flexibleRotor3Dtest.py

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  1#+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
  2# This is an EXUDYN example
  3#
  4# Details:  Flexible rotor test using two rigid bodies connected by 4 springs (corotating)
  5#           This test shows the unstable behavior if inner damping is larger than outer damping
  6#
  7# Author:   Johannes Gerstmayr
  8# Date:     2019-12-05
  9#
 10# 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.
 11#
 12#+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 13
 14import exudyn as exu
 15from exudyn.itemInterface import *
 16from exudyn.utilities import *
 17
 18import time
 19import numpy as np
 20
 21SC = exu.SystemContainer()
 22mbs = SC.AddSystem()
 23print('EXUDYN version='+exu.GetVersionString())
 24
 25L=1                     #total rotor axis length
 26m = 1                   #mass of one disc in kg
 27r = 0.5                 #radius for disc mass distribution
 28lRotor = 0.1            #length of one half rotor disk
 29k = 800                 #stiffness of (all/both) springs in rotor in N/m
 30Jxx = 0.5*m*r**2        #polar moment of inertia
 31Jyyzz = 0.25*m*r**2 + 1/12.*m*lRotor**2      #moment of inertia for y and z axes
 32
 33omega0=np.sqrt(2*k/(2*m)) #linear system; without flexibility of rotor
 34
 35#case 1: external damping: D0=0.002, D0int=0
 36#case 2: external damping with small internal damping: D0=0.002, D0int=0.001
 37#case 3: external damping with larger internal damping: D0=0.002, D0int=0.1
 38#case 4: no external damping with small internal damping: D0=0, D0int=0.001
 39attr = 'g-' #color in plot
 40D0 = 0.002              #0.002 default; dimensionless damping
 41D0int = 0.001*200 #*200      #default 0.001; dimensionless damping (not fully); value > 0.08 gives instability
 42
 43d = 2*omega0*D0*(2*m)       #damping constant for external damping in N/(m/s)
 44
 45kInt = 4*800            #stiffness of (all/both) springs in rotor in N/m
 46omega0int = np.sqrt(kInt/m)
 47dInt = 2*omega0int*D0int*m    #damping constant in N/(m/s)
 48
 49f0 = 0*omega0/(2*np.pi) #frequency start (Hz)
 50f1 = 2.*omega0/(2*np.pi) #frequency end (Hz)
 51
 52torque = 0.5            #driving torque; Nm
 53eps = 2e-3              #excentricity of mass in y-direction
 54omegaInitial = 0*4*omega0 #initial rotation speed in rad/s
 55
 56print('resonance frequency (rad/s)= '+str(omega0))
 57tEnd = 80               #end time of simulation
 58steps = 10000         #number of steps
 59
 60
 61#draw RGB-frame at origin
 62p=[0,0,0]
 63lFrame = 0.8
 64tFrame = 0.01
 65backgroundX = GraphicsDataCylinder(p,[lFrame,0,0],tFrame,[0.9,0.3,0.3,1],12)
 66backgroundY = GraphicsDataCylinder(p,[0,lFrame,0],tFrame,[0.3,0.9,0.3,1],12)
 67backgroundZ = GraphicsDataCylinder(p,[0,0,lFrame],tFrame,[0.3,0.3,0.9,1],12)
 68#mbs.AddObject(ObjectGround(referencePosition= [0,0,0], visualization=VObjectGround(graphicsData= [backgroundX, backgroundY, backgroundZ])))
 69
 70#rotor is rotating around x-axis
 71ep0 = eulerParameters0 #no rotation
 72ep_t0 = AngularVelocity2EulerParameters_t([omegaInitial,0,0], ep0)
 73print(ep_t0)
 74
 75p0 = [-lRotor*0.5,eps,0] #reference position
 76p1 = [ lRotor*0.5,eps,0] #reference position
 77v0 = [0.,0.,0.] #initial translational velocity
 78
 79#node for Rigid2D body: px, py, phi:
 80n0=mbs.AddNode(RigidEP(referenceCoordinates = p0+ep0, initialVelocities=v0+list(ep_t0)))
 81n1=mbs.AddNode(RigidEP(referenceCoordinates = p1+ep0, initialVelocities=v0+list(ep_t0)))
 82
 83#ground nodes
 84nGround0=mbs.AddNode(NodePointGround(referenceCoordinates = [-L/2,0,0]))
 85nGround1=mbs.AddNode(NodePointGround(referenceCoordinates = [ L/2,0,0]))
 86
 87#add mass point (this is a 3D object with 3 coordinates):
 88transl = 0.9 #<1 gives transparent object
 89gRotor0 = GraphicsDataCylinder([-lRotor*0.5,0,0],[lRotor,0,0],r,[0.3,0.3,0.9,transl],32)
 90gRotor1 = GraphicsDataCylinder([-lRotor*0.5,0,0],[lRotor,0,0],r,[0.9,0.3,0.3,transl],32)
 91gRotor0Axis = GraphicsDataCylinder([-L*0.5+0.5*lRotor,0,0],[L*0.5,0,0],r*0.05,[0.3,0.3,0.9,1],16)
 92gRotor1Axis = GraphicsDataCylinder([-0.5*lRotor,0,0],[L*0.5,0,0],r*0.05,[0.3,0.3,0.9,1],16)
 93gRotorCS = [backgroundX, backgroundY, backgroundZ]
 94rigid0 = mbs.AddObject(RigidBody(physicsMass=m, physicsInertia=[Jxx,Jyyzz,Jyyzz,0,0,0], nodeNumber = n0, visualization=VObjectRigidBody2D(graphicsData=[gRotor0, gRotor0Axis]+gRotorCS)))
 95rigid1 = mbs.AddObject(RigidBody(physicsMass=m, physicsInertia=[Jxx,Jyyzz,Jyyzz,0,0,0], nodeNumber = n1, visualization=VObjectRigidBody2D(graphicsData=[gRotor1, gRotor1Axis]+gRotorCS)))
 96
 97#marker for ground (=fixed):
 98groundMarker0=mbs.AddMarker(MarkerNodePosition(nodeNumber= nGround0))
 99groundMarker1=mbs.AddMarker(MarkerNodePosition(nodeNumber= nGround1))
100
101#marker for rotor axis and support:
102rotorAxisMarker0 =mbs.AddMarker(MarkerBodyPosition(bodyNumber=rigid0, localPosition=[-0.5*L+0.5*lRotor,-eps,0]))
103rotorAxisMarker1 =mbs.AddMarker(MarkerBodyPosition(bodyNumber=rigid1, localPosition=[ 0.5*L-0.5*lRotor,-eps,0]))
104
105
106#++++++++++++++++++++++++++++++++++++
107#supports:
108mbs.AddObject(CartesianSpringDamper(markerNumbers=[groundMarker0, rotorAxisMarker0],
109                                    stiffness=[k,k,k], damping=[d, d, d]))
110mbs.AddObject(CartesianSpringDamper(markerNumbers=[groundMarker1, rotorAxisMarker1],
111                                   stiffness=[0,k,k], damping=[0, d, d])) #do not constrain x-axis twice
112
113#++++++++++++++++++++++++++++++++++++
114#flexible rotor:
115nSprings = 4
116for i in range(nSprings):
117    #add corresponding markers
118    phi = 2*np.pi*i/nSprings
119    rSpring = 0.5
120    yPos = rSpring*np.sin(phi)
121    zPos = rSpring*np.cos(phi)
122    rotorM0 =mbs.AddMarker(MarkerBodyPosition(bodyNumber=rigid0, localPosition=[ 0.5*lRotor,yPos,zPos]))
123    rotorM1 =mbs.AddMarker(MarkerBodyPosition(bodyNumber=rigid1, localPosition=[-0.5*lRotor,yPos,zPos]))
124
125    mbs.AddObject(CartesianSpringDamper(markerNumbers=[rotorM0, rotorM1],
126                                        stiffness=[kInt,kInt,kInt], damping=[dInt, dInt, dInt]))
127
128#coordinate markers for loads:
129rotorMarkerUy=mbs.AddMarker(MarkerNodeCoordinate(nodeNumber= n1, coordinate=1))
130rotorMarkerUz=mbs.AddMarker(MarkerNodeCoordinate(nodeNumber= n1, coordinate=2))
131
132#add torque:
133rotorRigidMarker =mbs.AddMarker(MarkerBodyRigid(bodyNumber=rigid0, localPosition=[0,0,0]))
134mbs.AddLoad(Torque(markerNumber=rotorRigidMarker, loadVector=[torque,0,0]))
135
136#print(mbs)
137mbs.Assemble()
138#mbs.systemData.Info()
139
140simulationSettings = exu.SimulationSettings()
141simulationSettings.solutionSettings.solutionWritePeriod = 1e-5  #output interval
142simulationSettings.timeIntegration.numberOfSteps = steps
143simulationSettings.timeIntegration.endTime = 30#tEnd
144simulationSettings.timeIntegration.newton.useModifiedNewton=True
145simulationSettings.timeIntegration.generalizedAlpha.useIndex2Constraints = True
146simulationSettings.timeIntegration.generalizedAlpha.useNewmark = True
147simulationSettings.timeIntegration.verboseMode = 1
148simulationSettings.displayStatistics = True
149simulationSettings.displayComputationTime = True
150simulationSettings.linearSolverType = exu.LinearSolverType.EXUdense
151
152simulationSettings.timeIntegration.generalizedAlpha.spectralRadius = 1
153SC.visualizationSettings.general.useMultiThreadedRendering = False
154
155exu.StartRenderer()              #start graphics visualization
156mbs.WaitForUserToContinue()    #wait for pressing SPACE bar to continue
157
158#start solver:
159mbs.SolveDynamic(simulationSettings)
160
161SC.WaitForRenderEngineStopFlag()#wait for pressing 'Q' to quit
162exu.StopRenderer()               #safely close rendering window!
163
164#evaluate final (=current) output values
165u = mbs.GetNodeOutput(n1, exu.OutputVariableType.AngularVelocity)
166print('omega=',u)
167
168
169##+++++++++++++++++++++++++++++++++++++++++++++++++++++
170import matplotlib.pyplot as plt
171import matplotlib.ticker as ticker
172
173if True:
174    data = np.loadtxt('coordinatesSolution.txt', comments='#', delimiter=',')
175    n=steps
176    plt.rcParams.update({'font.size': 24})
177
178    plt.plot(data[:,0], data[:,3], 'r-') #numerical solution
179
180    ax=plt.gca() # get current axes
181    ax.grid(True, 'major', 'both')
182    ax.xaxis.set_major_locator(ticker.MaxNLocator(10))
183    ax.yaxis.set_major_locator(ticker.MaxNLocator(10))
184    plt.tight_layout()
185    plt.show()