.. _examples-hydraulicactuatorstaticinitialization: **************************************** HydraulicActuatorStaticInitialization.py **************************************** You can view and download this file on Github: `HydraulicActuatorStaticInitialization.py `_ .. code-block:: python :linenos: #+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ # This is an EXUDYN example # # Details: A one arm mechanism is actuated by the HydraulicActuatorSimple; # This particular example shows how a static computation can be performed with the hydraulic actuator; # For static computation, a distance constraint is used to replace the hydraulic actuator; # Hereafter, the dynamic simulation is initialized with the static equilibrium; this can be used for flexible booms # # Author: Johannes Gerstmayr # Date: 2023-09-07 # # Copyright:This file is part of Exudyn. Exudyn is free software. You can redistribute it and/or modify it under the terms of the Exudyn license. See 'LICENSE.txt' for more details. # #+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ import exudyn as exu from exudyn.utilities import * #includes itemInterface and rigidBodyUtilities import exudyn.graphics as graphics #only import if it does not conflict useGraphics = True #without test import numpy as np from math import sin, cos, sqrt,pi SC = exu.SystemContainer() mbs = SC.AddSystem() L = 1 #x-dim of arm b = 0.1 #y-dim of arm #+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ #one arm mechanism background = graphics.CheckerBoard(point=[0,0.5*L*0,-2*b],size=2) oGround=mbs.AddObject(ObjectGround(referencePosition= [0,0,0], visualization=VObjectGround(graphicsData= [background]))) massRigid = 12*10 inertiaRigid = massRigid/12*(L)**2 g = 9.81 # gravity graphicsList = [graphics.Brick(size= [L,b,0.1*b], color= graphics.color.dodgerblue, addEdges=True)] graphicsList += [graphics.Cylinder(pAxis=[-0.5*L,0,-0.7*b], vAxis= [0,0,1.4*b], radius = 0.55*b, color= graphics.color.lightgrey, addEdges=True, nTiles=32)] #print(graphicsList[2]) nRigid = mbs.AddNode(Rigid2D(referenceCoordinates=[0.5*L,0,0], initialVelocities=[0,0,0])); oRigid = mbs.AddObject(RigidBody2D(physicsMass=massRigid, physicsInertia=inertiaRigid,nodeNumber=nRigid, visualization=VObjectRigidBody2D(graphicsData= graphicsList))) mR1 = mbs.AddMarker(MarkerBodyPosition(bodyNumber=oRigid, localPosition=[-0.5*L,0.,0.])) #support point mR2 = mbs.AddMarker(MarkerBodyPosition(bodyNumber=oRigid, localPosition=[ 0.,0.,0.])) #end point #add joint mG0 = mbs.AddMarker(MarkerBodyPosition(bodyNumber=oGround, localPosition=[0,0,0])) mbs.AddObject(RevoluteJoint2D(markerNumbers=[mG0,mR1])) mbs.AddLoad(Force(markerNumber = mR2, loadVector = [0, -massRigid*g, 0])) #%%+++++++++++++++++++++++++++++++++++++++++++++++++++++ #add hydraulics actuator: mGH = mbs.AddMarker(MarkerBodyPosition(bodyNumber=oGround, localPosition=[0,-0.25*L-0.5*b*0,0.])) mRH = mbs.AddMarker(MarkerBodyPosition(bodyNumber=oRigid, localPosition=[-0.25*L,-0.5*b*0,0.])) LH0 = sqrt(2*(0.25*L)**2) #zero length of actuator #hydraulics parameters: V0 = 1. #oil volume (could actually change ...) V1 = V0 #oil volume (could actually change ...) A=[0.01,0.01] #piston area side 1/2 Eoil = 1e11 Av1 = 1 #valve opening (factor) Av2 = 0.0 #valve opening (factor) Qn = 2e-5 #nominal flow pS = 200.*1e5 #system pressure (200bar) pT = 0.*1e5 #tank pressure; dampingHA = 2e5 useHydraulics=True staticInitialization=True if useHydraulics: #ODE1 for pressures: nODE1 = mbs.AddNode(NodeGenericODE1(referenceCoordinates=[0,0], initialCoordinates=[2e6,2e6], #initialize with 20 bar numberOfODE1Coordinates=2)) oHA = mbs.AddObject(HydraulicActuatorSimple(markerNumbers=[mGH, mRH], nodeNumbers=[nODE1], offsetLength=LH0, strokeLength=LH0*0.5, chamberCrossSection0=A[0], chamberCrossSection1=A[1], hoseVolume0=V0, hoseVolume1=V1, valveOpening0=0, valveOpening1=0, oilBulkModulus=Eoil, actuatorDamping=dampingHA, nominalFlow=Qn, systemPressure=pS, tankPressure=pT, useChamberVolumeChange=False, visualization=VHydraulicActuatorSimple(cylinderRadius= 0.6*b, rodRadius= 0.3*b, baseMountLength = 0.4*b, baseMountRadius = 0.4*b, rodMountRadius = 0.3*b, pistonLength = 0.2*b, pistonRadius = 0.55*b, colorCylinder=graphics.color.blue, colorPiston=graphics.color.lightgrey), )) def PreStepUserFunction(mbs, t): LHact = mbs.GetObjectOutput(oHA, variableType=exu.OutputVariableType.Distance) x = (max(0.5, min(1.5,(1-cos(t*pi*2*0.5))) ) - 0.5)*0.1+LH0 #if t>2: x=LH0 Av0 = (x-LHact)*2 #valve position control ==> penalize set value LH0 #print('Av0=',Av0) Av1 = -Av0 mbs.SetObjectParameter(oHA, "valveOpening0", Av0) mbs.SetObjectParameter(oHA, "valveOpening1", Av1) return True sForce = mbs.AddSensor(SensorObject(objectNumber=oHA, storeInternal=True, outputVariableType=exu.OutputVariableType.Force)) sDistance = mbs.AddSensor(SensorObject(objectNumber=oHA, storeInternal=True, outputVariableType=exu.OutputVariableType.Distance)) sVelocity = mbs.AddSensor(SensorObject(objectNumber=oHA, storeInternal=True, outputVariableType=exu.OutputVariableType.Velocity)) sPressures = mbs.AddSensor(SensorNode(nodeNumber=nODE1, storeInternal=True, outputVariableType=exu.OutputVariableType.Coordinates)) #compute reference length of distance constraint (this is LH0 in this case, but could be else): mGHposition = mbs.GetMarkerOutput(mGH, variableType=exu.OutputVariableType.Position, configuration=exu.ConfigurationType.Reference) mRHposition = mbs.GetMarkerOutput(mRH, variableType=exu.OutputVariableType.Position, configuration=exu.ConfigurationType.Reference) dLH0 = NormL2(mGHposition - mRHposition) # print('LH0=', LH0) # print('dLH0=', dLH0) #use distance constraint to compute static equlibrium in static case oDC = mbs.AddObject(DistanceConstraint(markerNumbers=[mGH, mRH], distance=dLH0)) mbs.Assemble() #%%+++++++++++++++++++++++++++++++++++++++++++++++++++++ simulationSettings = exu.SimulationSettings() #takes currently set values or default values tEnd = 1 stepSize = 1e-3 simulationSettings.timeIntegration.numberOfSteps = int(tEnd/stepSize) simulationSettings.timeIntegration.endTime = tEnd simulationSettings.timeIntegration.startTime = 0 simulationSettings.timeIntegration.newton.relativeTolerance = 1e-8*100 #10000 simulationSettings.timeIntegration.newton.absoluteTolerance = 1e-10 simulationSettings.timeIntegration.verboseMode = 1 # simulationSettings.timeIntegration.simulateInRealtime = True #to see what happens ... simulationSettings.timeIntegration.newton.useModifiedNewton = True simulationSettings.timeIntegration.newton.numericalDifferentiation.minimumCoordinateSize = 1 simulationSettings.timeIntegration.generalizedAlpha.spectralRadius = 0.5 simulationSettings.displayStatistics = True simulationSettings.solutionSettings.solutionInformation = 'Hydraulics user function test' SC.visualizationSettings.openGL.multiSampling = 4 SC.visualizationSettings.openGL.lineWidth = 2 if useGraphics: exu.StartRenderer() # mbs.WaitForUserToContinue() simulationSettings.staticSolver.constrainODE1coordinates = True #True: set pressures to initial values if staticInitialization: exu.SolveStatic(mbs, simulationSettings, updateInitialValues=True) #results are new initial values force = mbs.GetObjectOutput(oDC, variableType=exu.OutputVariableType.Force) print('initial force=', force) mbs.SetObjectParameter(oDC, 'activeConnector', False) if useHydraulics: if staticInitialization: p0 = 2e6 + force/A[0] p1 = 2e6 #now we would like to reset the pressures: #1) chance initial in NodeGenericODE1 => then mbs.Assemble() => this would destroy the previously computed initial values #2) change the initial values in the system vector sysODE1 = mbs.systemData.GetODE1Coordinates(configuration=exu.ConfigurationType.Initial) nODE1index = mbs.GetNodeODE1Index(nODE1) print('sysODE1=',sysODE1) print('p0,p1=',p0,p1) sysODE1[nODE1index] = p0 sysODE1[nODE1index+1] = p1 #now write the updated system variables: mbs.systemData.SetODE1Coordinates(coordinates=sysODE1, configuration=exu.ConfigurationType.Initial) #mbs.SetObjectParameter(oHA, '') mbs.SetPreStepUserFunction(PreStepUserFunction) exu.SolveDynamic(mbs, simulationSettings, showHints=False) if useGraphics: SC.WaitForRenderEngineStopFlag() exu.StopRenderer() #safely close rendering window! if useHydraulics: exu.Print('hydraulics C++:') exu.Print('pressures=', mbs.GetSensorValues(sPressures)) exu.Print('velocity=', mbs.GetSensorValues(sVelocity)) #for stepSize=1e-6: error about 1e-5 compared to user function implementation; with initialVelocities=[0,0,2] and tEnd=0.4 # hydraulics C++: # pressures= [6441296.09086297 3008420.04232005] # velocity= [-0.0050061 0.20338669 0. ] # from exudyn.plot import PlotSensor # PlotSensor(mbs, sensorNumbers=sForce, components=exudyn.plot.componentNorm, labels=['connector force norm'], yLabel='force (N)', closeAll=True) # PlotSensor(mbs, sensorNumbers=sDistance, components=0) mbs.PlotSensor(sensorNumbers=[sPressures]*2, components=[0,1], labels=['p0', 'p1'], yLabel='pressure (N/m^2)') #PlotSensor(mbs, sensorNumbers=p01, components=0, labels=['differential hydraulic force'], yLabel='hydraulic force (N)') #compute error for test suite: sol2 = mbs.systemData.GetODE2Coordinates(); sol1 = mbs.systemData.GetODE1Coordinates(); u = np.linalg.norm(sol2); u += np.linalg.norm(sol1)*1e-6; exu.Print('solution of hydraulicActuatorSimpleTest =',u)