مدل‌سازی الاستواستاتیک و طراحی بهینه مکانیزم منعطف لوزی

نوع مقاله : مقاله پژوهشی

نویسندگان

دانشکده مهندسی مکانیک، دانشگاه صنعتی امیرکبیر، تهران، ایران

چکیده

مکانیزم‌های منعطف به دلیل ساختار یکپارچه‌ای که دارند، برای موقعیت‌دهی دقیق و تقویت دامنه عملگرهای پیزوالکتریک طراحی و استفاده می‌شوند. مدل‌سازی رفتار سینماتیکی این مکانیزم‌ها به دلیل ساختار پیوسته و تغییر شکل الاستیک دارای چالش‌‌هایی می‌باشد. در این مقاله ابتدا روشی بر مبنای ماتریس ساختاری به نام روش‌ الاستواستاتیک برای مدل‌سازی استاتیکی مکانیزم‌های منعطف ارائه می‌گردد. نوآوری این مدل، در کاهش محاسبات، با به‌کارگیری تقریب چرخش و جابه‌جایی کوچک می‌باشد. به دلیل ساختار یکپارچه و ساده، مکانیزم‌ لوزی برای موقعیت‌دهی میکرونی و تقویت دامنه عملگرهای پیزوالکتریک مورد استفاده قرار می‌گیرد. هدف اصلی، طراحی و بهینه‌سازی ابعادی مکانیزم منعطف لوزی با استفاده از مدل‌سازی الاستواستاتیک می‌باشد. هدف از بهینه‌سازی ابعادی، دستیابی به بزرگ‌نمایی بالا و سختی ورودی کم می‌باشد تا استفاده از مکانیزم منجر به کاهش دامنه مؤثر پیزوالکتریک نگردد. برای این مکانیزم مدل المان محدود و همچنین مدل تجربی ساخته شده، و در نهایت، خطای مدل‌سازی الاستواستاتیک با شبیه‌سازی در نرم‌افزار المان محدود و نتایج تجربی مقایسه می‌شود. نتایج گرفته شده از آزمون­های تجربی نشان می‌دهد که مدل‌سازی انجام شده برای مکانیزم لوزی حدود 1.5درصد خطا دارد.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

Elastostatic Modeling and Optimal Design of Rhombic Compliant Mechanism

نویسندگان [English]

  • Mohammad Saeed Erami
  • Hamed Ghafarirad
  • Afshin Taghvaeipour
  • Pouya Firuzy Rad
Department of Mechanical Engineering, Amirkabir University of Technology, Tehran, Iran
چکیده [English]

Compliant mechanisms are designed and used for precise positioning and amplification of piezoelectric actuators Due to their integrated structure. Modelling the kinematic behaviour of these mechanisms has challenges due to their continuous structure and elastic deformation. This article presents a structural matrix-based method called the elastostatic method for static modelling of compliant mechanisms. The innovation of elastostatic modelling reduces calculations by approximating rotation and small displacement. The main goal of this research is to design and optimize the rhombus flexible mechanism using elastostatic modelling. This mechanism is optimized in such a way that, in addition to positioning, it has high magnification and low input stiffness. The rhombus mechanism has an integrated and simple structure and is used for micron positioning and piezoelectric actuator amplification. In this research, the rhombus mechanism has been modeled using the elastostatic method, and its dimensions have been optimized according to the parameters of the mechanism; For this purpose, it is necessary to check the modeling error. The modelling error is compared with simulation in finite element software and experimental results. The results show that the modelling used to design the rhombus mechanism has a 1.5% error compared to experimental results.

کلیدواژه‌ها [English]

  • Elastostatic Modelling
  • Compliant Mechanism
  • Rhombic Mechanism
  • Optimization
  • Mechanism Design
[1] S. Park, S. Yang, A mathematical approach for analyzing ultra precision positioning system with compliant mechanism, Journal of Materials Processing Technology, 164 (2005) 1584-1589.
[2] J.S. Cuellar, G. Smit, D. Plettenburg, A. Zadpoor, Additive manufacturing of non-assembly mechanisms, Additive Manufacturing, 21 (2018) 150-158.
[3] S. Kota, J. Joo, Z. Li, S.M. Rodgers, J. Sniegowski, Design of compliant mechanisms: applications to MEMS, Analog integrated circuits and signal processing, 29(1) (2001) 7-15.
[4] A.J. Fleming, Y.K. Yong, An ultrathin monolithic XY nanopositioning stage constructed from a single sheet of piezoelectric material, IEEE/ASME Transactions on Mechatronics, 22(6) (2017) 2611-2618.
[5] P. Ouyang, R. Tjiptoprodjo, W. Zhang, G. Yang, Micro-motion devices technology: The state of arts review, The International Journal of Advanced Manufacturing Technology, 38(5) (2008) 463-478.
[6] C.N. Wang, T.D.-M. Le, Optimization parameter for microgripper based on triple-stair compliant mechanism using GTs-TOPSIS, The International Journal of Advanced Manufacturing Technology, 120(11) (2022) 7967-7983.
[7] R. Bharanidaran, T. Ramesh, A modified post-processing technique to design a compliant based microgripper with a plunger using topological optimization, The International Journal of Advanced Manufacturing Technology, 93(1) (2017) 103-112.
[8] H.A. Sodano, D.J. Inman, G. Park, A review of power harvesting from vibration using piezoelectric materials, Shock and Vibration Digest, 36(3) (2004) 197-206.
[9] J. Granstrom, J. Feenstra, H.A. Sodano, K. Farinholt, Energy harvesting from a backpack instrumented with piezoelectric shoulder straps, Smart materials and structures, 16(5) (2007) 1810.
[10] X. Sun, B. Yang, A new methodology for developing flexure-hinged displacement amplifiers with micro-vibration suppression for a giant magnetostrictive micro drive system, Sensors and Actuators A: Physical, 263 (2017) 30-43.
[11] G. Song, V. Sethi, Vibration Control of Civil Structures using Piezoceramic Smart Materials, Engineering, Construction, and Operations in Challenging Environments: Earth and Space 2004,  (2004) 546-553.
[12] K.-q. Qi, Y. Xiang, C. Fang, Y. Zhang, C.-s. Yu, Analysis of the displacement amplification ratio of bridge-type mechanism, Mechanism and Machine Theory, 87 (2015) 45-56.
[13] K.-B. Choi, J.J. Lee, G.H. Kim, H.J. Lim, S.G. Kwon, Amplification ratio analysis of a bridge-type mechanical amplification mechanism based on a fully compliant model, Mechanism and Machine Theory, 121 (2018) 355-372.
[14] J. Khurana, B. Hanks, M. Frecker, Design for additive manufacturing of cellular compliant mechanism using thermal history feedback, in:  International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, American Society of Mechanical Engineers, 2018, pp. V02AT03A035.
[15] M. Wang, D. Ge, L. Zhang, J.L. Herder, Micro-scale Realization of Compliant Mechanisms: Manufacturing Processes and Constituent Materials—A Review, Chinese Journal of Mechanical Engineering, 34(1) (2021) 1-22.
[16] R. Clement, J. Huang, Z. Sun, J. Wang, W. Zhang, Motion and stress analysis of direct-driven compliant mechanisms with general-purpose finite element software, The International Journal of Advanced Manufacturing Technology, 65(9) (2013) 1409-1421.
[17] W. Bejgerowski, J.W. Gerdes, S.K. Gupta, H.A. Bruck, Design and fabrication of miniature compliant hinges for multi-material compliant mechanisms, The International Journal of Advanced Manufacturing Technology, 57(5) (2011) 437-452.
[18] M. Liu, X. Zhang, S. Fatikow, Design and analysis of a multi-notched flexure hinge for compliant mechanisms, Precision Engineering, 48 (2017) 292-304.
[19] Y. Tian, B. Shirinzadeh, D. Zhang, Closed-form compliance equations of filleted V-shaped flexure hinges for compliant mechanism design, Precision Engineering, 34(3) (2010) 408-418.
[20] N. Lobontiu, J.S. Paine, E. Garcia, M. Goldfarb, Design of symmetric conic-section flexure hinges based on closed-form compliance equations, Mechanism and machine theory, 37(5) (2002) 477-498.
[21] J. Chen, C. Zhang, M. Xu, Y. Zi, X. Zhang, Rhombic micro-displacement amplifier for piezoelectric actuator and its linear and hybrid model, Mechanical Systems and Signal Processing, 50 (2015) 580-593.
[22] G. Ye, W. Li, Y.-q. Wang, X.-f. Yang, L. Yu, Kinematics analysis of bridge-type micro-displacement mechanism based on flexure hinge, in:  The 2010 IEEE International Conference on Information and Automation, IEEE, 2010, pp. 66-70.
[23] X. Shen, L. Zhang, D. Qiu, A lever-bridge combined compliant mechanism for translation amplification, Precision Engineering, 67 (2021) 383-392.
[24] H. Wu, L. Lai, L. Zhu, Analytical model and experimental verification of an elliptical bridge-type compliant displacement amplification mechanism, Review of Scientific Instruments, 92(5) (2021) 055109.
[25] G. Haertling, Compositional study of PLZT Rainbow ceramics for piezo actuators, in:  Proceedings of 1994 IEEE International Symposium on Applications of Ferroelectrics, IEEE, 1994, pp. 313-318.
[26] L.L. Howell, A. Midha, T.W. Norton, Evaluation of equivalent spring stiffness for use in a pseudo-rigid-body model of large-deflection compliant mechanisms,  (1996).
[27] S. Wu, Z. Shao, H. Su, H. Fu, An energy-based approach for kinetostatic modeling of general compliant mechanisms, Mechanism and Machine Theory, 142 (2019) 103588.
[28] M. Korayem, H. Rahimi, A. Nikoobin, M. Nazemizadeh, Maximum allowable dynamic payload for flexible mobile robotic manipulators, Latin American applied research, 43(1) (2013) 29-35.
[29] T. Yeom, T.W. Simon, M. Zhang, M.T. North, T. Cui, High frequency, large displacement, and low power consumption piezoelectric translational actuator based on an oval loop shell, Sensors and Actuators A: Physical, 176 (2012) 99-109.
[30] F. Ma, G. Chen, Modeling large planar deflections of flexible beams in compliant mechanisms using chained beam-constraint-model, Journal of Mechanisms and Robotics, 8(2) (2016).
[31] X. Pei, J. Yu, G. Zong, S. Bi, An effective pseudo-rigid-body method for beam-based compliant mechanisms, Precision Engineering, 34(3) (2010) 634-639.
[32] E. Abele, S. Rothenbücher, M. Weigold, Cartesian compliance model for industrial robots using virtual joints, Production Engineering, 2(3) (2008) 339-343.
[33] S. Shi, H. Wu, Y. Song, H. Handroos, M. Li, Y. Cheng, B. Mao, Static stiffness modelling of EAST articulated maintenance arm using matrix structural analysis method, Fusion Engineering and Design, 124 (2017) 507-511.
[34] S. Grazioso, G.D. Gironimo, L. Rosati, B. Siciliano, Modeling and simulation of hybrid soft robots using finite element methods: Brief overview and benefits, in:  International Symposium on Advances in Robot Kinematics, Springer, 2020, pp. 335-340.
[35] A. Taghvaeipour, J. Angeles, L. Lessard, On the elastostatic analysis of mechanical systems, Mechanism and Machine Theory, 58 (2012) 202-216.
[36] M. Ling, J. Cao, M. Zeng, J. Lin, D.J. Inman, Enhanced mathematical modeling of the displacement amplification ratio for piezoelectric compliant mechanisms, Smart Materials and Structures, 25(7) (2016