Planetary Gear

Gear transmission with sun gear, planetary gear and ring gear.

planetary gear

Description

The Planetary Gear unit simulates a gear train with sun, planetary and ring gears. Planetary gears are often found in transmission systems where they provide high gear ratios given compact overall dimensions. A driver connected to the drive shaft holds the planetary gears. The C, R and S ports are shafts connected to the planetary gear driver, ring gear and sun gear.

planetary gear 2

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

planetary gear 1

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 drive, sun, and ring gears, connect the Inertia blocks to the C, S, and R ports.

Thermal model

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

Equations

Ideal gears and gear ratios

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

where

- is the radius of the driving gear;
- is the radius of the sun gear;
- angular velocity of the sun gear;
- radius of the planetary gear;
- angular velocity of the planetary gear;
- radius of ring gear.

The gear ratio of the ring gear and the sun gear is equal:

where is the number of teeth on each gear.

In terms of this ratio, the key kinematic constraint is:

The four degrees of freedom reduce to two independent pairs of gears: ( , ) or ( , ).

The gear ratio of must be >1.

Torque transmission is carried out as follows:

where

- is the torque transmission ratio for the sun gear;
- is the torque transmission coefficient for ring gear;
- torque transmission losses.

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

Non-ideal constraints and losses in gears

In the non-ideal case, . For more details, see Modelling of mechanical gears with losses.

Assumptions and constraints

The inertia of the gears is negligible.
Gears are treated as solids.
Coulomb friction slows down the simulation. (See here for more details)

Ports

Conserving

# С — planetary gear drive
`rotational mechanics

Details

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

Program usage name

carrier_flange

# R — ring gear
`rotational mechanics

Details

A non-directional port associated with a ring gear.

Program usage name

ring_flange

# S — sun gear
`rotational mechanics

Details

A non-directional port associated with the sun gear.

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 sun (S) teeth ratio (NR/NS) — gear ratio from ring gear to sun gear

Details

A constant gear ratio, , of ring gear revolutions to sun gear revolutions, determined by the number of ring gear teeth divided by the number of sun gear teeth. The gear ratio must be strictly > 1.

Default value	`2.0`
Program usage name	`ring_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 transmission:

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 , such that .
`Temperature-dependent efficiency' - the torque transmission between gear pairs is determined by an interpolation table of temperature and efficiency.

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 — Efficiency of torque transmission from sun gear to planetary gear and from ring gear to planetary gear

Details

The vector of efficiency values, [ ], for the following gears: sun gear-planetary gear and ring gear-planetary gear, respectively.

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

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

Vector of torque transmission efficiency values, [ ], for the gear mesh of the sun gear and planetary gear.

Each element is an efficiency value related to the corresponding temperature value in the Temperature parameter value vector. 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, [ ], of ring gear to planetary gear.

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 full torque transmission efficiency values apply. Enter the threshold values in the order solar-planetary gear, ring-planetary gear, ring-planetary gear. 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	`Nms/rad` \| `ftlbfs/rad`
Default value	`[0, 0] Nms/rad`
Program usage name	`viscous_coefficient_vector`
Evaluatable	Yes

Inertia

# Inertia — inertia model

Details

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

Default value	`false (switched off)`
Program usage name	`enable_inertia`
Evaluatable	No

Details

Inertia of a planetary gear as a positive scalar.

Dependencies

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

Values	`gcm^2` \| `kgm^2` \| `lbmft^2` \| `lbmin^2` \| `slugft^2` \| `slugin^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

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

Additionally

* Hardware-in-the-loop modelling*

For optimum simulation performance, set the Friction model to the default value, No meshing losses - Suitable for HIL simulation.

Planetary Gear

Description

Thermal model

Equations

Ideal gears and gear ratios

Non-ideal constraints and losses in gears

Assumptions and constraints

Ports

Conserving

Parameters

Main

Meshing Losses

Viscous Losses

Inertia

Thermal Port

Additionally

See also