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Modelling and analysis for a pilot relief valve using CFD method and deformation theory of thin plates

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Abstract

The current work is concerned with modelling and analysis for a pilot relief valve, thus successfully bringing a systematic method for designing and analyzing similar valves. The essence of the work is to solve two important problems, one for positions of the pilot valve influenced by flow force and the other is for the opening of the relief valve governed by a thin annular plate. The computational fluid dynamics (CFD) method is used to present the flow force. Using a series of experiments, the flow rate versus pressure drop shows the rationality of the CFD results. In order to obtain the opening of relief valve with higher accuracy, the large deflection theory of thin plates is adopted. An equivalent method for replacing the concentrated force is innovatively proposed so that all of the loads of the plates can be given by a unified expression, which reduces the number of the governing equations and intermediate boundary conditions. For presenting a very simple and reliable method for solving the governing equation, an unconstrained nonlinear optimization is innovatively introduced to solve the deflection of the thin annular plate. Being verified by finite-element method (FEM) of the relief valve, the equivalent method and optimization can solve deflection of thin plates rapidly and accurately. Reflected through a complete model for the pilot relief valve, the theoretical flow rate of the pilot relief valve is consistent with experimental conclusion. Once again, the comparisons bring us insight into the accuracy of the method adopted in the current work.

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References

  1. Causemann P. Modern vibration damping systems. ATZ worldwide, 2003, 105: 10–13

    Google Scholar 

  2. Heißing B, Ersoy M. Chassis Hand Book: Chassis Components. Springer Science & Business Media, 2011

    Book  Google Scholar 

  3. Heißing B, Ersoy M. Chassis Hand Book: Chassis Control Systems. Springer Science & Business Media, 2011

    Book  Google Scholar 

  4. Zhang S. Testing the pressure transient flow-force for spool-type two-way valves. Dissertation of Doctor Degree. Columbia: University of Missouri-Columbia, 2011

    Google Scholar 

  5. Aung N Z, Yang Q, Chen M. CFD analysis of flow forces and energy loss characteristics in a flapper–nozzle pilot valve with different null clearances. Energy Conv Manag, 2014, 83: 284–295

    Article  Google Scholar 

  6. Qian J Y, Wei L, Jin Z J. CFD analysis on the dynamic flow characteristics of the pilot-control globe valve. Energy Conv Manag, 2014, 87: 220–226

    Article  Google Scholar 

  7. Lisowski E, Czyzycki W, Rajda J. Three dimensional CFD analysis and experimental test of flow force acting on the spool of solenoid operated directional control valve. Energy Conv Manag, 2013, 70: 220–229

    Article  Google Scholar 

  8. Lisowski E, Rajda J. CFD analysis of pressure loss during flow byhydraulic directional control valve constructed from logic valves. Energy Conv Manag, 2013, 65: 285–291

    Article  Google Scholar 

  9. Song X G, Cui L, Cao M S. A CFD analysis of the dynamics of a direct- operated safety relief valve mounted on a pressure vessel. Energy Conv Manag, 2014, 81: 407–419

    Article  Google Scholar 

  10. Beune A, Kuerten J G M, van Heumen M P C. CFD analysis with fluid–structure interaction of opening high-pressure safety valves. Comput Fluids, 2012, 15:108–116

    Article  Google Scholar 

  11. Nishawala V V. A study of large deflection of beams and plates. Dissertation of Master Degree. New Brunswick: Rutgers University, 2011

    Google Scholar 

  12. Kim K, Yoo C H. Analytical solution to flexural responses of annular sector thin-plates. Thin-Walled Struct, 2010, 48: 879–887

    Article  Google Scholar 

  13. Mohammadi M, Ghayour M, Farajpour A. Free transverse vibration analysis of circular and annular graphene sheets with various boundary conditions using the nonlocal continuum plate model. Compos: Part B-eng, 2013, 45: 32–42

    Article  Google Scholar 

  14. Mashat D S, Zenkour A M. Hygrothermal bending analysis of a sector- shaped annular plate with variable radial thickness. Compos Struct, 2014, 113: 446–458

    Article  Google Scholar 

  15. Hosseini-Hashemi S, Fadaee M, ’haghi M. A novel approach for in-plane/out-of-plane frequency analysis of functionally graded circular/annular plates. Int J Mech Sci, 2010, 52: 1025–1035

    Article  Google Scholar 

  16. Golmakani M E, Kadkhodayan M. Large deflection thermoelastic analysis of functionally graded stiffened annular sector plates. Int J Mech Sci, 2013, 69: 94–106

    Article  Google Scholar 

  17. Golmakani M E, Mehrabian M. Nonlinear bending analysis of ring-stiffened circular and annular general angle-ply laminated plates with various boundary conditions. Mech Res Commun, 2014, 59: 42–50

    Article  Google Scholar 

  18. Ghiasian S E, Kiani Y, Sadighi M, et al. Thermal buckling of shear deformable temperature dependent circular/annular FGM plates. Int J Mech Sci, 2014, 81: 137–148

    Article  Google Scholar 

  19. Ebrahimi F, Naei M H, Rastgoo A. Geometrically nonlinear vibration analysis of piezoelectrically actuated FGM plate with an initial large deformation. J Mech Sci Technol, 2009, 23: 2107–2124

    Article  Google Scholar 

  20. Breslavsky I, Amabili M, Legrand M. Physically and geometrically non-linear vibrations of thin rectangular plates. Int J Non-Linear Mech, 2014, 58: 30–40

    Article  Google Scholar 

  21. Zhou D, Lo S H, Cheung Y K. 3-D vibration analysis of annular sector plates using the Chebyshev–Ritz method. J Sound Vib, 2009, 320: 421–437

    Article  Google Scholar 

  22. Hashemi S H, Taher H R D, Omidi M. 3-D free vibration analysis of annular plates on Pasternak elastic foundation via p-Ritz method. J Sound Vib, 2008, 311: 1114–1140

    Article  Google Scholar 

  23. Gürses M, Akgöz B, Civalek Ö. Mathematical modeling of vibration problem of nano-sized annular sector plates using the nonlocal continuum theory via eight-node discrete singular convolution transformation. Appl Math Comput, 2012, 219: 3226–3240

    Google Scholar 

  24. Nikkhoo A, Hassanabadib M E, Azamc S E, et al. Vibration of a thin rectangular plate subjected to series of moving inertial loads. Mech Res Commun, 2014, 55: 105–113

    Article  Google Scholar 

  25. Xie X, Jin G, Ye T, et al. Free vibration analysis of functionally graded conical shells and annular plates using the Haar wavelet method. Appl Acoust, 2014, 85: 130–142

    Article  Google Scholar 

  26. Li Y Q, Li J. Free vibration analysis of circular and annular sectorial thin plates using curve strip Fourier p-element. J Sound Vib, 2007, 305: 457–466

    Article  Google Scholar 

  27. Allahverdizadeh A, Naei M H, Bahrami M N. Nonlinear free and forced vibration analysis of thin circular functionally graded plates. J Sound Vib, 2008, 310: 966–984

    Article  Google Scholar 

  28. Fua Z, Lin S, Xian X. Vibration of annular plate concentrators with conical cross-section. J Sound Vib, 2009, 321: 1026–1035

    Article  Google Scholar 

  29. Zhou Z H, Wong K W, Xu X S, et al. Natural vibration of circular and annular thin plates by Hamiltonian approach. J Sound Vib, 2011, 330: 1005–1017

    Article  Google Scholar 

  30. Hasheminejad S M, Ghaheri A, Rezaei S. Semi-analytic solutions for the free in-plane vibrations of confocal annular elliptic plates with elastically restrained edges. J Sound Vib, 2012, 331: 434–456

    Article  Google Scholar 

  31. Shojaee S, Izadpanah E, Valizadeh N, et al. Free vibration analysis of thin plates by using a NURBS-based isogeometric approach. Finite Elem Anal Des, 2012, 61: 23–34

    Article  MathSciNet  Google Scholar 

  32. Esen I. A new finite element for transverse vibration of rectangular thin plates under a moving mass. Finite Eleme Anal Des, 2013, 66: 26–35

    Article  MATH  MathSciNet  Google Scholar 

  33. Hosseini-Hashemi S, Derakhshani M, Fadaee M. An accurate mathematical study on the free vibration of stepped thickness circular/ annular Mindlin functionally graded plates. Appl Math Model, 2013, 37: 4147–4164

    Article  MATH  MathSciNet  Google Scholar 

  34. Es'haghi M. Accurate approach implementation in vibration analysis of thick sector plates. Int J Mech Sci, 2014, 79: 1–14

    Article  Google Scholar 

  35. Duan G, Wang X. Vibration analysis of stepped rectangular plates by the discrete singular convolution algorithm. Int J Mech Sci, 2014, 82: 100–109

    Article  Google Scholar 

  36. Li Q S, Liu J, Xiao H B. A new approach for bending analysis of thin circular plates with large deflection. Int J Mech Sci, 2004, 46: 173–180

    Article  MATH  Google Scholar 

  37. DaSilva P P, Krauth W. Numerical solution of the von Karman equations for a thin plate. Int J Mod Phys C, 1997, 8: 427–434

    Article  Google Scholar 

  38. Bencharif N, Ng S F. Linear and nonlinear deflection analysis of thick rectangular-plates. Comput Struct, 1994, 50: 763–776

    Article  Google Scholar 

  39. Hu C, Hartley G A. Boundary-element analysis of thin plates unilaterally edge supported. Eng Anal Bound Elem, 1993, 12: 47–55

    Article  Google Scholar 

  40. Ramachandra L S, Roy D. A novel technique in the solution of axisymmetric large deflection analysis of a circular plate. J Appl Mech, 2001, 68: 814–816

    Article  MATH  MathSciNet  Google Scholar 

  41. Gabriel B, Jiang F. Application of the modified method of multiple scales to the bending problems for circular thin plate at very large deflection and the asymptotics of solutions (I). Appl Math Mech, 1998, 19: 937–950

    Article  MATH  MathSciNet  Google Scholar 

  42. Cao J. Computer-extended perturbation solution for the large deflection of a circular plate, 2, central loading with clamped edge. Q J Mech Appl Math, 1997, 50: 333–347

    Article  MATH  Google Scholar 

  43. Cao J. Computer-extended perturbation solution for the large deflection of a circular plate, 1, uniform loading with clamped edge. Q J Mech Appl Mathe, 1996, 49: 163–178

    Article  MATH  Google Scholar 

  44. Ren H L, Ren P Z. Non-linear bending of a corrugated annular plate with a plane boundary region and a non-deformable rigid body at the center under compound load. Int J Non-Linear mech, 1993, 28: 353–364

    Article  Google Scholar 

  45. He J H. A Lagrangian for von Karman equations of large deflection problem of thin circular plate. Appl Math Comput, 2003, 143: 542–549

    Google Scholar 

  46. He J H. Variational iteration method: a kind of nonlinear analytical technique: some Examples. Int J Non-Linear Mech, 1999, 34: 699–708

    Article  MATH  Google Scholar 

  47. He J H. A modified perturbation technique depending upon an artificial parameter. Meccanica, 2000, 35: 299–311

    Article  MATH  MathSciNet  Google Scholar 

  48. He J H. Iteration perturbation method for strongly nonlinear oscillations. J Vib Control, 2001, 5: 631–642

    Google Scholar 

  49. He J H. Semi-inverse method of establishing generalized variational principles for fluid Mechanics with emphasis on turbomachineryaerodynamics. Int J Turbo Jet Engines, 1997, 14: 23–28

    Google Scholar 

  50. He J H. Semi-inverse method and generalized variational principles with multi-variables in Elasticity. Appl Math Mech, 2000, 21: 797–808

    Article  MATH  Google Scholar 

  51. Eftekhari S A, Jafari A A. A Mixed Method for Free and Forced Vibration of Rectangular Plates. Appl Math Model, 2012, 36: 2814–2831

    Article  MATH  MathSciNet  Google Scholar 

  52. Tornabene F, Viola E, Inman D J. 2-D differential quadrature solution for vibration analysis of functionally graded conical, cylindrical shell and annular plate structures. J Sound Vib, 2009, 328: 259–290

    Article  Google Scholar 

  53. Eftekhari S A, Jafari A A. A mixed modal-differential quadrature method for free and forced vibration of beams in contact with fluid. Meccanica, 2014, 49: 535–564

    Article  MATH  MathSciNet  Google Scholar 

  54. Zhang W, Wang D M, Yao M H. Using Fourier differential quadrature method to analyze transverse nonlinear vibrations of an axially accelerating viscoelastic beam. Nonlinear Dynam, 2014, 78: 839–856

    Article  MathSciNet  Google Scholar 

  55. Pu J, Zheng J. Structural dynamic responses analysis applying dif ferential quadrature method. J Zhejiang Univ Sci A, 2006, 7: 1831–1838

    Google Scholar 

  56. Yuan X J, Guo K H. Comparison of some existing models for throttling area of cone valve. Adv Mater Res, 2013, 823: 33–38

    Article  Google Scholar 

  57. McCloy D, Martin H R. Control of fluid power: analysis and design. New York: Halsted Press, 1980

    Google Scholar 

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Yuan, X., Guo, K. Modelling and analysis for a pilot relief valve using CFD method and deformation theory of thin plates. Sci. China Technol. Sci. 58, 979–998 (2015). https://doi.org/10.1007/s11431-015-5822-3

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