# Leadscrew

Leadscrew gear set of threaded rotating screw and translating nut, with adjustable thread and friction losses

**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,
*ω*_{S} and
*v*_{N} have the same sign. If the screw helix
is left-hand, *ω*_{S} and
*v*_{N} have opposite signs.

### Ideal Gear Constraint and Gear Ratio

Leadscrew imposes one kinematic constraint on the two connected axes:

ω_{S}L =
2πv_{N}
. | (1) |

The transmission ratio is *R*_{NS} =
2*π*/*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:

ω_{S} =
R_{NS}v_{N}
. | (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:

R_{NS}τ_{S}
+ F_{N} –
F_{loss} = 0 , | (3) |

with *F*_{loss} = 0 in the ideal case.

### Nonideal Gear Constraint and Losses

In the nonideal case, *F*_{loss} ≠ 0. For general considerations on nonideal gear modeling, see Model Gears with Losses.

**Geometric Surface Contact Friction**

In the contact friction case, *η*_{SN}
and *η*_{NS} are determined by:

The screw-nut threading geometry, specified by lead angle

*λ*and acme thread half-angle*α*.The surface contact friction coefficient

*k*.

η_{SN} =
(cosα –
k·tanα)/(cosα
+ k/tanλ) , | (4) |

η_{NS} =
(cosα –
k/tanλ)/(cosα +
k·tanα) . | (5) |

**Constant Efficiencies**

In the constant efficiency case, you specify
*η*_{SN} and
*η*_{NS}, independently of geometric
details.

**Self-Locking and Negative Efficiency**

*η*_{NS} has two distinct regimes,
depending on lead angle *λ*, separated by the
*self-locking point* at which *η*_{NS} = 0 and cos*α* =
*k*/tan*λ*.

In the

*overhauling regime*,*η*_{NS}> 0. The force acting on the nut can rotate the screw.In the

*self-locking regime*,*η*_{NS}< 0. An external torque must be applied to the screw to release an otherwise locked mechanism. The more negative is*η*_{NS}, the larger the torque must be to release the mechanism.

*η*_{SN} 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
–*μ*_{S}*ω*_{S}.
*ω*_{S} 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.

Coulomb friction slows down simulation. For more information, see Adjust Model Fidelity.

## Ports

Port | Description |
---|---|

S | Rotational conserving port representing the screw |

N | Translational conserving port representing the nut |

H | Thermal conserving port for thermal modeling |

## Parameters

## Extended Capabilities

## Version History

**Introduced in R2011a**