Sun-Planet
Planetary gearbox consisting of drive, planetary and sun gears with adjustable gear ratio and friction losses.
Description
The Sun-Planet unit is a planetary gear train with a carrier gear, planetary gear and sun gear. The planetary gear meshes with the carrier gear and rotates with it. The planetary and sun gear rotate at a fixed gear ratio that you specify, and in the same direction as the drive gear. The sun-planetary and ring-planetary gears are the basic elements of a planetary gear.
Thermal model
You can model the effects of heat flow and temperature changes by including the optional H heat port. To use the H heat port, set the Friction model parameter to `Temperature-dependent efficiency'.
Equations
Ideal gears and gear ratios
The Sun-Planet block imposes one kinematic and one geometric constraint on three linked axes:
The gear ratio for planetary and sun gear meshing is equal:
where is the number of teeth on each gear. In terms of this relationship, the key kinematic constraint is:
The three degrees of freedom are reduced to two independent pairs of gears: ( ).
The gear ratio must be >1.
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Torque transmission is realised as follows:
In the ideal case, there is no torque loss, i.e. .
Non-ideal limits and losses in gears
In the non-ideal case . For more details see Modelling of mechanical gears with losses.
Assumptions and limitations
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The inertia of the gears is negligible.
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Gears are treated as solids.
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Coulomb friction slows down the simulation. (See here for more details)
Ports
Conserving
#
С
—
drive pinion
`rotational mechanics
Details
A non-directional port associated with the drive gear.
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#
P
—
planetary gear
`rotational mechanics
Details
A non-directional port associated with a planetary gear.
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#
S
—
sun gear
`rotational mechanics
Details
A non-directional port associated with the sun gear.
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#
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'.
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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 |
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| 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:
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`No meshing losses - Suitable for HIL simulation' - the gearing is assumed to be perfect.
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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.
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| Default value |
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| 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 |
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| 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 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'.
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| 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 |
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| Program usage name |
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| 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.
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If Friction model is set to `Constant efficiency', the unit reduces losses to zero when no power is transmitted.
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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'.
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| 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.
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| Default value |
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| Program usage name |
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| 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'.
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| Default value |
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| Program usage name |
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| Evaluatable |
Yes |