Planetary Gear

Ideal planetary gear with sun, ring, and carrier

• Library:
• 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.

$\begin{array}{l}{\stackrel{˙}{\omega }}_{s}{J}_{s}={\stackrel{˙}{\omega }}_{s}{b}_{s}+{T}_{s}+{T}_{ps}\\ {\stackrel{˙}{\omega }}_{c}{J}_{c}={\stackrel{˙}{\omega }}_{c}{b}_{c}+{T}_{c}+{T}_{pc}\\ {\stackrel{˙}{\omega }}_{s}{J}_{r}={\stackrel{˙}{\omega }}_{r}{b}_{r}+{T}_{r}+{T}_{pr}\\ {\stackrel{˙}{\omega }}_{p}{J}_{p}={\omega }_{p}{b}_{p}+{T}_{rp}+{T}_{sp}+{T}_{cp}\end{array}$

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 DescriptionEquations

PwrInfo

PwrTrnsfrd — Power transferred between blocks

• Positive signals indicate flow into block

• Negative signals indicate flow out of block

PwrSun

Sun gear applied power

${\omega }_{s}{T}_{s}$

PwrCarrCarrier gear applied power

${\omega }_{c}{T}_{c}$

PwrRingRing 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

PwrDampLossMechanical 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

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

Ports

Input

expand all

Sun gear input torque, Ts, in N·m.

Dependencies

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

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

Dependencies

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

Ring gear applied torque, Tr, in N·m.

Dependencies

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

Carrier gear angular speed, ωc, in rad/s. Carrier gear applied torque, Tc, in N·m.

Dependencies

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

Output

expand all

Bus signal containing these block calculations.

SignalDescriptionUnits
Sun

SunTrq

Sun gear applied torque

N·m

SunSpd

Sun gear angular speed

Carr

CarrTrq

Carrier gear applied torque

N·m

CarrSpd

Carrier gear angular speed

Ring

RingTrq

Ring gear applied torque

N·m
PwrInfo

PwrTrnsfrd

PwrSun

Sun gear applied powerW
PwrCarrCarrier gear applied powerW
PwrRingRing gear applied powerW

PwrNotTrnsfrd

PwrDampLossMechanical damping lossW

PwrStored

PwrStoredPlntry

Rate change in rotational kinetic energy

W

Sun gear angular speed, ωs, in rad/s.

Dependencies

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

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

Dependencies

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

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

Dependencies

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

Sun gear angular speed, ωs, in rad/s. Sun gear applied torque, Ts, in N·m.

Dependencies

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

Ring gear angular speed, ωr, in rad/s. Ring gear applied torque, Tr, in N·m.

Dependencies

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

Parameters

expand all

Block Options

Specify the port configuration.

Dependencies

• SunTrq

• CarrTrq

• RingTrq

• SunSpd

• CarrSpd

• RingSpd

Specifying Two-way connection creates these ports:

• C

• S

• R

Sun-to-planet gear ratio, dimensionless.

Sun-to-ring gear ratio, dimensionless.

Sun gear inertia, Js, in kg·m^2.

Planet gear inertia, Jp, in kg·m^2.

Ring gear inertia, Jr, in kg·m^2.

Carrier gear inertia, Jc, in kg·m^2.

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

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

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

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

Initial sun gear angular speed, in rad/s.

Initial carrier gear angular speed, in rad/s.

Extended Capabilities

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