1. Classification of Electric Motors
| Main Category | Subcategory | Specific Type |
|---|---|---|
| AC Motors | Asynchronous Motors | – Squirrel-cage type
– Wound-rotor type |
| Synchronous Motors | —— | |
| DC Motors | —— | – Separately excited
– Shunt excited – Series excited – Compound excited |
Course Content Focus: Squirrel-Cage Asynchronous AC Motors
We will cover the following core topics:
- Basic structure
- Working principle
- Mechanical characteristics
- Control methods
2. Structure & Working Principle of Three-Phase Asynchronous Motors
Core Mechanism: From Magnetic Field to Rotation
-
Rotating Magnetic Field → Induced Electromotive Force (EMF)
When the magnetic pole rotates, the conductor cuts the magnetic field lines, generating an induced EMF:
- Right-Hand Rule: Used to determine the direction of (induced EMF).
-
- : Magnetic flux density
- : Length of the conductor
- : Speed of cutting magnetic field linesSymbols definition:
-
Closed Conductor → Induced Current
The induced EMF drives a current in the closed conductor loop.
-
Current-Carrying Conductor → Electromagnetic Force
A current-carrying conductor in a magnetic field experiences a force:
- Left-Hand Rule: Used to determine the direction of (electromagnetic force).
Key Conclusions
- The coil rotates in the same direction as the magnetic field.
- The coil rotates slower than the magnetic field () — this is the origin of the term “asynchronous.”
3. Structure of Three-Phase Asynchronous Motors
① Stator (Stationary Part)
- Three-Phase Stator Windings: The core component that generates the rotating magnetic field when energized.
② Rotor (Rotating Part)
- Function: Under the action of the rotating magnetic field, it generates induced EMF and current to drive rotation.
- Two main types:
- Wound-rotor type
- Squirrel-cage type (most widely used in industrial applications)
4. Generation of Rotating Magnetic Field
In asynchronous motors, the rotating magnetic field is created by three-phase alternating currents (instead of physical rotating magnets).
Three-Phase Current Equation
Magnetic Field Direction at Different Moments
- At : The resultant magnetic field points downward.
- As time elapses (), the magnetic field rotates continuously (one full rotation per electrical cycle).
5. Rotation Direction & Speed of Rotating Magnetic Field
① Rotation Direction
- Determined by the phase sequence of the three-phase current (e.g., A→B→C).
- To reverse the motor’s rotation: Swap any two of the three power supply lines.
② Rotation Speed (Synchronous Speed )
- Definition: The speed of the rotating magnetic field, measured in revolutions per minute (rpm).
- Formula:
- : Frequency of the power supply (Hz, typically 50 Hz in most regions).
- : Number of magnetic pole pairs of the motor.
Example: Synchronous Speed at 50 Hz
| Number of Pole Pairs () | Synchronous Speed (, rpm) |
|---|---|
| 1 | 3000 |
| 2 | 1500 |
| 3 | 1000 |
6. Concept of Pole Pairs ()
- : The winding configuration produces one pair of magnetic poles (N and S).
- : By splitting each phase winding into two segments and arranging them in stator slots, two pairs of magnetic poles are formed.
- Rule: As increases, the synchronous speed decreases (inverse proportionality).
7. Relationship Between Motor Speed () & Synchronous Speed ()
- The rotor rotates in the same direction as the magnetic field, but (a key feature of asynchronous motors).
- Critical reminder: If :
- No relative motion exists between the rotor and the magnetic field.
- No induced EMF/current in the rotor (conductors no longer cut magnetic field lines).
- No electromagnetic torque → The motor stops.
8. Slip (): The “Asynchronous” Factor
Definition
Slip is the relative difference between the synchronous speed and the actual rotor speed, expressed as a percentage:
Key Slip Values
- Startup (): (maximum slip).
- Near-synchronous speed (): (minimum slip).
- Normal operation: (varies by motor load).
Frequency of Rotor Induced Current ()
- : Frequency of the stator supply current (same as the power supply frequency).
9. Example Calculation: Slip & Rotor Current Frequency
Problem: A three-phase asynchronous motor has , , and rated speed . Calculate slip and rotor current frequency .
Solution:
- Calculate synchronous speed:
- Calculate slip:
- Calculate rotor current frequency:
10. Electromagnetic Torque of Three-Phase Asynchronous Motors
Definition
Electromagnetic torque () is the total torque generated by the electromagnetic force acting on current-carrying conductors in the rotor.
Core Formulas
-
Physical Expression (relates torque to magnetic flux and current):
- : Torque constant (depends on motor structure).
- : Magnetic flux per pole.
- : Rotor current.
- : Rotor power factor.
-
Parameter Expression (relates torque to supply and circuit parameters):
11. Key Torques in Motor Operation
① Rated Torque ()
- The torque output by the motor shaft when operating at rated voltage, rated speed (), and rated power ().
- Formula:
- : Rated power (Unit: kW).
- : Rated speed (Unit: rpm).
② Maximum Torque ()
- The maximum load torque the motor can drive. If the load torque , the motor stalls.
- Overload coefficient ():
- Typical value for three-phase asynchronous motors: .
③ Starting Torque ()
- The torque generated when the motor starts ().
- Significance: Determines the motor’s ability to start with a load. If , the motor cannot start.
12. Mechanical Characteristics of Three-Phase Asynchronous Motors
12. Mechanical Characteristics of Three-Phase Asynchronous MotorsDefinition
The relationship between rotor speed () and electromagnetic torque (), expressed as .
Key Features of the Characteristic Curve
- Startup phase: If , the motor starts; speed increases, and torque rises.
- Critical point (c): Torque reaches ; beyond this point, continues to increase while decreases along the curve.
- Stable operation (point b): , speed stabilizes (no further increase).
Adaptability to Load Changes
The motor’s electromagnetic torque automatically adjusts with changes in load — this is called the load self-adaptation capability.
13. Nameplate & Technical Parameters of Three-Phase Asynchronous Motors
Example: Nameplate Interpretation (Y132M-4)
| Parameter | Explanation |
|---|---|
| Model (Y132M-4) | – Y: Asynchronous motor
– 132: Shaft height (132 mm) – M: Medium frame – 4: Number of poles () |
| Rated speed () | Typically 1440 rpm (for , , ) |
| Connection method | Y/Δ (Star/Delta):
– Y-connection for 380 V line voltage – Δ-connection for 220 V line voltage |
| Rated voltage () | Line voltage for specified connection (e.g., 380/220 V). Allowable fluctuation: ±5%. |
| Rated current () | Line current for specified connection (e.g., 11.2 A for Δ-connection, 6.48 A for Y-connection). |
| Rated power () | Output power of the motor shaft (not the power absorbed from the grid). Efficiency (typical: 72% ~ 93% for squirrel-cage motors). |
| Power factor () | Typical value at rated load: 0.7 ~ 0.9 (low at no-load: 0.2 ~ 0.3). |
14. Speed Regulation Methods for Three-Phase Asynchronous Motors
| Regulation Method | Principle | Features |
|---|---|---|
| 1. Changing pole pairs () | Adjust by modifying the stator winding configuration. | Step speed regulation (discontinuous), simple structure. |
| 2. Changing slip () | Adjust by adding external resistance to the rotor (for wound-rotor motors). | Stepless regulation, low efficiency at high slip. |
| 3. Changing frequency () | Adjust via a variable-frequency power supply (rectifier + inverter). | Stepless regulation, high efficiency, excellent performance (most widely used in modern applications). |
15. Power Balance in Three-Phase Asynchronous Motors
Power Flow
Grid input power () → Stator copper loss () + Stator iron loss () → Electromagnetic power () → Rotor copper loss () → Mechanical power () → Output power ()
- : Mechanical loss (friction, windage).
- : Additional loss (due to harmonic fields, etc.).
16. Power Balance Relationship of Three-Phase Asynchronous Motors
Power Flow Breakdown
The power absorbed by the motor from the power grid () undergoes sequential conversion and loss before being output as mechanical power. The specific process is as follows:
| Power Component | Symbol | Definition & Calculation |
|---|---|---|
| Input Power (Grid) | Power drawn from the three-phase power supply, calculated as | |
| Stator Copper Loss | Power loss in stator windings due to resistance: | |
| Stator Iron Loss | Core loss from magnetic hysteresis and eddy currents (negligible at rated speed) | |
| Electromagnetic Power | Power transferred from stator to rotor via air-gap magnetic field: | |
| Rotor Copper Loss | Power loss in rotor windings: (proportional to slip ) | |
| Total Mechanical Power | Power converted to mechanical energy: | |
| Mechanical Loss | Loss from friction (bearings, brushes) and wind resistance | |
| Additional Loss | Extra loss from harmonic magnetic fields and irregular current distribution | |
| Rated Output Power | Useful mechanical power output by the motor shaft: |
Two Key Relationships
-
Mechanical Power vs. Electromagnetic Power
This shows that most electromagnetic power is converted to mechanical power; only a small portion (proportional to slip ) is lost as rotor copper loss.
-
Rotor Copper Loss vs. Electromagnetic Power
Implication: Higher slip () leads to greater rotor copper loss and lower motor efficiency. Thus, asynchronous motors operate with very small slip () under normal conditions.
17. Torque Balance Relationship
Dividing both sides of the power balance equation by the mechanical angular velocity () converts power balance to torque balance:
- : Electromagnetic torque (driving torque generated by the motor).
- : Load torque (torque required to drive the external mechanical load).
- : No-load torque (torque to overcome mechanical loss and additional loss, ).
18. Three Expressions of Electromagnetic Torque
① Physical Expression
Reflects the physical mechanism of torque generation (interaction between magnetic flux and current):
- : Torque coefficient (depends on motor structure and pole pairs ).
- : Main magnetic flux per pole.
- : Rotor current.
- : Rotor power factor (indicates the effective component of rotor current for torque generation).
Key Insight: Torque is determined by the product of the main magnetic flux and the active component of the rotor current.
② Parameter Expression
Relates torque to power supply parameters, motor structure parameters, and operating parameters:
- : Number of stator phases (usually 3).
- : Number of pole pairs.
- : Stator line voltage.
- : Stator and rotor winding resistances (per phase).
- : Stator and rotor leakage reactances (per phase).
- : Stator power supply frequency.
- : Slip.
Key Variables:
- : Torque is proportional to the square of the stator voltage (very sensitive to voltage fluctuations).
- is related to slip : Torque first increases and then decreases as changes, forming the “mechanical characteristic curve”.
③ Critical Slip and Maximum Torque
By taking the derivative of the parameter expression with respect to and setting it to zero, we obtain:
-
Critical Slip (): Slip corresponding to maximum torque ():
- is proportional to rotor resistance ; increasing shifts to higher values.
-
Maximum Torque ():
- : Maximum torque depends on voltage but is independent of rotor resistance .
19. Key Rules for Torque Variation
When other parameters (frequency, motor structure) are fixed:
- Voltage (): Maximum torque () is proportional to the square of ; critical slip () is unaffected by . A 10% voltage drop can reduce by ~19%.
- Rotor Resistance (): Increasing increases but does not change . This is the principle behind “rotor series resistance starting” for wound-rotor motors.
- Frequency (): Higher reduces both and ; higher leakage reactance () also lowers and .
20. Overload Capacity and Starting Torque
① Overload Capacity ()
Defined as the ratio of maximum torque to rated torque:
- Typical value for three-phase asynchronous motors: .
- Function: Ensures the motor can withstand short-term load surges (e.g., sudden increases in mechanical load) without stalling.
② Starting Torque () and Starting Torque Multiple ()
- Starting Torque (): Torque when the motor starts (), calculated by substituting into the parameter expression.
- Starting Torque Multiple ():
- Typical value: (varies by motor type).
- Significance: Determines the motor’s ability to start with a load. If , the motor cannot start.
21. Mechanical Characteristics with Rotor Series Resistance
21. Mechanical Characteristics with Rotor Series ResistanceFor wound-rotor asynchronous motors, adding external resistance () to the rotor circuit modifies the mechanical characteristics:
| Rotor Resistance | Critical Slip () | Maximum Torque () | Starting Torque () |
|---|---|---|---|
| (original) | Smaller | Unchanged | Smaller |
| Larger | Unchanged | Larger (if ) | |
| () | Larger still | Unchanged | Peaks when , then decreases |
Application: Used for high-torque starting (e.g., cranes, conveyors) and stepless speed regulation at low speeds.
22. Mechanical Characteristics with Stator Series Reactor
22. Mechanical Characteristics with Stator Series ReactorAdding a reactor () to the stator circuit reduces the effective voltage across the stator windings, leading to:
- Affected Parameters: Reduced and ; increased .
- Unaffected Parameter: Synchronous speed () (still determined by and ).
- Advantage: No additional active power loss (unlike stator series resistance).
- Disadvantage: High reactor cost; mainly used in low-power motors requiring soft starting.