Difference between revisions of "FCGear InvoluteGear"

From FreeCAD Documentation
Jump to navigation Jump to search
(Rephrased the computed properties section, giving more details and avoiding repetition)
(Marked this version for translation)
 
(14 intermediate revisions by 6 users not shown)
Line 5: Line 5:
 
{{Docnav
 
{{Docnav
 
|
 
|
|[[FCGear_InvoluteRack|FCGear InvoluteRack]]
+
|[[FCGear_InvoluteRack|InvoluteRack]]
|[[FCGear_Workbench|FCGear Workbench]]
+
|[[FCGear_Workbench|FCGear]]
 
|IconL=
 
|IconL=
 
|IconC=FCGear_workbench_icon.svg
 
|IconC=FCGear_workbench_icon.svg
Line 28: Line 28:
 
The movement is often transferred directly from one gear wheel to the other, but sometimes also via a chain. In addition, the direction of rotation can be changed. It is also possible to change a radial movement into a linear one via Involute Rack ([[File:FCGear_InvoluteRack.svg|22px|link=FCGear InvoluteRack]] [[FCGear_InvoluteRack|Create an Involute rack]]).
 
The movement is often transferred directly from one gear wheel to the other, but sometimes also via a chain. In addition, the direction of rotation can be changed. It is also possible to change a radial movement into a linear one via Involute Rack ([[File:FCGear_InvoluteRack.svg|22px|link=FCGear InvoluteRack]] [[FCGear_InvoluteRack|Create an Involute rack]]).
  
 +
</translate>
 +
[[Image:Involute-Gear example.png]]
 +
<translate>
 
<!--T:5-->
 
<!--T:5-->
:[[Image:Involute-Gear example.png]]
+
{{Caption|From left to right: Spur gearing, helical gearing, double helical gearing}}
:{{Caption|From left to right: Spur gearing, helical gearing, double helical gearing
 
}}
 
  
 
==Usage== <!--T:6-->
 
==Usage== <!--T:6-->
Line 60: Line 61:
 
* {{PropertyData|df}}: Root diameter, measured at the foot of the teeth.
 
* {{PropertyData|df}}: Root diameter, measured at the foot of the teeth.
 
* {{PropertyData|dw}}: Working pitch diameter.
 
* {{PropertyData|dw}}: Working pitch diameter.
 +
* {{PropertyData|transverse_pitch}}: Pitch in the plane of rotation.
  
 
<!--T:14-->
 
<!--T:14-->
Line 71: Line 73:
 
* {{PropertyData|height}}: Value of the gear width.
 
* {{PropertyData|height}}: Value of the gear width.
 
* {{PropertyData|module}}: Module is the ratio of the reference diameter of the gear divided by the number of teeth (see also the information in {{Emphasis|Notes}}).
 
* {{PropertyData|module}}: Module is the ratio of the reference diameter of the gear divided by the number of teeth (see also the information in {{Emphasis|Notes}}).
* {{PropertyData|numpoints}}: Default is 6, change of the involute profile. Changing the value can lead to unexpected results.
 
 
* {{PropertyData|properties_from_tool}}: If helix angle β is given and {{Emphasis|properties_from-tool}} is enabled, gear parameters are internally recomputed for the rotated gear.
 
* {{PropertyData|properties_from_tool}}: If helix angle β is given and {{Emphasis|properties_from-tool}} is enabled, gear parameters are internally recomputed for the rotated gear.
 
* {{PropertyData|shift}}: Default is 0,00, generates a positive and negative profile shift (see also the information in {{Emphasis|Notes}}).
 
* {{PropertyData|shift}}: Default is 0,00, generates a positive and negative profile shift (see also the information in {{Emphasis|Notes}}).
* {{PropertyData|simple}}: {{Emphasis|True}} generates a simplified display (without teeth and only a cylinder in pitch diameter).
 
 
* {{PropertyData|teeth}}: Number of teeth (see also the information in {{Emphasis|Notes}})
 
* {{PropertyData|teeth}}: Number of teeth (see also the information in {{Emphasis|Notes}})
 
* {{PropertyData|undercut}}: {{Emphasis|True}} changes the profil of the tooth root (see also the information in {{Emphasis|Notes}}).
 
* {{PropertyData|undercut}}: {{Emphasis|True}} changes the profil of the tooth root (see also the information in {{Emphasis|Notes}}).
Line 82: Line 82:
  
 
<!--T:17-->
 
<!--T:17-->
* {{PropertyData|pressure_parameter}}: Default is 20 (see also the information in {{Emphasis|Notes}}).
+
* {{PropertyData|pressure_angle}}: Default is 20° (see also the information in {{Emphasis|Notes}}).
 +
 
 +
<!--T:34-->
 +
{{Properties_Title|precision}}
 +
* {{PropertyData|numpoints}}: Default is 6, change of the involute profile. Changing the value can lead to unexpected results.
 +
* {{PropertyData|simple}}: {{Emphasis|True}} generates a simplified display (without teeth and only a cylinder in pitch diameter).
  
 
<!--T:18-->
 
<!--T:18-->
Line 106: Line 111:
 
* {{Emphasis|teeth}}: If the number of teeth is changed, the pitch diameter also changes ({{Emphasis|dw}}).
 
* {{Emphasis|teeth}}: If the number of teeth is changed, the pitch diameter also changes ({{Emphasis|dw}}).
 
* {{Emphasis|undercut}}: Undercut is used when the number of teeth of a gear is too small. Otherwise the mating gear will cut into the tooth root.  The undercut not only weakens the tooth with a wasp-like waist, but also removes some of the useful involute adjacent to the base circle.
 
* {{Emphasis|undercut}}: Undercut is used when the number of teeth of a gear is too small. Otherwise the mating gear will cut into the tooth root.  The undercut not only weakens the tooth with a wasp-like waist, but also removes some of the useful involute adjacent to the base circle.
* {{Emphasis|pressure_parameter}}: 20° is a standard value here. The pressure angle is defined as the angle between the line-of-action (common tangent to the base circles) and a perpendicular to the line-of-centers. Thus, for standard gears, 14.5° pressure angle gears have base circles much nearer to the roots of teeth than 20° gears.  It is for this reason that 14.5° gears encounter greater undercutting problems than 20° gears. Important. the pressure angle changes with a profile shift. Only change the parameter, if sufficient knowledge of the gear geometry is available.
+
* {{Emphasis|pressure_angle}}: 20° is a standard value here. The pressure angle is defined as the angle between the line-of-action (common tangent to the base circles) and a perpendicular to the line-of-centers. Thus, for standard gears, 14.5° pressure angle gears have base circles much nearer to the roots of teeth than 20° gears.  It is for this reason that 14.5° gears encounter greater undercutting problems than 20° gears. Important. the pressure angle changes with a profile shift. Only change the parameter, if sufficient knowledge of the gear geometry is available.
 
* {{Emphasis|reversed_backslash}}: If there are several gears, pay attention to which gear the parameter is set for.
 
* {{Emphasis|reversed_backslash}}: If there are several gears, pay attention to which gear the parameter is set for.
  
 
==Limitations== <!--T:24-->
 
==Limitations== <!--T:24-->
  
<!--T:25-->
+
<!--T:41-->
Limitation are not known yet.
+
A 2D tooth profile, obtained by setting the {{PropertyData|height}} to zero, cannot be used with features requiring a 2D shape. For example [[PartDesign_Pad|PartDesign Pad]] and [[PartDesign_AdditiveHelix|PartDesign AdditiveHelix]] features do not accept such a profile as base. For technical details, please refer to the related [https://github.com/looooo/freecad.gears/issues/97 issue on GitHub].
  
 
==Useful formulas== <!--T:29-->
 
==Useful formulas== <!--T:29-->
  
<!--T:30-->
+
===Standard Spur Gears=== <!--T:40-->
*'''External gearing'''
+
 
**{{Emphasis|addendum diameter}} = {{Emphasis|module}} * {{Emphasis|(teeth +2 )}}
+
<!--T:35-->
**{{Emphasis|dedendum diameter}} = {{Emphasis|pitch diameter (dw)}} - 2 * ({{Emphasis|module}} + {{Emphasis|clearance}})
+
Here “standard” refers to those spur gears with no profile shift coefficient (<math>x</math>).
**{{Emphasis|axle base}} = {{Emphasis|module}} * {{Emphasis|(teeth 1 + 2)}} : 2
+
 
 +
<!--T:36-->
 +
{| class="wikitable"
 +
|+ style="text-align: left;" | Basic formulas common to internal and external standard spur gears
 +
|-
 +
! Symbol !! Term !! Formula !! FCGear Parameter
 +
|-
 +
| <math>m</math> || ''Module'' || - || <math>\texttt{module}</math>
 +
|-
 +
| <math>z</math> || ''Number of Teeth'' || - || <math>\texttt{teeth}</math>
 +
|-
 +
| <math>\alpha</math>
 +
| ''Pressure Angle''
 +
| - <br> Typically,  <math>\alpha = 20^\circ</math>
 +
| <math>\texttt{pressure} {\_} \texttt{parameter}</math>
 +
|-
 +
| d
 +
| ''Reference Diameter'' or ''Pitch Diameter''
 +
| <math>z \cdot m</math>
 +
| -
 +
|-
 +
| <math>h^*_a</math>
 +
| ''Addendum Coefficient''
 +
| - <br> Typically,  <math>h^*_a = 1</math>
 +
| <math>h^*_a = 1 + \texttt{ head}</math>
 +
|-
 +
| <math>h^*_f</math>
 +
| ''Dedendum Coefficient''
 +
| - <br> Typically,  <math>h^*_f = 1.25</math>
 +
| <math>h^*_f = 1 + \texttt{ clearance}</math>
 +
|-
 +
| <math>h_a</math> || ''Addendum'' || <math>h_a = h^*_a \cdot m</math> || -
 +
|-
 +
| <math>h_f</math> || ''Dedendum'' || <math>h_f = h^*_f \cdot m</math> || -
 +
|-
 +
| <math>h</math>
 +
| ''Tooth Height'' or ''Tooth Depth''
 +
| <math>h = h_a + h_f</math> <br> Typically, <math>h = 2.25 \cdot m</math>
 +
| -
 +
|-
 +
| <math>x</math>
 +
| ''Profile Shift Coefficient''
 +
| - <br> For standard gears,  <math>x = 0</math>
 +
|  <math>\texttt{shift}</math>
 +
|}
 +
 
 +
<!--T:37-->
 +
{| class="wikitable"
 +
|+ style="text-align: left;" | Basic formulas specific to external standard spur gears
 +
|-
 +
! Symbol !! Term !! Formula
 +
|-
 +
| <math>d_a</math>
 +
| ''Tip Diameter''
 +
| <math>d_a = d + 2 \cdot h_a</math> <br>
 +
Typically, <math>d_a = (z + 2) \cdot m</math>
 +
|-
 +
| <math>d_f</math>
 +
| ''Root Diameter''
 +
| <math>d_f = d - 2 \cdot h_f</math> <br>
 +
Typically, <math>d_f = (z - 2.5) \cdot m</math>
 +
|}
  
<!--T:31-->
+
<!--T:38-->
*'''External and internal gearing'''
+
{| class="wikitable"
**{{Emphasis|number of teeth}} = {{Emphasis|pitch diameter (dw)}} : module
+
|+ style="text-align: left;" | Basic formulas specific to internal standard spur gears
**{{Emphasis|tooth high}} = 2 * {{Emphasis|module}} + {{Emphasis|clearance}}
+
|-
**{{Emphasis|clearance}} = {{Emphasis|0.1 * module}} til {{Emphasis|0.3 * module}}
+
! Symbol !! Term !! Formula
**{{Emphasis|module}} = {{Emphasis|pitch diameter (dw)}} : {{Emphasis|teeth}}
+
|-
 +
| <math>d_a</math>
 +
| ''Tip Diameter''
 +
| <math>d_a = d - 2 \cdot h_a</math> <br>
 +
Typically, <math>d_a = (z - 2) \cdot m</math>
 +
|-
 +
| <math>d_f</math>
 +
| ''Root Diameter''
 +
| <math>d_f = d + 2 \cdot h_f</math> <br>
 +
Typically, <math>d_f = (z + 2.5) \cdot m</math>
 +
|}
  
<!--T:32-->
+
<!--T:39-->
*'''Internal gearing'''
+
{| class="wikitable"
**{{Emphasis|addendum diameter}} = {{Emphasis|module}} * {{Emphasis|(teeth - 2)}}
+
|+ style="text-align: left;" | Basic formulas specific for a pair of external standard spur gears
**{{Emphasis|dedendum diameter}} = {{Emphasis|pitch diameter (dw)}} + 2 * ({{Emphasis|module}} + {{Emphasis|clearance}})
+
|-
**{{Emphasis|axle base}} = {{Emphasis|module}} * {{Emphasis|(teeth 1 - 2)}} : 2
+
! Symbol !! Term !! Formula
 +
|-
 +
| <math>a</math>
 +
| ''Center Distance''
 +
| <math>d = \frac{d_1 + d_2}{2}</math>
 +
|-
 +
| <math>c</math>
 +
| ''Tip and Root Clearance''
 +
| <math>c_1 = h_{f2} - h_{a1}</math> <br>
 +
<math>c_2 = h_{f1} - h_{a2}</math> <br>
 +
Typically, <math>c = 0.25 \cdot m</math>
 +
|}
  
 
<!--T:33-->
 
<!--T:33-->
Line 159: Line 246:
 
}}
 
}}
 
<translate>
 
<translate>
 +
 +
 
<!--T:28-->
 
<!--T:28-->
 
{{Docnav
 
{{Docnav
 
|
 
|
|[[FCGear_InvoluteRack|FCGear InvoluteRack]]
+
|[[FCGear_InvoluteRack|InvoluteRack]]
|[[FCGear_Workbench|FCGear Workbench]]
+
|[[FCGear_Workbench|FCGear]]
 
|IconL=
 
|IconL=
 
|IconC=FCGear_workbench_icon.svg
 
|IconC=FCGear_workbench_icon.svg

Latest revision as of 11:03, 22 January 2022

Other languages:
Deutsch • ‎English • ‎français • ‎italiano • ‎polski

FCGear InvoluteGear.svg FCGear InvoluteGear

Menu location
FCGear → Create an Involute gear
Workbenches
FCGear
Default shortcut
None
Introduced in version
v0.16
See also
FCGear CycloideGear

Description

Due to the favourable meshing ratio and the relatively simple production, involute gearing is the most common tooth form in mechanical engineering. Gear wheels can be found wherever movement and force are to be transferred from one part to another. For example, they can be found in machines, cars, watches or household appliances. The movement is often transferred directly from one gear wheel to the other, but sometimes also via a chain. In addition, the direction of rotation can be changed. It is also possible to change a radial movement into a linear one via Involute Rack (FCGear InvoluteRack.svg Create an Involute rack).

Involute-Gear example.png

From left to right: Spur gearing, helical gearing, double helical gearing

Usage

  1. Switch to the FCGear workbench icon.svg FCGear Workbench.
  2. Invoke the command several way:
  3. Change the gear parameter to the required conditions (see Properties → Data below).

Properties

Data

Base

  • DataPlacement: Placement is the location and orientation of an object in space.
  • DataLabel: User name of the object in the Tree view.

computed (All properties in this group are calculated automatically and thus read only)

  • Datada: Outside diameter, measured at the addendum (the tip of the teeth).
  • Datadf: Root diameter, measured at the foot of the teeth.
  • Datadw: Working pitch diameter.
  • Datatransverse_pitch: Pitch in the plane of rotation.

gear_parameter

  • Databeta: With the helix angle β a helical gear is created – positive value → rotation direction right, negative value → rotation direction left (see also the information in Notes).
  • Dataclearance: Default is 0,25 (see also the information in Notes).
  • Datadouble_gear: True creates a double helix gear (see also the information in Notes)
  • Datahead: Default is 0,00. This value is used to change the tooth height.
  • Dataheight: Value of the gear width.
  • Datamodule: Module is the ratio of the reference diameter of the gear divided by the number of teeth (see also the information in Notes).
  • Dataproperties_from_tool: If helix angle β is given and properties_from-tool is enabled, gear parameters are internally recomputed for the rotated gear.
  • Datashift: Default is 0,00, generates a positive and negative profile shift (see also the information in Notes).
  • Datateeth: Number of teeth (see also the information in Notes)
  • Dataundercut: True changes the profil of the tooth root (see also the information in Notes).

involute_parameter

  • Datapressure_angle: Default is 20° (see also the information in Notes).

precision

  • Datanumpoints: Default is 6, change of the involute profile. Changing the value can lead to unexpected results.
  • Datasimple: True generates a simplified display (without teeth and only a cylinder in pitch diameter).

tolerance

  • Databackslash: Default is 0,00. Backlash, also called lash or play, is the distance between the teeths at a gear pair.
  • Datareversed_backslash: True backlash decrease or False backlash increase (see also the information in Notes).

View

The parameter descriptions of the View tab will be found in Property editor, further below at Example of the properties of a PartDesign object.

Notes

  • beta: When beta is changed, pitch diameter also changes. The following formula illustrates how the parameters interact: d = m * Z / cos beta (Z = number of teeth, d = pitch diameter, m = module). This means for the spur gear: cos beta = 0 and for the helical gear: cos beta > 0. However, a helix angle of less than 10° has hardly any advantages over straight teeth.
  • clearance: At a gear pair, clearance is the distance between the tooth tip of the first gear and the tooth root of the second gear.
  • double_gear: To use the double helical gearing the helix angle β (beta) for the helical gearing must first be entered.
  • module: Using ISO (International Organization for Standardization) guidelines, Module size is designated as the unit representing gear tooth-sizes. Module (m): m = 1 (p = 3.1416), m = 2 (p = 6.2832), m = 4 (p = 12.566). If you multiply Module by Pi, you can obtain Pitch (p). Pitch is the distance between corresponding points on adjacent teeth.
  • shift: Profile shift is not merely used to prevent undercut. It can be used to adjust center distance between two gears. If a positive correction is applied, such as to prevent undercut in a pinion, the tooth thickness at top is thinner.
  • teeth: If the number of teeth is changed, the pitch diameter also changes (dw).
  • undercut: Undercut is used when the number of teeth of a gear is too small. Otherwise the mating gear will cut into the tooth root. The undercut not only weakens the tooth with a wasp-like waist, but also removes some of the useful involute adjacent to the base circle.
  • pressure_angle: 20° is a standard value here. The pressure angle is defined as the angle between the line-of-action (common tangent to the base circles) and a perpendicular to the line-of-centers. Thus, for standard gears, 14.5° pressure angle gears have base circles much nearer to the roots of teeth than 20° gears. It is for this reason that 14.5° gears encounter greater undercutting problems than 20° gears. Important. the pressure angle changes with a profile shift. Only change the parameter, if sufficient knowledge of the gear geometry is available.
  • reversed_backslash: If there are several gears, pay attention to which gear the parameter is set for.

Limitations

A 2D tooth profile, obtained by setting the Dataheight to zero, cannot be used with features requiring a 2D shape. For example PartDesign Pad and PartDesign AdditiveHelix features do not accept such a profile as base. For technical details, please refer to the related issue on GitHub.

Useful formulas

Standard Spur Gears

Here “standard” refers to those spur gears with no profile shift coefficient ().

Basic formulas common to internal and external standard spur gears
Symbol Term Formula FCGear Parameter
Module -
Number of Teeth -
Pressure Angle -
Typically,
d Reference Diameter or Pitch Diameter -
Addendum Coefficient -
Typically,
Dedendum Coefficient -
Typically,
Addendum -
Dedendum -
Tooth Height or Tooth Depth
Typically,
-
Profile Shift Coefficient -
For standard gears,
Basic formulas specific to external standard spur gears
Symbol Term Formula
Tip Diameter

Typically,

Root Diameter

Typically,

Basic formulas specific to internal standard spur gears
Symbol Term Formula
Tip Diameter

Typically,

Root Diameter

Typically,

Basic formulas specific for a pair of external standard spur gears
Symbol Term Formula
Center Distance
Tip and Root Clearance


Typically,

  • Helical and double helical gearing
    • pitch diameter (dw) = module * teeth : cos beta
    • axle base = (pitch diameter (dw) 1 + 2) : 2
    • addendum diameter = pitch diameter (dw) + 2 * module
    • module = pitch diameter (dw) * cos beta : teeth

Scripting

Use the power of python to automate your gear modeling:

import FreeCAD as App
import freecad.gears.commands
gear = freecad.gears.commands.CreateInvoluteGear.create()
gear.teeth = 20
gear.beta = 20
gear.height = 10
gear.double_helix = True
App.ActiveDocument.recompute()
Gui.SendMsgToActiveView("ViewFit")