# Shape Optimization of Discontinuous Armature Arrangement PMLSM for Reduction of Thrust Ripple
###### Abstract  
The aim of this paper is to present the optimal design process and an optimized model for a discontinuous armature arrangement permanent magnet linear synchronous motor (PMLSM). The stator tooth shapes are optimized to reduce detent force. When the shape of the stator is changed to reduce the detent force, the saturation magnetic flux density and the back electromotive force characteristics change. Multi-objective optimization is used to search for the local lowest point that can improve the detent force, saturation magnetic flux density, and back EMF characteristics. To reduce the detent force generated at the outlet edge, a trapezoidal auxiliary tooth was installed and the performance was analyzed. The experiment's response surface methodology is used as an optimization method and all the experimental samples are obtained from finite-element analysis. The validity of this method is verified by comparing the optimized FEA model to the initial FEA model. d 2021 15 November 2021 22 November 2021 22 November 2021 22 2021 22 22 22 22 22 22 22 22 22 22 22 22 22 22 2  
design to reduce the detent force [6]. Control-based reduction requires accurate current control and is significantly affected by the reliability of the sensor used [7]. Therefore, machine design is more effective for suppressing the detent force [8]. A stepped double auxiliary pole has been utilized with the armature to minimize the slot effect [9]. The magnet skew, which has been widely used to minimize the cogging force, has been applied to the discontinuous armature arrangement of the PMLSM to reduce the slot and end effects [10]. Auxiliary poles or auxiliary teeth have been widely used to reduce the end effect. The end effect can be reduced by installing auxiliary teeth at both ends of the mover [11; 12; 13]. Ripple components are reduced by adopting a modular mover [14; 15]. A method was proposed in which the detent force was reduced by the modularization of the mover through response surface methodology (RSM), considering multiple responses. Additionally, the target value of the rated thrust can be achieved [16]. Most existing studies have focused on reducing the detent force through the shape change of the stator or rotor. With the machine-design method, according to the change in the shape of the magnetic circuit, a disparity may exist between the characteristics of the back electromotive force (back EMF), which is induced during the movement of the mover, and the magnetic flux density generated in the tooth. The harmonic component of the back EMF and the saturation of the magnetic circuit are among the major causes of the thrust ripple [17]. The harmonic components of the back EMF and the generation of local magnetic saturation can significantly impact thrust pulsations [18; 19]. Therefore, in this study, not only do we consider the detent force discussed in the previous study but also the back-EMF distortion and local magnetic saturation, which can have a great effect on thrust pulsations. In addition, the detent force was subdivided into slot effect and end effect, and the effect of design parameters on each effect was analyzed. Both effects were reduced by using different kinds of approaches. To this end, two-dimensional (2D) finite-element analysis (FEA) and fractional factorial design were adopted to examine the effects of the seven design parameters of the PMLSM on each objective function. Each objective function was optimized according to the five main parameters, which were screened through a main-effect analysis. For optimization, the RSM with multiple responses was adopted, and the optimal shape for minimizing the detent force and back-EMF distortion and preventing tooth saturation was derived via the regression equation. The derived regression equation was tested through 2D FEA. Subsequently, a trapezoidal auxiliary tooth was installed at the ends of the armatures, and the end effect was analyzed according to the shape.