Leadscrew
R2026bLeadscrew gear set of threaded rotating screw and translating nut, with adjustable thread and friction losses
Leadscrew block
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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, ωS and vN have the same sign. If the screw helix is left-hand, ωS and vN have opposite signs.
Ideal Nut Constraint and Transmission Ratio
The block imposes one kinematic constraint on the two connected axes:
| ωSL = 2πvN. | (1) |
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. | (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 Floss = 0 in the ideal case.
Nonideal Nut Constraint and Losses
In the nonideal case, Floss ≠ 0. For general considerations on nonideal gear modeling, see Model Gears with Losses.
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 = (cosα – k·tanλ)/(cosα + k/tanλ), | (4) |
| ηNS = (cosα – k/tanλ)/(cosα + k·tanλ). | (5) |
In the constant efficiency case, you specify ηSN and ηNS, independently of geometric details.
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 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 Torque
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.
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
Conserving
Parameters
Extended Capabilities
Version History
Introduced in R2011a
