Abstract
The article deals with introduction into the issue of the general asymmetry under vertical oscillation of systems of spatially elastically supported bodies with context of vehicle application. The various models are mentioned, quarter, half and full model (with different DOF) and advantages and disadvantages are discussed. The basic calculation procedures were presented for symmetry and asymmetry of geometry and excitation. The excitation is produced by jump change of plate support (analytically and numerically solved by Heaviside’s function, in the experimental part by jump down from the wedges). The procedure to solve the basic 3D model is introduced for selected types of asymmetry of geometry and excitation. The practical approach is presented on the two-axle railroad vehicle. The vertical displacement, velocities, accelerations and angles of rotation of symmetry axes are considered. The time trend of the vertical displacement of the general point the aim of the calculation (3 DOF considered).
Highlights
The long time broad attention has been pursued to problem solutions which deal with oscillation of the railway or road wheel vehicles assuming various hypothesizes, models, operation conditions
What is missing is solution of the asymmetry effect at spatial vehicle models. Particular solution of these issues are presented on the half geometry, planar, plane symmetry
The system of simultaneous linear non-homogenous differential equations is determined by element definition of matrix M, B, K and components of vector F. These equations are motion equations of the spatial vehicle model with three degrees of freedom, with total asymmetry: distribution of system mass, geometry and stiffness of the elastic support, geometry and intensity of viscous dumping and with asymmetry of kinetic excitation defined by roughness of the road h(x) → h(t)
Summary
The long time broad attention has been pursued to problem solutions which deal with oscillation of the railway or road wheel vehicles assuming various hypothesizes, models, operation conditions. These axes are determined by mutually perpendicular symmetry axes of wheel-set and wheel-base of the vehicle and they are intersecting in the geometrical center of vehicle These three cases are: - asymmetry of the vehicle mass distribution with regard to axes of geometrical symmetry, - asymmetry of the elastic and dissipative elements distribution and their mechanical properties (assuming the linear bond of individual quantities and small displacements and rotation of system parts, - asymmetry of the kinematic excitation, i.e. array of the surface roughness of the road (or railway), which defines kinematic excitation of the system in the contact place wheel-road (or wheel-rail). It is obvious that the basic condition for successful investigation of the vertical oscillation of the vehicle by experimental or theoretical (analytical, numerical, simulation) method is selection or definition of the suitable spatial model [1]
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