Question

Machine Desgin course related

4. A compression spring is needed to fit over a 12mm diameter rod. To allow for some clearance, the inside diameter of the spring is to be 15mm. To ensure a reasonable coil, use a spring index of 8. The spring is to be used in a machine by compressing it from a free length of 125mm through a stroke of 75 mm to its solid length. The spring should have squared and ground ends, unpeened, and is to be made from cold-drawn wire. (a) Determine a suitable wire diameter. (b) Determine a suitable total number of coils. (c) Determine the spring constant. (d) Determine the static factor of safety when compressed to solid length. (e) Determine the fatigue factor of safety when repeatedly cycled from free length to solid length. Use the Gerber-Zimmerli fatigue-failure criterion.

Machine Design related, shigley's mechanical engineering

Answer 1

P8 = 0 al (cht-a) 8 Sh1:22 р щ Chi 2 ww si = pt щщ 51 = p - P8 щ 51 = p – а P8 - g 8 = ор = 2 elo (( с 8 indeac C = 8 bureas = D-d а щS1 а Inside diameter = o-d ( о k777 ан Әдім истор -P102 w983 орох Ә9 мярцо РӘцдааца 5pua Pцоод риъ Pə gonbѕ әлъч роҷs би1985 ачі w was a щщ (5t - Sa)) - 51 щщ 5. 30 Әң0.015 free length of to 3125 mm through a spring indesc of C-8 йој4a105 inside diameter of the spring Ib = 15 mm

D = 17.143 mm b) Total number of coils design of machine from Table 10- elements book Shigley by ts ANP WWRS 3 Sr ONE 250 mm AN So 2.143 24 coils SIN = 23.33 coils a AN 3 24 coils constant c) spring 1-01 from table Na = N6-2 Na 24-2 Na = 22 coils no from Table lo-5 G= 79-3GPa d2G R = 803 Na

3 K = (2.143)4 (79.3) 10 8 (17.143) 3 x 22 3 K=1.886 N/mm d) Static factor of safety when com Poessed to solid length from Table 10-4 m A = 1783 mPa.mm m = 0.190 R Sut A am 1783 Sut - 13 (2.143)0.190 Sut - 1942.6 mpa foom Table 10 -6 ssy zoals Sut Soy = 0.45 (1542.6) sy 694.17 mpa

-kys Fs mm Fs (1) (1.88c) (+s) N/mm - Fs = 141.4S N ЦC+2 Кр 11 ЦС-3 Ц. С8) +2 (1 ВВ ц (8) -3 kg 1.1+ 2 4 Кр • 1. L+ 2 Tg = KR BFC D tid 3 Sa - 1 172 8 (141.4S) (143) т (2.43)3 Mς с 133.3 mPa. Ssa (1 ng То 694, 12 ng с +3S, 3 ng - 0, 9ч

Gerbeo ordinate intercepto for e) 13 Ta Em = 0.5 Tg -0.5 (735.3) Ta - Tm= 367,65 mpa Ta 85 ta Tm 367.65 82 367.65 8:1 failure criterion using the Gerber fatigue with Zimmerli data 5 su = 0.67 Saub Ssu -0.67 (1942.6) Ssu = 10 33.54 MPa the Zimmerli data is 241 mpa 11 Sga Ssa 379mpa ssm Sse 1-(55m Issu)? 241 Sse 1-(379/1033.54)

S se - 278.44 mpa from Table 6-7 82 5 gu? 2 sse 8sou Ssa Fe + Paket esse 5 sa ?(1033.5u)? 2 (278-44) -1 + 1+ [2 (278.44) (1) (1033.54 ( S 260.7 mpa 'sa Ssa ng ta 260.7 ng 36 7.65 ng I 0.71