Three phase motor formula

📘 Essential Induction Motor Formulas (Quick Reference for Electrical Engineers)

1. High Inertia Loads (Acceleration Time & Torque)

Acceleration Time (t):

$$t = \frac{WK^2 \times \text{rpm}}{308 \times T_{av}}$$

Required Torque (Tav):

$$T_{av} = \frac{WK^2 \times \text{rpm}}{308 \times t}$$

• $WK^2$ = Inertia in lb·ft²

• $t$ = Accelerating time in seconds

• $T_{av}$ = Average accelerating torque in lb·ft

👉 Usage:

• Use first formula if you know torque and want to find acceleration time.

• Use second formula if you know acceleration time and want required torque.

Inertia Reflected to Motor

$$J_{motor} = J_{load} \times \left(\frac{N_{load}}{N_{motor}}\right)^2$$

---

2. Synchronous Speed, Frequency, and Poles

Synchronous Speed:

$$n_s = \frac{120 \times f}{P}$$

Frequency:

$$f = \frac{P \times n_s}{120}$$

Number of Poles:

$$P = \frac{120 \times f}{n_s}$$

• $n_s$ = synchronous speed (RPM)

• $f$ = frequency (Hz or CPS)

• $P$ = number of poles

---

3. Horsepower, Torque, and Speed Relationship

Horsepower:

$$HP = \frac{T \times n}{5250}$$

Torque:

$$T = \frac{5250 \times HP}{n}$$

Speed:

$$n = \frac{5250 \times HP}{T}$$

• $T$ = torque (lb·ft)

• $n$ = speed (RPM)

---

4. Motor Slip

$$\% Slip = \frac{n_s - n}{n_s} \times 100$$

• $n_s$ = synchronous speed (RPM)

• $n$ = actual motor speed (RPM)

---

5. Symbols (Quick Legend)

• $I$ = Current (A)

• $HP$ = Output power (horsepower)

• $n$ = Motor speed (RPM)

• $n_s$ = Synchronous speed (RPM)

• $P$ = Number of poles

• $f$ = Frequency (Hz)

• $T$ = Torque (lb·ft)

• $EFF$ = Efficiency (decimal)

• $PF$ = Power factor (decimal)

---

⚡ These formulas are widely used in motor calculations, programming of VFDs, and soft starters for acceleration, torque matching, and performance analysis.

---