Torsion spring

Linear torsion spring: τ = c·(φ_rel − φ_rel0).

  • rotational
  • Modelica Standard Library
  • 2 ports
  • 2 parameters
BlockTorsion springKindrotSpringLibraryRotational

Description

A linear torsion spring between two flanges. Connect it between two inertias to model shaft elasticity, or between an inertia and Fixed (rotational) to model a return spring.

Example

Rotational drivetrain A torque step drives a motor inertia through a 2:1 gear and a shaft spring into a damped load, with every rotational sensor.

Torque 1 N·mMotor 0.01 kg·m²Gear 2:1Shaft powerShaft torqueShaft 1000 N·m/radLoad 0.04 kg·m²Friction 0.1FrameMotor accelerationShaft twist rateLoad speed
In Gradara, select a Torsion spring block and press F1, then choose Open example. It opens as a new model in My models, ready to run.

Also in this example:Torque sensorFixed (rotational)Torsion damperInertia (ideal)Ideal gearTorque stepSpeed sensor (ideal)Acceleration sensorPower sensor (rotational)Relative speed sensor

Ports

Conserving terminals 2

  • aflange_arotational

    Flange a. Receives −τ.

  • bflange_brotational

    Flange b. Receives τ, the spring torque.

Parameters

  • Stiffnessc10000 N·m/rad

    ≥ 0

    Torsional stiffness, in N·m/rad. Zero or positive.

  • Unstretched anglephi_rel00 rad

    Relative angle at which the spring exerts no torque, in radians.

Equations

Modelica
φ_rel = flange_b.phi − flange_a.phi
τ = c · (φ_rel − phi_rel0)
flange_b.tau = τ, flange_a.tau = −τ

Implementation

Modelica Standard Library 4.1.0Modelica.Mechanics.Rotational.Components.Spring
MSL documentation

Assumptions and limitations

  • No damping and no mass. A stiff spring between two inertias makes the model stiff; add a little damping in parallel.

See also

Select a block in Gradara and press F1 to open its page offline.