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You already know that an induction motor runs at a speed slightly less than synchronous speed — this difference is the slip. But how does the motor's torque change as slip varies from 0 to 1? That relationship — the torque-slip characteristic — tells you everything about the motor's behaviour from no-load to standstill.
This curve determines whether the motor can start a heavy load, how it responds to sudden load changes, and why it stalls if overloaded. It's one of the most important performance curves in electrical machines.
What is the Torque-Slip Characteristic?
The torque-slip characteristic is a graph showing how the electromagnetic torque developed by an three-phase induction motor varies with slip (or equivalently, with rotor speed).
- X-axis: Slip (s) — from 0 (synchronous speed) to 1 (standstill)
- Y-axis: Torque (T) — electromagnetic torque developed
At s = 0, the rotor runs at synchronous speed (no relative motion, no torque). At s = 1, the rotor is stationary (starting condition). The curve between these extremes reveals the motor's complete operating behaviour.
Torque Equation of Induction Motor
The torque developed by an induction motor is given by:
Where:
- V₁ = Supply voltage per phase
- R₁ = Stator resistance
- R₂ = Rotor resistance (referred to stator)
- X₁ = Stator leakage reactance
- X₂ = Rotor leakage reactance (referred to stator)
- s = Slip
- ωₛ = Synchronous angular speed (2πNₛ/60)
This equation shows that torque depends on slip in a complex, non-linear way — which is why the torque-slip curve has its distinctive shape.
Torque-Slip Curve — Shape & Regions
The curve has three distinct regions:
Region 1: Low Slip (s ≈ 0 to s_max) — Stable Operating Region
At low slip, R₂/s >> (X₁ + X₂), so the reactance terms are negligible. The torque equation simplifies to:
Torque increases nearly linearly with slip. This is where the motor normally operates — between no-load and full-load.
Region 2: Maximum Torque Point (s = s_max)
At a specific slip called s_max (or s_m), the torque reaches its maximum value — called breakdown torque or pull-out torque. Beyond this point, increasing slip actually decreases torque.
If R₁ is neglected: s_max ≈ R₂ / (X₁ + X₂)
Region 3: High Slip (s_max to s = 1) — Unstable Region
At high slip, the rotor frequency is high, making rotor reactance (sX₂) dominant. The torque equation approximates to:
Torque decreases as slip increases. This region is unstable — if the motor enters this zone, it will stall.
Key Points on the Curve
Maximum (Breakdown) Torque
Critical observation: Maximum torque is independent of rotor resistance R₂. Changing R₂ changes where the maximum occurs (s_max) but not how much torque is available.
Effect of Rotor Resistance on Torque-Slip
This is one of the most important concepts for understanding motor starting and the double cage induction motor.
Increasing rotor resistance R₂:
- Shifts s_max to the right (maximum torque occurs at higher slip / lower speed)
- Does NOT change T_max (maximum torque value remains the same)
- Increases starting torque (at s = 1, higher R₂ means more torque)
- Reduces efficiency at rated load (more I²R losses in rotor)
When R₂ is increased such that s_max = 1, the starting torque equals the maximum torque — this is the ideal starting condition.
Stable vs Unstable Operating Region
The torque-slip curve divides into two operating regions separated by the breakdown point:
Stable Region (0 < s < s_max)
If load increases → slip increases → torque increases → motor meets the new load. The motor self-corrects. This is where normal operation occurs.
Unstable Region (s_max < s < 1)
If load increases → slip increases → torque decreases → motor cannot meet load → slip increases further → motor stalls. There is no self-correction — the motor collapses to standstill.
Practical rule: A motor must never be loaded beyond its breakdown torque. The safety margin between rated torque and breakdown torque (typically 2-3×) is the motor's overload capacity.
Connection to Double Cage Induction Motor
The double cage induction motor exploits the rotor resistance effect to get the best of both worlds:
- Outer cage: High resistance, low reactance → dominates at starting (s = 1) → provides high starting torque
- Inner cage: Low resistance, high reactance → dominates at running (low s) → provides high efficiency
At standstill (s = 1), rotor frequency is high (= supply frequency), so current flows mainly in the outer cage (low reactance path). As the motor accelerates and slip decreases, rotor frequency drops, reactance becomes negligible, and current shifts to the inner cage (low resistance path).
The result: a combined torque-slip curve that has high starting torque AND high running efficiency — without external resistance or slip rings.
Practical Significance
- Motor selection: The torque-slip curve determines if a motor can start a given load (T_start > T_load at standstill)
- Overload protection: Breakdown torque sets the absolute maximum load — exceeding it causes stalling
- Starting method selection: If starting torque is insufficient, use star-delta starter, autotransformer, or soft starter
- Speed control: Variable frequency drives (VFDs) shift the entire curve by changing supply frequency
- Motor design: Rotor bar shape (deep bar, double cage) is designed to optimize the torque-slip shape
Frequently Asked Questions
Why does torque decrease after the breakdown point?
At high slip, rotor frequency is high, making rotor reactance (sX₂) much larger than rotor resistance. The large reactance limits current flow and shifts the current phase angle, reducing the torque-producing component. The motor effectively becomes reactance-limited rather than resistance-limited.
Does maximum torque depend on supply voltage?
Yes. T_max is proportional to V₁². If supply voltage drops by 10%, maximum torque drops by approximately 19%. This is why motors may stall during voltage dips — the breakdown torque reduces below the load torque.
What is the typical ratio of breakdown torque to rated torque?
For standard squirrel cage motors, T_max/T_rated is typically 2 to 3. NEMA Design B motors have a minimum of 2.0. This ratio is the motor's overload margin — higher is better for applications with sudden load spikes.
Can we increase starting torque without reducing efficiency?
Yes — using a double cage or deep bar rotor. These designs provide high effective resistance at starting (high slip) and low resistance at running (low slip), giving both high starting torque and high running efficiency. External rotor resistance (wound rotor motors) achieves the same effect but with slip ring maintenance.
How does a VFD change the torque-slip curve?
A VFD changes the supply frequency, which shifts the synchronous speed. By maintaining constant V/f ratio, the entire torque-slip curve shifts along the speed axis without changing its shape. This allows full torque at any speed — unlike DOL starting where torque depends on the fixed curve.
Conclusion
The torque-slip characteristic is the complete performance map of an induction motor. It tells you the starting torque, the breakdown limit, the stable operating region, and how the motor responds to load changes. Understanding this curve is essential for motor selection, protection, and control.
The key insight: rotor resistance controls where maximum torque occurs on the slip axis, but not how much maximum torque is available. This principle drives the design of double cage rotors and the use of external resistance for wound rotor starting.
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