Sun-Planet

A planetary gearbox consisting of a drive, planetary and solar gears with an adjustable gear ratio and friction losses.

blockType: Engee1DMechanical.Transmission.Gears.Planetary.Auxiliary.SunPlanet

Path in the library:

/Physical Modeling/1D Mechanical/Gears/Planetary Subcomponents/Sun-Planet

Description

Block Sun-Planet It is a planetary gear train with carrier, planetary and solar gears. The planetary gear engages with the driving gear and rotates with it. The planetary and solar gears rotate at a fixed gear ratio that you specify and in the same direction as the driving gear. Solar–planetary and ring–planetary transmissions are the main elements of planetary transmission.

The thermal model

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

The equations

Ideal gears and transmission ratios

Block Sun-Planet imposes one kinematic and one geometric constraint on three connected axes:

The gear ratio for the engagement of the planetary and solar gears is:

where — the number of teeth on each gear. From the point of view of this relation, the key kinematic constraint is:

The three degrees of freedom are reduced to two independent pairs of gears: ( ).

Gear ratio it must be >1.

The transmission of torque is carried out as follows:

Ideally, there is no loss of torque, that is .

Imperfect limitations and losses in gears

In an imperfect case . For more information, see the article Modeling of mechanical gears with losses.

Assumptions and limitations

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

Ports

Conserving

# C — drive pinion
`rotational mechanics

Details

A non-directional port associated with the drive gear.

Program usage name

carrier_flange

# P — planetary gear
`rotational mechanics

Details

A non-directional port associated with a planetary gear.

Program usage name

planet_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 enable this port, set Friction model to `Temperature-dependent efficiency'.

Program usage name

thermal_port

Parameters

Main

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

Details

Transmission ratio revolutions of the planetary gear to revolutions of the sun gear. It is determined by the number of teeth of the planetary gear divided by the number of teeth of the sun gear. This value must be strictly `>1'.

Default value	`2`
Program usage name	`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, , such that .
`Temperature-dependent efficiency' - torque transmission between gear pairs, determined from an interpolation table of temperature and torque transmission 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

# Ordinary efficiency — Torque transmission efficiency

Details

Torque transmission efficiency, , for sun gear-planetary gear meshing. The value must fulfil the condition .

Dependencies

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

Default value	`0.98`
Program usage name	`efficiency_const`
Evaluatable	Yes

Details

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

Dependencies

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

Units	`K` \| `degC` \| `degF` \| `degR` \| `deltaK` \| `deltadegC` \| `deltadegF` \| `deltadegR`
Default value	`[280.0, 300.0, 320.0] K`
Program usage name	`temperature_vector`
Evaluatable	Yes

# Efficiency — vector of efficiency values

Details

Vector of efficiency values, , for ring-planetary gear meshing. The element of the vector must be in the interval (0,1].

Each element is the efficiency 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 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	`efficiency_vector`
Evaluatable	Yes

# Sun-carrier power threshold — minimum threshold power value
W | GW | MW | kW | mW | uW | HP_DIN

Details

The power threshold value above which the full torque transmission efficiency value is applied. Below this value, the efficiency value 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 between zero at rest and the values given in the interpolation tables for temperature and torque transfer efficiency.

Dependencies

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

Units	`W` \| `GW` \| `MW` \| `kW` \| `mW` \| `uW` \| `HP_DIN`
Default value	`0.001 W`
Program usage name	`power_threshold`
Evaluatable	Yes

Viscous Losses

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

Details

Coefficient of viscous friction, , for the movement of the sun and carrier gears.

Units	`Nms/rad` \| `ftlbfs/rad`
Default value	`0.0 Nms/rad`
Program usage name	`viscous_coefficient`
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 of temperature. 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'.

Units	`J/K` \| `kJ/K`
Default value	`50.0 J/K`
Program usage name	`thermal_mass`
Evaluatable	Yes