rollingCoinTest.py

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

  1#+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
  2# This is an EXUDYN example
  3#
  4# Details:  Rolling coin example;
  5#           examine example of Rill, Schaeffer, Grundlagen und Methodik der Mehrkörpersimulation, 2010, page 59
  6#           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
  7#           mass and inertia do not influence the results, as long as mass and inertia of a infinitely small ring are used
  8#           gravity is set to [0,0,-9.81m/s^2] and the radius is 0.01m
  9#
 10# Author:   Johannes Gerstmayr
 11# Date:     2020-06-19
 12#
 13# 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.
 14#
 15#+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 16
 17import exudyn as exu
 18from exudyn.utilities import *
 19
 20import numpy as np
 21
 22useGraphics = True #without test
 23#+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 24#you can erase the following lines and all exudynTestGlobals related operations if this is not intended to be used as TestModel:
 25try: #only if called from test suite
 26    from modelUnitTests import exudynTestGlobals #for globally storing test results
 27    useGraphics = exudynTestGlobals.useGraphics
 28except:
 29    class ExudynTestGlobals:
 30        pass
 31    exudynTestGlobals = ExudynTestGlobals()
 32#+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 33
 34SC = exu.SystemContainer()
 35mbs = SC.AddSystem()
 36
 37phi0 = 1./180.*np.pi#initial nick angle of disc, 1 degree
 38g = [0,0,-9.81]     #gravity in m/s^2
 39m = 1               #mass in kg
 40r = 0.01            #radius of disc in m
 41w = 0.001           #width of disc in m, just for drawing
 42p0 = [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]
 43initialRotation = RotationMatrixY(phi0)
 44
 45omega0 = [0,0,1800/180*np.pi]                   #initial angular velocity around z-axis
 46v0 = Skew(omega0) @ initialRotation @ [0,0,r]   #initial angular velocity of center point
 47#v0 = [0,0,0]                                   #initial translational velocity
 48#print("v0=",v0)#," = ", [0,10*np.pi*r*np.sin(phi0),0])
 49
 50#inertia for infinitely small ring:
 51inertiaRing = RigidBodyInertia(mass=1, inertiaTensor= np.diag([0.5*m*r**2, 0.25*m*r**2, 0.25*m*r**2]))
 52#print(inertiaRing)
 53
 54#additional graphics for visualization of rotation:
 55graphicsBody = GraphicsDataOrthoCubePoint(centerPoint=[0,0,0],size=[w*1.1,0.7*r,0.7*r], color=color4lightred)
 56
 57[n0,b0]=AddRigidBody(mainSys = mbs,
 58                     inertia = inertiaRing,
 59                     nodeType = str(exu.NodeType.RotationEulerParameters),
 60                     position = p0,
 61                     rotationMatrix = initialRotation, #np.diag([1,1,1]),
 62                     angularVelocity = omega0,
 63                     velocity=v0,
 64                     gravity = g,
 65                     graphicsDataList = [graphicsBody])
 66
 67#ground body and marker
 68gGround = GraphicsDataOrthoCubePoint(centerPoint=[0,0,-0.001],size=[0.12,0.12,0.002], color=color4lightgrey)
 69oGround = mbs.AddObject(ObjectGround(visualization=VObjectGround(graphicsData=[gGround])))
 70markerGround = mbs.AddMarker(MarkerBodyRigid(bodyNumber=oGround, localPosition=[0,0,0]))
 71
 72#markers for rigid body:
 73markerBody0J0 = mbs.AddMarker(MarkerBodyRigid(bodyNumber=b0, localPosition=[0,0,0]))
 74
 75#rolling disc:
 76oRolling=mbs.AddObject(ObjectJointRollingDisc(markerNumbers=[markerGround, markerBody0J0],
 77                                              constrainedAxes=[1,1,1], discRadius=r,
 78                                              visualization=VObjectJointRollingDisc(discWidth=w,color=color4blue)))
 79
 80
 81#sensor for trace of contact point:
 82if useGraphics:
 83    sTrail=mbs.AddSensor(SensorObject(objectNumber=oRolling, storeInternal=True,#fileName='solution/rollingDiscTrail.txt',
 84                               outputVariableType = exu.OutputVariableType.Position))
 85
 86    sVel=mbs.AddSensor(SensorObject(objectNumber=oRolling, storeInternal=True,#fileName='solution/rollingDiscTrailVel.txt',
 87                               outputVariableType = exu.OutputVariableType.Velocity))
 88
 89
 90
 91mbs.Assemble()
 92
 93simulationSettings = exu.SimulationSettings() #takes currently set values or default values
 94
 95tEnd = 0.5
 96if useGraphics:
 97    tEnd = 0.5
 98
 99h=0.0005 #no visual differences for step sizes smaller than 0.0005
100
101simulationSettings.timeIntegration.numberOfSteps = int(tEnd/h)
102simulationSettings.timeIntegration.endTime = tEnd
103#simulationSettings.solutionSettings.solutionWritePeriod = 0.01
104simulationSettings.solutionSettings.sensorsWritePeriod = 0.0005
105#simulationSettings.timeIntegration.verboseMode = 1
106simulationSettings.solutionSettings.writeSolutionToFile = False
107
108simulationSettings.timeIntegration.generalizedAlpha.useIndex2Constraints = True
109simulationSettings.timeIntegration.generalizedAlpha.useNewmark = True
110simulationSettings.timeIntegration.generalizedAlpha.spectralRadius = 0.5
111simulationSettings.timeIntegration.generalizedAlpha.computeInitialAccelerations=True
112
113
114SC.visualizationSettings.nodes.show = True
115SC.visualizationSettings.nodes.drawNodesAsPoint  = False
116SC.visualizationSettings.nodes.showBasis = True
117SC.visualizationSettings.nodes.basisSize = 0.015
118
119if useGraphics:
120    exu.StartRenderer()
121    mbs.WaitForUserToContinue()
122
123mbs.SolveDynamic(simulationSettings)
124
125p0=mbs.GetObjectOutput(oRolling, exu.OutputVariableType.Position)
126exu.Print('solution of rollingCoinTest=',p0[0]) #use x-coordinate
127
128exudynTestGlobals.testError = p0[0] - (0.002004099927340136) #2020-06-20: 0.002004099927340136; 2020-06-19: 0.002004099760845168 #4s looks visually similar to Rill, but not exactly ...
129exudynTestGlobals.testResult = p0[0]
130
131
132if useGraphics:
133    SC.WaitForRenderEngineStopFlag()
134    exu.StopRenderer() #safely close rendering window!
135
136    ##++++++++++++++++++++++++++++++++++++++++++++++q+++++++
137    #plot results
138    if True:
139
140
141        mbs.PlotSensor(sTrail, componentsX=[0],components=[1], closeAll=True, title='wheel trail')
142
143
144        # import matplotlib.pyplot as plt
145        # import matplotlib.ticker as ticker
146
147        # if True:
148        #     data = np.loadtxt('solution/rollingDiscTrail.txt', comments='#', delimiter=',')
149        #     plt.plot(data[:,1], data[:,2], 'r-',label='contact point trail') #x/y coordinates of trail
150        # else:
151        #     #show trail velocity computed numerically and from sensor:
152        #     data = np.loadtxt('solution/rollingDiscTrail.txt', comments='#', delimiter=',')
153
154        #     nData = len(data)
155        #     vVec = np.zeros((nData,2))
156        #     dt = data[1,0]-data[0,0]
157        #     for i in range(nData-1):
158        #         vVec[i+1,0:2] = 1/dt*(data[i+1,1:3]-data[i,1:3])
159
160        #     plt.plot(data[:,0], vVec[:,0], 'r-',label='contact point vel x')
161        #     plt.plot(data[:,0], vVec[:,1], 'k-',label='contact point vel y')
162        #     plt.plot(data[:,0], (vVec[:,0]**2+vVec[:,1]**2)**0.5, 'g-',label='|contact point vel|')
163
164        #     trailVel = np.loadtxt('solution/rollingDiscTrailVel.txt', comments='#', delimiter=',')
165        #     plt.plot(data[:,0], trailVel[:,1], 'r--',label='trail vel x')
166        #     plt.plot(data[:,0], trailVel[:,2], 'k--',label='trail vel y')
167        #     plt.plot(data[:,0], trailVel[:,3], 'y--',label='trail vel z')
168        #     plt.plot(data[:,0], (trailVel[:,1]**2+trailVel[:,2]**2)**0.5, 'b--',label='|trail vel|')
169
170        # ax=plt.gca() # get current axes
171        # ax.grid(True, 'major', 'both')
172        # ax.xaxis.set_major_locator(ticker.MaxNLocator(10)) #use maximum of 8 ticks on y-axis
173        # ax.yaxis.set_major_locator(ticker.MaxNLocator(10)) #use maximum of 8 ticks on y-axis
174        # plt.tight_layout()
175        # plt.legend()
176        # plt.show()