sliderCrankFloatingTest.py

You can view and download this file on Github: sliderCrankFloatingTest.py

  1#+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
  2# This is an EXUDYN example
  3#
  4# Details:  Slider crank model with verification in MATLAB for machine dynamics course
  5#           optionally, the slider crank is mounted on a floating frame, leading to vibrations
  6#           if the system is unbalanced
  7#           This example features 3D graphics of the links
  8#
  9# Author:   Johannes Gerstmayr
 10# Date:     2019-12-07
 11#
 12# 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.
 13#
 14#+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 15
 16import exudyn as exu
 17from exudyn.utilities import *
 18
 19import numpy as np
 20
 21useGraphics = True #without test
 22#+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 23#you can erase the following lines and all exudynTestGlobals related operations if this is not intended to be used as TestModel:
 24try: #only if called from test suite
 25    from modelUnitTests import exudynTestGlobals #for globally storing test results
 26    useGraphics = exudynTestGlobals.useGraphics
 27except:
 28    class ExudynTestGlobals:
 29        pass
 30    exudynTestGlobals = ExudynTestGlobals()
 31#+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 32
 33if useGraphics:
 34    import matplotlib.pyplot as plt
 35    import matplotlib.ticker as ticker
 36
 37SC = exu.SystemContainer()
 38mbs = SC.AddSystem()
 39
 40#++++++++++++++++++++++++++++++++
 41#ground object/node:
 42
 43#background = GraphicsDataRectangle(-0.5, -0.5, 1, 0.5, color=[1,1,1,1.]) #invisible background
 44##background2 = GraphicsDataOrthoCube(-1, -1, -1, 2, -0.8, -0.8, color=[0.3,0.5,0.5,1.])
 45#background2 = GraphicsDataCylinder(pAxis=[0,0.5,0],vAxis=[0,0,1],radius=0.3, color=[0.3,0.5,0.5,1.],
 46#                                   nTiles=16, angleRange=[0,pi*1.2], lastFace=True, cutPlain=True)
 47#
 48#background2 = GraphicsDataSphere(point=[0,0.5,0],radius=0.3,color=[0.3,0.5,0.5,1.],nTiles=8)
 49#
 50#background2 = GraphicsDataRigidLink(p0=[0,0.5,0],p1=[1,0.5,0], axis0=[0,0,1], axis1=[0,0,1],
 51#                                    radius=[0.1,0.1],thickness=0.2, width=[0.2,0.2],color=[0.3,0.5,0.5,1.],nTiles=16)
 52
 53solutionSliderCrankIndex2  = 0
 54
 55rangeTests = range(1,2) #(0,1): fixed frame, (1,2):floating frame
 56if exudynTestGlobals.performTests: #consider shorter integration time
 57    rangeTests = range(0,2)
 58
 59for testCases in rangeTests:
 60
 61    nGround = mbs.AddNode(NodePointGround(referenceCoordinates=[0,0,0])) #ground node for coordinate constraint
 62    mGround = mbs.AddMarker(MarkerNodeCoordinate(nodeNumber = nGround, coordinate=0)) #Ground node ==> no action
 63
 64
 65    #++++++++++++++++++++++++++++++++
 66    #floating body to mount slider-crank mechanism
 67    constrainGroundBody = (testCases == 0) #use this flag to fix ground body
 68
 69    #graphics for floating frame:
 70    #gFloating = GraphicsDataRectangle(-0.25, -0.25, 0.8, 0.25, color=[0.7,0.4,0.4,1.])
 71    gFloating = GraphicsDataOrthoCube(-0.25, -0.25, -0.1, 0.8, 0.25, -0.05, color=[0.3,0.3,0.3,1.])
 72
 73    if constrainGroundBody:
 74        floatingRB = mbs.AddObject(ObjectGround(referencePosition=[0,0,0], visualization=VObjectGround(graphicsData=[gFloating])))
 75        mFloatingN = mbs.AddMarker(MarkerBodyPosition(bodyNumber = floatingRB, localPosition=[0,0,0]))
 76    else:
 77        nFloating = mbs.AddNode(Rigid2D(referenceCoordinates=[0,0,0], initialVelocities=[0,0,0]));
 78        mFloatingN = mbs.AddMarker(MarkerNodePosition(nodeNumber=nFloating))
 79        floatingRB = mbs.AddObject(RigidBody2D(physicsMass=2, physicsInertia=1, nodeNumber=nFloating, visualization=VObjectRigidBody2D(graphicsData=[gFloating])))
 80        mRB0 = mbs.AddMarker(MarkerNodeCoordinate(nodeNumber = nFloating, coordinate=0))
 81        mRB1 = mbs.AddMarker(MarkerNodeCoordinate(nodeNumber = nFloating, coordinate=1))
 82        mRB2 = mbs.AddMarker(MarkerNodeCoordinate(nodeNumber = nFloating, coordinate=2))
 83
 84        #add spring dampers for reference frame:
 85        k=5000 #stiffness of floating body
 86        d=k*0.01
 87        mbs.AddObject(CoordinateSpringDamper(markerNumbers=[mGround,mRB0], stiffness=k, damping=d))
 88        mbs.AddObject(CoordinateSpringDamper(markerNumbers=[mGround,mRB1], stiffness=k, damping=d))
 89        mbs.AddObject(CoordinateSpringDamper(markerNumbers=[mGround,mRB2], stiffness=k, damping=d))
 90
 91
 92
 93    #++++++++++++++++++++++++++++++++
 94    #nodes and bodies
 95    omega=2*pi/60*300 #3000 rpm
 96    L1=0.1
 97    L2=0.3
 98    s1=L1*0.5
 99    s2=L2*0.5
100    m1=0.2
101    m2=0.2
102    m3=0.4
103    M=0.1 #torque (default: 0.1)
104    #lambda=L1/L2
105    J1=(m1/12.)*L1**2 #inertia w.r.t. center of mass
106    J2=(m2/12.)*L2**2 #inertia w.r.t. center of mass
107
108    ty = 0.05    #thickness
109    tz = 0.05    #thickness
110    #graphics1 = GraphicsDataRectangle(-0.5*L1,-0.5*ty,0.5*L1,0.5*ty,color4steelblue)
111    #graphics1 = GraphicsDataOrthoCube(-0.5*L1,-0.5*ty,-tz,0.5*L1,0.5*ty,0,color4steelblue)
112    graphics1 = GraphicsDataRigidLink(p0=[-0.5*L1,0,-0.5*tz],p1=[0.5*L1,0,-0.5*tz],
113                                      axis0=[0,0,1], axis1=[0,0,1],radius=[0.5*ty,0.5*ty],
114                                      thickness=0.8*ty, width=[tz,tz], color=color4steelblue,nTiles=16)
115
116    #graphics2 = GraphicsDataRectangle(-0.5*L2,-0.5*ty,0.5*L2,0.5*ty,color4lightred)
117    #graphics2 = GraphicsDataOrthoCube(-0.5*L2,-0.5*ty,0,0.5*L2,0.5*ty,tz,color4lightred)
118    graphics2 = GraphicsDataRigidLink(p0=[-0.5*L2,0,0.5*tz],p1=[0.5*L2,0,0.5*tz],
119                                      axis0=[0,0,1], axis1=[0,0,1],radius=[0.5*ty,0.5*ty],
120                                      thickness=0.8*ty, width=[tz,tz], color=color4lightred,nTiles=16)
121
122    #crank:
123    nRigid1 = mbs.AddNode(Rigid2D(referenceCoordinates=[s1,0,0],
124                                  initialVelocities=[0,0,0]));
125    oRigid1 = mbs.AddObject(RigidBody2D(physicsMass=m1,
126                                        physicsInertia=J1,
127                                        nodeNumber=nRigid1,
128                                        visualization=VObjectRigidBody2D(graphicsData= [graphics1])))
129
130    #connecting rod:
131    nRigid2 = mbs.AddNode(Rigid2D(referenceCoordinates=[L1+s2,0,0],
132                                  initialVelocities=[0,0,0]));
133    oRigid2 = mbs.AddObject(RigidBody2D(physicsMass=m2,
134                                        physicsInertia=J2,
135                                        nodeNumber=nRigid2,
136                                        visualization=VObjectRigidBody2D(graphicsData= [graphics2])))
137
138
139    #++++++++++++++++++++++++++++++++
140    #slider:
141    c=0.025 #dimension of mass
142    graphics3 = GraphicsDataOrthoCube(-c,-c,-c*2,c,c,0,color4grey)
143
144    #nMass = mbs.AddNode(Point2D(referenceCoordinates=[L1+L2,0]))
145    #oMass = mbs.AddObject(MassPoint2D(physicsMass=m3, nodeNumber=nMass,visualization=VObjectMassPoint2D(graphicsData= [graphics3])))
146    nMass = mbs.AddNode(Rigid2D(referenceCoordinates=[L1+L2,0,0]))
147    oMass = mbs.AddObject(RigidBody2D(physicsMass=m3, physicsInertia=0.001*m3, nodeNumber=nMass,visualization=VObjectRigidBody2D(graphicsData= [graphics3])))
148
149    #++++++++++++++++++++++++++++++++
150    #markers for joints:
151    mR1Left = mbs.AddMarker(MarkerBodyRigid(bodyNumber=oRigid1, localPosition=[-s1,0.,0.])) #support point # MUST be a rigidBodyMarker, because a torque is applied
152    mR1Right = mbs.AddMarker(MarkerBodyPosition(bodyNumber=oRigid1, localPosition=[ s1,0.,0.])) #end point; connection to connecting rod
153
154    mR2Left = mbs.AddMarker(MarkerBodyPosition(bodyNumber=oRigid2, localPosition=[-s2,0.,0.])) #connection to crank
155    mR2Right = mbs.AddMarker(MarkerBodyPosition(bodyNumber=oRigid2, localPosition=[ s2,0.,0.])) #end point; connection to slider
156
157    mMass = mbs.AddMarker(MarkerBodyPosition(bodyNumber=oMass, localPosition=[ 0.,0.,0.]))
158    mG0 = mFloatingN
159
160    #++++++++++++++++++++++++++++++++
161    #joints:
162    mbs.AddObject(RevoluteJoint2D(markerNumbers=[mG0,mR1Left]))
163    mbs.AddObject(RevoluteJoint2D(markerNumbers=[mR1Right,mR2Left]))
164    mbs.AddObject(RevoluteJoint2D(markerNumbers=[mR2Right,mMass]))
165
166    #++++++++++++++++++++++++++++++++
167    #markers for node constraints:
168    #mNodeSlider = mbs.AddMarker(MarkerNodeCoordinate(nodeNumber = nMass, coordinate=1)) #y-coordinate is constrained
169    #coordinate constraints for slider (free motion in x-direction)
170    #mbs.AddObject(CoordinateConstraint(markerNumbers=[mGround,mNodeSlider]))
171
172
173    #prismatic joint:
174    mRigidGround = mbs.AddMarker(MarkerBodyRigid(bodyNumber = floatingRB, localPosition = [L1+L2,0,0]))
175    mRigidSlider = mbs.AddMarker(MarkerBodyRigid(bodyNumber = oMass, localPosition = [0,0,0]))
176
177    mbs.AddObject(PrismaticJoint2D(markerNumbers=[mRigidGround,mRigidSlider], constrainRotation=True))
178
179
180    #user function for load; switch off load after 1 second
181    def userLoad(mbs, t, load):
182        if t <= 2: return load
183        return 0
184
185    #loads and driving forces:
186    mRigid1CoordinateTheta = mbs.AddMarker(MarkerNodeCoordinate(nodeNumber = nRigid1, coordinate=2)) #angle coordinate is constrained
187    mbs.AddLoad(LoadCoordinate(markerNumber=mRigid1CoordinateTheta, load = M, loadUserFunction=userLoad)) #torque at crank
188    #mbs.AddLoad(Torque(markerNumber = mR1Left, loadVector = [0, 0, M])) #apply torque at crank
189
190    #++++++++++++++++++++++++++++++++
191    #assemble, adjust settings and start time integration
192    mbs.Assemble()
193
194    simulationSettings = exu.SimulationSettings() #takes currently set values or default values
195
196    simulationSettings.timeIntegration.numberOfSteps = 50000 #1000 steps for test suite/error
197    simulationSettings.timeIntegration.endTime = 3              #1s for test suite / error
198
199    if exudynTestGlobals.performTests: #consider shorter integration time
200        simulationSettings.timeIntegration.numberOfSteps = 5000 #1000 steps for test suite/error
201        simulationSettings.timeIntegration.endTime = 0.3              #1s for test suite / error
202
203    #simulationSettings.timeIntegration.newton.relativeTolerance = 1e-8 #10000
204    simulationSettings.timeIntegration.verboseMode = 1 #10000
205
206    simulationSettings.solutionSettings.solutionWritePeriod = 2e-4
207    simulationSettings.timeIntegration.newton.useModifiedNewton = True
208    simulationSettings.timeIntegration.newton.relativeTolerance = 1e-8
209    simulationSettings.timeIntegration.newton.absoluteTolerance = 1e-8
210    simulationSettings.timeIntegration.generalizedAlpha.spectralRadius = 0.5
211
212    #++++++++++++++++++++++++++++++++++++++++++
213    #solve index 2 / trapezoidal rule:
214    simulationSettings.timeIntegration.generalizedAlpha.useNewmark = True
215    simulationSettings.timeIntegration.generalizedAlpha.useIndex2Constraints = True
216
217    dSize = 0.02
218    SC.visualizationSettings.nodes.defaultSize = dSize
219    SC.visualizationSettings.markers.defaultSize = dSize
220    SC.visualizationSettings.bodies.defaultSize = [dSize, dSize, dSize]
221    SC.visualizationSettings.connectors.defaultSize = dSize
222
223    #data obtained from SC.GetRenderState(); use np.round(d['modelRotation'],4)
224    SC.visualizationSettings.openGL.initialModelRotation = [[ 0.87758,  0.04786, -0.47703],
225                                                            [ 0.     ,  0.995  ,  0.09983],
226                                                            [ 0.47943, -0.08761,  0.8732]]
227    SC.visualizationSettings.openGL.initialZoom = 0.47
228    SC.visualizationSettings.openGL.initialCenterPoint = [0.192, -0.0039,-0.075]
229    SC.visualizationSettings.openGL.initialMaxSceneSize = 0.4
230    SC.visualizationSettings.general.autoFitScene = False
231    #mbs.WaitForUserToContinue()
232
233    if useGraphics:
234        exu.StartRenderer()
235
236    mbs.SolveDynamic(simulationSettings)
237
238    if useGraphics:
239        #+++++++++++++++++++++++++++++++++++++
240        #animate solution
241#        mbs.WaitForUserToContinue
242#        fileName = 'coordinatesSolution.txt'
243#        solution = LoadSolutionFile('coordinatesSolution.txt')
244#        AnimateSolution(mbs, solution, 10, 0.025, True)
245        #+++++++++++++++++++++++++++++++++++++
246
247        SC.WaitForRenderEngineStopFlag()
248        exu.StopRenderer() #safely close rendering window!
249
250    u = mbs.GetNodeOutput(nMass, exu.OutputVariableType.Position) #tip node
251    exu.Print('sol =', abs(u[0]))
252    solutionSliderCrankIndex2 += abs(u[0]) #x-position of slider
253
254
255exu.Print('solutionSliderCrankIndex2=',solutionSliderCrankIndex2)
256exudynTestGlobals.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
257exudynTestGlobals.testResult = solutionSliderCrankIndex2
258
259
260#plotResults = True#constrainGroundBody #comparison only works in case of fixed ground
261plotResults = useGraphics#constrainGroundBody #comparison only works in case of fixed ground
262if plotResults:
263    dataIndex2 = np.loadtxt('coordinatesSolution.txt', comments='#', delimiter=',')
264    #dataMatlab = np.loadtxt('slidercrankRefSolM0.1_tol1e-4.txt', comments='#', delimiter=',') #this is quite inaccurate
265    dataMatlab2 = np.loadtxt('slidercrankRefSolM0.1_tol1e-6.txt', comments='#', delimiter=',')
266
267    vODE2=mbs.systemData.GetODE2Coordinates()
268    nODE2=len(vODE2) #number of ODE2 coordinates
269
270    nAngle = mbs.systemData.GetObjectLTGODE2(oRigid1)[2] #get coordinate index of angle
271    plt.plot(dataIndex2[:,0], dataIndex2[:,1+nAngle], 'b-') #plot angle of crank;
272    plt.plot(dataIndex2[:,0], dataIndex2[:,1+nODE2+nAngle], 'r-') #plot angular velocity of crank
273    #plt.plot(dataMatlab[:,0], dataMatlab[:,2], 'g-') #plot angular velocity of crank from MATLAB
274    plt.plot(dataMatlab2[:,0], dataMatlab2[:,2], 'k-') #plot angular velocity of crank from MATLAB
275
276    #plt.plot(dataIndex3[:,0], dataIndex3[:,1+globalIndex], 'b-') #plot x-coordinate of slider
277
278    ax=plt.gca() # get current axes
279    ax.grid(True, 'major', 'both')
280    ax.xaxis.set_major_locator(ticker.MaxNLocator(10)) #use maximum of 8 ticks on y-axis
281    ax.yaxis.set_major_locator(ticker.MaxNLocator(10)) #use maximum of 8 ticks on y-axis
282    plt.tight_layout()
283    plt.show()