Planet-Planet

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Planetary gear consisting of driving, internal and external planetary gears with adjustable gear ratio and friction losses.

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

Path in the library:

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

Description

Block Planet-Planet It consists of a driving gear and two internal-external pairs of planetary gears. Both planetary gears are connected to the driving gear and rotate relative to it. The planetary gears rotate in the same direction with a fixed gear ratio, which is set by the user. For more information about the model, see The equations.

planet planet 1

The thermal model

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

The equations

Perfect gears and transmission ratios

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

The gear ratio of the outer planetary gear to the inner planetary gear is

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

Three degrees of freedom are reduced to two independent degrees of freedom. A pair of gears: .

The transmission of torque is carried out as follows:

Ideally, when there is no loss in torque transmission, .

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.

Ports

Conserving

# Po — outer planetary gear
rotational mechanics

Details

Undirected port connected to the outer planetary gear.

Program usage name

outer_planet_flange

# Pi — inner planetary gear
rotational mechanics

Details

Undirected port connected to the inner planetary gear.

Program usage name

inner_planet_flange

# C — drive gear
rotational mechanics

Details

Non-directional port connected to the drive gear.

Program usage name

carrier_flange

# H — thermal flow
heat

Details

An undirected port connected to the heat flow. The heat flow affects the efficiency of power transmission by changing the temperature of the gear.

Dependencies

To use this port, set the parameter Friction model the value Temperature-dependent efficiency.

Program usage name

thermal_port

Parameters

Main

# Outer planet (Po) to inner planet (Pi) teeth ratio (NPo/NPi) — gear ratio from the outer planetary gear to the inner gear

Details

Gear ratio The outer and inner planetary gears are determined by dividing the number of teeth of the outer planetary gear by the number of teeth of the inner planetary gear. The gear ratio must be strictly positive.

Default value	`2.0`
Program usage name	`ratio`
Evaluatable	Yes

Meshing Losses

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

Details

The friction model for the block is set as follows:

No meshing losses - Suitable for HIL simulation — gear engagement is considered ideal.
Constant efficiency — the transmission of torque between the gear pairs is reduced by a constant amount of efficiency so that .
Temperature-dependent efficiency — the transmission of torque between the gear pairs is determined by the interpolation table of temperature correspondence and the efficiency of torque transmission.

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	Yes

# Ordinary efficiency — Torque transmission efficiency

Details

Torque transmission efficiency to engage the outer and inner pairs of planetary gears. This value must be in the range of (0,1].

Dependencies

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

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

# Inner planet-carrier power threshold — minimum threshold power value for the internal support of the planetary gear
W | GW | MW | kW | mW | uW | HP_DIN

Details

Power threshold value , when exceeded, the full efficiency value is applied. If the value is lower than the specified value, the efficiency is smoothed using the hyperbolic tangent function.

If set for the parameter Friction model meaning Constant efficiency The unit reduces efficiency losses to zero when no power is transferred. If set for the parameter Friction model meaning Temperature-dependent efficiency The block smooths the efficiency coefficients between zero at rest and the values indicated in the tables of temperature and efficiency correspondence at power thresholds.

Dependencies

To use this parameter, set for the parameter Friction model meaning 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

Details

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

Dependencies

To use this parameter, set for the parameter Friction model meaning 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 — Transmission EFFICIENCY

Details

The vector of the ratio of output and input power, describing the flow of power from the outer planetary gear to the inner, . The block uses these values to build a one-dimensional reference table of temperature versus efficiency.

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

Dependencies

To use this parameter, set for the parameter Friction model meaning Temperature-dependent efficiency.

Default value	`[0.95, 0.9, 0.85]`
Program usage name	`efficiency_vector`
Evaluatable	Yes

Viscous Losses

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

Details

Coefficient of viscous friction for the movement of the inner planetary and driving gears.

Units	`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 thermal energy required to change the temperature of a component by one degree. The higher the heat capacity, the more resistant the component is to temperature fluctuations.

Dependencies

To use this parameter, set for the parameter Friction model meaning Temperature-dependent efficiency.

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

More detailed

Semi-natural modeling

Details

To ensure optimal simulation performance, set the parameter Friction model default value (No meshing losses - Suitable for HIL simulation).