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Planet-Planet - Represent set of carrier, inner planet, and outer planet gear wheels with specified planet-planet gear ratio

Library

Gears

Description

The Planet-Planet gear block represents a set of carrier, inner planet, and outer planet gear wheels. The outer planet is connected to and rotates with respect to the carrier. The inner planet rotates independently. The planets corotate with a fixed gear ratio that you specify and in opposite directions with respect to the carrier. A planet-planet gear is, along with a ring-planet gear, a basic element of a planetary gear set.

Axis Motions and Constraints

The Planet-Planet block imposes one kinematic and one geometric constraint on the three connected axes:

r_Cω_C = r_Poω_Po+ r_Piω_Pi , r_C = r_Po + r_Pi

In terms of the outer planet-to-inner planet gear ratio g_oi = r_Po/r_Pi, the effective kinematic constraint is

(1 + g_oi)ω_C = ω_Pi + g_oi·ω_Po ,

reducing the three axes to two independent degrees of freedom.

The gear ratio is also the ratio of the number of teeth on each gear and the ratio of the torques in each axis, g_oi = N_Po/N_Pi = τ_Po/τ_Pi.

Warning All gear ratios must be strictly positive. If any gear ratio equals 0 or becomes negative at any time, a SimDriveline simulation stops with an error.

In general, as shown in the first instance, the inner planet shaft does not have to be aligned with the carrier shaft.

Planet-Planet Gear Set

Viewing a Mechanical Drawing of the Planet-Planet Gear

Click here to open a detailed mechanical drawing of the planet-planet gear set.

Viewing a Planet-Planet Gear Animation

If you are connected to the Internet, have an AVI-compatible media streaming application installed on your system, and want to play a recorded animation of this system:

Click the following link. When the download dialog opens, choose Save to file and specify a file name and location on your system.
Click OK to save the AVI file to your system.
Once the downloading is complete, start the AVI animation on your system.

If you do not have an AVI-compatible application, consider using the MATLAB aviread and movie commands instead.

Download animation

Dialog Box and Parameters

Outer planet (Po)/Inner planet (Pi) gear ratio: Ratio g_oi of the outer planet gear radius wheel to the inner planet gear wheel radius. This gear ratio must be strictly positive. The default is 2.

Example

The drive_planet_planet_pic demo illustrates the planet-planet gear with an animation.