Question

2) Find the transfer function for the following rotational system (25%) G(s) = 02(*)/T(s) TO I N-m-s/rad fo 1 kg-m? = 25 8.(1) N>= 50 + 0000 4 N-m/rad HHHH

Answer 1

The given rotational system Control systems to attain the is a gear train, which are used mechanical matching of the motor to the in load. IN-8/rad At ding the Ni = 25 s i Na - 25 Oect) • Shaft 1 - Amalysis Inertia torque Jix system = torovues aceing on the = -f.w+T - J = moment of inertia of the system im Ky-ma. * = angular acceleration due to applied to revue, T. do dta C = angalore velocity = 40 f = Co-efficient of viscous - dumping in Nh/rad/sec. ... for Shaft-1 TO CE) Ft= J; &,+ fow, Tyle= J.MPOI Ct) + f douces) . dt. . at condicions and taking iapiace transporm Assuming, zero initial on both sides,

Ti (5) = Ji.SP.01 (8) + fi. s. o. Co) Given that Ji = 1 kg - ma Fi = 1 Nm / rad I sec .: Ti Cs) = 52.0CS) + 5. O,CS) =s.oics). [s+] Tics) = 5.C8+1). O,CS) Shaft a- For shaft Analysis 2, NOT NECESSARY Inertia torque = forques acting on the system Ja.da = sing restoring tovarne + Tact) 0 = -K; Oa (t) + Tact) Ta CE) = Ka. OaCt) - 2/ Taking Laplace transform, we get * Tai(8) = Ka. 02 (8) Given Kas 4 am imad ..Ta ()= 4.00(s) - THESE STEPS ARE Lee т, = Tulius оf aeqТ -1 - ra=radius of gear - 2 since linear distance travelled is same, m.0, = T. Od. along surface of each gean

No of gear teeth , Na gear rasius , n n NA NI work done by Assuming that gear-I = work there done is no by power loss, geam-a... . T. 0. = Ta. Oa . I - od Ti (3) - Da(8) - Ni Tacos = 0, C6) - Ne OCS - Na 25 Dals) a Na 50 Tics) S.(8+1) $co+1) Ĝls) = 02 (8) = Da so co? = a. Ji (st1