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lavalRotor2Dtest.rst

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lavalRotor2Dtest.py

You can view and download this file on Github: lavalRotor2Dtest.py

#+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
# This is an EXUDYN example
#
# Details:  Example with 2D laval rotor; shows backward and forward whirl effects using
#           Includes user load and Sweep
#
# Author:   Johannes Gerstmayr
# Date:     2019-12-03
#
# 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 length
mass = 1.6              #mass in kg
r = 0.5                 #radius for disc mass distribution
spring = 4000           #stiffness of (all/both) springs in rotor in N/m
omega0=np.sqrt(spring/mass) #linear system

zeta = 0.001*5
damper = 2*omega0*zeta*mass  #damping constant in N/(m/s)

f0 = 0.*omega0/(2*np.pi)
f1 = 1.*omega0/(2*np.pi)

torque = 0*1 #Nm
eps = 1e-2 #excentricity in y-direction
omegaInitial = 0.5*omega0

print('resonance frequency = '+str(omega0/2/np.pi)+'Hz')
tEnd = 50     #end time of simulation
steps = 10000  #number of steps


#linear frequency sweep in 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!!!

#user function for load
def userLoad(mbs, 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 userLoadBWx(mbs, t, load):
    return load*np.sin(omegaInitial*t)
def userLoadBWy(mbs, t, load):
    return -load*np.cos(omegaInitial*t) #negative sign: FW, positive sign: BW

#node for Rigid2D body: px, py, phi:
n1=mbs.AddNode(Rigid2D(referenceCoordinates = [0,eps,0],
                       initialCoordinates=[0,0,0],
                       initialVelocities=[0,0,omegaInitial]))

#ground node
nGround=mbs.AddNode(NodePointGround(referenceCoordinates = [0,0,0]))

#add mass point (this is a 3D object with 3 coordinates):
gRotor = GraphicsDataRectangle(-r*0.5,-r*0.5,r*0.5,r*0.5,[1,0,0,1])
rigid2D = mbs.AddObject(RigidBody2D(physicsMass=mass, physicsInertia=mass*r**2, nodeNumber = n1, visualization=VObjectRigidBody2D(graphicsData=[gRotor])))

#marker for ground (=fixed):
groundMarker=mbs.AddMarker(MarkerNodeCoordinate(nodeNumber= nGround, coordinate = 0))

#marker for rotor axis and support:
rotorAxisMarker =mbs.AddMarker(MarkerBodyPosition(bodyNumber=rigid2D, localPosition=[0,-eps,0]))
groundBody= mbs.AddObject(ObjectGround(referencePosition=[0,0,0]))
rotorSupportMarker=mbs.AddMarker(MarkerBodyPosition(bodyNumber=groundBody, localPosition=[0,0,0]))

#marker for springDamper for first (x-)coordinate:
coordXMarker = mbs.AddMarker(MarkerNodeCoordinate(nodeNumber= n1, coordinate = 0))
coordYMarker = mbs.AddMarker(MarkerNodeCoordinate(nodeNumber= n1, coordinate = 1))
coordPhiMarker = mbs.AddMarker(MarkerNodeCoordinate(nodeNumber= n1, coordinate = 2))

mbs.AddObject(CartesianSpringDamper(markerNumbers=[rotorSupportMarker, rotorAxisMarker], stiffness=[spring,spring,0], damping=[damper, damper,0]))

#add load:
mbs.AddLoad(LoadCoordinate(markerNumber = coordYMarker, load = 0, loadUserFunction=userLoad))
mbs.AddLoad(LoadCoordinate(markerNumber = coordPhiMarker, load = torque))#, loadUserFunction=userLoad))

mbs.AddLoad(LoadCoordinate(markerNumber = coordXMarker, load = amp, loadUserFunction=userLoadBWx))
mbs.AddLoad(LoadCoordinate(markerNumber = coordYMarker, load = amp, loadUserFunction=userLoadBWy))

print(mbs)
mbs.Assemble()

simulationSettings = exu.SimulationSettings()
simulationSettings.solutionSettings.solutionWritePeriod = 1e-5  #output interval
simulationSettings.timeIntegration.numberOfSteps = steps
simulationSettings.timeIntegration.endTime = tEnd

simulationSettings.timeIntegration.generalizedAlpha.spectralRadius = 1

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

#start solver:
mbs.SolveDynamic(simulationSettings)

exu.StopRenderer()               #safely close rendering window!

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

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

if True:
    data = np.loadtxt('coordinatesSolution.txt', comments='#', delimiter=',')
    n=steps
    #plt.plot(data[:,0], data[:,6], 'r-') #numerical solution
    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()