Optimization of Permanent Magnet Skew in Permanent Magnet Linear Synchronous Motors Using Finite Element and Statistical Method

The permanent magnet skew is one of the techniques mostly used on the Permanent Magnet Linear Syn-chronous Motors (PMLSMs) to reduce the thrust ripple; even though there is a reduction in the amplitude of ripple and at the same time a significantly decrease of the motor’s thrust. This article proposes a combined technique between the Finite Elements Method (FEM) and statistical regression, to obtain an objective function that will allow the achievement of the optimal Permanent Magnet (PM) skew angle, so that there is a greater reduction of ripple with the minimum thrust diminishment.

• FEM-Statistical Regression Method
• Optimization
• PM Skew
• PMLSM
• Ripple
• Thrust

1. Introduction

The PMLSMs are widely used for their excellent characteristics such as high force density, fast dynamic response, low thermal losses, and simple structure. However, the thrust ripple, which is the main disadvantage of PMLSM, results in a periodic force oscillation. Consequently, the periodic force oscillation causes mechanical vibration, acoustic noise, and speed oscillation, which will deterio-rate the performance of PMLSMs [1].

It is then necessary to look for a way of reducing the thrust’s ripple. To achieve the latter, a diversity of techniques are used and one of them is the skew of PM [1,2]. However, the skew also provokes a reduction in the thrust [3,4]; for which it will be necessary to implement a method to obtain the optimum skew angle so that there is a reduction in ripple without diminishing too much the motor’s thrust.

The existing Literature [5-14], considers diverse methods of optimization, but none establishes as objectives the maximization of thrust and the minimization of ripple. In addition, techniques that suppose certain degree of complexity like the genetic algorithms are used [6,11]. It is for that reason that this work considers a simpler technique that consists of using the data of thrust and ripple of the simulation by FEM, to obtain by means of quadratic regression the equations that follow the tendency of the data.

The equations are of second order, one for thrust (T) and another one for ripple (R), they are then combined to obtain an only objective function that is maximized and of which the optimal PMs skew is obtained.

The procedure is applied to two types of PMLSMs, the first one has a short pitch winding (PMLSM-1) and the second one has diametrical pitch winding (PMLSM-2). Figures 1 and 2, shows the structures of both motor.

Table 1 shows the most relevant dimensions of the two PMLSMs.

References

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