You can view and download this file on Github: sliderCrankFloatingTest.py
#+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
# This is an EXUDYN example
#
# Details: Slider crank model with verification in MATLAB for machine dynamics course
# optionally, the slider crank is mounted on a floating frame, leading to vibrations
# if the system is unbalanced
# This example features 3D graphics of the links
#
# Author: Johannes Gerstmayr
# Date: 2019-12-07
#
# 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 *
import numpy as np
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()
#+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
if useGraphics:
import matplotlib.pyplot as plt
import matplotlib.ticker as ticker
SC = exu.SystemContainer()
mbs = SC.AddSystem()
#++++++++++++++++++++++++++++++++
#ground object/node:
#background = GraphicsDataRectangle(-0.5, -0.5, 1, 0.5, color=[1,1,1,1.]) #invisible background
##background2 = GraphicsDataOrthoCube(-1, -1, -1, 2, -0.8, -0.8, color=[0.3,0.5,0.5,1.])
#background2 = GraphicsDataCylinder(pAxis=[0,0.5,0],vAxis=[0,0,1],radius=0.3, color=[0.3,0.5,0.5,1.],
# nTiles=16, angleRange=[0,pi*1.2], lastFace=True, cutPlain=True)
#
#background2 = GraphicsDataSphere(point=[0,0.5,0],radius=0.3,color=[0.3,0.5,0.5,1.],nTiles=8)
#
#background2 = GraphicsDataRigidLink(p0=[0,0.5,0],p1=[1,0.5,0], axis0=[0,0,1], axis1=[0,0,1],
# radius=[0.1,0.1],thickness=0.2, width=[0.2,0.2],color=[0.3,0.5,0.5,1.],nTiles=16)
solutionSliderCrankIndex2 = 0
rangeTests = range(1,2) #(0,1): fixed frame, (1,2):floating frame
if exudynTestGlobals.performTests: #consider shorter integration time
rangeTests = range(0,2)
for testCases in rangeTests:
nGround = mbs.AddNode(NodePointGround(referenceCoordinates=[0,0,0])) #ground node for coordinate constraint
mGround = mbs.AddMarker(MarkerNodeCoordinate(nodeNumber = nGround, coordinate=0)) #Ground node ==> no action
#++++++++++++++++++++++++++++++++
#floating body to mount slider-crank mechanism
constrainGroundBody = (testCases == 0) #use this flag to fix ground body
#graphics for floating frame:
#gFloating = GraphicsDataRectangle(-0.25, -0.25, 0.8, 0.25, color=[0.7,0.4,0.4,1.])
gFloating = GraphicsDataOrthoCube(-0.25, -0.25, -0.1, 0.8, 0.25, -0.05, color=[0.3,0.3,0.3,1.])
if constrainGroundBody:
floatingRB = mbs.AddObject(ObjectGround(referencePosition=[0,0,0], visualization=VObjectGround(graphicsData=[gFloating])))
mFloatingN = mbs.AddMarker(MarkerBodyPosition(bodyNumber = floatingRB, localPosition=[0,0,0]))
else:
nFloating = mbs.AddNode(Rigid2D(referenceCoordinates=[0,0,0], initialVelocities=[0,0,0]));
mFloatingN = mbs.AddMarker(MarkerNodePosition(nodeNumber=nFloating))
floatingRB = mbs.AddObject(RigidBody2D(physicsMass=2, physicsInertia=1, nodeNumber=nFloating, visualization=VObjectRigidBody2D(graphicsData=[gFloating])))
mRB0 = mbs.AddMarker(MarkerNodeCoordinate(nodeNumber = nFloating, coordinate=0))
mRB1 = mbs.AddMarker(MarkerNodeCoordinate(nodeNumber = nFloating, coordinate=1))
mRB2 = mbs.AddMarker(MarkerNodeCoordinate(nodeNumber = nFloating, coordinate=2))
#add spring dampers for reference frame:
k=5000 #stiffness of floating body
d=k*0.01
mbs.AddObject(CoordinateSpringDamper(markerNumbers=[mGround,mRB0], stiffness=k, damping=d))
mbs.AddObject(CoordinateSpringDamper(markerNumbers=[mGround,mRB1], stiffness=k, damping=d))
mbs.AddObject(CoordinateSpringDamper(markerNumbers=[mGround,mRB2], stiffness=k, damping=d))
#++++++++++++++++++++++++++++++++
#nodes and bodies
omega=2*pi/60*300 #3000 rpm
L1=0.1
L2=0.3
s1=L1*0.5
s2=L2*0.5
m1=0.2
m2=0.2
m3=0.4
M=0.1 #torque (default: 0.1)
#lambda=L1/L2
J1=(m1/12.)*L1**2 #inertia w.r.t. center of mass
J2=(m2/12.)*L2**2 #inertia w.r.t. center of mass
ty = 0.05 #thickness
tz = 0.05 #thickness
#graphics1 = GraphicsDataRectangle(-0.5*L1,-0.5*ty,0.5*L1,0.5*ty,color4steelblue)
#graphics1 = GraphicsDataOrthoCube(-0.5*L1,-0.5*ty,-tz,0.5*L1,0.5*ty,0,color4steelblue)
graphics1 = GraphicsDataRigidLink(p0=[-0.5*L1,0,-0.5*tz],p1=[0.5*L1,0,-0.5*tz],
axis0=[0,0,1], axis1=[0,0,1],radius=[0.5*ty,0.5*ty],
thickness=0.8*ty, width=[tz,tz], color=color4steelblue,nTiles=16)
#graphics2 = GraphicsDataRectangle(-0.5*L2,-0.5*ty,0.5*L2,0.5*ty,color4lightred)
#graphics2 = GraphicsDataOrthoCube(-0.5*L2,-0.5*ty,0,0.5*L2,0.5*ty,tz,color4lightred)
graphics2 = GraphicsDataRigidLink(p0=[-0.5*L2,0,0.5*tz],p1=[0.5*L2,0,0.5*tz],
axis0=[0,0,1], axis1=[0,0,1],radius=[0.5*ty,0.5*ty],
thickness=0.8*ty, width=[tz,tz], color=color4lightred,nTiles=16)
#crank:
nRigid1 = mbs.AddNode(Rigid2D(referenceCoordinates=[s1,0,0],
initialVelocities=[0,0,0]));
oRigid1 = mbs.AddObject(RigidBody2D(physicsMass=m1,
physicsInertia=J1,
nodeNumber=nRigid1,
visualization=VObjectRigidBody2D(graphicsData= [graphics1])))
#connecting rod:
nRigid2 = mbs.AddNode(Rigid2D(referenceCoordinates=[L1+s2,0,0],
initialVelocities=[0,0,0]));
oRigid2 = mbs.AddObject(RigidBody2D(physicsMass=m2,
physicsInertia=J2,
nodeNumber=nRigid2,
visualization=VObjectRigidBody2D(graphicsData= [graphics2])))
#++++++++++++++++++++++++++++++++
#slider:
c=0.025 #dimension of mass
graphics3 = GraphicsDataOrthoCube(-c,-c,-c*2,c,c,0,color4grey)
#nMass = mbs.AddNode(Point2D(referenceCoordinates=[L1+L2,0]))
#oMass = mbs.AddObject(MassPoint2D(physicsMass=m3, nodeNumber=nMass,visualization=VObjectMassPoint2D(graphicsData= [graphics3])))
nMass = mbs.AddNode(Rigid2D(referenceCoordinates=[L1+L2,0,0]))
oMass = mbs.AddObject(RigidBody2D(physicsMass=m3, physicsInertia=0.001*m3, nodeNumber=nMass,visualization=VObjectRigidBody2D(graphicsData= [graphics3])))
#++++++++++++++++++++++++++++++++
#markers for joints:
mR1Left = mbs.AddMarker(MarkerBodyRigid(bodyNumber=oRigid1, localPosition=[-s1,0.,0.])) #support point # MUST be a rigidBodyMarker, because a torque is applied
mR1Right = mbs.AddMarker(MarkerBodyPosition(bodyNumber=oRigid1, localPosition=[ s1,0.,0.])) #end point; connection to connecting rod
mR2Left = mbs.AddMarker(MarkerBodyPosition(bodyNumber=oRigid2, localPosition=[-s2,0.,0.])) #connection to crank
mR2Right = mbs.AddMarker(MarkerBodyPosition(bodyNumber=oRigid2, localPosition=[ s2,0.,0.])) #end point; connection to slider
mMass = mbs.AddMarker(MarkerBodyPosition(bodyNumber=oMass, localPosition=[ 0.,0.,0.]))
mG0 = mFloatingN
#++++++++++++++++++++++++++++++++
#joints:
mbs.AddObject(RevoluteJoint2D(markerNumbers=[mG0,mR1Left]))
mbs.AddObject(RevoluteJoint2D(markerNumbers=[mR1Right,mR2Left]))
mbs.AddObject(RevoluteJoint2D(markerNumbers=[mR2Right,mMass]))
#++++++++++++++++++++++++++++++++
#markers for node constraints:
#mNodeSlider = mbs.AddMarker(MarkerNodeCoordinate(nodeNumber = nMass, coordinate=1)) #y-coordinate is constrained
#coordinate constraints for slider (free motion in x-direction)
#mbs.AddObject(CoordinateConstraint(markerNumbers=[mGround,mNodeSlider]))
#prismatic joint:
mRigidGround = mbs.AddMarker(MarkerBodyRigid(bodyNumber = floatingRB, localPosition = [L1+L2,0,0]))
mRigidSlider = mbs.AddMarker(MarkerBodyRigid(bodyNumber = oMass, localPosition = [0,0,0]))
mbs.AddObject(PrismaticJoint2D(markerNumbers=[mRigidGround,mRigidSlider], constrainRotation=True))
#user function for load; switch off load after 1 second
def userLoad(mbs, t, load):
if t <= 2: return load
return 0
#loads and driving forces:
mRigid1CoordinateTheta = mbs.AddMarker(MarkerNodeCoordinate(nodeNumber = nRigid1, coordinate=2)) #angle coordinate is constrained
mbs.AddLoad(LoadCoordinate(markerNumber=mRigid1CoordinateTheta, load = M, loadUserFunction=userLoad)) #torque at crank
#mbs.AddLoad(Torque(markerNumber = mR1Left, loadVector = [0, 0, M])) #apply torque at crank
#++++++++++++++++++++++++++++++++
#assemble, adjust settings and start time integration
mbs.Assemble()
simulationSettings = exu.SimulationSettings() #takes currently set values or default values
simulationSettings.timeIntegration.numberOfSteps = 50000 #1000 steps for test suite/error
simulationSettings.timeIntegration.endTime = 3 #1s for test suite / error
if exudynTestGlobals.performTests: #consider shorter integration time
simulationSettings.timeIntegration.numberOfSteps = 5000 #1000 steps for test suite/error
simulationSettings.timeIntegration.endTime = 0.3 #1s for test suite / error
#simulationSettings.timeIntegration.newton.relativeTolerance = 1e-8 #10000
simulationSettings.timeIntegration.verboseMode = 1 #10000
simulationSettings.solutionSettings.solutionWritePeriod = 2e-4
simulationSettings.timeIntegration.newton.useModifiedNewton = True
simulationSettings.timeIntegration.newton.relativeTolerance = 1e-8
simulationSettings.timeIntegration.newton.absoluteTolerance = 1e-8
simulationSettings.timeIntegration.generalizedAlpha.spectralRadius = 0.5
#++++++++++++++++++++++++++++++++++++++++++
#solve index 2 / trapezoidal rule:
simulationSettings.timeIntegration.generalizedAlpha.useNewmark = True
simulationSettings.timeIntegration.generalizedAlpha.useIndex2Constraints = True
dSize = 0.02
SC.visualizationSettings.nodes.defaultSize = dSize
SC.visualizationSettings.markers.defaultSize = dSize
SC.visualizationSettings.bodies.defaultSize = [dSize, dSize, dSize]
SC.visualizationSettings.connectors.defaultSize = dSize
#data obtained from SC.GetRenderState(); use np.round(d['modelRotation'],4)
SC.visualizationSettings.openGL.initialModelRotation = [[ 0.87758, 0.04786, -0.47703],
[ 0. , 0.995 , 0.09983],
[ 0.47943, -0.08761, 0.8732]]
SC.visualizationSettings.openGL.initialZoom = 0.47
SC.visualizationSettings.openGL.initialCenterPoint = [0.192, -0.0039,-0.075]
SC.visualizationSettings.openGL.initialMaxSceneSize = 0.4
SC.visualizationSettings.general.autoFitScene = False
#mbs.WaitForUserToContinue()
if useGraphics:
exu.StartRenderer()
mbs.SolveDynamic(simulationSettings)
if useGraphics:
#+++++++++++++++++++++++++++++++++++++
#animate solution
# mbs.WaitForUserToContinue
# fileName = 'coordinatesSolution.txt'
# solution = LoadSolutionFile('coordinatesSolution.txt')
# AnimateSolution(mbs, solution, 10, 0.025, True)
#+++++++++++++++++++++++++++++++++++++
SC.WaitForRenderEngineStopFlag()
exu.StopRenderer() #safely close rendering window!
u = mbs.GetNodeOutput(nMass, exu.OutputVariableType.Position) #tip node
exu.Print('sol =', abs(u[0]))
solutionSliderCrankIndex2 += abs(u[0]) #x-position of slider
exu.Print('solutionSliderCrankIndex2=',solutionSliderCrankIndex2)
exudynTestGlobals.testError = solutionSliderCrankIndex2 - 0.5916491633788333 #2020-01-15: 0.5916491633788333(corrected PrismaticJoint); 2019-12-26: 0.5916499441339551; 2019-12-15: 0.591689710999802 (absTol: 1e-8 now; 1e-2 before); before 2019-12-15: 0.5896009710727431
exudynTestGlobals.testResult = solutionSliderCrankIndex2
#plotResults = True#constrainGroundBody #comparison only works in case of fixed ground
plotResults = useGraphics#constrainGroundBody #comparison only works in case of fixed ground
if plotResults:
dataIndex2 = np.loadtxt('coordinatesSolution.txt', comments='#', delimiter=',')
#dataMatlab = np.loadtxt('slidercrankRefSolM0.1_tol1e-4.txt', comments='#', delimiter=',') #this is quite inaccurate
dataMatlab2 = np.loadtxt('slidercrankRefSolM0.1_tol1e-6.txt', comments='#', delimiter=',')
vODE2=mbs.systemData.GetODE2Coordinates()
nODE2=len(vODE2) #number of ODE2 coordinates
nAngle = mbs.systemData.GetObjectLTGODE2(oRigid1)[2] #get coordinate index of angle
plt.plot(dataIndex2[:,0], dataIndex2[:,1+nAngle], 'b-') #plot angle of crank;
plt.plot(dataIndex2[:,0], dataIndex2[:,1+nODE2+nAngle], 'r-') #plot angular velocity of crank
#plt.plot(dataMatlab[:,0], dataMatlab[:,2], 'g-') #plot angular velocity of crank from MATLAB
plt.plot(dataMatlab2[:,0], dataMatlab2[:,2], 'k-') #plot angular velocity of crank from MATLAB
#plt.plot(dataIndex3[:,0], dataIndex3[:,1+globalIndex], 'b-') #plot x-coordinate of slider
ax=plt.gca() # get current axes
ax.grid(True, 'major', 'both')
ax.xaxis.set_major_locator(ticker.MaxNLocator(10)) #use maximum of 8 ticks on y-axis
ax.yaxis.set_major_locator(ticker.MaxNLocator(10)) #use maximum of 8 ticks on y-axis
plt.tight_layout()
plt.show()