve. The mid-dle figure shows the conductance of the compen-sators. With the exception of two spikes it is openfrom t = 0 s until t = 1 s. This means that in thatinterval the pump pressure is commanded by thatbucket cylinder. After t = 1 s the boom cylinderrequires a considerably higher pressure and thebucket compensator therefore increases the resis-tance (smaller conductance). The bottom figureshows that the flow rate control works fine. Eventhough there is a severe disturbance (high pumppressure after t = 1 s due to the boom) the com-manded flow rate is fed with a small error to thebucket cylinder.Figure 15 Operation of bucket cylinder Peter Beater and Martin Otter Multi-Domain Simulation: Mechanics and Hydraulics of an Excavator The Modelica Association Modelica 2003, November 3-4, 200310. ConclusionFor the evaluation of different hydraulic circuits adynamic model of an excavator was built. It con-sists of a detailed model of the 3 dimensional me-chanics of the carriage, including boom, arm andbucket and the standard hydraulic components likepump or cylinder. The control system was notmodeled on a component basis but the system wasdescribed by a set of nonlinear equations.The system was modeled using the
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