Relationship between number of teeth and positioning accuracy on cylindrical magnetic gear

Transcription

1 International Journal of Applied Electromagnetics and Mechanics 45 (2014) DOI /JAE IOS Press Relationship between number of teeth and positioning accuracy on cylindrical magnetic gear Yoshinori Ando a,, Akira Baba b, Takuya Onuma b, Iwanori Murakami a and Kou Yamada a a Division of Mechanical Science and Technology, Gunma University, Tenjin-cho, Kiryu, Japan b Department of Mechanical System Engineering, Gunma University, Tenjin-cho, Kiryu, Japan Abstract. A magnetic gear can transmit a torque and a motion without the contact by the magnetic force. Today a magnetic gear are studied about increasing transmit torque and decreasing cogging torque. The property of the positioning is another significant property in use of a motion transmission by magnetic gears. Therefore it is important to measure the positioning property. The purpose of this research is to check the relationship between the number of the magnet of the gear and positioning property. Then we have developed three types of gear which have a different number of teeth severally. By using the developed three types of gear, the average and the standard deviation are calculated from experimental results. We reveal the influence of the number of the teeth to positioning property in several operation conditions. Keywords: Magnetic gear, positioning accuracy, number of teeth, magnetic flux leakage 1. Introduction A magnetic gear can transmit a torque and a motion without the contact by the magnetic force. So problems on the wear, the dust and the noise occurred by the contact of the gear s tooth can be solved. About transmitting a torque, magnetic gears have been studied about increasing the maximum transmitted torque and decreasing the cogging torque [1 7]. On transmitting a motion, the positioning property has almost not studied. The positioning accuracy of a magnetic gear is required when the magnetic gear is used in a part of the joint of a robot arm. So we have studied about the positioning property of a magnetic gear [8,9]. In this paper we have interest in the number of gear s magnets which means the number of teeth. By using the developed three types of gears that have the same diameter and the different number of teeth, the average and the standard deviation of the positioning error of the output gear are calculated when the input gear rotated the specified angle. Then we reveal the influence of the number of the teeth to positioning property in several operation conditions. 2. Developed magnetic gear In this study three types of gears that have the same diameter and the different number of teeth are used. The gears that have 8, 16 and 24 teeth (4, 8 and 12 pole pairs) are named Type-A, Type-B and Corresponding author: Yoshinori Ando, Department of Mechanical System Engineering, Gunma University, Tenjincho, Kiryu , Japan. Fax: ; ando@gunma-u.ac.jp /14/$27.50 c 2014 IOS Press and the authors. All rights reserved

2 76 Y. Ando et al. / Relationship between number of teeth and positioning accuracy on cylindrical magnetic gear (a) Type-A (b) Type-B (c) Type-C Fig. 1. Developed magnetic gears. Fig. 2. Structure of magnetic gears. Fig. 3. Photo of measurement system. Type-C respectively. Figure 1 shows developed magnetic gears. The center part of the gears is electromagnetic iron and the magnet is neodymium. The direction of the magnetization is the radial direction. These magnets are attached on the surface of the center part alternately between N pole and S pole. The structure of the gears shows in Fig. 2. In the experiment, the same type gears are used at input and output side. So gear ratio is 1:1. 3. Measurement system Figures 3 and 4 show the photo and the structure of measurement system. The measurement system is divided into the input part and the output part Input part The input part is consists of a DC motor with an incremental encoder and a reduction device, an input shaft and an input gear. The encoder has 1000 pulse/rotation. This encoder named Encoder-I. By Encoder-I and the 1/100 reduction device which the DC motor has, the rotation angle of input gear is measured with pulse/rotation Output part The output par is consists of an absolute encoder, an output shaft, an output gear and an incremental encoder. The absolute encoder and the incremental encode are named Encoder-A and Encoder-O.

3 Y. Ando et al. / Relationship between number of teeth and positioning accuracy on cylindrical magnetic gear 77 PC AIO DIO Counter Encoder-A Absolute encoder Output gear Encoder-O Incremental encoder Power supply Encoder-I Incremental encoder DC motor Input gear Parallel movable plate Rail guide Fig. 4. Structure of measurement system. Encoder-A has 12 bit resolution and is used to set an initial position of the output gear. The rotation angle of the input gear is measured with pulse/rotation by Encoder-O. 4. Experimental method To measure the error of the output gear when the input gear is rotated by 360 degrees, the following steps are done. Step 1: By rotating the input gear the output gear is stop to specified angle θ A which is measured by Encoder-A. Step 2: The input gear is rotate. Then the input gear is stop when Z-phase signal of Encoder-I was received. At that time the positions of the input and the output gear are named θ I1 and θ O1. Step 3: The input gear is rotated by 360 degrees by controlling the DC motor. Then the rotation angle of the input and the output gear is measured by Encoder-I and Encoder-O severally. The positions of the input and the output gear are named θ I2 and θ O2 when these gears stop. The signal of z-phase of incremental encoder can be hardly determined uniquely by effect of the 1/100 reduction device. Then in Step 2 this signal is specified by doing Step 1. So in Step 3 the input gear is rotated from same position every time after Step 1 and Step 2 are executed. These 3 step operations are repeated 120 times. A different type gear is exchanged and the same experimental method is done. The error e of the output gear is calculated as follows; e = θ output θ input, (1) where θ output and θ input are the rotation angles of the output and input gears respectively. So, θ output is θ O2 θ O1 and θ input is θ I2 θ I1. And a standard deviation σ is calculated by following equations σ 2 = 1 n 1 n (e i ē) 2, i=1 (2) where n is the number of data, ē is an average of error.

4 78 Y. Ando et al. / Relationship between number of teeth and positioning accuracy on cylindrical magnetic gear (a) θ A 240 (b) θ A 251 (c) θ A Fig. 5. Stop position of Type-A. (a) Type-A (b) Type-C 5. Experimental results Fig. 6. Average and standard deviation of the error e (gap 3 mm). To check the influence of the teeth number to the positioning accuracy, two conditions are focused on. One is positions of magnets of input and output gear when those gear stop. So in experiment 1, the stop position of gears is changed. Another is the gap between the input and output gear. So, the gap is changed in experiment Experiment 1(change of stop position) After the 3-step operations in clause 4 are repeated 120 times at each position, the stop position is changed to the next position. The stop position can be changed by changing θ A in step1 of experimental method since the input gear is rotated 360 degree in step3 of experimental method. When θ A is specified to 240 degree, the center of the magnet of the teeth is on the line connecting the centers of the input and output shaft. The stop position of Type-A is shown in Fig. 5. The range of change of the stop position is the angle of one magnet. The gap is 3 mm and 10 mm. Figures 6 and 7 show results of 3 mm and 10 mm. The horizontal axis θ A indicates the position of the gears. So at the center of the graph, the center of magnets of the input and output gear faces each other and the break in magnets faces each other when gears stop at both ends of the graph.

5 Y. Ando et al. / Relationship between number of teeth and positioning accuracy on cylindrical magnetic gear 79 (a) Type-A (b) Type-C Fig. 7. Average and standard deviation of the error e (gap 10 mm). (a) Average (b) Standard deviation Fig. 8. Average and standard deviation of the error e. At 3 mm gap case of all type the standard deviation is large at the center of the graph and small at the both ends of the graph. It is confirmed that the stop position of magnets affects positioning property. Therefore the positioning property becomes hard to fluctuate for the stop position by reducing the number of teeth. The cause of this characteristic is mentioned with the simulation in the next clause. In result of 10 mm gap case, the influence by stop position to positioning property isn t confirmed. But compared with result of gap 3 mm, the difference of averages and standard deviations among 3 types gear becomes large. This characteristic is examined in following Experiment 2 (change of gap) After the 3 step operations in clause 4 are repeated 120 times, the gap is changed. Here, θ A in step1 is 240 degree and the gap is specified to 5 mm, 7 mm and 9 mm. Then, the relationship of positioning property and the number of teeth is checked with results of the experiment 2 and the experiment 1 when θ A in step1 is 240 degree. Since there is the risk of damage to the gear, the gap is not set to less than 3 mm. Figure 8 shows the average and the standard deviation of the error e. By the number of gear s teeth, the difference of the average and standard deviation become the larger as the gap becomes the larger. It is revealed that the number of teeth influences the positioning property. The positioning property of the gear which has fewer teeth is fine even if the gap becomes large. The cause of this characteristic is mentioned in with the simulation in next clause.

6 80 Y. Ando et al. / Relationship between number of teeth and positioning accuracy on cylindrical magnetic gear Table 1 Each θ A for number of Ns Ns Type-A Type-B Type-C (a) Front view (b) Top view Fig. 9. Model of Type-A and virtual line. Fig. 10. Average and standard deviation of the error e. 6. Simulation of the magnetic flux density The cause of characteristics of experiment 1 and 2 is supposed the difference of the magnetic flux density. So the magnetic flux density on the virtual line which is equal distance from the center of the input and output shaft is calculated in same condition as experiment1 and 2 with analysis software. Figure 9 shows the model of Type-A and the virtual line Simulation 1 (same condition as experiment 1) The position of gear is changed to the stop position of experiment 1 and the magnetic flux density on the virtual line is calculated. The calculated parallel magnetic flux density to the line connecting the center of the shaft of input and output gear shows in Fig. 10. To make the position of 3 type gears uniform in Fig. 10, the horizontal axis is used Stop position number N S.WhenN S is 1 and 7, the center of magnet of input and output gear faces each other. And when N S is 4, the break in magnets is faces each other. Table 1 shows the stop position of 3 type gears for N S. So at the center of the graph the center of magnets of the input and output gear faces each other and at both ends of the graph the break in magnets faces each other as well as Figs 6 and 7. The calculated magnetic flux density isn t constant for the position of the gear. In 3 types gear the calculate magnetic flux density is low at the center of graph of Fig. 10 and high at the both ends of the graph. From results of experiment 1 and simulation 1, in the position where the center of magnets faces each other the magnetic flux density is high so the standard deviation is small, and in the position where the break in magnets faces each other the magnetic flux density is low so the standard deviation is large.

7 Y. Ando et al. / Relationship between number of teeth and positioning accuracy on cylindrical magnetic gear 81 Fig. 11. The absolute value of calculated maximum magnetic flux density. (a) Gap 3 mm (b) Gap 10 mm (a) Gap 3 mm (b) Gap 10 mm Fig. 12. The magnetic flux density of Type-A. Fig. 13. The magnetic flux density of Type-C. Since the stop position of the gear s magnet influences the positioning accuracy, the positioning accuracy of the gear which has fewer teeth is hard to fluctuate for the stop position Simulation 2 (same condition as experiment 2) In the position where the center of magnets faces each other, the gap is changed and the magnetic flux density on the virtual line is calculated. Figure 11 shows the absolute value of parallel magnetic flux density to the line connecting the center of the shaft of the input and output gears for several gaps. When the gap becomes large, the difference of the magnetic flux density is large among 3 type gears. The magnetic flux density of the gear which has fewer teeth is hard to reduce even if the gap is larger. The cause of this characteristic is guessed to be the amount of the leakage flux. Since the change of gap is large relatively to the size of the magnet in the gear which has more teeth, the leakage flux is more when the gap becomes larger. Then the magnetic flux acting between gears reduces and the positioning accuracy becomes worse. The state of the leakage flux by simulation is shown in Figs 12 and 13. The leakage flux of Type-A can be confirmed at the edge of the magnet. The difference of state of the leakage flux between the gaps of 3 mm and 10 mm is small. In Type-C the leakage flux is same state as Type-A when the gap is 3 mm. But when the gap is 10 mm, the leakage flux of Type-C can be confirmed also at the center of the magnet. Therefore, the positioning property of the gear which has fewer teeth is fine since the leakage flux is small, even if the gap becomes large.

8 82 Y. Ando et al. / Relationship between number of teeth and positioning accuracy on cylindrical magnetic gear 7. Conclusion From the experiment and the simulation the relationship between the number of teeth and the positioning accuracy is confirmed. Since the stop position of gear s teeth influence positioning accuracy, the positioning accuracy of the gear which has fewer teeth is hard to fluctuate for the change of the stop position. Among 3 types gear there is the difference of the positioning accuracy when the gap is changed. The positioning accuracy of the gear which has fewer teeth is fine since the leakage flux is small, even if the gap becomes large. From the above, the gear which has fewer teeth is highly useful for the positioning accuracy. Acknowledgments The part of this study is a joint venture research with Oita Prefecture under Collaboration of Regional Entities for the Advancement of Technological Excellence program in sub theme of Technologies for Developing Next-generation Electromagnetic Devices. We also wish to specially thank Tomoyuki Fujita from Nissei Corporation for cooperation and technical advices. References [1] Y. Ando, M.A. Qurni, M. Ito, T. Ugajin, I. Murakami and K. Yamada, Development of magnetic gear device design and performance test for cylindrical magnetic gear, Journal of JSAEM 18 (2010), [2] Y. Ando, M.A. Qurni, N. Aziz, T. Ugajin, I. Murakami and K. Yamada, Dynamical performance test of cylindrical magnet gear, Journal of JSAEM 19(3) (2011), [3] Y. Ando, M.A. Qurni N. Aziz, I. Murakami and K. Yamada, Analysis and experiment of cylindrical magnetic gear, The Book of Abstract of The Seventh Japanese-Mediterranean and Central European Workshop on Applied Electromagnetic Engineering for Magnetic, Superconducting and Nano Materials (JAPMED 7), Budapest, Hungary, (2011), [4] K. Tsurumoto and Y. Kumasaka, Prototype production and design of a non-circular magnetic gear for practical applications (Power Magnetics), Journal of the Magnetics Society of Japan 28(3) (2004), [5] M. Yamamoto, K. Hirata and M. Matsumura, Study of a new magnetic gear, Journal of JSAEM 17(2) (2009), [6] M. Oka, T. Todaka, M. Enokizono and K. Nagaya, Magnetic filed analysis of planet-type magnetic gear by using 2- dimensional finite element method, Journal of JSAEM 18(2) (2010), [7] K. Atallah and D. Howe, A novel high-performance magnetic gear, IEEE Transactions on Magnetics 37(4) (2001), [8] Y. Ando, A. Baba, T. Ugajin, I. Murakami and K. Yamada, Measurement of properties of positioning of cylindrical magnetic gear, Proceedings of MAGDA (2011), [9] Y. Ando, A. Baba, T. Ugajin, I. Murakami and K. Yamada, Study on positioning repeatability of magnetic gear, Proceedings of APSAEM 2012 (2012),