Planetary Gear

Ideal planetary gear with sun, ring, and carrier

• 

×

Libraries:
Powertrain Blockset / Drivetrain / Couplings

Description

The Planetary Gear block implements an ideal planetary gear coupling consisting of a rigidly coupled sun, ring, and carrier gears. The block calculates the dynamic response to the sun, carrier, and ring input torques.

In fuel economy and powertrain studies, you can use the Planetary Gear block as a power-split device by coupling it to common driveline elements such as transmissions, engines, clutches, and differentials.

These equations of motion represent the dynamic response of the planetary gear.

$$\begin{array}{l}{\dot{\omega }}_s{J}_s={\dot{\omega }}_s{b}_s+T_s+T_{ps}\\ {\dot{\omega }}_c{J}_c={\dot{\omega }}_c{b}_c+T_c+T_{pc}\\ {\dot{\omega }}_s{J}_r={\dot{\omega }}_r{b}_r+T_r+T_{pr}\\ {\dot{\omega }}_p{J}_p={\omega }_p{b}_p+T_{rp}+T_{sp}+T_{cp}\end{array}$$

To reduce the equations of motion, the block uses these kinematic and geometric constraints.

$$\begin{array}{l}{\omega }_c{r}_c=r_s{\omega }_s+r_p{\omega }_p\\ {\omega }_r{r}_r=r_c{\omega }_c+r_p{\omega }_p\\ r_c=r_s+r_p\\ r_r=r_c+r_p\end{array}$$

Power Accounting

For the power accounting, the block implements these equations.

Bus Signal			Description	Equations
PwrInfo	PwrTrnsfrd — Power transferred between blocks Positive signals indicate flow into block Negative signals indicate flow out of block	PwrSun	Sun gear applied power	${\omega }_s{T}_s$
		PwrCarr	Carrier gear applied power	${\omega }_c{T}_c$
		PwrRing	Ring gear applied power	${\omega }_r{T}_r$
	PwrNotTrnsfrd — Power crossing the block boundary, but not transferred Positive signals indicate an input Negative signals indicate a loss	PwrDampLoss	Mechanical damping loss	$-\left(b_s{\omega }_s^2+b_c{\omega }_c^2+b_r{\omega }_r^2+b_p{\omega }_p^2\right)$
	PwrStored — Stored energy rate of change Positive signals indicate an increase Negative signals indicate a decrease	PwrStoredPlntry	Rate change in rotational kinetic energy	${\dot{\omega }}_s{\omega }_s{J}_s+ {\dot{\omega }}_c{\omega }_c{J}_c+{\dot{\omega }}_r{\omega }_r{J}_r+ {\dot{\omega }}_p{\omega }_p{J}_p$

The equations use these variables.

ωc, ωp, ωr, ωs	Carrier, planet, ring, and sun gear angular speed
rc, rp, rr, rs	Carrier, planet, ring, and sun gear angular radius
Jc, Jp, Jr, Js	Carrier, planet, ring, and sun gear inertia
bc, bp, br, bs	Carrier, planet, ring, and sun gear damping
Tc, Tp, Tr, Ts	Applied carrier, planet, ring, and sun gear torque
Tps	Torque applied from planet gear on sun gear
Tpc	Torque applied from planet gear on carrier gear
Tpr	Torque applied from planet gear on ring gear
Trp	Torque applied from ring gear on planet gear
Tsp	Torque applied from sun gear on planet gear
Tcp	Torque applied from carrier gear on planet gear

Examples

Build Conventional Vehicle Model

Build a vehicle with an internal combustion engine using the conventional vehicle reference application.

Ports

Input

SunTrq — Sun gear applied torque

scalar

Sun gear input torque, T_s, in N·m.

Dependencies

To create this port, for Port Configuration, select Simulink.

CarrTrq — Carrier gear applied torque

scalar

Carrier gear input torque, T_c, in N·m.

Dependencies

To create this port, for Port Configuration, select Simulink.

RingTrq — Ring gear applied torque

scalar

Ring gear applied torque, T_r, in N·m.

Dependencies

To create this port, for Port Configuration, select Simulink.

C — Carrier gear angular speed and torque

two-way connector port

Carrier gear angular speed, ω_c, in rad/s. Carrier gear applied torque, T_c, in N·m.

Dependencies

To create this port, for Port Configuration, select Two-way connection.

Output

Info — Bus signal

bus

Bus signal containing these block calculations.

Signal			Description	Units
Sun	SunTrq		Sun gear applied torque	N·m
	SunSpd		Sun gear angular speed	rad/s
Carr	CarrTrq		Carrier gear applied torque	N·m
	CarrSpd		Carrier gear angular speed	rad/s
Ring	RingTrq		Ring gear applied torque	N·m
PwrInfo	PwrTrnsfrd	PwrSun	Sun gear applied power	W
		PwrCarr	Carrier gear applied power	W
		PwrRing	Ring gear applied power	W
	PwrNotTrnsfrd	PwrDampLoss	Mechanical damping loss	W
	PwrStored	PwrStoredPlntry	Rate change in rotational kinetic energy	W

SunSpd — Sun gear angular speed

scalar

Sun gear angular speed, ω_s, in rad/s.

Dependencies

To create this port, for Port Configuration, select Simulink.

CarrSpd — Carrier gear angular speed

scalar

Carrier gear angular speed, ω_c, in rad/s.

Dependencies

To create this port, for Port Configuration, select Simulink.

RingSpd — Ring gear angular speed

scalar

Ring gear angular speed, ω_r, in rad/s.

Dependencies

To create this port, for Port Configuration, select Simulink.

S — Sun gear angular speed and torque

two-way connector port

Sun gear angular speed, ω_s, in rad/s. Sun gear applied torque, T_s, in N·m.

Dependencies

To create this port, for Port Configuration, select Two-way connection.

R — Ring gear angular speed and torque

two-way connector port

Ring gear angular speed, ω_r, in rad/s. Ring gear applied torque, T_r, in N·m.

Dependencies

To create this port, for Port Configuration, select Two-way connection.

Parameters

Block Options

Port Configuration — Specify configuration

Simulink (default) | Two-way connection

Specify the port configuration.

Dependencies

Specifying Simulink creates these ports:

• SunTrq

• CarrTrq

• RingTrq

• SunSpd

• CarrSpd

• RingSpd

Specifying Two-way connection creates these ports:

• C

• S

• R

Sun to planet ratio, Nsp — Ratio

30/23 (default) | scalar

Sun-to-planet gear ratio, dimensionless.

Sun to ring ratio, Nsr — Ratio

30/78 (default) | scalar

Sun-to-ring gear ratio, dimensionless.

Sun inertia, Js — Inertia

.003 (default) | scalar

Sun gear inertia, J_s, in kg·m^2.

Planet inertia, Jp — Inertia

.001 (default) | scalar

Planet gear inertia, J_p, in kg·m^2.

Ring inertia, Jr — Inertia

.01 (default) | scalar

Ring gear inertia, J_r, in kg·m^2.

Carrier inertia, Jc — Inertia

.002 (default) | scalar

Carrier gear inertia, J_c, in kg·m^2.

Sun viscous damping, bs — Damping

.001 (default) | scalar

Sun gear viscous damping, b_s, N·m· s/rad.

Ring viscous damping, br — Damping

.001 (default) | scalar

Ring gear viscous damping, b_r, N·m· s/rad.

Planet viscous damping, bp — Damping

.001 (default) | scalar

Planet gear viscous damping, b_p, N·m· s/rad.

Carrier viscous damping, bc — Damping

.001 (default) | scalar

Carrier gear viscous damping, b_c, N·m· s/rad.

Initial sun velocity, ws_o — Angular speed

0 (default) | scalar

Initial sun gear angular speed, in rad/s.

Initial carrier velocity, wc_o — Angular speed

0 (default) | scalar

Initial carrier gear angular speed, in rad/s.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

Introduced in R2017a