PartDesign InvoluteGear/de: Difference between revisions

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<languages/>

{{Docnav/de
{{Docnav/de
|[[PartDesign_Sprocket/de|Kettenrad]]
|[[PartDesign_WizardShaft/de|Wellenkonstruktionsassistent]]
|[[PartDesign_WizardShaft/de|EntwurfsassistentWellen]]
|[[PartDesign_MoveTip/de|Spitze setzen]]|[[PartDesign_Workbench/de|PartDesign]]
|[[PartDesign_Workbench/de|PartDesign]]
|IconL=WizardShaft.svg
|IconL=PartDesign_Sprocket.svg
|IconR=PartDesign_MoveTip.svg
|IconR=WizardShaft.svg
|IconC=Workbench_PartDesign.svg
|IconC=Workbench_PartDesign.svg
}}
}}
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{{GuiCommand/de
{{GuiCommand/de
|Name=PartDesign InvoluteGear
|Name=PartDesign InvoluteGear
|Name/de=PartDesign Evolventenzahnrad
|Name/de=PartDesign Evolventenrad
|Icon=PartDesign_InternalExternalGear.svg
|MenuLocation=Part Design → Evolventenzahnrad...
|MenuLocation=Part Design → Evolventenrad...
|Workbenches=[[PartDesign_Workbench/de|PartDesign]]
|Workbenches=[[PartDesign_Workbench/de|PartDesign]]
|SeeAlso=[[FCGear_Workbench/de|Arbeitsbereich FCGear]]
}}
}}


<span id="Description"></span>
== Beschreibung ==
==Beschreibung==
Mit diesem Werkzeug kannst Du ein 2D Profil eines Evolventenzahnrades erstellen. Dieses 2D Profil ist vollständig parametrisch und kann mit dem Grundelement [[PartDesign_Pad/de|PartDesign Polster]] aufgefüllt werden.
<br>
Ausführlichere Informationen findest Du in den Einträgen von Wikipedia für: [https://en.wikipedia.org/wiki/Gear Getriebe] und [https://en.wikipedia.org/wiki/Involute_gear Involute Gear] bzw. https://de.wikipedia.org/wiki/Zahnrad und
https://de.wikipedia.org/wiki/Evolventenverzahnung


Dieses Werkzeug erlaubt es ein 2D-Profil eines Evolventenrades oder einer Evolventenverzahnung zu erstellen. Dieses 2D-Profil ist vollständig parametrisch und kann mit den Formelementen [[PartDesign_Pad/de|PartDesign Aufpolsterung]] oder [[PartDesign_AdditiveHelix/de|PartDesign Wendel]] extrudiert werden.
[[File:PartDesign_Involute_Gear_01.png|left]]
{{clear}}


Für detailliertere Informationen siehe Wikipedia: [https://en.wikipedia.org/wiki/Gear Gear] und [https://en.wikipedia.org/wiki/Involute_gear Involute Gear] (engl.).
==Anwendung==
# Gehe zum Menü {{MenuCommand/de|Part Design → [[File:PartDesign InternalExternalGear.svg|24px]] Evolventenzahnrad...}}.
# Setze die Parameter für die Evolute.
# Klicke auf {{Button|OK}}.
# Das Evolventenrad wird außerhalb des aktiven Körpers erzeugt. Ziehe es per Drag & Drop in einen Körper, um weitere Funktionen wie z.B. Polsterung anzuwenden.


[[File:PartDesign_Involute_Gear_01.png|200px]]
== Parameter ==


<span id="Usage"></span>
*Anzahl Zähne: Setzt die Anzahl der Zähne.
==Anwendung==


<span id="Create_the_profile"></span>
*Module: Zahnabstand dividiert durch die Anzahl der Zähne.
===Profil erstellen===


# Wahlweise den richtigen Körper aktivieren.
* Eingriffswinkel: Winkel zwischen der Wirkungslinie und einer Normalen zu der Linie, die die Zahnradzentren verbindet. Standard ist 20 Grad. ([https://de.wikipedia.org/wiki/Evolventenverzahnung Weitere Informationen])
# Zum Menü {{MenuCommand|Part Design → [[File:PartDesign InternalExternalGear.svg|16px]] Involute gear...}} wechseln.
# Die Evolventenparameter anpassen.
# {{Button|OK}} klicken.
# Wurde noch kein Körper aktiviert: Das Zahnrad auf einen Körper ziehen und ablegen, um es mit weiteren Formelementen zu verwenden.


<span id="Create_a_spur_gear"></span>
* Hohe Präzision: Wahr oder Falsch
===Ein geradverzahntes Stirnrad erstellen===


# Das Zahnradprofil in der [[Tree_view/de|Baumansicht]] Auswählen.
* Außenrad: Wahr oder Falsch
# Die Schaltfläche {{Button|[[Image:PartDesign_Pad.svg|16px]] [[PartDesign_Pad/de|PartDesign Aufpolsterung]]}} drücken.
# Die {{PropertyData/de|Length}} des Blocks auf die gewünschte Zahnradbreite einstellen.
# {{Button|OK}} klicken.


<span id="Create_a_helical_gear"></span>
== Fehler ==
===Ein schrägverzahntes Stirnrad erstellen===


# Select the gear profile in the [[Tree_view|Tree view]].
# Press the {{Button|[[Image:PartDesign_AdditiveHelix.svg|16px]] [[PartDesign_AdditiveHelix|PartDesign AdditiveHelix]]}} button.
# Choose as Axis the normal of the gear profile, that is {{MenuCommand|Normal sketch axis}} {{Version|0.20}}. (In earlier versions the {{MenuCommand|Base Z axis}} can be used as long as the profile's plane has not been altered.)
# Choose a {{MenuCommand|Height-Turns}} mode.
# Set the {{PropertyData|Height}} to the desired face width of the gear.
# To set the desired helical angle an [[Expressions|Expression]] for the {{PropertyData|Turns}} is required.
## Click the blue [[Image:Bound-expression.svg|16px]] icon at the right of the input field.
## Enter the following formula: {{incode|Height * tan(25°) / (InvoluteGear.NumberOfTeeth * InvoluteGear.Modules * pi)}}, where {{incode|25°}} is an example for the desired helical angle (also known as beta-value) and {{incode|InvoluteGear}} is the {{PropertyData|Name}} of the profile.
## Click {{Button|OK}} to close the formula editor.
# Click {{Button|OK}} to close the task panel.

Hint: To make the helical angle an accessible parameter, use a ''dynamic property'':
# Select the profile.
# In the [[Property_editor|Property editor]] activate the {{MenuCommand|Show all}} option in the context menu.
# Again in the context menu, select {{MenuCommand|Add Property}}. Note: this entry is only available when {{MenuCommand|Show all}} is active.
# In the {{MenuCommand|Add Property}} dialog:
## Choose {{incode|App::PropertyAngle}} as Type.
## Set {{incode|Gear}} as Group.
## Set {{incode|HelicalAngle}} as Name (without a space).
## Click {{Button|OK}}.
# Now a new property {{PropertyData|Helical Angle}} (space added automatically), with an initial value of {{incode|0.0°}}, becomes available.
# Assign the desired helical angle to the new property.
# In the formula of the {{PropertyData|Turns}} property of the AdditiveHelix, you can now reference {{incode|InvoluteGear.HelicalAngle}} instead of the hard coded value of e.g. {{incode|25°}}; again assuming {{incode|InvoluteGear}} is the {{PropertyData|Name}} of the profile.

=== Cut a hub for an involute splined shaft ===

{{Version|0.21}}

# Activate the correct body.
# Create an internal involute gear profile with the required number of grooves and adapt the values of pressure angle, addendum-, dedendum- and root fillet coefficient. See also the table in [[#Notes|Notes]] below for feasible values. For example:
#* {{PropertyData|External Gear}}: False
#* {{PropertyData|Number Of Teeth}}: 12
#* {{PropertyData|Pressure Angle}}: 37.5°
#* {{PropertyData|Addendum Coefficient}}: 0.45
#* {{PropertyData|Dedendum Coefficient}}: 0.7
#* {{PropertyData|Root Fillet Coefficient}}: 0.3
# Select the gear profile in the [[Tree_view|Tree view]].
# Press the {{Button|[[Image:PartDesign_Pocket.svg|16px]] '''Pocket'''}} button.
# Set the pocket's {{PropertyData|Type}} to '''Through All'''.
# Check the pocket's {{PropertyData|Symmetric To Plane}} option.
# Click {{Button|OK}}.

<span id="Properties"></span>
==Eigenschaften==

* {{PropertyData|Addendum Coefficient}}: The height of the tooth from the pitch circle up to its tip, normalized by the module. Default is 1.0 for the standard full-depth system. {{Version|0.21}}

* {{PropertyData|Dedendum Coefficient}}: The height of the tooth from the pitch circle down to its root, normalized by the module. Default is 1.25 for the standard full-depth system. {{Version|0.21}}

* {{PropertyData/de|External Gear}} (Stirnrad): Wahr oder Falsch

* {{PropertyData/de|High Precision}} (Hohe Präzision): Wahr oder Falsch

* {{PropertyData/de|Modules}} (der Modul): Teilkreisdurchmesser geteilt durch die Anzahl der Zähne.

* {{PropertyData/de|Number Of Teeth}}: Legt die Anzahl der Zähne fest.

* {{PropertyData/de|Pressure Angle}} (Eingriffswinkel): Winkel zwischen der Wirkungslinie und einer Normalen zu der Linie, die die Zahnradmitten verbindet. Standard ist 20°. Siehe ([https://de.wikipedia.org/wiki/Evolventenverzahnung Evolventenverzahnung])

* {{PropertyData|Profile Shift Coefficient}}: The distance by which the reference profile is shifted outwards, normalized by the module. Default is zero. Profile shift may be positive or negative. {{Version|0.21}}

* {{PropertyData|Root Fillet Coefficient}}: The radius of the fillet at the root of the tooth, normalized by the module. Default is 0.38 as defined by the ISO rack. {{Version|0.21}}

== Notes ==

* In order for two gears to mesh they need to share the same module and pressure angle. [[Expressions|Expressions]] may help to ensure consistency. Their center distance needs to be {{incode|(NumberOfTeeth + OtherGear.NumberOfTeeth) * Modules / 2}} (that is in case of the sum profile shift being zero). Subtract the number of teeth in case of an internal gear.

* Profile shifting can be used to prevent undercut on gears with a small number of teeth. Another application is to adjust the center distance of two gears with a given number of teeth and module.

* When visually checking for proper meshing or interferences a much lower value for {{PropertyView|Deviation}} is helpful, e.g. 0.05 instead of the default 0.5. Otherwise the representation in the [[3D_view|3D view]] may be too coarse.

* For standard gears the most common pressure angle is 20 °, followed by 14,5 °. Other applications, notably [https://en.wikipedia.org/wiki/Spline_(mechanical) splines], use higher angles.

* The standard full-depth system uses an addendum coefficient of 1.0 and a dedendum coefficient of 1.25, resulting in a clearance of 0.25 (the difference between the addendum of the one gear and the dedendum of the other). The actual tooth length is the sum of both coefficients, multiplied by the module.

* Tooth length reduction may be required to prevent undercut or to strengthen the teeth (see [https://khkgears.net/new/gear_knowledge/gear-nomenclature/stub-teeth.html stub teeth]). For internal gears the addendum (here pointing inwards) may need shortening to avoid certain interferences or non-involute flanks; when indicated in combination with longer teeth of the pinion.

* For splined shafts and hubs ISO 4156 defines the following parameters:
: {| class="wikitable"
|-
! Pressure Angle !! 30 ° (flat root) !! 30 ° (fillet root) !! 37,5 ° !! 45 °
|-
| Addendum Coefficient || 0.5 || 0.5 || 0.45 || 0.4
|-
| Dedendum Coefficient || 0.75 || 0.9 || 0.7 || 0.6
|-
| Root Fillet Coefficient || 0.2 || 0.4 || 0.3 || 0.25
|}

==Limitations==

* It is currently not possible to adjust the tooth thickness. Tooth and tooth space are distributed equally on the pitch circle. Thus the only way to control backlash is to adjust the center distance in a gear paring.
* There is currently no [https://www.tec-science.com/mechanical-power-transmission/involute-gear/undercut/ undercut] in the generated gear profile. That means gears with a low number of teeth can interfere with the teeth of the mating gear. The lower limit depends on the {{PropertyData|Pressure Angle}} and is around 17 teeth for 20° and 32 for 14.5°. Most practical applications tolerate a missing undercut for gears a little smaller than this theoretical limit though.

<span id="Tutorials"></span>
==Tutorien==

Video: [https://www.youtube.com/watch?v=8VNhTrnFMfE How to make gears in FreeCAD]

<span id="Related"></span>
==Verwandt==
==Verwandt==


* [[FCGear_Workbench/de|Zahnrad-Arbeitsbereich]]
* Arbeitsbereich [[FCGear_Workbench/de|FCGear]]



{{Docnav/de
{{Docnav/de
|[[PartDesign_Sprocket/de|Kettenrad]]
|[[PartDesign_WizardShaft/de|Wellenkonstruktionsassistent]]
|[[PartDesign_WizardShaft/de|EntwurfsassistentWellen]]
|[[PartDesign_MoveTip/de|Spitze setzen]]|[[PartDesign_Workbench/de|PartDesign]]
|[[PartDesign_Workbench/de|PartDesign]]
|IconL=WizardShaft.svg
|IconL=PartDesign_Sprocket.svg
|IconR=PartDesign_MoveTip.svg
|IconR=WizardShaft.svg
|IconC=Workbench_PartDesign.svg
|IconC=Workbench_PartDesign.svg
}}
}}

Latest revision as of 15:28, 2 June 2023

Other languages:

PartDesign Evolventenrad

Menüeintrag
Part Design → Evolventenrad...
Arbeitsbereich
PartDesign
Standardtastenkürzel
Keiner
Eingeführt in Version
-
Siehe auch
Arbeitsbereich FCGear

Beschreibung

Dieses Werkzeug erlaubt es ein 2D-Profil eines Evolventenrades oder einer Evolventenverzahnung zu erstellen. Dieses 2D-Profil ist vollständig parametrisch und kann mit den Formelementen PartDesign Aufpolsterung oder PartDesign Wendel extrudiert werden.

Für detailliertere Informationen siehe Wikipedia: Gear und Involute Gear (engl.).

Anwendung

Profil erstellen

  1. Wahlweise den richtigen Körper aktivieren.
  2. Zum Menü Part Design → Involute gear... wechseln.
  3. Die Evolventenparameter anpassen.
  4. OK klicken.
  5. Wurde noch kein Körper aktiviert: Das Zahnrad auf einen Körper ziehen und ablegen, um es mit weiteren Formelementen zu verwenden.

Ein geradverzahntes Stirnrad erstellen

  1. Das Zahnradprofil in der Baumansicht Auswählen.
  2. Die Schaltfläche PartDesign Aufpolsterung drücken.
  3. Die Daten-EigenschaftLength des Blocks auf die gewünschte Zahnradbreite einstellen.
  4. OK klicken.

Ein schrägverzahntes Stirnrad erstellen

  1. Select the gear profile in the Tree view.
  2. Press the PartDesign AdditiveHelix button.
  3. Choose as Axis the normal of the gear profile, that is Normal sketch axis introduced in version 0.20. (In earlier versions the Base Z axis can be used as long as the profile's plane has not been altered.)
  4. Choose a Height-Turns mode.
  5. Set the DatenHeight to the desired face width of the gear.
  6. To set the desired helical angle an Expression for the DatenTurns is required.
    1. Click the blue icon at the right of the input field.
    2. Enter the following formula: Height * tan(25°) / (InvoluteGear.NumberOfTeeth * InvoluteGear.Modules * pi), where 25° is an example for the desired helical angle (also known as beta-value) and InvoluteGear is the DatenName of the profile.
    3. Click OK to close the formula editor.
  7. Click OK to close the task panel.

Hint: To make the helical angle an accessible parameter, use a dynamic property:

  1. Select the profile.
  2. In the Property editor activate the Show all option in the context menu.
  3. Again in the context menu, select Add Property. Note: this entry is only available when Show all is active.
  4. In the Add Property dialog:
    1. Choose App::PropertyAngle as Type.
    2. Set Gear as Group.
    3. Set HelicalAngle as Name (without a space).
    4. Click OK.
  5. Now a new property DatenHelical Angle (space added automatically), with an initial value of 0.0°, becomes available.
  6. Assign the desired helical angle to the new property.
  7. In the formula of the DatenTurns property of the AdditiveHelix, you can now reference InvoluteGear.HelicalAngle instead of the hard coded value of e.g. 25°; again assuming InvoluteGear is the DatenName of the profile.

Cut a hub for an involute splined shaft

introduced in version 0.21

  1. Activate the correct body.
  2. Create an internal involute gear profile with the required number of grooves and adapt the values of pressure angle, addendum-, dedendum- and root fillet coefficient. See also the table in Notes below for feasible values. For example:
    • DatenExternal Gear: False
    • DatenNumber Of Teeth: 12
    • DatenPressure Angle: 37.5°
    • DatenAddendum Coefficient: 0.45
    • DatenDedendum Coefficient: 0.7
    • DatenRoot Fillet Coefficient: 0.3
  3. Select the gear profile in the Tree view.
  4. Press the Pocket button.
  5. Set the pocket's DatenType to Through All.
  6. Check the pocket's DatenSymmetric To Plane option.
  7. Click OK.

Eigenschaften

  • DatenAddendum Coefficient: The height of the tooth from the pitch circle up to its tip, normalized by the module. Default is 1.0 for the standard full-depth system. introduced in version 0.21
  • DatenDedendum Coefficient: The height of the tooth from the pitch circle down to its root, normalized by the module. Default is 1.25 for the standard full-depth system. introduced in version 0.21
  • Daten-EigenschaftExternal Gear (Stirnrad): Wahr oder Falsch
  • Daten-EigenschaftHigh Precision (Hohe Präzision): Wahr oder Falsch
  • Daten-EigenschaftModules (der Modul): Teilkreisdurchmesser geteilt durch die Anzahl der Zähne.
  • Daten-EigenschaftNumber Of Teeth: Legt die Anzahl der Zähne fest.
  • Daten-EigenschaftPressure Angle (Eingriffswinkel): Winkel zwischen der Wirkungslinie und einer Normalen zu der Linie, die die Zahnradmitten verbindet. Standard ist 20°. Siehe (Evolventenverzahnung)
  • DatenProfile Shift Coefficient: The distance by which the reference profile is shifted outwards, normalized by the module. Default is zero. Profile shift may be positive or negative. introduced in version 0.21
  • DatenRoot Fillet Coefficient: The radius of the fillet at the root of the tooth, normalized by the module. Default is 0.38 as defined by the ISO rack. introduced in version 0.21

Notes

  • In order for two gears to mesh they need to share the same module and pressure angle. Expressions may help to ensure consistency. Their center distance needs to be (NumberOfTeeth + OtherGear.NumberOfTeeth) * Modules / 2 (that is in case of the sum profile shift being zero). Subtract the number of teeth in case of an internal gear.
  • Profile shifting can be used to prevent undercut on gears with a small number of teeth. Another application is to adjust the center distance of two gears with a given number of teeth and module.
  • When visually checking for proper meshing or interferences a much lower value for AnsichtDeviation is helpful, e.g. 0.05 instead of the default 0.5. Otherwise the representation in the 3D view may be too coarse.
  • For standard gears the most common pressure angle is 20 °, followed by 14,5 °. Other applications, notably splines, use higher angles.
  • The standard full-depth system uses an addendum coefficient of 1.0 and a dedendum coefficient of 1.25, resulting in a clearance of 0.25 (the difference between the addendum of the one gear and the dedendum of the other). The actual tooth length is the sum of both coefficients, multiplied by the module.
  • Tooth length reduction may be required to prevent undercut or to strengthen the teeth (see stub teeth). For internal gears the addendum (here pointing inwards) may need shortening to avoid certain interferences or non-involute flanks; when indicated in combination with longer teeth of the pinion.
  • For splined shafts and hubs ISO 4156 defines the following parameters:
Pressure Angle 30 ° (flat root) 30 ° (fillet root) 37,5 ° 45 °
Addendum Coefficient 0.5 0.5 0.45 0.4
Dedendum Coefficient 0.75 0.9 0.7 0.6
Root Fillet Coefficient 0.2 0.4 0.3 0.25

Limitations

  • It is currently not possible to adjust the tooth thickness. Tooth and tooth space are distributed equally on the pitch circle. Thus the only way to control backlash is to adjust the center distance in a gear paring.
  • There is currently no undercut in the generated gear profile. That means gears with a low number of teeth can interfere with the teeth of the mating gear. The lower limit depends on the DatenPressure Angle and is around 17 teeth for 20° and 32 for 14.5°. Most practical applications tolerate a missing undercut for gears a little smaller than this theoretical limit though.

Tutorien

Video: How to make gears in FreeCAD

Verwandt


PartDesign-Arbeitsbereich
Anwenderdokumentation
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