Torque & Speed

Part of Generators and Motors

The relationship between torque and speed in motors and generators, and how to match machine characteristics to the load for reliable, efficient operation.

Why This Matters

Power is the product of torque and speed: P = T × ω. This relationship governs everything about how motors and generators interact with their mechanical environment. A motor that produces the right power but at the wrong speed cannot do useful work without a transmission. A generator connected to a prime mover that produces too much torque at low speed will either overvolt the output or force the generator to operate inefficiently.

Understanding torque-speed relationships allows proper matching of machines to their applications, correct sizing of transmission systems, and accurate diagnosis of problems. When a motor fails to accelerate its load to full speed, or a generator produces the wrong voltage, the torque-speed diagram is the analytical tool that explains why and points to the solution.

The Fundamental Relationship

Mechanical power equals torque times angular velocity: P = T × ω, where T is in Newton-meters and ω is in radians per second. In practical units: P (watts) = T (Nm) × 2π × N (RPM) / 60. Rearranged: T = 9550 × P(kW) / N(RPM). A 10 kW motor running at 1450 RPM produces: T = 9550 × 10 / 1450 = 65.9 Nm of torque.

This calculation lets you size couplings, gearboxes, and shafts correctly. A coupling that must transmit this torque with a 2× safety factor must be rated for 130 Nm. A shaft of a given diameter and material has a calculable maximum torque — verify that rated torque does not approach this limit.

The relationship also reveals that the same power can be delivered at high torque/low speed or low torque/high speed. A gearbox changes the ratio between them while conserving power (minus losses). This is the fundamental principle of all power transmission: high torque is needed to do work (turn a mill, cut metal), while high speed is often what the prime mover provides naturally. Gearing matches supply to demand.

DC Motor Torque-Speed Curves

A DC motor (shunt, series, or compound) has characteristic torque-speed curves that determine its suitability for different applications.

Shunt DC motor (field in parallel with armature): nearly constant speed from no load to full load. Torque increases linearly as speed decreases slightly from no-load to full-load speed. This is the “ideal” motor for most machine tool applications where constant speed is required regardless of cutting load variations. The shunt motor maintains speed by increasing current as load increases. Catastrophic failure mode: if the field circuit opens, flux drops to residual, back-EMF drops, armature current rises to dangerous levels, and the motor overspeeds or burns out. Never run a shunt motor without confirmed field connection.

Series DC motor (field in series with armature): very high starting torque (field current equals armature current, so torque ∝ I², not just I). Speed varies dramatically with load — at no load, the motor races to dangerous overspeed because reducing current reduces both field and back-EMF. Series motors should never be run unloaded. They are ideal for traction (trams, locomotives, cranes) where high starting torque is needed and the load is always present. Historically important as the first practical traction motor.

Compound motor: combines both windings, with characteristics between shunt and series. The cumulative compound motor has high starting torque and more stable no-load speed than a pure series motor. For general industrial use requiring high starting torque and reasonable speed regulation, the compound motor is often the best choice.

AC Induction Motor Torque-Speed Curve

The AC induction motor torque-speed characteristic has a distinctive shape worth understanding in detail.

From standstill (zero speed, maximum slip), the motor produces starting torque (typically 1.0–2.5 times rated torque). As it accelerates, torque may initially increase before reaching breakdown torque (typically 2.0–3.5 times rated torque at about 70–80% of synchronous speed). After breakdown torque, torque decreases steeply until the motor reaches near-synchronous speed. At rated load, the motor runs at 2–5% slip, near synchronous speed.

The two critical regions: starting (0–20% of synchronous speed) and operating (90–100% of synchronous speed). Between them is an unstable region — if the load torque exceeds the motor’s breakdown torque, the motor will not pass through this region to reach operating speed. It stalls, drawing locked-rotor current (5–7 times rated) and quickly overheats.

For starting high-inertia loads (fans, flywheel-equipped machines), verify that the motor can accelerate the load in the available time without excessive heating during the acceleration period. The energy dissipated in the rotor during starting equals the kinetic energy stored in the load at full speed — high inertia loads cause rotor heating even when the motor itself is correctly sized.

Matching Motor Speed to Load Requirements

Most driven machines have a required speed: pumps, fans, and compressors have a design speed that determines their flow or pressure. Machine tools need specific spindle speeds for given materials and cutting tools. Generators need a specific speed for their design frequency and voltage.

If the motor speed and load speed match, direct coupling is ideal (no losses, no additional components to maintain). If they do not match, a transmission is required.

Fixed ratio transmission: belt, chain, or gear reduction or step-up. Choose the ratio to give load speed = motor speed × ratio. Include the efficiency of the transmission (90–98% for well-maintained gearing) when sizing the motor.

Variable ratio transmission: mechanical variable-speed drives (cone pulleys, variable pitch V-belt pulleys, hydraulic couplings) allow speed adjustment. This adds cost and complexity but is necessary for machine tools that operate at different speeds for different materials or operations.

Variable frequency drive (VFD): an electronic inverter that changes the frequency (and voltage) of the AC supply to an induction motor, varying the synchronous speed and thus the motor speed. Sophisticated, requires electronics manufacturing capability, but provides precise, efficient speed control with no mechanical transmission losses. As a rebuilding civilization develops electronics capability, VFDs become increasingly attractive.

Generator Torque Requirements from Prime Movers

A generator presents a torque demand to its prime mover that depends on electrical load. At no load, only friction and windage torque are required. As load increases, required torque increases proportionally to the power drawn.

The prime mover’s torque-speed curve must intersect the load (generator) torque curve at a stable operating point. A waterwheel (roughly constant torque over a range of speeds) is well-matched to a generator (roughly constant torque requirement at constant speed). A steam engine (torque drops with speed if throttle is fixed) and an induction generator (which presents increasing torque demand up to breakdown torque) requires careful matching and governor control.

Speed drooping is the key characteristic for parallel generator operation. When two generators run in parallel and load increases, both prime movers should reduce speed slightly — the “droop” characteristic. The generator that droops proportionally to its rating takes its fair share of the load increase. A generator with no droop (perfectly constant speed governor) picks up all load changes immediately, which destabilizes the parallel system. Design governors for 3–5% droop from no-load to full-load speed.

Diagnosing Torque-Speed Problems

If a motor fails to reach full speed under load:

• Check supply voltage under load (low voltage reduces torque proportionally to V²)
• Verify load torque requirement (may be higher than expected due to friction, binding, or incorrect sizing)
• Check for high slip → high rotor losses → overheating as warning signs of undersized motor

If a motor overspeeds (DC series or shunt motor):

• Check load is connected (series motor must always be loaded)
• Check field circuit continuity (shunt or compound motor: open field = runaway)
• Measure armature voltage and field current with motor running

If a generator produces high voltage at no load but voltage collapses under load:

• Winding resistance is too high — measure voltage drop across winding resistance under load current
• Excessive air gap — insufficient flux for the excitation current
• Soft magnetic core (wrong material, or not laminated) — excessive reactive voltage drop from core inductance