stiffFlyballGovernor2.py
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1#+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
2# This is an EXUDYN example
3#
4# Details: Stiff flyball governor with rigid and compliant joints (IFToMM benchmark problem);
5# Ref.: https://www.iftomm-multibody.org/benchmark/problem/Stiff_flyball_governor/
6# This version uses the newer C++ implemented Lie group solvers
7#
8# Model: Flyball governor as redundant multibody system
9#
10# Author: Johannes Gerstmayr, Stefan Holzinger
11# Date: 2020-02-13
12#
13# 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.
14#
15# *clean example*
16#+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
17
18## import libaries
19import exudyn as exu
20from exudyn.itemInterface import *
21from exudyn.utilities import *
22from exudyn.graphicsDataUtilities import *
23
24import numpy as np
25from numpy import linalg as LA
26
27## set up MainSystem mbs
28SC = exu.SystemContainer()
29mbs = SC.AddSystem()
30
31##
32useCompliantCase = False
33useLieGroup = useCompliantCase
34
35
36## create background graphics and ground object
37color = [0.1,0.1,0.8,1]
38r = 0.2 #radius
39L = 1 #length
40
41background0 = GraphicsDataRectangle(-L,-L,L,L,color)
42oGround=mbs.AddObject(ObjectGround(referencePosition= [0,0,0], visualization=VObjectGround(graphicsData= [background0])))
43
44# ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
45## set up body dimensions according to reference in m
46
47# shaft
48lengthShaft = 1 #z
49widthShaft = 0.01 #=height
50
51# rod
52lengthRod = 1
53widthRod = 0.01 #=height
54
55# slider
56dimSlider = 0.1 #x=y=z
57sSlider = 0.5
58
59# scalar distance between point A and B
60xAB = 0.1
61beta0 = np.deg2rad(30)
62initAngleRod = np.deg2rad(60)
63
64# initial angular velocity of shaft and slider
65omega0 = [0., 0., 0.16*2*np.pi]
66
67# ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
68## body masses according to reference in kg
69
70density = 3000
71
72mShaft = 0.3
73mRod = 0.3
74mSlider = 3
75mMassPoint = 5
76mRodMassPoint = mRod + mMassPoint
77
78
79# ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
80# gravity
81g = [0,0,-9.81]
82
83## setup inertia for rod along x-direction
84iRod = InertiaCuboid(density=density, sideLengths=[lengthRod,widthRod,0.01])
85iMass = InertiaMassPoint(mass=mMassPoint).Translated([lengthRod/2,0,0])
86iRodSum = iRod+iMass
87
88#compute reference point of rod (midpoint)
89refRod = -iRodSum.com
90iRodSum = iRodSum.Translated(refRod)
91
92if useLieGroup:
93 nodeType = exu.NodeType.RotationRotationVector
94else:
95 nodeType = exu.NodeType.RotationEulerParameters
96
97
98nRigidBodyNodes = 4
99#nRB=[-1]*nRigidBodyNodes #final node numbers
100
101## create inertia for shaft and slider
102inertiaList=[InertiaCuboid(density=density, sideLengths=[widthShaft,widthShaft,lengthShaft]),
103 InertiaCuboid(density=density, sideLengths=[dimSlider,dimSlider,dimSlider]),
104 iRodSum, iRodSum]
105
106## set up reference position list
107refPosList=[[0,0,lengthShaft/2], # shaft
108 [0,0,sSlider], # slider
109 [ xAB/2 + (lengthRod/2-refRod[0])*np.cos(beta0), 0, lengthShaft - (lengthRod/2-refRod[0])*np.sin(beta0)], # rodAC
110 [-xAB/2 - (lengthRod/2-refRod[0])*np.cos(beta0), 0, lengthShaft - (lengthRod/2-refRod[0])*np.sin(beta0)]] # rodBD
111
112## set up initial velocity vector list
113refVelList = [[0., 0., 0.], # shaft
114 [0., 0., 0.], # slider
115 [0,omega0[2]*refPosList[2][0],0], # rodAC
116 [0,omega0[2]*refPosList[3][0],0]] # rodBD
117
118## set up initial (global) angular velocity vector list
119refAngularVelList = [omega0, # shaft
120 omega0, # slider
121 omega0, # rodAC
122 omega0] # rodBD
123
124## create graphics objects for bodies
125graphicsRodAC = GraphicsDataOrthoCube(-(lengthRod/2-refRod[0]),-widthRod/2,-widthRod/2, lengthRod/2+refRod[0],widthRod/2,widthRod/2, [0.1,0.1,0.8,1])
126graphicsRodBD = GraphicsDataOrthoCube(-lengthRod/2-refRod[0],-widthRod/2,-widthRod/2, lengthRod/2-refRod[0],widthRod/2,widthRod/2, [0.1,0.1,0.8,1])
127graphicsSlider = GraphicsDataOrthoCube(-dimSlider/2,-dimSlider/2,-dimSlider/2, dimSlider/2,dimSlider/2,dimSlider/2, [0.1,0.1,0.8,1])
128graphicsShaft = GraphicsDataOrthoCube(-widthShaft/2,-widthShaft/2,-lengthShaft/2, widthShaft/2,widthShaft/2,lengthShaft/2, [0.1,0.1,0.8,1])
129
130#lists for 4 nodes/bodies: [shaft, slider, rodAC, rodBD]
131graphicsList=[graphicsShaft, graphicsSlider, graphicsRodAC, graphicsRodBD]
132
133#eulerParameters0 = [1, 0, 0, 0]
134rotParList = []
135if nodeType == exu.NodeType.RotationEulerParameters:
136 refRotParList = [eulerParameters0, # shaft
137 eulerParameters0, # slider
138 RotationMatrix2EulerParameters(RotationMatrixY(beta0)), # rodAC
139 RotationMatrix2EulerParameters(RotationMatrixY(-beta0))] # rodBD
140 refRotMatList = [EulerParameters2RotationMatrix(refRotParList[0]),
141 EulerParameters2RotationMatrix(refRotParList[1]),
142 EulerParameters2RotationMatrix(refRotParList[2]),
143 EulerParameters2RotationMatrix(refRotParList[3])]
144
145elif nodeType == exu.NodeType.RotationRxyz:
146 refRotParList = [[0,0,0], # shaft
147 [0,0,0], # slider
148 [0,beta0,0], # rodAC
149 [0,-beta0,0]] # rodBD
150 refRotMatList = [RotXYZ2RotationMatrix(refRotParList[0]),
151 RotXYZ2RotationMatrix(refRotParList[1]),
152 RotXYZ2RotationMatrix(refRotParList[2]),
153 RotXYZ2RotationMatrix(refRotParList[3])]
154
155elif nodeType == exu.NodeType.RotationRotationVector:
156 refRotParList = [[0,0,0], # shaft
157 [0,0,0], # slider
158 [0,beta0,0], # rodAC
159 [0,-beta0,0]] # rodBD
160 refRotMatList = [RotationVector2RotationMatrix(refRotParList[0]),
161 RotationVector2RotationMatrix(refRotParList[1]),
162 RotationVector2RotationMatrix(refRotParList[2]),
163 RotationVector2RotationMatrix(refRotParList[3])]
164
165# add rigid bodies to mbs
166nodeNumberList = [-1]*nRigidBodyNodes
167bodyNumberList = [-1]*nRigidBodyNodes
168for i in range(nRigidBodyNodes):
169 [n0,b0]=AddRigidBody(mainSys = mbs,
170 inertia = inertiaList[i],
171 nodeType = str(nodeType),
172 position = refPosList[i],
173 velocity = refVelList[i],
174 rotationMatrix = [],#refRotMatList[i],
175 rotationParameters = refRotParList[i],
176 angularVelocity = refAngularVelList[i],
177 gravity = g,
178 graphicsDataList = [graphicsList[i]])
179 nodeNumberList[i] = n0
180 bodyNumberList[i] = b0
181
182
183
184
185# ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
186## spring-damper parameters for connecting the rods with the slider
187
188# spring
189k = 8.e5*0.005 # spring stiffness in N/m
190l0 = 0.5 # relaxed spring length in m
191
192# damper
193c = 4.e4*0.005
194
195## connecting points
196# slider
197pointEslider = [dimSlider/2, 0., 0.]
198pointFslider = [-dimSlider/2, 0., 0.]
199
200# connectin points for connecting rods with slider
201connectingPointRodACWithSlider = [refRod[0], 0, 0]
202connectingPointRodBDWithSlider = [-refRod[0], 0, 0]
203
204# connecting points for connecting rods with shaft
205pointA = [xAB/2, 0, lengthShaft/2]
206pointB = [-xAB/2, 0, lengthShaft/2]
207pointARodAC = [-(lengthRod/2-refRod[0]), 0, 0]
208pointARodBD = [(lengthRod/2-refRod[0]), 0, 0]
209
210# connecting point of shaft with ground
211connectingPointShaftWithGround = [0, 0, -lengthShaft/2]
212
213# markers
214markerShaftCOM = mbs.AddMarker(MarkerBodyRigid(name='markerShaftCOM', bodyNumber=bodyNumberList[0], localPosition=[0,0,0]))
215markerShaftGround = mbs.AddMarker(MarkerBodyRigid(name='markerShaftGround', bodyNumber=bodyNumberList[0], localPosition=connectingPointShaftWithGround))
216markerShaftPointA = mbs.AddMarker(MarkerBodyRigid(name='markerShaftPointA', bodyNumber=bodyNumberList[0], localPosition=pointA))
217markerShaftPointB = mbs.AddMarker(MarkerBodyRigid(name='markerShaftPointB', bodyNumber=bodyNumberList[0], localPosition=pointB))
218
219markerSliderCOM = mbs.AddMarker(MarkerBodyRigid(name='markerSliderCOM', bodyNumber=bodyNumberList[1], localPosition=[0,0,0]))
220markerSliderPointE = mbs.AddMarker(MarkerBodyRigid(name='markerSliderPointE', bodyNumber=bodyNumberList[1], localPosition=pointEslider))
221markerSliderPointF = mbs.AddMarker(MarkerBodyRigid(name='markerSliderPointF', bodyNumber=bodyNumberList[1], localPosition=pointFslider))
222
223markerRodACShaft = mbs.AddMarker(MarkerBodyRigid(name='markerRodACShaft', bodyNumber=bodyNumberList[2], localPosition=pointARodAC))
224markerRodACSlider = mbs.AddMarker(MarkerBodyRigid(name='markerRodACSlider', bodyNumber=bodyNumberList[2], localPosition=connectingPointRodACWithSlider))
225
226markerRodBDShaft = mbs.AddMarker(MarkerBodyRigid(name='markerRodBDShaft', bodyNumber=bodyNumberList[3], localPosition=pointARodBD))
227markerRodBDSlider = mbs.AddMarker(MarkerBodyRigid(name='markerRodBDSlider', bodyNumber=bodyNumberList[3], localPosition=connectingPointRodBDWithSlider))
228
229
230
231oGround = mbs.AddObject(ObjectGround())
232markerGround = mbs.AddMarker(MarkerBodyRigid(name='markerGround', bodyNumber=oGround, localPosition=[0,0,0]))
233
234nj2=-1
235
236if not useCompliantCase:
237
238 mbs.AddObject(GenericJoint(markerNumbers=[markerGround, markerShaftGround], constrainedAxes=[1,1,1,1,1,0],
239 visualization=VObjectJointGeneric(axesRadius=0.01, axesLength=0.1)))
240
241 mbs.AddObject(GenericJoint(markerNumbers=[markerShaftCOM, markerSliderCOM], constrainedAxes=[1*0,1*0,0,1,1,1],
242 visualization=VObjectJointGeneric(axesRadius=0.01, axesLength=0.1)))
243
244 mbs.AddObject(GenericJoint(markerNumbers=[markerShaftPointA, markerRodACShaft], constrainedAxes=[1,1,1,1,0,1],
245 visualization=VObjectJointGeneric(axesRadius=0.01, axesLength=0.1)))
246
247 mbs.AddObject(GenericJoint(markerNumbers=[markerShaftPointB, markerRodBDShaft], constrainedAxes=[1,1,1,1,0,1],
248 visualization=VObjectJointGeneric(axesRadius=0.01, axesLength=0.1)))
249
250else:
251 kj=1e5*0.2
252 dj = kj*0.05
253
254 kj2 = kj*0.05 #rotatory springs can be softer!
255 dj2 = kj2*0.05
256
257 mbs.AddObject(RigidBodySpringDamper(markerNumbers=[markerGround, markerShaftGround],
258 stiffness=np.diag([kj,kj,kj,kj2,kj2,0]), damping=np.diag([dj,dj,dj,dj2,dj2,0])))
259
260 mbs.AddObject(RigidBodySpringDamper(markerNumbers=[markerShaftCOM, markerSliderCOM],
261 stiffness=np.diag([kj,kj,0,kj2,kj2,kj2]), damping=0*np.diag([dj,dj,0,0,0,0])))
262
263 nj2 = mbs.AddObject(RigidBodySpringDamper(markerNumbers=[markerShaftPointA, markerRodACShaft],
264 stiffness=np.diag([kj,kj,kj,kj2,0,kj2]), damping=0.*np.diag([dj,dj,dj,0,0,0])))
265
266 mbs.AddObject(RigidBodySpringDamper(markerNumbers=[markerShaftPointB, markerRodBDShaft],
267 stiffness=np.diag([kj,kj,kj,kj2,0,kj2]), damping=0.*np.diag([dj,dj,dj,0,0,0])))
268
269
270
271
272# spring-damper elements
273mbs.AddObject(SpringDamper(markerNumbers=[markerSliderPointE, markerRodACSlider], stiffness=k, damping=c, referenceLength=l0))
274mbs.AddObject(SpringDamper(markerNumbers=[markerSliderPointF, markerRodBDSlider], stiffness=k, damping=c, referenceLength=l0))
275
276mbs.AddSensor(SensorNode(nodeNumber = nodeNumberList[1], fileName='solution/flyballSliderPosition.txt',outputVariableType=exu.OutputVariableType.Position))
277mbs.AddSensor(SensorNode(nodeNumber = nodeNumberList[2], fileName='solution/flyballSliderRotation.txt',outputVariableType=exu.OutputVariableType.Rotation)) #Tait Bryan rotations
278mbs.AddSensor(SensorNode(nodeNumber = nodeNumberList[0], fileName='solution/flyballShaftAngularVelocity.txt',outputVariableType=exu.OutputVariableType.AngularVelocity))
279
280
281# ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
282mbs.Assemble()
283
284
285useGraphics=True
286if useGraphics: #only start graphics once, but after background is set
287 exu.StartRenderer()
288 #mbs.WaitForUserToContinue()
289
290# dynamicSolver = exu.MainSolverImplicitSecondOrder()
291
292tEnd = 10
293h = 2e-5 #RK44
294#h = 1e-3
295
296simulationSettings = exu.SimulationSettings() #takes currently set values or default values
297simulationSettings.timeIntegration.explicitIntegration.useLieGroupIntegration = useLieGroup
298
299simulationSettings.timeIntegration.numberOfSteps = int(tEnd/h)
300simulationSettings.timeIntegration.endTime = tEnd
301
302
303SC.visualizationSettings.markers.show = True
304#SC.visualizationSettings.markers.showNumbers = True
305
306#simulationSettings.displayComputationTime = True
307simulationSettings.timeIntegration.verboseMode = 1
308
309simulationSettings.solutionSettings.sensorsWritePeriod = simulationSettings.timeIntegration.endTime/2000
310simulationSettings.solutionSettings.solutionWritePeriod = simulationSettings.timeIntegration.endTime/2000
311
312if nodeType != exu.NodeType.RotationRotationVector:
313 simulationSettings.timeIntegration.generalizedAlpha.computeInitialAccelerations = True
314else:
315 simulationSettings.timeIntegration.generalizedAlpha.computeInitialAccelerations = False
316
317
318solverType = exu.DynamicSolverType.TrapezoidalIndex2
319if useLieGroup:
320 solverType = exu.DynamicSolverType.RK44
321 simulationSettings.timeIntegration.stepSizeSafety = 0.5 #almost no step rejection
322
323mbs.SolveDynamic(simulationSettings, solverType=solverType)
324print(mbs.sys['dynamicSolver'].it)
325
326
327if useGraphics: #only start graphics once, but after background is set
328 exu.StopRenderer() #safely close rendering window!
329
330
331for i in range(4):
332 om=mbs.GetNodeOutput(i,exu.OutputVariableType.AngularVelocity)
333 # exu.Print("om",i,"=",om)
334
335for i in range(4):
336 vel=mbs.GetNodeOutput(i,exu.OutputVariableType.Velocity)
337 # exu.Print("v",i,"=",vel)
338
339for i in range(2):
340 rot=mbs.GetNodeOutput(i+2,exu.OutputVariableType.RotationMatrix)
341 # exu.Print("Rot",i+2,"=",rot)
342
343result = mbs.GetNodeOutput(2,exu.OutputVariableType.Velocity)[1] #y-velocity of bar
344exu.Print('solution of stiffFlyballGovernor=',result)
345
346
347plist=[]
348plist += [mbs.GetObjectOutputBody(objectNumber = bodyNumberList[2], variableType = exu.OutputVariableType.Velocity, localPosition = list(pointARodAC), configuration =
349exu.ConfigurationType.Current)]
350plist += [mbs.GetObjectOutputBody(objectNumber = bodyNumberList[2], variableType = exu.OutputVariableType.Velocity, localPosition = connectingPointRodACWithSlider, configuration =
351exu.ConfigurationType.Current)]
352plist += [mbs.GetObjectOutputBody(objectNumber = bodyNumberList[3], variableType = exu.OutputVariableType.Velocity, localPosition = pointARodBD, configuration =
353exu.ConfigurationType.Current)]
354
355#locU = mbs.GetObjectOutput(objectNumber = nj2, variableType =exu.OutputVariableType.DisplacementLocal)
356#exu.Print('locU=', locU)
357#locR = mbs.GetObjectOutput(objectNumber = nj2, variableType =exu.OutputVariableType.Rotation)
358#exu.Print('locR=', locR)
359
360
361#Rxyz initial velocities:
362#om 0 = [0. 0. 6.28318531]
363#om 1 = [0. 0. 6.28318531]
364#om 2 = [ 0.00000000e+00 -8.54693196e-10 6.28318531e+00]
365#om 3 = [0.00000000e+00 8.54693196e-10 6.28318531e+00]
366#v 0 = [ 0.00000000e+00 0.00000000e+00 -4.90499796e-10]
367#v 1 = [ 0.00000000e+00 0.00000000e+00 -4.90499608e-10]
368#v 2 = [-1.91975841e-16 5.60155553e+00 -4.90500111e-10]
369#v 3 = [ 1.91975841e-16 -5.60155553e+00 -4.90500111e-10]
370
371if useGraphics:
372 import matplotlib.pyplot as plt
373 import matplotlib.ticker as ticker
374 plt.close('all')
375
376 data = np.loadtxt('solution/flyballSliderPosition.txt', comments='#', delimiter=',')
377 #plt.plot(data[:,0], data[:,3], 'r-') #z coordinate of slider
378 #data = np.loadtxt('solution/flyballShaftAngularVelocity.txt', comments='#', delimiter=',')
379 plt.plot(data[:,0], data[:,1], 'b-') #z coordinate of slider
380 plt.plot(data[:,0], data[:,2], 'g-') #z coordinate of slider
381 plt.plot(data[:,0], data[:,3], 'k-') #z coordinate of slider
382
383 data = np.loadtxt('solution/flyballSliderRotation.txt', comments='#', delimiter=',')
384 plt.plot(data[:,0], data[:,1], 'r--') #z coordinate of slider
385 plt.plot(data[:,0], data[:,2], 'g--') #z coordinate of slider
386 plt.plot(data[:,0], data[:,3], 'b--') #z coordinate of slider
387
388 if False:
389 #data = np.loadtxt('solution/flyballSliderPositionRxyz.txt', comments='#', delimiter=',') #rigid joints?
390 data = np.loadtxt('solution/flyballSliderPositionRK4Rxyz.txt', comments='#', delimiter=',') #compliant joints
391 #plt.plot(data[:,0], data[:,3], 'r:') #z coordinate of slider
392 plt.plot(data[:,0], data[:,1], 'b:') #z coordinate of slider
393 plt.plot(data[:,0], data[:,2], 'g:') #z coordinate of slider
394 plt.plot(data[:,0], data[:,3], 'k:') #z coordinate of slider
395
396# data = np.loadtxt('solution/flyballSliderPositionRK4Rxyz.txt', comments='#', delimiter=',')
397# plt.plot(data[:,0], data[:,3], 'g:') #z coordinate of slider
398# data = np.loadtxt('solution/flyballShaftAngularVelocityRK4Rxyz.txt', comments='#', delimiter=',')
399# plt.plot(data[:,0], data[:,3], 'k:') #z coordinate of slider
400
401 ax=plt.gca() # get current axes
402 ax.grid(True, 'major', 'both')
403 ax.xaxis.set_major_locator(ticker.MaxNLocator(10))
404 ax.yaxis.set_major_locator(ticker.MaxNLocator(10))
405 plt.tight_layout()
406 plt.show()