rigidRotor3DbasicBehaviour.py

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#+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
# This is an EXUDYN example
#
# Details:  Example with 3D rotor, showing basic behaviour of rotor
#           show COM, unbalance for low, critical and high rotation speeds
#
# Author:   Johannes Gerstmayr
# Date:     2019-12-05
#
# 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 sys
sys.path.append('../TestModels')            #for modelUnitTest as this example may be used also as a unit test

import exudyn as exu
from exudyn.itemInterface import *
from exudyn.utilities import * #includes itemInterface and rigidBodyUtilities
import exudyn.graphics as graphics #only import if it does not conflict

import time
import numpy as np

SC = exu.SystemContainer()
mbs = SC.AddSystem()
print('EXUDYN version='+exu.GetVersionString())

L=1                     #rotor axis length
isSymmetric = True
if isSymmetric:
    L0 = 0.5            #0.5 (symmetric rotor); position of rotor on x-axis
else :
    L0 = 0.9            #default: 0.9m; position of rotor on x-axis
L1 = L-L0               #
m = 2                   #mass in kg
r = 0.5*1.5             #radius for disc mass distribution
lRotor = 0.2            #length of rotor disk
k = 800                 #stiffness of (all/both) springs in rotor in N/m
Jxx = 0.5*m*r**2        #polar moment of inertia
Jyyzz = 0.25*m*r**2 + 1/12.*m*lRotor**2      #moment of inertia for y and z axes

omega0=np.sqrt(2*k/m) #linear system

D0 = 0.002              #dimensionless damping
d = 2*omega0*D0*m       #damping constant in N/(m/s)

f0 = 0*omega0/(2*np.pi) #frequency start (Hz)
f1 = 2.*omega0/(2*np.pi) #frequency end (Hz)

torque = 0*0.2            #driving torque; Nm ; 0.1Nm does not surpass critical speed; 0.2Nm works
eps = 10e-3              # excentricity of mass in y-direction
                        #symmetric rotor: 2e-3 gives large oscillations;
                        #symmetric rotor: 0.74*2e-3 shows kink in runup curve
#k*=1000

modeStr=['slow (omega0/2)',
         'critical (omega0)',
         'fast (2*omega0)' ]
mode = 2

#add constraint on euler parameters or euler angles
#add three cases

if mode == 0:
    omegaInitial = 0.5*omega0 #initial rotation speed in rad/s
elif mode == 1:
    omegaInitial = 1*omega0 #initial rotation speed in rad/s
    eps *= 0.1
    d *= 10
elif mode == 2:
    omegaInitial = 2*omega0 #initial rotation speed in rad/s

tEnd = 50              #end time of simulation
steps = 50000           #number of steps

fRes = omega0/(2*np.pi)
print('symmetric rotor resonance frequency (Hz)= '+str(fRes))
print('omega intial (Hz)= '+str(omegaInitial/(2*np.pi)))
#print('runup over '+str(tEnd)+' seconds, fStart='+str(f0)+'Hz, fEnd='+str(f1)+'Hz')


# #user function for load
# def userLoad(t, load):
#     #return load*np.sin(0.5*omega0*t) #gives resonance
#     if t>40: time.sleep(0.02) #make simulation slower
#     return load*Sweep(t, tEnd, f0, f1)
#     #return load*Sweep(t, tEnd, f1, f0) #backward sweep

# #backward whirl excitation:
# amp = 0.10  #in resonance: *0.01
# def userLoadBWy(t, load):
#     return load*SweepCos(t, tEnd, f0, f1) #negative sign: BW, positive sign: FW
# def userLoadBWz(t, load):
#     return load*Sweep(t, tEnd, f0, f1)
#def userLoadBWx(t, load):
#    return load*np.sin(omegaInitial*t)
#def userLoadBWy(t, load):
#    return -load*np.cos(omegaInitial*t) #negative sign: FW, positive sign: BW

#background1 = graphics.BrickXYZ(0,0,0,.5,0.5,0.5,[0.3,0.3,0.9,1])

#draw RGB-frame at origin
p=[0,0,0]
rDraw = 0.05*r
lFrame = rDraw*1.2
tFrame = 0.01*0.15
backgroundX = graphics.Cylinder(p,[lFrame,0,0],tFrame,[0.9,0.3,0.3,1],12)
backgroundY = graphics.Cylinder(p,[0,lFrame,0],tFrame*0.5,[0.3,0.9,0.3,1],12)
backgroundZ = graphics.Cylinder(p,[0,0,lFrame],tFrame*0.5,[0.3,0.3,0.9,1],12)
black=[0,0,0,1]
textCOM = {'type':'Text', 'text': 'COM', 'color': black, 'position': [lFrame*1.1,0,0]}
textSHAFT = {'type':'Text', 'text': 'SHAFT', 'color': black, 'position': [L-L0+0.1,-eps,0]}
textY = {'type':'Text', 'text': 'Y', 'color': black, 'position': [0,lFrame*1.05,0]}
textZ = {'type':'Text', 'text': 'Z', 'color': black, 'position': [0,0,lFrame*1.05]}

#rotor is rotating around x-axis
ep0 = eulerParameters0 #no rotation
ep_t0 = AngularVelocity2EulerParameters_t([omegaInitial,0,0], ep0)
print(ep_t0)

p0 = [L0-0.5*L,eps,0] #reference position, displaced by eccentricity eps !
v0 = [0.,0.,0.] #initial translational velocity

#node for Rigid2D body: px, py, phi:
n1=mbs.AddNode(NodeRigidBodyEP(referenceCoordinates = p0+ep0,
                               initialVelocities=v0+list(ep_t0)))

#ground nodes
nGround0=mbs.AddNode(NodePointGround(referenceCoordinates = [-L/2,0,0]))
nGround1=mbs.AddNode(NodePointGround(referenceCoordinates = [ L/2,0,0]))

#add mass point (this is a 3D object with 3 coordinates):
gRotor = graphics.Cylinder([-lRotor*0.2,0,0],[lRotor*0.4,0,0],rDraw,
                              [0.3,0.3,0.9,1],128)
gRotor2 = graphics.Cylinder([-L0,-eps,0],[L,0,0],r*0.01*0.25,[0.6,0.6,0.6,1],16)
gRotorCOM = graphics.Cylinder([-lRotor*0.1,0,0],[lRotor*0.6*0.1,0,0],r*0.01*0.5,
                                 [0.3,0.9,0.3,1],16)
gRotor3 = [backgroundX, backgroundY, backgroundZ, textCOM, textY, textZ, textSHAFT]
rigid = mbs.AddObject(RigidBody(physicsMass=m,
                                physicsInertia=[Jxx,Jyyzz,Jyyzz,0,0,0],
                                nodeNumber = n1,
                                visualization=VObjectRigidBody2D(graphicsData=[gRotor, gRotor2, gRotorCOM]+gRotor3)))

mbs.AddSensor(SensorBody(bodyNumber=rigid,
                          fileName='solution/rotorDisplacement.txt',
                          localPosition=[0,-eps,0],
                          outputVariableType=exu.OutputVariableType.Displacement))
# mbs.AddSensor(SensorBody(bodyNumber=rigid,
#                          fileName='solution/rotorAngularVelocity.txt',
#                          outputVariableType=exu.OutputVariableType.AngularVelocity))

#marker for ground (=fixed):
groundMarker0=mbs.AddMarker(MarkerNodePosition(nodeNumber= nGround0))
groundMarker1=mbs.AddMarker(MarkerNodePosition(nodeNumber= nGround1))

#marker for rotor axis and support:
rotorAxisMarker0 =mbs.AddMarker(MarkerBodyPosition(bodyNumber=rigid, localPosition=[-L0,-eps,0]))
rotorAxisMarker1 =mbs.AddMarker(MarkerBodyPosition(bodyNumber=rigid, localPosition=[ L1,-eps,0]))


#++++++++++++++++++++++++++++++++++++
mbs.AddObject(CartesianSpringDamper(markerNumbers=[groundMarker0, rotorAxisMarker0],
                                    stiffness=[k,k,k], damping=[d, d, d],
                                    visualization=VCartesianSpringDamper(drawSize=0.002)))
mbs.AddObject(CartesianSpringDamper(markerNumbers=[groundMarker1, rotorAxisMarker1],
                                   stiffness=[0,k,k], damping=[0, d, d],
                                   visualization=VCartesianSpringDamper(drawSize=0.002))) #do not constrain x-axis twice


#add torque:
# rotorRigidMarker =mbs.AddMarker(MarkerBodyRigid(bodyNumber=rigid, localPosition=[0,0,0]))
# mbs.AddLoad(Torque(markerNumber=rotorRigidMarker, loadVector=[torque,0,0]))

#constant velocity constraint:
constantRotorVelocity = True
if constantRotorVelocity :
    mRotationAxis = mbs.AddMarker(MarkerNodeRotationCoordinate(nodeNumber = n1, rotationCoordinate=0))
    mGroundCoordinate =mbs.AddMarker(MarkerNodeCoordinate(nodeNumber= nGround0, coordinate=0))
    mbs.AddObject(CoordinateConstraint(markerNumbers=[mGroundCoordinate, mRotationAxis],
                                       offset=omegaInitial, velocityLevel=True,
                                       visualization=VCoordinateConstraint(show=False))) #gives equation omegaMarker1 = offset


#print(mbs)
mbs.Assemble()
#mbs.systemData.Info()

simulationSettings = exu.SimulationSettings()
simulationSettings.solutionSettings.solutionWritePeriod = 1e-5  #output interval
simulationSettings.solutionSettings.sensorsWritePeriod = 1e-5  #output interval

descrStr = "Laval rotor, resonance="+str(round(fRes,3))+", "+modeStr[mode]
simulationSettings.solutionSettings.solutionInformation = descrStr

simulationSettings.timeIntegration.numberOfSteps = steps
simulationSettings.timeIntegration.endTime = tEnd
simulationSettings.timeIntegration.generalizedAlpha.useIndex2Constraints = True
simulationSettings.timeIntegration.generalizedAlpha.useNewmark = True

simulationSettings.timeIntegration.generalizedAlpha.spectralRadius = 1
SC.visualizationSettings.window.renderWindowSize = [1600,1080]
SC.visualizationSettings.general.textSize = 22

exu.StartRenderer()              #start graphics visualization
mbs.WaitForUserToContinue()    #wait for pressing SPACE bar to continue

#simulate some time to get steady-state solution:
mbs.SolveDynamic(simulationSettings)
state = mbs.systemData.GetSystemState()

#now simulate the steady state solution and record
simulationSettings.timeIntegration.numberOfSteps = 10000
simulationSettings.timeIntegration.endTime = 2.5

#create animations (causes slow simulation):
createAnimation=True
if createAnimation:
    mbs.WaitForUserToContinue()    #wait for pressing SPACE bar to continue
    simulationSettings.solutionSettings.recordImagesInterval = 0.01
    if mode == 1:
        simulationSettings.timeIntegration.endTime = 1
        simulationSettings.solutionSettings.recordImagesInterval = 0.0025
    if mode == 2:
        simulationSettings.timeIntegration.endTime = 0.5
        simulationSettings.solutionSettings.recordImagesInterval = 0.001

    SC.visualizationSettings.exportImages.saveImageFileName = "images/frame"

    mbs.systemData.SetSystemState(state, configuration=exu.ConfigurationType.Initial)
    mbs.SolveDynamic(simulationSettings)

#SC.WaitForRenderEngineStopFlag()#wait for pressing 'Q' to quit
exu.StopRenderer()               #safely close rendering window!

#evaluate final (=current) output values
u = mbs.GetNodeOutput(n1, exu.OutputVariableType.AngularVelocity)
print('omega final (Hz)=',u/(2*np.pi))
#print('displacement=',u[0])
c = mbs.GetNodeOutput(n1, exu.OutputVariableType.Coordinates)
c_t = mbs.GetNodeOutput(n1, exu.OutputVariableType.Coordinates_t)
print("nc=",c)
print("nc_t=",c_t)

##+++++++++++++++++++++++++++++++++++++++++++++++++++++
import matplotlib.pyplot as plt
import matplotlib.ticker as ticker

if True:
    plt.close('all') #close all plots

    dataDisp = np.loadtxt('solution/rotorDisplacement.txt', comments='#', delimiter=',')

    plt.plot(dataDisp[:,0], dataDisp[:,3], 'b-') #numerical solution
    plt.xlabel("time (s)")
    plt.ylabel("z-displacement (m)")

    plt.figure()
    plt.plot(dataDisp[:,2], dataDisp[:,3], 'r-') #numerical solution
    plt.xlabel("y-displacement (m)")
    plt.ylabel("z-displacement (m)")

    #plt.plot(data[n-500:n-1,1], data[n-500:n-1,2], 'r-') #numerical solution

    ax=plt.gca() # get current axes
    ax.grid(True, 'major', 'both')
    ax.xaxis.set_major_locator(ticker.MaxNLocator(10))
    ax.yaxis.set_major_locator(ticker.MaxNLocator(10))
    plt.tight_layout()
    plt.show()