Leadscrew

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

• Library:

• 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:

ωSL = 2πvN .

(1)

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:

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 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.

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 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.

Thermal Modeling

You can model the effects of heat flow and temperature change by exposing an optional thermal port. To expose the port, in the Meshing Losses tab, set the Friction model parameter 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.

Dependencies

Variable settings are exposed only when, in the Meshing Losses settings, the Friction model parameter is set to Temperature-dependent efficiency.

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 — Nut displacement per revolution

0.015 m (default) | positive scalar

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

Screw helix type — Rotational directional sense

Right-hand (default) | Left-hand

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

Friction model — Screw friction model

No meshing losses — Suitable for HIL simulation (default) | Constant efficiency | Temperature-dependent efficiency

• 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 parametrization — Friction losses from nonideal meshing of gear threads

Friction coefficient and geometrical parameters (default) | Efficiencies

• 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.

Lead angle — Thread helix angle

15 deg (default) | positive scalar

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.

Acme thread half angle — Thread half-angle

14.5 deg (default) | positive scalar

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.

Friction coefficient — Thread friction coefficient

0.08 (default) | positive scalar

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.

Screw-nut efficiency — Efficiency from screw to nut

0.75 (default) | positive scalar in the range of (0,1]

Efficiency η_SN of the power transfer from screw to nut.

Dependencies

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

Nut-screw efficiency — Efficiency from nut to screw

0.45 (default) | positive scalar in the range of (0,1]

Efficiency η_NS of the power transfer from gear to worm.

Dependencies

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

Temperature — Array for tabular parameterization of efficiency

[280 300 320] K (default) | vector

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 Nut-screw efficiency arrays.

Dependencies

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

Screw-nut efficiency — Array of screw-to-nut efficiencies

[0.75 0.7 0.65] (default) | vector

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.

Nut-screw efficiency — Array of nut-to-screw efficiencies

[0.5 0.45 0.4] (default) | vector

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 — Power below which numerical smoothing is applied

0.001 W (default) | positive scalar

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 — Fluid dynamic friction coefficient

0N*m/(rad/s) (default) | positive scalar

Viscous friction coefficient μ_S for the screw.

Thermal Port

Thermal mass — Thermal mass

50 J/K (default) | positive scalar

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.

Initial temperature — Initial temperature

300 K (default) | positive scalar

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.

Extended Capabilities

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