kindred/create
1
1
Fork 0
Code Issues 37 Pull Requests Actions Packages Projects 9 Releases 2 Wiki Activity

PD: Implement Profile Shift for InvoluteGear

Browse Source 
This commit adds the ability to shift the involute profile inside or
outside. Profile shift is implemented as coefficient, i.e. normalized by
the module, so that it the whole profile scales with the module without
chaning shape.
To verify the profile, the tests implement an "over pins measurement"
using formulae found in literature.
Backward compatibility with FreeCAD-v0.20 is garanteed by already
existing tests, not touched by this commit.

This addresses issue #5618.
This commit is contained in:
Jonas Bähr
2023-03-17 00:05:05 +01:00
parent 21d705ad4b
commit 9404c032f4
4 changed files with 200 additions and 16 deletions
Download Patch File Download Diff File Expand all files Collapse all files

140
src/Mod/PartDesign/PartDesignTests/TestInvoluteGear.py
View File

@@ -21,8 +21,10 @@
import unittest
import pathlib
from math import pi, tan, cos, acos
import FreeCAD
Quantity = FreeCAD.Units.Quantity # FIXME from FreeCAD.Units import Quantity doesn't work
from FreeCAD import Vector
from Part import makeCircle, Precision
import InvoluteGearFeature
@@ -150,6 +152,66 @@ class TestInvoluteGear(unittest.TestCase):
self.assertNoIntersection(hub.Shape, makeCircle(tip_diameter/2 - delta), "Teeth extent below tip circle")
self.assertNoIntersection(hub.Shape, makeCircle(root_diameter/2 + delta), "Teeth extend beyond root circle")
def testShiftedExternalGearProfile(self):
gear = InvoluteGearFeature.makeInvoluteGear('InvoluteGear')
gear.NumberOfTeeth = 9 # odd number to have a tooth space on the negative X-axis
gear.ProfileShiftCoefficient = 0.6
self.assertSuccessfulRecompute(gear)
self.assertClosedWire(gear.Shape)
# first, verify the radial dimensions
xm = gear.ProfileShiftCoefficient * gear.Modules
Rref = gear.NumberOfTeeth * gear.Modules / 2
Rtip = Rref + gear.AddendumCoefficient * gear.Modules + xm
Rroot = Rref - gear.DedendumCoefficient * gear.Modules + xm
delta = Quantity("20 um") # 20 micron is as good as it gets
self.assertIntersection(gear.Shape, makeCircle(Rref), "Expecting intersection at reference circle")
self.assertNoIntersection(gear.Shape, makeCircle(Rtip + delta), "Teeth extent beyond tip circle")
self.assertNoIntersection(gear.Shape, makeCircle(Rroot - delta), "Teeth extend below root circle")
# to verify the angular dimensions, we use an "over pin measurement"
Dpin, Rc = external_pin_diameter_and_distance(
z=gear.NumberOfTeeth,
m=gear.Modules.getValueAs('mm'),
a=gear.PressureAngle.getValueAs('rad'),
x=gear.ProfileShiftCoefficient)
Rpin = Quantity(f"{Dpin/2} mm")
delta = Quantity("1 um") # our angular precision is much greater then the radial one
self.assertIntersection(gear.Shape, makeCircle(Rpin + delta, Vector(-Rc)),
msg="Expecting intersection with enlarged pin")
self.assertNoIntersection(gear.Shape, makeCircle(Rpin - delta, Vector(-Rc)),
msg="Expecting no intersection with reduced pin")
def testShiftedInternalGearProfile(self):
gear = InvoluteGearFeature.makeInvoluteGear('InvoluteGear')
gear.NumberOfTeeth = 11 # odd number to have a tooth space on the negative X-axis
gear.ExternalGear = False # to ensure "clean" flanks we need to tweak some more props
gear.ProfileShiftCoefficient = 0.4
gear.AddendumCoefficient = 0.6
gear.DedendumCoefficient = 0.8
self.assertSuccessfulRecompute(gear)
self.assertClosedWire(gear.Shape)
# first, verify the radial dimensions
xm = gear.ProfileShiftCoefficient * gear.Modules
Rref = gear.NumberOfTeeth * gear.Modules / 2
# For internal, too, positive shift is outwards. So this is *not* inverted.
Rtip = Rref - gear.AddendumCoefficient * gear.Modules + xm
Rroot = Rref + gear.DedendumCoefficient * gear.Modules + xm
delta = Quantity("20 um") # 20 micron is as good as it gets
self.assertIntersection(gear.Shape, makeCircle(Rref), "Expecting intersection at reference circle")
self.assertNoIntersection(gear.Shape, makeCircle(Rtip - delta), "Teeth extent below tip circle")
self.assertNoIntersection(gear.Shape, makeCircle(Rroot + delta), "Teeth extend beyond root circle")
# to verify the angular dimensions, we use an "over pin measurement"
Dpin, Rc = internal_pin_diameter_and_distance(
z=gear.NumberOfTeeth,
m=gear.Modules.getValueAs('mm'),
a=gear.PressureAngle.getValueAs('rad'),
x=gear.ProfileShiftCoefficient)
Rpin = Quantity(f"{Dpin/2} mm")
delta = Quantity("1 um") # our angular precision is much greater then the radial one
self.assertIntersection(gear.Shape, makeCircle(Rpin + delta, Vector(-Rc)),
msg="Expecting intersection with enlarged pin")
self.assertNoIntersection(gear.Shape, makeCircle(Rpin - delta, Vector(-Rc)),
msg="Expecting no intersection with reduced pin")
def testZeroFilletExternalGearProfile_BaseAboveRoot(self):
gear = InvoluteGearFeature.makeInvoluteGear('InvoluteGear')
# below 42 teeth, with default dedendum 1.25, we have some non-involute flanks
@@ -261,3 +323,81 @@ class TestInvoluteGear(unittest.TestCase):
def assertSolid(self, shape, msg=None):
self.assertEqual(shape.ShapeType, 'Solid', msg=msg)
def inv(a):
"""the involute function"""
return tan(a) - a
def external_pin_diameter_and_distance(z, m, a, x):
"""Calculates the ideal pin diameter for over pins measurement and its distance
for extrnal spur gears.
z is the number of teeth
m is the module, in millimeter
a is the pressure angle, in radians
x is the profile shift coefficient
returns the tuple of ideal pin diameter and its center distance from the gear's center
"""
# Equations taken from http://qtcgears.com/tools/catalogs/PDF_Q420/Tech.pdf
# Table 10-13 (1-4) and Table 10-14 (4a)
# 1. Half Tooth Space Angle at Base Circle
nu = pi / (2 * z) - inv(a) - 2 * x * tan(a) / z
# 2. The Pressure Angle at the Point Pin is Tangent to Tooth Surface
ap = acos(z * m * cos(a) / (z * m + 2 * x * m))
# 3. The Pressure Angle at Pin Center
phi = tan(ap) + nu
# 4. Ideal Pin Diameter
dp = z * m * cos(a) * (inv(phi) + nu)
# 4a. Over Pins Measurement, even number of teeth
# As we return the distance from the gear's center, we need dm to pass thought this center
# and that's only the case for a dm for an even number of teeth. However, this center distance
# is also valid for an odd number of teeth, as we don't measure pin-to-pin but pin-to-center.
dm = z * m * cos(a) / cos(phi) + dp
# Eq. 10-12 on page T46
rc = (dm - dp) / 2
return (dp, rc)
def internal_pin_diameter_and_distance(z, m, a, x):
"""Calculates the ideal pin diameter for over pins measurement and its distance
for intrnal spur gears.
z is the number of teeth
m is the module, in millimeter
a is the pressure angle, in radians
x is the profile shift coefficient
returns the tuple of ideal pin diameter and its center distance from the gear's center
"""
# Equations taken from http://qtcgears.com/tools/catalogs/PDF_Q420/Tech.pdf
# Table 10-17 (1-4) and Table 10-18 (4a)
# 1. Half Tooth Space Angle at Base Circle
nu = pi / (2 * z) + inv(a) + 2 * x * tan(a) / z
# 2. The Pressure Angle at the Point Pin is Tangent to Tooth Surface
ap = acos(z * m * cos(a) / (z * m + 2 * x * m))
# 3. The Pressure Angle at Pin Center
phi = tan(ap) - nu
# 4. Ideal Pin Diameter
dp = z * m * cos(a) * (nu - inv(phi))
# 4a. Over Pins Measurement, even number of teeth
# As we return the distance from the gear's center, we need dm to pass thought this center
# and that's only the case for a dm for an even number of teeth. However, this center distance
# is also valid for an odd number of teeth, as we don't measure pin-to-pin but pin-to-center.
dm = z * m * cos(a) / cos(phi) - dp
rc = (dm + dp) / 2
return (dp, rc)