You can view and download this file on Github: sliderCrank3Dtest.py
#+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
# This is an EXUDYN example
#
# Details: Slidercrank 3D (iftomm benchmark problem)
# Ref.: https://www.iftomm-multibody.org/benchmark/problem/... spatial rigid slider-crank mechanism
#
# Author: Johannes Gerstmayr
# Date: 2020-02-16
#
# 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 *
from exudyn.lieGroupIntegration import *
import numpy as np
from numpy import linalg as LA
useGraphics = True #without test
#+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
#you can erase the following lines and all exudynTestGlobals related operations if this is not intended to be used as TestModel:
try: #only if called from test suite
from modelUnitTests import exudynTestGlobals #for globally storing test results
useGraphics = exudynTestGlobals.useGraphics
except:
class ExudynTestGlobals:
pass
exudynTestGlobals = ExudynTestGlobals()
#+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
SC = exu.SystemContainer()
mbs = SC.AddSystem()
###############################################################################
# given parameters:
g = [0,0,-9.81]
lAB = 0.08 #crank length
lBC = 0.3 #conrod
theta0 = 0 #initial crank angle
omega0 = [6,0,0] #initial crank angular velocity
#initial values for bodies 1 and 2 computed from initial value problem with constant angular velocity
v1Init = [1.2e-01, -2.400e-01, 0]
#omega1Init = [7.29730172e-01, -1.39497250e+00, 4.79376439e-01]
omega1Init = [1.6941176470530785, -0.8470588235366621, 0.705882352947701] #appr. 10 digits accuracy
#initial values: 0.12,-0.24,0,-0.9343942376,-2.73093948,-0.6316790456
v2Init = [0.24,0,0]
omega2Init = [0,0,0]
zA = 0.12 #z-position of crank CoR
yA = 0.1 #y-position of crank CoR
#initial x-position of slider:
xD = np.sqrt(lBC**2 - yA**2 - (zA + lAB)**2);
exu.Print('slider initial position =', xD)
#initial positions of points A-C
pA = [0, yA, zA]
pB = VAdd([0, yA, zA], [0,0,lAB])
pC = [xD, 0, 0]
vCB = np.array(pC) - np.array(pB)
exu.Print('vCB len=', LA.norm(vCB))
#xAxis1 = (1/lBC)*vCB #local x-axis of conrod
[xAxis1,zAxis1, vDummy] = GramSchmidt(vCB, pA) # compute projected pA to xAxis1 ==> gives z axis
yAxis1 = -np.cross(xAxis1, zAxis1)
rotMatBC=np.array([xAxis1, yAxis1, zAxis1]).transpose()
#mass and inertia
mAB = 0.12
mBC = 0.5
mSlider = 2
iAB = np.diag([0.0001,0.00001,0.0001]) #crank inertia
#iBC = np.diag([0.004,0.0004,0.004]) #conrod inertia; iftomm: x=axis of conrod; McPhee: y=axis of conrod
iSlider = np.diag([0.0001,0.0001,0.0001]) #slider inertia; McPhee: no inertia of slider / does not rotate
#Maple / McPhee ?
#<Text-field prompt="> " style="Maple Input" layout="Normal">m1:= 0.12; m2:= 0.5; m3:= 2; L1:= 0.08; L2:= 0.3; Ay:= 0.1; Az:= 0.12;</Text-field>
#<Text-field prompt="> " style="Maple Input" layout="Normal">Ixx1:= 0.0001; Ixx2:= 0.0004; Iyy2:= 0.004; Izz2:= 0.004; G:= 9.81;</Text-field>
#we choose x-axis as conrod axis!
iBC = np.diag([0.0004,0.004,0.004]) #conrod inertia; iftomm: x=axis of conrod; McPhee: y=axis of conrod
inertiaAB = RigidBodyInertia(mass=mAB, inertiaTensor=iAB)
inertiaBC = RigidBodyInertia(mass=mBC, inertiaTensor=iBC)
inertiaSlider = RigidBodyInertia(mass=mSlider, inertiaTensor=iSlider)
fixedVelocity = False #constrain angular velocity of crank
nodeType=exu.NodeType.RotationEulerParameters
#nodeType=exu.NodeType.RotationRxyz
################ Body0: CRANK
#graphicsAB = GraphicsDataOrthoCube(-d/2,-d/2,0, d/2,d/2, lAB, [0.1,0.1,0.8,1])
graphicsAB = GraphicsDataRigidLink(p0=[0,0,0],p1=[0,0,lAB], axis0=[1,0,0],
radius=[0.01,0.01], thickness = 0.01,
width = [0.02,0.02], color=color4steelblue)
[n0,b0]=AddRigidBody(mainSys = mbs, inertia=inertiaAB, nodeType=str(nodeType),
position=pA, angularVelocity=omega0, gravity=g,
graphicsDataList=[graphicsAB])
################ Body1: CONROD
graphicsBC = GraphicsDataRigidLink(p0=[-0.5*lBC,0,0],p1=[0.5*lBC,0,0], axis1=[0,0,0],
radius=[0.01,0.01], thickness = 0.01,
width = [0.02,0.02], color=color4lightred)
pBC = ScalarMult(0.5,VAdd(pB,pC))
[n1,b1]=AddRigidBody(mainSys = mbs, inertia=inertiaBC, nodeType=str(nodeType),
position=pBC, velocity=v1Init, angularVelocity=omega1Init,
rotationMatrix=rotMatBC, gravity=g, graphicsDataList=[graphicsBC])
################ Body2: SLIDER
d = 0.03
graphicsSlider = GraphicsDataOrthoCube(-d/2,-d/2,-d/2, d/2,d/2, d/2, [0.5,0.5,0.5,0.5])
[n2,b2]=AddRigidBody(mainSys = mbs, inertia=inertiaSlider, nodeType=str(nodeType),
position=pC, velocity=v2Init, angularVelocity=[0,0,0],
graphicsDataList=[graphicsSlider])
oGround = mbs.AddObject(ObjectGround())
markerGroundA = mbs.AddMarker(MarkerBodyRigid(name='markerGroundA', bodyNumber=oGround, localPosition=pA))
markerGroundD = mbs.AddMarker(MarkerBodyRigid(name='markerGroundD', bodyNumber=oGround, localPosition=[0,0,0]))
markerCrankA = mbs.AddMarker(MarkerBodyRigid(bodyNumber=b0))
markerCrankB = mbs.AddMarker(MarkerBodyRigid(bodyNumber=b0, localPosition=[0,0,lAB]))
markerConrodB = mbs.AddMarker(MarkerBodyRigid(bodyNumber=b1, localPosition=[-0.5*lBC,0,0]))
markerConrodC = mbs.AddMarker(MarkerBodyRigid(bodyNumber=b1, localPosition=[ 0.5*lBC,0,0]))
markerSlider = mbs.AddMarker(MarkerBodyRigid(bodyNumber=b2))
mbs.AddObject(GenericJoint(markerNumbers=[markerGroundA, markerCrankA], constrainedAxes=[1,1,1,0,1,1],
visualization=VObjectJointGeneric(axesRadius=0.005, axesLength=0.02)))
mbs.AddObject(GenericJoint(markerNumbers=[markerGroundD, markerSlider], constrainedAxes=[0,1,1,1,1,1],
visualization=VObjectJointGeneric(axesRadius=0.005, axesLength=0.02)))
mbs.AddObject(GenericJoint(markerNumbers=[markerCrankB, markerConrodB], constrainedAxes=[1,1,1,0,0,0],
visualization=VObjectJointGeneric(axesRadius=0.005, axesLength=0.02)))
#classical cardan, x=locked
#mbs.AddObject(GenericJoint(markerNumbers=[markerConrodC, markerSlider], constrainedAxes=[1,1,1,1,0,0],
# visualization=VObjectJointGeneric(axesRadius=0.005, axesLength=0.02)))
mbs.AddObject(GenericJoint(markerNumbers=[markerSlider, markerConrodC], constrainedAxes=[1,1,1,0,0,1], # xAxisMarker0=free, yAxisMarker1=free
visualization=VObjectJointGeneric(axesRadius=0.005, axesLength=0.02)))
if useGraphics:
sCrankAngle=mbs.AddSensor(SensorNode(nodeNumber = n0, storeInternal=True,#fileName='solution/crankAngle.txt',
outputVariableType=exu.OutputVariableType.Rotation))
sCrankAngVel=mbs.AddSensor(SensorNode(nodeNumber = n0, storeInternal=True,#fileName='solution/crankAngularVelocity.txt',
outputVariableType=exu.OutputVariableType.AngularVelocity))
sSliderPos=mbs.AddSensor(SensorNode(nodeNumber = n2, storeInternal=True,#fileName='solution/sliderPosition.txt',
outputVariableType=exu.OutputVariableType.Position))
sSliderVel=mbs.AddSensor(SensorNode(nodeNumber = n2, storeInternal=True,#fileName='solution/sliderVelocity.txt',
outputVariableType=exu.OutputVariableType.Velocity))
if fixedVelocity:
groundNode = mbs.AddNode(NodePointGround(referenceCoordinates=[0,0,0])) #add a coordinate fixed to ground
markerGroundCoordinate = mbs.AddMarker(MarkerNodeCoordinate(nodeNumber=groundNode, coordinate=0))
markerRotX = mbs.AddMarker(MarkerNodeCoordinate(nodeNumber=n0, coordinate=3)) #Euler angle x
mbs.AddObject(CoordinateConstraint(markerNumbers=[markerGroundCoordinate, markerRotX],
offset = 6, velocityLevel=True))
#+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
mbs.Assemble()
#mbs.systemData.Info()
simulationSettings = exu.SimulationSettings() #takes currently set values or default values
fact = 1000 #1000 for testing
outputFact = 1000
simulationSettings.timeIntegration.numberOfSteps = 1*fact
simulationSettings.timeIntegration.endTime = 0.2 #0.2 for testing
simulationSettings.solutionSettings.solutionWritePeriod = simulationSettings.timeIntegration.endTime/outputFact
simulationSettings.solutionSettings.sensorsWritePeriod = simulationSettings.timeIntegration.endTime/outputFact
simulationSettings.solutionSettings.writeSolutionToFile = useGraphics
simulationSettings.timeIntegration.verboseMode = 1
simulationSettings.timeIntegration.generalizedAlpha.useIndex2Constraints = True
simulationSettings.timeIntegration.generalizedAlpha.useNewmark = True
simulationSettings.timeIntegration.generalizedAlpha.spectralRadius = 0.5 #0.6 works well
simulationSettings.timeIntegration.generalizedAlpha.computeInitialAccelerations=True
SC.visualizationSettings.connectors.showJointAxes = True
SC.visualizationSettings.connectors.jointAxesLength = 0.02
SC.visualizationSettings.connectors.jointAxesRadius = 0.002
if useGraphics:
# simulationSettings.timeIntegration.numberOfSteps = 4*5000
# simulationSettings.timeIntegration.endTime = 5 #0.2 for testing
exu.StartRenderer()
mbs.WaitForUserToContinue()
mbs.SolveDynamic(simulationSettings)
#compute initial velocities:
#if fixedVelocity:
# v0 = mbs.GetNodeOutput(n0,exu.OutputVariableType.Coordinates_t)
# exu.Print('v0=',v0)
#
# v1 = mbs.GetNodeOutput(n1,exu.OutputVariableType.Coordinates_t)
# exu.Print('v1=',v1[0:3])
# omega1 = mbs.GetNodeOutput(n1,exu.OutputVariableType.AngularVelocity)
# exu.Print('omega1=',omega1[0],omega1[1],omega1[2])
#
# v2 = mbs.GetNodeOutput(n2,exu.OutputVariableType.Coordinates_t)
# exu.Print('v2=',v2[0:3])
#+++++++++++++++++++++++++++++++++++++++++++++
#compute TestModel error for EulerParameters and index2 solver
sol = mbs.systemData.GetODE2Coordinates();
solref = mbs.systemData.GetODE2Coordinates(configuration=exu.ConfigurationType.Reference);
#exu.Print('sol=',sol)
u = 0
for i in range(14): #take coordinates of first two bodies
u += abs(sol[i]+solref[i])
exu.Print('solution of 3D slidercrank iftomm benchmark=',u)
exudynTestGlobals.testError = u - (3.36427617809219) #2020-04-22(corrected GenericJoint): 3.36427617809219;2020-02-19: 3.3642838177004832
exudynTestGlobals.testResult = u
if useGraphics:
#SC.WaitForRenderEngineStopFlag()
exu.StopRenderer() #safely close rendering window!
if useGraphics:
import matplotlib.pyplot as plt
import matplotlib.ticker as ticker
plt.close("all")
[fig1, ax1] = plt.subplots()
[fig2, ax2] = plt.subplots()
# data1 = np.loadtxt('solution/crankAngularVelocity.txt', comments='#', delimiter=',')
data1 = mbs.GetSensorStoredData(sCrankAngVel)
ax1.plot(data1[:,0], data1[:,1], 'r-', label='crank angular velocity')
# data1 = np.loadtxt('solution/crankAngle.txt', comments='#', delimiter=',')
data1 = mbs.GetSensorStoredData(sCrankAngle)
ax1.plot(data1[:,0], data1[:,1], 'b-', label='crank angle')
if False: #only if available ...
data1 = np.loadtxt('../../../docs/verification/Slidercrank3DiftommBenchmark/Spatial_rigid_slider-crank_mechanism_Masarati.txt', comments='#', delimiter=',')
ax1.plot(data1[:,0], data1[:,2], 'r:', label='Ref Masarati: crank angle')
data1 = np.loadtxt('../../../docs/verification/Slidercrank3DiftommBenchmark/Spatial_rigid_slider-crank_mechanism_Masoudi.txt', comments='#', delimiter='\t')
ax1.plot(data1[:,0], data1[:,2], 'k:', label='Ref Masoudi: crank angle')
data1 = np.loadtxt('../../../docs/verification/Slidercrank3DiftommBenchmark/Spatial_rigid_slider-crank_mechanism_Chaojie.txt', comments='#', delimiter=',')
ax1.plot(data1[:,0], data1[:,2], 'g:', label='Ref Chaojie: crank angle')
# data2 = np.loadtxt('solution/sliderPosition.txt', comments='#', delimiter=',')
data2 = mbs.GetSensorStoredData(sSliderPos)
ax2.plot(data2[:,0], data2[:,1], 'b-', label='slider position')
#data2 = np.loadtxt('solution/sliderPosition_1e-4.txt', comments='#', delimiter=',')
#ax2.plot(data2[:,0], data2[:,1], 'r-', label='slider position, dt=1e-4')
# data2 = np.loadtxt('solution/sliderVelocity.txt', comments='#', delimiter=',')
# ax2.plot(data2[:,0], data2[:,1], 'r-', label='slider velocity')
if False: #only if available ...
data2 = np.loadtxt('../../../docs/verification/Slidercrank3DiftommBenchmark/Spatial_rigid_slider-crank_mechanism_Masarati.txt', comments='#', delimiter=',')
ax2.plot(data2[:,0], data2[:,1], 'r:', label='Ref Masarati: slider position')
data2 = np.loadtxt('../../../docs/verification/Slidercrank3DiftommBenchmark/Spatial_rigid_slider-crank_mechanism_Masoudi.txt', comments='#', delimiter='\t')
ax2.plot(data2[:,0], data2[:,1], 'k:', label='Ref Masoudi: slider position')
data2 = np.loadtxt('../../../docs/verification/Slidercrank3DiftommBenchmark/Spatial_rigid_slider-crank_mechanism_Chaojie.txt', comments='#', delimiter=',')
ax2.plot(data2[:,0], data2[:,1], 'g:', label='Ref Chaojie: slider position')
axList=[ax1,ax2]
figList=[fig1, fig2]
for ax in axList:
ax.grid(True, 'major', 'both')
ax.xaxis.set_major_locator(ticker.MaxNLocator(10))
ax.yaxis.set_major_locator(ticker.MaxNLocator(10))
ax.set_xlabel("time (s)")
ax.legend()
ax1.set_ylabel("crank angle / angular velocity")
ax2.set_ylabel("slider position (m)")
for f in figList:
f.tight_layout()
f.show() #bring to front