superposition of e.g. hxx(min)(n) andhxy(min)(n) does not apply. Therefore onlyhxx(min)(n) or hyy(min)(n) are used in the inverse filters. Thus, for the results to be accurate, the effect of the cross FRFs have to be negligible. The similarity between the signals is estimated by calculating the ratio of the energy in the difference between reference and inverse filtered force, E f R tð Þ f I tð Þ ð Þ and the energy in the reference signal, E(fR(t)), according to: η ¼min 1þ RfIfI 0ð Þ f 2 I 2 RfRfI τð Þ fRfI RfRfR 0ð Þ f 2 R ! ð1:7Þ where RfRfR 0ð Þ and RfIfI 0ð Þ are the autocorrelations at zero time delay between reference and inverse filtered forces, respectively. RfRfI τð Þ refers to the cross correlation between reference and inverse filtered forces, where τ is the time delay 0 500 1000 1500 2000 2500 3000 −600 −400 −200 0 Phase [Deg] Frequency [Hz] 0 500 1000 1500 2000 2500 3000 0 2 4 6 8 Frequency [Hz] Magnitude [N/N] Measured FRF, H yy Estimated (ETFE), H yy(min) Combined FRF Measured FRF, H yy Estimated (ETFE), H yy(min) Combined FRF Combined FRF without linear phase Fig. 1.4 Magnitude and phase responses of Hyy(ω), Hyy(min)(ω) and the combined FRF, nb ¼200 and na ¼55. The dynamometer’s dominant modes are: 1120 Hz, 1430 Hz, 1630 Hz, 1750 Hz and 2550 Hz Table 1.1 Equipment and cutting data used in the cutting force measurements Machine tool MORI SEIKI NV5000 Cutting tool Sandvik R331.35-050A20EM100 Insert Sandvik N331.1A-08 45 08H-NL H10 Work piece material AISI 7075 Force dynamometer Kistler 9255B Charge amplifier Kistler 5011 Cutter diameter, Dcap 50 [mm] Radial cutting depth, ae 10; 25; 40 [mm] Axial cutting depth, ap 3 [mm] Number of teeth, zc 1 Cutting speeds, vc 200; 400; 800; 1200; 1490; 2000 [m/min] Tooth passing frequencies, ft 21.2; 42.4; 84.8; 127.3; 158.1; 212.2 [Hz] Feed rates, fz 0.05; 0.1; 0.15; 0.2; 0.25 [mm/tooth] 6 M. Magnevall and T. Beno
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