You can view and download this file on Github: HydraulicActuator2Arms.py
#+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
# This is an EXUDYN example
#
# Details: A two arm mechanism is actuated by the HydraulicActuatorSimple;
# The actuator contains internal dynamics based on GenericODE1 node
#
# Author: Johannes Gerstmayr
# Date: 2022-06-16
#
# 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 *
#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
addArm2 = True
#+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
#one arm mechanism
background = [GraphicsDataCheckerBoard(point=[L,0,-2*b],size=5)]
background += [GraphicsDataCylinder(pAxis=[0,-0.25*L-0.5*b,-0.5*b], vAxis= [0,0,1.*b], radius = 0.25*b,
color= color4grey, addEdges=True, nTiles=32)]
oGround=mbs.AddObject(ObjectGround(referencePosition= [0,0,0], visualization=VObjectGround(graphicsData= background)))
massRigid = 12*10
inertiaRigid = massRigid/12*(L)**2
g = 9.81 # gravity
#++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
#++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
#arm1
#graphics for arm1
colCyl = color4orange
colArm = color4dodgerblue
graphicsList = [GraphicsDataOrthoCubePoint(size= [L,0.75*b,1.4*b], color= colArm, addEdges=True)]
graphicsList += [GraphicsDataCylinder(pAxis=[-0.5*L,0,-0.75*b], vAxis= [0,0,1.5*b], radius = 0.55*b,
color= colArm, addEdges=True, nTiles=32)]
graphicsList += [GraphicsDataCylinder(pAxis=[-0.5*L,0,-0.8*b], vAxis= [0,0,1.6*b], radius = 0.25*b,
color= color4grey, addEdges=True, nTiles=32)]
#bolt
graphicsList += [GraphicsDataCylinder(pAxis=[-0.25*L,-0.5*b,-0.7*b], vAxis= [0,0,1.4*b], radius = 0.15*b,
color= color4grey, addEdges=True, nTiles=32)]
graphicsList += [GraphicsDataCylinder(pAxis=[-0.25*L,-0.5*b,-0.6*b], vAxis= [0,0,0.25*b], radius = 0.3*b,
color= colArm, addEdges=True, nTiles=32)]
graphicsList += [GraphicsDataCylinder(pAxis=[-0.25*L,-0.5*b, 0.6*b], vAxis= [0,0,-0.25*b], radius = 0.3*b,
color= colArm, addEdges=True, nTiles=32)]
if addArm2:
graphicsList += [GraphicsDataCylinder(pAxis=[ 0.25*L,-0.5*b,-0.7*b], vAxis= [0,0,1.4*b], radius = 0.15*b,
color= color4grey, addEdges=True, nTiles=32)]
graphicsList += [GraphicsDataCylinder(pAxis=[ 0.25*L,-0.5*b,-0.6*b], vAxis= [0,0,0.25*b], radius = 0.3*b,
color= colArm, addEdges=True, nTiles=32)]
graphicsList += [GraphicsDataCylinder(pAxis=[ 0.25*L,-0.5*b, 0.6*b], vAxis= [0,0,-0.25*b], radius = 0.3*b,
color= colArm, addEdges=True, nTiles=32)]
#+++++++++++++++++++++++++++++++++++++++++++++++++++
#print(graphicsList)
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
mCOM1 = mbs.AddMarker(MarkerBodyPosition(bodyNumber=oRigid, localPosition=[ 0.,0.,0.]))
mR1end = mbs.AddMarker(MarkerBodyPosition(bodyNumber=oRigid, localPosition=[0.5*L,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 = mCOM1, loadVector = [0, -massRigid*g, 0]))
#%%+++++++++++++++++++++++++++++++++++++++++++++++++++++
#add hydraulics actuator:
mGH = mbs.AddMarker(MarkerBodyPosition(bodyNumber=oGround, localPosition=[0,-0.25*L-0.5*b,0.]))
mRH = mbs.AddMarker(MarkerBodyPosition(bodyNumber=oRigid, localPosition=[-0.25*L,-0.5*b,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 = 1e12
Av1 = 1 #valve opening (factor)
Av2 = 0.0 #valve opening (factor)
Qn = 2e-5 #nominal flow
pS = 200.*1e5 #system pressure (200bar)
pT = 1e-16+0.*1e5 #tank pressure;
actuatorDamping = 2e5
#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*0.7,
chamberCrossSection0=A[0], chamberCrossSection1=A[1],
hoseVolume0=V0, hoseVolume1=V1,
valveOpening0=0, valveOpening1=0,
oilBulkModulus=Eoil, actuatorDamping=actuatorDamping, nominalFlow=Qn,
systemPressure=pS, tankPressure=pT,
useChamberVolumeChange=False,
visualization=VHydraulicActuatorSimple(cylinderRadius= 0.55*b, rodRadius= 0.3*b,
baseMountLength = 0.4*b, baseMountRadius = 0.4*b,
rodMountRadius = 0.3*b, pistonLength = 0.2*b, pistonRadius = 0.5*b,
colorCylinder=colCyl, colorPiston=color4lightgrey),
))
#++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
#++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
#arm2
#graphics for arm2
oHA2 = -1
if addArm2:
graphicsList = [GraphicsDataOrthoCubePoint(size= [L,0.75*b,1.4*b], color= colArm, addEdges=True)]
graphicsList += [GraphicsDataCylinder(pAxis=[-0.5*L,0,-0.75*b], vAxis= [0,0,1.5*b], radius = 0.55*b,
color= colArm, addEdges=True, nTiles=32)]
graphicsList += [GraphicsDataCylinder(pAxis=[-0.5*L,0,-0.8*b], vAxis= [0,0,1.6*b], radius = 0.25*b,
color= color4grey, addEdges=True, nTiles=32)]
#bolt
graphicsList += [GraphicsDataCylinder(pAxis=[-0.25*L,-0.5*b,-0.7*b], vAxis= [0,0,1.4*b], radius = 0.15*b,
color= color4grey, addEdges=True, nTiles=32)]
graphicsList += [GraphicsDataCylinder(pAxis=[-0.25*L,-0.5*b,-0.6*b], vAxis= [0,0,0.25*b], radius = 0.3*b,
color= colArm, addEdges=True, nTiles=32)]
graphicsList += [GraphicsDataCylinder(pAxis=[-0.25*L,-0.5*b, 0.6*b], vAxis= [0,0,-0.25*b], radius = 0.3*b,
color= colArm, addEdges=True, nTiles=32)]
#+++++++++++++++++++++++++++++++++++++++++++++++++++
#print(graphicsList)
nRigid2 = mbs.AddNode(Rigid2D(referenceCoordinates=[1.*L,-0.5*L,-0.5*pi], initialVelocities=[0,0,0]));
oRigid2 = mbs.AddObject(RigidBody2D(physicsMass=massRigid, physicsInertia=inertiaRigid,nodeNumber=nRigid2,
visualization=VObjectRigidBody2D(graphicsData= graphicsList)))
mR1 = mbs.AddMarker(MarkerBodyPosition(bodyNumber=oRigid2, localPosition=[-0.5*L,0.,0.])) #support point
mCOM2 = mbs.AddMarker(MarkerBodyPosition(bodyNumber=oRigid2, localPosition=[ 0.,0.,0.]))
#add joint
mbs.AddObject(RevoluteJoint2D(markerNumbers=[mR1end,mR1]))
mbs.AddLoad(Force(markerNumber = mCOM2, loadVector = [0, -massRigid*g, 0]))
#%%+++++++++++++++++++++++++++++++++++++++++++++++++++++
#add hydraulics actuator:
mH12 = mbs.AddMarker(MarkerBodyPosition(bodyNumber=oRigid, localPosition=[0.25*L,-0.5*b,0.]))
mH2 = mbs.AddMarker(MarkerBodyPosition(bodyNumber=oRigid2, localPosition=[-0.25*L,-0.5*b,0.]))
LH02 = sqrt(2*(0.25*L-0.5*b)**2) #zero length of actuator
#ODE1 for pressures:
nODE1_2 = mbs.AddNode(NodeGenericODE1(referenceCoordinates=[0,0],
initialCoordinates=[2e6,2e6], #initialize with 20 bar
numberOfODE1Coordinates=2))
oHA2 = mbs.AddObject(HydraulicActuatorSimple(markerNumbers=[mH12, mH2],
nodeNumbers=[nODE1_2],
offsetLength=LH02, strokeLength=LH02*0.7,
chamberCrossSection0=A[0], chamberCrossSection1=A[1],
hoseVolume0=V0, hoseVolume1=V1,
valveOpening0=0, valveOpening1=0,
oilBulkModulus=Eoil, actuatorDamping=actuatorDamping, nominalFlow=Qn,
systemPressure=pS, tankPressure=pT,
useChamberVolumeChange=False,
visualization=VHydraulicActuatorSimple(cylinderRadius= 0.45*b, rodRadius= 0.2*b,
baseMountLength = 0.3*b, baseMountRadius = 0.3*b,
rodMountRadius = 0.2*b, pistonLength = 0.1*b, pistonRadius = 0.4*b,
colorCylinder=colCyl, colorPiston=color4lightgrey),
))
#add some simpistic trajectory and valve control
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)*0.15+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)
if oHA2 != -1:
LHact2 = mbs.GetObjectOutput(oHA2, variableType=exu.OutputVariableType.Distance)
x = (max(0.5, min(1.5,(1-cos(2*t*pi*2*0.5))) ) - 0.5)*0.2+LH02
#if t>2: x=LH0
Av0 = (x-LHact2)*2 #valve position control ==> penalize set value LH0
#print('Av0=',Av0)
Av1 = -Av0
mbs.SetObjectParameter(oHA2, "valveOpening0", Av0)
mbs.SetObjectParameter(oHA2, "valveOpening1", Av1)
return True
mbs.SetPreStepUserFunction(PreStepUserFunction)
sForce = mbs.AddSensor(SensorObject(objectNumber=oHA, storeInternal=True, outputVariableType=exu.OutputVariableType.Force))
sDistance = mbs.AddSensor(SensorObject(objectNumber=oHA, storeInternal=True, outputVariableType=exu.OutputVariableType.Distance))
sPressures = mbs.AddSensor(SensorNode(nodeNumber=nODE1, storeInternal=True, outputVariableType=exu.OutputVariableType.Coordinates))
sForce2 = mbs.AddSensor(SensorObject(objectNumber=oHA2, storeInternal=True, outputVariableType=exu.OutputVariableType.Force))
sDistance2 = mbs.AddSensor(SensorObject(objectNumber=oHA2, storeInternal=True, outputVariableType=exu.OutputVariableType.Distance))
sPressures2 = mbs.AddSensor(SensorNode(nodeNumber=nODE1_2, storeInternal=True, outputVariableType=exu.OutputVariableType.Coordinates))
sVelocity = mbs.AddSensor(SensorObject(objectNumber=oHA, storeInternal=True, outputVariableType=exu.OutputVariableType.Velocity))
mbs.Assemble()
#%%+++++++++++++++++++++++++++++++++++++++++++++++++++++
simulationSettings = exu.SimulationSettings() #takes currently set values or default values
tEnd = 30
stepSize = 0.001
simulationSettings.solutionSettings.sensorsWritePeriod = 2*stepSize
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 = 'Hydraulic actuator test'
SC.visualizationSettings.openGL.multiSampling = 4
SC.visualizationSettings.openGL.lineWidth = 2
SC.visualizationSettings.openGL.shadow = 0.5
SC.visualizationSettings.window.renderWindowSize = [1600,1200]
exu.StartRenderer()
mbs.WaitForUserToContinue()
#use %timeit to measure time!
mbs.SolveDynamic(simulationSettings, showHints=False)
if True: #use this to reload the solution and use SolutionViewer
SC.visualizationSettings.general.autoFitScene = False
mbs.SolutionViewer() #can also be entered in IPython ...
exu.StopRenderer() #safely close rendering window!
mbs.PlotSensor(sensorNumbers=[sForce,sForce2], components=[exudyn.plot.componentNorm]*2, labels=['connector force arm1','connector force arm1'], yLabel='force (N)', closeAll=True)
mbs.PlotSensor(sensorNumbers=[sDistance,sDistance2], components=0)
mbs.PlotSensor(sensorNumbers=[sPressures]*2+[sPressures2]*2, components=[0,1,0,1], labels=['p0 arm1', 'p1 arm1', 'p0 arm2', 'p1 arm2'], yLabel='pressure (N/m^2)')
#p01 = mbs.GetSensorStoredData(sPressures)
#p01[:,1] = A[0]*p01[:,1] - A[1]*p01[:,2]
#mbs.PlotSensor(sensorNumbers=p01, components=0, labels=['differential hydraulic force'], yLabel='hydraulic force (N)')