5 5. 0 6 5. C r C a ISO 8 JIS B 58 5.. 96 Lundberg Palmgren ISO 5. 5. C r b m f c(icosα) 0.7 Z D w.8 b m f c(ilwe cosα) 7 9 Z 4 D we 9 7 α = 90 b m f c Z D w.8 b m f c L we 7 9 Z 4 D we 9 7 C a α 90 b m f c(cosα) 0.7 tanαz D w.8 b m f c(lwe cosα) 7 9 tanαz 4 D we 9 7 b m f c i α ( ) Z D w (mm) L we (mm) D we (mm) D w 5.4 mm D.8 w.647d.4 w 5. b m b m...5. 5. f c D wcosα/dpw 0.0 9. 9.9 0.0 5.8.4 0.0 40. 4. 0.04 4.8 5.9 0.05 46.7 7. 0.06 49. 8.6 0.07 5. 9.9 0.08 5.8. 0.09 54.. 0.0 55.5.4 0. 57.5 5.6 0.4 58.8 7.7 0.6 59.6 9.7 0.8 59.9.7 0.0 59.9.5 0. 59.6 5. 0.4 59.0 6.8 0.6 58. 8. 0.8 57. 9.4 0.0 56.0 40. 0. 54.6 40.9 0.4 5. 4. 0.6 5.7 4. 0.7 50.9 4. 0.8 50.0 4.0 0.9 49. 40.7 0.40 48.4 40.4 D pw (mm) 5.4 f c D wecosα/dpw 0.0 5. 0.0 60.8 0.0 66.5 0.04 70.7 0.05 74. 0.06 76.9 0.07 79. 0.08 8. 0.09 8.8 0.0 84. 0. 86.4 0.4 87.7 0.6 88.5 0.8 88.8 0.0 88.7 0. 88. 0.4 87.5 0.6 86.4 0.8 85. 0.9 84.5 0.0 8.8 4 5
5.. Lundberg Palmgren Lundberg- Palmgren L-P Hertz ISO τ 0 Z 0 V N S Lundberg ln S τ 0 c N e V Z 0 h (5.) S τ 0 (MPa) Z 0 (mm) N V V az 0 πd a (mm) d (mm) c e h u L 0 6 N = ul τ 0 c u e L e V ln h Z 0 S = C τ 0 c u e L e V h (5.) Z 0 C (5.) S u τ 0 Z 0 V L F u τ 0 Z 0 V F L 90 % 90 % (5.) S = 0.9 F L L = F C τ 0 Z 0 V u 6 Z 0 d a V 5. τ 0 Z 0 V τ 0 Z 0 V τ 0 = Tσ max Z 0 = ζ b T ζ b/a 5. V V = az 0 πd Hertz σ max = Q πab a = μ Q E 0 ρ b = v Q E 0 ρ Q (N) σ max (MPa) a (mm) b (mm) E 0 m = E 0 E E m μ ν ρ (5.) Z 0 τ 0 V ln S T c u e L e πdd w h ζ h μ c v c+h E 0 D w ρ (c+h )/ Q D w D w π (c h+)/ (5.) Q c S = 0.9 ln(/s) (5.) Q D w (c h+)/ L e T c u e πdd w h ζ h μ c v c+h E 0 D w ρ (c+h )/ Lundberg e = 0/9 c = / h = 7/ (5.4) C E 0/ π A ϕ QL = A ϕd w.8 (5.5) ϕ = T T. ζ 0.4 μ.8 v.5 u D w ζ (D w ρ). d T ζ b/a = 0. (5.6) d 0 6 Q c L = (5.5) Q c = A ϕd w.8 (5.7) 7
ϕ Σρ d Σρ ρ ρ 4 = D w D w γ = D w cosα D pw γ γ fd w D pw α r f = r i r e D w D w ρ γ = γ f Hertz cosτ cosτ = D w γ γ ρ + fd w D w ρ cosτ = γ γ + f (5.8) + (5.9) (5.8) (5.9) ( + cosτ) D w ρ γ = γ ( cosτ) D w ρ = f (5.0) D w ρ = d d = D pw D w cosα 4 ( + cosτ)( γ) (5.8) (5.9) (5.0) (5.) (5.) 4 ϕ ζ T (5.) (5.0) Ω ϕ Ω Ω = cosτ + cosτ = f ( γ) (5.4) f Ω = ( + cosτ). T T. ζ ζ Lundberg Ω Ω Ω =.Ω 0.4 (5.4) (5.5) (5.6) (5.) ϕ = 0.0707 f f 0.4 ( γ).9 D w D pw 0.4 μ.8 v.5 (5.5) 0. u 5 u u = Z (d m D w cosα) D pw = Z D w cosα D pw u = 0.5Z ( γ) ϕ = 0.089 f f (5.7) Q c = 0.089A f f 0.4 ( γ).9 ( γ) γ cosα 0.4 ( γ).9 ( γ) γ cosα (5.6) 0. Z (5.7) 0. Z D w.8 0.089A = 98. = D pw D w cosα D pw Q c = 98. f f 0.4 ( γ).9 ( γ) γ cosα 0. Z D w.8 (5.8) = D pw ( γ) Σρ d (5.6) ϕ = T T. ζ ζ 0.4 μ.8 v.5 (+cosτ). ( γ). 4. D w D pw 0. γ 0. u (5.) 8 9
6 Q m L (5.5) (5.7) Q m L = Q c L = Q c Q m (5.9) i e 7 C r (.9) C r = ZQ max J r (ε) cosα ε J r (ε) Q C Q max Q mi Q mi = = Z j = Z Q i j = π π 0 Q ψ dψ 0 6 (L = ) (5.9) Q m Q C Q ci = Q mi = π π 0 Q ψ dψ Q ψ = Q max ε ( cosψ).5 (5.0) (5.) ΔS n S e S e = ΔS ΔS ΔS ΔSn ln S e = ln ΔS + ln ΔS + ln (5.) ln S e = C Q (c h+)/ L e πd C = T c u e ζ h μ c v c+h ΔS + + ln E 0 ρ (c+h )/ ΔS n (5.) (5.4) l Δl ΔS n Q (ψ) ln ΔS n = C Q (ψ) (c h+)/ L e Δl Δ (πd) = Δl (5.) ln S e = C L e + ψ0 ψ 0 Q (ψ) 0 dl c = / h = 7/ dl dψ dl = (d/) dψ ln S e = C L e d + ψ0 ψ 0 Q (ψ) 0 dψ (5.5) (5.4) (5.5) C Q 0 L e πd = C L e d + ψ0 ψ 0 Q (ψ) 0 dψ 0 6 Q ce Q ci = Q max π + ψ0 ψ 0 ε ( cosψ) 4.5 dψ / = Q max J (ε) (5.) Q ce = π + ψ0 ψ 0 Q (ψ) 0 dψ 0 J (ε) = π + ψ0 ψ 0 ε ( cosψ) 4.5 dψ / ψ 0. 0
Q ψ = Q max ε ( cosψ).5 Q ce = Q max = Q max J (ε) J (ε) = π + ψ0 ψ 0 ε ( cosψ) 5 dψ 0 (5.6) π + ψ0 ψ 0 ε ( cosψ) 5 dψ 0 J J ε ε 5.5 5.5 J J ε J J J J 0 0 0 0 0 0. 0.475 0.4608 0.587 0.56 0. 0.406 0.500 0.577 0.607 0. 0.550 0.547 0.6079 0.659 0.4 0.54 0.567 0.609 0.657 0.5 0.565 0.5875 0.6495 0.6744 0.6 0.5808 0.6045 0.665 0.6888 0.7 0.5970 0.696 0.679 0.705 0.8 0.604 0.60 0.6906 0.77 0.9 0.648 0.645 0.708 0.79 0.67 0.6566 0.7 0.7.5 0.665 0.68 0.766 0.75.67 0.7064 0.790 0.7705 0.78.5 0.7707 0.7777 0.86 0.80 5 0.8675 0.869 0.8989 0.904 8 Q max C r C r = ZQ max J r (ε) cosα (5.) (5.6) Q C C r C ri = ZQ ci J r (ε) J (ε) cosα C re = ZQ ce J r (ε) J (ε) cosα ε = 0.5 J r(0.5) = 0.88 J (0.5) = 0.565 J (0.5) = 0.5875 (5.8) C ri = 9.9 C re = 8. f f f f 0.4 ( γ).9 ( + γ) γ 0. (cosα) 0.7 Z D w.8 0.4 ( + γ).9 L = C r P Li = C ri P ( γ) γ 0. (cosα) 0.7 Z D w.8 Le = 5..4 L0 9 = L i 0 9 + L e 0 9 C re P C r = (C ri 0 + C re 0 ) 0. = Cri + C re C ri 0 0. (5.7) (5.8) (5.9) (5.0) (5.)
i P C i C i L L L = C P L = C P i i L e = L e + L e + + L e i C P e = C P i e + C P i e + + C e = (ic ) e i e = 0/9 C = i 0.7 C 4 C P i e = i (5.7) (5.8) (5.) (5.) C r = f c (i cosα) 0.7 Z D w.8 f c = 9.9λ +.04 γ + γ.7 f i f e f e f i ic P 0.4 0 0. γ0. ( γ).9 ( + γ) f i f i 0.4 e (5.) (5.) (5.4) f c ISO f i f e λ Lundberg Palmgren ISO 99 b m b m 5. 4 5. 90 % 5.. 5. L 0 = C P L 0 = C 0 P L 0 0 6 C (N) C r C a P (N) P r P a L 0h = 06 60n L 0 L 0h h n (min ) (5.5) (5.6) (5.7) 90 % L na = a a a L 0 L 0 0 6 a a a 5 (5.8)
a 90 % 90 % 5.6 90 % 5.6 % L n a 90 L 0 95 L 5 0.64 96 L 4 0.55 97 L 0.47 98 L 0.7 L na (5.8) a a ISO a 007 ISO 8 aiso 0 JIS B 58 aiso L nm (5.9) 99 L 0.5 99.9 L 0. 0.09 L nm = a aiso L 0 (5.9) a a a 5.7 a a a a 99.95 L 0.05 0.077 5.7 mm /s 0 mm /s D pw n 0 000 D pw (mm) n (min ) NTN a TS 60.00 TS 00 0.7 TS4 50 0.48 aiso aiso ISO 8:007 (5.40) aiso = f e C C u κ (5.40) P C u NTN e C e C 5.8 D pw (d+d)/ κ κ ν ν 5.4 κ = ν ν (5.4) ν n (D pw) 5. (5.4) (5.4) 6 7
5.8 e C D pw 00 mm e C D pw 00 mm 0.8 0.6 0.9 0.8 0.6 0.5 0.8 0.6 0.5 0. 0.6 0.4 0. 0. 0.4 0. 0. 0 0 0 0. 0 5.9 aiso 0. κ 0.4 aiso = 0..567 aiso = 0..5859 0.4 κ aiso = 0..567 aiso = 0..5859 κ 4.649 κ 0.0548.99 κ 0.0548.9987 κ 0.9087.48 κ 0.9087 0.8 e C C u P e C C u P 0.8 e C C u P e C C u P 9. 0.4 9.85 9. 0.4 9.85 n 000 min ν = 45 000n 0.8 0.5 D pw n 000 min ν = 4 500n 0.5 0.5 D pw (5.4) (5.4) aiso 5.9 5. 5.6 P P = P r P = P a P =.5P a ν, mm /s 000 500 00 00 50 0 0 000 500 000 500 000 5 000 0 000 0 000 50 000 50 00 00 5 0 0 5 D pw, mm 0 0 50 00 00 500 000 000 0 5 n,min aiso = 0..567 aiso = 0..5859.9987 κ 0.0779.48 κ 0.0779 e C C u N κ P N P = P r P = P a P =.5P a 0.8 e C C u P e C C u P 9. 0.4 9.85 5. ν 8 9
aiso 50 0 0 5 0.5 0. 5. C u P e C κ aiso aiso 50 κ 4 κ = 4 κ 0. 5.4 5.6 NTN κ = 4 0.8 0.6 0.5 0.4 0. 0. 0.5 aiso 50 0 0 5 0.5 0. κ = 4 0.8 0.6 0.5 0.4 0. 0. 0.5 5.. F(L) = e αl β F(L) L α β (5.44) β β = 0/9 β = 9/8 lnln (5.44) = β ln L + ln α (5.45) F(L) F(0.) 90 % L 0 F(L' ) L' lnln 0. = β ln L 0 + ln α (5.46) 0. 0. 0.005 0.0 0.0 0.05 0. 0. 0.5 5 e CC u/p 5. aiso aiso 50 0 0 5 0.5 0. 0. κ = 4 0.8 0.6 0.5 0.4 0. 0. 0.5 0. 0.005 0.0 0.0 0.05 0. 0. 0.5 5e CC u/p 0. 0.005 0.0 0.0 0.05 0. 0. 0.5 5 e CC u/p 5.4 aiso aiso 50 0 0 5 0.5 0. 0. κ = 4 0. 0.8 0.6 0.5 0.4 0. 0. 0.5 0. 0.005 0.0 0.0 0.05 0. 0. 0.5 5 e CC u/p lnln F(L' ) = β ln L ' + ln α (5.47) (5.47) (5.46) (L 0) L ' L 0 = ln F(L' ) ln 0.9 β = a 5.7 0 % β = / ISO (5.48) 5.8 5.6 破損確率 % 0.00 5.00.00 0.50 0.0 0.05 σ 範囲 理論寿命 β=9/8 または 0/9 β=/ 0.0 0.000 0.00 0.0 0..0 寿命比 ( 破損確率 50 % のときを.0) 5.5 aiso 40 5.6 aiso 4 5.7 0 %
a = L ' L 0 = 0.95 0.0 ln F(L' ) ln 0.9 + 0.05 (5.48) 90.0 荷重 n n (min ) t n t + t + t + + t n = n m n m = t n + t n + + t n n n 5.00 95.0.00 0.50 99.0 99.5 n t n t n n t n 回転総数 n m 破損確率 (%) 0.0 0.05 過去の ISO および JIS による線図 最新の ISO および JIS による線図 99.9 99.9 信頼度 (%) 5.9 j n = ϕ j L m L j L j (5.49) 0.0 0.00 99.9 99.9 L j j 0 6 L m 0 6 ϕ j j 0.00 99.9 0.00 0.0 0.0.00 信頼度係数 a ϕ j = n j t j n m ϕ j = t j (5.50) 5.8 a 5.. Miner Miner Rule Miner Miner ϕ L m L + ϕ L m L + ϕ L m L + + ϕ n L m L n = L m Miner P L 0 6 L /L L L/L = 00 % L m = ϕ L + ϕ L + ϕ L + + ϕ n L n (5.5) n L L n 5.9 4 4
5..4 S(L) = F(L) = e αl β F(L) S(L) L α β (5.5) S C L D L L 5. (5.5) ln ln ln S C = α D L D β S C = α L β S C = α L β (5.55) 残存確率 S C 装置 軸受 軸受 (5.5) ln S(L) = αlβ (5.5) 5.0 残存確率 装置 軸受 軸受 (5.54) (5.55) α ln ln ln S D = S = S = L β ln L D S C L β ln L S C L β ln L S C L D L L 寿命 5. (5.56) 寿命 S D = S S L S D S S 5. (5.5) 残存確率 5.0 装置 ln S D = ln S + ln S (5.56) (5.57) (5.57) ln ln ln S D = α D L β S = α L β (5.54) S = α L β S D S S 軸受 軸受 L D β = L β + L β n L D e = L e + L e + + L n e (5.58) S(L) D S(L) S(L) S D S S L 寿命 L D L L L n e 0/9 9/8 5. 44 45
5..5 ISO JIS ε = 0.5 (Δ r) 0 Δ r 0 (.) ε = ( cosψ ) = Δ r δ r ' (4.7) (4.8) (5.6) 5. δ r = 0.00044 cosα Q D w (4.7) δ ψ ψ δmax ψ δmax δ r ' di + Dw de d e (mm) d i (mm) d i + D w (mm) D w (mm) δ r ' (mm) δ ψ ψ (mm) δ max (mm) ψ ( ) ψ ( ) Δ r (mm) δ r = 0.000077 cosα (.6) Q max = F r ZJ r (ε)cosα Q 0.9 L we 0.8 ε ε J r = = 0.00044F r Δ r D w Z cos 5 α 0.00044 0.0076 0.0076 D w Z cos 5 α = 0.448K F r r = Δ r f (ε) F r Δ r (4.8) (.6) (5.6) 5. ψ δ ψ = ψ / ε ε J r. 0.9 0.000077F = r Δ r L 0.8 we Z 0.9 cos.9 α = 0.5K F r 0.9 r = Δ r f (ε) (5.64) = δ r ' cosψ Δ r (5.59) ψ = 0 δ max = δ r ' Δ r (5.60) ψ 0 (5.6) (5.64) K r 5.0 5. ε J r ε. J r δ ψ = δ r ' cosψ Δ r = 0 cosψ = Δ r δ r ' (5.6) 46 47
5.0 K r ( 0 5 ) 68 69 60 6 6 00 9.4 0.08 0.74 8.975 0.08 0 8.45 8.79 8.975 9.70 9.88 0 6.46 7.005 7.54 8.845 7.494 0 5.06 6.65 8.05 8.0 6.947 04 5. 5.46 5.98 6.004 6.46 05.89.78 4.857 4.796 5.68 06.46.067.406.9.98 07.45.4.94.6.40 08 0.7.87.4.95.9 09 9.87 0.86.7.650.05 0 9.694 0.40 0.676.79.954 9.667 0.44 0.609.8.69 9.47 0.09 0.098 0.947.55 9.8 9. 9.644 0.770.097 4 8.665 9.80 9.68 0.605 0.86 5 8.5 9.09 9.95 9.95 0.64 6 8.0 8.70 9.4 0.0 0.44 7 8.98 8.87 8.89 9.57 0.56 8 7.969 8.540 8.898 9.785 0.08 9 7.755 8.8 8.498 9.56 9.99 0 7.555 8.549 8.498 9.59 9.6 6.94 7.854 8.49 8.999 9.8 4 6.89 7.80 7.974 8.88 9.8 6 7.050 7.55 7.654 8.688 9.0 8 6.68 7.59 7. 8.688 8.808 0 6.7 7.67 7.5 8.54 8.4 6.54 6.9 6.99 7.894 8.60 4 6.447 6.9 7.000 7.45 8.88 6 6.74 7.04 7.06 7.67 7.66 8 6. 6.778 6.745 7.47 7.66 40 6.045 6.84 6.8 7.050 7.98 5. K r ( 0 6 ) 0 4 04 8.97 6.649 8.06 5.65 05 7.9 7.70 5.70 6.649 4.509 6.7 06 6.499 6.754 4.786 6.05 4.509 5.40 07 6.404 5.70.879 5.4.99 4.795 08 5.656 5.06.879 4.765.64 4.90 09 5.040 4.870.69 4.69.077.744 0 4.800 4.9.8 4.069.908.476 4.9.969.0.64.697.476.964.678.596.46.59.95.809.4.76.64.95.84 4.5.49.50.990.00.587 5.8.047.50.794.887.6 6.08.974.6.57.887.469 7.98.808.97.546.797.7 8.879.67.946.49.697.50 9.76.596.89.5.55.08 0.654.48.74.0.4.978.59.96.565.90.55.805 4.65.000.4.84.4.66 6.07.900.4.644.08.57 8.95.796.8.57.040.49 0.855.68.4.58 0.989.87.7.585.06.446 0.90 4.645.5.00.60 0.877 6.55.45 0.954.86 0.80 8.49.76 0.909.4 0.789 40.87.09 0.870.4 0.789 44.7.94 0.790.4 0.759 48.79.00 0.709.05 0.684 5.5.00 0.68 0.960 0.655 56.075 0.958 0.609 0.90 0.605 60.005 0.94 0.586 48 49
ISO L = C P p P (N) Lundberg-Palmgren L = Q c Q m p L 0 6 Q c (N) Q m = (N) (5.65) F r ε ε = 0.5 (.6) L ε L = J r(ε) J (0.5) J r(0.5) J (ε) J r. J 5. p (5.70) J r J (5.7) (5.7) f (ε) 5. ε ε J r 0.00044F r = Δ r D w Z cos 5 α = 0.448K F r r = Δ r f (ε) ε ε J r. 0.9 0.000077F r = Δ r l 0.8 eff Z 0.9 cos.9 α (5.7) F Q r max(ε) = ZJ r(ε)cosα (5.66) = 0.5K F r 0.9 r = Δ r f (ε) (5.7) Q max(0.5) = F r ZJ r(0.5)cosα (5.67) Δ r J ε ε = 0.5 J (ε) = Q m(ε) Q J m(0.5) (0.5) = Q max(ε) Q max(0.5) (5.66) (5.67) (5.68) F r = Q m(ε) Z J r(ε) J (ε) cosα F r = Q m(0.5) Z J r(0.5) J (0.5) cosα Q m(0.5) Q m(ε) = J r(ε) J (0.5) J r(0.5) J (ε) (5.65) (5.69) L ε L = Q p c Q m(ε) Q p = c Q m(0.5) Q m(0.5) Q m(ε) p (5.68) (5.69) 5. J ε 0 0 0 0. 0.475 0.587 0. 0.406 0.577 0. 0.550 0.6079 0.4 0.54 0.609 0.5 0.565 0.6495 0.6 0.5808 0.665 0.7 0.5970 0.679 0.8 0.604 0.6906 0.9 0.648 0.708 0.67 0.7.5 0.665 0.766.67 0.7064 0.7705.5 0.7707 0.86 5 0.8675 0.8989 5. ε f (ε) L e L f (ε) L e L 0..7 0.94 5.5 0.0 0. 0. 0.546 4.500 0.469 0. 4.045 0.77 5.59 0.69 0.4.408 0.889.887 0.870 0.5 0.0 0.0 0.6 0.857.069..075 0.7.48.098.897.096 0.8.86.094.455.065 0.9.95.04.99 0.968.0.489 0.948.45 0.805.5.07 0.605 4.94 0.78.5.877 0.7 6.87 0.96.67 4.8 0.76 7.5 0..8 4.596 0. 8.08 0.00.0 5.05 0.50 9.87 0.067.5 6.4 0.078.904 0.09 7.09 0.04 4.570 0.05 4 8.874 0.07 9.7 0.005 5 0.489 0.008 4.90 0.00 0 7.48 0.00 48.95 0.000 50 5
5..6 Lundberg- Palmgren 5.4 ψ β β 0 4 L OSC = ΩL ROT β β 0 ψ Ⅱ β0 β 0 Ⅰ Ⅱ 5.4 (5.7) 5.4 Ω 5 0 0 45 90 80 5.6.66 0.86 4.84 0 9..8 5 0.64.4 5.4 5.5 Ω 50 5.84 8.58.84 0 0.00 8.570 6 8.80 7.40 9.50 7.40.848 7. 7.0 7.956 7.956 6.869 6.89 7.00 7.00.950.950 4.65 4.585.9 4.5.68.858.0.480.79.777.84.85.760.76.86.794.06.057.7.9 0.96 0.48 0.97 0.486 0.908 0.475 0.9 0.480 0.567 0.5 0.600 5.0 4.970.4 Ω = A S Y S + A O Y O + Y R X e + AX i + BX r (5.74) L OSC L ROT A A S A O X i X e X r Y O Y S Y R B i e r O S R Ω D w/d pw Z α ε A i /A e A i /A e D w/d pw D w/d pw α = 0 ε = 0.5 Ω Z D w/d pw Ω 5.4 揺動寿命係数 Ω 00 0 深溝 6 深溝 5 円ころ 5 0. 0 00 揺動半角 β ( ) 深溝 0 円ころ 0 円ころ 9 5.5 Ω 揺動寿命係数 Ω 0 0 0 7.0 5.0 4.0.0.0.0 0.7 0.5 0. 0. 玉軸受 ころ軸受 0. 4 5 7 0 0 0 50 00 00 揺動半角 β ( ) β 5.6 500 000 5 5
5.6 5.5 Ω Z = 6 Z = 0 0 % 5.6 (60 /Z) 5..7 ISO L i = Q ci Q mi p Le = L = (L i e + L e e ) ¹ e Q ce Q me p β c = 60 D pw Z D pw D w cosα = 60 Z D w cosα D pw D pw (mm) D w (mm) Z α ( ) (5.75) Q ci Q ce (N) Q mi Q me (N) L i L e L 0 6 5.7 j D w/d pw D w D d = 0.6 D pw D + d = 0.5 D d D + d d (mm) D (mm) A j δ a+θr icosψ j δ rcosψ j 5 4 α ij V A j α V α ej S 5.7 j f i f e S S = ( f i + f e )D w δ a δ r ψ j j α α ij α ej R i δ ij δ ej 54 55
5.7 tanα ij = V V tanα ej = A j V A j V V + V {( f i 0.5) D w + δ ij } = 0 (A j V ) + (A j V ) {( f e 0.5) D w + δ ej } = 0 Q ij = K i δ ij.5 Q ej = K e δ ej.5 K i K e 5.8 λ ej M Gj D w α ej (5.76) (5.77) (5.78) (5.79) Q ej Q c 5. (5.8) Q c = 98.λ f f 0.4 ( γ).9 ( γ) γ cosα 0. Z D w.8 f f i f e λ λ = 0.95 α ( ) Z D w (mm) D w 5.4 mm D w.8.647d w.4 γ = D w cosα D pw D pw (mm) (5.8) JIS λ (5.8) Q i (N) Q e (N) M G 6.. F C (N) λ λ i = 0 λ e = j j Q ij F Cj α ij λ ij M Gj D w M Gj 5.8 Q c = 550.8λv ( γ)9 7 ( γ) 4 γ cosα λν λν = 0.8 D we (mm) L we (mm) λν 9 Z 4 D we 9 7 L we 7 9 (5.84) Q ij sinα ij Q ej sinα ej M Gj D w (λ ij sinα ij λ ej sinα ej ) = 0 (5.80) Q ij cosα ij Q ej cosα ej + M Gj D w (λ ij cosα ij λ ej cosα ej ) + F Cj = 0 (5.8) (5.76) (5.8) j = Z Z Q ij Q ej Q mi = Z Z wi Q ij j = wi Qme = Z Z we we Q ej j = (5.8) wi we wi we 0/ 0/ 4 4.5 4.5 4 Q ij Q ej 56 57
4 Q c Q m L c L ci = Q ci Q mi p Lce = L c = (L ci e + L ce e ) ¹ e Q ce Q me p 0/ e 0/9 9/8 p L 0 ISO L 0 L = L c L 0 L 0 606 5.9 寿命 h 0 5 50 40 0 0 0 4 50 40 0 0 0 遠心力を考慮する 606 F r = 500 N ラジアル内部すきま 0 遠心力を考慮しない 4 0 4 内輪回転速度 min 5.9 5-606 F r = 000 N n = 500 min 0.0 mm 606 C r = 600 N L 0 = 600 000 5. K r =.9 0 5 (5.7) 0 6 = 996 (h) 60 500 Δ r f (ε) = 0.448K r F r 0.0 = 0.448.9 0 5 =.64 000 5. L ε/l 0 = 0.889 L ε L ε = 0.889 996 = 500 (h) 5- NU08 F r = 0 kn β = 80 50 / min NU08 d = 40 mm D = 80 mm Z = C r = 64.5 kn L ROT = ( 64.5 0 )0 0 6 60 50 = 5 506 (h) 5.6 Ω =.9 L OSC =.9 5 506 = 0 500 (h) β C β c 60 =. ( ) 0.5(80 40) 80 + 40 58 59
X Y X Y X Y X Y 5. 5.7 X Y JIS α f 0 F r /C 0r e F a F e F / a r F e / r F a F e F / a r F e / r 0.7 0.9.. 5.. P r P r = XF r + YF a (5.85) 0.45 0..99.99 0.689 0.6.7.7.0 0.8.55.55.8 0.0 0 0.56.45 0 0.56.45 F r (N) F a (N) X Y.07 0.4...45 0.8.5.5 5.7 0.4.04.04 JIS X Y 5.5 5.6 X Y 5.7 5.5 X Y F a / F r e F a / F r e α α' X Y 0 X 0.4ξ η Y 0.4 η tanα' 0.65 ξ tanα'.65 0.65ξ η 0.65 η tanα' 0 0.45cotα 0.4 0.67 0.4cotα e ξ tan α'.5tanα 5.6 ξ η α 0.67cotα 6.89 0.44 5 0.78 0.8 5.. α = 90 α 90 P a.47.65.9 0.57 0.4.4.57.8 0.74 0.4..46..07 0.46..8.4 0.47 0 0.44.9.4 0.7.9.4 0.5..6.8.57 0.55.0.4.66 5.5 0.56..6 7.4 0.56..6 0 0.8 0 0.9 0.76 0.78 0.6.4 40.4 0 0.5 0.57 0.55 0.57 0.9.05 sinα.5 cosα α = 5 α 5 α 5.5 sinα.5 sinα.75 f = 0.054 cosα cosα = 0.974cosα 0 F a cosα C 0r sinα P a = XF r + YF a F r (N) F a (N) X Y (5.86) 60 6
JIS X Y 5.8 P a =.F r + F a (5.87) 5.. X Y X Y JIS 5.0 F r /F a 0.55 X = tan50. α = 50 F a /F r e F a /F r.5tan50 F r /F a /.788 0.55 5.8 X Y JIS F a / F r e X Y α 0 tanα sinα.5tanα 45.8 60.9 0 tanα sinα 45 0.59 0.67 60 0.55 F r P r..0 0.9 0.8 0.7 0.6 0.5 0.4 0. 0. 0. A B 0 0 0.5.0.5.0.5 C cota F acota Y P r 5.0 AC C i /C e = 0 C i /C e = 0.75 C i C e ABC Lundberg-Palmgren ABC X Y F a / F r e X.5tanα sinα.5tanα sinα tanα tanα 45 0.66 0.66 60 0.9 0.9 Y e.5tanα.5tanα (5.88) (5.89) ε 5.0 F r P r = C i + C e F a cotα' P r = pe J r(0.5) J (0.5) C pe i + C e J (ε) J r(ε) J (ε) J (0.5) pe + pe + C e + C i C pe e + C i pe J r(0.5) J (0.5) J (ε) J (0.5) pe J (ε) J r(ε) ¹ pe pe ¹ pe J a(ε) J r(0.5) (5.88) (5.89) 6 6
(Y ) F r = 0. 5.5 ε = J ( ) = J ( ) = J a( ) = (5.89) F a cotα' P r = J (0.5) C pe i + ¹ pe J (0.5) C e C pe i + C e J (0.5) C pe i + ¹ pe J (0.5) C e Y = C pe i + C e J (0.5) J r(0.5) J r(0.5) J (0.5) cotα' (5.90) (5.9) P r = Y F a Y C i C e 0 (5.9) J (0.5)/J (0.5) J (0.5) J (0.5) Y ξ tanα' = e F a F r e OB AB P r = F r (5.86) X = Y = 0 F a F r > e OB C (a,0) BC a F a cotα' P r P r P r = a ξ a + a ξ a F r + cotα' a F r P r = F a (5.86) Y = J (0.5) J (0.5) J r(0.5) J (0.5) cotα' = J r(0.5) cotα' = 0.4 cotα' J (0.5) J (0.5) (5.9) X = a ξ a Y = cotα' a (5.96) η Y = Y η η = sinα.5 (5.9) (5.94) Y Y F r = 0 F a cotα' P r (5.86) P r = Y F a cotα' (5.9) (5.9) Y = 0.4cotα' η (5.96) (5.97) a = η 0.4 (5.98) (5.96) X = 0.4ξ η (5.97) (5.98) (5.99) (5.97) (5.99) 5.5 X Y F a cotα' P r = cotα' Y B (ξ,) OB F r P r = ξ F a cotα' P r F a F r = ξ tanα' (5.95) 64 65
5..4 5.9 5.9 BrgⅠ F rⅠ Fa BrgⅡ F rⅡ 0.5F r Y 0.5F r + F a Y F a = 0.5F r + F a Y - F ac (ε = 0.5) F a + F ac (ε = 0.5) F ac (ε = 0.5) F ac (ε 0.5) F ac (ε = 0.5) F ac (ε 0.5) F ac (ε 0.5) = F a + F ac (ε 0.5) F acⅠ (ε > 0.5) 軸受 Ⅰ F rⅠ F a 軸受 Ⅱ F rⅡ F acⅡ (ε < 0.5) 5. (5.0) BrgⅡ BrgⅠ Fa F rⅡ F rⅠ BrgⅠ BrgⅡ Fa F rⅠ F rⅡ BrgⅡ BrgⅠ Fa F rⅡ F rⅠ 0.5F r Y 0.5F r Y 0.5F r Y 0.5F r + F a Y 0.5F r Y - F a = 0.5F r F a Y + F a - 0.5F F a = r + F a Y F a = 0.5F r + F a Y 0.5F r F a Y - F ac (ε 0.5) F ac (ε = 0.5) (5.0) F ac (ε 0.5) = F a + F ac (ε = 0.5) P r P r = X F r + Y F ac (ε 0.5) (5.00) (5.0) (5.0) (5.0) X Y 5. 5.9 F r F r F a F ac F ac 0 ε = 0.5 F ac (ε = 0.5) = F r Y (5.00) 5. F acⅠ 66 軸受 Ⅰ F rⅠ F a 軸受 Ⅱ F rⅡ 5. F acⅡ P r = X F r + Y F a + F r Y P r P r = X F r + Y F ac (ε 0.5) (5.00) (5.0) P r = X F r + Y F r Y = X F r + F r X X 0.5 5 0 40 (5.05) P r = F r X 0.44 0.9 0.5 0.44 67 (5.04) (5.05) (5.06) 右に移動
F ac (ε = 0.5) F a + F ac (ε = 0.5) F ac (ε 0.5) F ac (ε = 0.5) F ac (ε 0.5) = F ac (ε = 0.5) F a (5.07) (5.08) 5.7 NTN F a /F r. F a F r 0.8 (e = 0.80) X = 0.6 Y =.4 P r P r = X F r + Y F ac (ε 0.5) P r = X F r + F r = F r (5.09) P r P r = X F r + Y F r Y F a (5.0) ) ) 5.9 5..5 4 NTN 4 0 4 4 4 4 0 5.0 F r tanα F a 0.6 ε ε = 0 (5.) NTN ε.7 5.0 F r tan0 F a 0.444 ( ε >.7 ε = 0) F a F r. (5.) P r =0.6F r +.4F a 5.0 ε ε F r (N) F a (N) α ( ) J r J a (5.) ε ε F rtanα F a J r (ε) Ja (ε) 0.5 0.5 0.4577 0 0.6 0.4.0465 0.568 0.744 0.7 0..096 0.06 0.78 0.8 0. 0.8005 0.758 0.445 0.9 0. 0.67 0.68 0.900.0 0 0.6000 0.547 0.444.5 0 0.458 0.89 0.5044.67 0 0.088 0.87 0.6060.5 0 0.850 0.9 0.740 5 0 0.08 0.07 0.8558 0 0 0 4 JIS C r C a C a = C r Y Y Y (5.4) 68 69
C a = C r' Y' = C r i 0.7 Y' (5.5) C r ' (N) C a (N) Y' Y (5.4) (5.5) C r ' = YC a 0.7 Y Y (F r = 0) L = C a F a P r ' = 0.6F r +.4F a C r ' =0.76C a 0.7 F a /F r. L = C r ' P r ' (5.6) 5-606 F r = 500 N F a = 500 N n = 000 min 606 C r = 600 N C 0r = 00 N f 0 =.6 f 0 F a.6 500 = = 0.60 C 0r 00 5.5 e = 0.5 F a 500 = = 0. 0.5 = ey =.8 F r 500 P r = 0.56 500 +.8 500 = 755 (N) L 0 = 600 755 0 6 = 0 400 (h) 60 000 5-4 08 06 F r =.8 kn F a = kn n = 000 min F r =.8 05 60 = 8.4 (kn) F r =.8 55 60 = 4.4 (kn) (+) F ac = 0.5 8.4.6 =.65 (kn) F ac = 0.5 4.4.6 =.75 (kn) 軸受 55 05 軸受 08 06 F r F a = kn F r =.8 kn F r F a = (kn) F ac F a + F ac 70 7
08 e = 0.7 5.6 X = 0.4 Y = 0.4.5/0.7.6 P r = 0.4 8.4 +.6 ( +.75) = 8.76 (kn) P r = 4.4 (kn) 06 C r = 60.5 (kn) 08 C r = 88 (kn) L 0 = L 0 = 88 8.76 60.5 4.4 0 0 6 = 00 (h) 60 000 0 0 6 = 4 600 (h) 60 000 5-5 4 4 QJ0 F r = kn F a = 5 kn n = 000 min QJ0 C a = 57.5 (kn) F a = 5 =.5 >. F r P r ' = 0.6 +.4 5 = 7.46 (kn) C r ' = 0.76 57.5 0.7 = 7 (kn) L = 7 7.46 0 6 = 4 400 (h) 60 000 5.4 5.4. 0.000 ISO 76 JIS B 59 5. 5. f 0 5. f 0 5. 5. m D w/ m.04 m.06 m.08 m.06 5. 5. 5. C 0r f 0 i ZD w cosα f 0 i ZL we D wecosα C 0a f 0 ZD w sinα f 0 ZL we D wesinα σ max 4 00 MPa 4 600 MPa 4 000 MPa f 0 Z D w (mm) D we (mm) L we (mm) i α ( ) 7 7
5. f 0.07.07 0.6 σ max 4 000 σ max 4 000 σ max 4 000 E(κ) κ γ γ m π 4 ( + γ) E(κ) κ γ γ m f 0 σ max 5. E(κ) γ = D wcosα/d pw D wecosα/d pw m D w/ D pw (mm) κ a/b a b 44 0 σ max 4 000 σ max 4 000 ( γ) ( γ) 5. f 0 γ 0.00 4.7.9 6.6 0.0 4.9.0 60.8 0.0 5..0 59.9 0.0 5.. 59. 0.04 5.5. 58. 0.05 5.7. 57.5 0.06 5.9. 56.7 0.07 6.. 55.9 0.08 6.. 55. 0.09 6.5. 54. 0.0 6.4.4 5.5 0. 6..4 5.7 0. 5.9.4 5.9 0. 5.6.5 5. 0.4 5.4.5 50.4 0.5 5..6 49.6 0.6 4.9.6 48.8 0.7 4.7.7 48.0 0.8 4.4.7 47. 0.9 4..8 46.5 0.0 4.0.8 45.7 0..7.8 45.0 0..5.9 44. 0...9 4.5 0.4.0.0 4.7 0.5.8.0 4.9 0.6.5. 4. 0.7.. 40.5 0.8.. 9.7 0.9.8. 9.0 0.0.6. 8. 0..4. 7.5 0...4 6.8 0. 0.9.4 6.0 0.4 0.7.5 5. 0.5 0.5.5 4.6 0.6 0..6 0.7 0.0.6 0.8 9.8.7 0.9 9.6.8 0.4 9.4.8 74 75
5.4. Hertz (5.0) (5.) Q max = 6.476 0 0 χ D w E γ γ f σ max C 0r (.9) C 0r = 0.ZQ max cosα (5.) (5.) σ max = Q max πab Q max = πab σ max (5.7) σ max Q max a b (5.) (5.) C 0r =.07 σ max 4 000 E χ γ γ f ZD w cosα a = b = χ E π E πχ Q ρ Q ρ v E v E χ χ = a/b E Σρ ν E (5.7) (5.9) Q max = π χ v E E ρ σmax E =.07 0 5 MPa ν = 0. (5.8) (5.9) i f 0 C 0r = f 0 izd w cosα f 0 =.07 σ max 4 000 E χ γ γ f σ max = Q max πl we b Q max = πl we b σ max σ max Q max L we b (5.4) (5.5) (5.6) Q max = 6.476 0 0 χ E ρ σmax Σρ (5.0) b = 8Q πl we ρ v E (5.7) ρ = ρ + ρ + ρ + ρ = D w γ γ f D w γ = D wcosα/d pw f f i = r i /D w f e = r e /D w r i r e (5.) Σρ ν E (5.6) (5.7) Q max = π v E L we ρ σ max 76 77
0.6 0.5 0.6 0.5 E =.07 0 5 MPa ν = 0. Q max =.76 0 5 L we ρ σ max Σρ ρ = D we γ D we γ = D wecosα/d pw (5.8) (5.9) (5.8) (5.9) 5.4. ISO 76 JIS B 59 P 0r = X 0 F r + Y 0 F a P 0r = F r (5.) (5.4) Q max =.8 0 5 ( γ)l we D we σ max (5.0) X 0 Y 0 5.4 (5.) (5.0) C 0r = 44 σ max 4 000 ( γ)zlwe D we cosα 5.4 X 0 Y 0 X 0 Y 0 X 0 Y 0 ISO i f 0 C 0r = f 0 izd we cosα f 0 = 44 σ max 4 000 (5.) ( γ) (5.) α = 5 0.5.04 α = 0 0.50.00 α = 5 0.46 0.9 α = 0 0.4 0.84 α = 5 0.5 0.8 0.76 α = 0 0. 0.66 α = 40 0.6 0.5 α = 45 0. 0.44 0.5 0.cotα 0.44cotα 0.5 0.cotα 0.44cotα 78 79
α 90 P 0a = X 0 F r + Y 0 F a α = 90 P 0a = F a X 0 Y 0 5.5 (5.5) (5.6) F r (.9) Q max = 5F r Zcosα (5.40) P 0r (5.9) (5.40) 5.5 X 0 Y 0 X 0 Y 0 5.4.4 X 0 Y 0 X 0 Y 0 ISO Stellrecht α F a F r 5. α' Z F a /Z Q a = F a Zsinα' (5.7) 5F r /Z Q r =.tanα.7 F r/fa 0.55 5F r Z =.5F r cosα' Zcosα' F r/fa 0.44cotα 0.44cotα F r/fa 0.67cotα α' F a Z F a Z Q a Q r Q a 5F r Z Q r 5. (5.8) 5P 0r Zcosα =.5 Zcosα' P 0r = F r + F a Zsinα' cosα F r + cosα F a cosα' 5sinα' Y 0 η 0 = 0.sinα (5.4) P 0r = cosα cosα F r + cosα' 5sinα' ( 0.sinα) F a (5.) (5.4) X 0 Y 0 cosα X 0 = cosα' cosα Y 0 = 5sinα' ( 0.sinα) (5.4) (5.4) (5.4) (5.44) X 0 Y 0 ISO Palmgren C 0r (F a = C 0r) X 0 Y 0 α = 5 α' = 6.6 (5.4) (5.44) X 0 Y 0 5. X 0 = Y 0 = cos5 = 0.557 0.6 cos6.6 cos5 = 0.459 0.5 5sin6.6 ( 0.sin5 ) X 0 Y 0 Q max = Q r + Q a =.5 F r + F a Zcosα' Zsinα' (5.9) 80 8
C 0r / (F a = C 0r /) X 0 Y 0 (5.6) (5.7) α' X 0 Y 0 5.6 / / X 0 Y 0 5.6 α α' X 0 Y 0 5 6. 5.6 0.8 0.5 0 5. 0. α (5.4) P 0r = 0.5F r + 0.cotα F a (5.45) ISO Y 0 0 % X 0 Y 0 (5.4) 5.4 X 0 = 0.5 Y 0 = 0.cotα 0.46 0 8.5 0.4 40 4.0 0.6 45 47. 0. 5.5 EHL EHL EHL 5.5. EHL 5.4 5.5 h 0 = 0.66 (η 0 U) R p h 0 R U U R 5.5 h h 0 5.4 η 0 η 0 = νρ 0 9 (N s/mm ) U (mm/s) U = U + U U U R (mm) R = (R R ) p (MPa) h 0 (mm) ω (rad/s) h (mm) ν (mm /s) ρ (kg/mm 0 6 ) ω R z U y (5.46) 8 8
EHL Hertz 5.6 Dowson-Higginson Hertz 油膜圧力分布 油膜厚さ分布 5.7 ω 0 Z 圧力スパイク h 0 ヘルツ面圧分布 5.6 y 5.7 Martin Grubin Dowson-Higginson Dowson-Higginson H.S.Cheng Dowson Archard-Cowking Hamrock-Dowson h 0 R = 4.9 U W h 0 R =.95 (GU ) 0.77 W 0.09 h 0 R =.6 G 0.6 0.7 U W 0. h 0 R =.65 G 0.54 0.7 U W 0. h 0 R =.65 h 0 R =.8 U W h 0 η 0 U R R =.04ϕ0.74 (GU ) 0.74 P max E 0.74 W 0.074 h 0 R =.6 G 0.49 0.68 U ( e W 0.07 0.68K ) 0. h 0 R G U W K K = a/b a b 84 85
Ertel-Grubin h 0 = 0.8 = K A B C D D we ( γ).09 η0 α ncosθ γ γ 0.77 E' L we Q max 0.09 0 5 η 0 : 絶対粘度,α: 圧力粘度係数動粘度は運転時の粘度を使用 K K = 0.8E' 0.09 E' = 8.5 (GPa) A A = D we ( γ).09 γ cosθ γ θ 0.77 L 0.09 D we (mm) γ = D we cosθ D pw (mm) D pw L we (mm) B B = (η 0 α) 0.77 5.7 η 0 (N s/mm ) α C C = n 0.77 n (min ) D D = Q max 0.09 Q max (kn) (η0α) 0.77 0 6 8 6 4.5 0 7 7 5 4.5 0 8 パラフィン系鉱油 ナフテン系鉱油 合成油 0 0 0 40 60 80 00 000 0 000 ν 0 ( 動粘度 SUS).0 0 6 8.6 6. 4.08.06.04.5.0 0 7 9.8 8.6 7.4 6. 5.0 4.08.06.04.5.0 0 8 (η0α) 0.74 5.7 86 87
Archard-Cowking h 0 = 0.0ϕ 0.74 = K A B C D D w ( γ).48 η0 α ncosθ γ γ K K = 0.0E' 0.074 E' = 8.5 (GPa) A A = ϕ 0.74 D w ( γ).48 γ cosθ γ ϕ θ D w (mm) γ = D w cosθ D pw B B = (η 0 α) 0.74 5.7 C C = n 0.74 n (min ) D D = Q max 0.74 E' Q max 0.074 0.74 Q max 0.074 Q max (kn) Q max = 5 F r Z F Q a max = Zsinθ 5.8 5.9 5.8 A 0 NUE 0 NUE () 0 - NUE NUE 04. 8.6 -.8 5.5-05 4.7.9. 5.5 8.8.4 06 8. 5. 5.9 8.6. 6. 07.7 8.4 8.. 5.6 8.5 08 4.4.4 0.4 5. 8.8 0.6 09 6.4 6.5.8 7.0..9 0 8.4 40.4 4. 8.8 7. 4.4. 44.5 7.9.6 4. 8. 5.4 48.8 9. 6. 45. 9.5 9.7 5.9 0.8 40.7 49.6.0 4 4.4 57. 4.5 4.5 5.7 5.4 5 4.5 6.8 6.0 44.5 58. 5.8 6 47.4 65.5 40.8 48.6 6.7 4.6 7 5. 69.9 4. 5.5 66.5 4. 8 55. 7.7 46. 56.7 70.8 48. 9 59. 79.8 47.7 60.9 75.8 49.4 0 6. 8.6 49. 65. 8. 50.7 7.0 89. 58. 7.9 9. 58.8 4 78.0 98.9 6. 79.9 0.4 6.9 6 84.6 07.9 70. 86.9.9 7.7 8 9. 6. 7. 96.4. 74.9 0 99.8 6.5 79.4 04.7 8.5 8.7 5 % 0-88 89
5.9 A 68 78 () 69 79 00 4.0 4.95 5.95 6.8 8.9 0 4.69 5.50 6.8 7.5 8.74 0 5.9 6.59 7.74 8.7 0.6 0 5.8 7.9 8.80 0..7 04 7.7 9.7 0.8.4. 05 8.9 0.5..9 6.5 06 0..8 4.7 7.0 9.8 07. 4. 6.8 0.0. 08. 6. 8.4.6 5.6 09. 7.8 0.7 4.7 9.9 0 5. 8.9. 6..5 7.6. 5.5 9.7 6. 9.9.6 7.0.7 40...8 8.4 6. 4. 4. 7.5.0 8.4 46.9 5.4 8.8.4 40.4 50.5 6 4.4 0. 7. 4.7 54. 7 8.5.9 8.6 47.0 57.9 8 9.7 5. 4. 5.0 6.6 9 0.8 6.5 4.8 54.6 65. 0.9 40.4 45. 58.4 70.8 6.0 4. 5.9 65.9 80.9 4 9.6 48.4 56.0 7.6 86.6 6 45. 5.8 6.0 77. 94.5 8 47.5 56.6 66. 8.8 0.4 0 5. 6.9 7.7 88. 08.8 60 70 5 % 6 7 6 7 5.5. Λ Λ = h 0 R + R h 0 R R (rms) (rms) (R a) R rms =.R a 油膜形成率 % 潤滑係数 F( または α) 00 80 60 40 0 5.8.5.0.5.0.5.0 表面痛みの起こる領域 0.4 0.6 0.8.0.0 4.0 6.0 0 油膜パラメータ Λ ASME 推奨 AB の平均曲線 ひどい滑り運動を伴う軸受で表面痛みの起こる可能性のある領域寿命増加領域 A B Harris 5.8 Λ 4 00 % L 0 Λ = 0.9.5 50 % 5.9 Tallian Skurka ASME ISO a ISO 0.5 A 曲線 :J.C.Skurka B 曲線 :T.E.Tallian 0 0.6 0.8 4 6 8 0 油膜パラメータ Λ 5.9 90 9
5.5. 5.0 d m n = D pw n ϕ T h 0 ' = ϕ h 0 h 0 ' ϕ ϕ = ϕ T (4.6 +.5L 0.6 ) (0.645/ϕ (0.5/( + 0.00L)) T) ϕt.0 0.8 0.6 0.4 50 鉱油 5 mm /s 0 0.0 0.8 0.6 0.4 ϕ T = + 0.0766G 0.687 Q L 0.447 L 0.57 e 0.875S G = αe' α (mm /N) α = {0.6 + 0.965 log (νρ)} 0 ν ρ (0.88) E' 0. 00 0. Q L = Q max L we E' R y R y = D we ( γ) γ = D we cosθ D pw 0. 5 0 0 50 00 00 500 d m n 0 4 Λ' = ϕ T Λ ϕ T Λ 5.5.4 0.46 0.7 Wolveridge Hamrock-Dowson 5. (x 0 x B) 5.0 b x 0 x B 5. Goksem b 0. Q max (kn) L we (mm) D we (mm) S = (u u ) (u + u ) u = D pw ( γ)(ω i ω c) u = D we ω r u (mm/s) u (mm/s) ω i (rad/s) ω c (rad/s) ω r (rad/s) D pw (mm) u = u S = 0 L = βη T (u + u ) T β T = ln 4k b T T v v η = ν ρ k b = 0.85 (W/mK) ρ (g/cm ) ν (mm /s) ν (98.9 ) (mm /s) T (K) T (98.9 = 7. K) 9 9
5-6 N09E Grubin F r = 4 450 N n = 6 000 min ν = 00 SUS Z = 5 R i = 0.5 μm R r = 0.5 μm h 0 = 0.8 D we ( γ).09 η0 α ncosθ γ γ = K A B C D K = 0.8 8.5 0.09 = 0.78 A = 6.4 5.8 B =.4 0 7 5.7 C = 6 000 0.77 = 558 D = = 0.97 0.09.65 4.6 4.45 Q max = =.65 (kn) 5 0.77 E' L Q max 0.09 h 0 = 0.78 6.4.4 0 7 558 0.97 = 0.00075 (mm) Λ = 5-7 0.75 (. 0.5) + (. 0.5) =. 700C Archard-Cowking F a = 7 000 N n = 8 000 min ν = 0 mm /s Z = R i = 0. μm R r = 0. μm h 0 = 0.0ϕ 0.74 = K A B C D D w ( γ).48 η 0 α ncosθ γ γ 0.74 E' Q max 0.074 K = 0.0 8.5 0.074 = 0.44 A = 45. 5.9 B = 7.5 0 8 5.7 0 mm /sec = 60 SUS NTN C = 8 000 0.74 = 77 D = 0.985 7 Q max = sin5 =. (kn) h 0 = 0.44 45. 7.5 0 8 77 0.985 = 0.00089 (mm) Λ = 5-8 0.89 (. 0.) + (. 0.) = 4.8 5-6 N09E 0 000 min 80 SUS N09E d = 45 mm D = 85 mm B =. 0 7 5.7 C = 809 h 0 = 0.78 6.4. 0 7 809 0.97 = 0.00085 (mm) Λ = d m n d m n = 0.85 (. 0.5) + (. 0.5) =.6 45 + 85 0 000 = 65 0 4 0.88 80 SUS = 5.8 mm /s = 5.8 0.88 cp.9 cp 5.0 ϕ T = 0.75 h 0 ' = 0.75 0.85 = 0.64 μm Λ' = 0.75.6 =.7 94 95
5-9 5-8 N09E 60 5.8 mm /s 98.9 7.5 mm /s 5.8 mm /s 80 SUS 5-8 h 0 = 0.00085 (mm) Λ =.6 G = αe α(mm /N) α = {0.6 + 0.965 log(5.8 0.88)} 0 = 0.070 ν (mm /s) ρ (0.88) E' E' = 8 500 (N/mm ) G = 0.070 8 500 = 89 Q L = Q max L we E' R y D we = mml we = 9 mm D pw = 65.5 mm L = 7 0.09 ( 6.66) 4 0.85 = 0.5959 η = 5.8 0.88 0 = 0.09 (Nsec/m ) β = 7.. 7.. ln 5.8 7.5 = 75 (K) k b = 0.85 W/mK ρ0.88 g/cm ν 5.8 mm /s ν (98.9 ) 7.5 mm /s T. K T (98.9 = 7. K) ϕ T = + 0.0766 89 0.687 0.00045 0.447 0.5959 0.57 = 0.75 ϕ = 0.75 (4.6 +.5 0.5959 0.6 ) (0.645/0.75)(0.5/( + 0.00 0.5959)) = 0.59 59 % h 0 ' = 0.59 0.85 = 0.50 μm Λ' = 0.59.6 =. R y = 65.5 = 4.576 (mm) Q max = 4.6F r Z Q L = = 4.6 4 450 5 65 = 0.45 0 9 8 500 4.576 S ω i = πn π 0 000 = = 047 (rad/s) 60 60 ω c = 65.5 ω r = u = 65.5 u = 65.5 65.5 09 65.5 047 = 45.6 (rad/s) = 65 (N) 047 = 09 (rad/s) ( 047 45.6) = 6 660 mm/s = 6.66 (m/s) = 6 660 mm/s = 6.66 (m/s) u = u S = 0 96 97
5.6 Palmgren F(L) = e αlβ F(L) L α β (5.47) 5.6. L 0 L 50 (5.47) ln F(L) = αl β 残存確率 F(t)% 99.9 90.0 80.0 70.0 60.0 50.0 40.0 0.0 0.0 0.0 5.0 4.0.0.0.0 0.5 0.4 0. 0. 0. 0. 0. 0. 0.40.5.0.0.0 4.05.0 0.0 0.0 0.040.050.0 寿命 5. t lng = k logg k =.0 log F(L) = α L β (5.48) α = α k (5.48) loglog F(L) (5.49) Y = loglog X = logl A = logα F(L) = β logl + logα (5.49) 5.0 5. 8 5. n = 8 5. L 0 L 50 5. Y = βx-a Y X 5. β 98 99
No 5.0 n 4 5 6 7 8 9 0 4 5 6 7 8 9 0.5000.99.06.59.94.09.094.080.074.0670.06.056.059.048.045.044.0400.078.058.04.707.5000.864.47.655.95.0.806.6.489.68.66.78.0.04.0975.09.0874.08.797.66.5000.48.648..87.594.66.75.0.87.75.644.550.465.90. 4 5 6 7 8 9 0 4 5 6 7 8 9 0 5..8409.685.578.5000.4404.95.557.44.98.760.568.40.54.5.009.905.8.8706.745.65.5596.5000.459.4.789.506.6.05.865.700.55.4.0.8909.7705.6787.6065.548.5000.4596.45.958.700.475.75.097.97.79.9057.7979.79.644.5878.5404.5000.465.450.4085.850.64.45.8.970.894.7406.6756.6.5747.547.5000.4695.445.484.968.774.959.868.764.708.6494.604.5650.505.5000.478.4484.464.90.85.785.740.677.600.595.5575.57.5000.4755 0.989.86.7987.74.6949.655.650.586.556.554.949.874.87.7599.75.675.659.60.576 4 5 6 7 8 9.948.88.849.7746.700.690.6547.66.957.8899.856.7875.7447.706.677 4.9548.8966.8450.799.7579.707 5.9576.905.855.8095.7698 6.9600.9078.860.888 7.96.96.8678 8 5..964.969 9.9659 0 残存確率 F(t)% 99.9 90.0 80.0 70.0 60.0 50.0 40.0 0.0 0.0 0.0 5.0 4.0.0.0.0 0.5 0.4 0. 0. 0. 0. 0. 0. 0.40.5.0.0.0 4.05.0 0.0 0.0 0.040.050.0 寿命 (h) 00 t (h) 7 586 65 84 500 89 68 408 (h) 84 0.080 65 0.0 7 0. 89 0.4404 408 0.5596 500 0.6787 586 0.7979 68 0.970 5.6. 00 DATA DATA00 5. 00 0 0 5. 0 No No0 0 0 0 0 0 0 0 0 0 0 00 0
0 5.4 g n j (λ) = n C j [ jλ j ( λ) n j ] n j (5.50) 5.5 5 % 95 % λ 5 λ 95 90 % G n j (λ 5 ) = 0.05 G n j (λ 95 ) = 0.95 5.6 G n j λ 0.5 λ λ m 5.0 G n j (λ m ) = λm 0 g n j (λ) dλ = 0.5 λ m λ m = ¹ n + j n ( ¹ n) (5.5) 0.068 0.6 メディアンランク 5 % 90 % 90 % 信頼幅 0.94 5 % 累積分布関数 : G n j (λ) による繰返し計算 0. 0. 0. 順位率 順位 番の分布 n = 0 の場合 5.5 n = 0 個数 順位 番の中央値 順位 番の中央値 順位 番の分布 0 0 0 順位 00 0.067 0.6 メディアンランク 0. 0. 0. 順位率 97.5 90 累積破損確率 (%) 50 0 n = 0 0.94 0.6 λ m 95 % ランク 5 % ランク 寿命線図 5.4 5 0.068 5 5 0 5 寿命 5.6 0 0
5.6. = n n + + (5.5) 5.4 5.5 (5.5) (5.5) 5.7 n n = 8 5.5 5.4 (h) 84 0.080 65 0.0 7 0. 89 0.4404 408 0.5596 500 0.6787 586 0.7979 68 0.970 (h) 84 0.08 65 0.0 7 89.000+(8+ )/(+5).67 0.4 408.67+(8+ )/(+5) 4.4 0.480 500 4.4+(8+ )/(+5) 5.50 0.69 586 68 5.50+(8+5.50)/(+) 7.5 0.877 残存確率 F(t)% 99.9 90.0 80.0 70.0 60.0 50.0 40.0 0.0 0.0 0.0 5.0 4.0.0.0.0 0.5 0.4 0. 0. 0. 0. 0. 0. 0.40.5.0.0.0 4.05.0 0.0 0.0 0.040.050.0 L0 L50 0 5.7 t = = 5 = 5.50 = 04 05