Sun-Planet Bevel

A planetary gearbox consisting of a drive gear, bevel planetary gears and sun gear, with adjustable gear ratio, gear orientation and friction losses.

sun planet bevel

Description

The Sun-Planet Bevel unit is a drive gear, tapered planetary gear and sun gear. The planetary gear is connected to the drive gear and rotates relative to it. The planetary gear and sun gear rotate with a fixed gear ratio. The direction of rotation of the planetary gear relative to the sun gear is set by the Assembly orientation parameter.

Thermal model

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

Equations

Ideal gears and gear ratios

The Sun-Planet Bevel block imposes one kinematic and one geometric constraint on three coupled axes:

where

- is the radius of the drive pinion;
- angular velocity of the drive pinion;
- radius of the sun gear;
- angular velocity of the sun gear;
- radius of the planetary gear;
- angular velocity of the planetary gear.

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

where

- is the gear ratio for the planetary and sun gear meshing. Since , ;
- is the number of teeth of the planetary gear;
- the number of teeth of the sun gear.

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

when the planetary gear and the sun gear rotate in the same direction;
when the planetary gear and the sun gear rotate in opposite directions.

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

The gear ratio, , must be >1.

Torque transmission is carried out as follows:

where

- torque loss;
- is the torque for the sun gear;
- torque for the planetary gear.

In the ideal case where there is no torque transmission loss, . The resulting torque transmission equation: .

Assumptions and limitations

The inertia of the gears is negligible.
Gears are treated as solids.

Ports

Conserving

# C — drive pinion
`rotational mechanics

Details

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

Program usage name

carrier_flange

# P — planetary gear
`rotational mechanics

Details

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

Program usage name

planet_flange

# S — sun gear
`rotational mechanics

Details

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

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

Details

Transmission ratio from the planetary gear to 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	`2.0`
Program usage name	`ratio`
Evaluatable	Yes

# Assembly orientation — relative direction of rotation of the gears
Left - Sun and planet gears rotate in same direction | Right - Sun and planet gears rotate in opposite direction

Details

The relative orientation of the solar and planetary gears and their direction of rotation. Left or right orientation implies that the gears rotate in the same or opposite direction respectively.

Values	`Left - Sun and planet gears rotate in same direction` \| `Right - Sun and planet gears rotate in opposite direction`
Default value	`Left - Sun and planet gears rotate in same direction`
Program usage name	`assembly_orientation`
Evaluatable	No

Meashing 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 value of torque transmission efficiency, , such that .
`Temperature-dependent efficiency' - torque transmission between gear pairs, 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

# Ordinary efficiency — Torque transmission efficiency

Details

Torque transmission efficiency, , for meshing a pair of planetary gears with a sun gear. The value must fulfil the condition .

Dependencies

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

Default value	`0.9`
Program usage name	`efficiency_const`
Evaluatable	Yes

Details

A vector of temperatures 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

# Efficiency — vector of efficiency values

Details

Vector of efficiency values, , for the outer planetary-inner planetary gear mesh. The unit uses these values to construct a one-dimensional temperature efficiency table. The element of the vector must be in the interval (0,1].

Each element is an efficiency related to the corresponding temperature value in the parameter value vector. 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, 0.90, 0.85]`
Program usage name	`efficiency_vector`
Evaluatable	Yes

# Sun-carrier power threshold — minimum power values
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 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 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 W`
Program usage name	`power_threshold`
Evaluatable	Yes

Viscous Losses

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

Details

Viscous friction coefficients, , for sun gear motion.

Values	`Nm/(rad/s)` \| `ftlbf/(rad/s)`
Default value	`0.0 N*m/(rad/s)`
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 unit of temperature. The greater the thermal mass, 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