Analysis of Electromagnetic and Vibration Characteristics of a Spoke Type PMBLDC Motor

Abstract

This paper investigates the electromagnetic and structural characteristics of a spoke type BLDC motor and provides a comparative study with respect to Interior Permanent Magnet motor (IPM).The electromagnetic analysis aims to determine the average torque and cogging torque of spoke type BLDC motor. The natural and induced vibration characteristics of the motor are evaluated by performing structural finite element analysis. The electromagnetic and vibration characteristics are assessed for different slot/pole combination to provide an insight on their influence on the performance of the motor. In addition, thermal analysis is performed to predict the temperature distribution and a comprehensive analysis of spoke type BLDC motor is presented.

Appendices

Appendix 1

See Table

Table 8 Specifications

8.

Appendix 2

In Spoke type BLDC motor the flux is confined to a single closed loop as shown in Fig. 

Fig. 19

Flux path per pole in spoke type BLDC

19 and the corresponding magnetic equivalent circuit is shown in Fig. 

Fig. 20

Magnetic equivalent circuit

20. Based on Norton equivalent circuit, the permanent magnet is theoretically represented by a flux source in parallel with an internal permeance [24].

The remanance flux from Permanent magnet is

$$\phi_{r} = B_{r} h_{m} L_{u}$$

Magnetic reluctance of Permanent magnet,

$$R_{pm} = \frac{{l_{m} }}{{\mu_{0} \mu_{r} h_{m} L_{u} }}$$

If we neglect the leakage at the bridge of the rotor, the air-gap flux density is

$$\phi_{g} = \, \phi_{r} \frac{{R_{m} }}{{R_{m} + 4R_{g} }}$$

Therefore the air-gap flux density can be simply calculated by dividing the air-gap flux by the air-gap surface as

$$B_{g} = \frac{{\phi_{g} }}{{\frac{{\pi R_{{rotL_{u} }} }}{2p}}}$$

The air-gap reluctance

$$R_{g} = \frac{{k_{c} l_{g} }}{{\mu_{0} \left( {l_{m} + 2g_{e} } \right)L_{u} }}$$

The average torque is

$$T_{ave} = mk_{1} k_{w} N_{tot} B_{g} R_{ro} Li_{ph}$$

The torque expression for the spoke type motor is given by the equation

$$T = R_{rot}^{2} \frac{{L_{u} }}{{\mu_{o} }}\oint {B_{r} B_{\theta } d\theta }$$

where R_rot is the rotor outer radius, L_u is the stack length,$\mu_{0}$ is the permeability of free space, B_r is radial flux density and B_θ is the tangential flux density of the magnetic field in the air gap.

The cogging torque is expressed as

$$T_{cog} = - \frac{dw}{{d\theta }} = - R_{s} \frac{dw}{{dx}}$$

where w is the magnetic field stored in the air-gap

$$w = l_{g} L_{u} \int {\frac{{b_{g}^{2} \left( x \right)}}{{2\mu_{o} }}dx}$$

where b_g(x) is the air gap magnetic flux density expressed as a function of the x co-ordinate. The magnetic flux density distribution in the air-gap b_g(x), due to permanent magnet b_pm and slotted stator core b_sl($x$) is given as

$$b_{g} \left( x \right) = \left[ {\frac{{b_{pm} \left( x \right)}}{{k_{c} }} + b_{sl} \left( x \right)} \right]$$

For buried permanent magnets such as in Spoke type BLDC motor, the cogging torque [25] is derived as follows

$$\begin{aligned} T_{C} \left( x \right) & = \frac{{R_{s} }}{2}\frac{{L_{u} l_{g} }}{{2\mu_{o} }}\frac{\partial }{\partial x}\mathop \smallint \limits_{x + a}^{x + b} b_{g}^{2} \left( x \right)dx \\ T_{c} \left( x \right) & = \frac{{l_{g} L_{u} }}{{2\mu_{0} }}\frac{{R_{s} }}{2}A_{T} \frac{{B_{mg} }}{{K_{c} }}\mathop \sum \limits_{K = 1,2,3 \ldots }^{\infty } \left\{ {\ell_{k} \left[ {\cos \left( {\frac{2k\pi }{{t_{1} }}\left( {x + b} \right)} \right) - \cos \left( {\frac{2k\pi }{{t_{1} }}\left( {x + a} \right)} \right)} \right]} \right\} \\ \end{aligned}$$

Thus the cogging torque can be computed by using the above equation.