Documentation

Leadscrew

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

Library

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-handed direction. If the screw helix is right-handed, ωS and vN have the same sign. If the screw helix is left-handed, ωS and vN 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.

Dialog Box and Parameters

Main

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.

Friction Losses

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

 Without Thermal Port

 With Thermal Port

Viscous Losses

Viscous friction coefficient

Viscous friction coefficient μS 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 Port

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 Gear Model

Ideal Gear Constraint and Gear Ratio

Leadscrew imposes one kinematic constraint on the two connected axes:

ωSL = 2πvN .

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 .

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 + FNFloss = 0 ,

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.

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 (ηSN, ηNS]

  • Viscous coupling of driveshafts with bearings, parametrized by viscous friction coefficient μ

The loss force has the general form:

Floss = FCoul·tanh(4vN/vth) + μωS/RNS .

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

Power FlowPower Loss ConditionOutput DriveshaftCoulomb Friction Force FCoul
ForwardωSτS > FNvNNut, vNRNS|τS|·(1 – ηSN)
ReverseωSτS < FNvNScrew, ωS|FN|·(1 – ηNS)

Geometric Surface Contact Friction

In the contact friction case, ηSN and ηNS 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.

ηSN = (cosαk·tanα)/(cosα + k/tanλ) ,

ηNS = (cosαk/tanλ)/(cosα + k·tanα) .

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 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.

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.

Limitations

  • Gear inertia is assumed negligible.

  • Gears are treated as rigid components.

  • Coulomb friction slows down simulation. See Adjust Model Fidelity.

Ports

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

Example

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

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