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

where:k – is the basic spring stiffness,T – is the transformation matrix for the transformation froma local into a global coordinate system,K k – is the element stiffness matrix,d – is the strain of a spring in the local coordinate system ofthe spring,f(d) – is the prescribed functional dependence of an internalforce and strain in a spring,– is the additional force from a nonlinear spring.F Kkdeformation “measured” in nonlinear members of computationalmodel flexible bindings and given teoretical characteristics. Thesenonlinear courses may in fact describe the properties of dampersand springs. The example of a bogie model that would be equipedwith flexible bindings and dampers with nonlinear characteristicsis depicted in Fig. 3.For a nonlinear damper the following holds:bB TT-bk = $ < F $ T - b b(39)fv b vFB +TT $ $k = > ^ h -$ T(40)-_fv ^ h -b$viHwhere:b – is the basic damping constant of a damper,T – is the transformation matrix for a transformation froma local into a global coordinate system,B k – is the matrix of an element damping,v – is the mutual velocity of node points of a damper in thelocal coordinate system of a damper,f(v) – is the prescribed functional dependence of an internalforce in a damper and a mutual velocity of node points ofF Bka damper in the local coordinate system of a damper,– is the additional force from a nonlinear damper.5. Test of modified HHT-methodFor this method validation we used the comparison of computerevaluated dependence courses of forces and velocities, orThe principle: the forces in nonlinear members were computedas the internal forces in the serial connected linear springs withhigh stiffness. The prescribed flexible member characteristics arerepresented by curves in the graphs. The linear dependency representsthe basic stiffness, or better, the basic stiffness constant.6. ConclusionFig. 3 An example of a bogie model (MSC.ADAMS)Simulation computations mainly supported by computationaltechnique are used for the vehicle vibration analysis. The proceduresand methods are used for the forced oscillation of a mechanicalFig. 4 A secondary suspension damper (left: given parameters, right: a comparison)30 ● COMMUNICATIONS 3/2008