SimDriveline™

Dual-Ratio Planetary

Represent set of carrier, sun, planet, and ring gear wheels with specified ring-planet and planet-sun gear ratios

Library

Gears

Description

The Dual-Ratio Planetary block represents a set of carrier, sun, planet, and ring gear wheels. The planet is a single gear wheel with two different radii meshing with the ring and the sun, respectively. The ring and planet corotate with one fixed gear ratio. The planet and sun corotate with another fixed gear ratio.

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

Axis Motions and Constraints

The Dual-Ratio Planetary 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_P1ω_P , r_C = r_S + r_P1

r_Rω_R = r_Cω_C+ r_P2ω_P , r_R = r_C + r_P2

In terms of the ring-to-planet gear ratio g_RP = r_R/r_P2 and the planet-to-sun gear ratio g_PS = r_P1/r_S, the key kinematic constraint is

(1 + g_RP·g_PS)ω_C = ω_S + g_RP·g_PS·ω_R

The four degrees of freedom are reduced to two independent degrees of freedom.

The gear ratios are also the ratios of the number of teeth on each gear and the ratios of the torques in each axis, g_RP = N_R/N_P2 = τ_R/τ_P2 and g_PS = N_P1/N_S = τ_P1/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_RP must be strictly greater than one.

Dual-Ratio Planetary Gear Set

Viewing a Mechanical Drawing of the Dual-Ratio Planetary Gear

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

Viewing a Dual-Ratio Planetary Gear Animation

If you are connected to the Internet and have an AVI-compatible media streaming application installed on your system, click here to play a recorded animation of the dual-ratio planetary gear set. The animation takes a short time to download and start.

Dialog Box and Parameters

Ring (R)/Planet (P) gear ratio

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

Planet (P)/Sun (S) gear ratio

Ratio g_PS of the planet gear wheel radius to the sun gear wheel radius. This ratio must be strictly positive. 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