Leadscrew

A set of lead screws, consisting of a rotating threaded screw and a transfer nut, with adjustable thread and friction losses.

blockType: Engee1DMechanical.Transmission.Gears.RotationalTranslational.Leadscrew

Path in the library:

/Physical Modeling/1D Mechanical/Gears/Rotational-Translational/Leadscrew

Description

Block Leadscrew It is a threaded rotary-translational transmission that causes two connected axes, a screw (S) and a nut (N), to rotate and move together in a fixed ratio that you specify.

You can choose whether the nut axis will rotate in the positive or negative direction when the right screw thread rotates positively. If the spiral of the screw is right-sided, and they have the same sign. If the spiral of the screw is left-handed, and they have opposite signs.

Limitation of the ideal nut and gear ratio

The block imposes one kinematic constraint on two connected axes:

Gear ratio: . Here — this is the pitch of the screw thread, the translational movement of the nut in one turn of the screw. In terms of this relation, the kinematic constraint has the form:

Two degrees of freedom are reduced to one independent degree of freedom. The symbol for a pair of direct—shift gears is (1,2) = (S,N).

The transmission of torque is carried out as follows:

at the same time in the ideal case.

Imperfect restrictions on nuts and losses

In an imperfect case .

Geometric surface contact friction

In case of contact friction and defined by:

The geometry of the screw-nut thread, determined by the angle of thread lift and the half angle of the thread .
Coefficient of surface contact friction .

Continuous efficiency

In the case of continuous efficiency, you specify and , regardless of the geometric details.

Self-locking and negative efficiency

It has two different modes depending on the angle of thread lift. , separated by a dot selock, in which and .

In the _ self-unscrewing mode_, . The force acting on the nut can rotate the screw.
In the _ self-lock mode_, . To unlock the locked mechanism, an external torque must be applied to the screw. The more negative it is the greater the torque must be to unlock the mechanism. conditionally positive.

Coupling efficiency

Effectiveness The coupling between the screw and nut is fully active only if the transmitted power exceeds the threshold power.

If the power is less than the threshold, the actual efficiency is automatically adjusted to unity at zero speed.

Viscous friction force

Coefficient of viscous friction controls the viscous friction torque generated on the screw due to the lubricated imperfect gear thread. The torque of viscous friction on the axis of the helical transmission is equal to .

— this is the angular velocity of the screw relative to its attachment.

Thermal modeling

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

Simulation in a hardware loop

For optimal real-time simulation performance, set the Friction model parameter to `No meshing losses - Suitable for HIL simulation'.

Assumptions and limitations

The inertia of the gears is negligible.
Gears are considered as rigid components.
Coulomb friction slows down the simulation.

Ports

Conserving

# S — screw
`rotational mechanics

Details

A mechanical rotary non-directional port associated with a propeller.

Program usage name

screw_flange

# N — mechanical progressive nut
`rotational mechanics

Details

A mechanical non-directional port associated with a nut.

Program usage name

nut_flange

# H — heat flux
`heat

Details

A heat 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

# Screw lead (displacement per revolution) — thread pitch
m | cm | ft | in | km | mi | mm | um | yd

Details

Screw displacement of the nut per one turn of the screw.

Units	`m` \| `cm` \| `ft` \| `in` \| `km` \| `mi` \| `mm` \| `um` \| `yd`
Default value	`0.015 m`
Program usage name	`lead`
Evaluatable	Yes

# Screw helix type — direction of rotation
Right-hand | Left-hand

Details

The direction of rotation of the screw corresponding to positive movement of the nut.

For `Right-hand' orientation, the angular velocity of the propeller and the speed of the nut have the same sign.

Values	`Right-hand` \| `Left-hand`
Default value	`Right-hand`
Program usage name	`screw_handedness`
Evaluatable	No

Meshing Losses

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

Details

Propeller Friction Model. The following options are available to choose from:

No meshing losses - Suitable for HIL simulation+ - propeller adhesion is perfect.
Constant efficiency - torque transmission between screw and nut is reduced due to friction.
Temperature-dependent efficiency - torque transmission is determined based on user supplied data: screw-to-nut efficiency, nut-to-screw efficiency and temperature.

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

# Friction parameterization — friction losses
Friction coefficient and geometrical parameters | Efficiencies

Details

Friction losses for non-ideal meshing of gear threads. The following options are available to choose from:

Friction coefficient and geometrical parameters - friction is determined by contact friction between surfaces.
Efficiencies - friction is defined by constant coefficients 0 < < 1.

Dependencies

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

Values	`Friction coefficient and geometrical parameters` \| `Efficiencies`
Default value	`Friction coefficient and geometrical parameters`
Program usage name	`friction_parameterization`
Evaluatable	No

# Lead angle — thread lift angle
deg | rad | rev | mrad

Details

Thread lift angle , where:

- master screw.
- screw pitch diameter.

The value of the angle must be greater than zero.

Dependencies

To use this parameter, set the Friction model parameter to `Constant efficiency' and the Friction parameterization parameter to `Friction coefficient and geometrical parameters'.

Units	`deg` \| `rad` \| `rev` \| `mrad`
Default value	`15.0 deg`
Program usage name	`lead_angle`
Evaluatable	Yes

# Acme thread half angle — half thread angle
deg | rad | rev | mrad

Details

The half angle of the thread in the normal plane. In the case of square threads = 0. The value must be greater than zero.

Dependencies

To use this parameter, set the Friction model parameter to `Constant efficiency' and the Friction parameterization parameter to `Friction coefficient and geometrical parameters'.

Units	`deg` \| `rad` \| `rev` \| `mrad`
Default value	`14.5 deg`
Program usage name	`acme_thread_half_angle`
Evaluatable	Yes

# Friction coefficient — thread friction coefficient

Details

Dimensionless coefficient of normal thread friction. The value must be greater than zero.

Dependencies

To use this parameter, set Friction model to `Constant efficiency' and Friction parameterization to `Friction coefficient and geometrical parameters'.

Default value	`0.08`
Program usage name	`friction_coefficicent`
Evaluatable	Yes

# Screw-nut efficiency — screw-to-nut efficiency

Details

Efficiency screw-to-nut efficiency.

Dependencies

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

Default value	`0.75`
Program usage name	`screw_to_nut_efficiency_const`
Evaluatable	Yes

# Nut-screw efficiency — nut-to-screw efficiency

Details

Efficiency nut-to-screw energy transfer efficiency.

Dependencies

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

Default value	`0.45`
Program usage name	`nut_to_screw_efficiency_const`
Evaluatable	Yes

Details

A vector of temperatures used to construct an interpolation table of temperature/efficiency correspondence. The vector values should be monotonically increasing. The temperature vector should be of the same dimensionality as the Screw-nut efficiency and Nut-screw efficiency parameter vectors.

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

# Screw-nut efficiency — array of efficiency factors from screw to nut

Details

An array of component efficiencies when using the propeller as a drive - that is, when transferring energy from the propeller to the nut. The array values are the efficiencies at the temperatures in the Temperature array. Both arrays must be of the same dimension.

Dependencies

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

Default value	`[0.75, 0.65, 0.60]`
Program usage name	`screw_to_nut_efficiency_vector`
Evaluatable	Yes

# Nut-screw efficiency — array of efficiency factors from nut to screw

Details

An array of component efficiencies when using the nut as a drive - that is, when transferring energy from the nut to the screw. The array values are the efficiencies at the temperatures in the Temperature array. Both arrays must be the same size.

Dependencies

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

Default value	`[0.50, 0.45, 0.40]`
Program usage name	`nut_to_screw_efficiency_vector`
Evaluatable	Yes

# Power threshold — power to enable numerical smoothing
W | GW | MW | kW | mW | uW | HP_DIN

Details

The threshold power above which the full efficiency factor applies. The hyperbolic tangent function smooths the efficiency factor between zero at rest and the current efficiency setpoint.

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

Viscous Losses

# Viscous friction coefficient — screw viscous friction coefficient
N*m/(rad/s) | ft*lbf/(rad/s)

Details

Viscous friction coefficient for the screw.

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 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.

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