Topology Optimization of Flywheel Rotors Using SIMP Method: A Preliminary Study

Article Preview

Abstract:

Flywheels are kinetic energy storage and retrieval devices as chemical batteries. However, the high charge and discharge rates, as well as the high cycling capability make flywheels attractive as compared to other energy storage devices. This research serves as a preliminary study that aims for developing a technique in designing a flywheel rotor based on the solid isotropic method with penalization (SIMP) method. Examples are presented to illustrate the optimum structural layouts obtained given various design objectives. For a static rotor, the objectives are maximizing the first torsional natural frequency, maximizing the moment of inertia and maximizing both of them, respectively. The problem is formulated using bound formulation and the method of moving asymptotes (MMA), a first-order optimization technique, was employed. Therefore the design sensitivity becomes a necessity. The so-called checkerboard problem in the topology optimization is avoided using the nodal design variable. Also, a threshold is used to reduce the numerical imperfection in each iteration. For the topology design of a rotating rotor, the centrifugal force induced in the high-speed rotation is considered. The objective is to maximize the rotor stiffness and is demonstrated in the last example. Results show clear topology layout of flywheel was obtained using proposed method.

You might also be interested in these eBooks

Info:

Periodical:

Pages:

427-434

Citation:

Online since:

October 2012

Authors:

Export:

Price:

Permissions CCC:

Permissions PLS:

Сopyright:

© 2012 Trans Tech Publications Ltd. All Rights Reserved

Share:

Citation:

[1] V. Prakash, M.R. Vadiraj, D.N. Venkatesh, and U. Shrinivasa, Parametric study of crankshaft natural frequencies, SAE Tech. pap. 940698, (1994).

DOI: 10.4271/940698

Google Scholar

[2] P. Carrato, and C. Fu, Modal analysis techniques for torsional vibration of diesel crankshafts, SAE Tech. pap. 861225, (1986).

DOI: 10.4271/861225

Google Scholar

[3] J. Du, N. Olhoff, Topological design of freely vibrating continuum structures for maximum values of simple and multiple eigenfrequencies and frequency gaps, Struct. Multidisc. Optim., 34 (2007) 91–110.

DOI: 10.1007/s00158-007-0101-y

Google Scholar

[4] J. Du, N. Olhoff, Topology optimization of continuum structures with respect to simple and multiple eigenfrequencies, In: Proceedings of the 6th World Congresses of Structural and Multidisciplinary Optimization, Rio de Janeiro, Brazil, (2005).

Google Scholar

[5] J.S. Jensen, N.L. Pedersen, On maximal eigenfrequency separation in two-material structures: the 1D and 2D scalar cases, J. Sound Vib., 289 (2006) 967-986.

DOI: 10.1016/j.jsv.2005.03.028

Google Scholar

[6] N.L. Pedersen, Maximization of eigenvalues using topology optimization, Struct. Multidisc. Optim., 20 (2000) 2-11.

DOI: 10.1007/s001580050130

Google Scholar

[7] N.L. Pedersen, Topology optimization of laminated plates with prestress, Comput. Struct., 80 (2002) 559-570.

DOI: 10.1016/s0045-7949(02)00026-3

Google Scholar

[8] D. Tcherniak, Topology optimization of resonating structures using SIMP method, Int. J. Numer. Meth. Eng., 54 (2002) 1605–1622.

DOI: 10.1002/nme.484

Google Scholar

[9] K. Svanberg, The method of moving asymptotes-a new method for structural optimization, Int. J. Numer. Meth. Eng., 24 (1987) 359–373.

DOI: 10.1002/nme.1620240207

Google Scholar

[10] C.S. Jog, R.B. Haber, Stability of finite element models for distributed-parameter optimization and topology design, Comput. Meth. Appl. Mech. Eng., 130 (1996) 203-226.

DOI: 10.1016/0045-7825(95)00928-0

Google Scholar

[11] K. Matsui, K. Terada, Continuous approximation of material distribution for topology optimization, Int. J. Numer. Meth. Eng., 59 (2004) 1925-(1944).

DOI: 10.1002/nme.945

Google Scholar

[12] S. Rahmatalla, C.C. Swan, Form finding of sparse structures with continuum topology optimization, J. Struct. Eng., 129 (2003) 1707-1716.

DOI: 10.1061/(asce)0733-9445(2003)129:12(1707)

Google Scholar

[13] S.F. Rahmatalla, C.C. Swan, A Q4/Q4 continuum structural topology optimization implementation, Struct. Multidisc. Optim., 27 (2004) 130-135.

DOI: 10.1007/s00158-003-0365-9

Google Scholar

[14] N. Olhoff, J Du, Topological design of continuum structures subjected to forced vibration, In: Proceedings of the 6th World Congresses of Structural and Multidisciplinary Optimization, Rio de Janeiro, Brazil (2005).

Google Scholar