Minimization of vibration power transmission from rotating machinery to a flexible supporting plate

This paper deals with the problem of optimum design of a foundation for rotating machinery with a view to minimize vibration transmission from a machine source to its supporting structure. The problem of analysis and optimization of the installation systems of machinery has been extensively researched on the assumption of a rigid supporting structure. The design based on a rigid supporting structure model is reasonable for the installation of machinery in many real engineering situations. However, this rigid support based model may not be appropriate for the problem studied herein where the machinery is to be installed on a relatively flexible supporting plate. Thus, a generalized mathematical model of mobility power flow is developed in this paper, with a rotating machine as vibration source, resilient mounts as isolator, and a flexible supporting plate as receiver. The objective of minimizing vibration transmission is realized by optimization of stiffness coefficients of resilient mounts with a constraint on the vibration level of the machine. The design objective is chosen as the minimization of the power flow transmitted to the flexible supporting plate through the resilient mounts at the excitation frequency of the machinery. Both a single excitation frequency and a range of excitation frequencies are considered. A gradient-based mathematical programing method is selected for its advantage of efficiently solving the current type of optimization problem with multiple mounts and multi-degree-of-freedom vibration transmission. The sensitivities of the objective and the constraint functions with respect to the design variables are derived analytically. The design and performance of the optimized machinery foundation is illustrated and discussed using several numerical examples. The optimized mounting system is suitable for the installation case of a rotating machine with a low or medium service speed on a flexible supporting plate structure.

[1]  S. Ljunggren.  Generation of waves in an elastic plate by a vertical force and by a moment in the vertical plane , 1983 .

[2]  C. Jog.  Topology design of structures subjected to periodic loading , 2002 .

[3]  K. Y. Lam,et al.  DESIGN OPTIMIZATION OF MARINE ENGINE-MOUNT SYSTEM , 2000 .

[4]  Jakob Søndergaard Jensen,et al.  Topology optimization of dynamics problems with Padé approximants , 2007 .

[5]  P. S. Heyns,et al.  Vibration isolation of a mounted engine through optimization , 1995 .

[6]  M. F. Golnaraghi,et al.  Optimal design of passive linear suspension using genetic algorithm , 2004 .

[7]  J. Plunt,et al.  On effective mobilities in the prediction of structure-borne sound transmission between a source structure and a receiving structure, part I: Theoretical background and basic experimental studies , 1982 .

[8]  R. G. White,et al.  Vibrational power flow from machines into built-up structures, part III: Power flow through isolation systems , 1980 .

[9]  Amr M. Baz,et al.  Mechanical filtering characteristics of passive periodic engine mount , 2010 .

[10]  Ole Sigmund,et al.  Systematic design of phononic band–gap materials and structures by topology optimization , 2003, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[11]  Shilin Xie,et al.  Design optimization of machinery mounting systems with an elastic support structure , 2007 .

[12]  Andrew Y. T. Leung,et al.  Vibrational power-flow analysis of a MIMO system using the transmission matrix approach , 2007 .

[13]  R. White,et al.  Vibrational power flow from machines into built-up structures, part II: Wave propagation and power flow in beam-stiffened plates , 1980 .

[14]  A. Haddow,et al.  Design of band-gap grid structures , 2005 .

[15]  C. T. Molloy.  Use of Four‐Pole Parameters in Vibration Calculations , 1957 .

[16]  Stephen J. Elliott,et al.  Active power minimization and power absorption in a plate with force and moment excitation , 1997 .

[17]  R. G. White,et al.  Vibrational power flow from machines into built-up structures, part I: Introduction and approximate analyses of beam and plate-like foundations , 1980 .

[18]  K. Svanberg.  The method of moving asymptotes—a new method for structural optimization , 1987 .

[19]  Hashem Ashrafiuon.  Design Optimization of Aircraft Engine-Mount Systems , 1993 .

[20]  Colin H. Hansen,et al.  Total power flow from a vibrating rigid body to a thin panel through multiple elastic mounts , 1992 .

[21]  Noboru Kikuchi,et al.  Analysis and design of passive band-stop filter-type vibration isolators for low-frequency applications , 2006 .

[22]  Bin Niu,et al.  Optimum design of band-gap beam structures , 2012 .

[23]  J. I. Soliman,et al.  Vibration isolation between non-rigid machines and non-rigid foundations , 1968 .

[24]  S. Ljunggren.  Generation of waves in an elastic plate by a torsional moment and a horizontal force , 1984 .

[25]  Kwang-Joon Kim,et al.  Multi-dimensional vibration power flow analysis of compressor system mounted in outdoor unit of an air conditioner , 2004 .

[26]  Cheuk Ming Mak,et al.  A power transmissibility method for assessing the performance of vibration isolation of building services equipment , 2002 .