Engee documentation

Compound Planetary Gear

Planetary gearbox with step planetary gear.

compound planetary gear

Description

The Compound Planetary Gear unit simulates a planetary gear train with compound planetary gears. Each compound planetary gear is a pair of rigidly coupled and coaxial gears of different radii. One of the two gears meshes with the centrally located sun gear and the other with the outer ring gear.

Two-stage planetary gear

compound planetary gear 1

This block models a two-stage planetary gear as a structural component based on the Sun-Planet and Ring-Planet blocks. The figure shows the equivalent block diagram of the two-stage planetary gear block.

compound planetary gear 2

To increase the accuracy of the gear model, you can specify properties such as gear inertia, gear losses, and viscous friction losses. By default, it is assumed that the inertia and viscous losses of the gear are negligible. This block allows you to specify the inertia of the internal planetary gears. To model the inertia of the driver, sun and ring gears, connect the Inertia block to ports C, S, and R.

Thermal model

You can model the effects of heat flow and temperature changes by enabling the optional H thermal port. To use the H thermal port, set the Friction model parameter to `Temperature-dependent efficiency'.

Equations

Ideal gears and gear ratios

The Compound Planetary Gear block imposes two kinematic and two geometric constraints:










where

  • - is the radius of the carrier gear;

  • - angular velocity of the carrier pinion;

  • - radius of the sun gear;

  • - angular velocity of the sun pinion;

  • - radius of the planetary gear entering into meshing with the sun gear;

  • - angular velocity of the planetary gear;

  • - radius of the planetary pinion meshing with the ring gear;

  • - radius of the ring gear.

The gear ratio for the meshing of the ring gear and the planetary gear is equal:

The gear ratio for the meshing of the planetary and sun gear is equal to:

where

  • - is the ratio between the ring gear and the planetary gear;

  • - number of teeth on the ring gear;

  • - the number of teeth of the planetary gear entering into meshing with the ring gear;

  • - gear ratio between the planetary gear and the sun gear;

  • - number of teeth of the planetary gear entering into meshing with the sun gear;

  • - number of teeth on the sun gear.

Regarding gear ratios, the key kinematic constraint is:

The four degrees of freedom are reduced to two independent pairs of gears: or .

The gear ratio of must be >1.

Torque transmission is realised as follows:




where

  • - is the torque transmission coefficient for the planetary gear meshing with the ring gear;

  • - is the torque transmission coefficient for the ring gear;

  • - torque transmission losses;

  • - torque transmission coefficient for the sun gear;

  • - torque transmission ratio for the planetary gear meshing with the sun gear.

In the ideal case where there is no torque transmission loss, .

Non-ideal gears and transmission losses

In the non-ideal case, (for more information, see Modelling of mechanical gears with losses).

Assumptions and limitations

  • The inertia of the gears is negligible.

  • The gears are treated as solids.

  • Coulomb friction slows down the simulation (see here for details).

Ports

Conserving

# С — planetary gear drive
`rotational mechanics

Details

A non-directional port associated with the driver of a planetary gear of a gearbox.

Program usage name

carrier_flange

# R — ring gear
`rotational mechanics

Details

A non-directional port associated with the ring gear of a gearbox.

Program usage name

ring_flange

# S — sun gear
`rotational mechanics

Details

A non-directional port associated with the sun gear of a gearbox.

Program usage name

sun_flange

# H — heat flux
`heat

Details

A non-directional port associated with heat flow.

The heat port allows modelling the heat flow between the unit and the connected network.

Dependencies

To use this port, set Friction model to `Temperature-dependent efficiency'.

Program usage name

thermal_port

Parameters

Main

# Ring (R) to planet (P) teeth ratio (NR/NP) — gear ratio from ring gear to planetary gear

Details

Constant ratio, , of ring gear revolutions to planetary gear revolutions. Determined by the number of teeth of the ring gear divided by the number of teeth of the planetary gear. The gear ratio must be strictly >1.

Default value

2.0
Program usage name

ring_to_planet_ratio
Evaluatable

Yes

# Planet (P) to sun (S) teeth ratio (NP/NS) — gear ratio from the planetary gear to the sun gear

Details

Constant ratio, , of planetary gear revolutions to solar gear revolutions. Determined by the number of teeth of the planetary gear divided by the number of teeth of the sun gear. The gear ratio must be strictly `>0'.

Default value

1.0
Program usage name

planet_to_sun_ratio
Evaluatable

Yes

Meshing Losses

# Friction model — friction model
No meshing losses - Suitable for HIL simulation | Constant efficiency | Temperature-dependent efficiency

Details

A model of friction in a transmission. Defined as:

  • No meshing losses - Suitable for HIL simulation - the gearing is assumed to be perfect.

  • Constant efficiency - torque transmission between gear pairs is reduced by a constant efficiency value, , so that .

  • Temperature-dependent efficiency - the torque transmission between gear pairs is determined by an interpolation table of temperature and efficiency correspondence.

Values

No meshing losses - Suitable for HIL simulation | Constant efficiency | Temperature-dependent efficiency
Default value

No meshing losses - Suitable for HIL simulation
Program usage name

friction_model
Evaluatable

No

# Sun-planet and ring-planet ordinary efficiency — vector of torque transmission efficiency values

Details

The vector of efficiency values, [ ], for the following meshes: sun gear - planetary gear and ring gear - planetary gear respectively. The element of the vector must be in the interval (0,1].

Dependencies

To use this parameter, set the Friction model parameter to Constant efficiency.

Default value

[0.96, 0.98]
Program usage name

efficiency_const_vector
Evaluatable

Yes

# Temperature — vector of temperature values
K | degC | degF | degR | deltaK | deltadegC | deltadegF | deltadegR

Details

A vector of temperature values used to construct an interpolation table of temperature and efficiency correspondence. The elements of the vector should be monotonically increasing.

Dependencies

To use this parameter, set the Friction model parameter to `Temperature-dependent efficiency'.

Values

K | degC | degF | degR | deltaK | deltadegC | deltadegF | deltadegR
Default value

[280.0, 300.0, 320.0] K
Program usage name

temperature_vector
Evaluatable

Yes

# Sun-planet efficiency — vector of torque transmission efficiency values from solar to planetary gears

Details

A vector of output to input power ratios describing the power flow from the sun gear to the satellite gear, . The unit uses these values to build an interpolation table of temperature and efficiency correspondence.

Each element is an efficiency value related to the corresponding temperature value in the vector of Temperature parameter values. The length of the vector must be equal to the length of the Temperature parameter vector. Each element of the vector must be in the range (0,1].

Dependencies

To use this parameter, set the Friction model parameter to `Temperature-dependent efficiency'.

Default value

[0.95, 0.9, 0.85]
Program usage name

sun_planet_efficiency_vector
Evaluatable

Yes

# Ring-planet efficiency — vector of torque transmission efficiency values from ring gear to planetary gear

Details

Vector of torque transmission efficiency values, , for ring gear and planetary gear.

The unit uses these values to build an interpolation table of temperature and efficiency correspondence.

Each element is an efficiency value related to the corresponding temperature value in the vector of Temperature parameter values. The length of the vector must be equal to the length of the Temperature parameter vector. Each element of the vector must be in the range (0,1].

Dependencies

To use this parameter, set the Friction model parameter to `Temperature-dependent efficiency'.

Default value

[0.95, 0.9, 0.85]
Program usage name

ring_planet_efficiency_vector
Evaluatable

Yes

# Sun-carrier and planet-carrier power thresholds — minimum threshold power values
W | GW | MW | kW | mW | uW | HP_DIN

Details

Vector of power threshold values above which the full torque transmission efficiencies apply. Enter the threshold values in the order sun gear-drive, planetary gear-drive. For values below these values, the efficiency is smoothed using a hyperbolic tangent function.

  • If Friction model is set to `Constant efficiency', the unit reduces losses to zero when no power is transmitted.

  • If Friction model is set to `Temperature-dependent efficiency', the unit smooths the efficiency values between zero at rest and the values specified in the temperature and efficiency interpolation tables.

Dependencies

To use this parameter, set Friction model to Constant efficiency or Temperature-dependent efficiency.

Values

W | GW | MW | kW | mW | uW | HP_DIN
Default value

[0.001, 0.001] W
Program usage name

power_threshold_vector
Evaluatable

Yes

Viscous Losses

# Sun-carrier and planet-carrier viscous friction coefficients — viscous friction coefficients between gears
N*m*s/rad | ft*lbf*s/rad

Details

The vector of viscous friction coefficients, [ ], for the motion of the sun gear and planetary gear, respectively.

Values

N*m*s/rad | ft*lbf*s/rad
Default value

[0, 0] N*m*s/rad
Program usage name

viscous_coefficient_vector
Evaluatable

Yes

Inertia

# Inertia — inertia model

Details

Select this check box to enable the inertia model for the gear.

Default value

false (switched off)
Program usage name

enable_inertia
Evaluatable

No

# Planet gear inertia — planetary gear inertia
g*cm^2 | kg*m^2 | lbm*ft^2 | lbm*in^2 | slug*ft^2 | slug*in^2

Details

Moment of inertia of the combined planetary gears as a positive scalar.

Dependencies

To use this parameter, select the checkbox for the Inertia parameter.

Values

g*cm^2 | kg*m^2 | lbm*ft^2 | lbm*in^2 | slug*ft^2 | slug*in^2
Default value

0.001 kg*m^2
Program usage name

I_planet
Evaluatable

Yes

Thermal Port

# Thermal mass — heat capacity
J/K | kJ/K

Details

The heat energy required to change the temperature of a component by one degree. The greater the heat capacity, the more resistant the component is to temperature change.

Dependencies

To use this parameter, set the Friction model parameter to `Temperature-dependent efficiency'.

Values

J/K | kJ/K
Default value

50.0 J/K
Program usage name

thermal_mass
Evaluatable

Yes

# Initial temperature — initial temperature
K | degC | degF | degR | deltaK | deltadegC | deltadegF | deltadegR

Details

The temperature of the block at the beginning of the simulation. The initial temperature sets the initial efficiency value of the components according to the vectors specified for them.

Dependencies

To use this parameter, set the Friction model parameter to `Temperature-dependent efficiency'.

Values

K | degC | degF | degR | deltaK | deltadegC | deltadegF | deltadegR
Default value

300.0 K
Program usage name

temperature_start
Evaluatable

Yes

See also

  1. Planetary Gear