Double-cage and deep-bar induction motors

Reference notes

This lesson covers the Bimbhra-style treatment of double-cage and deep-bar induction motors: how two concentric rotor cages (or one tall bar exploiting skin effect) break the single-cage trade-off between starting torque and full-load efficiency. Press Next → to walk through the construction, the frequency-dependent current split, the equivalent circuit, and the NEMA Design A/B/C/D classifications.

The single-cage trade-off

For a standard squirrel-cage rotor with a single set of bars, the slip at maximum torque is:

• High R₂ → s_m near 1 → high starting torque, but rotor copper loss = s · P_input ∝ R₂ · I² at any operating slip → high losses, low η at full load.
• Low R₂ → low losses at full load → high η, but low starting torque (peak torque at low slip).

You can't have both with one cage — unless you split the rotor into TWO concentric cages.

Double-cage rotor — construction

• Outer cage — bars near the rotor surface. HIGH R per bar (often brass, or thinner cross-section copper). LOW leakage reactance X_outer (flux couples readily from the air gap).
• Inner cage — bars deeper in the rotor iron. LOW R (thick copper bars). HIGH leakage reactance X_inner (flux must penetrate rotor iron to reach it).
• Both cages are short-circuited by their own end-rings, or sometimes share a common end-ring.

Frequency-dependent current split

Rotor frequency f_r = s · f₁. At slip s = 1 (start), f_r = 50 or 60 Hz. At full-load slip ~3 %, f_r ≈ 1–2 Hz.

• At start (s = 1, f_r ≈ f₁): inner-cage reactance X_inner = ω·L_inner is HIGH. Inner branch is essentially blocked. Most rotor current flows through the LOW-X outer cage. Outer cage has HIGH R → high starting torque.
• At run (s ≈ 0.03, f_r ≈ 1.5 Hz): inner-cage reactance is tiny. Inner cage's LOW R dominates the parallel combination. Most current flows in the inner cage → low rotor I²R losses → high η.

The motor effectively has two different rotor resistances active at different speeds, with no external switching required.

Equivalent circuit

The single rotor branch in the standard induction-motor equivalent circuit is replaced by two parallel branches, both referred to the stator side:

Air-gap torque is the sum of contributions from each cage, each weighted by the current that branch carries. The double-cage T-s curve combines a high starting torque (from the outer cage) with a high pull-out torque at low slip (from the inner cage), giving smoother behavior across the slip range than either single cage alone.

Deep-bar rotor — skin effect alternative

A simpler alternative achieves a similar T-s shape with just ONE cage of tall, narrow bars extending deep into the rotor iron:

• At high f_r (start): AC penetrates only the outer skin of each bar → small effective cross-section → high effective resistance → high starting torque.
• At low f_r (run): current distributes across the full bar cross-section → low effective resistance → low losses → high η.
• Cheaper to manufacture than true two-cage construction. Most modern NEMA Design B and C motors use deep-bar rotors. True double-cage is reserved for specialized high-starting-torque applications.

NEMA Design classifications

• Design A — low rotor R, low starting T (~150 %), low full-load slip (< 5 %), high inrush. Older general-purpose. Sometimes uses single-cage low-R rotor.
• Design B — the workhorse. T_start ≈ 150–180 % FLT, I_start ≈ 600 % FLA (LRA ≈ 6× FLA), slip 3–5 %, η 80–96 %. Centrifugal pumps, fans, compressors. Deep-bar rotor.
• Design C — high starting torque (~200–250 % FLT). Double-cage or deep-bar rotor. Conveyors, crushers, loaded compressors.
• Design D — very high starting T (≥ 275 %), high full-load slip (8–13 %). Punch presses, shears, oil-well pumps. The high slip lets motor speed dip during torque peaks, releasing flywheel KE = ½ J ω².

Starting current (LRA)

All NEMA designs have similar locked-rotor (starting) current — about 6× full-load amps (600 % FLA) for ~0.5–5 seconds while the motor accelerates from standstill. Feeders to large motors need ampacity that doesn't trip on inrush: time-delay fuses, magnetic-only motor-circuit-protector breakers, or soft-start / VFD ramping.

Keyboard shortcuts

• Click +/− on the canvas to sweep slip from start to sync; click NEMA letter buttons to compare design classes.