Question

You work for a gearbox company and have been charged with helping to design a geared countershaft for a speed reducing gearbox. The gearbox consists of a compound reverted gear train as shown below and is to be designed for an exact 16:1 speed reduction ratio. The input motor provides 10-horsepower which is carried through the gear train and operates at a speed of 2,000 rpm. You are asked to consider spur gears with a 20° pressure angle and 4 teeth/in diametral pitch for this project. 1. Determine the number of teeth and pitch diameters for each of the gears to minimize the gearbox size while avoiding gear tooth interference. 2. Calculate the rotational speed of the countershaft (i.e. intermediate shaft) and the output shaft. 3. Calculate the pitch line velocities and the radial and tangential loads acting at the two sets of gears. 4. Calculate the reaction loads at the proposed bearing locations. Using Table 11-2, specify a single ball-bearing that will work for both sides of the shaft. The bearing should be chosen to allow for 2 years of continuous operation. 5. Use the bore diameter of the chosen bearing to set dị. Calculate d2 and dz using the approximations shown and rounding up to the nearest 1/8”. Assume a fillet radius of 0.035” at the bearing shoulders and 1/16” at the gear shoulders. 6. Draw all appropriate shear, moment, and torque diagrams for the shaft. 7. At the point of maximum stress, determine the bending and torsional shear stresses. 8. Using Table A-20, specify a material for the shaft that will allow for infinite life. Provide the factors of safety against both first cycle yielding and fatigue using the ASME-Elliptic criterion. 9. Specify the tolerances on both the ID of the bearings and OD of the bearing lands for a locational interference fit. 10. Calculate the shaft angle at the bearing locations.

Answer 1

e- 16.1 Ng at & No We know that diameteral pitch Partially solved :- 0 speed zoolution ratio Input Power Palohp = 10x746 = 7160 watt speed of mitor n = 200pm. & pressure angle diameterad pitch & = 4 teeth / of no of teeth are Me, My Neels at gear 2, 3, 445 respectively then h₂ n er 16 = ( 40) with two equations and pour unknown numbers of teeth two free choices available. Choose M₂ & Me to be small arpossible as 16 teeth 8o , Mga Ant &No=& Me - 64 80 Ng=16, Moc 64, My = 16, Ns=64 dz N So, d₂ = N2 Pa - tun are number of teethos Pach To, = 16 e

do= 64 4 Id₂ = 16 inch simitsly d=99m cd=16h dz=16n. dzzon, daz16in, da atin, Porque an shaft-2 I= 6op 6ox 746x10 2KX 2000 Prin = 35.619 Nom 12 = 35619 N.mm or T₂ = bol boxio 27 20x2000 We know that speedsats n ne ( He is ng = 2000/16 14) in = 500rpm Speed of Intermediate shaft 3 = 500pm. similarly N5 ng na nal Me (non Thes 5000 16 ) alsopm 752 125rpm]

Vm= 418.08 in/s (co so, spead of output shaft is ns=1858pm. pitch live velocity of gears-2- adh n M/A 60 5x 4 2000 Pitch live relocity of gran 3 Adzin 60 AX 500X 16 to [= 410180gr/ pitch live velocity of goan. A y = Ade.no XX 4 X 500 60 No = 104.72 in semilarly Us=104.72 m/s Tangential force gan-2 W2 = 33000H - 33000x lo 787.82 llof 418.88 Wt 2187.82 lsf

4 Radial force Why a Wetand = 787.828 tanzo" Was 286.74 lsf forces on gear 2f3 are equal to Wtz = 207.82 lff Wro 286.74 lsf Similarly tangential fore an gear - 4 and 5 ito 330000 X 10 104.72 3151126 lbf Weg Radial force Warga Wag tanzo I wrea 1196.97 esf semilang lits - W = 3151126 3151126 lof = 11 4 6 197 lbf Wrang bling 4