Question

A straight-bevel gear mesh is utilized to transform the rotation about a horizontal shaft of a motor-driven pinion into rotation of an output gear about a vertical shaft as shown in Fig. 1. The pressure angle f = 20°. The pinion shaft rotates at 900 rpm.

a. Both pinion and gear are Grade 2 steel through-hardened at 250 Brinell and are uncrowned. The quality number is 9 and the desired life is 30,000 hours with a 0.999 reliability. For a design factor of 2.0, rate the speed reducer for power using the AGMA method. (10 points)

b. Select the appropriate tapered roller bearings for use at C and D assuming a bore of 1 in, and that the pinion transmits 8 hp to the gear. The axial load is carried by the bearing at C. The bearings are to have a desired life of 30,000 hours at a combined reliability of 0.99. Use an application factor of 1.5, an initial K = 1.5, and the following Weibull distribution parameter values: x0 = 0, theta0 = 4.5, and b = 1.5 at a rating life of 90·10^6 revolutions. (10 points)

3- - 3.88 - -- 1.293 15-tooth pinion P= 5 teeth/in 45-tooth gear Figure 1 (all dimensions shown are in inches) O

Answer 1

(Page 1) Solution Given Pa F = 2p - p = dp = datai - 5 teeth / in - pitch face width - 1.3125" finom tooth - 45 pinion speed = 900 pm 28 = 1S - 3.00 inch T X3x goo 12 - Idene 12 7 Solety No, of factor :- nevolution Ne - 6ox nx dite) hours 5 60x900x 30000 NL - 1620 X 106 see # Stress - 1620x10 & K cycle factar (KL) for No = rev. 4 3558 No alto 1.3558 (1620x106)0.0170 - 0.92951 Ik

(Rage-2) # For Reliability of o.999, KR = 0.50 - 0.25 log (IR) - KR = o.so - 0.25 log (1-0.999 - 1,25 # Stress cycle factor for pitting resistance for 1.640) cycle - a = 3.4822 X (NL)-0.0602 C = 3,4822 x (1620X100 a = 0,9714 # Dynamic factory (kW): - A- 50+56 (1-B) 3 - 0. 25 (12- Qut B = 0.25 (12-93 B = 0.52 A - 50 +56 (1-0.52) - 76.88 70.52 K1 - 76,88 +1706.85 76.88 - Ko = 1,167

For steel grade 2 :- Sat G & HB + SI 8° Sat = 48 (250)+ sa 80 Sat - 17960 psi z

page-u) km - Kmb to,00 3.6F² 4 Face width km = 1,25+ 0.0036 (1.3125) ² km = 1.2562 1 J (Bending strength Geometry factar for 20' pressure angle & go shaft ongle, for no ot pinion teeth - 158 Gear teeth -ng-45 , J = 0.181 J = 8. 181 . For Now straight bevel gear kx=1 put all the values - - It - Wt X(S) X (1) X 1.3125 0.528x1.256L 2 (0,180 0 St - 13.9664 Wt - Now permissible bending given by stress is

- (Pages) Swt - Sat KL SF KTKR Assuming temperature will be 25° F L T <250°F, so K=1 Sf = JH - 2 (design factor) Jet - 17980 X 0, 9215 2x 1x 1.25 Swt - 6684.964 psi - 2 Equating equation 1 & 2 St Y Swt 13.9864 Wt X 6684.964 We - 977, 96 lbt 7 H - Wt. Vt 33000 – 4.77,968 70 6.85 33000 1 - 10.237 hp]