Question

2. Gear dynamics. The gear train above is driven on the input shaft with a 0.5 hp electric motor.
All of the gears have a diametral pitch of 8 teeth per inch.
a) What are the diameters of Gears 1, 2, 3, and 4?
b) What is the pitch-line velocity of Gear 1, in ft/min?
c) Is the pitch-line velocity of Gear 2 the same as Gear 1?
d) What is the pitch-line velocity of Gear 3 (and, therefore, Gear 4), in ft/min?

An input shaft drives Gear 1 with 20 teeth at 1800 rpm which mates with
the 80-tooth Gear 2 which in on the intermediate shaft. Also on the intermediate shaft is Gear 3
with 18 teeth. It mates with Gear 4 on the output shaft, where Gear 4 has 90 teeth.

the gear train is as described, no physical picture

Answer 1

this is the compound gear train problem.By using velocity ratio and train value we can solve this problem.
Solution:- from the draw the year train Gear train as below: problem statement we can -- R s — P E Q are 1. Q & R are R&S care - meshed together on same shaft meshed together that all have given gears Pap Pro Pop Pds 8 teeth that diametral same diametral It is pitch per inch weknow pitch la olt where 0 - diameter of gear T- Number of teeth. wlst 11 07 Þ alt = m (module

know that diametral pitch Pa = T D. (In inches) bat m where m-module. -It have same is given that all gears diametral pitch. To TQ = 8 Фр Do 20 8 Papa Pp Dp = 2.5 inch Pda = = 80 = 8 Do Do = 10 inch 8 Par = 18 DR PdR 2.25 inch

lds 8 Ds Ds = 11.25inch Dp = 2.5 inch Da= 10inch DR = 2.25 inch 0.20033 + ft 0.8333 O. 1875 ft 0.93751 Os = 11:25 inch b) gear o or Pitch line velocity of Vp= TT Dp np. TX 0.20833 X1800 = 1178.07 #min Vp= 1178.07 ftimon c) Np To Тр Na 2. Na = na 1800 X 20 450 pm 80 Vo: Tonos TX0.8333 X450 VQ = 1178:05 ft (min Yes Saine. both Vp & Vo are

d) we know that X Ne = Np Na NR Ws NR Train value = No NQ Nos No =1 both HR Same shaft are on Ne Nj To A. To XG) Tp. TR 90 Np X NS 20 18 20 NS Nga 1800 go rpm 20 Viss TTDs ng - TTX0.9375X90 N = 265. ft (min Ts Ne Hs TR 90 NR= 90 450 rpm 18 VR = TX0.1875x450 VR: 265 filmin