**1. Introduction**

The topology of FRPMM is depicted in **Figure 1**. As can be seen, it has a slotted rotor without any windings or PMs, and a stator with armature windings and PMs mounted on each stator teeth. First of all, the structural characteristics of FRPMMs and the corresponding performance advantages need to be explained:


**Figure 1.** *Cross section of a FRPMM.*

3.The stator windings of FRPMMs are mostly concentrated windings, which are easy to manufacture. Moreover, the electromagnetic isolation of the concentrated windings is better than regular distributed windings, which means that if one winding has faults, the fault is not likely to spread to other windings, and thus the fault tolerance is good [7, 8]. In addition, the concentrated winding has a smaller winding factor, inductance, and a shorter electrical time constant than the distributed windings [9], and thus the dynamic response of concentrated winding is faster.

In most existing literatures, the design of FRPMMs is mainly based on the classical design method [25] with low accuracy or time-consuming finite element algorithm (FEA) [26]. Therefore, in this chapter, the specialized sizing equations for FRPMMs will be deduced and the analytical design method will be introduced, which can be directly employed in the initial design of FRPMMs and allows for fast

**Advantages**

1 Use rare-earth PMs 1. No excitation loss, high motor efficiency;

density

response

1. Easy to install

*Structural characteristics and corresponding advantages of FRPMM.*

temperature conditions;

2. Rare-earth with high-magnetic energy product increases torque

1. Simple rotor structure, suitable for high-speed operation and high

2. Avoids mechanical friction and electric sparks caused by commutators and brushes, thus improving the reliability; 3. Small rotational inertia, thus fast acceleration and deceleration

2. No reduction in the slot area or increase in the motor volume

1. Good fault tolerance and high reliability; 2. Easy processing and manufacturing; 3. Small inductance and electrical time constant

This chapter is organized as follows. First, the structure and operation principles are introduced in Section 2. Then in Section 3, the magnetic circuit model is built and the sizing equations are analytically derived. After that, in Section 4, the influences of several key parameters (slot-pole combination, airgap radius, electric loading, and equivalent magnetic loading) in the sizing equation on the torque density are analyzed. Also, the effects of the airgap structural parameters on the pulsating torque, power factor, and PM demagnetization performances are investigated. Moreover, in Section 5, the geometric design of stator and rotor are introduced. And in Section 6, the design procedure is illustrated. Besides, to make the analytical design method more readable, a case study is presented and a FRPMM

To clearly exhibit the operating principle, a three-phase FRPMM with two pole windings, six stator slots, and eight rotor teeth is cited as an example. The flux distributions at different rotor positions are illustrated in **Figure 2**. The magnetic flux field is excited only by the PMs, and the difference of each rotor movement is 11.25 mech. degrees (i.e., 1/4 rotor slot pitch). Taking flux linkage of phase A winding as an example, when the rotor position is 0 degree, the flux linkage is 0; when the rotor position is 11.25 mech. degree (90 elec. degree), the flux linkage reaches the positive maximum value; when the rotor position is 22.5 mech. degree (180 elec. degree), the flux linkage is 0; when the rotor position is 33.75 mech. degree (270 elec. degree), the flux linkage reaches the negative maximum value. Therefore, in the duration of one rotor slot pitch (360 elec. degrees), the winding flux linkage reverses the polarity, thus it is called "flux reversal machine." Then,

prototype is tested. Finally, conclusions are drawn in Section 7.

calculations of machine dimensions.

**No. Structural characteristic**

*Flux Reversal Machine Design*

*DOI: http://dx.doi.org/10.5772/intechopen.92428*

2 No windings or PMs in the rotor

3 Often use concentrated windings

4 PMs attached to the stator teeth surface

**Table 1.**

**69**

**2. Operation principle of FRPMM**

4.Compared to other stator-PM machines, that is, flux switching PM machines and doubly salient PM machines, FRPMMs have a simpler structure. The PMs of the flux switching PM machines and doubly salient PM machines are inserted into the stator core, which is not convenient for installation. In the flux switching PM machine, putting permanent magnets in the middle of the teeth will reduce the slot area and affect the output torque. In the doubly salient PM machine, placing PMs in the yoke will increase the volume of the motor and reduce the torque density. In the FRPMMs, the PMs are pasted on the inner surface of the stator teeth, thus eliminating the above problems [10].

Finally, the structural characteristics and performance advantages of the fluxreverse motor can be summarized in **Table 1**.

It can be seen that the FRPMMs have many performance advantages, and these advantages can be utilized in different applications. First of all, the high efficiency, the large torque density, the rapid acceleration, and deceleration response make FRPMMs suitable for various high-speed rotation areas, such as electric vehicles [11–13], electric spindle [14], fans [15, 16], etc. Secondly, the number of rotor pole pairs is usually high, which is also suitable for low-speed areas, meanwhile its torque density is high at the low speeds, making FRPMMs suitable for various lowspeed direct-drive occasions [17], for example wind power [18–20], direct drive servo system [21], wave power generation [22], etc. In addition, linear FRPMM has no PMs and copper windings in the secondary, which saves cost and is also very suitable for long rail transit linear motion applications [23, 24].

#### *Flux Reversal Machine Design DOI: http://dx.doi.org/10.5772/intechopen.92428*


#### **Table 1.**

3.The stator windings of FRPMMs are mostly concentrated windings, which are

concentrated winding has a smaller winding factor, inductance, and a shorter electrical time constant than the distributed windings [9], and thus the

4.Compared to other stator-PM machines, that is, flux switching PM machines and doubly salient PM machines, FRPMMs have a simpler structure. The PMs of the flux switching PM machines and doubly salient PM machines are inserted into the stator core, which is not convenient for installation. In the flux switching PM machine, putting permanent magnets in the middle of the teeth will reduce the slot area and affect the output torque. In the doubly salient PM machine, placing PMs in the yoke will increase the volume of the motor and reduce the torque density. In the FRPMMs, the PMs are pasted on the inner surface of the stator teeth, thus eliminating the above problems [10].

Finally, the structural characteristics and performance advantages of the flux-

It can be seen that the FRPMMs have many performance advantages, and these advantages can be utilized in different applications. First of all, the high efficiency, the large torque density, the rapid acceleration, and deceleration response make FRPMMs suitable for various high-speed rotation areas, such as electric vehicles [11–13], electric spindle [14], fans [15, 16], etc. Secondly, the number of rotor pole pairs is usually high, which is also suitable for low-speed areas, meanwhile its torque density is high at the low speeds, making FRPMMs suitable for various lowspeed direct-drive occasions [17], for example wind power [18–20], direct drive servo system [21], wave power generation [22], etc. In addition, linear FRPMM has no PMs and copper windings in the secondary, which saves cost and is also very

easy to manufacture. Moreover, the electromagnetic isolation of the concentrated windings is better than regular distributed windings, which means that if one winding has faults, the fault is not likely to spread to other

windings, and thus the fault tolerance is good [7, 8]. In addition, the

dynamic response of concentrated winding is faster.

suitable for long rail transit linear motion applications [23, 24].

reverse motor can be summarized in **Table 1**.

**Figure 1.**

**68**

*Cross section of a FRPMM.*

*Direct Torque Control Strategies of Electrical Machines*

*Structural characteristics and corresponding advantages of FRPMM.*

In most existing literatures, the design of FRPMMs is mainly based on the classical design method [25] with low accuracy or time-consuming finite element algorithm (FEA) [26]. Therefore, in this chapter, the specialized sizing equations for FRPMMs will be deduced and the analytical design method will be introduced, which can be directly employed in the initial design of FRPMMs and allows for fast calculations of machine dimensions.

This chapter is organized as follows. First, the structure and operation principles are introduced in Section 2. Then in Section 3, the magnetic circuit model is built and the sizing equations are analytically derived. After that, in Section 4, the influences of several key parameters (slot-pole combination, airgap radius, electric loading, and equivalent magnetic loading) in the sizing equation on the torque density are analyzed. Also, the effects of the airgap structural parameters on the pulsating torque, power factor, and PM demagnetization performances are investigated. Moreover, in Section 5, the geometric design of stator and rotor are introduced. And in Section 6, the design procedure is illustrated. Besides, to make the analytical design method more readable, a case study is presented and a FRPMM prototype is tested. Finally, conclusions are drawn in Section 7.
