• Libraries:
Simscape / Driveline / Gears / Rotational- Translational

## Description

The Leadscrew block represents a threaded rotational-translational gear that constrains the two connected driveline axes, screw (S) and nut (N), to, respectively, rotate and translate together in a fixed ratio that you specify. You can choose whether the nut axis translates in a positive or negative direction, as the screw rotates in a positive right-hand direction. If the screw helix is right-hand, ωS and vN have the same sign. If the screw helix is left-hand, ωS and vN have opposite signs.

### Ideal Gear Constraint and Gear Ratio

Leadscrew imposes one kinematic constraint on the two connected axes:

 ωSL = 2πvN . (1)

The transmission ratio is RNS = 2π/L. L is the screw lead, the translational displacement of the nut for one turn of the screw. In terms of this ratio, the kinematic constraint is:

 ωS = RNSvN . (2)

The two degrees of freedom are reduced to one independent degree of freedom. The forward-transfer gear pair convention is (1,2) = (S,N).

The torque-force transfer is:

 RNSτS + FN – Floss = 0 , (3)

with Floss = 0 in the ideal case.

### Nonideal Gear Constraint and Losses

In the nonideal case, Floss ≠ 0. For general considerations on nonideal gear modeling, see Model Gears with Losses.

Geometric Surface Contact Friction

In the contact friction case, ηSN and ηNS are determined by:

• The surface contact friction coefficient k.

 ηSN = (cosα – k·tanα)/(cosα + k/tanλ) , (4)
 ηNS = (cosα – k/tanλ)/(cosα + k·tanα) . (5)
Constant Efficiencies

In the constant efficiency case, you specify ηSN and ηNS, independently of geometric details.

Self-Locking and Negative Efficiency

ηNS has two distinct regimes, depending on lead angle λ, separated by the self-locking point at which ηNS = 0 and cosα = k/tanλ.

• In the overhauling regime, ηNS > 0. The force acting on the nut can rotate the screw.

• In the self-locking regime, ηNS < 0. An external torque must be applied to the screw to release an otherwise locked mechanism. The more negative is ηNS, the larger the torque must be to release the mechanism.

ηSN is conventionally positive.

### Meshing Efficiency

The efficiencies η of meshing between screw and nut are fully active only if the transmitted power is greater than the power threshold.

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

### Viscous Friction Force

The viscous friction coefficient μ controls the viscous friction torque experienced by the screw from lubricated, nonideal gear threads. The viscous friction torque on a screw driveline axis is –μSωS. ωS is the angular velocity of the screw with respect to its mounting.

### Thermal Modeling

You can model the effects of heat flow and temperature change by enabling the optional thermal port. To enable the port, set Friction model to ```Temperature-dependent efficiency```.

### Hardware-in-the-Loop Simulation

For optimal performance of your real-time simulation, set the Friction model to ```No meshing losses - Suitable for HIL simulation``` on the Meshing Losses tab.

### Variables

Use the Variables settings to set the priority and initial target values for the block variables before simulating. For more information, see Set Priority and Initial Target for Block Variables.

## Limitations

• Gear inertia is assumed to be negligible.

• Gears are treated as rigid components.

## Ports

PortDescription
SRotational conserving port representing the screw
NTranslational conserving port representing the nut
HThermal conserving port for thermal modeling

## Parameters

expand all

### Main

Translational displacement L of the nut per revolution of the screw.

Choose the directional sense of screw rotation corresponding to positive nut translation. For the `Right-hand` orientation, the screw angular velocity and the nut velocity have the same sign.

### Meshing Losses

• ```No meshing losses — Suitable for HIL simulation``` — Screw meshing is ideal.

• `Constant efficiency` — Transfer of torque between screw and nut is reduced by friction.

• ```Temperature-dependent efficiency``` — Torque transfer is determined from user-supplied data for screw-nut efficiency, nut-screw efficiency, and temperature.

• ```Friction coefficient and geometrical parameters``` — Friction is determined by contact friction between surfaces.

• `Efficiencies` — Friction is determined by constant efficiencies 0 < η < 1.

#### Dependencies

To enable this parameter, set Friction model to `Constant efficiency`.

Thread helix angle λ = arctan[L/(πd)], where:

• L is the worm lead.

• d is the worm pitch diameter.

The value must be greater than zero.

#### Dependencies

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

Half-angle of the acme thread α in the normal plane. In the case of a square thread, α = 0. The value must be greater than zero.

#### Dependencies

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

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

#### Dependencies

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

Efficiency ηSN of the power transfer from screw to nut.

#### Dependencies

To enable this parameter, set Friction model to `Constant efficiency` and Friction parameterization to `Efficiencies`.

Efficiency ηNS of the power transfer from gear to worm.

#### Dependencies

To enable this parameter, set Friction model to `Constant efficiency` and Friction parameterization to `Efficiencies`.

Array of temperatures used to construct a 1-D temperature-efficiency lookup table. The array values must increase left to right. The temperature array must be the same size as the Screw-nut efficiency and arrays.

#### Dependencies

To enable this parameter, set Friction model to ```Temperature-dependent efficiency```.

Array of component efficiencies with the screw as the driver— that is, with power from the screw to the nut. The array values are the efficiencies at the temperatures in the Temperature array. The two arrays must be the same size.

#### Dependencies

To enable this parameter, set Friction model to ```Temperature-dependent efficiency```.

Array of component efficiencies with the nut as the driver— that is, with power flowing from the nut to the screw. The array values are the efficiencies at the temperatures in the Temperature array. The two arrays must be the same size.

#### Dependencies

To enable this parameter, set Friction model to ```Temperature-dependent efficiency```.

Power threshold above which full efficiency factor is in effect. A hyperbolic tangent function smooths the efficiency factor between zero at rest and the current efficiency set point.

### Viscous Losses

Viscous friction coefficient μS for the screw.

### Thermal Port

Thermal energy required to change the component temperature by a single degree. The greater the thermal mass, the more resistant the component is to temperature change.

Component temperature at the start of simulation. The initial temperature alters the component efficiency according to an efficiency vector that you specify, affecting the starting meshing or friction losses.

## Version History

Introduced in R2011a