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You are part of a team trying to restore a historic electric locomotive, which is driven by a large induction motor. During the restoration process, the induction motor was refurbished and, due to its age, its rated torque has been reduced to half of its initial rated torque. Before refurbishment, you tried to test it, and applied a mechanical load with inertia JL = 600 kg.m? You measured the inertia of the motor's own rotor, and found it to be JM = 1,500 kg.m? The motor managed to accelerate to 906 rpm within 50 seconds. The synchronous speed is 960 rpm. Determine how much time it would take for the motor to accelerate to the rated speed, as well as the rotor actual speed after the refurbishment.
Formulae Sheet Mechanical power P= TXw Inertia of a solid cylinder Ion (Goin) dwm dwm T = Jeq dt = OM + D dt Relationship between torque, acceleration and inertia Kinetic energy stored in a motor-load system 1 W= = Um +Juwm? Gear ratios - Power factor, active, reactive and apparent power in a three-phase system, and their relationships пм TM ωι nu T2 WM P= V3 VL2114 | cos(6), or P = 3|Vp1|1p| cos(0) Q = 73|VL||4) sin(O). or Q = 3|vp||1p| sin(0) Q S = 3|Vp|lipl. = tan(O). pf = cos(0) Ni Hm = Im Ni Ni Bm = Am Hm = 4m ·= HOM, Im Permeability of air (po): Mo = 410 x 10-7 Field intensity along mean path Flux density (B) of ferromagnetic materials (henries ) m e(t) = No E Leap do Relationship between voltage, flux and current di hence also V = Nºw Magnetic reluctance Im Rm = Hm Am N2 L= Rm Inductance of a simple coil Electromagnetic torque in a generic motor DC machine induced electromagnetic torque and torque constant = DC machine induced electromotive force and voltage constant = Tem = 2B,(N 1)lr Tem = kria kr = C a dr) B; Ea = kęWm kg = Ca.r) B; Va = Eq + Rala = keWm + Rala Eloss = Pross At = 1,2R 4t Tem = kris NS k = 12V1B, DC machine equivalent circuit voltage DC machine electrical energy losses AC synchronous machine (2-pole) torque and AC machine torque constant
S = n-nsyn nsyn 3(Ira)?R Tem Wslip Induction motor slip relevant to the rotor and synchronous speeds (rpm) - NOTE: S is negative for motor, positive for generator Electromagnetic torque, as a function of slip and power loss (rotor resistivity / current) Space vector representation of current Space vector angles of current and flux density in a synchronous machine AC machine magneto-motive force (mm) space vector AC machine stator field density space vector AC machine magnetising current space vector = is(t) = ia(t)20° + ip(t) 120° + ic(t)/240° 0i, (t) = 0m(t) + 90° És(t) Ns is(t) p B (t) = MONS- T's(t) plg 3 īms(t) = zſm_wt Va kpwM Vtri) = = DC motor drive converter gain Electrical frequency, rotational speed (rpm) and number of pole-pairs in a synchronous machine nxp fel = 60