You can view and download this file on Github: rollingCoinTest.py
#+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
# This is an EXUDYN example
#
# Details: Rolling coin example;
# examine example of Rill, Schaeffer, Grundlagen und Methodik der Mehrkörpersimulation, 2010, page 59
# Note that in comparison to the literature, we use the local x-axis for the local axis of the coin, z is the normal to the plane
# mass and inertia do not influence the results, as long as mass and inertia of a infinitely small ring are used
# gravity is set to [0,0,-9.81m/s^2] and the radius is 0.01m
#
# Author: Johannes Gerstmayr
# Date: 2020-06-19
#
# 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
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()
phi0 = 1./180.*np.pi#initial nick angle of disc, 1 degree
g = [0,0,-9.81] #gravity in m/s^2
m = 1 #mass in kg
r = 0.01 #radius of disc in m
w = 0.001 #width of disc in m, just for drawing
p0 = [r*np.sin(phi0),0,r*np.cos(phi0)] #origin of disc center point at reference, such that initial contact point is at [0,0,0]
initialRotation = RotationMatrixY(phi0)
omega0 = [0,0,1800/180*np.pi] #initial angular velocity around z-axis
v0 = Skew(omega0) @ initialRotation @ [0,0,r] #initial angular velocity of center point
#v0 = [0,0,0] #initial translational velocity
#print("v0=",v0)#," = ", [0,10*np.pi*r*np.sin(phi0),0])
#inertia for infinitely small ring:
inertiaRing = RigidBodyInertia(mass=1, inertiaTensor= np.diag([0.5*m*r**2, 0.25*m*r**2, 0.25*m*r**2]))
#print(inertiaRing)
#additional graphics for visualization of rotation:
graphicsBody = graphics.Brick(centerPoint=[0,0,0],size=[w*1.1,0.7*r,0.7*r], color=graphics.color.lightred)
[n0,b0]=AddRigidBody(mainSys = mbs,
inertia = inertiaRing,
nodeType = str(exu.NodeType.RotationEulerParameters),
position = p0,
rotationMatrix = initialRotation, #np.diag([1,1,1]),
angularVelocity = omega0,
velocity=v0,
gravity = g,
graphicsDataList = [graphicsBody])
#ground body and marker
gGround = graphics.Brick(centerPoint=[0,0,-0.001],size=[0.12,0.12,0.002], color=graphics.color.lightgrey)
oGround = mbs.AddObject(ObjectGround(visualization=VObjectGround(graphicsData=[gGround])))
markerGround = mbs.AddMarker(MarkerBodyRigid(bodyNumber=oGround, localPosition=[0,0,0]))
#markers for rigid body:
markerBody0J0 = mbs.AddMarker(MarkerBodyRigid(bodyNumber=b0, localPosition=[0,0,0]))
#rolling disc:
oRolling=mbs.AddObject(ObjectJointRollingDisc(markerNumbers=[markerGround, markerBody0J0],
constrainedAxes=[1,1,1], discRadius=r,
visualization=VObjectJointRollingDisc(discWidth=w,color=graphics.color.blue)))
sForce=mbs.AddSensor(SensorObject(objectNumber=oRolling, storeInternal=True,#fileName='solution/rollingDiscTrail.txt',
outputVariableType = exu.OutputVariableType.ForceLocal))
#sensor for trace of contact point:
if useGraphics:
sTrail=mbs.AddSensor(SensorObject(objectNumber=oRolling, storeInternal=True,#fileName='solution/rollingDiscTrail.txt',
outputVariableType = exu.OutputVariableType.Position))
sVel=mbs.AddSensor(SensorObject(objectNumber=oRolling, storeInternal=True,#fileName='solution/rollingDiscTrailVel.txt',
outputVariableType = exu.OutputVariableType.Velocity))
mbs.Assemble()
simulationSettings = exu.SimulationSettings() #takes currently set values or default values
tEnd = 0.5
if useGraphics:
tEnd = 0.5
h=0.0005 #no visual differences for step sizes smaller than 0.0005
simulationSettings.timeIntegration.numberOfSteps = int(tEnd/h)
simulationSettings.timeIntegration.endTime = tEnd
#simulationSettings.solutionSettings.solutionWritePeriod = 0.01
simulationSettings.solutionSettings.sensorsWritePeriod = 0.0005
simulationSettings.solutionSettings.writeSolutionToFile = False
simulationSettings.timeIntegration.verboseMode = 1
# simulationSettings.displayStatistics = True
simulationSettings.timeIntegration.generalizedAlpha.useIndex2Constraints = True
simulationSettings.timeIntegration.generalizedAlpha.useNewmark = True
simulationSettings.timeIntegration.generalizedAlpha.spectralRadius = 0.5
simulationSettings.timeIntegration.generalizedAlpha.computeInitialAccelerations=True
SC.visualizationSettings.nodes.show = True
SC.visualizationSettings.nodes.drawNodesAsPoint = False
SC.visualizationSettings.nodes.showBasis = True
SC.visualizationSettings.nodes.basisSize = 0.015
if useGraphics:
exu.StartRenderer()
mbs.WaitForUserToContinue()
mbs.SolveDynamic(simulationSettings)
p0=mbs.GetObjectOutput(oRolling, exu.OutputVariableType.Position)
force=mbs.GetSensorValues(sForce)
exu.Print('force in rollingCoinTest=',force) #use x-coordinate
u = p0[0] + 0.1*(force[0]+force[1]+force[2])
exu.Print('solution of rollingCoinTest=',u) #use x-coordinate
exudynTestGlobals.testError = u - (1.0634381189385853) #2024-04-29: added force #2020-06-20: 0.002004099927340136; 2020-06-19: 0.002004099760845168 #4s looks visually similar to Rill, but not exactly ...
exudynTestGlobals.testResult = u
if useGraphics:
SC.WaitForRenderEngineStopFlag()
exu.StopRenderer() #safely close rendering window!
##++++++++++++++++++++++++++++++++++++++++++++++q+++++++
#plot results
if True:
mbs.PlotSensor(sTrail, componentsX=[0],components=[1], closeAll=True, title='wheel trail')
# import matplotlib.pyplot as plt
# import matplotlib.ticker as ticker
# if True:
# data = np.loadtxt('solution/rollingDiscTrail.txt', comments='#', delimiter=',')
# plt.plot(data[:,1], data[:,2], 'r-',label='contact point trail') #x/y coordinates of trail
# else:
# #show trail velocity computed numerically and from sensor:
# data = np.loadtxt('solution/rollingDiscTrail.txt', comments='#', delimiter=',')
# nData = len(data)
# vVec = np.zeros((nData,2))
# dt = data[1,0]-data[0,0]
# for i in range(nData-1):
# vVec[i+1,0:2] = 1/dt*(data[i+1,1:3]-data[i,1:3])
# plt.plot(data[:,0], vVec[:,0], 'r-',label='contact point vel x')
# plt.plot(data[:,0], vVec[:,1], 'k-',label='contact point vel y')
# plt.plot(data[:,0], (vVec[:,0]**2+vVec[:,1]**2)**0.5, 'g-',label='|contact point vel|')
# trailVel = np.loadtxt('solution/rollingDiscTrailVel.txt', comments='#', delimiter=',')
# plt.plot(data[:,0], trailVel[:,1], 'r--',label='trail vel x')
# plt.plot(data[:,0], trailVel[:,2], 'k--',label='trail vel y')
# plt.plot(data[:,0], trailVel[:,3], 'y--',label='trail vel z')
# plt.plot(data[:,0], (trailVel[:,1]**2+trailVel[:,2]**2)**0.5, 'b--',label='|trail vel|')
# ax=plt.gca() # get current axes
# ax.grid(True, 'major', 'both')
# ax.xaxis.set_major_locator(ticker.MaxNLocator(10)) #use maximum of 8 ticks on y-axis
# ax.yaxis.set_major_locator(ticker.MaxNLocator(10)) #use maximum of 8 ticks on y-axis
# plt.tight_layout()
# plt.legend()
# plt.show()