FreeCAD: Tu propio modelador paramétrico 3D

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FCGear InvoluteGear
Gear → Involute Gear
Workbenches
FCGear
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None
Introduced in version
v0.16
See also
FCGear CycloideGear

Descripción

The FCGear InvoluteGear command creates an involute gear wheel with spur gearing by default that can also be transformed into a helical gearing or a double helical gearing.

Debido a la favorable relación de engrane y su fabricación relativamente sencilla, el dentado de espiral es la forma de diente más común en la construcción de máquinas. Las ruedas dentadas se encuentran allí donde se desea transferir movimiento y fuerza de una pieza a otra. Se pueden encontrar, por ejemplo, en máquinas, coches, relojes o electrodomésticos. A menudo, el movimiento se transmite directamente de una rueda dentada a otra, pero a veces también a través de una cadena. Además, se puede cambiar el sentido de giro. También es posible cambiar un movimiento radial a uno lineal mediante un cremallera involuta.

De izquierda a derecha: engranaje recto, engranaje helicoidal, engranaje helicoidal doble

Uso

Cambie a entorno de trabajo FCGear.
Hay varias formas de invocar el comando:
- Presione el botón engranaje evolvente en la barra de herramientas.
- Seleccione la opción Gear → Engranaje evolvente del menú.
Cambie el parámetro de engranaje a las condiciones requeridas (ver Propiedades).

Propiedades

Datos

accuracy

Datosnumpoints (Integer): Default is 20. Change of the involute profile. Changing the value can lead to unexpected results.
Datossimple (Bool): Default is false, true generates a simplified display (without teeth and only a cylinder in pitch diameter).

base

Datosgear (PythonObject): Python gear object.
Datosheight (Length): Default is 5 mm. Value of the gear width.
Datosmodule (Length): Default is 1 mm. Module is the ratio of the reference diameter of the gear divided by the number of teeth (see Notes).
Datosnum_teeth (Integer): Default is 15. Number of teeth (see Notes).

computed

Datosaddendum_diameter (Length): Default is 17 mm. Outside diameter, measured at the addendum (the tip of the teeth).
Datosangular_backlash (Angle): (read-only) The angle by which this gear can turn without moving the mating gear.
Datospitch_diameter (Length): Default is 15 mm. The pitch diameter.
Datosroot_diameter (Length): (read-only) The root diameter, measured at the foot of the teeth.
Datostransverse_pitch (Length): Default is 3.14 mm. The transverse pitch.
Datostraverse_module (Length): Default is 1 mm. The traverse module of the generated gear.

fillets

Datoshead_fillet (Float): Default is 0 mm. A fillet for the tooth-head.
Datosroot_fillet (Float): Default is 0 mm. A fillet for the tooth-root.
Datosundercut (Bool): Default is false, true changes the profile of the tooth root (see Notes).

helical

Datosdouble_helix (Bool): Default is false, true creates a double helix gear (see Notes).
Datoshelix_angle (Angle): Default is 0°. With the helix angle β a helical gear is created – positive value → rotation direction right, negative value → rotation direction left (see Notes).
Datosproperties_from_tool (Bool): Default is false. If true and Datoshelix_angle is not zero, gear parameters are recomputed internally for the rotated gear.

hole

DatosAxle_hole (Bool): Default is false. true enables a central hole for an axle.
DatosAxle_holesize (Length): Default is 10 mm. Diameter of the hole for an axle.
Datosoffset_hole (Bool): Default is false, true enables an offset hole.
Datosoffset_holeoffset (Length): Default is 10 mm. The offset of the offset hole.
Datosoffset_holesize (Length): Default is 10 mm. The diameter of the offset hole.

involute

Datospressure_angle (Angle): Default is 20° (see Notes).
Datosshift (Float): Default is 0. Generates a positive and negative profile shift (see Notes).

tolerance

Datosbacklash (Length): Default is 0. Backlash, also called lash or play, is the distance between the teeth at a gear pair.
Datosclearance (Float): Default is 0.25 (see Notes).
Datoshead (Float): Default is 0. This value is used to change the tooth height.
Datosreversed_backlash (Bool): true backlash decrease or false (default) backlash increase see Notes).

version

Datosversion (String):

Notas

Datoshelix_angle (beta, β): Changing the helix angle does not change the pitch diameter, or more precise the transverse pitch diameter (dt) since the Datosmodule property represents the transverse module (mt) unless the Datosproperties_from_tool property is true. In that case it represents the normal module (mn), and all properties depending on the transverse module in the computed group will be divided by cos β and thus enlarged.
- Spur gear: $β = 0^{\circ}$ , $\cos (β) = 1$ and $m_{t} = m_{n}$
- Helical gear: $β > 0^{\circ}$ , $\cos (β) < 1$ and $m_{t} = \frac{m_{n}}{\cos (β)}$
- $d_{t} = z \cdot m_{t} = z \cdot \frac{m_{n}}{\cos (β)}$
However, a helix angle of less than 10° has hardly any advantages over straight teeth.
Datosclearance ( $c$ ): At a gear pair, clearance is the distance between the tooth tip of the first gear and the tooth root of the second gear.
Datosdouble_helix: Activates double helical gearing if the Datoshelix_angle property is larger than 0 ( $β > 0^{\circ}$ ).
Datosmodule (m): Using ISO (International Organization for Standardization) guidelines, Module size is designated as the unit representing gear tooth-sizes.
- The module multiplied by the number of teeth ( $z$ ) defines the pitch circle diameter ( $d$ ): $d = m \cdot z$
- The module multiplied by Pi ( $π$ ) defines the pitch ( $p$ ), the arc distance on the pitch circle between corresponding points of adjacent teeth: $p = m \cdot π$
Datosshift: 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.
Datosnum_teeth (number of teeth, $z$ ): If the number of teeth is changed, the pitch diameter ( $d$ ) also changes.
Datosundercut: 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.
Datospressure_angle ( $α$ ): 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.
Datosreversed_backlash: If there are several gears, pay attention to which gear the parameter is set for.

Limitaciones

A 2D tooth profile, obtained by setting the Datosheight 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.

Fórmulas útiles

Standard Spur Gears

Aquí "standard" se refiere a aquellos engranajes rectos sin coeficiente de cambio de perfil ( $x$ ).

Basic formulas common to internal and external standard spur gears
Symbol	Term	Formula	FCGear Parameter
$m$	Module	-	$module$
$z$	Number of Teeth	-	$num_teeth$
$α$	Pressure Angle	Typically, $α = 2 0^{\circ}$	$pressure_angle$
$d$	Reference Diameter or Pitch Diameter	$d = z \cdot m$	$pitch_diameter$
$h_{a}^{*}$	Addendum Coefficient	Typically, $h_{a}^{*} = 1$	$h_{a}^{*} = 1 + head$
$h_{f}^{*}$	Dedendum Coefficient	Typically, $h_{f}^{*} = 1.25$	$h_{f}^{*} = 1 + clearance$
$h_{a}$	Addendum	$h_{a} = h_{a}^{*} \cdot m$	-
$h_{f}$	Dedendum	$h_{f} = h_{f}^{*} \cdot m$	-
$h$	Tooth Height or Tooth Depth	$h = h_{a} + h_{f}$ Typically, $h = 2.25 \cdot m$	-
$x$	Profile Shift Coefficient	For standard gears, $x = 0$	$shift$

Basic formulas specific to external standard spur gears
Symbol	Term	Formula
$d_{a}$	Tip Diameter	$d_{a} = d + 2 \cdot h_{a}$ Typically, $d_{a} = (z + 2) \cdot m$
$d_{f}$	Root Diameter	$d_{f} = d - 2 \cdot h_{f}$ Typically, $d_{f} = (z - 2.5) \cdot m$

Basic formulas specific to internal standard spur gears
Symbol	Term	Formula
$d_{a}$	Tip Diameter	$d_{a} = d - 2 \cdot h_{a}$ Typically, $d_{a} = (z - 2) \cdot m$
$d_{f}$	Root Diameter	$d_{f} = d + 2 \cdot h_{f}$ Typically, $d_{f} = (z + 2.5) \cdot m$

Basic formulas specific for a pair of external standard spur gears
Symbol	Term	Formula
$a$	Center Distance	$a = \frac{d_{1} + d_{2}}{2}$
$c$	Tip and Root Clearance	$c_{1} = h_{f 2} - h_{a 1}$ $c_{2} = h_{f 1} - h_{a 2}$ Typically, $c = 0.25 \cdot m$

Standard Helical Gears

As above with no profile shifting but the helix angle ( $β$ ) is taken into account.

Helical and double helical gearing
Symbol	Term	Formula
$m_{t}$	Transverse Module	$m_{t} = \frac{m_{n}}{\cos (β)}$
$m_{n}$	Normal Module	$m_{n} = m_{t} \cdot \cos (β)$
$p_{t}$	Transverse Pitch	$p_{t} = π \cdot m_{t} = π \cdot \frac{m_{n}}{\cos (β)}$
$p_{n}$	Normal Pitch	$p_{n} = π \cdot m_{n} = π \cdot m_{t} \cdot \cos (β)$
$d$	Pitch Diameter	$d = z \cdot m_{t} = z \cdot \frac{m_{n}}{\cos (β)}$

Addendum and dedendum are also controlled by the normal module.
It depends on the Datosproperties_from_tool property if the Datosmodule property is used as normal module or transverse module.

Programación

Utilice el poder de Python para automatizar el modelado de sus engranajes:

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

InternalInvoluteGear

FCGear

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