Thick-Walled Cylinders and Press Fits by W.H.Dornfeld PressCylinder:

Transcription

1 Thck-Walled Cylndes and Pess Fts 004 by W.H.Dnfeld PessCylnde: 1

2 Stesses n Thck-Walled Cylndes Thck-Walled cylndes have an aveage adus less than 0 tmes the wall thckness. σ σl They ae essuzed ntenally and/ extenally. The ncal stesses ae σ c ccumfeental (h) σ c, adal σ, and lngtudnal (axal) σ l. 004 by W.H.Dnfeld PessCylnde:

3 Ccumfeental & adal Stesses F the geneal case f bth ntenal and extenal essue, the ccumfeental and adal stesses at adus n the wall ae: σ = Whee the ± s: ± ( 1 ± ) F the secal case f nly ntenal essue, = 0, and the stesses at adus ae: σ = + f ccumfeental, and - f adal stess. The sgn cnventn s the same. 004 by W.H.Dnfeld PessCylnde: / Eqns 10.0/10. Eqns 10.3/10.4 3

4 Lngtudnal Stesses The lngtudnal stess s smly gven by a Fce/Aea, whee the Fce s tmes the ccula nsde aea π, and the Aea s the annula aea f the cylnde css sectn, π( - ), : σ l = Ths s geneally nly cnsdeed f the case f ntenal essuzatn ( = 0). Un-numbeed Equatn just belw Eqn σ σl σ c 004 by W.H.Dnfeld PessCylnde: 4

5 Stesses vs. adus Fst, the easy bsevatn: adal stesses at the nne and ute sufaces ae equal t mnus the essuzatn. If a suface s unessuzed, the adal stess thee s ze. If a suface s essuzed, the adal stess thee = -, because t s n cmessn. Nw let s lk at an ntenally essuzed cylnde, and hw the adal and ccumfeental stesses vay acss the wall thckness at adus. σ 1 ± = ( + s ccumfeental, - s adal ) Eqns 10.3/ by W.H.Dnfeld PessCylnde: 5

6 Stesses f Intenal Pessuzatn Stess (KSI) Thck-Walled Cylnde wth ntenal essue f 5330 s adus (n.) σ HOOP STESS ADIAL STESS 1 ± = ( + s h, - s adal ) 004 by W.H.Dnfeld PessCylnde: 6

7 Stesses vs. adus - Intenal Pessue adal stess s as edcted: s at the nne, essuzed suface. 0 at the unessuzed ute suface. H stess s: Maxmum at the nne suface, 13.9 ks. Lwe, but nt ze, at the unessuzed ute suface, 8.5 ks. Lage n magntude than the adal stess Lngtudnal stess s (tust me): 4.3 ks, cnsdeed as a unfm, aveage stess acss the thckness f the wall. Nw let s lk at an extenally essuzed cylnde. 004 by W.H.Dnfeld PessCylnde: 7

8 Stesses f Extenal Pessuzatn Stess (KSI) Thck-Walled Cylnde wth extenal essue f 5330 s. ADIAL STESS HOOP STESS adus (n.) σ 1 ± = ( + s h, - s adal ) 004 by W.H.Dnfeld PessCylnde: 8

9 Stesses vs. adus - Extenal Pessue adal stess s as edcted: 0 at the unessuzed nne suface s at the ute, essuzed suface. H stess s: Mnmum at the ute suface, -8.9 ks. Maxmum at the (unessuzed) nne suface, -14. ks. Lage than the adal stess Lngtudnal stess s: Nt usually cnsdeed f extenal essuzatn. 004 by W.H.Dnfeld PessCylnde: 9

10 Pess Fts In a ess ft, the shaft s cmessed and the hub s exanded. Befe Hub adal ntefeence, δ Hub Afte Shaft Shaft 004 by W.H.Dnfeld PessCylnde: 10

11 Pess Fts Pess fts, ntefeence fts, ae smla t essuzed cylndes n that the lacement f an veszed shaft n an undeszed hub esults n a adal essue at the nteface. Hub 004 by W.H.Dnfeld PessCylnde: 11

12 Chaactestcs f Pess Fts 1) The shaft s cmessed and the hub s exanded. Hub ) Thee ae equal and ste essues at the matng sufaces. Shaft 3) The elatve amunt f cmessn and exansn deends n the stffness (elastcty and gemety) f the tw eces. 4) The sum f the cmessn and the exansn equals the ntefeence ntduced. 5) The ctcal stess lcatn s usually the nne damete f the hub, whee max tensle h stess ccus. 004 by W.H.Dnfeld PessCylnde: 1

13 Analyss f Pess Fts Stat by fndng the nteface essue. Eδ ( ) ( ) ( ) = Whee d s the ADIAL ntefeence f hub and shaft f the same mateal, wth mdulus f elastcty, E. Eqn 10.5, eaanged If the shaft s sld, = 0 and Eδ 1 = Eqn 10.53, eaanged 004 by W.H.Dnfeld PessCylnde: 13

14 Analyss f Pess Fts If the shaft and hub ae f dffeent mateals = E + + ν δ + Once we have the essue, we can use the cylnde equatns t cmute the h stesses at the nteface. A) The ID f the hub s tensle: σ B) The OD f the shaft s cmessve: c = σ E c = + + ν by W.H.Dnfeld PessCylnde: E,ν Eqn 10.51, eaanged Eqn Eqn E,ν n, = Pssn = - f shaft s sld 14

15 Stan Analyss f Pess Fts The ess ft has n axal essue, s σ l = 0, and t s a baxal stess cndtn. The ccumfeental stan whch equals the adal stan (because C = π). ε Because the adal change δ = ε, we get the ncease n Inne adus f the ute membe (hub): c = And the decease n Oute adus f the nne membe (shaft): σ c E + = + ν E δ ν σ E + = ν E δ Eqn Eqn by W.H.Dnfeld PessCylnde: 15

16 As a check, make sue that Ntes n Pess Fts δ + δ = δ The assembly fce equed wll be F max = πdlµ whee = the nteface essue µ = the ceffcent f fctn F d = L The tque caacty avalable s T = F = πdlµ whee = the ntefeence adus, as befe. T We cnvenently knw the nteface essue f these equatns! 004 by W.H.Dnfeld PessCylnde: 16

17 Shnk Fts If heatng clng a at t acheve a shnk ft, the equed adal ntefeence s: = d = α T whee s the nteface adus α s the ceffcent f themal exansn T s the temeatue change T select an amunt f ntefeence see ANSI/ASME tables f class FN1 (lght) t FN5 (Heavy-dve) fts. They gve ntefeence n 0.001" n damete f a ange f dametes Ex: FN4 f 0.95 t 1.19" damete, ntefeence = 1 t.3 mls n damete. 004 by W.H.Dnfeld PessCylnde: 17