#*************************************************************************** #* Copyright (c) 2021 Jonas Bähr * #* * #* This program is free software; you can redistribute it and/or modify * #* it under the terms of the GNU Lesser General Public License (LGPL) * #* as published by the Free Software Foundation; either version 2 of * #* the License, or (at your option) any later version. * #* for detail see the LICENCE text file. * #* * #* This program 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 program; if not, write to the Free Software * #* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 * #* USA * #* * #*************************************************************************** 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 FIXTURE_PATH = pathlib.Path(__file__).parent / "Fixtures" class TestInvoluteGear(unittest.TestCase): def setUp(self): self.Doc = FreeCAD.newDocument("PartDesignTestInvoluteGear") def tearDown(self): FreeCAD.closeDocument(self.Doc.Name) def testDefaultGearProfile(self): InvoluteGearFeature.makeInvoluteGear('TestGear') gear = self.Doc.getObject('TestGear') self.assertSuccessfulRecompute(gear) self.assertClosedWire(gear.Shape) def testDefaultInternalGearProfile(self): gear = InvoluteGearFeature.makeInvoluteGear('InvoluteGear') gear.ExternalGear = False self.assertSuccessfulRecompute(gear) self.assertClosedWire(gear.Shape) def testLowPrecisionGearProfile(self): gear = InvoluteGearFeature.makeInvoluteGear('InvoluteGear') gear.HighPrecision = False self.assertSuccessfulRecompute(gear) self.assertClosedWire(gear.Shape) def testLowPrecisionInternalGearProfile(self): gear = InvoluteGearFeature.makeInvoluteGear('InvoluteGear') gear.ExternalGear = False gear.HighPrecision = False self.assertSuccessfulRecompute(gear) self.assertClosedWire(gear.Shape) def testExternalGearProfileOrientation(self): gear = InvoluteGearFeature.makeInvoluteGear('TestGear') self.assertSuccessfulRecompute(gear) tip_diameter = (gear.NumberOfTeeth + 2 * gear.AddendumCoefficient) * gear.Modules delta = 0.01 # yes, we do not reach micrometer precision tip_probe = makeCircle(delta, Vector(tip_diameter/2, 0, 0)) self.assertIntersection(gear.Shape, tip_probe, msg=f"First tooth tip does not lay on the positive X-axis") def testInternalGearProfileOrientation(self): gear = InvoluteGearFeature.makeInvoluteGear('TestGear') gear.ExternalGear = False self.assertSuccessfulRecompute(gear) tip_diameter = (gear.NumberOfTeeth - 2 * gear.AddendumCoefficient) * gear.Modules delta = 0.01 # yes, we do not reach micrometer precision tip_probe = makeCircle(delta, Vector(tip_diameter/2, 0, 0)) self.assertIntersection(gear.Shape, tip_probe, msg=f"First tooth tip does not lay on the positive X-axis") def testCustomizedGearProfile(self): gear = InvoluteGearFeature.makeInvoluteGear('InvoluteGear') z = 12 m = 1 gear.NumberOfTeeth = z gear.Modules = f'{m} mm' gear.PressureAngle = '14.5 deg' self.assertSuccessfulRecompute(gear) self.assertClosedWire(gear.Shape) pitch_diameter = m * z default_addendum = 1 default_dedendum = 1.25 tip_diameter = pitch_diameter + 2 * default_addendum * m root_diameter = pitch_diameter - 2 * default_dedendum * m # the test purpose here is just to ensure the gear's parameters are used, # not super precise profile verification. Thus a lax delta is just file here. delta = 0.01 self.assertIntersection(gear.Shape, makeCircle(pitch_diameter/2), "Expecting intersection at pitch circle") self.assertNoIntersection(gear.Shape, makeCircle(tip_diameter/2 + delta), "Teeth extent beyond tip circle") self.assertNoIntersection(gear.Shape, makeCircle(root_diameter/2 - delta), "Teeth extend below root circle") def testCustomizedGearProfileForSplinedShaft(self): spline = InvoluteGearFeature.makeInvoluteGear('InvoluteSplinedShaft') z = 12 m = 2 add_coef = 0.5 ded_coef = 0.9 spline.NumberOfTeeth = z spline.Modules = f'{m} mm' spline.PressureAngle = '30 deg' spline.AddendumCoefficient = add_coef spline.DedendumCoefficient = ded_coef spline.RootFilletCoefficient = 0.4 self.assertSuccessfulRecompute(spline) self.assertClosedWire(spline.Shape) pitch_diameter = m * z tip_diameter = pitch_diameter + 2 * add_coef * m root_diameter = pitch_diameter - 2 * ded_coef * m # the test purpose here is just to ensure the gear's parameters are used, # not super precise profile verification. Thus a lax delta is just file here. delta = 0.01 self.assertIntersection(spline.Shape, makeCircle(pitch_diameter/2), "Expecting intersection at pitch circle") self.assertNoIntersection(spline.Shape, makeCircle(tip_diameter/2 + delta), "Teeth extent beyond tip circle") self.assertNoIntersection(spline.Shape, makeCircle(root_diameter/2 - delta), "Teeth extend below root circle") def testCustomizedGearProfileForSplinedHub(self): hub = InvoluteGearFeature.makeInvoluteGear('InvoluteSplinedHub') hub.ExternalGear = False z = 12 m = 2 add_coef = 0.5 ded_coef = 0.9 hub.NumberOfTeeth = z hub.Modules = f'{m} mm' hub.PressureAngle = '30 deg' hub.AddendumCoefficient = add_coef hub.DedendumCoefficient = ded_coef hub.RootFilletCoefficient = 0.4 self.assertSuccessfulRecompute(hub) self.assertClosedWire(hub.Shape) pitch_diameter = m * z tip_diameter = pitch_diameter - 2 * add_coef * m root_diameter = pitch_diameter + 2 * ded_coef * m # the test purpose here is just to ensure the gear's parameters are used, # not super precise profile verification. Thus a lax delta is just file here. delta = 0.01 self.assertIntersection(hub.Shape, makeCircle(pitch_diameter/2), "Expecting intersection at pitch circle") 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 gear.NumberOfTeeth = 41 gear.RootFilletCoefficient = 0 self.assertSuccessfulRecompute(gear) self.assertClosedWire(gear.Shape) def testZeroFilletExternalGearProfile_BaseBelowRoot(self): gear = InvoluteGearFeature.makeInvoluteGear('InvoluteGear') # above 41 teeth, with default dedendum 1.25, the root is within the involute flank gear.NumberOfTeeth = 42 gear.RootFilletCoefficient = 0 self.assertSuccessfulRecompute(gear) self.assertClosedWire(gear.Shape) def testZeroFilletInternalGearProfile(self): gear = InvoluteGearFeature.makeInvoluteGear('InvoluteGear') gear.ExternalGear = False gear.RootFilletCoefficient = 0 self.assertSuccessfulRecompute(gear) self.assertClosedWire(gear.Shape) def testUsagePadGearProfile(self): profile = InvoluteGearFeature.makeInvoluteGear('GearProfile') body = self.Doc.addObject('PartDesign::Body','GearBody') body.addObject(profile) pad = body.newObject("PartDesign::Pad","GearPad") pad.Profile = profile pad.Length = '5 mm' # that our gear's "Face Width" self.assertSuccessfulRecompute() self.assertSolid(pad.Shape) def testUsagePocketInternalGearProfile(self): profile = InvoluteGearFeature.makeInvoluteGear('GearProfile') profile.ExternalGear = False # boolean cuts with lots of B-splines are quite slow, so let's make it less complex profile.HighPrecision = False profile.NumberOfTeeth = 8 body = self.Doc.addObject('PartDesign::Body','GearBody') body.addObject(profile) cylinder = body.newObject('PartDesign::AdditiveCylinder','GearCylinder') default_dedendum = 1.25 rim_width = 3 * FreeCAD.Units.MilliMetre cylinder.Height = '5 mm' # that our gear's "Face Width" cylinder.Radius = profile.NumberOfTeeth * profile.Modules / 2 + default_dedendum * profile.Modules + rim_width pocket = body.newObject('PartDesign::Pocket','GearPocket') pocket.Profile = profile pocket.Reversed = True # need to "pocket upwards" into the cylinder pocket.Type = 'ThroughAll' self.assertSuccessfulRecompute() self.assertSolid(pocket.Shape) def testRecomputeExternalGearFromV020(self): FreeCAD.closeDocument(self.Doc.Name) # this was created in setUp(self) self.Doc = FreeCAD.openDocument(str(FIXTURE_PATH / "InvoluteGear_v0-20.FCStd")) created_with = f"created with {self.Doc.getProgramVersion()}" gear = self.Doc.InvoluteGear # from fixture fixture_length = 187.752 # from fixture, rounded to micrometer self.assertClosedWire(gear.Shape) # no recompute yet, i.e. check original self.assertAlmostEqual(fixture_length, gear.Shape.Length, places=3, msg=f"Total wire length does not match fixture for gear {created_with}") gear.enforceRecompute() self.assertSuccessfulRecompute(gear, msg=f"Cannot recompute gear {created_with}") relative_tolerance_per_tooth = 1e-3 # wild guess: changes of <0.1%/tooth are ok length_delta = fixture_length * relative_tolerance_per_tooth * gear.NumberOfTeeth self.assertAlmostEqual(fixture_length, gear.Shape.Length, delta=length_delta, msg=f"Total wire length changed after recomputing gear {created_with}") def testRecomputeInternalGearFromV020(self): FreeCAD.closeDocument(self.Doc.Name) # this was created in setUp(self) self.Doc = FreeCAD.openDocument(str(FIXTURE_PATH / "InternalInvoluteGear_v0-20.FCStd")) created_with = f"created with {self.Doc.getProgramVersion()}" gear = self.Doc.InvoluteGear # from fixture fixture_length = 165.408 # from fixture, rounded to micrometer self.assertClosedWire(gear.Shape) # no recompute yet, i.e. check original self.assertAlmostEqual(fixture_length, gear.Shape.Length, places=3, msg=f"Total wire length does not match fixture for gear {created_with}") gear.enforceRecompute() self.assertSuccessfulRecompute(gear, msg=f"Cannot recompute gear {created_with}") relative_tolerance_per_tooth = 1e-3 # wild guess: changes of <0.1%/tooth are ok length_delta = fixture_length * relative_tolerance_per_tooth * gear.NumberOfTeeth self.assertAlmostEqual(fixture_length, gear.Shape.Length, delta=length_delta, msg=f"Total wire length changed after recomputing gear {created_with}") def assertSuccessfulRecompute(self, *objs, msg=None): if (len(objs) == 0): self.Doc.recompute() objs = self.Doc.Objects else: self.Doc.recompute(objs) failed_objects = [o.Name for o in objs if 'Invalid' in o.State] if (len(failed_objects) > 0): self.fail(msg or f"Recompute failed for {failed_objects}") def assertClosedWire(self, shape, msg=None): self.assertEqual(shape.ShapeType, 'Wire', msg=msg) self.assertTrue(shape.isClosed(), msg=msg) def assertIntersection(self, shape1, shape2, msg=None): self.failUnless(self._check_intersection(shape1, shape2), msg or "Given shapes do not intersect.") def assertNoIntersection(self, shape1, shape2, msg=None): self.failIf(self._check_intersection(shape1, shape2), msg or "Given shapes intersect.") def _check_intersection(self, shape1, shape2): distance, _, _ = shape1.distToShape(shape2) return distance < Precision.intersection() 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)