FCGear InvoluteGear: Difference between revisions
(Added calculated properties "da" and "df", introduced with https://github.com/looooo/freecad.gears/pull/69) |
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{{Docnav |
{{Docnav |
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|[[FCGear_InternalInvoluteGear|InternalInvoluteGear]] |
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|[[FCGear_InvoluteRack|FCGear InvoluteRack]] |
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|[[FCGear_Workbench|FCGear |
|[[FCGear_Workbench|FCGear]] |
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|IconL= |
|IconL= |
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|IconR=FCGear_InternalInvoluteGear.svg |
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|IconC=FCGear_workbench_icon.svg |
|IconC=FCGear_workbench_icon.svg |
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|IconR=FCGear_InvoluteRack.svg |
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}} |
}} |
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{{GuiCommand |
{{GuiCommand |
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|Name=FCGear InvoluteGear |
|Name=FCGear InvoluteGear |
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|MenuLocation= |
|MenuLocation=Gear → Involute Gear |
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|Workbenches=[[ |
|Workbenches=[[FCGear_Workbench|FCGear]] |
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|Shortcut=None |
|Shortcut=None |
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|Version=v0.16 |
|Version=v0.16 |
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|SeeAlso=[[FCGear CycloideGear]] |
|SeeAlso=[[FCGear_CycloideGear|FCGear CycloideGear]] |
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}} |
}} |
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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. |
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 an [[FCGear_InvoluteRack|involute rack]]. |
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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]]). |
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</translate> |
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[[Image:Involute-Gear_example.png]] |
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<translate> |
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{{Caption|From left to right: Spur gearing, helical gearing, double helical gearing}} |
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:[[Image:Involute-Gear example.png]] |
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:{{Caption|From left to right: Spur gearing, helical gearing, double helical gearing |
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}} |
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==Usage== <!--T:6--> |
==Usage== <!--T:6--> |
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<!--T:7--> |
<!--T:7--> |
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# Switch to the [[Image:FCGear_workbench_icon.svg| |
# Switch to the [[Image:FCGear_workbench_icon.svg|16px]] [[FCGear_Workbench|FCGear Workbench]]. |
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# |
# There are several ways to invoke the command: |
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#* Press the [[File:FCGear_InvoluteGear.svg| |
#* Press the {{Button|[[File:FCGear_InvoluteGear.svg|16px]] [[FCGear_InvoluteGear|Involute Gear]]}} button in the toolbar. |
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#* |
#* Select the {{MenuCommand|Gear → [[File:FCGear_InvoluteGear.svg|16px]] Involute Gear}} option from the menu. |
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# Change the gear parameter to the required conditions (see |
# Change the gear parameter to the required conditions (see [[#Properties|Properties]]). |
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==Properties== <!--T:8--> |
==Properties== <!--T:8--> |
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An FCGear InvoluteGear object is derived from a [[Part_Feature|Part Feature]] object and inherits all its properties. It also has the following additional properties: |
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===Data=== <!--T:9--> |
===Data=== <!--T:9--> |
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{{Properties_Title| |
{{Properties_Title|accuracy}} |
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* {{PropertyData|numpoints|Integer}}: Default is {{Value|6}}. Change of the involute profile. Changing the value can lead to unexpected results. |
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* {{PropertyData|simple|Bool}}: Default is {{False}}, {{True}} generates a simplified display (without teeth and only a cylinder in pitch diameter). |
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{{Properties_Title|base}} |
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* {{PropertyData| |
* {{PropertyData|height|Length}}: Default is {{Value|5 mm}}. Value of the gear width. |
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* {{PropertyData| |
* {{PropertyData|module|Length}}: Default is {{Value|1 mm}}. Module is the ratio of the reference diameter of the gear divided by the number of teeth (see [[#Notes|Notes]]). |
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* {{PropertyData|teeth|Integer}}: Default is {{Value|15}}. Number of teeth (see [[#Notes|Notes]]). |
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* {{PropertyData| |
* {{PropertyData|angular_backlash|Angle}}: (read-only) |
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* {{PropertyData| |
* {{PropertyData|da|Length}}: (read-only) Outside diameter, measured at the addendum (the tip of the teeth). |
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* {{PropertyData| |
* {{PropertyData|df|Length}}: (read-only) Root diameter, measured at the foot of the teeth. |
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* {{PropertyData|dw|Length}}: (read-only) Working pitch diameter. |
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* {{PropertyData|transverse_pitch|Length}}: (read-only) Pitch in the plane of rotation. |
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{{Properties_Title| |
{{Properties_Title|fillets}} |
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* {{PropertyData|head_fillet|Float}}: Default is {{Value|0 mm}}. |
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* {{PropertyData|beta}}: 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 {{Emphasis|Notes}}). |
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* {{PropertyData| |
* {{PropertyData|root_fillet|Float}}: Default is {{Value|0 mm}}. |
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* {{PropertyData| |
* {{PropertyData|undercut|Bool}}: Default is {{False}}, {{True}} changes the profile of the tooth root (see [[#Notes|Notes]]). |
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* {{PropertyData|head}}: Default is 0,00. This value is used to change the tooth height. |
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* {{PropertyData|height}}: Value of the gear width. |
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* {{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}}). |
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* {{PropertyData|numpoints}}: Default is 6, change of the involute profile. Changing the value can lead to unexpected results. |
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* {{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. |
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* {{PropertyData|shift}}: Default is 0,00, generates a positive and negative profile shift (see also the information in {{Emphasis|Notes}}). |
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* {{PropertyData|simple}}: {{Emphasis|True}} generates a simplified display (without teeth and only a cylinder in pitch diameter). |
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* {{PropertyData|teeth}}: Number of teeth (see also the information in {{Emphasis|Notes}}) |
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* {{PropertyData|undercut}}: {{Emphasis|True}} changes the profil of the tooth root (see also the information in {{Emphasis|Notes}}). |
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{{Properties_Title| |
{{Properties_Title|helical}} |
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<!--T:49--> |
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* {{PropertyData| |
* {{PropertyData|beta|Angle}}: Default is {{Value|0 °}}. With the helix angle β a helical gear is created – positive value → rotation direction right, negative value → rotation direction left (see [[#Notes|Notes]]). |
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* {{PropertyData|double_helix|Bool}}: Default is {{False}}, {{True}} creates a double helix gear (see [[#Notes|Notes]]). |
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* {{PropertyData|properties_from_tool|Bool}}: Default is {{False}}. If {{True}} and {{PropertyData|beta}} is not zero, gear parameters are recomputed internally for the rotated gear. |
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{{Properties_Title|involute}} |
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* {{PropertyData|pressure_angle|Angle}}: Default is {{Value|20 °}} (see [[#Notes|Notes]]). |
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* {{PropertyData|shift|Float}}: Default is {{Value|0}}. Generates a positive and negative profile shift (see [[#Notes|Notes]]). |
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{{Properties_Title|tolerance}} |
{{Properties_Title|tolerance}} |
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* {{PropertyData| |
* {{PropertyData|backlash|Length}}: Default is {{Value|0}}. Backlash, also called lash or play, is the distance between the teeth at a gear pair. |
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* {{PropertyData| |
* {{PropertyData|clearance|Float}}: Default is {{Value|0.25}} (see [[#Notes|Notes]]). |
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* {{PropertyData|head|Float}}: Default is {{Value|0}}. This value is used to change the tooth height. |
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* {{PropertyData|reversed_backlash|Bool}}: {{True}} backlash decrease or {{False}} (default) backlash increase see [[#Notes|Notes]]). |
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{{Properties_Title|version}} |
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* {{PropertyData|version|String}}: |
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The parameter descriptions of the {{Emphasis|View}} tab will be found in [[Property_editor|Property editor]], further below at {{Emphasis|Example of the properties of a PartDesign object}}. |
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==Notes== <!--T:22--> |
==Notes== <!--T:22--> |
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* {{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}}). |
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* {{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. |
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* {{Emphasis| |
* {{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. |
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* {{Emphasis| |
* {{Emphasis|reversed_backlash}}: If there are several gears, pay attention to which gear the parameter is set for. |
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==Limitations== <!--T:24--> |
==Limitations== <!--T:24--> |
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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]. |
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Limitation are not known yet. |
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==Useful formulas== <!--T:29--> |
==Useful formulas== <!--T:29--> |
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===Standard Spur Gears=== <!--T:40--> |
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*'''External gearing''' |
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**{{Emphasis|addendum diameter}} = {{Emphasis|module}} * {{Emphasis|(teeth +2 )}} |
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**{{Emphasis|dedendum diameter}} = {{Emphasis|pitch diameter (dw)}} - 2 * ({{Emphasis|module}} + {{Emphasis|clearance}}) |
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**{{Emphasis|axle base}} = {{Emphasis|module}} * {{Emphasis|(teeth 1 + 2)}} : 2 |
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Here “standard” refers to those spur gears with no profile shift coefficient (<math>x</math>). |
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*'''External and internal gearing''' |
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**{{Emphasis|number of teeth}} = {{Emphasis|pitch diameter (dw)}} : module |
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**{{Emphasis|tooth high}} = 2 * {{Emphasis|module}} + {{Emphasis|clearance}} |
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**{{Emphasis|clearance}} = {{Emphasis|0.1 * module}} til {{Emphasis|0.3 * module}} |
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**{{Emphasis|module}} = {{Emphasis|pitch diameter (dw)}} : {{Emphasis|teeth}} |
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{| class="wikitable" |
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*'''Internal gearing''' |
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|+ style="text-align: left;" | Basic formulas common to internal and external standard spur gears |
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**{{Emphasis|addendum diameter}} = {{Emphasis|module}} * {{Emphasis|(teeth - 2)}} |
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|- |
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**{{Emphasis|dedendum diameter}} = {{Emphasis|pitch diameter (dw)}} + 2 * ({{Emphasis|module}} + {{Emphasis|clearance}}) |
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! Symbol !! Term !! Formula !! FCGear Parameter |
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**{{Emphasis|axle base}} = {{Emphasis|module}} * {{Emphasis|(teeth 1 - 2)}} : 2 |
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|- |
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| <math>m</math> || ''Module'' || - || <math>\texttt{module}</math> |
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|- |
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| <math>z</math> || ''Number of Teeth'' || - || <math>\texttt{teeth}</math> |
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|- |
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| <math>\alpha</math> |
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| ''Pressure Angle'' |
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| - <br> Typically, <math>\alpha = 20^\circ</math> |
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| <math>\texttt{pressure} {\_} \texttt{parameter}</math> |
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|- |
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| <math>d</math> |
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| ''Reference Diameter'' or ''Pitch Diameter'' |
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| <math>z \cdot m</math> |
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| - |
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|- |
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| <math>h^*_a</math> |
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| ''Addendum Coefficient'' |
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| - <br> Typically, <math>h^*_a = 1</math> |
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| <math>h^*_a = 1 + \texttt{ head}</math> |
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|- |
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| <math>h^*_f</math> |
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| ''Dedendum Coefficient'' |
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| - <br> Typically, <math>h^*_f = 1.25</math> |
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| <math>h^*_f = 1 + \texttt{ clearance}</math> |
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|- |
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| <math>h_a</math> || ''Addendum'' || <math>h_a = h^*_a \cdot m</math> || - |
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|- |
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| <math>h_f</math> || ''Dedendum'' || <math>h_f = h^*_f \cdot m</math> || - |
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|- |
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| <math>h</math> |
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| ''Tooth Height'' or ''Tooth Depth'' |
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| <math>h = h_a + h_f</math> <br> Typically, <math>h = 2.25 \cdot m</math> |
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| - |
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|- |
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| <math>x</math> |
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| ''Profile Shift Coefficient'' |
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| - <br> For standard gears, <math>x = 0</math> |
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| <math>\texttt{shift}</math> |
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|} |
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{| class="wikitable" |
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|+ style="text-align: left;" | Basic formulas specific to external standard spur gears |
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|- |
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! Symbol !! Term !! Formula |
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|- |
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| <math>d_a</math> |
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| ''Tip Diameter'' |
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| <math>d_a = d + 2 \cdot h_a</math> <br> |
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Typically, <math>d_a = (z + 2) \cdot m</math> |
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|- |
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| <math>d_f</math> |
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| ''Root Diameter'' |
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| <math>d_f = d - 2 \cdot h_f</math> <br> |
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Typically, <math>d_f = (z - 2.5) \cdot m</math> |
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|} |
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{| class="wikitable" |
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|+ style="text-align: left;" | Basic formulas specific to internal standard spur gears |
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|- |
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! Symbol !! Term !! Formula |
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|- |
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| <math>d_a</math> |
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| ''Tip Diameter'' |
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| <math>d_a = d - 2 \cdot h_a</math> <br> |
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Typically, <math>d_a = (z - 2) \cdot m</math> |
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|- |
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| <math>d_f</math> |
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| ''Root Diameter'' |
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| <math>d_f = d + 2 \cdot h_f</math> <br> |
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Typically, <math>d_f = (z + 2.5) \cdot m</math> |
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|} |
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<!--T:39--> |
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{| class="wikitable" |
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|+ style="text-align: left;" | Basic formulas specific for a pair of external standard spur gears |
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|- |
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! Symbol !! Term !! Formula |
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|- |
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| <math>a</math> |
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| ''Center Distance'' |
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| <math>d = \frac{d_1 + d_2}{2}</math> |
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|- |
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| <math>c</math> |
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| ''Tip and Root Clearance'' |
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| <math>c_1 = h_{f2} - h_{a1}</math> <br> |
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<math>c_2 = h_{f1} - h_{a2}</math> <br> |
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Typically, <math>c = 0.25 \cdot m</math> |
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|} |
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Use the power of |
Use the power of Python to automate your gear modeling: |
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</translate> |
</translate> |
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{{Code|code= |
{{Code|code= |
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}} |
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<translate> |
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{{Docnav |
{{Docnav |
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|[[FCGear_InternalInvoluteGear|InternalInvoluteGear]] |
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|[[FCGear_InvoluteRack|FCGear InvoluteRack]] |
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|[[FCGear_Workbench|FCGear |
|[[FCGear_Workbench|FCGear]] |
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|IconL= |
|IconL= |
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|IconR=FCGear_InternalInvoluteGear.svg |
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|IconC=FCGear_workbench_icon.svg |
|IconC=FCGear_workbench_icon.svg |
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|IconR=FCGear_InvoluteRack.svg |
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}} |
}} |
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Latest revision as of 23:48, 29 February 2024
FCGear InvoluteGear |
Menu location |
---|
Gear → 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 an involute rack.
From left to right: Spur gearing, helical gearing, double helical gearing
Usage
- Switch to the FCGear Workbench.
- There are several ways to invoke the command:
- Press the Involute Gear button in the toolbar.
- Select the Gear → Involute Gear option from the menu.
- Change the gear parameter to the required conditions (see Properties).
Properties
An FCGear InvoluteGear object is derived from a Part Feature object and inherits all its properties. It also has the following additional properties:
Data
accuracy
- Datanumpoints (
Integer
): Default is6
. Change of the involute profile. Changing the value can lead to unexpected results. - Datasimple (
Bool
): Default isfalse
,true
generates a simplified display (without teeth and only a cylinder in pitch diameter).
base
- Dataheight (
Length
): Default is5 mm
. Value of the gear width. - Datamodule (
Length
): Default is1 mm
. Module is the ratio of the reference diameter of the gear divided by the number of teeth (see Notes). - Datateeth (
Integer
): Default is15
. Number of teeth (see Notes).
computed
- Dataangular_backlash (
Angle
): (read-only) - Datada (
Length
): (read-only) Outside diameter, measured at the addendum (the tip of the teeth). - Datadf (
Length
): (read-only) Root diameter, measured at the foot of the teeth. - Datadw (
Length
): (read-only) Working pitch diameter. - Datatransverse_pitch (
Length
): (read-only) Pitch in the plane of rotation.
fillets
- Datahead_fillet (
Float
): Default is0 mm
. - Dataroot_fillet (
Float
): Default is0 mm
. - Dataundercut (
Bool
): Default isfalse
,true
changes the profile of the tooth root (see Notes).
helical
- Databeta (
Angle
): Default is0 °
. With the helix angle β a helical gear is created – positive value → rotation direction right, negative value → rotation direction left (see Notes). - Datadouble_helix (
Bool
): Default isfalse
,true
creates a double helix gear (see Notes). - Dataproperties_from_tool (
Bool
): Default isfalse
. Iftrue
and Databeta is not zero, gear parameters are recomputed internally for the rotated gear.
involute
- Datapressure_angle (
Angle
): Default is20 °
(see Notes). - Datashift (
Float
): Default is0
. Generates a positive and negative profile shift (see Notes).
tolerance
- Databacklash (
Length
): Default is0
. Backlash, also called lash or play, is the distance between the teeth at a gear pair. - Dataclearance (
Float
): Default is0.25
(see Notes). - Datahead (
Float
): Default is0
. This value is used to change the tooth height. - Datareversed_backlash (
Bool
):true
backlash decrease orfalse
(default) backlash increase see Notes).
version
- Dataversion (
String
):
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_backlash: 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 ().
Symbol | Term | Formula | FCGear Parameter |
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Module | - | ||
Number of Teeth | - | ||
Pressure Angle | - Typically, |
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Reference Diameter or Pitch Diameter | - | ||
Addendum Coefficient | - Typically, |
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Dedendum Coefficient | - Typically, |
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Addendum | - | ||
Dedendum | - | ||
Tooth Height or Tooth Depth | Typically, |
- | |
Profile Shift Coefficient | - For standard gears, |
Symbol | Term | Formula |
---|---|---|
Tip Diameter | Typically, | |
Root Diameter | Typically, |
Symbol | Term | Formula |
---|---|---|
Tip Diameter | Typically, | |
Root Diameter | Typically, |
Symbol | Term | Formula |
---|---|---|
Center Distance | ||
Tip and Root Clearance | |
- 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")