rigidRotor3Drunup.py

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#+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
# This is an EXUDYN example
#
# Details:  Example with 3D rotor, showing runup
#
# 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
#a local run must not open a plot window when windows are suppressed (#2477)
if exu.special.userInterface.suppressPlots: import matplotlib; matplotlib.use('Agg')
from exudyn.itemInterface import *
from exudyn.utilities import * #includes itemInterface and rigidBodyUtilities
import exudyn.graphics as graphics

import time
import numpy as np

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

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 = 0.2            #driving torque; Nm ; 0.1Nm does not surpass critical speed; 0.2Nm works
eps = 2e-3*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 = 200              #end time of simulation
steps = 40000           #number of steps

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')

#linear frequency sweep evaluated at time t, for time interval [0, t1] and frequency interval [f0,f1];
def Sweep(t, t1, f0, f1):
    k = (f1-f0)/t1
    return np.sin(2*np.pi*(f0+k*0.5*t)*t) #take care of factor 0.5 in k*0.5*t, in order to obtain correct frequencies!!!
def SweepCos(t, t1, f0, f1):
    k = (f1-f0)/t1
    return np.cos(2*np.pi*(f0+k*0.5*t)*t) #take care of factor 0.5 in k*0.5*t, in order to obtain correct frequencies!!!

# #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]
lFrame = 0.8
tFrame = 0.01
backgroundX = graphics.Cylinder(p,[lFrame,0,0],tFrame,[0.9,0.3,0.3,1],12)
backgroundY = graphics.Cylinder(p,[0,lFrame,0],tFrame,[0.3,0.9,0.3,1],12)
backgroundZ = graphics.Cylinder(p,[0,0,lFrame],tFrame,[0.3,0.3,0.9,1],12)
#mbs.AddObject(ObjectGround(referencePosition= [0,0,0], visualization=VObjectGround(graphicsData= [backgroundX, backgroundY, backgroundZ])))

#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 = graphics.Cylinder([-lRotor*0.5,0,0],[lRotor,0,0],r,[0.3,0.3,0.9,1],128)
gRotor2 = graphics.Cylinder([-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(mass=m, inertia=[Jxx,Jyyzz,Jyyzz,0,0,0], nodeNumber = n1, visualization=VObjectRigidBody2D(graphicsData=[gRotor, gRotor2]+gRotor3)))

mbs.AddSensor(SensorBody(bodyNumber=rigid, 
                         fileName='solution/runupDisplacement.txt',
                         outputVariableType=exu.OutputVariableType.Displacement))
mbs.AddSensor(SensorBody(bodyNumber=rigid, 
                         fileName='solution/runupAngularVelocity.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]))

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

simulationSettings = exu.SimulationSettings()
simulationSettings.solution.file.writePeriod = 1e-5  #output interval
simulationSettings.solution.sensors.writePeriod = 1e-5  #output interval

if isSymmetric:
    simulationSettings.solution.file.information = "Runup of Laval rotor, resonance="+str(round(fRes,3))+"Hz at 80-90 seconds"
else:
    simulationSettings.solution.file.information = "Runup of unsymmetric rotor"

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.solution.recordImagesInterval = 0.2
    SC.visualizationSettings.exportImages.saveImageFileName = "images/frame"
    SC.visualizationSettings.view0.window.renderWindowSize = [1600,1080]


SC.renderer.Start()              #start graphics visualization
SC.renderer.DoIdleTasks()    #wait for pressing SPACE bar to continue

#start solver:
mbs.SolveDynamic(simulationSettings)

#SC.renderer.DoIdleTasks()#wait for pressing 'Q' to quit
SC.renderer.Stop()               #safely close rendering window!

#evaluate final (=current) output values
u = mbs.GetNodeOutput(n1, exu.OutputVariableType.AngularVelocity)
print('omega=',u)
#print('displacement=',u[0])

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

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

    dataDisp = np.loadtxt(OutputFilePath('solution/runupDisplacement.txt'), comments='#', delimiter=',')
    dataOmega = np.loadtxt(OutputFilePath('solution/runupAngularVelocity.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((1/(2*np.pi))*dataOmega[:,1], dataDisp[:,3], 'b-') #numerical solution
    plt.xlabel("angular velocity (1/s)")
    plt.ylabel("z-displacement (m)")

    plt.figure()
    plt.plot(dataOmega[:,0], (1/(2*np.pi))*dataOmega[:,1], 'b-') #numerical solution
    plt.xlabel("time (s)")
    plt.ylabel("angular velocity (1/s)")

    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()