Ideal gear

Lossless gear: φ_a = ratio·φ_b.

  • rotational
  • Modelica Standard Library
  • 2 ports
  • 1 parameter
BlockIdeal gearKindidealGearLibraryRotational

Description

A lossless gear fixed to the housing, with no inertia, elasticity, or backlash. Flange a turns ratio times as far as flange b, and the torque is scaled by the same factor, so power is conserved.

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 Ideal gear 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 springTorsion damperInertia (ideal)Torque stepSpeed sensor (ideal)Acceleration sensorPower sensor (rotational)Relative speed sensor

Ports

Conserving terminals 2

  • aflange_arotational

    Input side flange. Angle φ_a = ratio · φ_b.

  • bflange_brotational

    Output side flange.

Parameters

  • Ratioratio2

    Transmission ratio φ_a/φ_b. A value above 1 reduces speed and raises torque at flange_b; a negative value reverses direction.

Equations

Modelica
flange_a.phi = ratio · flange_b.phi
0 = ratio · flange_a.tau + flange_b.tau

Implementation

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

Assumptions and limitations

  • No friction, efficiency loss, backlash, or tooth stiffness. Add Backlash or Torsion spring on either side for those effects.

Tips

  • An inertia J behind the gear appears as J/ratio² at flange_a.

Used in

These larger examples use it too. Open them from Examples in the app.

  • EV drivetrain

See also

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