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Planetary Gear - Represent set of carrier, sun, planet, and ring gear wheels with specified ring-sun gear ratio

Library

Gears

Description

The Planetary Gear block represents a set of carrier, ring, planet, and sun gear wheels. A planetary gear set can be constructed from planet-planet and ring-planet gears. The ring and sun corotate with a fixed gear ratio and in opposite directions with respect to the carrier.

To model the planet's rotational inertia, connect an Inertia block to the optional planet connector port.

Axis Motions and Constraints

The Planetary Gear block imposes two kinematic and two geometric constraints on the three connected axes and the fourth, internal wheel (planet):

r_Cω_C = r_Sω_S+ r_Pω_P , r_C = r_S + r_P

r_Rω_R = r_Cω_C+ r_Pω_P , r_R = r_C + r_P

In terms of the ring-to-sun gear ratio g_RS = r_R/r_S, the key effective kinematic constraint is

(1 + g_RS)ω_C = ω_S + g_RS·ω_R

The four degrees of freedom are reduced 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_RS = N_R/N_S = τ_R/τ_S.

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.

The gear ratio g_RS must be strictly greater than one.

Planetary Gear Set

Viewing a Mechanical Drawing of the Planetary Gear

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

Viewing a Planetary 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

Ring (R)/Sun (S) gear ratio

Ratio g_RS of the ring gear wheel radius to the sun gear wheel radius. This gear ratio must be strictly greater than 1. The default is 2.

Show planet connector port (P)

Selecting this check box makes the connector port for the planet gear visible and available for connection to other driveline blocks.

Use this connector port to connect an Inertia block if you want to model the planet gear's inertia. The default is unselected, with the planet gear's inertia neglected in the dynamics.

Example

The drive_planetary_pic demo illustrates the planetary gear with an animation.