A dynamic thermal identification method applied to condutor ... - IEM

526 V. L. Borges et al.Table 7.Summary of and l for polythene sample estimation. (m 2 s 1 ) 10 7 l (W m K 1 ) l (W m K 1 ) (HPM) Error (%)2.14 1.15% 0.383 1.68% 0.389 1.57samples tested. The calculation of the phase factor numerically is one of the importantadvantages of the technique proposed here. This procedure allows the use of a 3Dtransient model and consequently its application to conductor material identification.The estimation of thermophysical properties of complex forms (such as a cutting tool) isa subject for future study.Nomenclaturef ¼ frequency (Hz)G ¼ Green’s function (m 2 KW 1 )H( f ) ¼ frequency response function (m 2 KW 1 )jHð f Þj ¼ modulus of frequency response functionIm(S xy ) ¼ imaginary component of the cross-spectral density function (K 2 )Re(S xy ) ¼ real component of the cross-spectral density function (K 2 )S mq ¼ objective function (K 2 )S ¼ phase objective function (rad 2 )S xx ¼ autoespectral density function of x(t) (K 2 )S yy ¼ autoespectral density function of y(t) (K 2 )S xy ¼ cross-spectral density function (K 2 )t ¼ time (s)T 0 ¼ initial temperature ( CX(t) ¼ input signal in time domain ( C)Y(t) ¼ output signal in time domain ( C)X( f ) ¼ input signal in frequency domain ( C)Y( f ) ¼ input signal in frequency domain ( Cx, y, z ¼ geometric variables (m)Z ¼ generalized impedance (m 2 KW 1 )Greek symbols ¼ thermal diffusivity (m 2 s 1 )l ¼ thermal conductivity (W m K 1 ) ¼ heat flux (W m 2 ) ¼ density (kg m 3 ) ¼ temperature difference ( C)( f ) ¼ phase angle (rad)Subscriptst ¼ relative to calculated datae ¼ relative to experimental data