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Paula Lagos Estrada
7 Há anos
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5 Pinos transversais Chavetas Eixos ranhurados Recartilha e Estrias Ajuste prensado cônico Anéis cônicos Ajuste prensado cliíndrico...20

6 Snap Fit

8 snap fit Snap Fit

9 creep σ x ε)

10 µ µ

12 A A esm A cis A pino A l A c a C m C máx C mín C n C p C r d d f d 1 d 2 D D o D v f F a H h c i J ce J m J v L L e L ch

13 L m v n n n s p P atr P mec P v P joule P fe P sup P P c n n r r i r o Ra Ra i Ra 0 Rt i Rt 0 t t a m m m m m T T e T T m T i T o t a T vf T vp T req T vmáx U w z

14 α α i α o α m β θ σ σ adm σ esm δ δ d δ t τ τ adm µ ν o ν i ϕ ω s ω n µ

18 (Cortesia WEG Indústrias S.A.).

19 benchmarking (Cortesia WEG Indústrias S.A.). creep

24 P δ = δ r ro + r r r + r i + ν + ν i Eo ro r Ei r ri

25 δ r 0 r i r E 0 ν 0 E i ν creep

26 e σ 0 σ τ, σ = σ e t τ Tg Tg,

27 α α ε σ 0

28 Ansys Mathematica

29 T Fa

32 d 1 d 2 L β Fa d 2 -d 1 tg β β tg β d = d L

33 Fa = π d L Ptg β + ϕ ϕ P β ϕ P 0 P i

34 P i P D d

35 T 4 T 1 tg β q = tg β + µ n q Tn = T q β β µ q T 1 T 2 T 1 T 3 T 1

36 Pmáx Pmin American Gear Manufacturing Association Flexible Couplings Keyless Fits δ d d D δ δ d d = d D = r

37 ro r ri r D d l δ d mín = dmín Dmáx δ máx = dmáx Dmín d

38 δ d ε d D δd ε = = D D Ar An Pr Pn k Pr/2k

39 Ra < 0,8 µm L Ra i Ra 0 L = Rai + Ra

40 δ d = Rt + Rt r i o Rt i Rt o µm T l, L d. D

41 ε = ε = ε = ε = α T x y z α T δ d T = εd = α T D D δ d = α T D α T D T o o i i δ d = D α T α T T o o i i α i α o T i T o T T i T m T T - T m T

42 T T m E ν α ν δ = δd + δd r + δd T δd T

43 P max P min P( δ) := r r o + r E o r o r + ν o δ r r + r i + E i r r i ν i P(δ) δ r o r i r E o E i ν o ν i d µ da dt

44 T = A A dt T = µ r P δ da da = r dθ dz T = µ r P δ r dθ dz A L π T = µ r P δ dθ dz T = π µ r L P δ θ 0 θ 2π Pδ T L µ r dθ dz da θ z δ

46 (Cortesia WEG Equipamentos Elétrico, [30]). U, τ τ adm = U A cis T d = W L ch A cis = W L ch

47 A esm = L H/2 L ch σ esm U T d T σ adm = = = A L H d H L esm ch ch

49 x σ x = σ x = x = b x σ x = σ b f(x) σ(x) T = x f x A f(x) = σ(x) da da = L dx L

50 T = σ x x da A T = σ x x L dx A x = 0 x = b σ max = σ adm x T = σ adm x L dx A b L x= b T = σ x= adm x dx b σ adm L b T = b 2 = R 2 - a 2 T σ = L r a adm a a r a r,

51 fit, snap snap fit snap fit

52 A pino U τ U T τ adm = = A d A pino pino d A pino U A l σ U T σ adm = = A d h d l c pino d pino Al h c d pino h c

53 Snap Fit Snap fit Snap fit Snap fit Emerson Motors Snap Fit. T = P A c c µ d f P c A c d f

54 Snap Fit p d d D θ

55 T = i hd L rm P h d i L r m P π i = d p d. δ r m = d d h d δ P

56 T T π d d = δ L σ p π d δ = p L σ esm esm θ U δ L.

57 et al d T = iδ Le σ esm L e

58 (Cortesia WEG Indústrias S.A)

59 T = π µ r L P δ L

60 (Cortesia WEG). T = π µ r L P δ

62 C p n n n s C m C r C n n n.

63 C m C p C n C máx C mín C r n n n s et. al f n s f = = p f p 2p ω = s π f p f ω s 2p.

64 s, n n s = ns s ω n = ω s s n n n ω = n π n n t a = ω n C J m mmed + J ce C t a ω n rmed t a α m. et. al n = n Cmmed Cm n dn n n

65 n = n Crmed Cr n dn n n α m dω = dt ω = t n a ω t ω 0 t 0 T vp = J v α T vp J v α m T vp Microsoft Excell

66 s rad n t t dt d n a n m = = = = π ω ω ω α v v v v v m D D m J = =

67 (Cortesia WEG Indústrias S.A.) (Cortesia WEG Indústrias S.A.).

68 m v D v J v mvdv = = = kgm T = J α = = Nm vp v m P = P + P mec P mec P v P atr v atr

69 P joule P fe P sup Ptot = Pmec + Pjoule + Pfe + P P v T vf Pv = ω T vf ω s s J m

70 dω/dt α m P = J α ω mec m m s J m α m - ω s P tot I a P Joule U

71 R S I a P joule = I a R P 1 S + P I Ω I 1

72 T vf Pv = = = ω π s Nm T vmáx T vmáx T vp T = máx T vp vf T vf Treq = Tvmáx N f T req T vmáx N f

73 (WEG Indústrias S.A.).

74 creep

75 creep Creep Modulus Fonte: Crawford [1] σ log t creep ε s E log t ε σ ε creep

76 σ E ε et. al.

78 (Heat Distorcion Temperature)

79 σ ε) Fonte: Dupont [12].

80 (Cortesia: Dupont [12]).

81 µ

84 Æ Æ

86 Torque Products

94 D médio ) d P) D δd Se D médio mas P médio médio D + D = = d D = d δd médio médio =

100

101 σ T E T t = ε t δ = mm D = mm δ ε = = D σ MPa => E = = MPa

102 C 1 δ δ C P = = i i i i r r r r E r r r r r E r C ν ν (E 0 ν Creep Modulus C 1 µ

103 P(δ) L r T = π µ r L Pδ T = C µ Pδ C = π r L T = C µ C δ T = C µ δ C = r E r r + r r + ν π r + L r E i r r + ri r i ν i T e = Aδ + B T e δ A B

104 µ = A δ + B C δ µ A B C δ C A B

105 C A = µ N C C r r r r E r r r r r E r L r C i i i i = = = π ν ν π A = = µ µ

106 m N T B A T e e + = + = δ δ A C m N T T C T δ δ µ δ = = = B C δ δ = =

107 ε MPa h C h C E = = = ε σ C C m N T T C T δ δ µ δ = = = B δ δ = + =

108 Ansys 10.0, solid186 E 0

109 Fonte: Dupont [12]. Fonte: Dupont [12].

110 E C µ T = δd T A µ = = = C µ

111 T Te µ T L

112 Creep Modulus

113

114 Image Pro Express

115 Ra µm µm Ra µm

116 Ra µm Ra µm

117 Ra µm stress Ra µm

118 µm

119 Ra µm Ra µm

120 µm

121

122

123

124 et al Proc. Roy. Soc. London. A Proc. R. Soc. Lond. A Proc. Roy. Soc. Lond. A

125

126 E ε σ σ = Eε τ dε/dt ouε& τ = µε& µ, σ = f ε t f ε σ = ε t E t E(t),

127

128

129

130 ε σ ε σ = E ε σ ε& σ = µε& σ = σ = σ ε = ε + ε ε& ε& σ ε σ& σ ε& = ε& + ε& ε& = + E µ p 1 µe q 1 µ σ + p σ& = q ε&

131 σ(t), ε(t) t = 0 σ =σ 0 ε(t) ε(t) σ& = σ ε & t = q ε t = σ t + C t > 0 q C 1 σ 0 t = 0 σ& t + τ σ dt + p σ + τ σ τ = q ε + τ ε τ τ τ t = 0 ε(0 + ) ε 0, p σ = q ε ε = p q σ µ E σ ε = σ = µ E

132 t 0 + C 1 C p σ = ε = σ = q E C 1 ε t = σ p + t q 0 < t < t 1 ε 1 t = t 1 σ(t). ε& t = σ + p σ& =

133 p t t e p t p t dt p d p dt d = = = = = = σ σ σ σ σ σ σ σ σ σ σ σ σ & λ σ σ t e t = t t 1 λ σ t e C t = t > t 1. λ = p 1 t > t 1 ε σ E 0 λ e.

134 Tg Tg E rel, σ(t) ε 0. σ 0 =ε 0 E 0. E rel σ t t = ε σ = ε e t λ = E e t λ E 0 λ E 0 λ E 0 e t = λ. l C 2 σ(t 1 + ). ε& σ(t 1 - ) =σ(t 1 + ) = σ 0. C 2

135 σ t = σ = C e C = σ e t p t p C 2 σ t t t λ = σ e σ σ σ ε σ = Eε σ = µε& σ σ σ

136 σ = σ + σ σ = E ε + µε& σ = q ε + q ε& σ =σ 0 ε t σ t ρ = + C e q ρ 1 = q 1 /q 0 t = 0 σ 0 σ ε& ε(0+) = 0 C 1 = -σ 0/ q 0 ε σ q ρ t = e t 0<t< t 1 t ε ε = σ q ε σ = E E

137 t = t 1 ε = ε 1 σ σ = q ε = σ e t λ f (t) (0, ) e st f t dt s L f L f f f

138 L f s L f f f + = t + f t f f f n t f [0 + ; ), L f n s n L f s n f s n ( ) f (n- ) n n f n f f h t f = f f = f M f n = f n L f s ht L f t L f t f s t s dt e t a+s a e t sa+s t a a e t s a+s t n n n s

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