Leadscrew

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

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Simscape / Driveline / Gears / Rotational-Translational

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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. For model details, see Leadscrew Gear Model.

Thermal Modeling

You can model the effects of heat flow and temperature change through an optional thermal conserving port. By default, the thermal port is hidden. To expose the thermal port, right-click the block in your model and, from the context menu, select Simscape > Block choices. Select a variant that includes a thermal port. Specify the associated thermal parameters for the component.

Leadscrew Gear Model

Ideal Gear Constraint and Gear Ratio

Leadscrew imposes one kinematic constraint on the two connected axes:

ω_SL = 2πv_N .

The transmission ratio is R_NS = 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:

ω_S = R_NSv_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_NSτ_S + F_N – F_loss = 0 ,

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) ,

η_NS = (cosα – k/tanλ)/(cosα + k·tanα) .

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 cosα = k/tanλ.

• 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_Sω_S. ω_S 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. 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

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. The alternate option is Left-hand.

Meshing Losses

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

 Without Thermal Port

Friction model

Select how to implement from nonideal meshing of gear threads. The default is No meshing losses — Suitable for HIL simulation.

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

• Constant efficiency — Transfer of torque and force between screw and nut is reduced by friction. If you select this option, the panel expands.

   Constant Efficiency

  Friction parametrization

  Select how to characterize the friction between gear threads. The default is Friction coefficient and geometrical parameters.

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

    Lead angle

    Thread helix angle λ = arctan[L/(πd)]. d is the mean thread diameter. Must be greater than zero. The default is 15.

    From the drop-down list, choose units. The default is degrees (deg).

    Acme thread half angle

    Half-angle of the acme thread α in the normal plane. If a square thread is simulated, α = 0. Must be greater than zero. The default is 14.5.

    From the drop-down list, choose units. The default is degrees (deg).

    Friction coefficient

    Dimensionless coefficient of kinetic friction in the thread. Must be greater than zero. The default is 0.08.

  • Efficiencies — Friction is determined by constant efficiencies 0 < η < 1. If you select this option, the panel changes from its default.

     Efficiencies

    Screw-nut efficiency

    Efficiency η_SN of the power transfer from screw to nut.

    Nut-screw efficiency

    Efficiency η_NS of the power transfer from nut to screw.

  Power threshold

  Power threshold above which the full efficiency factor is in effect. Below this value, a hyperbolic tangent function smooths the efficiency factor, lowering the efficiency losses to zero when no power is transmitted. The default value is 0.001 W.

 With Thermal Port

Temperature

Array of temperatures used to construct a 1-D temperature-efficiency lookup table. The array values must increase from left to right. The temperature array must be the same size as the Efficiency array. The default array is [280 300 320] K.

Screw-nut efficiency

Array of component efficiencies with the screw as the driver—that is, with power flowing 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. The default array is [0.75 0.7 0.65].

Nut-screw 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. The default array is [0.5 0.45 0.4].

Power threshold

Power threshold above which the full efficiency factor is in effect. A hyperbolic tangent function smooths the efficiency factor between zero at rest and the value provided by the temperature-efficiency lookup table at the power threshold. The default value is 0.001 W.

Viscous Losses

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 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 alters the component efficiency according to an efficiency vector that you specify, affecting the starting meshing or friction losses. The default value is 300 K.

Real-Time Simulation

Hardware-in-the-Loop Simulation

For optimal simulation performance, use the Meshing Losses > Friction model parameter default setting, No meshing losses - Suitable for HIL simulation.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.