Motor Starting Torque Calculator – IEEE, IEC

Accurate motor starting torque calculation is critical for ensuring reliable motor performance and system protection. Understanding IEEE and IEC standards helps engineers design efficient motor control systems.

This article explores motor starting torque calculators based on IEEE and IEC guidelines, including formulas, tables, and real-world examples. It provides a comprehensive technical resource for electrical engineers and professionals.

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• Calculate starting torque for a 5 HP, 415 V, 3-phase induction motor.
• Determine starting torque using IEC standard for a 10 kW motor with 400 V supply.
• Find starting torque for a 7.5 HP motor with locked rotor current of 30 A.
• Compute starting torque for a 15 kW motor with slip of 0.05 and rated torque of 50 Nm.

Common Values for Motor Starting Torque – IEEE and IEC Standards

Fundamental Formulas for Motor Starting Torque Calculation (IEEE & IEC)

Motor starting torque is a key parameter that defines the torque produced by a motor at the instant of startup. It is essential for overcoming the initial inertia and load torque.

• Starting Torque (T_start): The torque generated by the motor at zero speed (starting condition).
• Rated Torque (T_rated): The torque at rated load and speed.
• Slip (s): The difference between synchronous speed and rotor speed, expressed as a fraction.

1. Starting Torque Calculation

The starting torque can be calculated using the following formula derived from the motor equivalent circuit:

• V: Phase voltage (Volts)
• R₁: Stator resistance (Ohms)
• R₂: Rotor resistance referred to stator (Ohms)
• X₁: Stator reactance (Ohms)
• X₂: Rotor reactance referred to stator (Ohms)
• s: Slip at starting (usually s = 1)
• ω_s: Synchronous angular velocity (rad/s), ω_s = 2π × f / p
• f: Supply frequency (Hz)
• p: Number of pole pairs

2. Synchronous Speed (N_s)

The synchronous speed is the speed of the rotating magnetic field in the stator and is given by:

• N_s: Synchronous speed (rpm)
• f: Supply frequency (Hz)
• P: Number of poles

3. Rated Torque (T_rated)

Rated torque is calculated from the rated power and synchronous speed:

• T_rated: Rated torque (Nm)
• P_rated: Rated power (kW)
• N_rated: Rated speed (rpm)

4. Starting Torque as Percentage of Rated Torque

Starting torque is often expressed as a percentage of rated torque:

5. Locked Rotor Current (I_locked)

Locked rotor current is the current drawn by the motor at starting (slip s = 1):

• Z_start: Starting impedance of the motor

Detailed Real-World Examples of Motor Starting Torque Calculation

Example 1: Calculating Starting Torque for a 5 HP Induction Motor (IEEE Standard)

A 5 HP (3.73 kW), 415 V, 50 Hz, 4-pole, three-phase squirrel cage induction motor has the following parameters:

• Stator resistance, R₁ = 0.5 Ω
• Rotor resistance referred to stator, R₂ = 0.4 Ω
• Stator reactance, X₁ = 1.2 Ω
• Rotor reactance referred to stator, X₂ = 1.0 Ω
• Slip at starting, s = 1

Calculate the starting torque and express it as a percentage of rated torque.

Step 1: Calculate synchronous speed (N_s)

Using the formula:

Step 2: Calculate synchronous angular velocity (ω_s)

Note: Number of pole pairs p = P/2 = 4/2 = 2

Step 3: Calculate starting torque (T_start)

Calculate denominator first:

Calculate numerator:

Note: Phase voltage V = Line voltage / √3 = 415 / 1.732 = 240 V

Finally, calculate starting torque:

Step 4: Calculate rated torque (T_rated)

Note: Rated speed assumed 1450 rpm (typical slip 0.033)

Step 5: Calculate starting torque as percentage of rated torque

This motor produces a starting torque approximately 3.16 times its rated torque, suitable for heavy starting loads.

Example 2: IEC Standard Starting Torque Calculation for a 10 kW Motor

A 10 kW, 400 V, 50 Hz, 6-pole three-phase induction motor has the following parameters:

• Locked rotor current, I_locked = 120 A
• Rated current, I_rated = 18 A
• Rated speed, N_rated = 980 rpm
• Slip at starting, s = 1
• Rated torque, T_rated = (9.55 × 10) / 980 = 97.45 Nm

Calculate the starting torque using the IEC method, assuming starting torque is proportional to the square of the starting current ratio.

Step 1: Calculate starting current ratio

Step 2: Calculate starting torque

IEC standard approximates starting torque as:

Where k is a constant typically between 0.1 and 0.3 depending on motor design. Assume k = 0.2 for this motor.

Step 3: Calculate starting torque as percentage of rated torque

This high starting torque indicates the motor is capable of handling heavy starting loads, consistent with IEC guidelines.

Additional Technical Insights and Considerations

• Impact of Rotor Resistance: Increasing rotor resistance improves starting torque but reduces efficiency at rated speed.
• Slip at Starting: Typically s = 1 at start; slip decreases as motor accelerates.
• Starting Methods: Direct-on-line (DOL), star-delta, autotransformer starting affect starting torque and current.
• Standards Compliance: IEEE Std 112 and IEC 60034 provide detailed test methods and definitions for starting torque.
• Thermal Considerations: High starting torque often correlates with high starting current, impacting thermal stress.
• Application Matching: Correct starting torque ensures motor can overcome load inertia and friction without stalling.

References and Further Reading

• IEEE Std 112-2017 – Test Procedure for Polyphase Induction Motors and Generators
• IEC 60034 – Rotating Electrical Machines
• Electrical4U: Starting Torque of Induction Motor
• Engineering Toolbox: Induction Motors