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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.

Ports

S is a rotational conserving port. N is a translational conserving port. They represent the screw and the nut, respectively.

Dialog Box and Parameters

Main

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

Friction model

Select how to implement friction losses from nonideal meshing of gear threads. The default is No friction losses.

• No friction 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.

Viscous Losses

Viscous friction coefficient

Viscous friction coefficient μS for the screw. The default is 0.

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 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 negligible. It does not impact gear dynamics.

• Gears are rigid. They do not deform.

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

Example

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