WOLFRAM SYSTEM MODELER
PlanetaryGearClass containing a basic planetary gear model |
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Diagram
Wolfram Language
In[1]:=
SystemModel["RotatingMachinery.Gears.PlanetaryGears.PlanetaryGear"]
Out[1]:=
Information
Planetary Gear
Planetary gear consisting of three elements: sun gear, planet gears and ring gear, [1–4]. The sun gear is located at the center. The planet gears are mounted on a carrier and revolve around the sun gear. Both systems are located inside the ring gear.
The sun and planet gears are externally meshed and the ring gear is internally meshed. Many different variations and arrangements of planetary gears can be found, including applications such as clocks, car mirrors, toys, turbine engines and the more familiar automatic car gearboxes and wind turbines.
Figure 1 shows an animation of the planetary gear, and also naming of the wheels.
Figure 1: Planetary gear.
Figure 2 displays the parameters of the planetary gear system, including number of teeth, modules and profile shift. The initial angles of the gearwheels are also calculated in the parameters tab so that the gears teeth are in contact.
Figure 2: Planetary gear parameters tab.
The theory around planetary gears can be found [5].
References
[1] Dahl, M., H. Wettergren, and H. Tidefelt. "Modelica Spur Gears with Hertzian Contact Forces." Proceedings of the 12th International Modelica Conference, Prague, Czech Republic, May 15-17, 2017. Linköping Electronic Conference Proceedings 132, no. 82 (2017): 755-763. http://dx.doi.org/10.3384/ecp17132755.
[2] Van der Lunden, F. L. J. and P. H. Vazques de Souza Silva. "Modelling and Simulating the Efficiency and Elasticity of Gearboxes." Proceedings of the 7th International Modelica Conference, Como; Italy, Sep 20-22, 2009. Linköping Electronic Conference Proceedings 43, no. 29 (2009): 270-277. http://dx.doi.org/10.3384/ecp09430052.
[3] Kosenko, I. and I. Gusev. "Implementation of the Spur Involute Gear Model on Modelica." Proceedings of the 8th International Modelica Conference, Dresden; Germany, Mar 20-22, 2011. Linköping Electronic Conference Proceedings 63, no. 35 (2011): 315-328. https://ep.liu.se/ecp/063/035/ecp11063035.pdf.
[4] B. Paul. Kinematics and Dynamics of Planar Machinery. Prentice Hall, 1979.
[5] Wikipedia. "Epicylic Gearing". https://en.wikipedia.org/wiki/Epicyclic_gearing.
Parameters (16)
| m |
Value: Type: Module (m) Description: Gear module |
|---|---|
| alpha0 |
Value: 20 * Modelica.Constants.pi / 180 Type: Angle (rad) Description: Reference profile angle |
| zs |
Value: Type: Integer Description: Number of teeth for sunwheel |
| xs |
Value: 0 Type: Real Description: Profile shift for sunwheel |
| zp |
Value: Type: Integer Description: Number of teeth for planetwheel |
| xp |
Value: 0 Type: Real Description: Profile shift for planetwheel |
| zr |
Value: Type: Integer Description: Number of teeth for ringwheel |
| xr |
Value: 0 Type: Real Description: Profile shift for ringwheel |
| initialAnglePlanetShaft1 |
Value: 0 Type: Angle_deg (°) Description: Angle of planet shaft. Normally 360/3*i |
| initialAnglePlanetShaft2 |
Value: 120 Type: Angle_deg (°) Description: Angle of planet shaft. Normally 360/3*i |
| initialAnglePlanetShaft3 |
Value: 240 Type: Angle_deg (°) Description: Angle of planet shaft. Normally 360/3*i |
| initialRotationSunWheel |
Value: initialAnglePlanetShaft1 - 360 / zs * floor(initialAnglePlanetShaft1 / 360 * zs) Type: Angle_deg (°) Description: Gear wheel 1 initial angle of rotation |
| initialRotationPlanetWheel1 |
Value: 180 + initialAnglePlanetShaft1 - 360 / zp * (floor((180 + initialAnglePlanetShaft1) / 360 * zp) + 0.5) Type: Angle_deg (°) Description: Planet wheel 1 initial angle of rotation |
| initialRotationPlanetWheel2 |
Value: initialRotationPlanetWheel1 + (initialAnglePlanetShaft2 - initialAnglePlanetShaft1) * (zp / zp + zs / zp - 1) Type: Angle_deg (°) Description: Planet wheel 2 initial angle of rotation |
| initialRotationPlanetWheel3 |
Value: initialRotationPlanetWheel1 + (initialAnglePlanetShaft3 - initialAnglePlanetShaft1) * (zp / zp + zs / zp - 1) Type: Angle_deg (°) Description: Planet wheel 3 initial angle of rotation |
| InitialRotationWheelRingWheel |
Value: initialAnglePlanetShaft1 + initialRotationPlanetWheel1 * zp / zs Type: Angle_deg (°) Description: Sun wheel initial angle of rotation |
Connectors (4)
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frame_sun_b |
Type: Frame_b Description: Coordinate system fixed to the component with one cut-force and cut-torque (non-filled rectangular icon) |
|---|---|---|
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frame_sun_a |
Type: Frame_a Description: Coordinate system fixed to the component with one cut-force and cut-torque (filled rectangular icon) |
|
frame_carrier |
Type: Frame_a Description: Coordinate system fixed to the component with one cut-force and cut-torque (filled rectangular icon) |
|
frame_ring |
Type: Frame_a Description: Coordinate system fixed to the component with one cut-force and cut-torque (filled rectangular icon) |
Components (15)
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sunWheel |
Type: SpurGear Description: Spur gear with mass, rotations and visualization |
|---|---|---|
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ringWheel |
Type: SpurGear Description: Spur gear with mass, rotations and visualization |
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planetaryWheel1 |
Type: PlanetWheel Description: Planet wheel to be used in PlanetaryGears |
 |
fixedTranslation |
Type: FixedTranslation Description: Fixed translation of frame_b with respect to frame_a |
|
fixedTranslation1 |
Type: FixedTranslation Description: Fixed translation of frame_b with respect to frame_a |
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gearForceCalculation |
Type: GearForceCalculation Description: Class calculating gear mesh contact forces |
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gearForceCalculationInner |
Type: GearForceCalculationInner Description: Class calculating internal gear mesh contact forces |
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planetaryWheel2 |
Type: PlanetWheel Description: Planet wheel to be used in PlanetaryGears |
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gearForceCalculation1 |
Type: GearForceCalculation Description: Class calculating gear mesh contact forces |
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gearForceCalculationInner1 |
Type: GearForceCalculationInner Description: Class calculating internal gear mesh contact forces |
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planetaryWheel3 |
Type: PlanetWheel Description: Planet wheel to be used in PlanetaryGears |
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gearForceCalculation2 |
Type: GearForceCalculation Description: Class calculating gear mesh contact forces |
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gearForceCalculationInner2 |
Type: GearForceCalculationInner Description: Class calculating internal gear mesh contact forces |
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cylindricalBeam |
Type: CylindricalBeam Description: Class with a flexible cylindrical beam |
|
cylindricalBeam1 |
Type: CylindricalBeam Description: Class with a flexible cylindrical beam |
Used in Examples (2)
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RotatingMachinery.Examples.Gears.PlanetaryGears A basic planetary gear application; WindTurbine Part I |
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RotatingMachinery.Examples.Gears.PlanetaryGears Assembly of a planetary gear and a three-shafted gearbox; Part I and Part II |