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Motor

Motor Starting Torque

Calculate DC motor starting (stall) torque, stall current, no-load speed, and peak power at startup.

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Formula

T_s = Kt × V/R, I_s = V/R

Kt— Torque constant (N·m/A)
R— Winding resistance (Ω)

How It Works

Starting torque is the rotational force a motor must overcome to accelerate the load from rest to operating speed. It must exceed static friction torque (breakaway torque) plus the torque required to accelerate the combined load and motor rotor inertia. The acceleration torque is T_accel = J_total × α, where J_total is the total reflected inertia (kg·m²) and α is the required angular acceleration (rad/s²). The motor's selected starting torque rating must exceed T_breakaway + T_accel with an adequate safety margin (typically 1.5–2×).

Worked Example

A conveyor must reach 200 RPM in 2 seconds. Load inertia at the motor shaft (reflected through gearbox) is 0.05 kg·m². Motor rotor inertia is 0.005 kg·m². Static friction torque is 1.2 N·m. Step 1 — Angular acceleration required: α = ω / t = (200 × π/30) / 2 = 20.94 / 2 = 10.47 rad/s² Step 2 — Total inertia: J_total = J_load + J_motor = 0.05 + 0.005 = 0.055 kg·m² Step 3 — Acceleration torque: T_accel = J_total × α = 0.055 × 10.47 = 0.576 N·m Step 4 — Total required starting torque: T_start = T_friction + T_accel = 1.2 + 0.576 = 1.776 N·m Step 5 — Motor selection with 2× safety factor: T_motor_min = 1.776 × 2 = 3.55 N·m rated starting torque Result: Select a motor with at least 3.55 N·m starting torque. If only continuous torque is available, ensure the starting torque specification (often 1.5–2.5× continuous) meets this requirement.

Practical Tips

  • ✓For high-inertia loads (flywheels, large fans), consider a soft-start or ramp-up profile to limit peak starting current and mechanical shock on couplings and gearboxes
  • ✓Test breakaway torque experimentally — place a torque wrench on the output shaft and measure the torque needed to initiate rotation from a cold standstill, which is always higher than warm running friction
  • ✓Permanent-magnet DC motors and BLDC motors typically have starting torque equal to stall torque, making them well-suited for high-inertia starts compared to induction motors whose starting torque is limited

Common Mistakes

  • ✗Neglecting static breakaway friction, which can be 3–5× higher than running friction in applications with seals, grease, or long periods of standstill
  • ✗Using continuous rated torque instead of locked-rotor or peak torque for starting calculations — these can differ by 2–3×
  • ✗Forgetting to reflect load inertia through the gear ratio squared (J_reflected = J_load / GR²) when the encoder or motor is on the input side of a gearbox

Frequently Asked Questions

Stall torque is the maximum torque a motor can produce at zero speed when driven at rated voltage — it is a motor characteristic. Starting torque is the torque required by the application to begin rotation — it is a load characteristic. The motor's stall torque must exceed the load's required starting torque for the system to start.
In star connection, each motor winding sees 1/√3 of line voltage, reducing torque to 1/3 of direct-on-line (DOL) starting torque. This also reduces inrush current to 1/3 of DOL. The starter switches from star to delta once the motor approaches full speed. This is only suitable when the load torque at startup is less than 1/3 of full-load torque.
Permanent-magnet DC and BLDC motors produce maximum torque at zero speed, making them inherently well-suited for high starting-torque applications. Series-wound DC motors also produce very high starting torque. AC induction motors require star-delta, autotransformer, or soft-starter equipment to increase starting torque capability above direct-on-line values.

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