Question

I. The countershaft shown in the Fig Q1 has two spur gears mounted on it with teeth cut wi a 20 pressure angle. The shaft (grooved) is to be made of cold-drawn AISI 1040 steel havin Sut 779 MPa and S,-593 MPa, an elongation of 19% and HB-262. You are asked to size the shaft for safe operation according to DE-Elliptic criterion by using a factor of safety of 2.5 and a reliability of 99 percent. The stress-concentration factors for the grooves, K and Ks, are 2.14 and 1.75 respectively for a fillet radius of r 2 mm. The shaft is supported by two cylindrical roller bearings at D and C, which have bore diameters of do-40 mm and dc-55 mm. a) Find the reactions at points D and C and draw the shear force, bending moment and torque diagrams for xy-plane. (8 pts) b) Do the same as in a) for xz-plane. (7 pts) Dimensions in millimeters. 12 kN 20° Gear 3, 700 0. .4 Gear 4, 350 D. 20 450 250 450 9

Answer 1

F- 24oooN a) Readi ons at Dand C un χ-y pla ne 2 R> So 4So By equilibtum Cendihons Rp+ Rc - 12312-125N Re 6602-475N Rp - 5T10-25N VA = 5710-25-1200osin2ổ SF aと A, VA- 1606 N - - 6602- 415N

moment dragsa CHoad At 2D-57ID-25N Rc G602-47SN 450 450 250 3-146kN-m 57I0-25 Shers I6o6 -6602, 415 2-9711 2-569 b 3

<b> Reachtno at D and c > x-z plane 12000 CB20 4So 2 450 Ro+Rc -11276-31 N Rp -116-31 +q315-21 Ackual load diacsan 25o 3.946 kV-

12000 S)o SF at A> VA- -16 -13237-4N SF at B , VB-_13237-N-t 240004)20 9315-21 n/ Vc - 931521N Bendun Moment olam_ Rc- 4315 21N Lood Dag 6 250 4SO VCN) G31S-2 12131-H Lendi*t D-982 4-19