Patent ID: 6945083

Claim:
A method of measuring eccentricity of a hollow billet in conjunction with a rolling thereof, comprising the steps of: (a) displacing said hollow billet in translation in a direction along a transport path of the hollow billet and along a longitudinal axis of the hollow billet; (b) juxtaposing with said hollow billet a measuring device capable of measuring a wall thickness of said hollow billet, thereby taking a plurality of wall thickness measurements of said hollow billet over a time interval; (c) during said time interval displacing said measuring device relative to said path; and (d) calculating eccentricity of the hollow billet from said measurements, the calculation of eccentricity of the hollow billet in step (d) including determining a pattern of a wall thickness (s) of the hollow billet as a function of a longitudinal coordinate (z) in a direction of the longitudinal axis of the hollow billet and an angle φ around the longitudinal axis in accordance with the relationship S (φ, z )= s 0 ( z )+ s 1 ( z ) cos (φ+δ( z )), where s 0 is the mean wall thickness of the hollow billet, s 1 is the wall thickness amplitude superimposed on the wall thickness s 0 and δ is the annular position dependent on the longitudinal coordinate (z) of the wall thickness, and subjecting the result to a Fourier transformation to obtain the course of the wall thickness as a function of the longitudinal coordinate (z) and the annular position φ to an approximation of the form S (φ, z )≅ξ s 0 *+s i,1 cos(φ+2 π/p i z +ξ i,1 ) wherein s 0 * and s i,1 are the determining Fourier coefficients in the thickness of the hollow billet by a summation (i) over the number (n) of the elements of the Fourier series and p i and ξ i,1 represent the Fourier coefficients for the pitch and for the starting position angle from summation (i) over the number (n) of the Fourier series elements, the frequency transformation being a consideration of the movement of the measuring head.