181
Optimal Design of Stator Slot Geometry to Reduce Torque Ripple for
High-Speed Spindle Motors
Wawan Purwanto
#, Dwi Sudarno Putra
*, Toto Sugiarto
## Department of Engineering, Universitas Negeri Padang, Air Tawar Barat, Padang, 25131, Indonesia
E-mail: wawan5527@gmail.com; wawan5527@ft.unp.ac.id
Abstract—This paper describes the optimal design for the geometry of a stator slot to reduce torque ripple for use in high-speed spindle motor applications. The proposed method consists of the following three steps: first, choose the parameters of the stator slot that has a strong influence on the stator current, stator winding loss, iron loss, total loss, efficiency, and torque by using the analysis of the effects of stator slot geometry; second, create factors and levels in the Taguchi method to obtain the optimal combination of the stator slot parameters from the analysis effect of the parameter results; third, using Genetic Algorithms (GAs) to determine the optimal value from the optimal combination of the results of the Taguchi method. Optimal design and performance analysis was performed using the Finite element Method (FEM) and verification by using equivalent circuit analysis. The optimization results were evaluated by comparing them with original performance. According to the test results and analysis, the optimal design of the stator slot geometry produce better performance than original design.
Keywords— finite element analysis; spindle motor; induction motor; stator slot; torque ripple
I. INTRODUCTION
Many industries have begun launching electric energy ef-ficient programs, with various attempts made to improve out-put power and efficiency, particularly in the new designs of induction motors [1]-[3]. Small changes in the optimal design of induction motors can increase their efficiency and output power, which has an impact on conserving electrical energy and extending the lifetime of an induction motor. Stator slots have a critical function in creating stator teeth flux density, stator leakage, torque ripple, winding loss, temperature rise, and radial force [4]-[6].
The geometry of the stator slots used in induction motors provides a flux path and an appropriate design of the stator slots can be maximizing flux distribution while minimizing motor losses. Stator windings generate magnetic fields in the stator slot. The cross-section area of the stator slot affects the stator winding loss, core loss, iron loss, and high-speed induc-tion motors require a minimum loss [6]-[8]. Given of the sig-nificance of stator slots, this study investigated the optimal design of the stator slot geometry to reduce torque ripple and improve the efficiency and torque of a spindle motor.
The stator slot design of a spindle motor is critical in satis-fying performance specifications, because the torque speed characteristics are largely determined by the configuration of the stator geometry [10,11]. A crucial focus is on the slot ge-ometry of the stator, because it is one of the most critical fac-tors for improving the performance of induction mofac-tors [6]. These paper, describes the design of stator slot geometry in high-speed spindle motors. The proposed method involved the following three steps. The first step is define the parame-ters that have a strong influence on the stator winding loss, iron loss, the total loss, the stator current, torque, and effi-ciency through the analysis of the effect of the stator slots pa-rameters.
The second step is the stator slot parameters which have a strong influence on the results of the first step, will be a factor
in the Taguchi method to obtain the optimal combination of the geometry of the stator slots. The third step is the optimal combination produced in the second step will be adopted as a guide to determine the optimum value of the stator slot pa-rameters by using GAs. The results of the Taguchi method and GAs optimization will be tested by using FEM, perfor-mance analysis and verified by the equivalent circuit analysis. Equivalent circuit analysis was formed based on the results of GAs.
In this paper, steady-state performance characteristics of the original design and both optimal designs are plotted to fa-cilitate a comparison and discussion. Finally, optimal overall performance is presented and a recommendation is offered for developing a spindle motor with the optimal specifications.
II. ANALYSIS OF STATOR SLOT GEOMETRY AND TORQUE RIPPLE REDUCTION
A. Optimal Stator Slot to Reduce Torque Ripple
Proper design of the conductor per slots with stator slot ge-ometry can make current along the surface of the stator core with sinusoidal distribution, than can get closer to the mag-netic potential curve in sinusoidal. Current concentration in the slot can cause high frequency, this is affecting magneto-motive forces (mmfs) concentration and cause current and torque ripple [5].
Stator slot support for optimal supply current in the stator winding, it is will causes produce higher magnetic flux den-sity in the stator slot-air gap-rotor slot. On the other hand, teeth zone magnetomotive force (mmf) is formed along the stator teeth-air gap-rotor teeth path. So, it is will causes higher starting torque.
182 reactance, the induction distribution produced by the funda-mental mmf waveform along the air-gap is distorted. It is causing the low starting torque and higher current and torque ripple.
The stator slot flux density across air gap on slotted arma-ture core alternates between a maximum value and a mini-mum value. It is defined as carter’s coefficient that plays very important role in computing of the performance of the induc-tion motor [4].
B. Stator Flux Density and Torque Ripple
The method can be used to achieve optimum flux density and reduce torque ripple is based on the reduction of current ripple, because the flux density and torque ripple is a function of the ripple current. The rotor flux density estimated based on stator current model. The stator flux estimation based on the stator voltage equation [5].
The rate of change of the stator current depends on the ap-plied voltage and the magnitude of the back electromotive force which depend on the speed of stator flux. At the high speed operation the applied voltage vector magnitude should be high to maintain V/f constant. If the position of the voltage vector is selected, the angle of torque is changing rapidly. For low speed operation, if the position of the voltage vector is selected to increase the flux and torque value than the current ripple increase.
Depends on the speed reference, the selection of optimum space voltage vectors for increase or decrease in the flux and torque ripple value is depend of back electromotive force and speed on the rotor flux. Very important to adjust the geometry of the stator slots, wire diameter, and working specifications of the spindle motor with a space voltage vectors selected. If the applied voltage vector does not match the resulting torque ripple can be significant. The torque ripple during a control period can be expressed as [7]:
In this study, the spindle motor had a rated output 14 kW, four Poles, a ∆ connection, 380 V, and could be operated at up to 30.000 rpm. The analyzed spindle motor was con-structed as a rounded semi closed stator slot type, shown in Fig. 1 with general spindle motor specification as shown in Table 1. The stator geometry is typically related to the number of conductors per slot. In this study, the number of conductors per slot was 8 turns per slot with a wire diameter of 0.32 mm. The optimization process and procedure is as shown in Fig. 2.
Fig. 1 Rounded semi-closed slot type
Fig. 2 Outline of the optimization design
183 The performance of the spindle motor in the L9 matrix exper-iments was obtained using a 2D FEM.
TABLEI
GENERAL SPINDLE MOTOR SPECIFICATIONS
Parameter Value Parameter value
Inner diameter of stator (mm) 70 hs0 (mm) 0.5 Outer diameter of stator (mm) 120 hs1 (mm) 0.5 Length of the stator core (mm) 120 hs2 (mm) 5.5 Outer diameter of rotor (mm) 69.5 bs0 (mm) 1.3 Inner diameter of rotor (mm) 38 bs1 (mm) 3.2 Number of stator slot 36 bs2 (mm) 4.7 Number of rorot slot 32 rs (mm) 0.8
GAs is iterative problem solving techniques and it is used in many engineering fields for finding an optimal solution. GAs is advantageous because they provide a flexible, simple, and intuitive approach to optimization with gives a high prob-ability of success [6-9]. The optimization procedure involves finding a vector x = (x1, x2, ... xn), representing a set of n design variables bounded by xL≤ xi≤ xU, i = 1, 2 ... n, so that the objective function f(x) is maximized (or minimized) with a set of k constraints Gj(x) ≤ 0, j = 1, 2 ... k. The objective function is the motor spindle efficiency and torque was defined in [6]. In this study, a GAs was used to determine the optimal value of the Taguchi method stator slot geometry parameter results. In this study GAs results with the popula-tion set at N = 500, crossover pc = 0.85 and mutation pm = 0.05.
IV.ANALYSIS RESULTS AND DISCUSSION
A. Spindle Motor Performance Analysis
Table 2 shows a comparison of the stator slot geometry based on the original design, Taguchi method, and GAs, and Table 3 shows a comparison of performance from the original design with the improved performance results, which was ver-ified by equivalent circuit analysis. The tables show copper loss in the stator winding reduced from the original design to the Taguchi method, and GAs, the efficiency increased from 74.98% of the original design to 93.26% of the Taguchi method, and 93.32% of GAs.
Improving the performance can reduce the potential likeli-hood of the stator temperature increasing, because of the de-crease in the stator current density and stator thermal load. The stator current density was reduced from 130.32 A/mm2 of original design to 13.95 A/mm2 of Taguchi method and 12.89 A/mm2 of GAs. The stator thermal load was reduced from the original design to Taguchi method, and GAs. These results show that the cross-sectional area of the stator slots fitted with the stator winding can improve the spindle motor perfor-mance.
TABLEII
COMPARISON RESULTS OF STATOR SLOT GEOMETRY
Parameter Original design
Taguchi method GAs
hs0 (mm) 0.5 0.5 0.5
hs1 (mm) 0.5 0.65 0.65
hs2 (mm) 5.5 8 7.4
bs0 (mm) 1.3 1.3 1.3
bs1 (mm) 3 3 3
bs2 (mm) 4.7 4.7 4.79
rs (mm) 0.8 2 2
184 TABLEIII
COMPARISON RESULTS OF SPINDLE MOTOR PERFORMANCE
Parameter Original design Taguchi method GAs Equivalent circuit analysis
Copper loss of stator winding (W) 3944.95 272.86 262.15 265.54
Copper loss of rotor winding (W) 185.02 103.72 115.46 115.36
Iron core loss (W) 103.22 197.72 186.44 185.6
B. Current and Torque Ripple analysis
Fig. 4 Stator current with time characteristics in spindle motor
Fig. 3 shows the torque ripple characteristics generated by the spindle motor. The GAs and Taguchi method produced lower torque ripple than the original design, as shown in Fig. 3(a) and (c). The torque ripple was influenced by the high sta-tor current and winding loss. In the original design, the high stator current caused high torque ripple, as shown in Fig. 3(b).
In the initial rotation, higher stator current ripple was pro-duced of Taguchi method and GAs, as shown in Fig. 4(a) and (c), however, in normal operating conditions, the optimal de-sign results were more stable with lower torque and stator cur-rent ripple compared with the original design. In the original design, the high stator current ripple causes high torque ripple, as shown in Fig. 4(b). This condition was also caused reduc-tion the efficiency and torque produced by the original design.
V. CONCLUSION
This paper presents an optimal design for the stator slots geometry to reduce torque ripple for developing of high-speed induction motors for spindle applications. An analysis of the parameters revealed that the stator slot geometry significantly influences the performance of the spindle motor. The Taguchi method and genetic algorithm could be applied for optimal design of the stator slot geometry. The test results and analysis showed that the performance and minimum torque ripple un-der the Taguchi method and GAs was superior to that unun-der the original design performance.
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