Question

3-116, 3-119 The table gives data concerning the shrink fit of two cylinders of differing materials and dimensional specification in inches. Elastic constants for different materials may be found in Table A-5. Identify the radial interference 8, then find the interference pressure p, and the tangential normal stress on both sides of the fit surface. If dimensional tolerances are given at fit surfaces, repeat the problem for the highest and lowest stress levels. Problem Inner Cylinder Outer Cylinder Number Material di Material D 3-116 Steel 0 2 .002 Steel 2.000 3.00 3-119 Steel Steel 3.00 2.003/2.006 2.000/2.002 do D.

Answer 1

Date:_ Page no:1 solution of Problem. 3-466 and 3-119 3-116 soln Given Data: The inner diameter of Innes cylinder, di coin The outer diameter of Immet cylinder, do = 2.002 im. The immex diameter of the outer cylinder. De = 2:00 in The outer diameter of outer cylinder, Do = 3.00 in The inner and outer cylinders are made of steel using the standard tables Taking Properties from physical constants of material tables, Modulus of elasticity g Ei= FO 30 MPSC poisson's satie, Vi = Vo = 0.292. Radial interference i s= (do) - (0) 22 8 = 2.002 - 2.00 2 2 Is = 0.001 in Ans. The interference Pressure is, L where P = ES T (20²-R²) (R2-8²7 2 R3 L (€²-&2) to = outer radius of outer cylinder ti= inner radius of inner cylinder Re immer Ladius of outer cylinde -

Date: __ Page no Page no: C For the given cylinders, - ti e di co R - . Di = 2 = 1 in ko - DO - 3 - 15 im so. P- (30 X106) (0.001) [((1.5)2-(192) ((172-(0)2) 2 (4) 3 (2.5)2-(0)2 P-8333. 33 33 Psi Ans. Now calculate the tangential stresses on each side of the interference surfaces are, Coolil - - p R²+ e; 2 - TE=R R²-22 Coti -(8333-3333 ) : (1)2 + (012 - (4) 2-c002 Topi --- 8333-3333 psi | Ams: (otol = p 8² + R² TE=R & 2-R² Guo - (8333-33.3.3) (1.5)2 + (1)2 11.5)2-(1) Toto = 21666.6667 Psi Ams

Date: Page no: 3 3-119 Sol Given Data :- The innie diameter of inner cylinder di= o im The outer diameter of innet cylinder do= 2.003/2006 in. The innes diameter of outer cylinder, Di= 2.000/2.002 in. The outer diameter of outer cylinder, Do= 3.00 in The material is steel (two steel cylinders). taking Properties from A-5 table & Ei Eo = 30 mp si Vi= Vos 0.292 The radial interference, Smin = (do) min -(01) max 2 Smin = 2.003 - 2.002 2 2. Smin = 0.0005 in Smax = (dol max. -.(Di) min 2 2.006 - 2.000 Smax = Ismax = 0.003 in

Date: Page no:4) The interference Pressure is, P = ES T (80² -R2) CR2_{:2). 2 R3 I (8²-8; 2) - For the given cylinders, - 2 R- Di = t - 0.5 in to = Do = 3 = 1.5 in minimum interference Pressuke is, (S=smin = 0.0005) Pmin - (30x10%) (0.0005) I ((115) ² (0.582) (10.5)2-(0)2) 260.513 L {(1.582-(0)2) - 13,333 Psi Ans. | Pmin Mogrimum interference Plessure is, (S: Smax = 0.003 in) Pomar = (30x106)(0.003) T (61.5)2-(0.5)) (10.5)2-(012) 2 x (0.53 ((1.5)2-(0)2) 80,000 psi An Pmax.

Date: page no: (5.) The minimum tomgential stresses on each side of interference surfaces are Tommi = - Pmin R² + 2; ² R²-4; 2 - 13,333 (0.5)2+con '&=R ( o iler- - 13,333 0.12 - 2012 TER 't=R To mim) - -13,233 Pisi_ Ansi for mim hotter - Pmim to? + R2 (thumou 13,333 (1.5)2 + (0-5) (11.5)2 - (0.5² (omnoler - 16, 666 esi Ans. The maximum tangential stresses on each side of the interference surfaces atla Cormors militar = - mox (p2+ &). --80,000 (0.5)2+(012) C(0.52 -102, (of manjila -80,000 Psi for mox jole - e - Pmax ( 20 ² + R2 - 30,000 ( 1257 - (of many of 100,000 psi. Ans. ER -80.000 / (1.502 +0.5021 I (1.512-(0:53