Question

Shown below is a machine with a rotating unbalance equal to: mr = 0.20 lb-sec2. The machine operates at a speed o = 55 rad/sec. The machine is supported on a spring K and damper C. Find the force transmitted to the supporting structure through the spring(k) and damper(C) by the machine at this operating speed. Rotating Unbalance M = 1 lb-sec/in m C = 17.6 lb-sec/in Ту K = 484.0 lb/in M ww с

Answer 1

Question : Unit conversion (1) (2) NS 1 16-sece = 175.34 kg in. Į 16 -see 175.34 in. 1 16 175.34 N in. 1 Ib = 0.454 kg acceleration due to gravity, g (4) (5) 386 in. = 9.81 m S² sec? (6) 1 in. = 0.0254 m Given data: 2 mg = 0.20 Ib-see? 0 -2 lb- 3 = ? ( ) 0.20 X 0.454 x 9.81 0.8907 kym mr 175.34 kg M = 1 lb-see? in 17.6 lb sec.in (3) C = 17.6% 175.34 :. c= 3085.984 NS m (1 ) k = 484 16 طر = 484 x 175.34 zl E = 84 864-56 N m (5) 3 55 rad see.

Solution Natural frequency, Wn 84864.56 175:34 wzom м. Wn- 2.2 HC :. = - 2.5 r = w 55 22 Wn 11 damping ratio, с 2Jmk 3085.984 2x 175-348 4 864.56 ؟ = 0.4 force transmitted to supporting structure, FI Fol St (2&8)? (1–82)+(2&r)? f = my W² 1+(2&m)? (1-72)2 + (287)? fi = 0.89.7x552 | Jit (2x0.472-5)2 (1-2-53)2+(2X0-952-53 Fy = 1072.398 N