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pendulumFriction.py
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pendulumFriction.py
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#+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
# This is an EXUDYN example
#
# Details: Mathematical pendulum with friction;
# Remark: uses two friction models: CoordinateSpringDamper and CartesianSpringDamper
#
# Author: Johannes Gerstmayr
# Date: 2019-12-26
#
# 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 exudyn as exu
from exudyn.utilities import * #includes itemInterface and rigidBodyUtilities
import exudyn.graphics as graphics #only import if it does not conflict
from exudyn.FEM import *
import numpy as np
useGraphics = True #without test
#+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
#you can erase the following lines and all exudynTestGlobals related operations if this is not intended to be used as TestModel:
try: #only if called from test suite
from modelUnitTests import exudynTestGlobals #for globally storing test results
useGraphics = exudynTestGlobals.useGraphics
except:
class ExudynTestGlobals:
pass
exudynTestGlobals = ExudynTestGlobals()
#+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
SC = exu.SystemContainer()
mbs = SC.AddSystem()
L = 0.8 #length of arm
mass = 2.5
g = 9.81
r = 0.05 #just for graphics
d = r/2
#add ground object and mass point:
graphicsBackground = GraphicsDataRectangle(-1.2*L,-1.2*L, 1.2*L, 0.2*L, [1,1,1,1]) #for appropriate zoom
oGround = mbs.AddObject(ObjectGround(referencePosition = [0,0,0],
visualization = VObjectGround(graphicsData = [graphicsBackground])))
graphicsSphere = graphics.Sphere(point=[L/2,0,0], radius=r, color=[1.,0.2,0.2,1], nTiles = 16)
graphicsSphere2 = graphics.Sphere(point=[0,0,0], radius=r, color=graphics.color.steelblue, nTiles = 16)
graphicsLink = graphics.BrickXYZ(-L/2,-d/2,-d/2, L/2,d/2, d/2, [0.5,0.5,0.5,0.5])
inertia = InertiaCuboid(density=mass/(L*d*d), sideLengths=[L,d,d])
exu.Print("mass=",inertia.mass)
nR0 = mbs.AddNode(Rigid2D(referenceCoordinates=[L/2,0,0])) #body goes from [0,0,0] to [L,0,0]
oR0 = mbs.AddObject(RigidBody2D(nodeNumber=nR0, physicsMass = inertia.mass, physicsInertia=inertia.inertiaTensor[2][2],
visualization = VObjectRigidBody2D(graphicsData = [graphicsLink,graphicsSphere])))
#markers:
mGround0 = mbs.AddMarker(MarkerBodyPosition(bodyNumber=oGround, localPosition = [0,0,0]))
mR0 = mbs.AddMarker(MarkerBodyPosition(bodyNumber=oR0, localPosition=[-L/2,0,0]))
mTip0 = mbs.AddMarker(MarkerBodyPosition(bodyNumber=oR0, localPosition=[L/2,0,0]))
mNodeR0 = mbs.AddMarker(MarkerNodePosition(nodeNumber=nR0))
mR0COM = mbs.AddMarker(MarkerBodyRigid(bodyNumber=oR0, localPosition=[0,0,0]))
oRJ0 = mbs.AddObject(RevoluteJoint2D(markerNumbers=[mGround0,mR0]))
#
mbs.AddLoad(Force(markerNumber = mNodeR0, loadVector = [0, -mass*g, 0]))
zeroZoneFriction = 1e-3 #zero-zone for velocity in friction
fFriction = 1 #friction force (norm); acts against velocity
#user function for friction against velocity vector, including zeroZone
def UserFunctionSpringDamper(mbs, t, itemIndex, u, v, k, d, offset):
vNorm = NormL2(v)
f=[v[0],v[1],v[2]]
if abs(vNorm) < offset[0]:
f = ScalarMult(offset[1]/offset[0], f)
else:
f = ScalarMult(offset[1]/vNorm, f)
return f
mbs.AddObject(CartesianSpringDamper(markerNumbers=[mGround0, mTip0],
offset=[zeroZoneFriction, fFriction, 0],
springForceUserFunction=UserFunctionSpringDamper))
if useGraphics:
sRot1 = mbs.AddSensor(SensorBody(bodyNumber = oR0, fileName='solution/pendulumFrictionRotation0.txt',
outputVariableType=exu.OutputVariableType.Rotation))
sRot2 = mbs.AddSensor(SensorMarker(markerNumber = mR0COM, fileName='solution/pendulumFrictionRotation0marker.txt',
writeToFile = useGraphics,
outputVariableType=exu.OutputVariableType.Rotation))
sPos = mbs.AddSensor(SensorMarker(markerNumber = mR0COM, writeToFile = False,
outputVariableType=exu.OutputVariableType.Position))
mbs.Assemble()
simulationSettings = exu.SimulationSettings()
f = 4000
simulationSettings.timeIntegration.numberOfSteps = int(1*f)
simulationSettings.timeIntegration.endTime = 0.0001*f
simulationSettings.solutionSettings.solutionWritePeriod = simulationSettings.timeIntegration.endTime/5000
simulationSettings.solutionSettings.sensorsWritePeriod = simulationSettings.timeIntegration.endTime/2000
#simulationSettings.displayComputationTime = True
simulationSettings.timeIntegration.verboseMode = 1
#simulationSettings.timeIntegration.newton.useModifiedNewton = False
simulationSettings.timeIntegration.generalizedAlpha.useNewmark = True
simulationSettings.timeIntegration.generalizedAlpha.useIndex2Constraints = simulationSettings.timeIntegration.generalizedAlpha.useNewmark
simulationSettings.timeIntegration.generalizedAlpha.spectralRadius = 0.60 #0.62 is approx. the limit
simulationSettings.timeIntegration.generalizedAlpha.computeInitialAccelerations = True
simulationSettings.solutionSettings.coordinatesSolutionFileName= "solution/coordinatesSolution.txt"
simulationSettings.solutionSettings.writeSolutionToFile=False
#simulationSettings.displayStatistics = True
SC.visualizationSettings.nodes.defaultSize = 0.05
if useGraphics:
exu.StartRenderer()
mbs.WaitForUserToContinue()
mbs.SolveDynamic(simulationSettings)
p0=mbs.GetObjectOutputBody(oR0, exu.OutputVariableType.Position, localPosition=[0,0,0])
exu.Print("p0=", p0)
p0 = mbs.GetSensorValues(sPos) #obtain values from marker
exu.Print("p0=", p0, '(marker)')
u=NormL2(p0)
exu.Print('solution of pendulumFriction=',u)
exudynTestGlobals.testError = u - (0.3999999877698205) #2020-04-22: 0.3999999877698205
exudynTestGlobals.testResult = u
if useGraphics:
SC.WaitForRenderEngineStopFlag()
exu.StopRenderer() #safely close rendering window!
mbs.PlotSensor([sRot1, sRot2], components=[0,2], closeAll=True, markerStyles=['x','+'])
# import matplotlib.pyplot as plt
# import matplotlib.ticker as ticker
# data = np.loadtxt('solution/pendulumFrictionRotation0.txt', comments='#', delimiter=',')
# plt.plot(data[:,0], data[:,1], 'b-', label='rotation 0') #ccordinate 1 = rotation, scalar for ObjectRigidBody2D
# data = np.loadtxt('solution/pendulumFrictionRotation0marker.txt', comments='#', delimiter=',')
# plt.plot(data[:,0], data[:,3], 'r-', label='rotation 0') #ccordinate 3 = rotation, Z-coordinate because marker always 3D
# 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.xlabel("time (s)")
# plt.ylabel("angle (rad)")
# plt.tight_layout() #better arrangement of plot
# plt.legend()
# plt.show()