rigidRotor3DFWBW.py

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#+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
# This is an EXUDYN example
#
# Details:  Example with 3D rotor; rotates around X-axis
#           showing forward (FW) and backward (BW) whirls and FW/BW whirl resonances
#
# 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 *
from math import cos, sin

import time
import numpy as np

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

L=1                     #rotor axis length
isSymmetric = True
symStr = "General"
if isSymmetric:
    L0 = 0.5            #0.5 (symmetric rotor); position of rotor on x-axis
    symStr = "Laval"
    s = "symmetric"
else :
    L0 = 0.9            #default: 0.9m; position of rotor on x-axis
    s = "unsymmetric"

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

omegaInitial = 0*4*omega0 #initial rotation speed in rad/s

tEnd = 20              #end time of simulation
steps = int(tEnd*1000)           #number of steps

modeStr = "BW" #"FW" or "BW"
sign = 1
if modeStr == "BW": sign = -1

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

#3D load vector
loadFact = 1
n1 = 0 #rotor node number, will be defined later
def UFload(mbs, t, load):
    #compute angle of rotation (only true if rotation about 1 axis)
    phi = mbs.GetNodeOutput(nodeNumber=n1, variableType=exu.OutputVariableType.Rotation)[0]
    return [0, sign*loadFact*cos(phi), loadFact*sin(phi)]

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

#draw RGB-frame at origin
p=[0,0,0]
lFrame = 0.9
tFrame = 0.01
backgroundX = GraphicsDataCylinder(p,[lFrame,0,0],tFrame,[0.9,0.3,0.3,1],12)
backgroundY = GraphicsDataCylinder(p,[0,lFrame,0],tFrame,[0.3,0.9,0.3,1],12)
backgroundZ = GraphicsDataCylinder(p,[0,0,lFrame],tFrame,[0.3,0.3,0.9,1],12)

#visualize forces:
lVec = r*0.8
f1=0.08 #arrow size
f2=0.04 #arrow size 2
rigid = 0 #will be set later!
#ground user function, but draws load on body
def UFgraphics(mainSystem, bodyNr):
    t=mainSystem.systemData.GetTime()
    #get rotation for rigid body:
    rot = mbs.GetObjectOutputBody(rigid, exu.OutputVariableType.Rotation,
                                [0,0,0], exu.ConfigurationType.Visualization)
    omega = mbs.GetObjectOutputBody(rigid, exu.OutputVariableType.AngularVelocity,
                                [0,0,0], exu.ConfigurationType.Visualization)
    phi = rot[0]
    phi += 0.9*0.05*omega[0] #graphics is always delayed ...
    #print("rot=", phi)

    #g0=GraphicsDataSphere(point=p0,radius=0.01, color=color4green)
    #g1=GraphicsDataSphere(point=p1,radius=0.01, color=color4red)
    xVec = 0.5+lRotor
    p0 = [xVec,0,0]
    p1 = [xVec,sign*lVec*cos(phi), lVec*sin(phi)]
    p2 = [xVec,sign*(1-f1)*lVec*cos(phi)-f2*lVec*sin(phi), (1-f1)*lVec*sin(phi)+f2*sign*lVec*cos(phi)]
    p3 = [xVec,sign*(1-f1)*lVec*cos(phi)+f2*lVec*sin(phi), (1-f1)*lVec*sin(phi)-f2*sign*lVec*cos(phi)]
    gLine = {'type':'Line', 'data': p0+p1+p2+p1+p3, 'color':color4red}
    return [gLine]#,g0,g1] #return list of graphics data

mbs.AddObject(ObjectGround(referencePosition= [0,0,0],
                           visualization=VObjectGround(graphicsDataUserFunction=UFgraphics)))

#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
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 = GraphicsDataCylinder([-lRotor*0.5,0,0],[lRotor,0,0],r,[0.3,0.3,0.9,1],128)
gRotor2 = GraphicsDataCylinder([-L0,0,0],[L,0,0],r*0.05,[0.3,0.3,0.9,1],16)
gRotor3 = [backgroundX, backgroundY, backgroundZ]
rigid = mbs.AddObject(RigidBody(physicsMass=m, physicsInertia=[Jxx,Jyyzz,Jyyzz,0,0,0], nodeNumber = n1, visualization=VObjectRigidBody2D(graphicsData=[gRotor, gRotor2]+gRotor3)))

mbs.AddSensor(SensorBody(bodyNumber=rigid,
                         fileName='solution/runupDisplacement'+modeStr+'.txt',
                         outputVariableType=exu.OutputVariableType.Displacement))
mbs.AddSensor(SensorBody(bodyNumber=rigid,
                         fileName='solution/runupAngularVelocity'+modeStr+'.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]))
mbs.AddObject(CartesianSpringDamper(markerNumbers=[groundMarker1, rotorAxisMarker1],
                                   stiffness=[0,k,k], damping=[0, d, d])) #do not constrain x-axis twice

#coordinate markers for loads:
rotorMarkerUy=mbs.AddMarker(MarkerNodeCoordinate(nodeNumber= n1, coordinate=1))
rotorMarkerUz=mbs.AddMarker(MarkerNodeCoordinate(nodeNumber= n1, coordinate=2))

#add torque:
rotorRigidMarker =mbs.AddMarker(MarkerBodyRigid(bodyNumber=rigid, localPosition=[0,0,0]))
mbs.AddLoad(Torque(markerNumber=rotorRigidMarker,
                   loadVector=[torque,0,0],
                   visualization={'show':False}))

#BW/FW load vector:
mbs.AddLoad(Force(markerNumber=rotorRigidMarker,
                  loadVector=[0,0,0],
                  loadVectorUserFunction=UFload))

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

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

simulationSettings.solutionSettings.solutionInformation = "Runup of "+s+" rotor: "+modeStr + ", " + symStr

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

simulationSettings.timeIntegration.generalizedAlpha.spectralRadius = 1

#create animations (causes slow simulation):
createAnimation=True
if createAnimation:
    simulationSettings.solutionSettings.recordImagesInterval = 0.05
    SC.visualizationSettings.exportImages.saveImageFileName = "images/frame"
    SC.visualizationSettings.window.renderWindowSize = [1600,1080]
    SC.visualizationSettings.openGL.multiSampling = 4

#visualize loads:
# SC.visualizationSettings.loads.fixedLoadSize=False
# SC.visualizationSettings.loads.loadSizeFactor=100
# SC.visualizationSettings.loads.drawSimplified = False

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

    #start solver:
    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)=',(1./(2.*np.pi))*u)
    #print('displacement=',u[0])


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

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


    dataDispFW = np.loadtxt('solution/runupDisplacementFW.txt', comments='#', delimiter=',')
    dataOmegaFW = np.loadtxt('solution/runupAngularVelocityFW.txt', comments='#', delimiter=',')
    dataDispBW = np.loadtxt('solution/runupDisplacementBW.txt', comments='#', delimiter=',')
    dataOmegaBW = np.loadtxt('solution/runupAngularVelocityBW.txt', comments='#', delimiter=',')
    plt.rcParams.update({'font.size': 12})

    if False:
        plt.plot(dataDispFW[:,0], dataDispFW[:,3], 'r-', label='FW') #numerical solution
        plt.plot(dataDispBW[:,0], dataDispBW[:,3], 'b-', label='BW') #numerical solution
        plt.xlabel("time (s)")
        plt.ylabel("z-displacement (m)")
        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.legend()
        plt.tight_layout()

    plt.figure()
    plt.plot((1/(2*np.pi))*dataOmegaFW[:,1], dataDispFW[:,3], 'r-', label='FW', linewidth=0.7) #numerical solution
    plt.plot((1/(2*np.pi))*dataOmegaBW[:,1], dataDispBW[:,3], 'b-', label='BW', linewidth=0.7) #numerical solution
    plt.xlabel("angular velocity (1/s)")
    plt.ylabel("z-displacement (m)")
    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.legend()
    plt.tight_layout()

    #save figure:
    #plt.savefig("rotorBWFWrunup"+symStr+".pdf")

    # plt.figure()
    # plt.plot(dataOmegaFW[:,0], (1/(2*np.pi))*dataOmegaFW[:,1], 'r-') #numerical solution
    # plt.xlabel("time (s)")
    # plt.ylabel("angular velocity (1/s)")
    # 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.figure()
    # plt.plot(dataDispFW[:,2], dataDispFW[:,3], 'r-') #numerical solution
    # plt.xlabel("y-displacement (m)")
    # plt.ylabel("z-displacement (m)")
    # 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.plot(data[n-500:n-1,1], data[n-500:n-1,2], 'r-') #numerical solution

    plt.show()