1. Introduction

PM claw pole stepping motors execute rotational motion in a sequence of discrete angular steps. Well suited for open-loop digital control, they are widely used for precision motion and positioning. These motors can be found in numerous industrial and consumer products, including computers and peripherals, disk drives, printers, robotic devices, and in electronic cameras, where they are used for lens focusing^{[1, 2]}.

The analysis model of this paper is optical disk drives. For this application, the motor has a smaller size, pole pairs, and output compared to general PM type claw-pole stepping motors. Considering the comparable small size of the motor, a small variation of the motor design factor could lead to a large difference of the output characteristics. For this reason, more precise modeling should be introduced with a careful analysis process for better analysis results. Especially for PM type claw-pole stepping motors, magnetization along the z-axis makes 3-D analysis necessary for correct analysis results^{[3, 4]}.

In this paper, Response Surface Method (RSM) is used for design optimization and 3D Finite Element Analysis (FEA) is carried out changing several design parameters, which are considered as the most influential on detent torque viz., air gap length (tapered air gap), pole width, and pole high.

To decide the parameters for improving the steady state characteristics, Approximate Reaction Function is generated by using Central Composite Design (CCD) and final the optimum model, which satisfies the given holing and has minimum detent torque is suggested.

In the case of a claw pole PM step motor, an upper part and a lower part are usually assembled with an error. This error increases the detent-torque in the motor. However, because the motor is very small, it is very difficult to assemble the two parts precisely. This paper proposes a new construction method that is able to lessen the assembling error. Through analysis of assembling error (from 0 to 3 degree), it shows the effect of construction error on the detent-torque.

Moreover, the simulation results are verified and compare with the experimental results.

2. Main Discourse

2.1.Structure of PM claw pole stepping motor

A PM claw pole stepping motor consists of two separate bobbin-wound drive coils that enclose axial sections of a cylindrical radial polarized multi pole permanent magnet rotor. The rotor is usually made from isotropic grade ceramic ferrite. This is a two-phase motor with each coil comprising a separate drive phase. Each coil is mounted on a soft-magnetic stator element that consists of two opposing toothed components and a flux return ring. As the two phases (A, B) have 8 pairs of teeth poles, the analysis model of this paper has a 22.5 degree step angle. The drive coils are assembled by first sliding the coil and flux return ring on one of the toothed components and then inserting the remaining toothed element into the assembly in such a way that the stator teeth are equally spaced^[5]. Although the PM claw pole stepping motor has a very complicated structure, Fig. 1 depicts the structure as a plain.

Fig. 1. PM type stepping motor with claw pole in one phase

2.2.Drive of PM claw pole stepping motor

In the PM claw pole stepping motor each rotation step is initiated by activating a single phase. Specifically, when one phase is activated (with the other phase off) the rotor experiences a torque that rotates it into magnetic alignment with that phase. The stator teeth of the two phases are offset from one another by half-a-tooth pitch in an angular sense. Therefore, by sequentially activating the two phases the rotor can be repetitively stepped with an angular measure equal to half a pole pitch.

Fig. 2 shows the basic circuit for a two-phase PM claw pole stepping motor.

The main specifications of the analysis model is shown in Table 1. Although the PM of each stack is isolated from each other, an influence due to the leakage magnetic flux exists. This is because the cross section of the stator of each stack is coupled. As the stacks are magnetically dependent on each other, analysis has been conducted considering both stacks.

Fig. 3 presents the element division and magnetic flux density distribution using FEA. The number of elements is about 300,000 and the number of nodes is about 90,000.

Fig. 2. A basic circuit for a two-phase PM claw pole stepping motor

Fig. 3. Mesh shape and distribution of magnetic flux density

Table 1. The specifications of the PM type stepping motor with claw-poles

Section Specification
Stator	Phase number	2
	Poles per phase	8
	Outer a diameter	7.45[mm]
	Length	12.2[mm]
	Step angle	22.5[deg]
Rotor	Number of poles	8
PM	Flux density	0.43[T] @20℃
Air gap	Length	0.195[mm]

2.3.Analysis results of simulation-based DOE

There are two important concepts on the variation of rotor position of PM claw pole stepping motors. First is detent torque and second is holding torque.

Detent torque is the maximum torque of no exciting state and the rotor keeps its position fixed by this torque. The holding torque is the maximum torque that can be externally induced to the motor shaft allowing the motor to recover the initial state with rated current excitation^[3].

This paper is based on the assumption that the range of the design factors is equally thought to be two and RSM was applied to the analysis model. The influence and tendency of the design factors on the holding torque and detent torque are shown in Fig. 4. As the result is shown in Fig. 4, as the tapered air gap and pole width increase, detent torque is decreased, and choosing the proper pole height becomes important between the given range.

Fig. 4. Effect of selected design variables on design objectives

2.4.Effect of Assemble error of PM type stepping motor

Fig. 5(a) shows the construction error of the claw pole PM step motor. The claw pole PM step motor is composed of two poles that are out of alignment by 22.5 mechanic degrees and 90 electrical degrees. If the center of a permanent magnet takes same point with the center of the pole, there is a lowest detent-torque as the upper part detent-torque and a lower part take 180 degree of the phase difference.

A claw pole PM step motor is very small. Stack A and Stack B are separated from each other and they are wrapped in a housing. This construction method is the cause of construction error, which leads to a rise in detent-torque.

Fig. 5(b) shows the detent-torque of the model that is applied from zero to three degree construction error. As indicated by result of Fig. 5(b), the more construction error increases, the more detent-torque increases and it shows the phase rises at that same time. The detent torque causes vibration and acoustic noises to the PM motors. which degrades the control characteristics. Therefore, construction error should be minimized during the design process.

Fig. 5. Detent torque caused by construction error

3. Analysis Results of the Design

The original model and improved model are shown in Fig. 9. Fig. 6 shows the detent torque of original model and improved model designed by using DOE.

The detent torque distribution of the both conventional model and the improved model are shown in Fig. 6. Like in Fig. 9, the tapered pole shape lessens and there is less air gap between stator ploe and permanent magnet which is stator and when the width and height of pole is designed using DOE, it can be confirmed that detent torque is decreased. At this moment, detent torque of the modified model is diminished about 58.2% compared to the original model. As reluctance is increase in an air gap by tapered and saturation of pole is decrease by design of pole shape, this phenomenon is considered.

The comparison of the holding torque between the conventional model and the proposed model is shown in Fig. 7. If the holding torque is high, the motor is said to be robust to disturbances. This is why many motor designs are focused on increasing the holding torque. In this paper, the holding torque was computed when the motor is driven with 2 phase bipolar excitation method when a current of 0.27 A. The comparison of the holding torque between the conventional model and the proposed model is shown in Fig. 7. The holding torque was increased about 5.6%.

Fig. 8 shows the Back-EMF of the analysis model when the motor speed is 4050rpm ^[2].

Fig. 9 is shown tapered shape to decrease the detent torque. The tapered shape is due to decreasing the detent torque and the sine wave magnetic flux in the air gap.

Fig. 6. Detent torque waveforms

Fig. 7. Holding torque waveforms

Fig. 8. EMF waveforms

Fig. 9. Alternative topologies of PM claw pole stepping motor

4.Comparison between the Analysis Results and the Experimental Result

The proposed motor could not be manufactured because of its cost, but the validity was verified indirectly with the conventional claw pole motor.

Fig. 10 shows the experimental setup to measure the characteristics of the holding torque for the stepping motor by using the torque-meter.

After the stepping motor is connected with torque-meter, the torque is measured^[3].

The experimental result of the holding torque is shown in Fig. 11. Here the unit of y-axis is Nm×10-3 and gf˙is cm. As can be seen in the Figure, the shape of the simulation waveform is nearly the same as the measurement waveform. The cause of the error between the simulation and the experimental results are not considered a difficulty of complete magnetization in the permanent magnet during design process.

Fig. 10. Test equipment to measure the characteristics of the holding torque

Fig. 11. Experimental and simulation result of the holding torque

5. Conclusion

This paper analyzed a model which is consist of design parameters, tapered air gap, pole width, and pole high as they are considered to have an important effect in characteristic, using 3-D FEM and is optimized designed optimal using RSM. Using FEM and RSM together, the dersired results were achieved. Then comparing to simulation and experimental results of original model the propriety of this study was confirmed.

When the design detent decreasing and power improvement of PM claw pole stepping motors, this paper will br very useful in future.