Understanding the Calculation of Motor Starting Torque

Motor starting torque is the initial torque a motor generates to overcome inertia. Calculating it ensures proper motor selection and system reliability.

This article covers detailed formulas, variable explanations, common values, and real-world examples for precise motor starting torque calculation.

• Calculate starting torque for a 5 HP induction motor with 460 V supply.
• Determine starting torque for a 3-phase squirrel cage motor with locked rotor current of 30 A.
• Find starting torque for a motor driving a conveyor belt requiring 50 Nm torque at startup.
• Compute starting torque for a 10 kW motor with a starting current of 80 A and rated torque of 60 Nm.

Comprehensive Tables of Common Motor Starting Torque Values

Fundamental Formulas for Calculating Motor Starting Torque

Calculating motor starting torque involves understanding the relationship between torque, power, speed, and current. The primary formula to calculate torque (T) in Newton-meters (Nm) from power (P) in watts and angular velocity (ω) in radians per second is:

Where angular velocity ω is related to rotational speed (N) in revolutions per minute (rpm) by:

Combining both, torque can be expressed as:

Where:

• T = Torque (Nm)
• P = Power (W)
• N = Speed (rpm)
• π = Pi, approximately 3.1416

For starting torque, the speed N is zero at the instant of start, so direct calculation from power and speed is not possible. Instead, starting torque is often calculated from motor current and torque constants or from locked rotor torque data.

Starting Torque from Locked Rotor Torque

Locked rotor torque (LRT) is the torque the motor produces at zero speed when the rotor is locked. It is often expressed as a percentage of rated torque:

Rated torque can be calculated from rated power and rated speed:

Where:

• T_start = Starting torque (Nm)
• LRT% = Locked rotor torque percentage (%)
• T_rated = Rated torque (Nm)
• P_rated = Rated power (W)
• N_rated = Rated speed (rpm)

Starting Torque from Starting Current and Torque Constant

Another approach uses the motor torque constant (K_t) and starting current (I_start):

The torque constant K_t relates current to torque and depends on motor design. For DC motors, it is often given in Nm/A. For AC induction motors, it is derived from rated torque and rated current:

Where:

• I_start = Starting current (A)
• I_rated = Rated current (A)

Torque-Speed Characteristic Equation for Induction Motors

The torque-speed characteristic of an induction motor is given by:

Where:

• T = Torque (Nm)
• s = Slip (unitless, 0 to 1)
• E₂ = Rotor induced emf (V)
• R₂ = Rotor resistance (Ω)
• X₂ = Rotor reactance (Ω)
• ω_s = Synchronous angular velocity (rad/s)

At starting, slip s = 1, so starting torque simplifies to:

This formula is essential for motor designers and engineers analyzing starting performance.

Detailed Explanation of Variables and Typical Values

• Power (P): Usually given in kilowatts (kW) or horsepower (HP). 1 HP = 746 W. Typical motor powers range from fractional kW to several MW.
• Speed (N): Rated speed in rpm, commonly 1500 or 1800 rpm for 4-pole or 6-pole motors at 50 Hz.
• Torque (T): Measured in Newton-meters (Nm). Rated torque is the torque at rated power and speed.
• Slip (s): Difference between synchronous speed and rotor speed, expressed as a fraction. At start, s=1.
• Rotor Resistance (R₂): Resistance of rotor winding, typically in milliohms to ohms.
• Rotor Reactance (X₂): Reactance of rotor winding, depends on frequency and inductance.
• Starting Current (I_start): Current drawn at start, often 5-7 times rated current for squirrel cage motors.
• Locked Rotor Torque (LRT): Torque at zero speed, usually 100-250% of rated torque depending on motor design.
• Torque Constant (K_t): Ratio of torque to current, varies by motor type.

Real-World Application Examples of Motor Starting Torque Calculation

Example 1: Starting Torque Calculation for a 5 HP Induction Motor

A 5 HP (3.73 kW) 3-phase squirrel cage induction motor operates at 1750 rpm with a rated current of 12 A and locked rotor torque of 180% of rated torque. Calculate the starting torque.

Step 1: Calculate rated torque:

Step 2: Calculate starting torque using locked rotor torque percentage:

Step 3: Verify starting current (given as 12 A) and compare with rated current (assumed 12 A). Starting current is typically higher; if actual starting current is 60 A (5× rated), then torque constant can be estimated:

Starting torque from current:

This indicates the motor can produce a starting torque significantly higher than locked rotor torque, confirming the motor’s capability to start under load.

Example 2: Motor Starting Torque for a Conveyor Belt Application

A conveyor belt requires a starting torque of 50 Nm to overcome static friction and load inertia. The motor selected is a 3 kW, 4-pole, 400 V induction motor running at 1500 rpm. Determine if the motor’s starting torque is sufficient.

Step 1: Calculate rated torque:

Step 2: Assume locked rotor torque is 170% of rated torque:

The starting torque of 32.5 Nm is less than the required 50 Nm, indicating the motor is undersized for this application.

Step 3: Select a motor with higher power or use a motor with higher locked rotor torque. For example, a 5.5 kW motor:

Starting torque:

This motor provides sufficient starting torque to meet the conveyor belt requirements.

Additional Considerations in Motor Starting Torque Calculations

• Load Characteristics: The nature of the load (constant torque, variable torque, or constant power) affects starting torque requirements.
• Starting Methods: Direct-on-line (DOL), star-delta, soft starters, and variable frequency drives influence starting torque and current.
• Temperature Effects: Motor resistance changes with temperature, affecting starting torque.
• Supply Voltage Variations: Voltage dips reduce starting torque proportionally to the square of voltage.
• Standards and Norms: IEC 60034 and NEMA MG1 provide guidelines on motor starting torque and performance.

References and Further Reading

• NEMA – National Electrical Manufacturers Association
• IEC 60034 – Rotating Electrical Machines
• Electrical4U – Starting Torque of Induction Motor
• Engineering Toolbox – Torque and Power Calculations