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simulation of torsion moment at the wheel set of the railway vehicle ...

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Fig.1 3D model <strong>of</strong> <strong>vehicle</strong> (MSC.ADAMS/Rail [10])finite element method <strong>the</strong>ory. Because <strong>of</strong> special model parameters<strong>set</strong>ting (in accordance with <strong>the</strong> ADAMS system), it behaves like<strong>the</strong> system <strong>of</strong> no-mass frames. We can proclaim th<strong>at</strong> from <strong>the</strong> point<strong>of</strong> view <strong>of</strong> commercial programme packages fe<strong>at</strong>ures, <strong>the</strong> DELTAprogramme with its working fe<strong>at</strong>ures is closer to <strong>the</strong> FEM (ANSYS– <strong>the</strong> Transient analysis part) system than to MBS (ADAMS)system. It is possible to take into account <strong>the</strong> flexibility <strong>of</strong> modelledbodies when <strong>the</strong> real stiffness and cross-sections parametersare known and <strong>set</strong> as input parameters for a comput<strong>at</strong>ion. Theprogramme was built in <strong>the</strong> environment <strong>of</strong> <strong>the</strong> programme languageDELPHI for an oper<strong>at</strong>ion in <strong>the</strong> environment <strong>of</strong> <strong>the</strong> MSWindows XP oper<strong>at</strong>ional system. It was designed on <strong>the</strong> base <strong>of</strong> anopened component system. The programme DELTA allows performingst<strong>at</strong>ic and dynamic mechanical systems analyses. An input<strong>of</strong> d<strong>at</strong>a <strong>of</strong> a <strong>vehicle</strong> mechanical system is carried out with <strong>the</strong> help<strong>of</strong> node points and elements: a linear spring, nonlinear spring,a beam, a linear damper, nonlinear damper and mass point.Boundary and starting conditions:– prescribed displacements, velocities and acceler<strong>at</strong>ions <strong>of</strong> nodes;– prescribed revolutions, angular velocities and angular acceler<strong>at</strong>ions<strong>of</strong> nodes;– prescribed forces and torques acting in nodal points;– prescribed acceler<strong>at</strong>ions acting on a <strong>vehicle</strong>.Methods for dynamics solution:– <strong>the</strong> eigenfrequencies and eigenvectors assessment with <strong>the</strong> help<strong>of</strong> Jacobi’s rot<strong>at</strong>ion method;– a response analysis evoked by harmonic excit<strong>at</strong>ion;– a direct solution <strong>of</strong> a model oscill<strong>at</strong>ion in <strong>the</strong> time domain with<strong>the</strong> following methods: <strong>the</strong> differential method, <strong>the</strong> HHT- method,<strong>the</strong> method <strong>of</strong> linear acceler<strong>at</strong>ions, <strong>the</strong> Newmark method, <strong>the</strong>Wilson- method and <strong>the</strong> Crank-Nicolson method.Equ<strong>at</strong>ions solution methods (solver) are Frontal elimin<strong>at</strong>ionand L-U decomposition.The otput is graphical and textual. The eigenfrequencies andeigenvectors assessment was performed with <strong>the</strong> Jacobi’s rot<strong>at</strong>ionmethod. A response analysis from harmonic excit<strong>at</strong>ion and a directsolution <strong>of</strong> model oscill<strong>at</strong>ion were performed in <strong>the</strong> time domain.Fig.2 The DELTA programme main screenwhen <strong>the</strong> menu are openedThe Newmark modified method was used for <strong>the</strong> direct solutionin <strong>the</strong> time domain. This method is known as <strong>the</strong> ”HHTmethod“.The method was modified for <strong>the</strong> solution <strong>of</strong> dynamicsystems with nonlinear members. The usage <strong>of</strong> this method hasbeen recently very relevant in <strong>the</strong> field <strong>of</strong> technical comput<strong>at</strong>ionsperformance. The main advantage is in <strong>the</strong> decrease <strong>of</strong> time whichis necessary for computing. The linear algebraic equ<strong>at</strong>ions systemwas computed with <strong>the</strong> help <strong>of</strong> <strong>the</strong> Frontal elimin<strong>at</strong>ion method.This method is suitable for big systems <strong>of</strong> linear equ<strong>at</strong>ion solution,known in connection with numerical analyses based on <strong>the</strong> Finiteelement method <strong>the</strong>ory. The comput<strong>at</strong>ional model was built up from80 nodal points and 132 elements. The model has 456 degrees <strong>of</strong>freedom, <strong>the</strong> comput<strong>at</strong>ional front width is 66. All <strong>the</strong> amount <strong>of</strong>track sections is 257, which represents <strong>the</strong> 1285 seconds <strong>of</strong> <strong>vehicle</strong>running.COMMUNICATIONS 3/2008 ●11

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