Overview
Surrogate model methods (design space reduction, response surface and space mapping) and scalar objective search algorithms (genetic algorithms, particle swarm and differential evolution) are probably the most widely used and favoured methods for electrical machine optimisation in recent years [64]. The use of the Taguchi method in electrical machine design is relatively new. This section intends to provide a detailed review and discussion of the published work relating to the use of Taguchi method in electrical machine design.
2.4.1
Publication Overview
Taguchi method has been used widely in engineering design [59,60, 62,63]. However, the first reported use of the method in the field of electrical machine design was possibly by Chen, Low and Bruhl in their 1998 paper [65], in which they implemented the method on a brushless DC PM CD-ROM spindle motor to further reduce the cogging torque while maintaining a high average torque. This publication stimulated vast research in- terest in applying Taguchi method to improve the performance of different brushless PM motors [66–72]. Figure 2.5 is a histogram3 of the research publications relating to the
Taguchi method in the field of electrical machines, where the number of publications including journals and conferences are summarised. It is clear that there is a growing interest in Taguchi method in past decade.
The geographical distribution of the publications in Fig. 2.5 is presented in a pie-chart in Fig. 2.6. Apparently, the Taguchi method is more favoured by Asian countries with Taiwan producing almost a third of the total publications. Nearly 50% of the publications from Taiwan was from Hwang’s group making them the most active contributor in this
3Note: The literature study in this dissertation covers primarily the research work published in English
Figure 2.5: Number of annual publications relating to the use of Taguchi method in electrical machines
field. Hwang’s group focused on PMSM design, where they used Taguchi method to optimise interior [80, 92] and surface-mounted [81, 83, 88, 104] PM rotor designs , axial flux [132] and linear PMSMs [135] as well as stator slots [84, 110]. In 2016, Lin and Hwang also applied the method to induction machine design [122]. It should be noted that the relatively low contribution from Japanese researchers in the related research is likely inaccurate as research work published in Japanese were not included. The number of publication from non-Asian regions is rather limited, which may be attributed to the fact that Taguchi method is less known outside Asia. Most of the published work outside Asia was published in recent five years.
2.4.2
Current Status of Taguchi Method in Electrical Machine
Design
In this section, the scope, objectives and implementation aspects of Taguchi method in the field of electrical machines are discussed.
According to literature, Taguchi method has been applied to various types of electrical machines such as brushless DC PM [65,66,68,70–77], radial flux PMSM [56,67,69,78–119], IM [120–122], RSM or switch reluctance machines (SRM) [123–131], axial flux PMSM [132, 133], linear or tubular flux type machines [134–138], piezoelectric motor [139], ac- tive magnetic bearing [140], Halbach array PM machine [141], and superconducting wind generator [143]. Figure 2.7(a) shows the percentage representation of each machine type in the Taguchi method publications. It can be seen clearly that the Taguchi method was largely implemented on PM machines design optimisation.
In literature, Taguchi method has been employed for different design optimisation objectives, which include minimisation objectives such as cogging (Tc) and torque ripple
(Tr), total harmonic distortion (THD) and active machine mass, legitimate objectives
such as efficiency, torque production, electromagnetic (EM) properties (flux or flux den- sity properties) back-EMF, and other objectives like power factor, rotor saliency ratio, temperature distribution and acoustic noise, as illustrated in Fig. 2.7(b). The most com- mon use of the method is to improve the performance of the existing machine that was realised by other design methods. This is done by using either the smaller-is-best quality characteristic (QC) to minimise a specific objective or the bigger-is-best QC to maximise a specific objective. It is possible to minimise one objective while maximising another. However, this requires multi-objective optimisation, for which the Taguchi method is not well suited. Overall more than 50% of the published work involved the torque perfor- mance related objectives such as minimising Tc or Tr while maintaining a high average
(Ta) torque or just maximising the peak torque production.
(a) (b)
Figure 2.7: Percentage breakdown of Taguchi method related publications regarding (a) Ma- chine types (b) optimisation objectives
As with any other optimisation methods, the number of parameters directly influences the total number of simulations and the complexity to analyse and realise the final design. With Taguchi method, the available OAs also need to be considered when selecting the
number of parameters for the optimisation. In addition to the main design parameters, the use of outer design can also be included which requires the use (in the majority of cases) of a second OA. It was found that for the main OA the L9 is the most favoured, fol-
lowed by the L18and the L16 as shown in Fig. 2.8. These arrays can be used to determine
the optimum conditions for 4, 8 and 5 parameters, respectively. There were limited publi- cations which utilised outer array design as part of the design framework [68,71,93,99,102] as it increases the total number of trial simulations.
Figure 2.8: Orthogonal arrays used in publications
During the review, two instances were found in which researchers used both the DOE and Taguchi method for performance improvement optimisation of a single-phase LS- PMSM. For both publications, the same LS-PMSM design was used. Ahn et al. in [82] used the DOE method to improve the steady-state efficiency through limiting the leakage flux in the rotor by optimising the PM barriers shape. In [56], Kim et al. improved both starting torque and efficiency through the use of a weighted normalised function. Although the starting torque was included as a performance objective it was determined from a static 2D FEM simulation thus the transient performance was not directly optimised. The final results were experimentally verified.
2.4.3
Citation Metrics
To identify the key publications from the published work and to establish unique contri- bution made by researchers to overcome the limitations of the Taguchi method a citation matrics is compiled using [56,65–152]. The citation matrics presented in Fig. 2.9 shows the number of citations for each selected paper of significance received from other Taguchi method related publications. It was found that Kim et al. in [79] and Hwang et al. in [81, 83, 132, 135] applied practically the same approach as that of Chen et al. in [65]. However, Kim et al. in [56,85], Shin et al. in [86] and Hwang et al. in [104] each proposed methods for multi-objective optimisation using Taguchi method. There has not been any published research incorporating the Taguchi method into an iterative design procedure.
Figure 2.9: Taguchi machine design publication citations index