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# * Copyright (c) 2012 Jan Rheinländer <jrheinlaender@users.sourceforge.net> *
# * *
# * This file is part of the FreeCAD CAx development system. *
# * *
# * This library is free software; you can redistribute it and/or *
# * modify it under the terms of the GNU Library General Public *
# * License as published by the Free Software Foundation; either *
# * version 2 of the License, or (at your option) any later version. *
# * *
# * This library is distributed in the hope that it will be useful, *
# * but WITHOUT ANY WARRANTY; without even the implied warranty of *
# * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the *
# * GNU Library General Public License for more details. *
# * *
# * You should have received a copy of the GNU Library General Public *
# * License along with this library; see the file COPYING.LIB. If not, *
# * write to the Free Software Foundation, Inc., 59 Temple Place, *
# * Suite 330, Boston, MA 02111-1307, USA *
# * *
# ******************************************************************************/
import FreeCAD, FreeCADGui
from .SegmentFunction import SegmentFunction, IntervalFunction, StressFunction, TranslationFunction
from .ShaftFeature import ShaftFeature
from .ShaftDiagram import Diagram
import math
class ShaftSegment:
def __init__(self, l, d, di):
self.length = l
self.diameter = d
self.innerdiameter = di
self.constraintType = "None"
self.constraint = None
class Shaft:
"The axis of the shaft is always assumed to correspond to the X-axis"
# Names (note Qy corresponds with Mz, and Qz with My)
Fstr = ["Nx", "Qy", "Qz"] # Forces
Mstr = ["Mx", "Mz", "My"] # Moments
wstr = ["", "wy", "wz"] # Translations
sigmaNstr = ["sigmax", "sigmay", "sigmaz"] # Normal/shear stresses
sigmaBstr = ["taut", "sigmabz", "sigmaby"] # Torsion/bending stresses
# For diagram labeling
Qstrings = (
("Normal force [x]", "x", "mm", "N_x", "N"),
("Shear force [y]", "x", "mm", "Q_y", "N"),
("Shear force [z]", "x", "mm", "Q_z", "N"),
)
Mstrings = (
("Torque [x]", "x", "mm", "M_t", "Nm"),
("Bending moment [z]", "x", "mm", "M_{b,z}", "Nm"),
("Bending moment [y]", "x", "mm", "M_{b,y}", "Nm"),
)
wstrings = (
("", "", "", "", ""),
("Translation [y]", "x", "mm", "w_y", "mm"),
("Translation [z]", "x", "mm", "w_z", "mm"),
)
sigmaNstrings = (
("Normal stress [x]", "x", "mm", "\\sigma_x", "N/mm²"),
("Shear stress [y]", "x", "mm", "\\sigma_y", "N/mm²"),
("Shear stress [z]", "x", "mm", "\\sigma_z", "N/mm²"),
)
sigmaBstrings = (
("Torque stress [x]", "x", "mm", "\\tau_t", "N/mm²"),
("Bending stress [z]", "x", "mm", "\\sigma_{b,z}", "N/mm²"),
("Bending stress [y]", "x", "mm", "\\sigma_{b,y}", "N/mm²"),
)
def __init__(self, parent):
self.parent = parent
self.doc = parent.doc
self.feature = ShaftFeature(self.doc)
# List of shaft segments (each segment has a different diameter)
self.segments = []
# The diagrams
self.diagrams = {} # map of function name against Diagram object
# Calculation of shaft
self.F = [None, None, None] # force in direction of [x,y,z]-axis
self.M = [None, None, None] # bending moment around [x,z,y]-axis
self.w = [None, None, None] # Shaft translation due to bending
self.sigmaN = [
None,
None,
None,
] # normal stress in direction of x-axis, shear stress in direction of [y,z]-axis
self.sigmaB = [
None,
None,
None,
] # # torque stress around x-axis, maximum bending stress in direction of [y,z]-axis
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):
self.segments.append(ShaftSegment(l, d, di))
self.feature.addSegment(l, d, di)
# We don't call equilibrium() here because the new segment has no constraints defined yet
# Fix face reference of fixed segment if it is the last one
for i in range(1, len(self.segments)):
if self.segments[i].constraintType != "Fixed":
continue
if i == len(self.segments) - 1:
self.segments[index].constraint.References = [
(self.feature.feature, "Face%u" % (2 * (index + 1) + 1))
]
else:
# Remove reference since it is now in the middle of the shaft (which is not allowed)
self.segments[index].constraint.References = [(None, "")]
def updateSegment(self, index, length=None, diameter=None, innerdiameter=None):
oldLength = self.segments[index].length
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.feature.updateSegment(
index,
oldLength,
self.segments[index].length,
self.segments[index].diameter,
self.segments[index].innerdiameter,
)
self.equilibrium()
self.updateDiagrams()
def updateConstraint(self, index, constraintType):
if constraintType is not None:
# Did the constraint type change?
if (self.segments[index].constraintType != "None") and (
self.segments[index].constraintType != constraintType
):
self.doc.removeObject(self.segments[index].constraint.Name)
self.segments[index].constraint = None
self.segments[index].constraintType = constraintType
# Create constraint if it does not exist yet or has changed
if self.segments[index].constraint is None:
if constraintType == "Force":
# TODO: Create a reference point and put the force onto it
constraint = self.doc.addObject("Fem::ConstraintForce", "ShaftConstraintForce")
constraint.Force = 1000.0
self.segments[index].constraint = constraint
elif constraintType == "Fixed":
# TODO: Use robust reference as soon as it is available for the face
constraint = self.doc.addObject("Fem::ConstraintFixed", "ShaftConstraintFixed")
if index == 0:
constraint.References = [(self.feature.feature, "Face1")]
elif index == len(self.segments) - 1:
constraint.References = [
(self.feature.feature, "Face%u" % (2 * (index + 1) + 1))
]
self.segments[index].constraint = constraint
elif constraintType == "Bearing":
# TODO: Use robust reference as soon as it is available for the cylindrical face reference
constraint = self.doc.addObject(
"Fem::ConstraintBearing", "ShaftConstraintBearing"
)
constraint.References = [(self.feature.feature, "Face%u" % (2 * (index + 1)))]
constraint.AxialFree = True
self.segments[index].constraint = constraint
elif constraintType == "Pulley":
constraint = self.doc.addObject(
"Fem::ConstraintPulley", "ShaftConstraintPulley"
)
constraint.References = [(self.feature.feature, "Face%u" % (2 * (index + 1)))]
self.segments[index].constraint = constraint
elif constraintType == "Gear":
constraint = self.doc.addObject("Fem::ConstraintGear", "ShaftConstraintGear")
constraint.References = [(self.feature.feature, "Face%u" % (2 * (index + 1)))]
self.segments[index].constraint = constraint
self.equilibrium()
self.updateDiagrams()
def editConstraint(self, index):
if self.segments[index].constraint is not None:
FreeCADGui.activeDocument().setEdit(self.segments[index].constraint.Name)
def getConstraint(self, index):
return self.segments[index].constraint
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()[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):
for ax in range(3):
if self.F[ax] is not None:
if self.F[ax].name in self.diagrams:
self.diagrams[self.F[ax].name].update(
self.F[ax], self.getLengthTo(len(self.segments)) / 1000.0
)
if self.M[ax] is not None:
if self.M[ax].name in self.diagrams:
self.diagrams[self.M[ax].name].update(
self.M[ax], self.getLengthTo(len(self.segments)) / 1000.0
)
if self.w[ax] is not None:
if self.w[ax].name in self.diagrams:
self.diagrams[self.w[ax].name].update(
self.w[ax], self.getLengthTo(len(self.segments)) / 1000.0
)
if self.sigmaN[ax] is not None:
if self.sigmaN[ax].name in self.diagrams:
self.diagrams[self.sigmaN[ax].name].update(
self.sigmaN[ax], self.getLengthTo(len(self.segments)) / 1000.0
)
if self.sigmaB[ax] is not None:
if self.sigmaB[ax].name in self.diagrams:
self.diagrams[self.sigmaB[ax].name].update(
self.sigmaB[ax], self.getLengthTo(len(self.segments)) / 1000.0
)
def showDiagram(self, which):
if which in self.Fstr:
ax = self.Fstr.index(which)
text = self.Qstrings[ax]
if self.F[ax] is None:
# No data
return
if self.F[ax].name in self.diagrams:
# Diagram is already open, close it again
self.diagrams[self.F[ax].name].close()
del self.diagrams[self.F[ax].name]
return
self.diagrams[self.F[ax].name] = Diagram()
self.diagrams[self.F[ax].name].create(
text[0],
self.F[ax],
self.getLengthTo(len(self.segments)) / 1000.0,
text[1],
text[2],
1000.0,
text[3],
text[4],
1.0,
10,
)
elif which in self.Mstr:
ax = self.Mstr.index(which)
text = self.Mstrings[ax]
if self.M[ax] is None:
# No data
return
if self.M[ax].name in self.diagrams:
# Diagram is already open, close it again
self.diagrams[self.M[ax].name].close()
del self.diagrams[self.M[ax].name]
return
self.diagrams[self.M[ax].name] = Diagram()
self.diagrams[self.M[ax].name].create(
text[0],
self.M[ax],
self.getLengthTo(len(self.segments)) / 1000.0,
text[1],
text[2],
1000.0,
text[3],
text[4],
1.0,
20,
)
elif which in self.wstr:
ax = self.wstr.index(which)
text = self.wstrings[ax]
if self.w[ax] is None:
# No data
return
if self.w[ax].name in self.diagrams:
# Diagram is already open, close it again
self.diagrams[self.w[ax].name].close()
del self.diagrams[self.w[ax].name]
return
self.diagrams[self.w[ax].name] = Diagram()
self.diagrams[self.w[ax].name].create(
text[0],
self.w[ax],
self.getLengthTo(len(self.segments)) / 1000.0,
text[1],
text[2],
1000.0,
text[3],
text[4],
1000.0,
30,
)
elif which in self.sigmaNstr:
ax = self.sigmaNstr.index(which)
text = self.sigmaNstrings[ax]
if self.sigmaN[ax] is None:
# No data
return
if self.sigmaN[ax].name in self.diagrams:
# Diagram is already open, close it again
self.diagrams[self.sigmaN[ax].name].close()
del self.diagrams[self.sigmaN[ax].name]
return
self.diagrams[self.sigmaN[ax].name] = Diagram()
self.diagrams[self.sigmaN[ax].name].create(
text[0],
self.sigmaN[ax],
self.getLengthTo(len(self.segments)) / 1000.0,
text[1],
text[2],
1000.0,
text[3],
text[4],
1.0e-6,
10,
)
elif which in self.sigmaBstr:
ax = self.sigmaBstr.index(which)
text = self.sigmaBstrings[ax]
if self.sigmaB[ax] is None:
# No data
return
if self.sigmaB[ax].name in self.diagrams:
# Diagram is already open, close it again
self.diagrams[self.sigmaB[ax].name].close()
del self.diagrams[self.sigmaB[ax].name]
return
self.diagrams[self.sigmaB[ax].name] = Diagram()
self.diagrams[self.sigmaB[ax].name].create(
text[0],
self.sigmaB[ax],
self.getLengthTo(len(self.segments)) / 1000.0,
text[1],
text[2],
1000.0,
text[3],
text[4],
1.0e-6,
20,
)
def addTo(self, dict, location, value):
if location not in dict:
dict[location] = value
else:
dict[location] += value
def equilibrium(self):
# Build equilibrium equations
try:
import numpy as np
except ImportError:
FreeCAD.Console.PrintMessage("numpy is not installed on your system\n")
raise ImportError("numpy not installed")
# Initialization of structures. All three axes are handled separately so everything is 3-fold
# dictionaries of (location : outer force/moment) with reverse sign, which means that the segment functions for the section force and section moment
# created from them will have signs as by the convention in
# http://www.umwelt-campus.de/ucb/fileadmin/users/90_t.preussler/dokumente/Skripte/TEMECH/TMI/Ebene_Balkenstatik.pdf (page 10)
# (see also example on page 19)
forces = [{0.0: 0.0}, {0.0: 0.0}, {0.0: 0.0}]
moments = [{0.0: 0.0}, {0.0: 0.0}, {0.0: 0.0}]
# Boundary conditions for shaft bending line
tangents = [[], [], []] # Tangents to shaft bending line
translations = [[], [], []] # Shaft displacement
# Variable names, e.g. Fx, Mz. Because the system must be exactly determined, not more than two independent variables for each
# force/moment per axis are possible (if there are more no solution is calculated)
variableNames = [[""], [""], [""]]
# # dictionary of (variableName : location) giving the x-coordinate at which the force/moment represented by the variable acts on the shaft
locations = {}
# Coefficients of the equilibrium equations in the form a = b * F1 + c * F2 and d = e * M1 + f * M2
# LHS (variables a1, a2, a3, d3) initialized to zero
coefficientsF = [[0], [0], [0]]
coefficientsM = [[0], [0], [0]]
for i in range(len(self.segments)):
cType = self.segments[i].constraintType
constraint = self.segments[i].constraint
if cType == "Fixed":
# Fixed segment
if i == 0:
# At beginning of shaft
location = 0
elif i == len(self.segments) - 1:
# At end of shaft
location = self.getLengthTo(len(self.segments)) / 1000.0 # convert to meters
else:
# TODO: Better error message
FreeCAD.Console.PrintMessage(
"Fixed constraint must be at beginning or end of shaft\n"
)
return
for ax in range(3):
# Create a new reaction force
variableNames[ax].append("%s%u" % (self.Fstr[ax], i))
coefficientsF[ax].append(1)
# Register location of reaction force
locations["%s%u" % (self.Fstr[ax], i)] = location
# Boundary conditions for the translations
tangents[ax].append((location, 0.0))
translations[ax].append((location, 0.0))
coefficientsM[0].append(0) # Reaction force contributes no moment around x axis
coefficientsM[1].append(
location
) # Reaction force contributes a positive moment around z axis
coefficientsM[2].append(
-location
) # Reaction force contributes a negative moment around y axis
for ax in range(3):
# Create a new reaction moment
variableNames[ax].append("%s%u" % (self.Mstr[ax], i))
coefficientsF[ax].append(0)
coefficientsM[ax].append(1)
locations["%s%u" % (self.Mstr[ax], i)] = location
elif cType == "Force":
# Static force (currently force on midpoint of segment only)
force = constraint.DirectionVector.multiply(constraint.Force)
# TODO: Extract value of the location from geometry
location = (self.getLengthTo(i) + self.segments[i].length / 2.0) / 1000.0
# The force itself
for ax in range(3):
if abs(force[ax]) > 0.0:
coefficientsF[ax][0] = (
coefficientsF[ax][0] - force[ax]
) # neg. because this coefficient is on the LHS of the equilibrium equation
self.addTo(
forces[ax], location, -force[ax]
) # neg. to fulfill the convention mentioned above
# Moments created by the force (by definition no moment is created by the force in x-direction)
if abs(force[1]) > 0.0:
coefficientsM[1][0] = (
coefficientsM[1][0] - force[1] * location
) # moment around z-axis
self.addTo(moments[1], location, 0)
if abs(force[2]) > 0.0:
coefficientsM[2][0] = (
coefficientsM[2][0] + force[2] * location
) # moment around y-axis
self.addTo(moments[2], location, 0) # No outer moment acts here!
elif cType == "Bearing":
location = (
constraint.BasePoint.x / 1000.0
) # TODO: This assumes that the shaft feature starts with the first segment at (0,0,0) and its axis corresponds to the x-axis
# Bearing reaction forces. TODO: the bearing is assumed to not induce any reaction moments
start = 0 if constraint.AxialFree == False else 1
for ax in range(start, 3):
variableNames[ax].append("%s%u" % (self.Fstr[ax], i))
coefficientsF[ax].append(1)
locations["%s%u" % (self.Fstr[ax], i)] = location
# Boundary condition
translations[ax].append((location, 0.0))
if constraint.AxialFree == False:
coefficientsM[0].append(0) # Reaction force contributes no moment around x axis
coefficientsM[1].append(
location
) # Reaction force contributes a positive moment around z axis
coefficientsM[2].append(
-location
) # Reaction force contributes a negative moment around y axis
elif cType == "Gear":
force = constraint.DirectionVector.multiply(constraint.Force)
location = constraint.BasePoint.x / 1000.0
lever = [
0,
constraint.Diameter
/ 2.0
/ 1000.0
* math.sin(constraint.ForceAngle / 180.0 * math.pi),
constraint.Diameter
/ 2.0
/ 1000.0
* math.cos(constraint.ForceAngle / 180.0 * math.pi),
]
# Effect of the gear force
for ax in range(3):
if abs(force[ax]) > 0.0:
# Effect of the force
coefficientsF[ax][0] = coefficientsF[ax][0] - force[ax]
self.addTo(forces[ax], location, -force[ax])
# Moments created by the force (by definition no moment is created by the force in x-direction)
if abs(force[1]) > 0.0:
coefficientsM[1][0] = (
coefficientsM[1][0] - force[1] * location
) # moment around z-axis
self.addTo(moments[1], location, 0)
if abs(force[2]) > 0.0:
coefficientsM[2][0] = (
coefficientsM[2][0] + force[2] * location
) # moment around y-axis
self.addTo(moments[2], location, 0) # No outer moment acts here!
# Moments created by the force and lever
if abs(force[0]) > 0.0:
momenty = force[0] * lever[2]
momentz = force[0] * lever[1]
coefficientsM[1][0] = coefficientsM[1][0] + momentz # moment around z-axis
self.addTo(moments[1], location, momentz)
coefficientsM[2][0] = coefficientsM[2][0] - momenty # moment around y-axis
self.addTo(moments[2], location, -momenty)
if abs(force[1]) > 0.0:
moment = force[1] * lever[2]
coefficientsM[0][0] = coefficientsM[0][0] + moment
self.addTo(moments[0], location, moment)
if abs(force[2]) > 0.0:
moment = force[2] * lever[1]
coefficientsM[0][0] = coefficientsM[0][0] - moment
self.addTo(moments[0], location, -moment)
elif cType == "Pulley":
forceAngle1 = (
(constraint.ForceAngle + constraint.BeltAngle + 90.0) / 180.0 * math.pi
)
forceAngle2 = (
(constraint.ForceAngle - constraint.BeltAngle + 90.0) / 180.0 * math.pi
)
# FreeCAD.Console.PrintMessage("BeltForce1: %f, BeltForce2: %f\n" % (constraint.BeltForce1, constraint.BeltForce2))
# FreeCAD.Console.PrintMessage("Angle1: %f, Angle2: %f\n" % (forceAngle1, forceAngle2))
force = [
0,
-constraint.BeltForce1 * math.sin(forceAngle1)
- constraint.BeltForce2 * math.sin(forceAngle2),
constraint.BeltForce1 * math.cos(forceAngle1)
+ constraint.BeltForce2 * math.cos(forceAngle2),
]
location = constraint.BasePoint.x / 1000.0
# Effect of the pulley forces
for ax in range(3):
if abs(force[ax]) > 0.0:
# Effect of the force
coefficientsF[ax][0] = coefficientsF[ax][0] - force[ax]
self.addTo(forces[ax], location, -force[ax])
# Moments created by the force (by definition no moment is created by the force in x-direction)
if abs(force[1]) > 0.0:
coefficientsM[1][0] = (
coefficientsM[1][0] - force[1] * location
) # moment around z-axis
self.addTo(moments[1], location, 0)
if abs(force[2]) > 0.0:
coefficientsM[2][0] = (
coefficientsM[2][0] + force[2] * location
) # moment around y-axis
self.addTo(moments[2], location, 0) # No outer moment acts here!
# Torque
moment = constraint.Force * (1 if constraint.IsDriven is True else -1)
coefficientsM[0][0] = coefficientsM[0][0] + moment
self.addTo(moments[0], location, moment)
areas = [None, None, None]
areamoments = [None, None, None]
bendingmoments = [None, None, None]
torquemoments = [None, None, None]
for ax in range(3):
FreeCAD.Console.PrintMessage("Axis: %u\n" % ax)
self.printEquilibrium(variableNames[ax], coefficientsF[ax])
self.printEquilibrium(variableNames[ax], coefficientsM[ax])
if len(coefficientsF[ax]) <= 1:
# Note: coefficientsF and coefficientsM always have the same length
FreeCAD.Console.PrintMessage("Matrix is singular, no solution possible\n")
self.parent.updateButtons(ax, False)
continue
# Handle special cases. Note that the code above should ensure that coefficientsF and coefficientsM always have same length
solution = [None, None]
if len(coefficientsF[ax]) == 2:
if coefficientsF[ax][1] != 0.0 and coefficientsF[ax][0] != 0.0:
solution[0] = coefficientsF[ax][0] / coefficientsF[ax][1]
if coefficientsM[ax][1] != 0.0 and coefficientsM[ax][0] != 0.0:
solution[1] = coefficientsM[ax][0] / coefficientsM[ax][1]
if abs(solution[0] - solution[1]) < 1e9:
FreeCAD.Console.PrintMessage(
"System is statically undetermined. No solution possible.\n"
)
self.parent.updateButtons(ax, False)
continue
else:
# Build matrix and vector for linear algebra solving algorithm
# TODO: This could easily be done manually... there are only 2 variables and 6 coefficients
A = np.array([coefficientsF[ax][1:], coefficientsM[ax][1:]])
b = np.array([coefficientsF[ax][0], coefficientsM[ax][0]])
try:
solution = np.linalg.solve(A, b) # A * solution = b
except np.linalg.linalg.LinAlgError as e:
FreeCAD.Console.PrintMessage(str(e))
FreeCAD.Console.PrintMessage(". No solution possible.\n")
self.parent.updateButtons(ax, False)
continue
# Complete dictionary of forces and moments with the two reaction forces that were calculated
for i in range(2):
if solution[i] is None:
continue
FreeCAD.Console.PrintMessage(
"Reaction force/moment: %s = %f\n" % (variableNames[ax][i + 1], solution[i])
)
if variableNames[ax][i + 1][0] == "M":
moments[ax][locations[variableNames[ax][i + 1]]] = -solution[i]
else:
forces[ax][locations[variableNames[ax][i + 1]]] = -solution[i]
FreeCAD.Console.PrintMessage(forces[ax])
FreeCAD.Console.PrintMessage("\n")
FreeCAD.Console.PrintMessage(moments[ax])
FreeCAD.Console.PrintMessage("\n")
# Forces
self.F[ax] = SegmentFunction(self.Fstr[ax])
self.F[ax].buildFromDict("x", forces[ax])
self.parent.updateButton(1, ax, not self.F[ax].isZero())
self.F[ax].output()
# Moments
if ax == 0:
self.M[0] = SegmentFunction(self.Mstr[0])
self.M[0].buildFromDict("x", moments[0])
elif ax == 1:
self.M[1] = self.F[1].integrated().negate()
self.M[1].name = self.Mstr[1]
self.M[1].addSegments(moments[1]) # takes care of boundary conditions
elif ax == 2:
self.M[2] = self.F[2].integrated()
self.M[2].name = self.Mstr[2]
self.M[2].addSegments(moments[2]) # takes care of boundary conditions
self.parent.updateButton(2, ax, not self.M[ax].isZero())
self.M[ax].output()
# Areas and area moments
location = 0.0
areas[ax] = IntervalFunction() # A [m²]
areamoments[ax] = IntervalFunction() # I [m⁴]
bendingmoments[ax] = IntervalFunction() # W_b [m³]
torquemoments[ax] = IntervalFunction() # W_t [m³]
for i in range(len(self.segments)):
od = self.segments[i].diameter / 1000.0
id = self.segments[i].innerdiameter / 1000.0
length = self.segments[i].length / 1000.0
areas[ax].addInterval(
location, length, math.pi / 4.0 * (math.pow(od, 2.0) - math.pow(id, 2.0))
)
areamoment = math.pi / 64.0 * (math.pow(od, 4.0) - math.pow(id, 4.0))
areamoments[ax].addInterval(location, length, areamoment)
bendingmoments[ax].addInterval(location, length, areamoment / (od / 2.0))
torquemoments[ax].addInterval(location, length, 2 * (areamoment / (od / 2.0)))
location += length
# Bending line
if ax > 0:
if len(tangents[ax]) + len(translations[ax]) == 2:
# TODO: Get Young's module from material type instead of using 210000 N/mm² = 2.1E12 N/m²
self.w[ax] = TranslationFunction(
self.M[ax].negated(),
2.1e12,
areamoments[ax],
tangents[ax],
translations[ax],
)
self.w[ax].name = self.wstr[ax]
self.parent.updateButton(3, ax, not self.w[ax].isZero())
else:
self.parent.updateButton(3, ax, False)
# Normal/shear stresses and torque/bending stresses
self.sigmaN[ax] = StressFunction(self.F[ax], areas[ax])
self.sigmaN[ax].name = self.sigmaNstr[ax]
self.parent.updateButton(4, ax, not self.sigmaN[ax].isZero())
if ax == 0:
self.sigmaB[ax] = StressFunction(self.M[ax], torquemoments[ax])
else:
self.sigmaB[ax] = StressFunction(self.M[ax], bendingmoments[ax])
self.sigmaB[ax].name = self.sigmaBstr[ax]
self.parent.updateButton(5, ax, not self.sigmaB[ax].isZero())
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")
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