Torque Characteristics of Permanent Magnet Motors

Permanent Magnet Synchronous Motors (PMSMs) are known for their high efficiency and robust performance. A key aspect of their operation is the generation of torque, which can be categorized into two main components: magnet torque and reluctance torque.

The total torque T produced by a PMSM can be expressed as the sum of magnet torque (Tm) and reluctance torque (Tr):

T = Tm+Tr

• Magnet Torque (Tm): This component arises from the interaction between the magnetic field of the permanent magnets and the stator's magnetic field.
• Reluctance Torque (Tr): This component is generated due to the differences in magnetic reluctance in the magnetic circuit, which can occur when the rotor aligns with the stator field in certain positions.

Magnet torque is proportional to the number of pole pairs, the magnetic flux generated by the rotor magnets, and the current flowing through the stator windings.

Tm = 3/2?P?Φm?I

Where:

P = Number of pole pairs

Φm = Magnetic flux (Wb) linked with the rotor

I = Current in the stator windings (A)

Magnet torque is maximized when Iq is high (i.e. when the current is aligned with the q-axis).

Conversely, in synchronous reluctance machines (SynRMs), since there are no permanent magnets, Φm is zero, resulting in no magnet torque:

Reluctance torque occurs due to the variation in inductance between the d-axis and q-axis of the motor. The greater the difference between these two inductances, the more significant the reluctance torque.

Tr = 3/2?P?(Ld?Lq)?Id?Iq

d-axis Inductance (Ld): Inductance aligned with the rotor’s magnetic field.

q-axis Inductance (Lq): Inductance orthogonal to the d-axis.

A larger difference between d-axis and q-axis inductance results in a higher reluctance torque.

The d-q axis transformation is fundamental in analyzing AC machines like PMSMs. The motor's torque is strongly affected by the d-axis and q-axis currents:

• Magnet Torque: Strongly influenced by the q-axis current, which is responsible for torque production.
• Reluctance Torque: Determined by the difference between the inductances in the d-axis and q-axis, where higher saliency leads to increased reluctance torque.

For Surface-Mounted Magnets:

Surface-mounted magnets have higher torque density due to their direct interaction with the stator field. This configuration maximizes magnet torque since the magnets are close to the stator's magnetic field.

For Interior Magnets:

Embedded magnets improve thermal stability and protect against demagnetization but may slightly reduce the effective magnetic flux. In interior magnet designs, the reluctance torque tends to increase due to enhanced saliency, while the magnet torque may be slightly lower compared to surface-mounted configurations.

Synchronous electric motors can be seen as existing on a continuum based on their torque production methods. On one end, the surface permanent-magnet motor generates torque solely through the interaction between permanent magnets in the rotor and electromagnets in the stator. On the opposite end, the synchronous reluctance motor produces torque using magnetic reluctance, which is the opposition of a material to magnetic flux. Most motor designs aim to maximize torque by combining these two mechanisms.

To summarize, understanding torque components in Permanent Magnet Synchronous Motors is crucial for designing efficient electric motor systems. The placement of magnets—whether surface-mounted or embedded—significantly influences the torque characteristics. The distinct contributions of magnet torque and reluctance torque underscore the importance of d-q axis currents in achieving optimal motor performance.

Sumeet Singh, PhD - Product Manager for eMotor Electromagnetic Simulation at EMWorks Inc., Montreal