Motor Sizing Calculator

Motor Power Calculation

The fundamental relationship between power, torque, and speed:

P = T x omega = T x (2 x pi x n / 60)

Where:

• P = Mechanical power (Watts)
• T = Torque (N-m)
• omega = Angular velocity (rad/s)
• n = Rotational speed (RPM)

In imperial units: HP = T(lb-ft) x n(RPM) / 5252

Service Factors for Different Applications

• 1.0 - Continuous duty, uniform load (blowers, fans)
• 1.15 - Normal industrial duty (pumps, conveyors)
• 1.25 - Moderate shock or overloads (machine tools)
• 1.35-1.5 - Heavy shock loads (compressors, punch presses)
• 2.0+ - Severe shock loads (rock crushers, rolling mills)

Inertia and Acceleration Torque

The torque required to accelerate a rotating mass:

T_accel = J x alpha = J x (delta_omega / delta_t)

Acceleration time calculation:

t = J x omega / (T_motor - T_load)

Where J is the total system inertia reflected to the motor shaft.

Reflected Inertia Through Gearbox

When a gearbox reduces speed by ratio N:1, the load inertia is divided by N squared:

J_reflected = J_load / N^2

This is why gearboxes are effective for high-inertia loads - a 5:1 reducer makes the load appear 25x lighter to the motor.

Motor Efficiency and Power Factor

Motor efficiency relates mechanical output to electrical input:

eta = P_mechanical / P_electrical

Power factor relates real power to apparent power:

PF = P_real / S_apparent = P / (V x I)

For 3-phase motors: P = sqrt(3) x V x I x PF x eta

NEMA vs IEC Frame Sizes

• NEMA (National Electrical Manufacturers Association) - Used in North America. Frame size indicates shaft height and mounting dimensions (e.g., 143T, 256T).
• IEC (International Electrotechnical Commission) - Used worldwide. Frame size is the shaft centerline height in mm (e.g., 80, 100, 132).

NEMA motors typically use imperial dimensions; IEC uses metric. Adapters are available for mounting interchangeability.

Starting Current Considerations

• DOL (Direct-On-Line): Starting current 6-8x FLA. Simple but high inrush.
• Star-Delta: Reduces starting current to ~33% of DOL but also reduces torque.
• Soft Starter: Gradually ramps voltage, typically 2-4x FLA starting current.
• VFD: Full torque at low current (1-1.5x FLA), best for frequent starts.