Esercizi di Elementi costruttivi delle macchine sulla fatica

Sez. 3

Ga: Mf: 21 Mf πd²

N/πd² - S Σ27,68 N/mm²

NE No t Lowmin. : Cs = S_m/σ_d - S ? σ_d

k = 0.95 - 3σ stress

k = 0.5 - 2+0.6 stress - N

Materials

• ciclo 0: Gm [N/mm²] 0, Ga [N/mm²] 300
• ciclo 2 100: 40, 130
• ciclo 3 12: 55, 280
• ciclo 4 10: 80, 250

S = a N^b ➞ log S = log a + b log N

log (0.5 Su) = log a + b log (1-0.5) ➞ log a - 3b

log (0.5 S_u) = log a + b[log (2) + log 0.5]

= log a + 6b + b log 2

log (0.5 S_u) = log (0.5 Su) - 3b

b = log (0.5 S_u) - log (0.5 Su)/3t log 2

➔ b = -0.077

log a = log (0.5 Su) + 3b ➞ a = 120 ➞ log (0.5 Su) r=3b

= 120 N/mm²

σ_aeq / 1 = √(σ_a² - S_u)

1 - Gm/Su

= 146.25 ➞ N2 = (σ_aeq / σ_a)^1/1b

D_i = Σ n_i/N_i

Life = 1/D_i

Life = k/3600 [hr]

Sez. 3

Non lavoriamo:

K = EOF

acciaio S 355 (F=360)

Del:

0,95α → 5 ciclo = N

0,5 Su = 2,66 culo = N

• ciclo 0 → m/cb | Gm (N/mm²) | Ga (N/mm²)
• ciclo 0 → 18 | 0 | 300
• ciclo 1 → 100 | 40 | 130
• ciclo 2 → 12 | 55 | 280
• ciclo 3 → 40 | 80 | 250

S = α N^b → log S = log α + b log N

• log (0,9 Su) = log α + b log (10³) = log α + 3b
• log (0,5 Su) = log α + b log (1,26⁶) = log α + b [log (2) + log 1,206]
• = log α + 6bτ + b log 2
• log (0,5 Su) = log (0,9 Su) - 3bτ 6b + b log 2 = log (0,5 Su) + b [3 + log 2]

b = ^{log (0,5 Su) - log (0,9 Su)}/_{3τ + log 2} = -0,77

= 130 N/mm²

Ga_eq¹ = ^α1/_{1 - ^Gm/Su = 300 → N1 = ^{(Gaeq/α )1/b}}

Ga_eq² = ^α2/_{1 - ^Gm/Su = 146,25 → N2 = ^{(Gaeq/α )1/b}}

D_i = ^{∑ m_i}/_Ni

Life m = ¹/_Dpr ,

Life τ = Life m ^k/_{3600 hτ}

Dati

Sf = 620 N/mm²

Sp = 398 N/mm²

F: 2000 N

M = 60 000 Nmm

L: 500 mm

l₁: 220 mm

l₂: 60 mm

r: 4 mm

D = 36 mm d = 35 mm

C_s + φ = 45

n = 10⁶ cicli

Reazioni Vincolari

1) H_B = 0

2) V_A + V_B – F = 0 => V_B = 680 N

3) –F⋅330 + V_A⋅500 = 0

V_A = 1320 N

Verifica sezioni 1, 2, 3

Sez. 1

τ_m = _16·Tle/^πd3 = 5,16 N/mm²

τ_{m eq} √3 ⋅ τ_m = 3,16 N/mm²

(Von-Mises)

σ_a = _32·Mf/^πd3 = 6.92 N/mm²

Goodman

_σm/^S_u + _σa/^S_m = ₁/^C_s

S_m = 1/2 S_u C_L C_P C_S C_T C_R = 138,16 N/mm²

1 a_j 0,5 1 0,8 #

C_s = ₁/^{(_τm/S_u + _σa/S_m)} = 2,66 > C_sf = 2,5

Sez. 2

Y/d = 0,023

D/d = 1,054

Mc: 2,2

r = 1 mm

HRC: # & /3 #

V = 12,7 N/mm²

S_u = 600 # HS

M_f = π/4 (Me+Mz) ρ = 1.78

σ_{a Hf}: _32·Mf/^πd3 = 15,68 N/mm

C_S = ₁/^{(_τm/S_u + _σa/S_m)} = 7,37 > C_sf

ciclo 1

110 226 384 2070 1686 612 55 38 55

ciclo 2

80 408.8 76.20 432 832.4 48 190 70 230

ciclo 3

125 660.8 292 247.50 3450 123 111.5 150 215.5

F_a = (F_nom + F_min) / 2

32 d₁³

N_d = (_a.eq/a)^1/b = 2800.10⁶

D₁ = 110 / 2800.10⁶ = 39.2.10^-8

N_d2 = 3000.10⁶ →

D₂ = 2.6.10^-8

N_d3 = 76.10⁶ →

D₃ = 25 / 76.10⁶ = 32.8.10^-8

Life D_tot = D₁ + D₂ + D₃ = 39.2.10^-8

Life = 1 / D_tot = 2.56.10⁶

Life_f = Life * 1/3600 = 320860 h

Dati: D=30 mm d=15 mm

l=1 mm l=4000 mm

t=455

Φ₁=3.45

C₅=0.9 C₁=1 C₉=0.9

S_ut=900 MPa

S^ν(=750)=150 MPa

S^(ν>)=810 MPa

Svolgimento Andi:220 sede sez B

Ricavo Coef a e b con Wishler (infatti 2x2ma poiche ho S_m(x=0.9))

S_m=Sⁿ C₆ C₅ C₁

150 . 0.9 . 0.7 . 1 = 283.5 MPa

log (0.5 S_ue) = log a + b log (-0.5^a)

log a = log (0.5 S_ue) - 3b

-3.322583

log (S_m) = log a + b log (2 - 1.6)

-3.322583

log (S_m) - log (0.5 S_ue) = b (3 + log 2 - 3)

b=log(S_m) - log (0.5 S_ue) / 3 + log 2

-0.133448 MPa