FCGear CycloidGear/it: Difference between revisions

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{{Docnav/it
{{Docnav/it
|[[FCGear_InvoluteRack/it|Cremagliera]]
|[[FCGear_InvoluteRack/it|Cremagliera]]
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|IconR=FCGear_BevelGear.svg
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{{GuiCommand/it
{{GuiCommand/it
|Name=FCGear CycloideGear
|Name=FCGear CycloideGear
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|Shortcut=None
|Shortcut=None
|Version=v0.16
|Version=v0.16
|SeeAlso=[[FCGear InvoluteGear]]
|SeeAlso=[[FCGear InvoluteGear/it|Ingranaggio a spirale]]
}}
}}
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==Descrizione==
==Descrizione==
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Cycloidal gears are very sensitive to an inaccurate adjustment of the centre distance, which then leads to a change in the transmission ratio. For these reasons, cycloidal gears are hardly found in mechanical engineering but are only used in special cases such as in the watch industry, for roots type blowers or for the drive of gear racks.
Cycloidal gears are very sensitive to an inaccurate adjustment of the centre distance, which then leads to a change in the transmission ratio. For these reasons, cycloidal gears are hardly found in mechanical engineering but are only used in special cases such as in the watch industry, for roots type blowers or for the drive of gear racks.


:[[Image:Cycloid-Gear example_1.png]]
[[Image:Cycloid-Gear_example_1.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==
==Usage==


# Switch to the [[Image:FCGear_workbench_icon.svg|22px]] [[FCGear Workbench]].
# Switch to the [[Image:FCGear_workbench_icon.svg|16px]] [[FCGear_Workbench|FCGear Workbench]].
# Invoke the command several way:
# There are several ways to invoke the command:
#* Press the [[File:FCGear_CycloideGear.svg|22px|link=FCGear CycloideGear]] [[FCGear_CycloideGear|Create a Cycloide gear]] button in the tool bar.
#* Press the {{Button|[[File:FCGear_CycloidGear.svg|16px]] [[FCGear_CycloidGear|Cycloid Gear]]}} button in the toolbar.
#* Using the {{MenuCommand|Gear Menu → Cycloide gear}}.
#* Select the {{MenuCommand|Gear → [[File:FCGear_CycloidGear.svg|16px]] Cycloid Gear}} option from the menu.
# Change the gear parameter to the required conditions (see {{Emphasis|Properties → Data}} below).
# Change the gear parameter to the required conditions (see [[#Properties|Properties]]).


==Properties==
==Properties==
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===Data===
===Data===


An FCGear CycloidGear object is derived from a [[Part_Feature|Part Feature]] object and inherits all its properties. It also has the following additional properties:
⚫
{{Properties_Title|Base}}


{{Properties_Title|accuracy}}
* {{PropertyData|Placement}}: [[Placement|Placement]] is the location and orientation of an object in space.
* {{PropertyData|Label}}: User name of the object in the [[Tree_view|Tree view]].


⚫
* {{PropertyData|numpoints|Integer}}: Default is {{Value|15}}. Change of the involute profile. Changing the value can lead to unexpected results.
⚫
{{Properties_Title|cycloid_parameter}}


⚫
{{Properties_Title|base}}
⚫
* {{PropertyData|inner_diameter}}: Default is 5,00. Rolling circle of hypocycloid (see also the information in {{Emphasis|Notes}}).
⚫
* {{PropertyData|outer_diameter}}: Default is 5,00. Rolling circle of epicycloid (see also the information in {{Emphasis|Notes}}).


⚫
* {{PropertyData|height|Length}}: Default is {{Value|5 mm}}. Value of the gear width.
⚫
{{Properties_Title|gear_parameter}}
⚫
* {{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]]).
⚫
* {{PropertyData|teeth|Integer}}: Default is {{Value|15}}. Number of teeth.


⚫
{{Properties_Title|computed}}
⚫
* {{PropertyData|backslash}}: Default is 0,00. Backlash, also called lash or play, is the distance between the teeths at a gear pair.
⚫
* {{PropertyData|beta}}: With the helix angle β a helical gear is created (positive value → rotation direction right, negative value → rotation direction left).
⚫
* {{PropertyData|clearance}}: Default is 0,25 (see also the information in {{Emphasis|Notes}}).
⚫
* {{PropertyData|double_helix}}: {{Emphasis|True}} creates a double helix gear (see also the information in {{Emphasis|Notes}})
⚫
* {{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|numpoints}}: Default is 15, change of the involute profile. Changing the value can lead to unexpected results.
⚫
* {{PropertyData|teeth}}: Number of teeth.


* {{PropertyData|angular_backlash|Angle}}: (read-only)
=== View ===
* {{PropertyData|dw|Length}}: (read-only) Working pitch diameter.


{{Properties_Title|cycloid}}
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}}.

⚫
* {{PropertyData|inner_diameter|Float}}: (read-only) Diameter of the rolling circle of hypocycloid, normalized by the {{PropertyData|module}} (see [[#Notes|Notes]]).
⚫
* {{PropertyData|outer_diameter|Float}}: Default is {{Value|7.5}}. Diameter of the rolling circle of epicycloid, normalized by the {{PropertyData|module}} (see [[#Notes|Notes]]).

{{Properties_Title|fillets}}

* {{PropertyData|head_fillet|Float}}: Default is {{Value|0 mm}}.
* {{PropertyData|root_fillet|Float}}: Default is {{Value|0 mm}}.

{{Properties_Title|helical}}

⚫
* {{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.
⚫
* {{PropertyData|double_helix|Bool}}: Default is {{False}}, {{True}} creates a double helix gear (see [[#Notes|Notes]]).

{{Properties_Title|tolerance}}

⚫
* {{PropertyData|backlash|Length}}: Default is {{Value|0}}. Backlash, also called lash or play, is the distance between the teeth at a gear pair.

⚫
* {{PropertyData|clearance|Float}}: Default is {{Value|0.25}} (see [[#Notes|Notes]]).
* {{PropertyData|head|Float}}: Default is {{Value|0}}. Additional length of the tip of the teeth, normalized by the {{PropertyData|module}}.

{{Properties_Title|version}}

* {{PropertyData|version|String}}:


==Notes==
==Notes==


* Cycloidal gears must always be specially matched to each other and can generally not be exchanged at will!
* Cycloidal gears must always be specially matched to each other and can generally not be exchanged at will: In a gear pair, the value of {{Emphasis|inner_diameter}} on one gear must equal the {{Emphasis|outer_diameter}} on the other, and vice versa. See also the information in {{Emphasis|Properties cycloid parameter view}} below.
* In a gear pair, both gears have the same values for {{Emphasis|inner_diameter}} and {{Emphasis|outer_diameter}}. See also the information in {{Emphasis|Properties cycloid parameter view}} below.
* {{Emphasis|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.
* {{Emphasis|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.
* {{Emphasis|double_helix}}: To use the double helical gearing the helix angle β ({{Emphasis|beta}}) for the helical gearing must first be entered.
* {{Emphasis|double_helix}}: To use the double helical gearing the helix angle β ({{Emphasis|beta}}) for the helical gearing must first be entered.
* {{Emphasis|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.
* {{Emphasis|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.


==Limitations==
==Special cases==


=== Straight line as hypocycloid ===
Limitation are not known yet.

To obtain a straight line, directly towards the center, as hypocycloid, use the following [[Expressions|expression]] for the {{PropertyData|inner_diameter}}: {{incode|teeth / 2}}. Such a tooth form is often found in historical clockworks and thus called "clock toothing". A larger {{PropertyData|clearance}} makes the effect even more visible.

=== Full hypocycloid/epicycloid as tooth ===

To obtain a gear made of complete hypocycloid and epicycloid curves use the following [[Expressions|expressions]]:
* {{PropertyData|inner_diameter}}: {{incode|0.5 + 1e-6}}
* {{PropertyData|outer_diameter}}: {{incode|inner_diameter}}
* {{PropertyData|clearance}}: {{incode|(-1 + inner_diameter/1mm) * 2}}
* {{PropertyData|head}}: {{incode|(-1 + outer_diameter/1mm) * 2}}

The reference diameter is ''d = m * z'', with ''m'' being the {{PropertyData|module}} and ''z'' being the {{PropertyData|teeth}}.
For a complete hypocycloid, the rolling diameter has to be ''d_i = d / (z*2) = m*z / (z*2)''. And if we now normalize this by the module, we get ''d_in = m*z / (z*2) / m = 1 / 2''. The additional explicit tolerance value ({{incode|1e-6}} in the expression above) is required to overcome coincidence issues.

Now the cycloids' rolling circle diameters have to match the gear's addedum/dedendum. The addendum, i.e. the tooth length above the reference circle, is 1 + {{PropertyData|head}}. The dedendum, i.e. the tooth length below the reference circle, is 1 + {{PropertyData|clearance}}. Both are normalized by the module, thus we need a head/clearance value of ''1 - d_in''. The additional {{incode| / 1mm}} and {{incode| * 2}} are required to overcome shortcomings already fixed in the development version of the FCGear Workbench, but porting those fixes back to the stable version may break existing models.

Such "gears" allow the the number of teeth to be as low as ''two'' and are used as rotary vanes in pumps or compressors (cf. [https://en.wikipedia.org/wiki/Roots-type_supercharger Roots-type Supercharger]).

=== Infinitely large epicycloid ===

If the radius of the epicycloid's rolling circle becomes infinitely large, it becomes a rolling straight line. Such a degenerated epicycloid is called involute. Gears with such a tooth form are handled by the [[FCGear_InvoluteGear|involute gear]] command. It is by far the most common tooth form Today.

==Useful formulas==

See [[FCGear_InvoluteGear#Useful_formulas|FCGear InvoluteGear]].


==Properties cycloid parameter view==
==Properties cycloid parameter view==


[[File:CycloidGear inner-outer-diameter 2.svg|400px|thumb|left]]
[[File:CycloidGear inner-outer-diameter 2.svg|400px]]



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{{Docnav
<div class="mw-translate-fuzzy">
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|[[FCGear_InvoluteRack|FCGear InvoluteRack]]
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{{Docnav/it
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|[[FCGear_BevelGear|FCGear BevelGear]]
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|[[FCGear_InvoluteRack/it|Cremagliera]]
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|[[FCGear Workbench|FCGear Workbench]]
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|[[FCGear_BevelGear/it|Ingranaggio conico]]
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|[[FCGear Workbench/it|FCGear]]
|IconL=FCGear_InvoluteRack.svg
|IconL=FCGear_InvoluteRack.svg
|IconC=FCGear_workbench_icon.svg
|IconC=FCGear_workbench_icon.svg
|IconR=FCGear_BevelGear.svg
|IconR=FCGear_BevelGear.svg
}}
}}
</div>


[[Category:Addons{{#translation:}}]]
[[Category:Addons{{#translation:}}]]

Latest revision as of 15:07, 5 October 2022

Other languages:

Ingranaggio cicloidale

Posizione nel menu
FCGear → Create a Cycloide gear
Ambiente
FCGear
Avvio veloce
None
Introdotto nella versione
v0.16
Vedere anche
Ingranaggio a spirale

Descrizione

Cycloidal gears are very sensitive to an inaccurate adjustment of the centre distance, which then leads to a change in the transmission ratio. For these reasons, cycloidal gears are hardly found in mechanical engineering but are only used in special cases such as in the watch industry, for roots type blowers or for the drive of gear racks.

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

Usage

  1. Switch to the FCGear Workbench.
  2. There are several ways to invoke the command:
    • Press the Cycloid Gear button in the toolbar.
    • Select the Gear → Cycloid Gear option from the menu.
  3. Change the gear parameter to the required conditions (see Properties).

Properties

Data

An FCGear CycloidGear object is derived from a Part Feature object and inherits all its properties. It also has the following additional properties:

accuracy

  • Datinumpoints (Integer): Default is 15. Change of the involute profile. Changing the value can lead to unexpected results.

base

  • Datiheight (Length): Default is 5 mm. Value of the gear width.
  • Datimodule (Length): Default is 1 mm. Module is the ratio of the reference diameter of the gear divided by the number of teeth (see Notes).
  • Datiteeth (Integer): Default is 15. Number of teeth.

computed

  • Datiangular_backlash (Angle): (read-only)
  • Datidw (Length): (read-only) Working pitch diameter.

cycloid

  • Datiinner_diameter (Float): (read-only) Diameter of the rolling circle of hypocycloid, normalized by the Datimodule (see Notes).
  • Datiouter_diameter (Float): Default is 7.5. Diameter of the rolling circle of epicycloid, normalized by the Datimodule (see Notes).

fillets

  • Datihead_fillet (Float): Default is 0 mm.
  • Datiroot_fillet (Float): Default is 0 mm.

helical

  • Datibeta (Angle): Default is 0 °. With the helix angle β a helical gear is created – positive value → rotation direction right, negative value → rotation direction left.
  • Datidouble_helix (Bool): Default is false, true creates a double helix gear (see Notes).

tolerance

  • Datibacklash (Length): Default is 0. Backlash, also called lash or play, is the distance between the teeth at a gear pair.
  • Daticlearance (Float): Default is 0.25 (see Notes).
  • Datihead (Float): Default is 0. Additional length of the tip of the teeth, normalized by the Datimodule.

version

  • Dativersion (String):

Notes

  • Cycloidal gears must always be specially matched to each other and can generally not be exchanged at will: In a gear pair, the value of inner_diameter on one gear must equal the outer_diameter on the other, and vice versa. See also the information in Properties cycloid parameter view below.
  • 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_helix: 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.

Special cases

Straight line as hypocycloid

To obtain a straight line, directly towards the center, as hypocycloid, use the following expression for the Datiinner_diameter: teeth / 2. Such a tooth form is often found in historical clockworks and thus called "clock toothing". A larger Daticlearance makes the effect even more visible.

Full hypocycloid/epicycloid as tooth

To obtain a gear made of complete hypocycloid and epicycloid curves use the following expressions:

  • Datiinner_diameter: 0.5 + 1e-6
  • Datiouter_diameter: inner_diameter
  • Daticlearance: (-1 + inner_diameter/1mm) * 2
  • Datihead: (-1 + outer_diameter/1mm) * 2

The reference diameter is d = m * z, with m being the Datimodule and z being the Datiteeth. For a complete hypocycloid, the rolling diameter has to be d_i = d / (z*2) = m*z / (z*2). And if we now normalize this by the module, we get d_in = m*z / (z*2) / m = 1 / 2. The additional explicit tolerance value (1e-6 in the expression above) is required to overcome coincidence issues.

Now the cycloids' rolling circle diameters have to match the gear's addedum/dedendum. The addendum, i.e. the tooth length above the reference circle, is 1 + Datihead. The dedendum, i.e. the tooth length below the reference circle, is 1 + Daticlearance. Both are normalized by the module, thus we need a head/clearance value of 1 - d_in. The additional / 1mm and * 2 are required to overcome shortcomings already fixed in the development version of the FCGear Workbench, but porting those fixes back to the stable version may break existing models.

Such "gears" allow the the number of teeth to be as low as two and are used as rotary vanes in pumps or compressors (cf. Roots-type Supercharger).

Infinitely large epicycloid

If the radius of the epicycloid's rolling circle becomes infinitely large, it becomes a rolling straight line. Such a degenerated epicycloid is called involute. Gears with such a tooth form are handled by the involute gear command. It is by far the most common tooth form Today.

Useful formulas

See FCGear InvoluteGear.

Properties cycloid parameter view


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