DC machines

In short

A DC machine converts mechanical energy into direct-current electrical energy (generator) or DC electrical energy into rotation (motor), using a field system, an armature winding and a commutator that mechanically rectifies the alternating EMF induced in the coils. The same machine works either way — only the direction of power flow changes — which is why the EMF equation, armature reaction and commutation are common to both. DC machines carry heavy weight in electrical machines papers, GATE EE (EMF/torque equations, characteristics, speed control, efficiency tests) and in PSU and campus interviews at NTPC, Power Grid, Indian Railways, BHEL, CIL, Siemens, ABB, L&T, Crompton and Kirloskar. Although induction and BLDC drives have replaced DC motors in most new installations, DC machines remain the teaching foundation for all rotating machines and still run cranes, rolling mills, traction legacy stock, electroplating plants and small servo and automotive drives.

Explained

Construction and basic action

• Yoke (frame): outer cast-steel or rolled-steel shell; carries the main flux and supports the machine mechanically.
• Field poles and pole shoes: laminated poles bolted to the yoke; the pole shoe spreads the flux over the armature surface and reduces reluctance.
• Field winding: many turns of fine wire (shunt, across the supply) or few turns of thick conductor (series, in the armature path); produces the main flux φ per pole.
• Armature core: slotted laminations of silicon steel, 0.35–0.5 mm thick, insulated with varnish to cut eddy-current loss; hysteresis loss is reduced by low-loss silicon steel.
• Armature winding: coils placed in slots, always a closed winding, connected to commutator segments; lap or wave connected.
• Commutator: hard-drawn copper segments separated by mica, mounted on the shaft; it is the rotating mechanical rectifier/inverter.
• Brushes: carbon or electro-graphite, held in spring-loaded holders; carbon gives a useful contact drop (about 1 V per brush, so ≈2 V per pair) that limits circulating current during commutation.
• Generator action: the conductor moves in a field, e = Blv; Fleming's right-hand rule gives the direction of induced EMF.
• Motor action: current-carrying conductor in a field experiences F = BIl; Fleming's left-hand rule gives the force direction.
• Why a commutator: the EMF in any armature coil is always alternating; the commutator reverses external connections as the coil passes the magnetic neutral axis, so the brush terminals see unidirectional voltage.

Armature windings — lap versus wave

• Pole pitch: number of armature slots (or conductors) per pole. Coil span (back pitch Yb): nearly one pole pitch for full EMF.
• Lap (parallel) winding: A = m·P parallel paths (m = multiplicity, 1 for simplex); front pitch Yf = Yb − 2 (progressive). Gives low voltage, high current; needs equalizer rings to kill circulating currents caused by unequal path flux.
• Wave (series) winding: A = 2m paths only, independent of poles; average pitch Ya = (Yb + Yf)/2 = (Z ± 2)/P. Gives high voltage, low current; needs no equalizers, needs dummy coils if the winding does not close.
• Brush sets: lap winding needs P brush arms; wave winding needs only 2 (though P are often used to reduce current density).
• Choice rule of thumb: large current low-voltage machines (electroplating, welding generators) → lap; high-voltage small-current machines → wave.

EMF, torque and armature reaction

• EMF equation: Eg = φZNP/(60A). Derivation outline: flux cut per conductor per revolution = φP; in N/60 revolutions per second EMF per conductor = φPN/60; conductors in series per path = Z/A; multiply.
• Terminal relations: generator V = Eg − Ia·Ra − brush drop; motor V = Eb + Ia·Ra + brush drop. Back EMF Eb is what makes a DC motor self-regulating — more load lowers speed, lowers Eb, raises Ia, raises torque.
• Torque: electromagnetic (armature) torque Ta = φZPIa/(2πA) = 9.55·Eb·Ia/N (N·m, N in rpm); shaft torque Tsh = Ta − loss torque. Ta ∝ φ·Ia always.
• Armature reaction: the MMF of armature current distorts and weakens the main field. It has a cross-magnetising component (shifts the magnetic neutral axis — forward of rotation in a generator, backward in a motor) and a demagnetising component (reduces φ because the strengthened pole tip — the trailing tip in a generator — saturates), which makes the generator's terminal voltage droop and a motor's speed rise slightly with load.
• Remedies: shift brushes to the new neutral axis (crude; only for fixed load), compensating (pole-face) windings in series with the armature to cancel cross-MMF under the pole arc, and interpoles between the main poles.

Commutation

• Commutation is the reversal of current in a coil during the time (about 1–2 ms) it is short-circuited by a brush. Ideal is linear commutation; the coil's self-inductance causes under-commutation (reactance voltage L·di/dt), leaving residual current that sparks at the trailing brush edge, pitting the commutator.
• Reactance voltage = L × 2Ic/Tc, where Ic is the coil current (= Ia/A) and Tc is the commutation period.
• Remedies: resistance commutation (high-resistance carbon brushes), EMF commutation using interpoles (narrow poles on the neutral axis, series-connected so their flux is proportional to Ia, inducing a voltage that reverses the coil current in step with load — the standard method), and reduced armature inductance.
• Interpole polarity: same as the next main pole ahead in the direction of rotation for a generator; same as the previous (preceding) main pole for a motor.

Types of excitation and characteristics

• Separately excited: field from an independent DC source; widest flux control, used in Ward-Leonard drives and in testing.
• Shunt: field across the armature; series: field in series with armature; compound: both — cumulative (series aids shunt) or differential (series opposes); connected long shunt or short shunt.
• Generator characteristics: (a) OCC / magnetisation curve Eo vs If at constant speed — starts at residual voltage, linear, then saturates; (b) internal E vs Ia; (c) external V vs IL — droops for shunt (armature drop + armature reaction + field weakening), rises with load for series up to saturation then falls, flat for level-compound (voltage at full load = no-load voltage), rising for over-compound (compensates line drop), steeply drooping for differential compound (used in old welding sets).
• Self-excitation needs: residual magnetism, field connected to help residual flux (else reverse field connections or swap rotation), and field circuit resistance below the critical resistance (slope of the tangent to the OCC at the origin). Below the critical speed the machine will not build up at all.
• Shunt motor: φ nearly constant, so T ∝ Ia and speed falls only 5–10% from no load to full load — an "almost constant speed" motor for lathes, fans, pumps, machine tools, line shafts.
• Series motor: before saturation φ ∝ Ia, so T ∝ Ia² and N ∝ 1/Ia — very high starting torque, speed-torque curve is a hyperbola. Must never be started unloaded (flux → 0, speed runs away). Used in traction, cranes, hoists, starter motors.
• Cumulative compound motor: high starting torque like a series motor but a definite no-load speed — rolling mills, punching presses, lifts, flywheel loads.

Starting, braking and speed control

• Why a starter: at standstill Eb = 0, so Ia = V/Ra. For a 230 V machine with Ra = 0.5 Ω that is 460 A against a rated 40 A — enough to burn the winding and flash the commutator. A starting resistance in series, cut out in steps as the motor speeds up and Eb rises, limits it to 1.5–2 times rated current.
• Three-point starter: handle moves over studs; has a no-volt release (NVR) coil in series with the shunt field (releases the handle on supply failure or open field) and an overload release (OLR) that short-circuits the NVR coil on overload. Drawback: on field weakening for speed control, the NVR current falls and may trip.
• Four-point starter: NVR coil has its own branch with a protective resistance, independent of the field — so wide field-weakening speed control is possible; field open-circuit protection must be provided separately.
• Speed control (from N ∝ (V − IaRa)/φ):
  1. Flux (field) control: rheostat in the shunt field raises speed above rated (base) speed at constant power; range about 1:2 to 1:4, limited by armature-reaction instability and commutation.
  2. Armature-resistance control: series resistance lowers speed below rated, but at poor efficiency (I²R wasted) and poor speed regulation; still used in cranes and hoists.
  3. Armature-voltage control: best method — Ward-Leonard (motor-generator set; smooth, reversible, four-quadrant, very wide range) or modern thyristor/chopper drives (single- or three-phase full converters; a chopper for battery and traction supplies).
  4. Series motor only: field diverter, tapped field, series-parallel grouping of two motors (traction).
• Braking: rheostatic (dynamic) — armature feeds a resistor, kinetic energy is dissipated; regenerative — Eb > V, power returns to the supply (needs a receptive source); plugging (counter-current) — armature supply reversed, fastest but wasteful. Reversal of a DC motor is done by reversing either the armature or the field connections, not both.

Losses, efficiency and testing

• Losses: (i) copper — armature Ia²Ra, shunt field V·Ish, series/interpole/compensating winding; (ii) iron — hysteresis (∝ f·Bmax^1.6) and eddy current (∝ f²·t²·Bmax²); (iii) mechanical — friction and windage; (iv) brush contact loss and stray load loss (often taken as about 1% of output). Iron + mechanical = constant (stray no-load) losses.
• Condition for maximum efficiency: variable loss = constant loss, i.e. Ia²Ra = Wc.
• Swinburne's test: run the machine at no load as a motor at rated voltage and speed, measure no-load input; subtract no-load armature copper loss to get constant losses, then compute efficiency at any load. Cheap and needs little power, but gives no temperature rise or commutation check, cannot be used on a series motor, and ignores the change in armature reaction with load.
• Hopkinson's test (back-to-back): two identical machines coupled, one motoring and one generating, with only the losses drawn from the supply. Gives full-load performance and temperature rise with small power input; needs two identical machines.
• Field's test: for two identical series machines, separating stray losses.
• Retardation (running-down) test: finds moment of inertia and stray losses from the deceleration rate of the armature.
• Standards and practice (India): IS/IEC 60034 series (rotating electrical machines) covers ratings, performance, losses and efficiency, temperature-rise limits by insulation class (A/E/B/F/H), degrees of protection (IP, IS/IEC 60034-5) and cooling (IC codes); IS 4722 covers rotating machine ratings; IS 325 is the familiar three-phase induction motor standard, not DC. Installation and safety follow the Electricity Act 2003, the CEA (Measures relating to Safety and Electric Supply) Regulations, 2023 (which replaced the 2010 regulations), and IS 732 for wiring; BEE star labelling and the Energy Conservation Act apply to induction motors — DC machines are generally outside mandatory star labelling. Exact clause numbers and amendment dates should be checked against the current published standard before use in design or tender work.

Key points

• Commutator - rotating mechanical rectifier; makes the alternating coil EMF unidirectional at the brushes.
• EMF equation - Eg = φZNP/60A; EMF ∝ φN for a given machine.
• Torque equation - Ta = φZPIa/2πA = 0.159 φZIa(P/A); torque ∝ φIa.
• Back EMF - Eb = V − IaRa in a motor; it automatically adjusts armature current to the load.
• Lap winding - A = mP paths, low voltage/high current, P brush arms, needs equalizers.
• Wave winding - A = 2m paths, high voltage/low current, 2 brush arms, may need dummy coils.
• Armature reaction - cross-magnetising distortion plus demagnetising effect; shifts the MNA forward in a generator, backward in a motor.
• Interpoles - series-connected auxiliary poles on the neutral axis that cancel reactance voltage and give spark-free commutation at all loads.
• Compensating winding - pole-face winding in series with the armature; cancels armature-reaction MMF under the pole arc, used in fast-changing loads (mills, Ward-Leonard).
• Critical field resistance - the field resistance equal to the slope of the OCC tangent at the origin; above it a shunt generator cannot self-excite.
• Shunt motor - approximately constant speed, T ∝ Ia; speed regulation 5–10%.
• Series motor - T ∝ Ia² below saturation, N ∝ 1/Ia; never run on no load.
• Compound motor - cumulative gives series-like starting torque with a safe no-load speed; differential is rarely used (unstable).
• Starter - limits Ia to 1.5–2 × rated at start; three-point starter trips on field weakening, four-point starter does not.
• Speed control - field control above base speed (constant power), armature-voltage control below base speed (constant torque).
• Maximum efficiency - occurs when variable copper loss equals constant (iron + friction) loss.
• Swinburne vs Hopkinson - Swinburne is a cheap no-load loss test; Hopkinson is a full-load regenerative (back-to-back) test needing two identical machines.
• Speed regulation - (No-load speed − full-load speed)/full-load speed × 100; voltage regulation of a generator = (Eno-load − Vfull-load)/Vfull-load × 100.

Formulas and examples

Example 1 — EMF, lap and wave. A 4-pole DC generator has 500 armature conductors, flux 0.03 Wb per pole, running at 1,200 rpm.

• Lap (A = P = 4): Eg = (0.03 × 500 × 1200 × 4)/(60 × 4) = 72,000/240... compute stepwise: φZNP = 0.03 × 500 × 1200 × 4 = 72,000; 60A = 240; Eg = 300 V.
• Wave (A = 2): 60A = 120 → Eg = 600 V. Same machine, double the voltage, half the current capacity.

Example 2 — Shunt motor: current, torque, speed. A 230 V DC shunt motor has Ra = 0.4 Ω, Rsh = 115 Ω, and draws 32 A from the line at 1,000 rpm. Total brush drop 2 V.

1. Ish = 230/115 = 2 A → Ia = 32 − 2 = 30 A.
2. Eb = 230 − (30 × 0.4) − 2 = 230 − 12 − 2 = 216 V.
3. Mechanical power developed = Eb·Ia = 216 × 30 = 6,480 W.
4. Armature torque Ta = 9.55 × 6,480/1,000 = 61.9 N·m.
5. If the load is removed so that Ia falls to 3 A (flux unchanged): Eb2 = 230 − 1.2 − 2 = 226.8 V → N2 = 1,000 × 226.8/216 = 1,050 rpm. Speed regulation = (1,050 − 1,000)/1,000 = 5%.

Example 3 — Series motor torque and speed. A 4-pole 250 V series motor takes 25 A and runs at 600 rpm; Ra + Rse = 0.6 Ω. Flux is proportional to current up to 30 A.

1. Eb1 = 250 − 25 × 0.6 = 235 V; Ta1 = 9.55 × 235 × 25/600 = 93.5 N·m.
2. Load increases so the current becomes 30 A: Eb2 = 250 − 30 × 0.6 = 232 V.
3. N2 = N1 × (Eb2/Eb1) × (φ1/φ2) = 600 × (232/235) × (25/30) = 600 × 0.98723 × 0.8333 = 493.6 rpm.
4. Torque ratio = (30/25)² = 1.44 → Ta2 ≈ 93.5 × ... check directly: Ta2 = 9.55 × 232 × 30/493.6 = 134.6 N·m; ratio 134.6/93.5 = 1.44, confirming T ∝ Ia².

Example 4 — Starting resistance. The same 230 V shunt motor (Ra = 0.4 Ω, full-load Ia = 30 A) is to be started with the armature current limited to 1.5 × full load.

• Permitted starting current = 45 A → total armature-circuit resistance needed = 230/45 = 5.111 Ω.
• External starting resistance = 5.111 − 0.4 = 4.71 Ω, cut out in steps as Eb builds up. Without it, Ia = 230/0.4 = 575 A, i.e. 19 times full load.

Example 5 — Swinburne's test and maximum efficiency. A 230 V shunt machine takes 5 A at no load; Ra = 0.4 Ω, Rsh = 115 Ω.

1. No-load input = 230 × 5 = 1,150 W. Ish = 2 A, Ia0 = 3 A.
2. No-load armature copper loss = 3² × 0.4 = 3.6 W → constant losses Wc = 1,150 − 3.6 = 1,146.4 W (includes the 460 W field loss, iron, friction and windage).
3. As a motor at 50 A line: Ia = 48 A; armature Cu loss = 48² × 0.4 = 921.6 W; total loss = 921.6 + 1,146.4 = 2,068 W; input = 230 × 50 = 11,500 W; output = 9,432 W → η = 82.0%.
4. As a generator delivering 50 A: Ia = 52 A; armature Cu loss = 52² × 0.4 = 1,081.6 W; output = 11,500 W; input = 11,500 + 1,081.6 + 1,146.4 = 13,728 W → η = 83.8%.
5. Maximum efficiency as a motor: excluding the field loss from Wc for the armature-circuit condition is a common simplification; using the full Wc, Ia = √(1,146.4/0.4) = 53.5 A, so maximum efficiency occurs near 55 A line current.

Where it is used

• Steel and rolling mills (SAIL, Tata Steel, JSW): large DC mill motors with compensating windings and thyristor drives for reversing stands; retrofit and maintenance work is a steady job area.
• Cranes, hoists, winders and mining equipment (BEML, Coal India, port cranes): series and compound motors for high starting torque, with rheostatic and regenerative braking.
• Railways: DC series traction motors on legacy locomotives and EMUs, and DC series motors in starter motors and auxiliaries; new Indian Railways stock uses three-phase induction drives, so DC traction is largely maintenance and conversion work.
• Electroplating, electrolysis, anodising and welding plants: low-voltage high-current DC generators and rectifier sets, with lap-wound armatures.
• Machine tools, printing presses, paper and textile mills: shunt and separately excited motors in Ward-Leonard or converter-fed drives where wide, smooth speed control is needed.
• Job roles: maintenance and electrical engineer in heavy industry, drives and automation engineer (Siemens, ABB, Schneider, L&T), testing engineer in machine manufacturing (BHEL, Crompton, Kirloskar Electric), and tender/technical roles in state utilities where the DC machine fundamentals are the entry test syllabus.

Interview questions

• Q: Why does a DC machine need a commutator? A: The EMF induced in each armature coil is inherently alternating; the commutator reverses the external connection as the coil crosses the neutral axis, so the brush terminals get unidirectional voltage (and in a motor it keeps torque unidirectional).
• Q: Why is the starting current of a DC motor so high? A: At standstill the back EMF is zero, so Ia = V/Ra, and Ra is only a fraction of an ohm — often 10–20 times rated current; a starter resistance limits it until Eb builds up.
• Q: Why must a DC series motor never be started on no load? A: Flux is proportional to armature current, so at very light load the flux nearly vanishes and speed rises to a destructive value (N ∝ 1/Ia); it is therefore always coupled directly, never by belt or chain.
• Q: What is armature reaction and what are its two effects? A: The armature MMF acting on the main field — it is cross-magnetising (distorts the flux and shifts the magnetic neutral axis) and, because of saturation, slightly demagnetising (reduces the useful flux and so the generated voltage).
• Q: Difference between interpoles and a compensating winding? A: Interpoles are narrow poles on the neutral axis that neutralise the reactance voltage in the commutating coil; a compensating winding is embedded in the pole faces and neutralises armature-reaction MMF under the pole arc. Both are connected in series with the armature.
• Q: How do you reverse the direction of a DC shunt motor? A: Reverse either the armature connections or the field connections, not both; armature reversal is normally used because the field has high inductance and reversing it is slow and can cause dangerous flux loss.
• Q: Why is a four-point starter preferred when field-weakening speed control is used? A: In a three-point starter the no-volt release coil is in series with the shunt field, so weakening the field reduces the holding current and the handle trips; in a four-point starter the NVR coil has a separate branch and is independent of field current.
• Q: Will a shunt generator build up voltage if it is driven in the wrong direction? A: No — the field current then opposes the residual flux and the voltage collapses; you must either reverse the rotation or reverse the field winding connections, after re-establishing residual magnetism by flashing the field if needed.
• Q: What decides whether lap or wave winding is used? A: The required voltage and current — lap gives P parallel paths (high current, low voltage), wave gives only two paths (high voltage, low current), for the same number of conductors and speed.
• Q: Why does a DC shunt motor's speed rise slightly when a field rheostat is removed from the circuit… or rather, why does weakening the field increase speed? A: Speed N ∝ (V − IaRa)/φ; reducing φ reduces back EMF momentarily, so Ia and torque rise until the motor accelerates to restore Eb at a higher speed.
• Q: Why is Swinburne's test not applicable to a DC series machine? A: It is a no-load test, and a series machine cannot be run safely at no load because its flux collapses and its speed runs away; Field's test is used instead.
• Q: Where does regenerative braking fail to work, and what do you use instead? A: It needs a supply able to absorb power — with a battery or diode rectifier that cannot invert, regeneration is impossible, so rheostatic (dynamic) braking into a resistor or plugging is used.

Common mistakes

• Using the wrong number of parallel paths A — taking A = 2 for a lap winding or A = P for a wave winding — which scales the EMF by a factor of P/2.
• Mixing up the armature and line current: in a shunt motor Ia = IL − Ish, in a shunt generator Ia = IL + Ish; getting the sign wrong changes Eb and the torque.
• Forgetting the brush contact drop (about 2 V total) when a question gives it, or adding it when it is not given.
• Treating T ∝ Ia² for a series motor beyond saturation — once the iron saturates the flux stops rising and torque becomes nearly proportional to Ia.
• Using Ta (electromagnetic torque, from Eb·Ia) where the shaft torque is asked, forgetting friction, windage and iron-loss torque.
• Confusing interpoles with main poles when stating polarity, and forgetting that interpole and compensating windings carry the full armature current.
• In efficiency problems, omitting the shunt field copper loss from the constant losses, or claiming maximum efficiency at full load instead of where variable loss equals constant loss.

Related topics

Transformers · Induction motors · Induction motor testing, starting and speed control · Synchronous machines · Special machines: stepper and BLDC motors · Electrical machine design basics