6223 Torque Production

Torque is produced in the SRM by the tendency of the rotor to attain the minimum reluctance position when a stator phase is excited. The general expression for instantaneous torque for such a device that operates under the reluctance principle is as follows:

where W' is the co-energy defined as

Obviously, instantaneous torque is not constant. Total instantaneous torque of the machine is given by the sum of the individual phase torques:

SRM electromechanical properties are defined by the static T—i— characteristics of a phase, an example of which is shown in Figure 6.8. Average torque is a more important parameter from the user's perspective and can be derived mathematically by integrating Equation 6.20:

Average torque is also an important parameter during the design process.

When magnetic saturation can be neglected, instantaneous torque expression becomes:

FIGURE 6.8 Torque-angle-current characteristics of a four-phase SRM for four constant current levels. (From Husain, I., Switched reluctance machines, in The Power Electronics Handbook, Skvarenina, T.L., Ed., CRC Press, Boca Raton, FL, 2002.)

FIGURE 6.8 Torque-angle-current characteristics of a four-phase SRM for four constant current levels. (From Husain, I., Switched reluctance machines, in The Power Electronics Handbook, Skvarenina, T.L., Ed., CRC Press, Boca Raton, FL, 2002.)

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FIGURE 6.9 Phase currents for motoring and generating modes with respect to rotor position and idealized inductance profiles. (From Husain, I., Switched reluctance machines, in The Power Electronics Handbook, Skvarenina, T.L., Ed., CRC Press, Boca Raton, FL, 2002.)

The linear torque expression also follows from the energy conversion term (last term) in Equation 6.17. The phase current needs to be synchronized with the rotor position for effective torque production. For positive or motoring torque, the phase current i s switched so that the rotor i s moving from the unaligned position toward the aligned position. The linear SRM model is insightful in understanding these situations. Equation 6.22 clearly shows that for motoring torque, the phase current must coincide with the rising inductance region. On the other hand, the phase current must coincide with the decreasing inductance region for braking or generating torque. The phase currents for motoring and generating modes of operation are shown in Figure 6.9, with respect to the phase inductance profiles. Torque expression also shows that the direction of current is immaterial in torque production. The optimum performance of the drive system depends on the appropriate positioning of phase currents relative to the rotor angular position. Therefore, a rotor position transducer is essential to provide the position feedback signal to the controller.

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