FCGear CycloidGear/de

Beschreibung
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.



Anwendung

 * 1) Zum Arbeitsbereich [[Image:FCGear_workbench_icon.svg|16px]] FCGear wechseln.
 * 2) Es gibt mehrere Möglichkeiten den Befehl aufzurufen:
 * 3) * Die Schaltfläche drücken.
 * 4) * Den Menüeintrag auswählen.
 * 5) Die Einstellungen den geforderten Randbedingungen entsprechend ändern (siehe Eigenschaften).

Daten
Ein FCGear-CycloidGear-Objekt wird von einem Part-Formelement abgeleitet und erbt alle seine Eigenschaften. Außerdem hat es die folgenden zusätzlichen Eigenschaften:


 * : Default is 15, change of the involute profile. Changing the value can lead to unexpected results.


 * : Value of the gear width.
 * : Module is the ratio of the reference diameter of the gear divided by the number of teeth (see Notes).
 * : Number of teeth.


 * : (read-only)
 * : Working pitch diameter. (read-only)


 * : Default is 5,00. Diameter of the rolling circle of hypocycloid, normalized by the  (see Notes).
 * : Default is 5,00. Diameter of the rolling circle of epicycloid, normalized by the  (see Notes).




 * : With the helix angle β a helical gear is created (positive value → rotation direction right, negative value → rotation direction left).
 * : creates a double helix gear (see Notes).


 * : Default is 0,00. Backlash, also called lash or play, is the distance between the teeths at a gear pair.


 * : Default is 0,25 (see Notes).
 * : Additional length of the tip of the teeth, normalized by the . Default is 0.



Hinweise

 * 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 on one gear must equal the  on the other, and vice versa. See also the information in  below.
 * : At a gear pair, clearance is the distance between the tooth tip of the first gear and the tooth root of the second gear.
 * : To use the double helical gearing the helix angle β for the helical gearing must first be entered.
 * : 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.

Straight line as hypocycloid
To obtain a straight line, directly towards the center, as hypocycloid, use the following expression for the :. Such a tooth form is often found in historical clockworks and thus called "clock toothing". A larger 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:

The reference diameter is d = m * z, with m being the and z being the. 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 ( 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 +. The dedendum, i.e. the tooth length below the reference circle, is 1 +. Both are normalized by the module, thus we need a head/clearance value of 1 - d_in. The additional and  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.

Nützliche Formeln
Siehe FCGear Evolventenzahnrad.