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

Gears/Rotational-Translational

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-handed direction. If the screw helix is right-handed, *ω*_{S} and *v*_{N} have
the same sign. If the screw helix is left-handed, *ω*_{S} and *v*_{N} have
opposite signs. For model details, see Leadscrew Gear Model.

The block models the effects of heat flow and temperature change
through an optional thermal port. To expose the thermal port, right-click
the block and select **Simscape** > **Block choices** > **Show thermal
port**. Exposing the thermal port causes
new parameters specific to thermal modeling to appear in the block
dialog box.

**Screw lead**Translational displacement

*L*of the nut per revolution of the screw. The default is`0.015`

.From the drop-down list, choose units. The default is meters (

`m`

).**Screw helix type**Choose the directional sense of screw rotation corresponding to positive nut translation. The default is

`Right-hand`

.

Parameters for friction losses vary with the block variant chosen—one with a thermal port for thermal modeling and one without it.

**Viscous friction coefficient**Viscous friction coefficient

*μ*_{S}for the screw. The default is`0`

.From the drop-down list, choose units. The default is newton-meters/(radians/second) (

`N*m/(rad/s)`

).

**Thermal mass**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. The default value is

`50`

J/K.**Initial temperature**Component temperature at the start of simulation. The initial temperature influences the starting meshing or friction losses by altering the component efficiency according to an efficiency vector that you specify. The default value is

`300`

K.

Leadscrew imposes one kinematic constraint on the two connected axes:

*ω*_{S}*L* =
2*π**v*_{N} .

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} .

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 ,

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

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

In a nonideal screw-nut pair (S,N), the angular velocity and geometric constraints are unchanged. But the transferred torque, force, and power are reduced by:

Coulomb friction between thread surfaces on S and N, characterized by friction coefficient

*k*or constant efficiencies (*η*_{SN},*η*_{NS}]Viscous coupling of driveshafts with bearings, parametrized by viscous friction coefficient

*μ*

The loss force has the general form:

*F*_{loss} = *F*_{Coul}·tanh(4*v*_{N}/*v*_{th})
+ *μ**ω*_{S}/*R*_{NS} .

The hyperbolic tangent regularizes the sign change in the Coulomb friction force when the nut velocity changes sign.

Power Flow | Power Loss Condition | Output Driveshaft | Coulomb Friction Force F_{Coul} |
---|---|---|---|

Forward | ω_{S}τ_{S} > F_{N}v_{N} | Nut, v_{N} | R_{NS}|τ_{S}|·(1
– η_{SN}) |

Reverse | ω_{S}τ_{S} < F_{N}v_{N} | Screw, ω_{S} | |F_{N}|·(1
– η_{NS}) |

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} =
(cos*α* – *k*·tan*α*)/(cos*α* + *k*/tan*λ*)
,

*η*_{NS} =
(cos*α* – *k*/tan*λ*)/(cos*α* + *k*·tan*α*)
.

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

*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.

The efficiencies *η* of meshing between
screw and nut are fully active only if the absolute value of the nut
velocity is greater than the velocity tolerance.

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

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.

Gear inertia is assumed negligible.

Gears are treated as rigid components.

Coulomb friction slows down simulation. See Adjust Model Fidelity.

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

S | Rotational conserving port representing the screw |

N | Translational conserving port representing the nut |

H | Thermal conserving port for thermal modeling |

The sdl_stepping_mechanismsdl_stepping_mechanism example model uses the Leadscrew gear to translate a load in one direction (ratcheting).

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