class Shaft:
"The axis of the shaft is always assumed to correspond to the X-axis"
# List of shaft segments (each segment has a different diameter)
segments = []
# The sketch
sketch = 0
#featureWindow = None
# The diagrams
diagrams = {} # map of function name against Diagram object
# Calculation of shaft
Qy = 0 # force in direction of y axis
Qz = 0 # force in direction of z axis
Mbz = 0 # bending moment around z axis
Mby = 0 # bending moment around y axis
Mtz = 0 # torsion moment around z axis
def __init__(self, doc):
self.sketch = ShaftFeature(doc)
def getLengthTo(self, index):
"Get the total length of all segments up to the given one"
result = 0.0
for i in range(index):
result += self.segments[i].length
return result
def addSegment(self, l, d, di):
#print "Adding segment: ", l, " : ", d
self.segments.append(ShaftSegment(l,d,di))
self.sketch.addSegment(l, d, di)
# We don't call equilibrium() here because the new segment has no loads defined yet
def updateSegment(self, index, length = None, diameter = None, innerdiameter = None):
oldLength = self.segments[index].length
#print "Old length of ", index, ": ", oldLength, ", new Length: ", length, " diameter: ", diameter
if length is not None:
self.segments[index].length = length
if diameter is not None:
self.segments[index].diameter = diameter
if innerdiameter is not None:
self.segments[index].innerdiameter = innerdiameter
self.sketch.updateSegment(index, oldLength, self.segments[index].length,
self.segments[index].diameter, self.segments[index].innerdiameter)
self.equilibrium()
self.updateDiagrams()
def updateLoad(self, index, loadType = None, loadSize = None, loadLocation = None):
if (loadType is not None):
self.segments[index].loadType = loadType
if (loadSize is not None):
self.segments[index].loadSize = loadSize
if (loadLocation is not None):
if (loadLocation >= 0) and (loadLocation <= self.segments[index].length):
self.segments[index].loadLocation = loadLocation
else:
# TODO: Show warning
FreeCAD.Console.PrintMessage("Load location must be inside segment\n")
#self.feature.updateForces() graphical representation of the forces
self.equilibrium()
self.updateDiagrams()
def updateEdge(self, column, start):
App.Console.PrintMessage("Not implemented yet - waiting for robust references...")
return
if self.sketchClosed is not True:
return
# Create a chamfer or fillet at the start or end edge of the segment
if start is True:
row = rowStartEdgeType
idx = 0
else:
row = rowEndEdgeType
idx = 1
edgeType = self.tableWidget.item(row, column).text().toAscii()[0].upper()
if not ((edgeType == "C") or (edgeType == "F")):
return # neither chamfer nor fillet defined
if edgeType == "C":
objName = self.doc.addObject("PartDesign::Chamfer","ChamferShaft%u" % (column * 2 + idx))
else:
objName = self.doc.addObject("PartDesign::Fillet","FilletShaft%u" % (column * 2 + idx))
if objName == "":
return
edgeName = "Edge%u" % self.getEdgeIndex(column, idx, edgeType)
self.doc.getObject(objName).Base = (self.doc.getObject("RevolutionShaft"),"[%s]" % edgeName)
# etc. etc.
def getEdgeIndex(self, column, startIdx):
# FIXME: This is impossible without robust references anchored in the sketch!!!
return
def updateDiagrams(self):
if (self.Qy == 0) or (self.Mbz == 0):
return
if self.Qy.name in self.diagrams:
# Update diagram
self.diagrams[self.Qy.name].update(self.Qy, self.getLengthTo(len(self.segments)) / 1000.0)
else:
# Create diagram
self.diagrams[self.Qy.name] = Diagram()
self.diagrams[self.Qy.name].create("Shear force", self.Qy, self.getLengthTo(len(self.segments)) / 1000.0, "x", "mm", 1000.0, "Q_y", "N", 1.0, 10)
if self.Mbz.name in self.diagrams:
# Update diagram
self.diagrams[self.Mbz.name].update(self.Mbz, self.getLengthTo(len(self.segments)) / 1000.0)
else:
# Create diagram
self.diagrams[self.Mbz.name] = Diagram()
self.diagrams[self.Mbz.name].create("Bending moment", self.Mbz, self.getLengthTo(len(self.segments)) / 1000.0, "x", "mm", 1000.0, "M_{b,z}", "Nm", 1.0, 10)
def equilibrium(self):
# Build equilibrium equations
forces = {0.0:0.0} # dictionary of (location : outer force)
moments = {0.0:0.0} # dictionary of (location : outer moment)
variableNames = [""] # names of all variables
locations = {} # dictionary of (variableName : location)
coefficientsFy = [0] # force equilibrium equation
coefficientsMbz = [0] # moment equilibrium equation
for i in range(len(self.segments)):
lType = self.segments[i].loadType
load = -1 # -1 means unknown (just for debug printing)
location = -1
if lType == "Fixed":
# Fixed segment
if i == 0:
location = 0
variableNames.append("Fy%u" % i)
coefficientsFy.append(1)
coefficientsMbz.append(0)
variableNames.append("Mz%u" % i)
coefficientsFy.append(0)
coefficientsMbz.append(1) # Force does not contribute because location is zero
elif i == len(self.segments) - 1:
location = self.getLengthTo(len(self.segments)) / 1000
variableNames.append("Fy%u" % i)
coefficientsFy.append(1)
coefficientsMbz.append(location)
variableNames.append("Mz%u" % i)
coefficientsFy.append(0)
coefficientsMbz.append(1)
else:
# TODO: Better error message
FreeCAD.Console.PrintMessage("Fixed constraint must be at beginning or end of shaft\n")
return
locations["Fy%u" % i] = location
locations["Mz%u" % i] = location
elif lType == "Static":
# Static load (currently force only)
load = self.segments[i].loadSize
location = (self.getLengthTo(i) + self.segments[i].loadLocation) / 1000 # convert to meters
coefficientsFy[0] = coefficientsFy[0] - load
forces[location] = load
coefficientsMbz[0] = coefficientsMbz[0] - load * location
moments[location] = 0
#elif lType == "None":
# # No loads on segment
FreeCAD.Console.PrintMessage("Segment: %u, type: %s, load: %f, location: %f\n" % (i, lType, load, location))
self.printEquilibrium(variableNames, coefficientsFy)
self.printEquilibrium(variableNames, coefficientsMbz)
# Build matrix and vector for linear algebra solving algorithm
try:
import numpy as np
except ImportError:
FreeCAD.Console.PrintMessage("numpy is not installed on your system\n")
raise ImportError("numpy not installed")
if (len(coefficientsFy) < 3) or (len(coefficientsMbz) < 3):
return
A = np.array([coefficientsFy[1:], coefficientsMbz[1:]])
b = np.array([coefficientsFy[0], coefficientsMbz[0]])
solution = np.linalg.solve(A, b)
# Complete dictionary of forces and moments
if variableNames[1][0] == "F":
forces[locations[variableNames[1]]] = solution[0]
else:
moments[locations[variableNames[1]]] = solution[0]
if variableNames[2][0] == "F":
forces[locations[variableNames[2]]] = solution[1]
else:
moments[locations[variableNames[2]]] = solution[1]
FreeCAD.Console.PrintMessage(forces)
FreeCAD.Console.PrintMessage(moments)
self.Qy = SegmentFunction("Qy")
self.Qy.buildFromDict("x", forces)
self.Qy.output()
self.Mbz = self.Qy.integrated().negate()
self.Mbz.addSegments(moments) # takes care of boundary conditions
self.Mbz.name = "Mbz"
self.Mbz.output()
def printEquilibrium(self, var, coeff):
# Auxiliary method for debugging purposes
for i in range(len(var)):
if i == 0:
FreeCAD.Console.PrintMessage("%f = " % coeff[i])
else:
FreeCAD.Console.PrintMessage("%f * %s" % (coeff[i], var[i]))
if (i < len(var) - 1) and (i != 0):
FreeCAD.Console.PrintMessage(" + ")
FreeCAD.Console.PrintMessage("\n")
