Question

(b) Fig Q1 shows a two-stage spur gearbox. The input shaft is coupled to a motor. The shaft “b” turns freely in bearings C and D, except for the gear-tooth forces. Assuming 100% gear efficiency, determine the resultant radial loads applied to bearings C and D, and sketch the shaft "b" as a free body in equilibrium. (28 Marks) (Total 33 Marks) INPUT 22 TEETH m = 5 mm 0 = 20 24 TEETH SHAFT"b 18 TEETH IDLER 66 TEETH OUTPUT 1 kw 200 rpm 84 TEETH VIEW FROM A Fig Q1: Two-stage spur gearbox.

Answer 1

Torque transmitted by shaft output shaft. PX 60 000 x 60 21214200 0:42 To=47.74 Nm El Dia of 84 teeth gear miz: 8445 420mm Also: : 0:42m To DX > Pe : 2 To: 26.47,74 -227.33 N Tangential force on 84 teeth gear : 227.33 N e &: pressure angle : 200 Radial force on 84 teeth gear 22 Pt tanø 1 .227. 33 tanzo = 82.74 N. (Downward) Tangential and Radial force on 18 teeth gear . le. idler gear is same as the 84 teeth gear. Also the Targential and Radial force on 24 teeth gegn on shaft 'b' is same as the idler gear ar 84 teeth gear... . (Picha 227.33 N. - and pr=82.74 N (Upward) Torque on genees Shaft b = Tango (P+) 24 x 0/2 - To = 227.33x 24x5. - T363q.8 Non = 13.639 Nm. Tangential force on 66 teeth gear (P+)64 - 2x To 2x13639.8 - 82.66 N. Radial force on 66 teeth gear: (Pesax to = 30.08 N. (povnu Des - 66x5

Px=30:08 Tangential and Radial force on 22 teeth gear is same as 66 teeth gear - So...-- (Puls : 82.66No om and CPr)zz - 30.08N cupward). free body diagram of shaft B. 300 T = 13-639 Nm ID k to b = 32.744 _- Ryh F.BD. Shaft B Let Rvc and Rvd are Resultent Rodial Lood. at c and a respectively. Tokily Moment about C. de Mc20 82.74x130 + Rupx 90 – 30.08x30 - 0 90 = 30.08x30 - 82.74x130 > Rvox 907 - 9853.8 Rud : -109.48N (Down ward) Total lood Ruet Rud =-30.88 - 82.74 - Ruc30.08- 82.74 +109.48 - Ruc= 56.82 N. (Upward) Resultant Rodial Lood on C: Ruc: 56.82N ↑ Upward Resultant Radial Load on D: Rud: 109.98 N / Dounaan.