The paper discusses a method of quantitative comparison of cylindricity profiles measured with different strategies. The method is based on applying so-called Legendre-Fourier coefficients. The comparison is carried out by computing the correlation coefficient between the profiles. It is conducted by applying a normalized cross-correlation function and it requires approximation of cylindrical surfaces using the Legendre-Fourier method. As the example two sets of measurement data are employed: the first from the CMM and the second one from the traditional radial measuring instrument. The measuring data are compared by analyzing the values of selected cylindricity parameters and calculating the coefficient of correlation between profiles.
The standard approach to the wave propagation in an inhomogeneous elastic layer leads to the displacement in a form of a product of a function of space and a harmonic function of time. This product represents the standing, and not the running wave. The part depending on the space variable is governed by the linear ordinary second order differential equation. In order to calculate the propagation speed in the present paper the inhomogeneous material is separated by a plane into two parts. Between the two inhomogeneous parts the virtual homogeneous elastic extra layer is added. The elasticity modulus and the mass density of the extra layer have the same values as the inhomogeneous material on the separation plane. In further calculations the extra layer is assumed to be infinitesimally thin. The virtual layer allows to decompose the motion into two waves: a wave running to the right and a wave running to the left. Energy conservation equation is derived.