This paper discusses the influence of the magnetic properties of the stator core on cogging torque in 8-pole 12-slot surface-mounted permanent-magnet synchronous motors from the perspective of magnetic energy. In the finite element analyses of magnetic fields with modeled stator BH curves, cogging torque decreases drastically when the shape of magnets is changed from an arc to a semi-cylindrical structure. The influence of the stator BH curve on cogging torque is dominant in the low-cogging-torque motor with semi-cylindrical magnets. This is because magnetic energies in the gap and the magnets cancel each other and the magnetic energy in the stator core is dominant in the low-cogging-torque motor. Low maximum permeability and low magnetizing force in a high-B region are preferable for stator magnetic properties to reduce cogging torque. This is explained by the behavior of harmonics in the stator magnetic energy variation. The influences of steel grade, compressive stress, and punching in the stator core on cogging torque analyses are consistent with the results for the modeled BH curves. Low grade electrical steel sheets, high compressive stress, and magnetic annealing are effective to reduce cogging torque in the described motor design.
1. Introduction Electrical steel sheets are widely used for magnetic cores in electrical machines such as motors and transformers. To produce motor cores, for example, electrical steel sheets are punched, stacked, vertically fixed by interlocking or welding and finally combined with a frame by shrink fitting. In the vertical fixing process, interlocking is an especially suitable method for mass production. On the other hand, it is well known that electrical steel sheets are magnetically deteriorated by such manufacturing processes. After the processes, permeability decreases and iron loss increases, which lead e.g. to a lower performance of motors. To take these influences into account, finite element method (FEM) analyses considering magnetic deterioration are performed. For such FEM analyses, magnetic data for electrical steel sheets considering such manufacturing processes are required. It has been reported that compressive stress [1][2][3], which often appears in motor cores with shrink fitting, and punching [4][5][6][7] deteriorate electrical steel sheets significantly. However, there are few reports on magnetic deterioration by interlocking electrical steel sheets and it is required to systematically study the influence of interlocking. In this contribution, measurement results for ring cores with interlocking are presented and the cause of the magnetic deterioration is discussed. 2. Experimental procedure Interlocking was applied to ring cores made of electrical steel sheets. This is because it is difficult to apply interlocking to samples for Epstein frames or single sheet testers. The structure of the studied ring cores is shown in Fig. 1 (a). The material used is non-oriented electrical steel containing about 3 wt% of silicon and some other elements to improve soft magnetic properties. The thickness of the sheets t 1 is 0.5 mm. The outer and inner diameters of the ring cores, d o and d i respectively, are 60 mm and 48 mm. The overall height of the stack T is 5 mm. There are 0, 2, 4, or 8 interlocks equally distributed along the circumference of the ring cores. The length and the width of each interlock, a and b respectively, are 4 mm and 1 mm. Fig. 1 (b) shows the schematic drawing of the cross section of an interlock. BH curves and iron losses at the frequency of 50 Hz were measured. 3. Magnetic model We assume here that an interlocked ring core is represented by a magnetic series circuit with undamaged and damaged regions. If there is no leakage of flux from the ring core, the following equations are valid. l/μ a =Nd/μ + +(l-Nd)/μ -(1) W a =NdW + /l+(l-Nd)W -/l (2) Here, μ a and W a show the measured permeability and iron loss. μ + and μ -show the permeability of damaged and undamaged regions. W + and W -show the iron losses of damaged and undamaged regions. N is the number of interlocks in a ring core. l is the average length of the entire magnetic circuit approximated by π(d o + d i )/2. d is the length of a damaged region. These equations show that the inverse of permeability and iron loss should ...
This paper investigates an efficient iron loss calculation method for soft magnetic materials of power transformers. To accurately estimate iron losses in the materials such as structural steels and magnetic shielding, the magnetic field analysis taking account of the nonlinear magnetic properties is considered to be effective. In this paper, quasi-DC magnetic properties of the soft magnetic materials are measured and the iron losses are calculated by using a three-dimensional finite element method. Furthermore, the effect of considering hysteretic properties on the accuracy of the iron loss calculation is discussed based on a theoretical representation of eddy current loss in a conductive rectangular plate.
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