FCGear BevelGear

Menu location
FCGear BevelGear
Gear → Bevel Gear
Workbenches
Gear
Default shortcut
None
Introduced in version
v0.16
See also
None

Description

The FCGear BevelGear command creates a basic bevel gear, a solid object that needs to be trimmed to the correct final shape in following steps.

Partly because of the noise they generate, bevel gears are not used as often as other types of gear. But they are still used in certain sectors, such as food packaging and canned food, lawn and garden equipment, machines such as drills and mills, compression systems for the gas and oil market and flow control valves.

Spiral bevel gears have curved teeth to provide softer engagement and greater tooth to tooth contact compared to a straight bevel gear. This reduces the vibration and noise. They can be used at high speeds and are typically used in motorcycle and bicycle transmissions.

From left to right: Spur gearing, spiral gearing

Usage

Switch to the Gear Workbench.
There are several ways to invoke the command:
- Press the Bevel Gear button in the toolbar.
- Select the Gear → Bevel Gear option from the menu.
A BevelGear object is created according to the default settings.
Change the gear parameter to the required conditions (see Properties).

Properties

Data

base

Datagear (PythonObject): Python gear object.
Dataheight (Length): Default is 5. Value of the bevel gear width, measured from the pitch circle.
Datamodule (Length): Default is 1. Module is the ratio of the pitch diameter of the gear divided by the number of teeth (see Notes).
Datanum_teeth (Integer): Default is 15. Number of teeth.
Datareset_origin (Bool): If true (default) the origin of the gear is at the center of the pitch circle (bottom of the gear) (see Notes).
If false the origin of the gear is at the tip of the pitch cone.

computed

Dataangular_backlash (Angle): (read-only)
Datadw (Length): (read-only) Working pitch diameter.

helical

Databeta (Angle): Default is 0°. With the helix angle β a helical bevel gear is created – positive value → rotation direction right, negative value → rotation direction left.

involute

Datapitch_angle (Angle): Default is 45°. Taper angle of the pitch cone.

involute_parameter

Datapressure_angle (Angle): Default is 20° (see Notes).

precision

Datanumpoints (Integer): Default is 6. Change of the involute profile. Changing the value can lead to unexpected results.

tolerance

Databacklash (Length): Default is 0. Backlash, also called lash or play, is the distance between the teeth at a gear pair.
Dataclearance (Float): Default is 0.1 (see Notes).

version

Dataversion (String):

Notes

Bevel gears are quite complex, because their properties not only depend on the gear ratio but also on the angle between the gear axes. The default bevel gear is built for perpendicular axes and a 1:1 ratio (this is called a miter gear).
Datapitch angle ( $δ$ ): The taper angle of the pitch cone is half the angle between gear axes for a 1:1 ratio, that is 45° for perpendicular axes. Pitch angles for other combinations of ratio and angles between axes can be determined geometrically within a sketch.
Dataclearance ( $c$ ): At a gear pair, clearance is the distance between the tooth tip of the first gear and the tooth root of the second gear.
Datamodule (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: $p = m \cdot π$
Datapressure_angle ( $α$ ): Only change the parameter, if sufficient knowledge of the gear geometry is available.
Datareset_origin: It is recommended to set the parameter to false to have the origin of the gear at the tip of the pitch cone. This way we can extend the bevel gear beyond the pitch circle plane using the module property.
The weak point of this tool is that it builds the geometry from the pitch diameter towards the tip and ignores the fact that there is also geometry in the opposite direction, the back cone. That is why we have to determine the cross-section of the gear at the pitch circle belonging to our chosen module to define cutting geometry and then use an extended (scaled from the tip) bevel gear to be cut. (see Datareset_origin above)

Useful formulas

Basic formulas common to standard bevel gear pairs
Symbol	Term	Formula 1 This Gear	Formula 2 Other Gear
$m$	Module	-	-
$z$	Number of Teeth	-	-
$Σ$	Shaft Angle	-	-
$u$	Gear Ratio	$u_{1} = \frac{z_{2}}{z_{1}}$	$u_{2} = \frac{z_{1}}{z_{2}} = \frac{1}{u_{1}}$
$δ$	Pitch Cone Angle	$δ_{1} = \arctan (\frac{\sin (Σ)}{u_{1} + \cos (Σ)})$	$δ_{2} = \arctan (\frac{\sin (Σ)}{u_{2} + \cos (Σ)})$
$R_{e}$	Cone Distance	$R_{e} = \frac{z_{1} \cdot m}{2 \cdot \sin (δ_{1})}$	$R_{e} = \frac{z_{2} \cdot m}{2 \cdot \sin (δ_{2})}$
$ϑ_{a}$	Addendum Angle	$ϑ_{a} = \arctan (\frac{m}{R_{e}})$	$ϑ_{a} = \arctan (\frac{m}{R_{e}})$
$c$	Clearance	$0.1 \leq c \leq 0.3$	$0.1 \leq c \leq 0.3$
$ϑ_{f}$	Dedendum Angle	$ϑ_{f} = \arctan (\frac{m + c}{R_{e}})$	$ϑ_{f} = \arctan (\frac{m + c}{R_{e}})$
$δ_{a}$	Face Angle	$δ_{a_{1}} = δ_{1} + ϑ_{a}$	$δ_{a_{2}} = δ_{2} + ϑ_{a}$
$δ_{f}$	Root Angle	$δ_{f_{1}} = δ_{1} - ϑ_{f}$	$δ_{f_{2}} = δ_{2} - ϑ_{f}$
$δ_{s}$	Back Cone Angle	$δ_{s_{1}} = 9 0^{\circ} - δ_{1}$	$δ_{s_{2}} = 9 0^{\circ} - δ_{2}$

Basic formulas common to standard bevel gears
Symbol	Term	Formula	FCGear Parameter
$m$	Module	-	$module$
$z$	Number of Teeth	-	$num_teeth$
$δ$	Pitch Cone Angle	-	$pitch_angle$
$p$	Pitch	$p = m \cdot π$	-
$d$	Pitch Diameter	$d = z \cdot m$	$d w$
$d_{a}$	Addendum Diameter	$d_{a} = d + 2 \cdot m \cdot \cos (δ)$	-
$R_{e}$	Cone Distance	$R_{e} = \frac{d}{2 \cdot \sin (δ)} = \frac{z \cdot m}{2 \cdot \sin (δ)}$	-
$b$	Width of Teeth	$b \leq \frac{R_{e}}{3}$	-
$h_{a}$	Addendum	$h_{a} = m$	-
$h_{f}$	Dedendum	$h_{f} = m + c$	-
$h$	Tooth Height or Tooth Depth	$h = h_{a} + h_{f} = 2 \cdot m + c$	-

Pitch diameter AKA reference diameter
Face angle AKA tip angle
Pitch cone angle AKA reference cone angle
Shaft angle AKA axis angle

Substantive reference cone angle [TECH.]

Scripting

Use the power of Python to automate your gear modeling:

import FreeCAD as App
import FreeCADGui as Gui
import freecad.gears.commands
gear = freecad.gears.commands.CreateBevelGear.create()
gear.num_teeth = 20
gear.beta = 20
gear.height = 5
App.ActiveDocument.recompute()
Gui.SendMsgToActiveView("ViewFit")

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