What Is Torque?

Torque is the rotational equivalent of force: a vector quantity that describes the tendency of a force to cause angular acceleration about a given axis. Mathematically, torque is the cross product of the moment arm vector and the applied force vector, giving a result in newton-meters (N·m) in the International System of Units. Its magnitude depends on both the magnitude of the force and the perpendicular distance from the axis of rotation to the line of action of the force. Torque is a foundational concept in mechanical engineering, electrical machine design, robotics, and automotive systems.

The physical principle governing torque follows from Newton's second law generalized to rotation: net torque equals the product of the moment of inertia and angular acceleration. This relationship makes torque the central quantity in the design of any rotating system, from a simple fastener to a large synchronous generator. Torque pulsations, periodic oscillations in torque output arising from electromagnetic or mechanical asymmetries, are a primary concern in motor design because they cause vibration and acoustic noise in both industrial machines and electric vehicles.

Torque in Rotational Mechanics

In classical mechanics, torque analysis determines whether a rigid body remains in rotational equilibrium or accelerates. For a body in static equilibrium, the sum of all torques about any axis must equal zero; this principle governs the design of structures such as crane booms, gear trains, and bridge load paths. Dynamic torque analysis solves for angular motion under time-varying loads. The NIST program on torque realization describes how national metrology efforts establish primary torque standards traceable to fundamental SI units, enabling calibration of torque instruments across the full range from sub-millinewton-meters in micro-electromechanical systems to megainewton-meters in large wind turbines. Gear ratios transform torque between rotating shafts while trading angular velocity: doubling the gear ratio halves the speed and doubles the torque, conserving power in ideal conditions.

Torque in Electric Machines

In electric motors and generators, electromagnetic torque arises from the interaction between the magnetic flux in the air gap and the current-carrying conductors of the rotor. For a permanent magnet synchronous motor, the instantaneous torque equals the product of the flux linkage and the quadrature current component divided by the rotor flux magnitude. Induction motors produce torque through slip, the difference in rotational speed between the stator's rotating magnetic field and the rotor, which induces rotor currents by transformer action. Managing torque pulsations requires careful design of the slot and pole geometry, and in variable-speed drives, sophisticated control algorithms suppress ripple to acceptable levels. IEEE Xplore research on direct torque control of induction motors presents the foundational comparison between field-oriented and direct torque control strategies that now underpin most industrial drive designs.

Torque Measurement

Measuring torque on a rotating shaft requires techniques that accommodate both the continuous rotation and the requirement for high-accuracy calibration. Strain-gauge torquemeters bond resistive gauges to an elastic shaft section; torsional strain deforms the gauges, changing their resistance in a manner proportional to applied torque. Telemetry or slip rings transfer the signal from the rotating shaft to stationary instrumentation. Magnetostrictive sensors exploit the change in magnetic permeability of shaft material under torsional stress, enabling non-contact measurement. IEEE research on sensor design for torque-controlled actuators compares strain-gauge and encoder-based sensing principles for robotic joints, where measurement bandwidth and zero-offset stability are critical.

Applications

Torque has applications across a wide range of engineering systems, including:

• Electric vehicle powertrain design where motor torque commands determine acceleration and regenerative braking
• Industrial motor drives requiring precise torque regulation in steel rolling mills and paper machines
• Automotive transmissions and torque converters for efficient power delivery
• Robotics, where joint torque sensing enables compliant and force-controlled manipulation
• Wind turbines, where aerodynamic torque is converted to electrical power by the generator