||Adaptive Control for Active Magnetic Bearing Applied to Milling Process
||Department of Mechanical Engineering
Active Magnetic Bearing
Spindle Position Regulation
Fuzzy Logic Algorithm
模具為工業生產的基礎且模具之品質直接影響成品之品質，而其中金屬模具通常必須仰賴銑切程序製作。然而，產品生產所需耗費之能源以及所衍生之污染大多源自如金屬切削等加工製造過程。近年來由於全球逐漸關注環境保護以及能源節約之重要性，因此「綠色加工」之概念也越來越受重視。為改善配置傳統剛性軸承之機台於銑切過程中引發之問題，如軸承磨損導致之加工件尺寸誤差或油漬污染等缺點。本論文針對銑切製程提出整合高速馬達之磁浮銑切模組(High-Speed Magnetic Milling Module, HSM3)設計，整合項目包括：高速驅動馬達、創新內嵌式柱陣列型磁浮致動器(Embedded Cylindrical-Array Magnetic Actuator, ECAMA)以及用於偵測主軸偏擺之自間隙感測模組。本論文所提出之ECAMA為專門針對銑切主軸動態控制的非接觸式磁致動器，為大幅改善傳統主動式磁浮軸承(Active Magnetic Bearing, AMB)架構下磁控力不足之問題，ECAMA內之電磁線圈均纏繞於特別設計之「工字型」矽鋼鐵心上，並沿軸向排列以增加線阻匝數。一旦自間隙感測模組感測並回傳主軸偏擺之動態資訊後，便可以透過調變線圈電流達到主軸位置動態控制之目的。
本論文提出基於參考模型之模糊適應性控制(Fuzzy Model-Reference Adaptive Control, FMRAC)策略，並採用實驗法建立包括主軸動態、銑切動態以及電磁力之數學模型，以增強ECAMA於銑切製程下對主軸位置動態之調控效果。本論文所提出之ECAMA設計經實驗初步驗證，與同尺寸之傳統改良式AMB結構相比，可提昇磁控力約200%，換句話說，ECAMA較傳統式AMB更適合磁浮銑切應用。此外，ECAMA對於銑切主軸位置動態調控之性能，亦透過三種不同材質的加工工件實際切削以獲得實證。
Molding industry is the main basis for production and the quality of goods is directly dependent of the mold quality. Metal molds are usually developed by milling process. However, most energy consumption and induced pollutions occur during the manufacture process such as metal cutting. Therefore, Green Machining (GM) has been emphasized for environmental protection and reduction of energy consumption in the past decades. For the purpose to improve the defects for milling process caused by traditional bearings, e.g., the dimension discrepancy of finished workpiece due to bearing wear or oil pollution by lubricant, an innovative type of High-Speed Magnetic Milling Module (HSM3), which consists of a high-speed motor, a novel Embedded Cylindrical-Array Magnetic Bearing (ECAMA) and a gap self-sensing module for the measurement of spindle position deviation, is developed in this research for milling applications. The proposed ECAMA is a non-contact type of magnetic actuator and realistically employed to regulate the position deviation of milling spindle. To enhance the induced magnetic force, the coils are wound on the deliberately designed I-shape silicon steel cores, instead of conventional yokes. The I-shape silicon steel cores are constructed along the axial direction to reduce the radial size of ECAMA. Once the spindle position deviation is measured by the gap self-sensing module embedded in HSM3, the spindle can be regulated via the induced magnetic force by tuning the applied coil currents.
The control strategy, named as Fuzzy Model-Reference Adaptive Control (FMRAC) in this dissertation, is synthesized to account for the input nonlinearities of the spindle dynamics. In addition, in order to ensure the superior performance of spindle position regulation in realistic world, the models of spindle dynamics, milling process and induced magnetic force are all constructed by experiments.
The performance of the proposed ECAMA is verified and evaluated by experiments. In comparison with the traditional Active Magnetic Bearing (AMB) design, the magnetic attraction force by ECAMA can be increased by 200% under the same condition of identical overall size. That implies the proposed ECAMA has more promising potential to be equipped in the metal cutting machines than traditional AMBs. Based on the experimental results, the spindle position deviation can be successfully suppressed under various types of cutting force.
Table of Content...VI
List of Tables...XVII
List of Figures...XVIII
1.1 Evolution of Green Machining (GM)...3
1.2 Literature Review on Active Magnetic Bearing (AMB) and Modeling of Milling Dynamics...5
1.3 Research Motivation and Objectives...8
1.4 Organization of Dissertation...10
2. Design of High-Speed Magnetic Milling Module...13
2.1 Proposed High-Speed Magnetic Milling Module (HSM3)...13
2.1.1 Components of HSM3...13
2.1.2 Specification of HSM3...15
2.2 Embedded Cylindrical-Array Magnetic Actuator (ECAMA)...15
2.2.1 Components of ECAMA...15
2.2.2 Magnetic Flux Route Around Spindle and ECAMA...16
2.2.3 Induced Magnetic Force by ECAMA...17
2.2.4 Mathematical Model of Spindle Dynamics...19
3. Analysis of Magnetic Properties for Embedded Cylindrical-Array Magnetic Actuator...31
3.1 Specification of ECAMA...31
3.2 Design of Parameters...32
3.3 Analysis of Magnetic Flux Density...36
3.4 Characterization of Induced Magnetic Force...40
4. Adaptive Control for Spindle Position Regulation...53
4.1 Control Goals...54
4.2 Fuzzy Model-Reference Adaptive Control (FMRAC)...55
4.3 Modeling of Spindle and Cutting Dynamics...61
4.3.1 Modeling of Spindle Dynamics under Idle Mode...62
4.3.2 Modeling of Milling Dynamics...63
4.4 Performance of FMRAC...65
5. Experimental Setup and Simulation Results...77
5.1 Prototype of High-Speed Magnetic Milling Module (HSM3)...77
5.1.1 Components of HSM3...77
5.1.2 Measurement of Induced Magnetic Force by ECAMA...78
5.1.3 Characteristics of Self-Sensing Module for Spindle Position Deviation Measurement...79
5.2 Construction of Reference Spindle Dynamic Model and Fuzzy Milling Dynamic Model...80
5.2.1 Modeling of Spindle Dynamics...80
5.2.2 Modeling of Milling Dynamics...81
5.2.3 Fuzzy Models for Spindle Dynamics and Milling Dynamics...83
5.3 Performances Verification of High-Speed Magnetic Milling Module...84
5.3.1 Setup of Test Rig...84
5.3.2 Measurement of Spindle Position Deviation and Finish of Workpiece...85
6. Conclusions and Future Works...107
6.3 Future Works...110
Allaire P. E., Humphris R. R., Kelm R. D., “Dynamics of A Digitally Controlled Magnetic Bearing,” Nippon Kikai Gakkai Ronbunshu, Vol. 51, No. 465, pp. 1095-1100, 1985.
Auchet, S., Chevrier, P., Lacour, M., Lipinski, P., “A New Method of Cutting Force Measurement Based on Command Voltages of Active Electro-Magnetic Bearings,” International Journal of Machine Tools and Manufacture, Vol. 44, No. 14, pp. 1441-1449, 2004.
Cheng, Y., Adel, E. H., “Hybrid Adaptive Control of Two-link Flexible Manipulators Grasping Payload”, IEEE transactions on Automatic Control, Vol.30, pp. 201-216, 1995.
Chiang, S.-T., Tsai, C.-M., Lee, A.-C., “Analysis of Cutting Forces in Ball-End Milling,” Journal of Materials Processing Technology, Vol. 47, pp. 231-249, 1995.
Chiang, S.-T., Liu, D.-I., Lee, A., Chieng W., “Adaptive Control Optimization in End Milling Using Neural Network,” International Journal of Machines and Tools Manufacture, Vol. 34, pp. 637-660, 1995.
Closs, M., Buhler, P., Schweitzer, G., “Miniature Active Magnetic Bearing for Very High Rotational Speeds,” Proceedings of 6th International Symposium on Magnetic Bearings, Virginia, USA, 1998.
Craig, J. J., Hsu, P., Sastry, S. S., “Adaptive Control of Mechanical Manipulators,” The International Journal of Robotics Research, Vol. 6, No 2, pp. 16–28, 1987.
Elliott, H., “Hybrid Adaptive Control of Continuous Time System”, IEEE transactions on Automatic Control., Vol. 27, I. 2, pp.419-426, 1982.
Fukata, S., Yutani, K., Kouya, Y., “Characteristics of Magnetic Bearings Biased with Permanent Magnets in the Stator,” Japan Society of Mechanical Engineering, Series C, Vol. 41, No. 2, pp. 206–213, 1998.
Franklin, G. F., Powell, J. D., Abbas, E. N., “Feedback Control of Dynamics Systems 3rd Ed.,” Addison Wesley, 1994.
Hegazi, A. S., “Comparison Between Conventional and High Speed Milling Processes,” Journal of Engineering and Applied Science, Vol. 53, No. 1, pp, 45-61, 2006.
Imoberdorf, P., Zwyssig, C., Round, S. D., Kolar, J. W., “Combined Radial-Axial Magnetic Bearing for A 1 kW, 500,000 rpm Permanent Magnet Machine,” 22nd Annual IEEE Applied Power Electronics Conference, Anaheim, California, USA, 2007.
Kiu, J., Han, R., Zhang, L., Huo, H., “Study on Lubricating Characteristic and Tool Wear with Water Vapor as Coolant and Lubricant in Green Cutting,” Wear, Vol. 262, No. 3-4, pp. 442-452, 2007.
Kim, H., Lee, C., “Analysis of Eddy-current Loss for Design of Small Active Magnetic Bearings with Solid Core and Rotor,” IEEE Transactions on Magnetics, Vol. 40, No. 5, pp. 3293–3301, 2004.
Kim, M. K., Cho, M. W., Kim K., “Application of The Fuzzy Control Strategy to Adaptive Force Control of Non-Minimum Phase End Milling Operations,” International Journal of Machines and Tools Manufacture, Vol. 33, pp. 677-696, 1994.
Komori, M., Yamane, T., “Magnetic Levitation System with A Millimeter Sized Cylindrical Rotor,” Mechatronics, Vol. 10, pp. 595–607, 2000.
Kondo, T., “Environmentally Friendly Machining Technology,” Proceedings of the 7th International Conference on Machine on Tool Engineering, pp. 245-257, 1996.
Kuo, B. C., “Automatic Control Systems 7th,” Prentice Hall, 1997.
Kyung, J. H., Lee, C. W., “Controller Design for A Magnetically Suspended Milling Spindle Based on Chatter Stability Analysis,” Japan Society of Mechanical Engineering, Series C, Vol. 46, No. 2, pp. 416-422, 2003.
Lauderbaugh L. K., Ulsoy A. G., “Dynamic Modeling for Control of Milling Process,” Journal of Engineering for Industry, Vol. 110, No. 4, pp. 367-375, 1998.
Lee, C., Jeong, H., “Dynamic Modeling and Optimal Control of Coneshaped Active Magnetic Bearing System,” Control Engineering Practice, Vol. 4, pp. 1393–1403, 1996.
Li H. Z., Li X. P., Chen X. Q., “A Novel Chatter Stability Criterion for The Modeling and Simulation of The Dynamic Milling Process in The Time Domain,” International Journal of Advanced Manufacturing Technology, Vol. 22, No. 9-10, pp. 619-625, 2003.
Morita, N., Yoshida, Y., Kishioka, Sh., Ueno, Sh., Ueno, “Study on High-Speed Milling of Hard Materials,” Japan Society of Mechanical Engineers, Part C, Vol. 63, No. 616, pp. 4347-4353, 1997.
Maslen, E., Allaire, P., Noh, M., Sortore, C., “Magnetic Bearing Design for Reduced Power Consumption,” Journal of Tribology, Vol. 118, pp. 839–846, 1996.
Mohamed, A., Emad, F., “Conical Magnetic Bearings with Radial and Thrust Control,” IEEE Transaction on Automatic Control, Vol. 37, No. 12, pp. 1859–1868, 1992.
Peng Y. H., “On The Performance Enhancement of Self-Tuning Adaptive Control for Time-Varying Machining Processes,” International Journal Advanced Manufacturing Technology, Vol. 24, No. 5, pp. 395-403, 2004.
Spirig, M., Schmied, J., Jenckel, P., Kanne, U., “Three Practical Examples of Magnetic Bearing Control Design Using A Modern Tool,” Journal of Engineering for Gas Turbines and Power, Vol. 124, No. 4, pp. 1025-1031, 2002.
Swanson, E. E., Heshmat, H., Walton, II., “Performance of A Foil-Magnetic Hybrid Bearing,” Journal of Engineering for Gas Turbines and Power, Vol. 124, No. 2, pp. 375-382, 2002.
Storace, A. F., Sood, D., Lyons, J. P., Preston, M. A., “Integration of Magnetic Bearings in the Design of Advanced Gas Turbine Engines,” Journal of Engineering for Gas Turbines and Power, Vol. 117, No. 4, pp. 655-665, 1995.
Sortore, C., Allaire, P., Maslen, E., Humphris, R., Studer, P., “Permanent Magnet Biased Magnetic Bearings-design, Construction and Testing,” Proceedings of 2nd International Symposium on Magnetic Bearings, Tokyo Japan, 1990.
Tang, D. W., Wang, C. Y., Hu, Y. N., “Finite-Element Simulation of Conventional and High-Speed Peripheral Milling of Hardened Mold Steel,” Metallurgical and Materials Transactions A: Physical Metallurgy and Materials Science, Vol. 40, No. 13, pp. 3245-3257, 2009.
Tarng, Y. S., Hwang, S. T., “Adaptive Learning Control of Milling Operations,” Mechatronics, Vol. 5, pp. 937-948, 1995.
Tsai, N.-C., Shih, L.-W., Lee, R.-M., “Counterbalance of Cutting Force for Advanced Milling Operations,” Mechanical Systems and Signal Processing, Vol. 24, No. 4, pp. 1191-1208, 2010.
Tsai, N.-C., Hsu, S.-L., “On Sandwiched Magnetic Bearing Design,” Electromegnetics, Vol. 27, No. 6, pp. 371-385, 2007.
Tsai N.-C., Kuo C.-H., Lee R.-M., “Regulation on Radial Position Deviation for Vertical AMB Systems,” Mechanical System and Signal Processing, Vol. 21, pp. 2777-2793, 2007.
Wang, X., Yue, W., Han, Z., “Study on High Speed Cutting Technology for Green Manufacturing,” Advanced Materials Research, Vol. 305, pp. 25-30, 2011.
Wang, S.-M., Chiou, C.-H., Cheng, Y.-M., “An Improved Dynamic Cutting Force Model for End-Milling Process,” Journal of Materials Processing Technology, Vol. 148, pp. 317–327, 2004.
Wassim, H. M., Tomohisa, H., Sergey, N. G., “Hybrid Adaptive Control for Nonlinear Impulsive Dynamical Systems”, Proceedings of the American Control Conference, Denver, Colorado, USA, 2003.
Yang M. Y., Lee T. M., “Hybrid Adaptive Control Based on The Characteristics of CNC End Milling,” International Journal of Machine Tools & Manufacture, Vol. 42, pp. 489-499, 2002.
Zaman, M.T., Kumar, S. A., Rahamn, M., Sreeram, S., “A Three-Dimensional Analytical Cutting Force Model for Micro End Milling Operation,” International Journal of Machine Tools & Manufacture, Vol. 46, pp. 353–366, 2006.
Zhang, J. Z., Petros, I. A., “Safe Adaptive Control for Performance Improvement”, Proceedings of the 45th IEEE Conference on Decision & Control, San Diego, California, USA, 2006.