Due to the tram speed, and according to the relation between the frequencies f and the train speed V, f = V/λ, the wavelength λ on a tram rail surface is commonly around 10 50 mm.
The rail corrugation on rail surface is very frequent in all railway infrastructures and is also classified as short-wave defect (long wavelength irregularities are, instead, defined as irregularities of wavelengths of 300 mm or longer, that may be either geometric irregularities in the track or on the wheel, or irregularities of the track stiffness [10]).
The nonlinear normal force between wheel and rail surface is solved using Hertz's theory [19]: F_{n} = C_{h} delta^{1.5} (20)where the constant C h depends from the contact surfaces bending and from material characteristics and δ is the value of the elastic penetration between the two bodies.
With the assumption that the power spectral density of the unevennesses on the rail surface is in proportion to the third power of the wavelength, or to (wavenumber)−3, the amplitudes of the vibrations in railway tracks supported by rail-pads and roadbeds with various magnitudes of elastic constants are analyzed and the values for each one-third octave band are estimated.
Nonlinear effects due to the shape and roughness of the wheel and the rail surfaces are included in the point contact model by pre-calculation of functions for the contact stiffness and contact filters.
In Fig. 2a, the value of H in the rail surface area is high as a whole and has small mutations.
The detection of rail surface defects is an important part of railway daily inspection, according to the requirements of modern railway automatic detection technology on real-time detection and adaptability.
The track area usually consists of rail, ballast, sleeper, and fasteners; their characteristics and H values are different in the detecting image, as shown in Fig. 2. (1) In Fig. 2a, the value of H in the rail surface area is high as a whole and has small mutations.
Conventionally, the rail's surfaces are ground by a single-wheel grinder.
In this study we examine analytically the anticipated changes in these quantities if the transverse curvature of the wheel and rail running surfaces are varied over realistic limits.
