Understanding Torque Ratios in Three-Phase Induction Motors

This article study about various torque ratios of three phase induction motors. Because these torque ratios involved a critical role in operation. To understanding motor performance under various conditions such as startup, full load, and at maximum torque this study is more important. These torque ratios are used to compare the torque generated by the motor during different operating conditions. This comparison more useful to electrical engineers to analyze about efficiency, design suitability, starting and running characteristics of the motor.

In this article, most important torque ratios mentioned used in induction motors explained

1. Starting torque to maximum torque ratio
2. Full load torque to maximum torque ratio

Torque ratios represent the relationship between different torque values that a three-phase induction motor develops under varying load conditions

1. Starting Torque (T_st)– Starting torque develops when motor is being started
2. Maximum Torque (T_m) – Also known as breakdown torque, this is the highest torque a motor can be developed at maximum load condition.
3. Full Load Torque (T_FL) – Torque developed at rated or full-load operating condition.

By Detailed study about torque ratios , Electrical engineers can get following information about an induction motor

1. Starting capacity
2. Load handling ability
3. Overall performance

Before studying about various torque ratios in three phase induction motors, it is necessary to know about few fundamental terms as briefed follows,

The torque developed at the time of motor standstill is known as starting torque. In other word when rotor speed (N) = 0 and slip (s) =1, the torque developed in rotor is called as starting torque. This torque tends rotor to rotate from standstill condition

The general equation of starting torque is

\[T_{st} = \frac{kE_2 ^2 R_2}{R_2 ^2 + X_2 ^2}\]

Here,

E₂ = Rotor induced EMF in volts

R₂ = Rotor Resistance in Ohms

X₂ = Rotor Reactance in Ohms

k = proportionality constant varies with motor design conditions

Running torque is some times referred as general torque of motor. It is defined as torque generated during running condition of motor at any load conditions

Equation of running torque is expressed as

\[T_{r} = \frac{ksE_2 ^2 R_2}{R_2 ^2 + s^2 X_2 ^2}\]

The above equation shows that running torque of an induction motor depends upon its slip(s) value.

Maximum torque refers to the highest torque a motor can generate before stalling. It occurs at a particular slip value (sm), given by sm = R₂ / X₂. The slip generated at that load condition is called as maximum slip (s_m)

Maximum torque in an induction motor occurs at a specific value of slip, known as the slip for maximum torque (s_m), which is given by s_m = R₂ / X₂

\[Maximum Torque (T_m) = \frac{kE_2 ^2}{2X_2}\]

Now let us study about various torque ratios in details

This ratio comparison helps to understand how strong the motor is at startup compared to its maximum capability.

\[\frac{Starting Torque }{Maximum Torque} = \frac{T_{st} }{ T_m}\]

\[\frac{T_{st}}{ T_m} = \frac{ksE_2 ^2 R_2}{R_2 ^2 + s^2 X_2 ^2} . \frac{2X_2}{kE_2 ^2} \]

After simplifying above equation

\[\frac{R_2}{R_2 ^2 + s^2 X_2 ^2} . 2X_2 ^2\]

Further dividing both numerator and denominator by X₂²

\[\frac{\frac{2R_2}{X_2 ^2}}{(\frac{R_2 }{X_2})^2 +1}\]

As we know that maximum slip (s_m) = R₂/X₂

Hence Substituting S_m instead R₂/X₂

\[\frac{2s_m}{(s_m)^2 +1}\]

Further substitute ‘a’ where S_m

\[\frac{T_{st}}{ T_m} = \frac{2a}{(a)^2 +1} \]

This is the final expression for ratio of starting torque and maximum torque. This ratio is so helpful to select motor according to starting demands in various loads like pumps, conveyors, elevators, lift, compressors and hoists etc.

A high starting-to-maximum torque ratio indicates that the motor can deliver substantial torque at startup, making it suitable for heavy starting loads such as compressors, conveyors, or hoists. A low ratio suggests the motor may struggle under such conditions.

Starting torque (Tst) indicates how much torque the motor produces at slip = 1 (i.e., at standstill), while maximum torque (Tm) represents the highest torque the motor can produce during operation. Comparing these two values provides valuable insight into whether the motor can overcome the initial load inertia and how close the starting torque is to the motor’s peak capability.

This understanding helps prevent motor damage due to stalling and overloading during startup. If the starting torque is too low, the motor may be unable to start under load-connected conditions. As a result, high slip can occur, leading to overheating and potential damage to the stator and rotor windings.

Therefore, studying the T_st to T_m ratio is useful for improving the efficiency and reliability of the motor while maintaining sufficient starting capability

This ratio describe us how close the motor runs to its maximum capability under normal load.

\[\frac{Full load Torque}{Maxmum Torque} = \frac{T_{FL}}{T_m} \]

\[ \frac{ksE_2 ^2 R_2}{R_2 ^2 + s^2 X_2 ^2} .\frac{2X_2}{kE_2 ^2} \]

Simplifying above equation

\[\frac{2s R_2 X_2}{R_2 ^2 + s^2 X_2 ^2}\]

Further dividing both numerator and denominator by X₂²

\[\frac{2s \frac{R_2}{X_2}}{(\frac{R_2}{X_2})^2 .s^2}\]

As we know that maximum slip (s_m) = R₂/X₂

Hence substituting S_m instead R₂/X₂

\[\frac{2s_m s}{s_m ^2 + s^2}\]

Further substitute ‘a’ where S_m

\[ \frac{T_{FL}}{T_m} = \frac{2as}{a^2 + s^2}\]

This is the final expression for ratio of full load torque and maximum torque.

This ratio provides insight into the motor’s operating range and stability. A lower ratio (e.g., < 0.5) indicates that the motor operates well within its safe range, offering a wide margin before reaching the breakdown torque. On the other hand, a higher ratio (e.g., > 0.9) suggests the motor is operating close to its maximum torque limit. In such cases, any further increase in load may lead to stalling or cause the motor to enter the breakdown region.

Therefore, studying this ratio is essential to ensure that the motor is not run too close to its peak torque. This helps prevent potential damage, reduces the likelihood of high slip, and ultimately contributes to a longer motor lifespan

Motor manufacturers often use this analysis to design motors for various load conditions, such as steady and variable loads. By selecting the appropriate motor size based on the torque ratio study, they can ensure optimal performance for the intended application. This approach not only enhances reliability but also improves energy efficiency by preventing over-sizing or under-sizing of the motor.

Understanding and calculating torque ratios in three-phase induction motors is essential for both theoretical learning and practical motor selection. Whether you’re preparing for exams or engineering industrial drive systems, mastering these torque relationships ensures efficient and reliable motor performance.

By studying these torque ratios following information can be obtained

Ratio of starting torque to Maximum torque is useful for

• Selecting suitable size of motor for depending on load condition
• Ensuring motor is starting with proper starting torque without electrical stress.
• Optimizing motor design and application.

Ratio of full load torque to Maximum torque is useful for

• Helps to get information how close motor operates to its breakdown point.
• Guides in selecting motors for steady vs. fluctuating loads. Provide guides for proper size motor for static and fluctuating load conditions
• Prevents motor from over heating, stalling and increases lifespan
• To achieve efficient and safe motor operation.