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Motor Starting Torque

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

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Formula

Ts=Kt×V/R,Is=V/RT_s = Kt × V/R, I_s = V/R
Kt— Torque constant (N·m/A)
R— Winding resistance (Ω)

How It Works

This calculator determines the starting torque required to accelerate a motor-driven load from rest to operating speed. Mechanical engineers, conveyor designers, and industrial automation specialists use it to select motors that overcome static friction and accelerate loads within specified time constraints. Undersizing starting torque causes motor stalling; oversizing wastes capital cost and energy.

Per NEMA MG-1-12.38, starting torque must exceed the sum of breakaway torque (static friction) plus acceleration torque: T_start ≥ T_breakaway + T_accel. The acceleration component follows Newton's second law for rotation: T_accel = J_total × α, where J_total is total reflected inertia (kg·m²) and α is angular acceleration (rad/s²). Breakaway friction typically equals 1.5-3× running friction per Tribology Handbook (Neale, 1995).

NEMA motor designs specify starting torque as a percentage of rated torque: Design A provides 70-100%, Design B (most common) provides 100-200%, Design C provides 200-250%, and Design D provides 250-300%. A 10 HP Design B motor rated at 25 N·m continuous delivers 25-50 N·m locked-rotor torque. For high-inertia loads, the motor must sustain high torque for several seconds during acceleration—exceeding thermal limits if the start takes longer than 10-15 seconds per NEMA MG-1-12.50.

Worked Example

A packaging line conveyor must reach 60 m/min (1 m/s) in 2.5 seconds. Total reflected load inertia is 0.8 kg·m², motor rotor inertia is 0.05 kg·m². Breakaway friction requires 12 N·m. Drive drum radius is 0.15 m.

Step 1 — Calculate required angular velocity: ω = v / r = 1.0 / 0.15 = 6.67 rad/s = 63.7 RPM

Step 2 — Calculate angular acceleration: α = ω / t = 6.67 / 2.5 = 2.67 rad/s²

Step 3 — Calculate acceleration torque: J_total = J_load + J_motor = 0.8 + 0.05 = 0.85 kg·m² T_accel = J × α = 0.85 × 2.67 = 2.27 N·m

Step 4 — Calculate total starting torque: T_start = T_breakaway + T_accel = 12 + 2.27 = 14.27 N·m

Step 5 — Apply safety factor per NEMA guidelines: With 1.5× margin: T_motor_min = 14.27 × 1.5 = 21.4 N·m starting torque Select motor with rated torque ≥ 10.7 N·m (assuming Design B at 200% locked-rotor)

Result: A 1.1 kW motor (rated ~10-12 N·m continuous, 20-24 N·m starting) meets requirements with adequate margin. Starting time of 2.5 seconds is within NEMA thermal limits for Design B motors.

Practical Tips

  • ✓Per NEMA MG-1-12.50, limit starting duration to 2 × rated locked-rotor time (typically 10-15 seconds) to prevent winding overheating; for longer acceleration, use a soft-starter to reduce current and thermal stress
  • ✓Test breakaway torque experimentally: per industrial commissioning practice, apply a torque wrench to the output shaft after 8+ hours standstill—cold breakaway is always higher than warm running friction by 50-200%
  • ✓For star-delta starting, available torque is only 33% of DOL torque (voltage² relationship); ensure load starting torque is <25% of motor DOL locked-rotor torque when using reduced-voltage starters

Common Mistakes

  • ✗Using running friction instead of breakaway: Per Tribology Handbook, static friction coefficient is 1.5-3× kinetic friction—a conveyor requiring 8 N·m running torque may need 12-24 N·m to initiate motion after overnight standstill
  • ✗Confusing continuous and locked-rotor torque: Per NEMA MG-1, Design B motors deliver 100-200% of continuous torque at stall; using continuous torque in starting calculations undersizes the motor by 50-100%
  • ✗Ignoring gear ratio effect on reflected inertia: Inertia transforms as J_reflected = J_load × (N_motor/N_load)² = J_load / GR²; a 10:1 gearbox reduces reflected inertia by 100×, dramatically lowering acceleration torque requirements

Frequently Asked Questions

Per NEMA MG-1: Stall (locked-rotor) torque is a motor specification—the maximum torque at zero speed when energized at rated voltage. Starting torque is an application requirement—the torque needed to initiate and complete acceleration. The motor's stall torque must exceed the application's starting torque. Design B motors provide 100-200% stall-to-rated ratio; Design D provides 250-300% for high-inertia loads.
Per IEC 60947-4-1, star connection applies V_line/√3 to each winding, reducing torque to (1/√3)² = 33% of DOL value. Current also drops to 33%. Transition to delta restores full torque once the motor approaches synchronous speed. Star-delta is suitable only when starting torque requirement is <33% of motor locked-rotor torque—typically light loads or high-inertia flywheels that accelerate slowly.
Per Krishnan's 'Electric Motor Drives': Permanent-magnet DC and BLDC motors produce maximum torque at zero speed (100% stall-to-continuous ratio), making them ideal for high starting-torque applications. Series-wound DC motors provide 200-300% starting torque. AC induction motors require reduced-voltage or soft-starters to extend starting duration without overheating, as their starting current is 5-8× rated current per NEMA MG-1.

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