A heavy machine tool mounted on the first floor of a building, Fig. 6.43(a), has been modeled as a three-degree-of-freedom system as indicated in Fig. 6.43(b).

(a) For \(k_{1}=875 \mathrm{kN} / \mathrm{m}\), \(k_{2}=87 \mathrm{kN} / \mathrm{m}, k_{3}=350 \mathrm{kN} / \mathrm{m}, c_{1}=c_{2}=c_{3}=2000 \mathrm{~N}-\mathrm{s} / \mathrm{m}, m_{f}=8700 \mathrm{~kg}, m_{b}=1800 \mathrm{~kg}\), \(m_{h}=350 \mathrm{~kg}\), and \(F(t)=4000 \cos 60 t \mathrm{~N}\), find the steady-state vibration of the system using the mechanical impedance method described in Section 5.6.

(b) If the maximum response of the machine tool head \(\left(x_{3}\right)\) has to be reduced by \(25 \%\), how should the stiffness of the mounting \(\left(k_{2}\right)\) be changed?

(c) Is there any better way of achieving the goal stated in (b)? Provide details.

Figure 6.43(a):-

Transcribed Image Text:

Wall Mounting Machine tool head (equivalent mass, mn) F(t), cutting force Machine tool base (equivalent mass, mp) (a) Floor (equivalent mass, m)