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تحلیل دینامیکی میکرو المان منعطف موازی با مدل قیدی تیر و تئوری گرادیان کرنشی اصلاح یافته | ||
| نشریه مهندسی مکانیک امیرکبیر | ||
| مقاله 6، دوره 54، شماره 4، تیر 1401، صفحه 821-842 اصل مقاله (2.55 M) | ||
| نوع مقاله: مقاله پژوهشی | ||
| شناسه دیجیتال (DOI): 10.22060/mej.2022.20518.7251 | ||
| نویسندگان | ||
| محمد ارحامی1؛ حمید معین فرد* 2 | ||
| 1دانشکده مهندسی، دانشگاه فردوسی مشهد، ایران | ||
| 2دانشکده مهندسی، دانشگاه فردوسی مشهد، ایران -قطب علمی رایانش نرم و پردازش هوشمند اطالعات، دانشگاه فردوسی مشهد، ایران | ||
| چکیده | ||
| در این پژوهش، رفتار دینامیکی میکرو المان منعطف موازی تحت بار انتهایی، مورد بررسی قرار می‌گیرد. ابتدا با تئوری گرادیان کرنشی اصلاح یافته و به کمک مدل قیدی تیر، انرژی کرنشی یک میکرو تیر منعطف، برحسب مؤلفه‌های جابجایی انتهای تیر به دست آمده، و از آن برای تعیین انرژی کرنشی المان منعطف موازی استفاده می‌شود. در ادامه، با روش لاگرانژ، مدل دینامیکی میکرو المان منعطف استخراج شده و حول نقطه تعادل، خطی‌سازی می‌گردد. سپس محدوده مجاز برای اعمال نیروهای استاتیکی به سکوی حرکتی، به نحوی که هم تئوری مورد استفاده از دقت کافی برخوردار باشد، و هم پایداری دینامیکی سیستم تحت اغتشاشات دینامیکی کوچک خدشه‌دار نشود، مشخص می‌گردد. نتایج بدست آمده حاکی از این است که تئوری الاستیسیته کلاسیک، سخت‌گیری بیش از حدی برای مشخص کردن دقیق ناحیه پایداری مکانیزم دارد. همچنین فرکانس‌های طبیعی سیستم نیز استخراج شده و اثر ابعاد و مؤلفه‌های استاتیکی نیرو بر آن‌ها، مورد مطالعه قرار گرفته است. مشاهده می‌شود که با کاهش ابعاد، فرکانس طبیعی بی‌بعد عرضیِ سیستم افزایش می‌یابد، اما فرکانس طبیعی بی‌بُعد طولی سیستم، به دلیل عدم وجود گرادیان کرنش در مُد طولی، ثابت می‌ماند. همچنین مشاهده شد که نیروی استاتیکی کششی باعث افزایش، و نیروی استاتیکی خمشی باعث کاهش فرکانس‌های طبیعی سیستم می‌شوند. با توجه به بی‌بعد بیان شدن روابط و نتایج ارائه شده در این پژوهش، می‌توانند به سادگی برای تحلیل دینامیکی مکانیزم‌های منعطف پیچیده‌تر، استفاده شوند. | ||
| کلیدواژه‌ها | ||
| المان منعطف موازی؛ مدل قیدی تیر؛ تحلیل دینامیکی؛ تئوری گرادیان کرنشی؛ تحلیل پایداری | ||
| عنوان مقاله [English] | ||
| Dynamic Analysis of Micro -Scale Parallelogram Flexures Using Beam Constraint Model and Modified Strain Gradient Theory | ||
| نویسندگان [English] | ||
| Mohammad Arhami1؛ Hamid Moeenfard2 | ||
| 1PhD Student, School of Mechanical Engineering, Ferdowsi University of Mashhad, Mashhad, Iran | ||
| 2Associate Professor, School of Mechanical Engineering, Ferdowsi University of Mashhad, Mashhad, Iran Center of Excellence in Soft Computing and Intelligent Information Processing (SCIIP), Ferdowsi University of Mashhad, Mashhad, Iran | ||
| چکیده [English] | ||
| In this paper, the dynamic behavior of a small-scale parallelogram (P) flexure is studied. First, using the beam constrain model and the modified strain gradient theory, the nonlinear strain energy of a small-scale beam is obtained in terms of its tip displacements. This energy expression is utilized to derive the strain energy of a P-flexure. Then the governing dynamic equations of motion are derived using Lagrange equations and are linearized around the operating equilibrium point. This linear model is employed to determine the allowable forces which do not lead to instability of the system. Moreover, the natural frequencies of the system are also extracted and the size effect as well as the static components of the applied loads on them are studied in detail. It is observed that by reducing the dimensions, the normalized transverse natural frequency of the system is increased. However, since there is no strain gradient in an axial mode, the axial normalized frequency is remained constant reducing the dimensions of the system. Moreover, it was observed that the tensile static forces lead to an increase, and transverse forces lead to a decrease in normalized natural frequency of the system. The procedure utilized for dynamic modeling of parallelogram flexures in this paper can be further extended for modeling more complex flexure systems. | ||
| کلیدواژه‌ها [English] | ||
| Parallelogram flexure, Beam constraint model, Dynamic analysis, Modified strain gradient theory, Stability analysis | ||
| مراجع | ||
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[1] L.L. Howell, Compliant mechanisms, in: 21st Century Kinematics, Springer, 2013, pp. 189-216. [2] L.L. Howell, S.P. Magleby, B.M. Olsen, Handbook of compliant mechanisms, John Wiley & Sons, 2013. [3] C.-H. Liu, G.-F. Huang, C.-H. Chiu, T.-Y. Pai, Topology synthesis and optimal design of an adaptive compliant gripper to maximize output displacement, Journal of Intelligent & Robotic Systems, 90(3-4) (2018) 287-304. [4] M. Lofroth, E. Avci, Development of a novel modular compliant gripper for manipulation of micro objects, Micromachines, 10(5) (2019) 313. [5] X. Zhang, X. Xiang, Y. Wang, G. Ding, X. Xu, Z. Yang, A Heterogeneous Integrated MEMS Inertial Switch With Compliant Cantilevers Fixed Electrode and Electrostatic Locking to Realize Stable On-State, Journal of Microelectromechanical Systems, 28(6) (2019) 977-986. [6] Q. Xu, Z. Yang, B. Fu, J. Li, H. Wu, Q. Zhang, Y. Sun, G. Ding, X. Zhao, A surface-micromachining-based inertial micro-switch with compliant cantilever beam as movable electrode for enduring high shock and prolonging contact time, Applied Surface Science, 387 (2016) 569-580. [7] Q.-D. Truong, D.-A. Wang, Design and characterization of a mouse trap based on a bistable mechanism, Sensors and Actuators A: Physical, 267 (2017) 360-375. [8] N. Le Chau, N.T. Tran, T.-P. Dao, A multi-response optimal design of bistable compliant mechanism using efficient approach of desirability, fuzzy logic, ANFIS and LAPO algorithm, Applied Soft Computing, 94 (2020) 106486. [9] M.M. Elsisy, M.H. Arafa, C.A. Saleh, Y.H. Anis, Modeling of a Symmetric Five-Bar Displacement Amplification Compliant Mechanism for Energy Harvesting, Sensors, 21(4) (2021) 1095. [10] M.A. Abdelnaby, M. Arafa, Energy harvesting using a flextensional compliant mechanism, Journal of Intelligent Material Systems and Structures, 27(19) (2016) 2707-2718. [11] A. Zhang, G. Chen, A comprehensive elliptic integral solution to the large deflection problems of thin beams in compliant mechanisms, Journal of Mechanisms and Robotics, 5(2) (2013). [12] L. Campanile, A. Hasse, A simple and effective solution of the elastica problem, Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 222(12) (2008) 2513-2516. [13] P. Liu, P. Yan, Modeling and Analysis of Beam Flexure Based Double Parallel Guiding Mechanisms: A Modified Pseudo-Rigid-Body Approach, in: ASME 2016 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, 2016. [14] S. Awtar, S. Sen, A generalized constraint model for two-dimensional beam flexures: Nonlinear strain energy formulation, Journal of mechanical Design, 132(8) (2010). [15] G. Chen, F. Ma, G. Hao, W. Zhu, Modeling large deflections of initially curved beams in compliant mechanisms using chained beam constraint model, Journal of Mechanisms and Robotics, 11(1) (2019) 011002. [16] S. Awtar, A.H. Slocum, Closed-form nonlinear analysis of beam-based flexure modules, in: ASME 2005 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, American Society of Mechanical Engineers Digital Collection, 2005, pp. 101-110. [17] S. Awtar, S. Sen, A Generalized Constraint Model for Two-Dimensional Beam Flexures: Nonlinear Load-Displacement Formulation, Journal of Mechanical Design, 132(8) (2010). [18] S. Awtar, A.H. Slocum, E. Sevincer, Characteristics of beam-based flexure modules, (2007). [19] S. Sen, S. Awtar, Nonlinear strain energy formulation of a generalized bisymmetric spatial beam for flexure mechanism analysis, Journal of Mechanical Design, 136(2) (2014). [20] M. Bakhtiari-Shahri, H. Moeenfard, Topology optimization of fundamental compliant mechanisms using a novel asymmetric beam flexure, International Journal of Mechanical Sciences, 135 (2018) 383-397. [21] H. Malaeke, H. Moeenfard, A novel flexure beam module with low stiffness loss in compliant mechanisms, Precision Engineering, 48 (2017) 216-233. [22] 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). [23] C. He, Q. Xie, Z. Yang, S. Xue, Modelling large planar deflections of flexible bundled conductors in substations using a modified chained-beam constraint model, Engineering Structures, 185 (2019) 278-285. [24] H. Moeenfard, S. Awtar, Modeling geometric nonlinearities in the free vibration of a planar beam flexure with a tip mass, Journal of Mechanical Design, 136(4) (2014). [25] M. Radgolchin, H. Moeenfard, Analytical modeling of nonlinear flexural-extensional vibration of flexure beams with an interconnected compliant element, Mechanics Research Communications, 89 (2018) 23-33. [26] M.N. Aghaei, H. Moeenfard, M. Moavenian, Nonlinear extensional-flexural vibrations in variable cross section beams with eccentric intermediate mass, International Journal of Mechanical Sciences, 196 (2021) 106248. [27] H. Malaeke, H. Moeenfard, Analytical modeling of large amplitude free vibration of non-uniform beams carrying a both transversely and axially eccentric tip mass, Journal of Sound and Vibration, 366 (2016) 211-229. [28] M.B. Akbarzadeh, H. Moeenfard, S. Awtar, Nonlinear dynamic modeling of a parallelogram flexure, Mechanism and Machine Theory, 153 (2020) 103985. [29] C.J. Silva, M.F. Daqaq, Nonlinear flexural response of a slender cantilever beam of constant thickness and linearly-varying width to a primary resonance excitation, Journal of Sound and Vibration, 389 (2017) 438-453. [30] M.R. Sayag, E.H. Dowell, Linear versus nonlinear response of a cantilevered beam under harmonic base excitation: theory and experiment, Journal of Applied Mechanics, 83(10) (2016). [31] S. Iqbal, R.I. Shakoor, Y. Lai, A.M. Malik, S.A. Bazaz, Experimental evaluation of force and amplification factor of three different variants of flexure based micro displacement amplification mechanism, Microsystem Technologies, 25(7) (2019) 2889-2906. [32] A. Vafaie, M. Tahmasebipour, Y. Tahmasebipour, A novel capacitive micro-accelerometer made of steel using micro wire electrical discharge machining method, Journal of Micromechanics and Microengineering, 29(12) (2019) 125018. [33] Y. Gao, C. Yan, H. Huang, T. Yang, G. Tian, D. Xiong, N. Chen, X. Chu, S. Zhong, W. Deng, Microchannel‐Confined MXene Based Flexible Piezoresistive Multifunctional Micro‐Force Sensor, Advanced Functional Materials, 30(11) (2020) 1909603. [34] P. Trocha, M. Karpov, D. Ganin, M.H. Pfeiffer, A. Kordts, S. Wolf, J. Krockenberger, P. Marin-Palomo, C. Weimann, S. Randel, Ultrafast optical ranging using microresonator soliton frequency combs, Science, 359(6378) (2018) 887-891. [35] A. Kravchenko, V. Komenko, W.-J. Fischer, Silicon-On-Nothing Micro-Pirani Gauge for Interior-Pressure Measurement, in: Multidisciplinary Digital Publishing Institute Proceedings, 2018, pp. 1079. [36] A. Jain, Development of Indigenous Micro-gyroscope Technology, (2019). [37] S. Afrang, H. Mobki, M. Hassanzadeh, G. Rezazadeh, Design and simulation of a MEMS analog micro-mirror with improved rotation angle, Microsystem Technologies, 25(3) (2019) 1099-1109. [38] B. Leimkuhler, C. Matthews, Molecular Dynamics, Springer, 2016. [39] V. Parvaneh, M. Shariati, A.M.M. Sabeti, Investigation of vacancy defects effects on the buckling behavior of SWCNTs via a structural mechanics approach, European Journal of Mechanics-A/Solids, 28(6) (2009) 1072-1078. [40] S. Karparvarfard, M. Asghari, R. Vatankhah, A geometrically nonlinear beam model based on the second strain gradient theory, International Journal of Engineering Science, 91 (2015) 63-75. [41] J.G. Korvink, E.B. Rudnyi, A. Greiner, Z. Liu, MEMS and NEMS simulation, in: MEMS: a practical guide to design, analysis, and applications, Springer, 2006, pp. 93-186. [42] J.A. Pelesko, D.H. Bernstein, Modeling Mems and Nems, CRC press, 2002. [43] F. Yang, A. Chong, D.C.C. Lam, P. Tong, Couple stress based strain gradient theory for elasticity, International Journal of Solids and Structures, 39(10) (2002) 2731-2743. [44] D.C. Lam, F. Yang, A. Chong, J. Wang, P. Tong, Experiments and theory in strain gradient elasticity, Journal of the Mechanics and Physics of Solids, 51(8) (2003) 1477-1508. [45] F. Rajabi, S. Ramezani, A nonlinear microbeam model based on strain gradient elasticity theory, Acta Mechanica Solida Sinica, 26(1) (2013) 21-34. [46] R.S. Joshi, A.C. Mitra, S.R. Kandharkar, Design and analysis of compliant micro-gripper using pseudo rigid body model (PRBM), Materials Today: Proceedings, 4(2) (2017) 1701-1707. [47] B. Ding, Y. Li, Design and analysis of a decoupled XY micro compliant parallel manipulator, in: 2014 IEEE International Conference on Robotics and Biomimetics (ROBIO 2014), IEEE, 2014, pp. 1898-1903. [48] T.-P. Dao, S.-C. Huang, Design and analysis of a compliant micro-positioning platform with embedded strain gauges and viscoelastic damper, Microsystem Technologies, 23(2) (2017) 441-456. [49] J. Reddy, Nonlocal theories for bending, buckling and vibration of beams, International Journal of Engineering Science, 45(2-8) (2007) 288-307. [50] M. Kahrobaiyan, M. Asghari, M. Rahaeifard, M. Ahmadian, A nonlinear strain gradient beam formulation, International Journal of Engineering Science, 49(11) (2011) 1256-1267. [51] F. Beer, E. Johnston, J. DeWolf, D. Mazurek, Mechanics of Materials. 7th_Edition, New York. MeGraw-Hill Education Ltd, (2015). [52] L. Cui, C. Okwudire, S. Awtar, Modeling complex nonminimum phase zeros in flexure mechanisms, Journal of Dynamic Systems, Measurement, and Control, 139(10) (2017). | ||
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