Calculation on proportion of rotor shape for torque ripple reduction of axially laminated type synchronous reluctance motor

Abstract

This paper deals with computation on the ratio of rotor core width and insulator width to maximize the torque density and to minimize the torque ripple of axially multi-layer type synchronous reluctance motor (ALA-SynRM) for electric valve actuators. The thickness of the rotor core and flux barrier has the greatest effect on the flux path. Therefore, the optimum design on proportion of rotor shape for ALA-SynRM is proposed in this paper by coupled finite element method (FEM) and response surface method (RSM). Also, the characteristics dependence on the presence or absence of a rotor core rib, which causes magnetic saturation, was analyzed by calculating the inductance. Finally, the results of analysis are demonstrated through the simulation and by an experiment.

Keywords

Axially laminated type synchronous reluctance motor (ALA-SynRM)electric valve actuator Box-Behnken method proportion of rotor structure

1. Introduction

An actuator is an essential component in high demand caused by its application in a wide range of fields including industrial equipment, construction, robotics, shipbuilding, electrical vehicles, and aircrafts. The driving power source of actuators have been hydraulic and pneumatic in nature but, recently, actuators comprising electric drive systems have become popular because they simplified installation, and eased control and management. Induction motors are very often applied as actuator of driving source, but the demand for better actuators increases due to the low torque at low speed, efficiency problems, and reactivity/stability issues of induction motors [1, 2, 3]. Therefore, the feasibility of adopting an optimal design method and fabrication of an electric-actuator-driving synchronous reluctance motor (SynRM) was studied, as presented in this paper, with specific targets of high efficiency and high torque.

Figure 1.

SynRMs according to laminated direction.

Two types of synchronous reluctance motors are shown in Fig. 1. Segment type synchronous reluctance motor has ribs in the flux barriers whereas axially laminated anisotropic (ALA) SynRM has good mechanical strength and higher saliency ratio [4, 5] due to its higher saliency ratio [6, 7]. The segment type SynRM has characteristics suitable for mass production and easy manufacturing processes. The ALA type SynRMs are capable of greater torque per unit weight because of the absence of rib in its mechanical structure. Such a structural characteristics of ALA type has good properties due to the large difference ( $L_{d}-L_{q}$ ) and ratio ( $L_{d}$ / $L_{q}$ ) significantly. As can be seen from the previous studies of references, it can be confirmed that the rotors with an axial lamination have higher saliency ratio as compared to those with lateral lamination [8].

Therefore, in this paper, the ALA type SynRM is selected as an alternative of the electric actuator drive source and the methods of improving its torque density are studied. The torque and torque ripple characteristics, in consideration of the influence of the core magnetic saturation, are also analyzed by calculating the $d$ -axis and $q$ -axis inductances. The main design parameters of the rotor shape are the thickness of the flux barrier, the iron core and the presence of the rib. The proposed model is analyzed using the response surface method (RSM) coupled finite element method (FEM).

Finally, the torque characteristics of the optimal design model are verified by comparing the finite element analysis simulation with the experimental results.

2. Proposed model design

2.1 Range of the design

The stator of an axially laminated synchronous reluctance motor (ALA-SynRM) is similar to that of an induction motor, whereas the rotor is laminated in the axial direction of the shaft as shown in Fig. 1b. Alternate layers of the core sheets capable of punching and flux barrier (insulator) sheets are punched together in order to create an improved flux path between the cores. A non-magnetic material (spider) is used for the same purpose to assemble the structure between the shaft and the core. Magnetic flux flows well in a direction parallel to the laminated surface ( $d$ -axis) but is blocked in a direction perpendicular ( $q$ -axis) to the laminate surface because of the high reluctance. Therefore, it is important to design the rotor structure in accordance with the thickness of the core, the thickness of the flux barrier for high torque density. In addition to these rotor design variables, more design variables exist. However, in this paper, only these parameters are selected for optimizing the design with minimal analysis time.

2.2 Mathematical modeling

As mentioned above, inductance values in the $d$ - and $q$ -axis of ALA-SynRM affect the torque and power factor [9], so that relevant equations are represented as follows Eqs (1)–(3). The reluctance torque of an ALA type SynRM can be expressed by

$T_{e}=\frac{3}{2}\cdot\frac{P}{2}(L_{d}-L_{q})i_{d}\cdot i_{q}=\frac{3}{2}% \cdot\frac{P}{2}(L_{d}-L_{q})\cdot\frac{1}{2}I_{a}^{2}\cdot\sin 2\theta$ (1)

where $P$ is the number of pole pairs and $I_{a}$ is the rms value of the input current. Equation (1) is only valid for a 3-phase model.

The $d$ - and $q$ -axis current can be wrote with the current phase angle ( $\theta$ )

$i_{d}=I_{a}\cos\theta,\;\;\;i_{q}=I_{a}\sin\theta$ (2)

where $\theta$ is the angle of the stator current vector with respect to the rotor $d$ -axis, as shown in Fig. 2. If the model is ideal, $\theta$ is in the range 0 to 9 ${}^{\circ}$ , and exhibits best performances at 45 ${}^{\circ}$ . Otherwise, we calculate the optimal angle by varying the value of $\theta$ and observing the main effect on the model for each angle step.

Figure 2.

Vector diagram of the current and voltage.

In SynRM, the power factor (PF) can be calculated by a function of the salient pole ratio [9].

$PF=\frac{\xi-1}{\xi+1}\;,\;\;\;\;\xi=\frac{L_{d}}{L_{q}}$ (3)

2.3 Design parameters

Figure 3 shows the stator and the rotor of an ALA-SynRM and the design variables used for the optimal design. According to previous researches, main factors that affect the $L_{d}$ , and $L_{q}$ in optimum design are the width of the open slot, the thicknesses of the flux barrier and the rotor core layers [10].

$K_{w}=\sum(W_{i})/\sum(W_{c})$ (4)

Here,

$\sum(W_{i})$ : The total flux barrier width

$\sum(W_{c})$ : The overall core width

Table 1

Stator and rotor design variable range of the objective fuction

Function		Minimize	Torque ripple
		Maximize	Torque
Design variable and	Stator	1.5 $\leqslant$ Open Slot $\leqslant$ 2.0
mechanical constraint	Rotor	8.85 $\leqslant$ Position $\leqslant$ 9.85
		2.7 $\leqslant$ Core thickness $\leqslant$ 3.5
		1.0 $\leqslant$ Insulator thickness $\leqslant$ 1.5

Figure 3.

Design variables and variation direction of the initial model.

Therefore, the design parameter of the stator is the width of the open slot and design parameters of the rotor are the thickness of the iron core, the thickness of the insulating material and these position. Figure 4 shows the torque and torque ripple values for the design variable range considered. In particular, it can be seen that the change in the core thickness has a strong effect on the torque characteristics. In this paper, the $K_{w}$ of initial model is determined $K_{w}=$ 1 in consideration of previous research result [10]. When $K_{w}=$ 1 the configuration of the rotor is constructed of alternate sheets in which the iron core and insulator are equal.

Figure 4.

Main effect analysis by each design variables.

2.4 Optimal design

Response surface methodology (RSM) is a collection of statistical and mathematical techniques useful for developing, analysing, improving, and optimising the output or response of processes that are influenced by several independent input variables [11]. RSM was used by researchers developing the surface deposition model and surface roughness model [12]. There are many design of experiment (DOE) methods in the RSM, and this paper uses the Box-Behnken method. This method requires lesser number of experiments compared to other response surface methods for the optimization of same set of parameters and factors. If the range of the variable is determined, it may be advantageously used at the analysis time. Multi-characteristic optimal design cannot be performed in the DOE because it does not use S/N (signal/noise) ratio according to the smaller and larger the better characteristics.

Furthermore, there are many other parameters for optimizing the two objective functions in addition to the four parameters mentioned above [13, 14]. Therefore, we select the optimum model using an experimental design screening method to analyse the effects of these parameters on performance. Table 1 shows the range of design parameters for the objective function, and constraint conditions for the design of the stator and the rotor. The thickness of the iron core and the insulating sheet of an ALA-SynRM are considered. These thicknesses are limited by mechanical constraints such as the thickness of bolt head and the external diameter of the rotor. These parameters are designed considering the saturation of the iron core as well as the manufacturability. Table 2 shows the resulting values for torque and torque ripple due to changes in design parameters using the Box-Behnken method. Comparing the results, best parameters that result in maximum torque and a minimum torque ripple are selected for testing 7.

Table 2
Experimental results of the objective function, the design variable using the Box-Behnken method

Analysis	Design variable (stator)	Design variable(rotor)			Result
	Open slot [mm]	Position [mm]	Core [mm]	Insulator [mm]	Torque [Nm]	Ripple [%]
1	1.9	9.35	3.15	1.20	1.8447	31.80
2	1.7	9.35	2.80	1.20	1.9678	32.73
$\vdots$	$\vdots$	$\vdots$	$\vdots$	$\vdots$	$\vdots$	$\vdots$
6	1.5	8.85	3.15	1.20	1.9240	29.61
7	1.9	9.35	2.80	1.35	1.9328	17.86
$\vdots$	$\vdots$	$\vdots$	$\vdots$	$\vdots$	$\vdots$	$\vdots$
15	1.7	9.85	2.80	1.50	1.9646	25.69

3. Analysis of the proposed model

3.1 Results of the analysis model

The $d$ -axis and the $q$ -axis inductances are calculated using a 2-D finite element method. Enter the input current of one phase on the stator for the calculation of the inductance, takes the value of magnetic vector potential depends on the position of the rotor and flux linkage to the coil is calculated. Figure 5 shows the results of calculated flux linkage. Using this result and the Eq. (5), one can compute the inductance.

$L_{d}=\frac{3}{2}\frac{\lambda_{a\_\max}}{I_{\textit{a\_peak}}},\;\;\;\;L_{q}=% \frac{3}{2}\frac{\lambda_{a\_\min}}{I_{\textit{a\_peak}}}$ (5)

Figure 5.

$d$ -/ $q$ -axis flux linkage for calculation of $L_{d}$ and $L_{q}$ by FEM.

Figure 6.

Comparison of d-/q-axis inductance difference and ratio.

Figure 6 shows the variation curves of the inductance difference ( $L_{d}-L_{q}$ ) and the ratio ( $L_{d}/L_{q}$ ) corresponding to an input current range that results in the desired torque density. It is typical inductances pattern of the SynRMs, $d$ -axis inductance reducing from saturation at the start, and the inductance value falling with small increases in the amount of current. It can be seen that the $q$ -axis inductance is less than that of the $d$ -axis, thus meeting the design objectives of the salient pole structure motor. Figure 7 shows the flux density distribution for the comparison of initial and optimum model at the rated conditions.

Figure 7.

Comparison of the flux density at rated conditions (@ output torque: 1.8 [Nm], speed: 1800 [rpm]).

Figure 8.

Torque and torque ripple according to the $K_{w}$ .

Figure 9.

Photograph of experiment equipment and manufactured rotor shape.

Figure 10.

Comparison of the analysis result with FEM and experimentation.

Figure 8 shows torque characteristics of according to the $K_{w}$ . In the case of rated speed (1800 rpm) and rated current (1.8 A), it is observed that the maximum torque and minimum torque ripple point are nearly closed to $K_{w}=$ 0.5.

One should notice that the design solutions should be related to the proportion of rotor structure, and this will be the important data in motor design of similar types.

4. Experimental verification

To validate the performance of the proposed design model, an experiment was carried out using prototype motor in accordance with the targeted design. Experimental set up consisted of dynamometer, torque sensors, power quality analyzers, power supplies, and vector control inverters and the appearance of the rotor fully assembled, as shown in Fig. 9.

In order to obtain the higher characteristics owing to rotor structure, the characteristic of the optimum model with those of the initial model compared through Box-Behnken design. The torque characteristics of optimal model are represented as good results in Fig. 10. Finally, it can be demonstrated the results of analysis through the simulation and by an experiment. Figure 11 shows the comparison of the analysis results of the torque, back-EMF and current phase angle with that of experiment. Table 3 shows the comparison results of both model.

5. Conclusions

This paper deals with a design method for the optimal design of ALA-SynRM using response surface method coupled finite element method for use as a direct drive electric valve actuator.

Table 3

Comparison of experimental results at rated condition

	Input current [A]	E.M.F [V]	Torque [Nm]	Torque ripple [%]	Output power [W]	$K_{w}$
Initial	1.95	106.02	1.8036	35.82	340	1
Optimal	1.80	115.80	1.8315	17.86	340	0.5

Figure 11.

Comparison of the analysis result with FEM and experimentation.

And a method of design related to the torque density, the power factor, and torque ripple of ALA-SynRM according to the $K_{w}$ has been proposed. Setting the design parameters for the stator and rotor for the best design, and by combining the data derived from the response surface method with the finite element method the results were derived. After selecting a specified range of variables through a primary analysis, further analysis time was reduced by utilizing Box-Behnken method.

In addition, this paper presents a design solution that is found through the comparison of inductance difference and torque ripple, according to the rotor shape proportion under the above condition. Through this study, it was determined that the motor torque is reduced due to the $K_{w}$ in the rotor of the ALA type.

Consequently, the appropriateness of design solution in a machine’s optimization method is verified through the simulation and by an experiment. Therefore, computation of $K_{w}$ approach can be considered as a design method for optimum design of ALA-SynRM and other machines.

Footnotes

Acknowledgments

This work was supported by the Human Resource Training Program for Regional Innovation and Creativity through the Ministry of Education and National Research Foundation of Korea (NRF-2015H1C1A1033580).

References

Taghavi

S.M.

and Pillay

, A mechanically robust rotor with transverse laminations for a wide-speed-range synchronous reluctance traction motor, IEEE Transactions on Industry Applications 51 (2015), 4404–4414.

Soong

W.L.

and Ertugrul

, Field-weakening performance of interior permanent-magnet motors, IEEE Transactions on Industry Applications 38 (2002), 1251–1258.

Lee

J.H.

, Efficiency evaluations of synchronous reluctance motor using coupled FEM and preisach modeling, IEEE Transaction on Magnetics 39 (2003), 3271–3274.

Ikaheimo

Kolehmainen

Kansakangas

Kivela

and Moghaddam

R.R.

, Synchronous high-speed reluctance machine with novel rotor construction, IEEE Transactions on Industrial Electronics 61 (2014), 2969–2975.

Arkadan

A.A.

ElBsat

M.N.

and Mneimneh

M.A.

, Particle swarm design optimization of ALA rotor SynRM for traction applications, IEEE Transactions on Magnetics 45 (2009), 956–959.

Platt

, Reluctance motor with strong rotor anisotropy, IEEE Transactions on Industry Applications 28 (1992), 652–658.

Boldea

Z.X.

and Nasar

S.A.

, Performance evaluation of axially laminated anisotropic rotor reluctance synchronous motors, IEEE Transactions on Industry Applications 30 (1994), 977–985.

Vagati

Canova

Chiampi

Pastorelli

and Repetto

, Design refinement of synchronous reluctance motors through finite-element analysis, IEEE Transactions on Industry Applications 36 (2000), 1094–1102.

Staton

D.A.

Miller

T.J.E.

and Wood

S.E.

, Maximising the saliency ratio of the synchronous reluctance motor, Electric Power Applications, IEEE Proceedings 140 (1993), 249–259.

10.

Choi

Y.C.

Kim

H.S.

and Lee

J.H.

, Optimum design criteria for maximum torque density and minimum torque ripple of SynRM according to the rated wattage using response surface methodology, IEEE Transactions on Magnetics 44 (2008), 4135–4138.

11.

Montgomery

D.C.

, Design and Analysis of Experiments. John Wiley and Sons, New York, 2001.

12.

Sidhu

H.S.

and Banwait

S.S.

, Analysis and Multi-objective Optimisation of Surface Modification Phenomenon by EDM Process with Copper-Tungsten Semi-sintered P/M Composite Electrodes, American Journal of Mechanical Engineering 2 (2014), 130–142.

13.

Khuri

A.I.

and Cornell

J.A.

, Response Surfaces Design and Analyses. Marcel Dekker Inc., 1987.

14.

Antony

, Design of Experiments for Engineers and Scientists. Burrerworth-Heinemann, 2003.