Analysis of analytical hydrodynamic bearing models on a reciprocating compressor

Reciprocating compressors are one of the most common machines, as they are usually found in household refrigerators and air conditioners. The reciprocating compressor is a rotor-crankshaft-piston machine supported by lubricated bearings. They are sealed to retain and store the refrigerating gas, therefore, the maintenance of the compressor is difficult and expensive. Thus reciprocating compressors should be designed to last the life span of the appliance. Most models of reciprocating compressors considers rigid bearings, which completely neglects the influence of the hydrodynamic bearings on the dynamic behavior of the compressor. This work shows the modeling and analysis of a reciprocating compressor with flexible bearings. The rotor which is part of the motor is supported by a pair of hydrodynamic bearings that are modeled using three different analytical models: Capone, Vance and Butenschön. Analytical models of bearing are much faster than numerical ones, such as the ones that use the finite difference (FDM) or finite element method (FEM). The three models have different approaches to solve the Reynolds equation and, therefore, distinct results were found using each one of them. The model was developed in the OpenModelica software using the elements of the Mechanics.Multibody library. The Butenschön model was implemented in C and Fortran 95 and integrated to OpenModelica as an external library.6030732

Dynamic Loads Of Reciprocating Compressors With Flexible Bearings

The paper analyzes the visco-elastic bearing loads in the dynamic model of a reciprocating refrigeration compressor. The model incorporates the gyroscopic interactions due to the radial movement of the bearings. The Newton-Euler method is used in the analysis, establishing the necessary differential equations that describe the movement of the system, leading also to the calculation of orbital displacements of the bearings. © 2012 Elsevier Ltd. All rights reserved.52130143Stoecker, W.F., (1998) Industrial Refrigeration Handbook, , McGraw-HillTassou, S.A., Grace, I.N., Fault diagnosis and refrigerant leak detection in vapour compression refrigerant systems (2005) International Journal of Refrigeration, 28, pp. 680-688House, J.M., Lee, K.D., Norford, L.K., Controls and diagnostics for air distribution systems (2003) Journal of Solar Energy Engineering, Transactions of the ASME, 125, pp. 310-317Prata, A.T., Fernandes, J.R.S., Fagotti, F., Dynamic analysis of piston secondary motion for small reciprocating compressors (2000) Journal of Tribology, 122, pp. 752-760Cho, J.R., Moon, S.J., A numerical analysis of the interaction between the piston oil film and the component deformation in a reciprocating compressor (2005) Tribology International, 38, pp. 459-468Kim, T.J., Han, J.S., Comparison of the dynamic behavior and lubrication characteristics of a reciprocating compressor crankshaft in both finite and short bearing models (2004) Tribology Transactions, 47, pp. 61-69Goodwin, M.J., Nikolajsen, J.L., Reciprocating machinery bearing analysis: Theory and practice (2003) Proceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology, 217, pp. 409-426Levecque, N., Mahfoud, J., Violette, D., Ferraris, G., Dufour, R., Vibration reduction of a single cylinder reciprocating compressor based on multi-stage balancing (2011) Mechanism and Machine Theory, 46 (1), pp. 1-9Sultan, I.A., Kalim, A., Improving reciprocating compressor performance using a hybrid two level optimization approach (2011) Engineering Computations, 28 (5), pp. 616-636Shabana, A.A., (1989) Dynamics Multibody Systems, , John Wiley & Sons IllinoisDufour, R., Der Hagopian, J., Lalanne, M., Transient and steady state dynamic behavior of single cylinder compressors: Prediction and experiments (1995) Journal of Sound and Vibration, 181 (1), pp. 23-41Couto, P.R.C., Análise de Mancais Radiais Hidrodinâmicos Com Aplicação em Compressores Herméticos de Refrigeraç ão, , Ph. D. Thesis, Federal University of Santa Catarina, Florianopolis 2006 [in Portuguese]Wisbeck, H.J., Manke, A.L., Prata, A.T., Bearing System in Dynamic Loading Including Solid Contact and Wear (2002) Paper, 1532. , International Compressor Engineering ConferenceRao, J.S., (1983) Rotor Dynamics, , John Wiley & SonsStachowiak, G.W., Batchelor, A.W., (2001) Engineering Tribology, , 2nd ed. Buttterworth HeinemannOtto, S.R., Denier, J.P., (2005) An Introduction to Programming and Numerical Methods in MATLAB, , Springer - Verlag Londo

Vibration Of A Long, Tip Pulled Deflected Beam

A study was conducted to address the problem of building a simple dynamic model of a long beam deformed by a tip pulling cable. The exact static deformation shape of a long beam was obtained through the solution of the nonlinear beam governing differential equations. The exact deformed configuration for beams with a uniform cross section and transversal end load was found through the recursive solution of elliptic integrals. The deformed configuration of beams with an inclined pulling force was found via numerical approximations, using adequate methods such as the Runge-Kutta method, the finite element method, and the quasi-linearization finite difference method. A strategy to calculate the static deformation of a long beam pulled by a tip cable was also proposed in the study.52715591563Puig, L., Barton, A., Rando, N., A review on large deployable structures for astrophysics missions (2010) Acta Astronautica, 67 (1-2), pp. 12-26. , July-Aug. doi:10.1016/j.actaastro.2010.02.021Tibert, G., (2002) Deployable Tensegrity Structures for Space Applications, pp. 9-30. , Royal Inst, of Technology, StockholmPellegrino, S., (2001) Deployable Structures, pp. 1-35. , Springer MilanFrisch-Fay, R., (1962) Flexible Bars, pp. 33-64. , Butterworths LondonTimoshenko, S., Gere, J., (1961) Theory of Elastic Stability, pp. 66-70. , 2nd ed. McGraw-Hill New YorkOhtsuki, A., Analysis of the characteristics of fishing rods based on the large-deformation theory (2001) Materials and Science in Sports, pp. 161-170. , edited by Sam, F.H. , Minerals, Metals and Materials Society , Warrendale, PAShvartsman, B., Large deflections of a cantilever beam subjected to a follower force (2007) Journal of Sound and Vibration, 304 (3-5), pp. 969-973. , doi:10.1016/j.jsv.2007.03.010Holland, D., Stanciulescu, I., Virgin, L., Plaut, R., Vibration and large deflection of cantilevered elastica compressed by angled cable (2006) AIAA Journal, 44 (7), pp. 1468-1476. , doi:10.2514/1.18000Howell, L.L., (2001) Compliant Mechanisms, pp. 42-55. , Wiley , New YorkAl-Sadder, S., Al-Rawi, R., Finite difference scheme for large-deflection analysis of non-prismatic cantilever beams subjected to different types of continuous and discontinuous loadings (2006) Applied Mechanics, 75 (8-9), pp. 459-473. , doi:10.1007/s00419-005-0422-5Yau, J., Close-form solutions of large deflections for a guyed cantilever column pulled by an inclinations cable (2010) Journal of Marine Science and Technology, 18 (1), pp. 130-136Ferris, D., Afonia, A., Small vibrations of flexible bars by using the finite element method with equivalent uniform stiffness and mass methodology (1993) Journal of Sound and Vibration, 163 (2), pp. 343-358. , doi:10.1006/jsvi.1993.1170Sallstrom, J., Poelaert, D., Janssens, F., Small displacements about equilibrium of a beam subjected to large static loads (1996) AIAA Journal, 34 (11), pp. 2384-2391. , Nov. doi: 10.2514/3.13405Santillan, S., Virgin, L., Plaut, R., Post-buckling and vibration of heavy beam on horizontal or inclined rigid foundation (2006) Journal of Applied Mechanics, 73 (4), pp. 664-671. , July doi: 10.1115/1.2165237Santillan, S., Virgin, L., Plaut, R., Equilibria and vibration of a heavy pinched loop (2005) Journal of Sound and Vibration, 288 (1-2), pp. 81-90. , Nov. doi:10.1016/j.jsv.2004.12.016Santillan, S., Virgin, L., Plaut, R., Static and dynamic behavior of highly deformed risers and pipelines (2010) Journal of Offshore Mechanics and Arctic Engineering, 132 (2). , Paper 021401. doi:10.1115/1.4000555Petyt, M., (2010) Introduction to Finite Element Vibration Analysis, pp. 45-115. , 2nd ed. Cambridge Univ. Press New YorkCraig, R., Kurdila, A., (2006) Fundamentals of Structural Dynamics, pp. 417-453. , 2nd ed. Wiley New YorkKwon, Y., Bang, H., (1997) The Finite Element Method Using Matlab, pp. 197-304. , CRC Press Boca Raton, FLCook, R., Malkus, D., Plesha, M., (1989) Concepts and Applications of Finite Element Method, pp. 31-57. , 3rd ed., Wiley, New Yor