Abstract
The design of vibratory feeders ensuring effective product feeding is particularly demanding since the flexibility of the device components severely affects the dynamic response. Traditional design approaches are based on expensive and time-consuming trial and error iterations, which include building and testing tentative devices. In order to overcome these limitations, this paper proposes a novel systematic approach for designing linear vibratory feeders, based on an inverse dynamic structural modification approach. After synthesising a reduced-order model, the design is cast as an inverse eigenvalue problem and solved numerically through the minimization of a convex quadratic function. Constraints on the design variables, i.e. inertial and elastic parameters, are represented through a convex domain and included in the optimization problem. The numerical and experimental results obtained prove the effectiveness of the method and its ease of application, that make is suitable for both the design of new feeders and the optimization of existing ones.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Redford AH, Boothroyd G (1967) Vibratory feeding. Proc Inst Mech Eng 182(1):135–152
Lim GH (1997) On the conveying velocity of a vibratory feeder. Comput Struct 62(1):197–203. doi:10.1016/S0045-7949(96)00223-4
Kerita JN (2008) Optimum vibration angle for transporting granular materials on linear conveyors. Int J Precis Eng Manuf 9(2):3–7
Ramalingam M, Samuel GL (2009) Investigation on the conveying velocity of a linear vibratory feeder while handling bulk-sized small parts. Int J Adv Manuf Technol 44(3–4):372–382
Erdesz K, Nemeth J (1988) Methods of calculation of vibrational transport rate of granular materials. Powder Technol 55(3):161–170. doi:10.1016/0032-5910(88)80100-1
Okabe S, Yokoyama Y, Boothroyd G (1988) Analysis of vibratory feeding where the track has directional friction characteristics. Int J Adv Manuf Technol 3(4):73–85. doi:10.1007/BF02601835
Liangsheng W (2003) Direct method of inverse eigenvalue problems for structure redesign. ASME J Mech Des 125:845–847
Bucher I, Braun S (1992) The structural modification inverse problem: an exact solution. Mech Syst Signal Process 7(3):217–238
Li T, He J (1999) Local structural modification using mass and stiffness changes. Eng Struct 21:1028–1037
Kyprianou A, Mottershead JE, Ouyang H (2004) Assignment of natural frequencies by an added mass and one or more springs. Mech Syst Signal Process 18:263–289
Park YH, Park YS (2000) Structural modification based on measured frequency response functions: an exact eigenproperties reallocation. J Sound Vib 237(3):411–426
Hernandes JA, Suleman A (2014) Structural synthesis for prescribed target natural frequencies and mode shapes. Shock and Vib 2014, Article ID 173786, 8 pages. doi: 10.1155/2014/173786
Richiedei D, Trevisani A, Zanardo G (2011) A constrained convex approach to modal design optimization of vibrating systems. ASME J Mech Des 133(6)
Ouyang H, Richiedei D, Trevisani A, Zanardo G (2012) Eigenstructure assignment in undamped vibrating systems: a convex-constrained modification method based on receptances. Mech Syst Signal Process 27:397–409
Ouyang H, Richiedei D, Trevisani A, Zanardo G (2012) Discrete mass and stiffness modifications for the inverse eigenstructure assignment in vibrating systems: theory and experimental validation. Int J Mech Sci 64(1):211–220
Hernandes JA, Ferreira RTL, de Faria AR., Meleiro RM (2008) An assessment of structural optimization using Catia V5. SAE Technical Paper. No. 2008-36-0183
Palomba I, Richiedei D, Trevisani A (2014) A ranking method for the selection of the interior modes of reduced order resonant system models, Proceedings of the ASME 2014 12th Biennial Conference on Engineering Systems Design and Analysis ESDA2014 June 25–27, 2014, Copenhagen, Denmark
Hehenberger P, Follmer M, Geirhofer R, Zeman K (2013) Model-based system design of annealing simulators. Mechatronics 23:247–256
Hehenberger P (2014) Perspectives on hierarchical modeling in mechatronic design. Adv Eng Inform 28(3):188–197
Caracciolo R, Richiedei D (2014) Optimal design of ball-screw driven servomechanisms through an integrated mechatronic approach. Mechatronics 24(7):819–832. doi:10.1016/j.mechatronics.2014.01.004
Van Den Berg S, Mohanty P, Rixen DJ (2004) Investigating the causes of non-uniform cookie flow in vibratory conveyors: part 1. Exp Tech 28:46–49
Van Den Berg S, Mohanty P, Rixen DJ (2004) Investigating the causes of non-uniform cookie flow in vibratory conveyors: part 2. Exp Tech 29:32–35
Grant M, Boyd S (2008) Graph implementations for non smooth convex programs. Recent advances in learning and control (a tribute to M. Vidyasagar), V. Blondel, S. Boyd, and H. Kimura, Lecture Notes in Control and Information Sciences, Springer. http://stanford.edu/~boyd/graph_dcp.html.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Caracciolo, R., Richiedei, D., Trevisani, A. et al. Designing vibratory linear feeders through an inverse dynamic structural modification approach. Int J Adv Manuf Technol 80, 1587–1599 (2015). https://doi.org/10.1007/s00170-015-7096-0
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00170-015-7096-0