Question

4. (12 points) A compound reverted spur gear train is to be designed to reduce the speed of a 180HP engine's rotating shaft from 3500rpm to 100rpm exactly. (a) (5 points) Specify appropriate numbers of teeth (N2, N3, N4 and N5) to minimize the gearbox size. A pressure angle of 20° is used for all the gears. Interference of gears is not acceptable. (b) (5 points) If all the gears are cut with 20° full-depth system. Assume a diametral pitch of 6 teeth/in, and allowable stress of 60kpsi. Find a suitable face width for gear 5 (see the following figure). (c) (2 points) Provide at least two (2) solutions (by modifying some parameters above, while keeping the same gear train value) to further reduce the size of the gear box. 2 N 5 3

Answer 1

Solution: H= 180 HP, Wi = 3500 rpm, wo : 100 rpm, d=209 Wo (a) 100 3500 I 35 Wo wi N3 Ns N2 NG Let N2 MA N; N = già Smallest number of teeth on pinion without interference is given by the formula Np of (mtalima +(1+2m) sino) 2k C\+2m) sinad Let k=d, m=5.916, 2 (5.916+ 15.916) 6)+(1+2x5.916) six?? Np - (1+ 285.916) sin220 = 1.332 (5.916 +6.042) .. Np = = 15.9 ñ 16 16 teeth Net Ny=N5 N22 Na -5.9168 16= =94.6 teeth Let Me - Nu=94 16 94 16 g4 x 3500 = 101.4 rpm

Since Wo > 100 tpm; eat N2= N42 95 teeth Woe 16 16 X gs" gs x 3500.- 99.3 a 100 rpro INS N5= 16 teeth N2 = N4=gs teeth ...(Ans) = 2.67 in (b) for gear S, N5= 16 teeth, p=6 teeth lin Call 60 kpsi ,&= 20° Pitch diameter d= Ns 16 P Pitch line velocity Vaildn 7(2-67)x100 12 Velocity form factor for cut profile 6 69.9ftl 12 ku= 1200 + V 1200+ 69.9 -1058 1200 1200 Horsepower transmitted is given by lip 33000x hip last i = lot. 33000 i. Wat 33000 X 180 84978.5 ebb a 69.9 Wta FY fall Wit => F KVP Call Y KuP

Where Y= form factor = 0.296 for 16 teeth : Fa 84978.5 x 1.048 x6 60000 X0.296 F = 30.4 in (Large face width is justifiable for geartrain transmitting 180 HP power) of train (c) size of the gearbon can be reduced by 6) Decreasing the diameter of the year and increasing dimetral pitch. This will keep value of gear constant at the cost of increase in number of teeth. (1) Transmission shaft length can be reduced by incorporating stronger shafts with adequately designed bearings to accomodate extra load.