Behavior Analysis of PPWS Sockets for Suspension Bridges Considering Frictional Contact

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Received August 21 2012, Revised February 22 2013, Accepted June 3 2013

Copyright ⵑ 2013 by the Korean Society of Civil Engineers

This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0)

ABSTRACT

A sophisticated finite element model is illustrated to analyze the behavior of Prefabricated Parallel Wire Strand(PPWS) sockets for main cables of suspension bridges. An orthotropic model is proposed for the casting material by considering both effects of individual wires and a casting alloy, and the contact between surfaces of a socket and a casting alloy is idealized by using the Coulomb friction and the surface-based contact model. The proposed FE model is verified by comparing the strain distributions obtained from the tensile test and FE analysis. The mechanical behavior of a socket is investigated with respect to the variation of the frictional coefficient. The result shows that the friction between surfaces significantly diminishes the stress concentration of a socket and a casting alloy, and the normal stress from the design equation represents the averaged value of the upper and lower quartiles in the distribution of contact stresses between a socket and a casting alloy.

Key words : Parallel wire strand, Socket, Frictional contact, Finite element analysis, Suspension bridges

Ⅹಾ

⩥ᙹƱᵝ⍡ᯕትᬊ⠪⧪vᖁᜅ✙௽ऽ(PPWS) ᗭ⍴᮹ᨥၡ⦽ᙹ⊹⧕ᕾᮥ᭥⦽ᮁ⦽᫵ᗭ⧕ᕾ༉ߙᮥᱽᦩ⦹ᩡŁ, ᱽᦩࡽ⧕ᕾ༉ߙᮥᯕᬊ⦹ᩍ

ᗭ⍴᮹Ñ࠺ᮥᇥᕾ⦹ᩡ݅. }ᄥvᖁŝᗭ⍴ԕᇡᵝ᯦⧊ɩᰍ᮹ᩢ⨆ᮥŁಅ⦽ḢƱᯕႊᖒᰍഭ༉ߙᮥᱢᬊ⦹ᩡŁ, Coulomb ษₑၰ⢽໕ ᱲⅪ༉ߙᮥ᯦ࠥ⦹ᩍᗭ⍴ԕ໕ŝᵝ᯦⧊ɩᰍ⢽໕᮹ᱲⅪᔢ┽ෝǍ⩥⦹ᩡ݅. ᯙᰆᝅ⨹ᮝಽᇡ░⊂ᱶࡽᗭ⍴᫙໕᮹ᄡ⩶ᮉŝᮁ⦽᫵ᗭ⧕ᕾ

đŝෝእƱ⦹ᩍᱽᦩࡽᮁ⦽᫵ᗭ⧕ᕾ༉ߙ᮹┡ݚᖒᮥá᷾⦹ᩡŁ, ษₑĥᙹ᮹ᄡ⪵ᨱ঑ෙᗭ⍴᮹Ñ࠺ᮥ⧕ᕾ⦹ᩡ݅. ⧕ᕾđŝ, ᗭ⍴ԕ໕ ŝᵝ᯦⧊ɩᰍ⢽໕᮹ษₑᮡᗭ⍴ŝᵝ᯦⧊ɩᰍᨱၽᔾ⦹۵᮲ಆḲᵲᮥⓍí᪥⪵᜽⎑ᮝ໑, ᗭ⍴ᖅĥჶᨱᕽᱶ᮹ࡽᙹḢ᮲ಆ᜾ᮡᗭ⍴ԕ ໕ŝᵝ᯦⧊ɩᰍ⢽໕᮹ᱲⅪ᮲ಆᇥ⡍ᨱᕽᔢ⦹ᇡᔍᇥ᭥s᮹⠪Ɂᮥݡ⢽⦹۵äᮝಽӹ┡ԍ݅.

áᔪᨕ ⠪⧪vᖁᜅ✙௽ऽ, ᗭ⍴, ษₑᱲⅪ, ᮁ⦽᫵ᗭ⧕ᕾ, ⩥ᙹƱ

1. ᕽು

Ǎ᳑ᬊಽ⥥۵ᗭᱶᅙᙹಽ༉ᦥḥᜅ✙௽ऽ݅ၽ᮹᧲Ҿ݉ᮥŁᱶษq⦹Ł, ᯝᱶÑญ᮹ᱶ₊݉ᔍᯕᨱᖅ⊹⦹ᩍᯙᰆಆᨱᱡ⧎⧁

ᙹ ᯩࠥಾ Łᦩࡽ Ǎ᳑ෝ ☖⋎⦽݅. ᯕ్⦽ ಽ⥥ Ǎ᳑۵ ᵲపᯕ aᄮŁ ๅᬑ ᮁᩑ⦹໑, vࠥ ⬉ᮉᯕ ׳݅۵ ᰆᱱᯕ ᯩᨕᕽ, ☁༊, Õ⇶, ᖁၶၰ⧕ᔢǍ᳑ྜྷ॒ŝzᯕᯙᰆḡ႑Ǎ᳑aฯᯕᱢᬊࡹ۵ᇥ᧝ᨱᕽᵝ᫵ᇡᰍಽๅᬑ⡎մíᱢᬊࡹᨕ᪵݅. ᧲Ҿ݉ᮥ

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Łᱶ ษq⦹ᩍ ᯙᰆಆᨱ ᱡ⧎⦹۵ ಽ⥥⩶ Ǎ᳑ᨱᕽ۵ ᧲ Ҿ݉

ษq ႊჶ᮹ vࠥ ⬉ᮉᖒᯕ ʑᚁᱢᮝಽ ๅᬑ ᵲ᫵⦹݅. ಽ⥥⩶

Ǎ᳑ᨱᕽ᧲Ҿ݉᮹ษqႊჶᮡᯝၹᱢᮝಽⓍíᰍഭᱢᯙษₑ/ᇡ

₊✚ᖒᮥᯕᬊ⦹۵ႊჶŝʑĥᱢᯙᩑđ✚ᖒᮥᯕᬊ⦹۵ႊჶᮝ ಽǍᇥࡽ݅(Verreet, 1999; Wire rope technical board, 2005;

Feyrer, 2010).

ᰍഭᱢᯙษₑ/ᇡ₊✚ᖒᮥᯕᬊ⦽ษqႊჶᮡಽ⥥᧲Ҿ݉ᨱ

ᔞ᯦ࡽᬱ⇵⩶ᗭ⍴ᨱԊᯕӹᦥᩑ⪚ᮡ⧊ᖒᙹḡෝ₥ᬭքᨕ, ಽ⥥᪡ᵝ᯦ᰍᔍᯕ᮹ษₑ/ᇡ₊ᨱ᮹⦹ᩍ⍡ᯕት᮹ᯙᰆಆᨱᱡ⧎

⦹۵ႊჶᮝಽ, ݡ⢽ᱢᯙᱢᬊᩩಽ۵ᦥᩑ⧊ɩᮥᵝ᯦⦽}ႊ⩶

⪚ᮡ⠱ᘥ⩶ᜅ⠁░ᗭ⍴ᯕᯩ݅. ᰍഭᱢᯙษₑ/ᇡ₊✚ᖒᮥᯕᬊ⦽

ษq ႊჶᮡ ᗭ⍴᮹ ᱽ᳑ ၰ ᵝྜྷ ᯲ᨦ ॒ŝ zᯕ ⣩ḩ šญa

݅ᗭӽ⧕⦽᯲ᨦᮥᙹ⧪⦹ᩍ᧝⦽݅۵݉ᱱᯕᯩ۵ၹ໕, ษqࡽ

᧲ Ҿ݉Łᱶ݉᮹ vࠥ۵ ಽ⥥ᅙℕ᮹ ᯙᰆಆᮥ ᪥ᱥ⯩ḡḡ⧁

ᙹᯩ݅۵ᱱᨱᕽvࠥ⬉ᮉᯕ׳݅(Verreet, 1999; Wire rope technical board, 2005; Feyrer, 2010). ⦽⠙, ʑĥᱢᯙᩑđ✚ᖒᮥ

ᯕᬊ⦽ษqႊჶᮡಽ⥥᮹ᱽ᳑ၰ᯲ᨦᖒᨱᵝᦩᱱᮥࢵႊჶᮝಽ, Splice, Clamp ၰWedge ॒ᮥ⪽ᬊ⦽ษqႊჶᮥั⦽݅. ʑĥᱢ ᯙ ᩑđ ✚ᖒᮥ ᯕᬊ⦽ ษq ႊჶ᮹ vࠥ ⬉ᮉᮡ ಽ⥥ ᯱℕ᮹

ᯙᰆvࠥݡእ, ᧞80%ⴇ95% ᔍᯕᨱᇥ⡍⦹۵äᮝಽ᦭ಅᲙ

ᯩ݅(Verreet, 1999; Wire rope technical board, 2005; Feyrer, 2010).

⩥ᙹƱᵝ⍡ᯕትᬊ⠪⧪vᖁᜅ✙௽ऽ(ᯕ⦹PPWS: Prefabricated Parallel Wire Strand)۵ᯝᱶᅙᙹ᮹vᖁᮥᮂb⩶⩶┽ಽྗᨕ

ᜅ✙௽ऽ⪵ ⦹Ł᧲ Ҿ݉ᮥ ᬱ⇵⩶ᗭ⍴ŝ ᵝྜྷ ⧊ɩᮝಽŁᱶ

ษq⦹ᩍᱽ⣩⪵⦽äᯕ݅(Yoo et al., 2011). PPWS۵⩥ᙹƱ

Ʊ⇶᧲Ҿ݉ᨱ᭥⊹⦽ݡ⩶᧖⍅ญḡትಾᨱᖅ⊹ࡹᨕᵝ⍡ᯕትᬊ

ᯙᰆᇡᰍಽᕽʑ܆⦹ʑভྙᨱ, ᜅ✙௽ऽ᮹vࠥෝ᪥ᱥ⯩ḡḡ⧁

ᙹᯩ۵ษqႊჶ, ᷪ, ᗭ⍴ŝᵝྜྷ⧊ɩᮝಽŁᱶ᜽┅۵ᰍഭᱢᯙ

ษₑ/ᇡ₊✚ᖒᮥᯕᬊ⦽ษqႊჶᮥ₥┾⦹Łᯩ݅. ⩥ᙹƱPPWS ᬊᗭ⍴ᮡᗭ⩶ಽ⥥᮹ᜅ⠁░ᗭ⍴ŝǍ᳑⩶᜾ᔢᮝಽ۵ᮁᔍ⦹ḡ อ, vᖁ᮹⠪⧪႑⊹, Łᯙᰆvࠥ, ᵝ᯦ᰍ᮹✚ᖒၰᗭ⍴Ǎ᳑᮹

ݡ⩶⪵॒ŝzᮡ₉ᯕaᯩᨕᕽᗭ⍴ษqǍ᳑᮹vࠥ⬉ᮉᖒŝ

ᦩᱶᖒᮥᄥࠥಽá☁⧕᧝⧁⦥᫵ᖒᯕᯩ݅. PPWS᮹᧲Ҿ݉

ษqႊჶ᮹vࠥ⬉ᮉᖒᮥá☁⦹Łᗭ⍴ษqǍ᳑᮹ᦩᱶᖒᮥ

❱݉⦹ʑ᭥⧕ᕽ۵ᬱ⇵⩶ᗭ⍴ŝᗭ⍴ԕᇡᨱᵝ᯦ࡽᵝྜྷ⧊ɩ᮹

᮲ಆ ᇥ⡍᪡ ᩎ⦺ᱢ Ñ࠺ᮥ ᱶ⪶⯩ ᩩ⊂⧁ ᙹ ᯩᨕ᧝ ⦽݅.

Ł᪉ᬊᮖࡽᵝྜྷ᯲ᨦᮥ☖⦹ᩍᗭ⍴ᨱᵝ᯦ࡽ⧊ɩᰍ۵ᩩ⊂⦹

ʑᨕಅᬕᰍഭᱢᯙᇩɁᯝᖒᮥaḡ໑, ᵝ᯦⧊ɩᰍ᪡}ᄥvᖁ᮹

ᇡ₊ၰᗭ⍴ᅙℕ᪡ᵝ᯦⧊ɩᰍ᮹ษₑÑ࠺ᮡᙹ⊹ᱢᮝಽᱶప⪵

⦹ʑaๅᬑᨕಖ݅. ᯕ᪡zᮡᯕᮁಽᬱ⇵⩶ᗭ⍴᮹᮲ಆᇥ⡍

ၰÑ࠺ᨱš⦽ŝÑ᮹ᩑǍ۵ᵝಽᝅ⨹ᱢᯙႊჶᮥ☖⦹ᩍᯕ൉ᨕ

Კ᪵݅(Komura et al., 1990; Flory et al., 1995). ə్ӹᯕ᪡

zᮡᝅ⨹ᱢᩑǍᨱᕽ۵ᗭ⍴᫙ᇡ᮹᮲ಆᇥ⡍᪡ᗭ⍴ᱥℕǍ᳑᮹

Ñ࠺ᨱš⧕ᕽ۵ᮁ᮹ၙ⦽ᩑǍđŝෝᅕᩍᵝᨩᮝӹ, ᝅ⨹ᱢ⊂ᱶ ᯕᇩa܆⦽ ᗭ⍴ ԕᄞŝᵝ᯦ ⧊ɩᰍ᮹ ᮲ಆᇥ⡍ᨱ ݡ⧕ᕽ۵

Ñ࠺ᮥ ᪥ᱥ⦹í ᇥᕾ⦹ḡ ༜⦹ᩡ݅۵ ⦽ĥa ᯩ݅.

⦽⠙, ᜅ⠁░ᗭ⍴᮹Ñ࠺ᨱš⦽⧕ᕾᱢᩑǍ(Komura et al., 1990; Seo et al., 2010; Yoo et al., 2010a; Yoo et al., 2010b)ᨱᕽ

ࠥᰍഭᱢᱲⅪŝษₑÑ࠺ᮥᨥၡ⦹íၹᩢ⦹ḡᦫŁᗭ⍴ᅙℕอ

ᮥݡᔢᮝಽၽᔾ᮲ಆ᮹ᇥ⡍ෝá☁⦽ᩑǍđŝaݡᇡᇥᯕᨩ݅.

ᗭ⍴᮹ ᱲⅪŝ ษₑᮥ Łಅ⦹ḡ ᦫᮡ ᩑǍ۵ ᬱ⇵⩶ ᗭ⍴ᨱᕽ

⦥ᙹᱢᮝಽၽᔾ⦹۵ᡱʑ⬉ŝ(Wedge effect)ෝᱶ⪶⦹íၹᩢ⦹

ḡ༜⦽݅۵ᱱᨱᕽᱽ⦽ᱢᯕ௝⧁ᙹᯩ݅. ⧊ᖒᙹḡෝᵝ᯦ᰍಽ

⪽ᬊ⦽ᗭ⩶ಽ⥥Ǎ᳑᮹ᗭ⍴ᨱݡ⦽ᨥၡ⦽ᙹ⊹⧕ᕾᱢᩑǍ (Brandon et al., 2001; Brandon and Ridge, 2003)a ḥ⧪ࡽ

ၵ۵ᯩᮝӹ, ⩥ᙹƱᵝ⍡ᯕትᬊPPWS۵ᗭ⩶ಽ⥥Ǎ᳑ᨱእ⦹ᩍ

ḡḡ⦹۵ᜅ✙௽ऽ᮹ᯙᰆಆᯕๅᬑⓍŁ, ᗭ⍴᮹Ⓧʑaݡ⩶ᯕ௝

۵₉ᯕᱱᯕᯩᨕᯕᩎ᜽PPWSᬊᗭ⍴᮹ᩑǍđŝಽ⪽ᬊ⦹ʑᨱ ۵ ᇡᱢ⧊⦹݅.

ᅙםྙᨱᕽ۵⩥ᙹƱᵝ⍡ᯕትಽᯕᬊࡹ۵PPWSᬊݡ⩶ᗭ⍴

᮹ Ñ࠺ᮥ ᇥᕾ⦹Ł ᗭ⍴ ԕᄞ ၰ ᵝ᯦ ⧊ɩᰍ᮹ ᮲ಆ ᇥ⡍ෝ

᳑ᔍ⦹ʑ᭥⦹ᩍษₑᱲⅪᮥŁಅ⦽ᨥၡ⦽ᮁ⦽᫵ᗭ⧕ᕾႊჶᮥ

ᱽᦩ⦹ᩡ݅. ᗭ⍴ Ǎ᳑᮹ Ñ࠺ᮥ ᱶ⪶⯩ ༉ᔍ⦹ʑ ᭥⦹ᩍ ᗭ⍴

ᅙℕ۵॒ႊᖒᰍഭಽ༉ߙย⦹ᩡŁ, ᗭ⍴ԕᇡ᮹ᵝ᯦⧊ɩᰍ۵

⧊ɩᰍᨱྜ⩡ ᯩ۵ }ᄥvᖁ᮹ ᩢ⨆ᮥ Łಅ⦹ᩍḢƱ ᯕႊᖒ

ᰍഭಽ ༉ߙย ⦹ᩡ݅. ੱ⦽, ᯙᰆ ᝅ⨹ᨱ ᮹⦹ᩍ ᨜ᨕḥ ᗭ⍴

᫙໕᮹ᄡ⩶ᮉŝᮁ⦽᫵ᗭ⧕ᕾᮝಽᇡ░ᔑᱶࡽᄡ⩶ශᮥእƱ⦹ᩍ

⧕ᕾ༉ߙ᮹┡ݚᖒᮥá᷾⦹ᩡ݅. ᗭ⍴ԕ໕ŝᗭ⍴ԕᇡᵝ᯦

⧊ɩᰍ᮹ษₑᨱ঑ෙᗭ⍴Ǎ᳑᮹᮲ಆᇥ⡍ෝᅕᩡŁ, ࢱ໕ᔍᯕ᮹

ษₑĥᙹaၽᔾ᮲ಆၰ᮲ಆḲᵲᨱၙ⊹۵ᩢ⨆ᮥ᳑ᔍ⦹ᩡ݅.

ੱ⦽, ᗭ⍴ᖅĥჶᨱᕽᱶ᮹ࡽࢱ⢽໕ᔍᯕ᮹ᙹḢ᮲ಆŝᮁ⦽᫵ᗭ

⧕ᕾᨱᕽᔑᱶࡽᱲⅪ᮲ಆᮥእƱ⦹ᩍᖅĥ᜾᮹ ᮹ၙෝᰍŁₑ

⦹ᩡ݅.

2. PPWSᬊᗭ⍴᮹Ǎ᳑ၰᖅĥჶ

2.1 ীಭଭࠬԮ֜୺ࢫՋܛ൉ন

PPWSᬊᗭ⍴᮹ษqǍ᳑۵Fig. 1ŝzᯕᬱ⇵⩶ᮝಽᱽ᯲ࡽ

ᗭ⍴ᅙℕ᪡ԕᇡᵝ᯦⧊ɩᰍၰᵝ᯦⧊ɩᰍᨱႊᔍ⩶ᮝಽ⠝ℱᲙ

ྜ⩡ᯩ۵}ᄥvᖁᮝಽǍᖒࡹᨕᯩ݅. ᯕ్⦽ᗭ⍴᮹ษqǍ᳑۵

ᗭ⩶ಽ⥥᮹ᜅ⠁░ᗭ⍴ŝᮁᔍ⦽äᮝಽ, ᗭ⍴ԕᇡᨱᵝ᯦ࡽ

⧊ɩᰍ᪡ᵝ᯦⧊ɩᰍᨱྜ⩡ᯩ۵}ᄥvᖁ᮹ᇡ₊ಆၰᗭ⍴

ԕ໕ŝᵝ᯦⧊ɩᰍ᮹ᦶ⇶᮲ಆᨱ᮹⦹ᩍ ᜅ✙௽ऽᨱᱥݍࡹ۵

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Fig. 1. Structure and components of PPWS socket

Fig. 2. Distribution of the normal stress due to the contact between internal face of socket and casting alloy.

ᯙᰆಆᮥḡḡ⧁ᙹᯩࠥಾŁᦩࡽäᯕ݅. ᜅ✙௽ऽᨱᯙᰆಆᯕ

᯲ᬊ⧁ভ, ᬱ⇵⩶ᗭ⍴᮹aᰆⓑÑ࠺᮹✚Ḷᮡᬱ⇵⩶ᱥ໕ᇡᨱᕽ

ၽᔾ⦹۵ᡱʑ⬉ŝ(Wedge effect)ᯕ݅. ᡱʑ⬉ŝ۵ᜅ✙௽ऽᨱ

ᯙᰆಆᯕ ᯲ᬊ ⧁ ভ, ᬱ⇵⩶ ᗭ⍴᮹ ᱥ໕ᇡᨱ ๅᬑ ⓑ ᮲ಆᯕ

Ḳᵲࡹ۵⩥ᔢᮥั⦹໑(Brandon et al., 2001), ᬱ⇵⩶ᗭ⍴᮹

ᯕ్⦽᮲ಆḲᵲ⩥ᔢᮡ}ᄥvᖁŝᵝ᯦⧊ɩᰍ᮹ᇡ₊ᖒ܆ᮥ

v⪵᜽┅۵ᙽʑ܆ŝ⧉̹, ᗭ⍴ᯝᇡᨱŝࠥ⦽᮲ಆᮥၽᔾ᜽┅۵

ᩎʑ܆ᮥ ࠺᜽ᨱ ᮁၽ⦽݅.

2.2 ীಭডծ࣑

PPWSᬊᗭ⍴᮹ᯝၹᱢᯙᖅĥჶᮡ⨩ᬊ᮲ಆᖅĥჶᮥʑၹᮝ ಽ⦽݅. ᔢᖙ⦽ᗭ⍴᮹ᖅĥჶᮡšಉྙ⨭(Komura et al., 1995;

JSA, 1995; Yoo et al., 2013)ᮥₙŁ⧁ᙹᯩᮝ໑, ᅙםྙᨱᕽ۵

}ఖᱢᯙ ᖅĥ }ֱᨱ ݡ⧕ᕽอ eఖ⯩ ʑᚁ⦽݅.

ᗭ⍴᮹⦹ᵲᱡ⧎ᬱญ۵ᜅ✙௽ऽᨱ᯲ᬊ⦹۵ᯙᰆಆᮥᗭ⍴ŝ

ᵝ᯦⧊ɩᰍ᮹ᦶ⇶᮲ಆᮝಽᱡ⧎⦹۵äᯕ݅. ঑௝ᕽᜅ✙௽ऽ᮹

ᯙᰆಆᮥᵝ᯦⧊ɩᰍ᪡ᗭ⍴ᅙℕᨱ᪥ᱥ⦹íᱥݍ⦹ʑ᭥⧕ᕽ۵

ᵝ᯦⧊ɩᰍᨱྜ⩡ᯩ۵}ᄥvᖁŝᵝ᯦⧊ɩᰍᔍᯕᨱ∊ᇥ⦽

ᇡ₊vࠥa ၽ⩥ࡹᨕ᧝ ⦽݅. }ᄥ vᖁŝ ᵝ᯦ ⧊ɩᰍ ᔍᯕᨱ

∊ᇥ⦽ᇡ₊vࠥa⪶ᅕࡹᨩ݅Łaᱶ⦹໕, ᗭ⍴ԕᇡ᮹ᵝ᯦⧊ɩ ᰍᨱ۵ ᗭ⍴ ԕᄞ᮹ ḡḡᨱ ᮹⦹ᩍ ᦶ⇶᮲ಆᯕ ၽᔾ⦹໑, ᗭ⍴

ᅙℕ۵⇶ႊ⨆᮲ಆ(Axial stress)ŝᬱᵝႊ⨆᮲ಆ(Hoop stress) ၰᬱᵝḢbႊ⨆᮲ಆ(Radial stress)ᯕ༉ࢱၽᔾ⦹۵ᔝ⇶᮲ಆ

ᔢ┽ᨱᯩíࡽ݅. ᯕভ, ᵝ᯦⧊ɩᰍ᪡ᗭ⍴ᅙℕ᮹᮲ಆᔢ┽ෝ

đᱶ⦹ʑ᭥⧕ᕽ۵ᬱ⇵⩶ᮝಽᱽ᯲ࡽᗭ⍴ԕ໕ŝᵝ᯦⧊ɩᰍ

ᔍᯕᨱᱲⅪᮝಽၽᔾ⦹۵ᙹḢ᮲ಆᮥĥᔑ⧁⦥᫵aᯩᮝ໑, ࢱ

໕᮹ᙹḢ᮲ಆᮡFig. 2᪡zᯕ᯲ᬊ-ၹ᯲ᬊ᮹šĥᨱᯩ݅. ᗭ⍴᮹

ᖅĥŝᱶᨱᕽ۵ᱲⅪᨱ᮹⦹ᩍၽᔾࡹ۵ᗭ⍴ԕᄞ᮹ᙹḢ᮲ಆŝ

ᵝ᯦⧊ɩᰍ⢽໕ᨱ᯲ᬊ⦹۵ᙹḢ᮲ಆᮡᗭ⍴᮹⇶ႊ⨆ᨱ঑௝

ᯝᱶ⦽äᮝಽaᱶ⦽݅. ᗭ⍴ԕᄞၰᵝ᯦⧊ɩᰍ⢽໕᮹ᙹḢ᮲ಆ

ᮡ ᗭ⍴ԕᄞ᮹Ğᔍbŝᗭ⍴ԕ໕ၰᵝ᯦⧊ɩᰍ⢽໕᮹ษₑᮥ

Łಅ⦹ᩍ ᜾ (1)ŝ zᯕ ӹ┡ԝ ᙹ ᯩ݅(Komura et al., 1995;

JSA, 1995; Yoo et al., 2013).

ň_Ɓá ćņÞÎÏÞľßÞŇßâ_Ïß^¥ƃÞľ âŇß (1)

ᩍʑᕽ, ۵ᜅ✙௽ऽᨱ᯲ᬊ⦹۵⨩ᬊᰆಆᮥ᮹ၙ⦹Ł, ľ۵

ᗭ⍴ԕᄞ᮹Ğᔍbᮥ᮹ၙ⦽݅.Ň۵ᗭ⍴ԕᇡ⢽໕ŝᵝ᯦⧊ɩᰍ

⢽໕᮹ษₑbᮥ᮹ၙ⦹۵äᮝಽ, ษₑĥᙹෝł௝Łᱶ᮹⦹໕, ł á ÞŇß᮹ šĥa ᯩ݅. ⦽⠙, ÎŝÏ۵ ᗭ⍴ ԕᇡᨱᕽ

ᬱ⇵⩶ᮝಽᵝ᯦ࡽ⧊ɩᰍᨱᕽǍ᳑ᱢᮝಽᮁ⬉⦽Ǎeᨱݡ⦽

ᱥ໕ŝ⬥໕᮹ḢĞᯕ໑, ¥ƃᮡᵝ᯦⧊ɩᰍ᮹ᮁ⬉ʙᯕෝ᮹ၙ⦽

݅. ᬱ⇵⩶ᮝಽ ᱽ᯲ࡽ ᗭ⍴ ԕᇡ ᱥ໕ᇡ᮹ ᯝᱶ Ǎeᮡ }ᄥ

vᖁᯕ₉ḡ⦹۵እᵲᯕⓍŁ}ᄥvᖁᔍᯕ᮹eĊᯕⓍḡᦫʑ

ভྙᨱ ⧊ɩᰍa ᱽݡಽ ᵝ᯦ࡹḡ ᦫᮥ a܆ᖒᯕ ᯩ݅Ł ᅕ۵

äᯕ┡ݚ⦹݅. ⧊ɩᰍᨱᕽǍ᳑ᱢᮝಽᮁ⬉⦹݅۵äᮡ⧊ɩᰍa

(4)

Table 1. Material properties of strand, socket and casting alloy

Prop. Strand Socket Casting alloy

Material

High-strength wire (T.S. 1960MPa

class)

SCW450 (KS D 4101)

Zinc-copper alloy (Zn 98%+Cu 2%) Young's

modulus 210000MPa 210000MPa 86614 MPa Poisson

ratio 0.3 0.3 0.27

Fig. 3. Geometry of the designed socket

(a) Outside (b) Inside

Fig. 4. Finite element model for a socket

∊ᇥ⯩ᵝ᯦ࡹᨕ}ᄥvᖁŝᵝ᯦⧊ɩᰍᔍᯕᨱ᪥ᱥ⦽ᇡ₊vࠥ

a ⪶ᅕࡽ äᮥ ᮹ၙ⦽݅.

2.3 ীಭଭ୍߹ࢄনࢫ׆෇෴ঃ

ᗭ⍴ᅙℕ۵ᯝၹᱢᮝಽKS D 4101ᨱ໦᜽ࡽ┥ᗭvᵝv⣩ᮝ ಽᱽ᯲ࡹ໑, ᵝ᯦⧊ɩᰍಽ۵ᦥᩑ98%᪡࠺2%᮹ᖒᇥᮥw۵

ᦥᩑ-࠺⧊ɩᯕᔍᬊࡽ݅(HSBA-HBS 3503, 1989). ᅙםྙᨱᕽ ۵ᜅ✙௽ऽ᮹ᯙᰆvࠥ1960MPaɪ, vᖁᅙᙹ127ᅙၰvᖁ

ḡ෥5.4mmᯙPPWSᨱݡ⦹ᩍᗭ⍴᮹ᖅĥჶᨱ঑௝⧕ݚᗭ⍴ᮥ

ᖅĥ⦹Ł, ⬥ᗮᱩᨱᕽʑᚁࢁᮁ⦽᫵ᗭ⧕ᕾ༉ߙ᮹á᷾ŝᗭ⍴

Ñ࠺ᇥᕾ᮹ʑᅙ༉ߙಽᔍᬊ⦹ᩡ݅. Table 1ᮡᜅ✙௽ऽ᪡ᗭ⍴

ᅙℕၰᵝ᯦⧊ɩᰍ᮹ᰍഭྜྷᖒᮥᱶญ⦽äᯕ݅. Table 1ᨱᕽ

ᜅ✙௽ऽ᪡ ᗭ⍴ ᅙℕ᮹ ྜྷᖒᮡ ₙŁྙ⨭(Yoo et al., 2011)ᨱ

ʑᚁࡽ sᮥ ᔍᬊ⦹ᩡᮝ໑, ᵝ᯦ ⧊ɩᰍ᮹ Ğᬑᨱ۵ šಉྙ⨭

(NADCA, 2006)ᨱʑᚁࡽᦥᩑ⧊ɩ᮹ᯱഭෝ⪽ᬊ⦹ᩡ݅. ᯕ

ভ, ᗭ⍴ԕᄞŝᵝ᯦⧊ɩᰍ⢽໕ᔍᯕ᮹ษₑĥᙹ۵ᯝၹᱢᮝಽ

ᵝv⣩ŝᦥᩑ⧊ɩᔍᯕ᮹ษₑĥᙹಽᯙᬊࡹ۵0.2ෝᱢᬊ⦹ᩡ݅

(Podolny and Scalzi, 1986). ᯕ᪡zᮡᰍഭྜྷᖒᮥʑᵡᮝಽ

ᖅĥࡽ PPWS ᗭ⍴᮹ ᱽᬱᮡ Fig. 3ŝ z݅.

3. ᙹ⊹⧕ᕾ༉ߙၰá᷾

3.1 ীಭ఼࣭ଭକ෉૬ীࡦ܄

ᖅĥࡽPPWS ᗭ⍴Ǎ᳑᮹Ñ࠺ᮥᇥᕾ⦹ʑ᭥⦹ᩍษₑᱲⅪ

༉ߙ᮹⧕ᕾᯕa܆⦽ABAQUSෝᯕᬊ⦹ᩡ݅. ᗭ⍴ᅙℕ᮹ᮁ⦽

᫵ᗭ⧕ᕾ༉ߙᮡ᫵ᗭݚ8ᱩᱱ᮹3₉ᬱ᯦ႊ᫵ᗭ(C3D8R)ෝᯕᬊ

⦹ᩍ᯲ᖒࡹᨩ݅. ᵝv⣩ᮝಽᱽ᯲ࡽᗭ⍴ᅙℕ۵ᰍഭ᮹ႊ⨆ᨱ

঑௝ᰍഭᱢ✚ᖒᯕ࠺ᯝ⦽॒ႊᖒ(Isotropic) ᰍഭಽ༉ߙย⦹ᩡ

ᮝ໑, ᰍഭྜྷᖒᮡTable 1ᨱʑᚁࡽsᮥᯕᬊ⦹ᩡ݅. Fig. 4۵

ᗭ⍴ ᅙℕ᮹ ᮁ⦽᫵ᗭ ⧕ᕾ ༉ߙᮥ ӹ┡ԙ äᯕ݅.

3.2 Թ࣢Գটࢫச଺෍୍ׁ

}ᄥvᖁŝᵝ᯦⧊ɩᰍ۵bbTable 1ᨱʑᚁࡽäŝzᯕ

ᰍഭႊ⨆ᨱ঑௝✚ᖒᯕ࠺ᯝ⦽॒ႊᖒᰍഭᯕ݅. ᗭ⍴ԕᇡᨱ

ᵝ᯦ࡽ ⧊ɩᰍᨱᕽ }ᄥ vᖁᮡ ᇡ₊ ᖒ܆ᮥ ⪶ᅕ⦹ʑ ᭥⦹ᩍ

ႊᔍ⩶ᮝಽ⠝ℱᲙᕽŁᱶࡹᨕᯩ݅(Fig. 1 ₙ᳑). ə్ӹ, ᯕ᪡

zᮡ}ᄥvᖁŝᵝ᯦⧊ɩᰍ᮹ʑ⦹⩶ᔢᮥᮁ⦽᫵ᗭ⧕ᕾ༉ߙಽ

ᱶ⪶⯩Ǎ⩥⦹۵äᮡÑ᮹ᇩa܆⦹ʑভྙᨱ, ᅙםྙᨱᕽ۵

ᗭ⍴ԕᇡ᮹ ᰍഭෝ }ᄥvᖁŝ ᵝ᯦ ⧊ɩᰍ᮹ᰍഭᱢ ✚ᖒᮥ

(5)

Fig. 5. Orthotropic material model for a single wire and casting alloy

༉ࢱ Łಅ⧁ ᙹ ᯩ۵ ⦹ӹ᮹ ᅖ⧊ᰍഭಽ aᱶ⦹ᩡ݅.

Fig. 5۵ ᗭ⍴ ԕᇡᨱᕽ ᵝ᯦ ⧊ɩᰍ᪡ ⧊ɩᰍ ᔍᯕᨱ ྜ⩡

ᯩ۵}ᄥvᖁᮥ⪶ݡ⦹ᩍӹ┡ԙäᯕ݅. Fig. 5ᨱᕽᅕ۵ၵ᪡

zᯕ }ᄥ vᖁŝ ᵝ᯦ ⧊ɩᰍෝ ⦹ӹ᮹ ᅖ⧊ᰍഭಽ aᱶ⦹۵

Ğᬑ, ᯕᰍഭ۵ᗭ⍴᮹Ḣbႊ⨆(2⇶ŝ3⇶)ᨱݡ⧕ᕽ۵ᕽಽ

࠺ᯝ⦽ᰍഭ✚ᖒᮥaḡḡอ, ᗭ⍴⇶ႊ⨆(1⇶)ᨱݡ⧕ᕽ۵⇶ႊ⨆

ᮝಽʙí႑⊹ࡽvᖁ᮹ᩢ⨆ᨱ᮹⦹ᩍᱥ⩡݅ෙᰍഭᱢ✚ᖒᮥ

aḡíࢉᮥ᦭ᙹᯩ݅. ঑௝ᕽ, }ᄥvᖁᯕᵝ᯦⧊ɩᰍԕᨱᕽ

॒eĊᮝಽŁᱶࡹᨕᯩ݅Łaᱶ⦹໕, vᖁŝᵝ᯦⧊ɩᰍෝݡᄡ

⦹۵ᅖ⧊ᰍഭ۵ᗭ⍴᮹⇶ႊ⨆ŝḢbႊ⨆ᮝಽᰍഭᱢ✚ᖒᯕ

ᕽಽ ݅ෙ ḢƱ ᯕႊᖒ(Orthotropic) ᰍഭಽ Łಅࢁ ᙹ ᯩ݅

(Brandon et al., 2001).

ᯕ్⦽ᅖ⧊ᰍഭ᮹ྜྷᖒᮡᅖ⧊ᰍഭෝǍᖒ⦹۵ᰍഭ᮹✚ᖒᨱ

bᰍഭa₉ḡ⦹۵ᇡ⦝ᮉ᮹Œᮥᖁ⩶ᱢᯙ⧊ᮝಽӹ┡ԙ⪝⧊ჶ

⊺(rule of mixtures)ᨱ ঑௝ đᱶ⧁ ᙹ ᯩ݅(Brandon et al., 2001). ⪝⧊ჶ⊺ᨱ঑௝ᅖ⧊ᰍഭ᮹┥ᖒĥᙹ۵݅ᮭ᜾ᨱ᮹⦹ᩍ

đᱶࡽ݅.

_ÎÎá _ƕƇƐƃ¯_ƕƇƐƃâ_ſƊƊƍƗ¯_ſƊƊƍƗ (2)

ᩍʑᕽ, _ÎÎᮡᗭ⍴⇶ႊ⨆᮹┥ᖒĥᙹෝ᮹ၙ⦹Ł,᪡¯۵

bbǍᖒᰍഭ᮹┥ᖒĥᙹ᪡ᇡ⦝ᮉᮥ᮹ၙ⦽݅. ᯕভ, ᦥ௹℉ᯱ

ƕƇƐƃ۵}ᄥvᖁᨱݡ⦽ྜྷᖒs, ᦥ௹℉ᯱſƊƊƍƗ۵ᵝ᯦⧊ɩᰍ ᮹ ྜྷᖒ sᮥ ᮹ၙ⦽݅.

⦽⠙, ᗭ⍴ ⇶ Ḣbႊ⨆(_ÏÏ ၰ_ÐÐ)᮹ ┥ᖒĥᙹ۵᜾ (3)ᨱ

᮹⦹ᩍđᱶࡽ݅. ᯕভ, }ᄥvᖁᮡᵝ᯦⧊ɩԕᨱᕽᗭ⍴⇶ႊ⨆

ᮝಽ॒eĊᮝಽ႑⊹ࡽ݅Łaᱶ⦹ᩡᮝအಽ, ᗭ⍴⇶᮹Ḣbႊ⨆

ᮝಽ۵ ႊ⨆ŝ šĥᨧᯕ ࠺ᯝ⦽ ྜྷᖒsᮥ w۵݅.

_ÏÏá _ÐÐá ć¯_ƕƇƐƃî_ƕƇƐƃâ¯Î _ſƊƊƍƗî_ſƊƊƍƗ (3)

ᰍഭ᮹⥥᪡ᘂእ۵⦽⇶ᨱ᯲ᬊࡹ۵᮲ಆᨱ᮹⦹ᩍၽᔾ⦹۵

ḢƱ⇶᮹ᄡ⩶ශಽᱶ᮹ࡹအಽᗭ⍴⇶ႊ⨆᮹᮲ಆᨱ᮹⦹ᩍ⇶

Ḣbႊ⨆᮹ᄡ⩶ශᮥŁಅ⦹໕, ᅖ⧊ᰍഭ᮹⥥᪡ᘂእ۵⪝⧊ჶ⊺

ᨱ ᮹⦹ᩍ ݅ᮭŝ zᯕ đᱶࡽ݅.

Ń_ÎÏá Ń_ÎÐá Ń_ƕƇƐƃ¯_ƕƇƐƃâŃ_ſƊƊƍƗ¯_ſƊƊƍƗ (4)

Ń_ÏÐá Ń_ſƊƊƍƗ

ᩍʑᕽ, ᗭ⍴⇶ႊ⨆ᮥʑᵡᮝಽᗭ⍴ᙹḢႊ⨆᮹᮲ಆᨱݡ⦽

ḢƱ ႊ⨆᮹ ⥥᪡ᘂእ(ŃÏÐ)۵ }ᄥ vᖁ᮹ ᩢ⨆ᮡ Ñ᮹ ᨧ݅Ł

ᅕŁ, ᵝ᯦⧊ɩᰍᨱ᮹⧕ᕽอđᱶࡹ۵äᮝಽaᱶ⦹ᩡ݅. ᅖ⧊ᰍ ഭ᮹✚ᖒᮥđᱶ⦹۵ษḡส⧎ᮝಽᰍഭ᮹ᱥ݉┥ᖒĥᙹ۵݅ᮭ

᜾ᨱ ᮹⦹ᩍ đᱶࡽ݅.

_ÎÏá _ÎÐá ć¯_ƕƇƐƃî _ƕƇƐƃâ¯Î _ſƊƊƍƗî _ſƊƊƍƗ (5) _ÏÐá ćÏÞÎ âŃÏÐß

_ÏÏ

᜾(2)ⴇ᜾(5)۵}ᄥvᖁŝᵝ᯦⧊ɩᰍ᮹ᇡ⦝ᮉᨱ঑௝

đᱶࡹ۵ḢƱᯕႊᖒᅖ⧊ᰍഭ᮹ᰍഭᱢ✚ᖒᮥĥᔑ⦹۵᜾ᯕ݅.

ᯕ ভ, ᗭ⍴ ԕᇡ۵ ᬱ⇵⩶ᯕအಽ ᗭ⍴᮹ ⇶ ႊ⨆ᨱ ঑௝ }ᄥ

vᖁŝ ᵝ᯦ ⧊ɩᰍa ₉ḡ⦹۵ ᇡ⦝ᮉᮡ Ⓧí ᄡ⪵⦹í ࡽ݅.

ᷪ, ᗭ⍴ᱥ໕ᇡᨱᕽ۵ᵝ᯦⧊ɩᰍᨱእ⦹ᩍ}ᄥvᖁᯕ₉ḡ⦹۵

ᇡ⦝ᮉᯕⓍíࡹအಽᅖ⧊ᰍഭ᮹✚ᖒᨱ۵}ᄥvᖁᯕၙ⊹۵

(6)

Fig. 6. Finite element model for a strand and casting alloy

Table 2. Calculated properties of the orthotropic material for casting alloy

Part _ÎÎ (MPa) _ÏÏ(=_ÐÐ) (MPa) Ń_ÎÏ(=Ń_ÎÐ) Ń_ÏÐ _ÎÏ(= _ÎÐ) (MPa) _ÏÐ (MPa)

alloy0 175452 150121 0.292 0.270 58393 59103

alloy1 136585 113661 0.282 0.270 44518 44748

alloy2 116227 100833 0.277 0.270 39590 39698

alloy3 106109 95478 0.275 0.270 37526 37590

alloy4 100433 92715 0.273 0.270 36459 36502

ᩢ⨆ᯕⓍ݅. ၹݡಽ, ᗭ⍴᮹⬥໕ᇡᨱᕽ۵}ᄥvᖁᨱእ⦹ᩍ

ᵝ᯦⧊ɩᯕ₉ḡ⦹۵ᇡ⦝ᮉᯕⓍʑভྙᨱᅖ⧊ᰍഭ᮹✚ᖒᨱ

}ᄥvᖁᯕၙ⊹۵ᩢ⨆ᮡᔢݡᱢᮝಽ᯲݅. ᅙםྙᨱᕽ۵ᗭ⍴

⇶ႊ⨆ᮝಽݍ௝ḡ۵ᅖ⧊ᰍഭ᮹ ✚ᖒᮥᅕ݅ᱶ⪶⯩Łಅ⦹ʑ

᭥⦹ᩍ ᜅ✙௽ऽ᪡ᵝ᯦ ⧊ɩᰍෝ ᗭ⍴ʙᯕ ႊ⨆ᮝಽ ⅾ݅ᖐ

Ǎeᮝಽӹ٥ᨕ༉ߙย⦹ᩡ݅. Fig. 6ᮡ݅ᖐǍeᮝಽӹڹᨕ

༉ߙยࡽᜅ✙௽ऽ᪡ᵝ᯦⧊ɩᰍ᮹༉ߙย⩶ᔢᮥӹ┡ԙäᯕ݅.

ੱ⦽, Table 2۵ ᜾ (2)ⴇ᜾ (5)ෝ ᯕᬊ⦹ᩍ b Ǎeᨱ ݡ⦹ᩍ

ĥᔑ⦽ ᅖ⧊ᰍഭ᮹ ྜྷᖒsᮥ ᱶญ⦽ äᯕ݅. ⦽⠙, ᅖ⧊ᰍഭ᮹

༉ߙยᨱᔍᬊࡽᮁ⦽᫵ᗭ۵3₉ᬱ᯦ႊ⩶᫵ᗭ(C3D8R)᪡ᡱʑ⩶

᫵ᗭ(C3D6)ෝ ᯕᬊ⦹ᩡ݅.

3.3 ীಭ఼࣭૕ச଺෍ׁଭ୦ోࡦ܄

ᗭ⍴ŝᵝ᯦⧊ɩᰍ۵Fig. 4᪡zᯕᯝᱶĞᔍbᮥw۵ᡱʑ

⩶┽ಽ đ⧊ࡹᨕ ᯩʑ ভྙᨱ, ᗭ⍴ Ǎ᳑ᨱ ᯙᰆಆᯕ ᯲ᬊ⧉ᨱ

঑௝ᕽ ᗭ⍴ ԕᄞŝ ᵝ᯦ ⧊ɩᰍ᮹ ⢽໕ᨱᕽ۵ Fig. 2᪡ zᯕ

᯲ᬊ-ၹ᯲ᬊ ⩶┽᮹ ᙹḢ᮲ಆᯕ ၽᔾ⦽݅. ᗭ⍴ Ǎ᳑᮹ ᖅĥ᜽, ᗭ⍴ ԕᄞŝ ᵝ᯦ ⧊ɩᰍ᮹ ⢽໕ᨱᕽ ᱲⅪᨱ ᮹⦹ᩍ ၽᔾ⦹۵

ᙹḢ᮲ಆᮡ ᜾ (1)ಽ ĥᔑࡹᨩ݅.

ᗭ⍴ԕᄞŝᵝ᯦⧊ɩᰍ᮹⢽໕ᨱၽᔾ⦹۵ᱲⅪᨱ᮹⦽ᙹḢ᮲ ಆᮡᮁ⦽᫵ᗭ⧕ᕾᨱᕽ⢽໕ᱲⅪྙᱽಽ⊹⪹ࢁᙹᯩ݅. ᕽಽ

ᇥญࡹᨕ ༉ߙย ࡽ ࢱ ᄡ⩶ℕ᮹ ⢽໕ ᱲⅪᮥ ᙹ⊹⧕ᕾᱢᮝಽ

Ǎ⩥⦹ʑ᭥⧕ᕽ۵᮲ಆᮥᱥݍ⦹۵⢽໕ᮝಽ ᱶ᮹ࡹ۵ᵝ⢽໕ (Master surface)ŝ ᮲ಆᮥ ᱥݍ ၼ۵ ⢽໕ᮝಽ ᱶ᮹ࡹ۵ ᱲⅪ

ݡ᮲⢽໕(Slave surface)᮹༉ߙยᯕ⦥᫵⦹݅. ࢱᄡ⩶ℕ᮹⢽໕

ᱲⅪ ⩥ᔢᮥ Ǎ⩥⦹ʑ ᭥⦽ ᙹ⊹⧕ᕾᱢ ʑჶᮡ Ⓧí ᱩᱱ ᱲⅪ

༉ߙ(node based contact)ŝ⢽໕ᱲⅪ༉ߙ(surface based contact) ಽ Ǎᇥࡽ݅. ࢱ ᱲⅪ ༉ߙᮡ ᵝ⢽໕ŝ ᱲⅪ ݡ᮲ ⢽໕ ᔍᯕ᮹

ᱲⅪᩍᇡෝ❱ᄥ⦹۵ʑჶ᮹₉ᯕಽǍᇥࡹ۵äᮝಽ, ᱩᱱᱲⅪ

༉ߙᮡࢱ ⢽໕ᨱᕽ ᱶ᮹ࡽᱩᱱᮥ ʑᵡᮝಽ ᧲ᱲⅪ໕ᯕ ᕽಽ

ᱲ⧩۵ḡᇥญࡹᨩ۵ḡෝ❱ᄥ⦹۵⧕ᕾᱢʑჶᯕ௝⧁ᙹᯩŁ,

⢽໕ᱲⅪ ༉ߙᮡ ⢽໕ᔢᨱ᭥⊹⦽ ᱩᱱ ᔍᯕෝᖁ⩶ ᅕeჶᨱ

᮹⦹ᩍ⢽໕⪵⦽⬥, ࢱᱲⅪ໕᮹ᱲⅪᩍᇡෝ❱ᄥ⦹۵⧕ᕾʑჶᯕ

௝⧁ᙹᯩ݅(Simulia, 2010). ᱩᱱᱲⅪ༉ߙ᮹Ğᬑᨱ۵ĥᔑపᯕ

ᔢݡᱢᮝಽᱢᮡၹ໕, ࢱ⢽໕ᔍᯕᨱᱶ᮹ࡽᱩᱱ᮹ᔢݡᱢ᭥⊹ᨱ

঑௝ᱲⅪ໕᮹ᱲⅪᔢ┽ෝᱶ⪶⯩❱ᄥ⦹ḡ༜⧁a܆ᖒᯕᯩ݅.

⦽⠙, ⢽໕ᱲⅪ༉ߙᮡࢱᱲⅪ໕᮹ᱲⅪᔢ┽ෝᱶ⪶⯩༉ᔍ⧁

ᙹᯩᮝӹ, ᱩᱱeᖁ⩶ᅕeᮝಽᯙ⦹ᩍĥᔑపᯕŝࠥ⦹íฯᦥḡ ۵ྙᱽᱱᯕᯩ݅. ᅙםྙᨱᕽ۵ĥᔑప᮹⇶ᗭᅕ݅۵ࢱᱲⅪ໕

ᔍᯕ᮹ᱲⅪᔢ┽ၰᨥၡ⦽ᱲⅪ᮲ಆ᮹ĥᔑᯕᅕ݅ᵲ᫵⦽äᮝಽ

❱݉ࡹᨕ ⢽໕ ᱲⅪ ༉ߙᮥ ᱢᬊ⦹ᩡ݅.

⢽໕ᱲⅪ༉ߙᨱᕽᵝ⢽໕ŝᱲⅪݡ᮲⢽໕᮹ᯝၹᱢᯙᖁ┾

ʑᵡᮡᵝ⢽໕᮹Ğᬑ, ⢽໕᮹ᮁ⦽᫵ᗭMeshaᱲⅪݡ᮲⢽໕ᨱ

እ⦹ᩍ݅ᗭ᳑ၡ⦹í⩶ᖒࡹ໑, ၽᔾᱲⅪ᮲ಆᮥ܆࠺ᱢᯙ᯦ᰆᨱ ᕽᱥݍ⦹۵ᄡ⩶ℕ᮹⢽໕ᨱᱶ᮹ࡽ݅۵äᯕ݅. ᯕ్⦽ʑᵡᮝಽ

ᅝভ, ᗭ⍴ᅙℕ᪡}ᄥvᖁၰᵝ᯦⧊ɩᰍෝݡᄡ⦹۵ᅖ⧊ᰍഭಽ

ᕽಽᇥญࡹᨕ༉ߙยࡽᅙםྙ᮹ᮁ⦽᫵ᗭ༉ߙᨱᕽ۵ᅖ⧊ᰍഭ ᮹⢽໕ᮥᵝ⢽໕ᮝಽ⦹Ł, ᗭ⍴ᅙℕ᮹ԕ໕ᮥᱲⅪݡ᮲⢽໕ᮝಽ

ᱶ᮹⦹۵äᯕ┡ݚ⦹݅. Fig. 7ᮡᅙםྙᨱᕽ༉ߙยࡽࢱᄡ⩶ℕ ᮹ ᵝ⢽໕ŝ ݡ᮲ ᱲⅪ⢽໕ᮥ ӹ┡ԙ äᯕ݅.

(7)

(a) Master surface (b) Slave surface Fig. 7. Definition of contact surfaces on a socket

3.4 ীಭٛ࣠րச଺෍୍ׁଭࠬఝࡦ܄:

Coulomb friction

ᗭ⍴ԕᄞŝᵝ᯦⧊ɩᰍ᮹⢽໕ᮡᕽಽᱲⅪ⦹ᩍᯩʑভྙᨱ

ᜅ✙௽ऽᨱᯙᰆಆᯕ᯲ᬊ⧉ᨱ঑௝ࢱ⢽໕ᔍᯕ᮹ᱲⅪᨱ᮹⦽

ᙹḢ᮲ಆᮡ᷾a⦹໑, ᯕᨱ঑௝⢽໕ᨱ᯲ᬊ⦹۵ษₑಆᮡ᷾a⦹

íࡽ݅. ᅙםྙᨱᕽ۵ࢱ⢽໕᮹ษₑಆᮥ༉ߙย⦹ʑ᭥⦽ႊჶᮝ ಽᯝၹᱢᮝಽձญᥑᯕŁᯩ۵Coulomb friction ༉ߙᮥᱢᬊ⦹

ᩡ݅(Waismann et al., 2011). Coulomb friction ༉ߙᮡ ݅ᮭ

᜾ᮝಽ ᱶ᮹ࡽ݅.

ŉ á łƎ (6)

ᩍʑᕽ, ŉ۵ ࢱ ⢽໕ ᔍᯕᨱ ၽᔾ⦹۵ ษₑ᮲ಆᮥ ᮹ၙ⦹Ł, ł۵ࢱ⢽໕᮹ᖒḩᨱ঑௝đᱶࡹ۵ษₑĥᙹෝӹ┡ԙ݅.Ǝ۵

ࢱ⢽໕ᔍᯕᨱᕽᱲⅪᨱ᮹⦹ᩍၽᔾ⦹۵ᙹḢ᮲ಆᮝಽᱶ᮹ࡹ໑, ᯝၹᱢᮝಽ ᱲⅪ᮲ಆ(Contact stress)ᮝಽ ӹ┡ԙ݅. Coulomb friction ༉ߙᨱᕽᱲⅪ᮲ಆƎ۵ᗭ⍴ᖅĥჶ(᜾(1))ᨱᕽࢱ⢽໕ᨱ

᯲ᬊ⦹۵᮲ಆᮝಽᱶ᮹⦽ၵᯩ۵ᗭ⍴ԕᄞŝᵝ᯦⧊ɩᰍ⢽໕ᨱ

ᇥ⡍⦹۵ ᙹḢ᮲ಆŝ ࠺ᯝ⦽ ᮹ၙᯕ݅.

ᅙםྙᨱᕽ۵᯲ᖒࡽᮁ⦽᫵ᗭ༉ߙ᮹┡ݚᖒᮥá᷾⦹ʑ᭥⦹

ᩍᗭ⍴ԕᄞŝᵝ᯦⧊ɩᰍᔍᯕ᮹⢽໕ᔢ┽ෝŁಅ⦽ษₑĥᙹෝ

⧕ᕾᨱᱢᬊ⦹ᩡŁ, ⧕ᕾđŝෝᝅ⨹ᨱᕽ᨜ᮡđŝ᪡እƱ⦹ᩡ݅.

ᷪ, ᗭ⍴ᖅĥ᜽ᨱ۵ࢱ⢽໕ᔍᯕ᮹ษₑĥᙹಽ┥ᗭvŝᦥᩑ

⧊ɩ⢽໕ᔍᯕ᮹ษₑĥᙹಽᯝၹᱢᮝಽᔍᬊࡹ۵0.2ෝᱢᬊ⦹ᩡ

ᮝӹ(Podolny and Scalzi, 1986), ᅙםྙ᮹ᮁ⦽᫵ᗭ⧕ᕾᨱᕽ۵

ᝅᱽᗭ⍴ᱽ᳑᜽, ᗭ⍴ԕᄞᯕᦥᩑࠥɩࡹᨩ݅۵ᱱᮥqᦩ⦹ᩍ

ᦥᩑࠥɩࡽ⢽໕ᔍᯕ᮹ษₑĥᙹsᨱaʭᬕ0.7ᮥᱢᬊ⦹ᩍ

⧕ᕾ⦹ᩡ݅(Yoo et al., 2013). ੱ⦽, ษₑĥᙹaᗭ⍴᮹Ñ࠺ၰ

᮲ಆᇥ⡍ᨱၙ⊹۵ᩢ⨆ᮥ᳑ᔍ⦹ʑ᭥⦹ᩍษₑĥᙹsᮥᄡ⪵᜽

┅໑ ⧕ᕾᮥ ᙹ⧪⦹ᩍ đŝෝ ᇥᕾ⦹ᩡ݅.

3.5 լծ୺Սࢫ෇ண୺Ս

ᕽಽᇥญࡹᨕ༉ߙยࡽᗭ⍴ᅙℕ᪡ᗭ⍴ԕᇡᅖ⧊ᰍഭ᮹

vℕᬕ࠺(rigid body motion)ᮥǍᗮ⦹ʑ᭥⦹ᩍb༉ߙᨱ⧊ݚ⦽

Ğĥ᳑Õᮥᱢᬊ⦹ᩡ݅. ᗭ⍴ᅙℕ᮹Ğᬑᨱ۵ᝅᱽÑ࠺᳑Õŝ

࠺ᯝ⦹ࠥಾ ᗭ⍴ ᱥ໕ᮥ ⦡Ǎᗮ ᜽⎑Ł, ᗭ⍴ ԕᇡ ᅖ⧊ᰍഭ᮹

Ğᬑᨱ۵ԕᇡᅖ⧊ᰍഭ᪡ᩑđࡽᜅ✙௽ऽᇡ᮹ᦿ໕ᮥ⬂Ǎᗮ

᜽⎑݅. ⦽⠙, ༉ߙᨱ᯲ᬊ⦹۵⦹ᵲᮡᅖ⧊ᰍഭ᪡ᩑđࡽᜅ✙௽ऽ ᮹ᦿ໕ᯕᯙᰆಆᮥၼᦥᗭ⍴⇶ႊ⨆ᮝಽᄡ᭥ෝᯝᮝ┅۵ᄡ᭥

⦹ᵲ᳑Õᮥᱢᬊ᜽⎑݅. ᯕভ, ⇶ႊ⨆᮹ᄡ᭥۵ᗭ⍴ᱥ໕ᇡᨱ

⦡Ǎᗮࡽᱩᱱᨱᕽၽᔾ⦹۵⇶ႊ⨆ၹಆ᮹ⅾ⧊ᯕᜅ✙௽ऽ᮹

⨩ᬊ ᯙᰆಆ(=2280 kN)ᯕ ࡹࠥಾ ᰍ⦹ ࡹᨩ݅.

4. ᮁ⦽᫵ᗭ⧕ᕾ༉ߙ᮹á᷾

4.1 ਆൈ޻݁଴ୋਓ෠

ᅙםྙᨱᕽᱢᬊ⦽ᮁ⦽᫵ᗭ༉ߙ᮹┡ݚᖒᮥá᷾⦹ʑ᭥⦽

ႊჶᮝಽ, ᯙᰆᝅ⨹(Yoo et al., 2011)ᨱᕽ⊂ᱶࡽᗭ⍴⢽໕᮹

ᄡ⩶ᮉ ᇥ⡍᪡, ࠺ᯝ⦽ ᳑Õᮥ ᱢᬊ⦹ᩍ ⧕ᕾ⦽ ᮁ⦽᫵ᗭ ⧕ᕾ

đŝෝ እƱ⦹ᩡ݅.

PPWS ᯙᰆ᜽⨹ℕ᮹ᜅ✙௽ऽ۵ⅾ127ᅙ᮹}ᄥvᖁ(Ŗ⋎

ḡ෥5.4mm)ᯕᮂb⩶ᮝಽ⠪⧪⦹íḲᗮࡽäᮝಽ᧲݉ᮡᅙ

םྙᨱᕽᖅĥࡽᗭ⍴ᮝಽŁᱶษqࡹᨩᮝ໑, ᗭ⍴ᱥ໕eÑญ۵

5.5mᯕᨩ݅. ᯙᰆᝅ⨹ᮡ᜽⨹ℕ᮹᧲݉ᮥbbŁᱶ݉ŝaಆʑa

ᇡ₊ࡽa࠺݉ᨱᖅ⊹⦹Łaಆʑᨱᱱḥᱢᮝಽ ⦹ᵲᮥa⦹۵

ႊჶᮝಽᙹ⧪ࡹᨩ݅. aಆ⦹ᵲᮡᜅ✙௽ऽԕᇡ᮹}ᄥvᖁᯕ

(8)

Fig. 8. Location of strain gauges on a socket

(a) Axial strain (b) Hoop strain

Fig. 9. Comparison of strains measured from test and obtained from analysis ᯝᱶᅙᙹᯕᔢ❭݉ࡹᨕᱥℕ᜽⨹ℕ᮹⦹ᵲ-ᄡ᭥łᖁᯕᱶᱱᨱ

ࠥݍ⧁ ভ ʭḡ ᷾a ᜽⎑݅(Yoo et al., 2011). ᯙᰆ ᝅ⨹ ᵲ, ᗭ⍴ ⢽໕᮹ ᄡ⩶ශᮥ ⊂ᱶ⦹ʑ ᭥⦹ᩍ Fig. 8ŝ zᯕ Łᱶ݉

ᗭ⍴᫙⢽໕ᨱ3⇶ᄡ⩶ශíᯕḡෝᇡ₊⦹ᩡ݅. ᗭ⍴᮹ʙᯕႊ⨆

ၰᬱᵝႊ⨆ᨱ঑௝ᵲᦺŝ᳭, ᬑ⊂ᨱÙℱíᯕḡෝᖅ⊹⦹ᩍ

ᗭ⍴ ⢽໕᮹ ⇶ႊ⨆ ᄡ⩶ශ(Axial strain)ŝ ᬱᵝ ႊ⨆ ᄡ⩶ශ (Hoop strain)ᮥ ༉ࢱ ⊂ᱶ⧁ ᙹ ᯩࠥಾ ⦹ᩡ݅.

4.2 କ෉૬ীැজէր૕ਓ෠౸୨էրଭण֗

Fig. 9۵ ᜅ✙௽ऽᨱ ⨩ᬊᯙᰆಆᯕ᯲ᬊ⦹۵ Ğᬑ, ᝅ⨹ᨱᕽ

⊂ᱶࡽᗭ⍴᫙⢽໕᮹ᄡ⩶ශŝ࠺ᯝ⦽᳑Õᨱᕽ⧕ᕾࡽᮁ⦽᫵ᗭ

⧕ᕾ༉ߙᨱᕽᗭ⍴⢽໕᮹ᄡ⩶ශᮥእƱ⦽äᯕ݅. ᯕভ, ᗭ⍴ᮡ

Fig. 3᮹ᱽᬱᮥ঑෕໑, 3.3ᱩᨱᕽʑᚁ⦽ၵݡಽᝅᱽᗭ⍴ᱽ᳑᜽

ᄡ⪵ࡽᗭ⍴ԕ⢽໕᮹ᦥᩑࠥɩ᳑ÕᮥŁಅ⦹ᩍ, ᗭ⍴ԕ⢽໕ŝ

ᵝ᯦⧊ɩᰍ⢽໕᮹ษₑĥᙹෝ0.7ಽᱢᬊ⦹ᩍ⧕ᕾ⦹ᩡ݅. Fig.

9(a)۵ᗭ⍴⇶ႊ⨆᮹ᄡ⩶ශ(Axial strain)ᮥእƱ⦽äᯕŁ, Fig.

9(b)۵ᗭ⍴ᬱᵝႊ⨆᮹ᄡ⩶ශ(Hoop strain)ᮥእƱ⦽äᯕ݅.

Fig. 9ᨱᕽ ʑ⪙ಽ ⢽᜽ࡽ ᱱᮡ Fig. 8᮹ ᗭ⍴ ⢽໕ ᭥⊹ᨱᕽ

ᝅ⨹ᨱ᮹⦹ᩍ⊂ᱶࡽᄡ⩶ශᮥӹ┡ԙäᯕŁ, ᝅᖁᮡᮁ⦽᫵ᗭ

⧕ᕾᨱᕽ ᨜ᮡ đŝෝ ӹ┡ԙ äᯕ݅.

ᝅ⨹ᨱᕽ ᨜ᨕḥ ᗭ⍴ ⢽໕᮹ ⇶ႊ⨆ ᄡ⩶ශᮡ ᗭ⍴᮹ ᬱᵝ

ႊ⨆ᨱ ঑௝ ᵲᦺ(C)ŝ ᳭(L), ᬑ⊂(R)ᨱ Ùℱ Ñ᮹ ᯝ⊹⦹ᩍ, ᯙᰆᝅ⨹ࠥᵲᨱᗭ⍴ᨱ⠙ᝍ⦹ᵲᯕ᯲ᬊ⦹۵॒᮹እᱶᔢᱢᯙ

Ğᬑ۵ᨧᨩᮭᮥ⪶ᯙ⧁ᙹᯩ݅. ⦽⠙, ᝅ⨹ᨱᕽ⊂ᱶ⦽ᗭ⍴

ᬱᵝႊ⨆᮹ᄡ⩶ශᮡᗭ⍴᮹ᬱᵝႊ⨆ᨱ঑௝݅ᗭ₉ᯕෝᅕᩡᮝ ӹ, ݡℕᱢᯙ ᄡ⩶ශ᮹ Ğ⨆ᮡ Ñ᮹ ᯝ⊹ ⦹ᩡ݅.

Fig. 9ᨱᕽ⪶ᯙ⧁ᙹᯩ۵ၵ᪡zᯕᮁ⦽᫵ᗭ⧕ᕾᨱᕽᔑᱶࡽ

ᗭ⍴ ᫙⢽໕᮹ ᄡ⩶ශ ᇥ⡍۵ ᝅ⨹ᨱᕽ ⊂ᱶࡽ ᄡ⩶ශ ᇥ⡍᪡

᯹ᯝ⊹⦹ᩡ݅. ᅙםྙᨱᕽᱢᬊ⦽ษₑᱲⅪ༉ߙŝ⢽໕ᔍᯕ᮹

ษₑĥᙹၰ ḢƱ ᯕႊᖒᅖ⧊ᰍഭಽ Ǎ⩥ࡽ }ᄥvᖁŝ ᵝ᯦

⧊ɩᰍ᮹ᮁ⦽᫵ᗭ⧕ᕾ༉ߙᮡᝅᱽᗭ⍴Ǎ᳑᮹Ñ࠺ᮥ᯹ၹᩢ⦹

Ł ᯩᮭᮥ ᦭ ᙹ ᯩ݅.

5. ᗭ⍴Ǎ᳑᮹Ñ࠺⧕ᕾ

5.1 ীಭଭଦߚंඑ

ᗭ⍴ԕ໕ŝᵝ᯦⧊ɩᰍ⢽໕᮹ษₑĥᙹၰࢱǍ᳑᮹ᱲⅪᨱ

᮹⦽ ᙹḢ᮲ಆᯕ ᗭ⍴ Ǎ᳑ᨱ ၙ⊹۵ ᩢ⨆ᮥ ᳑ᔍ⦹ʑ ᭥⦹ᩍ

ࢱ⢽໕᮹ษₑĥᙹෝᄡ⪵᜽┅໑⧕ᕾ⦹Łđŝෝᇥᕾ⦹ᩡ݅.

ᯕভ, ࢱ⢽໕ᔍᯕ᮹ษₑĥᙹ۵ษₑᯕၽᔾ⦹ḡᦫ۵ᯕᔢᱢᯙ

(9)

Outside

(a) Internal surface (b) External surface

Fig. 10. Effective stresses on a socket with respect to fictional coefficients

ᔢ┽(ł=0.0)ಽᇡ░ 0.05, 0.2, 0.45 ၰ 0.7ಽ ᄡ⪵᜽⎑݅.

ᗭ⍴ᮡᜅ✙௽ऽ᮹ᯙᰆಆᨱ᮹⦹ᩍ⇶ႊ⨆᮲ಆŝᬱᵝႊ⨆

᮲ಆ ၰᬱᵝ Ḣbႊ⨆ ᮲ಆᯕ༉ࢱ ၽᔾ⦹۵ ᔝ⇶᮲ಆᔢ┽ᨱ

ᯩíࡽ݅. ঑௝ᕽ, ᗭ⍴᮹ᱥၹᱢᯙ᮲ಆᇥ⡍ၰ᮲ಆḲᵲࠥෝ

❱݉⦹ʑ᭥⧕ᕽ۵ᔝ⇶᮲ಆᔢ┽ᨱᕽᮁ⬉᮲ಆ(Effective stress)

ᮥĥᔑ⦹ᩍ❱݉⦹۵ äᯕ⬉ᮉᱢᯕ݅. Table 3ᮡษₑĥᙹa

ᄡ⪵⧉ᨱ঑௝ᗭ⍴ԕ໕ŝ᫙໕ᨱၽᔾ⦹۵ᮁ⬉᮲ಆ᮹ᇥ⡍ෝ

ӹ┡ԙäᯕ݅. ษₑᯕᱥ⩡ᨧ۵ᯕᔢᱢᯙᔢ⫊ᮥaᱶ⦽Ğᬑ, ᡱʑ⬉ŝᨱ᮹⦹ᩍᗭ⍴ԕ໕᮹ᱥ໕ᇡᨱŝࠥ⦽᮲ಆᯕ⡎մí

Ḳᵲࢉᮥ ᦭ ᙹ ᯩᮝ໑, ᗭ⍴ ᫙໕᮹ Ğᬑᨱࠥ ᗭ⍴ ༊ ᇡ᭥ᨱ

ᔢݚ⦽Ⓧʑ᮹᮲ಆᯕḲᵲࡹŁᯩ݅. ə్ӹๅᬑၙᗭ⦽᧲ᯕ௝ࠥ

ᯝ݉ษₑಆᯕ᯲ᬊ⦹۵Ğᬑᨱ۵ᗭ⍴ԕ໕ŝ᫙໕᮹᮲ಆḲᵲ

⩥ᔢᮡษₑᯕ ᨧ۵ Ğᬑᨱእ⦹ᩍ ᔢݚప ᪥⪵ࡹŁᯩᮭᮥ ᦭

ᙹᯩ݅. ᯕ۵ᡱʑ⬉ŝᨱ᮹⦹ᩍᗭ⍴᮹ᱥ໕ᇡᨱḲᵲࡹ۵ᮁ⬉᮲ ಆᯕᗭ⍴ԕ໕ŝᵝ᯦⧊ɩᰍᔍᯕ᮹ษₑᨱ᮹⦹ᩍ⬉ŝᱢᮝಽ

qᘥࡹŁ ᯩᮭᮥ ᅕᩍᵝ۵ äᯕ݅.

ษₑᨱ᮹⦹ᩍᗭ⍴ᨱၽᔾ⦹۵ᮁ⬉᮲ಆᯕqᘥࡹ۵⬉ŝ۵

ᗭ⍴᮹ ⇶ႊ⨆ᨱ ঑௝ ᗭ⍴ ԕ໕ŝ ᫙໕᮹ ᮁ⬉᮲ಆᮥ ӹ┡ԙ

Fig. 10ᮥ ☖⧕ᕽ ᅕ݅ ໦⪶⦹í ⪶ᯙ⧁ ᙹ ᯩ݅. ษₑᯕ ᨧ۵

ᯕᔢᱢᯙ Ğᬑ, ᗭ⍴ ԕ໕᮹ ᱥ໕ᇡᨱ۵ ᗭ⍴ ᰍḩ᮹ ⧎ᅖvࠥ

(10)

Fig. 11. The maximum effective stress on a socket with respect to frictional coefficients

Fig. 12. The minimum principal stress of casting alloy (275MPa)ෝ⭉ᦍᔢ⫭⦹۵ᮁ⬉᮲ಆᯕၽᔾ⦹۵ၹ໕, ᗭ⍴⬥໕

᮹ᮁ⬉᮲ಆᮡɪĊ⦹íqᗭ⦹ᩍ, ᗭ⍴ᱥ໕ᇡᨱŝࠥ⦽᮲ಆᯕ

ḲᵲࡹŁᯩᮭᮥ᦭ᙹᯩ݅. ⦽⠙, ᗭ⍴ԕ໕ŝᵝ᯦⧊ɩ⢽໕᮹

ษₑĥᙹa ᷾a⦹ᩍࠥ ᡱʑ ⬉ŝᨱ ᮹⦽ ᗭ⍴ ᱥ໕ᇡ᮹ ᮲ಆ

Ḳᵲ⩥ᔢᮡəݡಽӹ┡ӹŁᯩ݅. ə్ӹᯕ్⦽᮲ಆḲᵲ⩥ᔢᮡ

ษₑĥᙹa᷾a⧉ᨱ঑௝Ⓧí᪥⪵ࡹᨕ, ᗭ⍴ᖅĥݚ᜽ᱢᬊ⧩޹

ษₑĥᙹ 0.2ʭḡ ᗭ⍴ ᱥ໕᮹ ᮲ಆ Ḳᵲᇡ᮹ ↽ݡ ᮁ⬉᮲ಆᮡ

ɪĊ⯩qᗭ⦹Ł, əᯕᔢ᮹ษₑĥᙹaᱢᬊࡽĞᬑᨱၽᔾ⦹۵

↽ݡ ᮁ⬉᮲ಆᮡᗭ⍴ ᰍḩ᮹ ⧎ᅖvࠥᯕԕಽ ᇥ⡍⧉ᮥ ᦭ᙹ

ᯩ݅. ᗭ⍴᫙໕᮹Ğᬑᨱࠥᗭ⍴ԕ໕᮹᮲ಆᇥ⡍᪡ᮁᔍ⦽Ğ⨆ᮥ

ᅕᯙ݅.

Fig. 11ᮡษₑĥᙹᨱ঑௝ᗭ⍴ᨱၽᔾ⦹۵↽ݡᮁ⬉᮲ಆ᮹

ᄡ⪵ෝӹ┡ԙäᯕ݅. ᅙםྙᨱᕽŁಅ⦽ษₑĥᙹᵲᨱᕽ↽ݡ᮹

Ğᬑ(ł=0.7)ᨱ ᗭ⍴᮹ ԕᄞᨱ ၽᔾ⦽ ↽ݡ ᮁ⬉᮲ಆᮡ ษₑᯕ

ᨧ۵ Ğᬑ᮹ ᗭ⍴ ԕ໕ ᮁ⬉᮲ಆᨱ እ⦹ᩍ ᧞ 80% aప Ⓧí

qᗭࡽ݅. ੱ⦽, ᯕsᮡᗭ⍴ᖅĥ᜽ᨱᯝၹᱢᮝಽᱢᬊ⦹Łᯩ۵

ษₑĥᙹ 0.2᮹ Ğᬑᨱ እ⧕ᕽࠥ ᧞ 20% aప qᗭࡽ äᯕ݅.

đŝᱢᮝಽᗭ⍴ԕᄞၰ᫙ᄞᨱၽᔾ⦹۵↽ݡᮁ⬉᮲ಆᮡᗭ⍴

ԕᄞŝᵝ᯦⧊ɩᰍ⢽໕᮹ษₑĥᙹ᷾aᨱ᮹⦹ᩍᔢݚపqᘥ

ࢁᙹᯩᨩᮝ໑, ⩥⧪ᗭ⍴ᖅĥჶᨱᕽᯝၹᱢᮝಽᱢᬊ⦹Łᯩ۵

ษₑĥᙹᯙ0.2 ᯕᔢᨱᕽᗭ⍴ԕ/᫙ᄞ᮹↽ݡᮁ⬉᮲ಆᮡᗭ⍴

ᰍḩ᮹ ⨩ᬊ᮲ಆ ᯕԕಽ ᇥ⡍⧉ᮥ ⪶ᯙ⧁ ᙹ ᯩᨩ݅.

ᯕ᪡zᮡ⧕ᕾđŝ۵ᗭ⍴ᱽ᳑݉ĥᨱᕽษₑĥᙹෝ᷾ḥ

᜽┍ᙹᯩ۵ࠥᰆ⪚ᮡࠥɩ॒ŝzᮡe݉⦽⢽໕⃹ญ᯲ᨦอᮥ

☖⧕ᕽࠥ ᗭ⍴ŝ ᵝ᯦ ⧊ɩᰍᨱ ᯲ᬊ⦹۵ ᮲ಆᮥ ᔢݚప ᪥⪵

᜽┍ᙹᯩ݅۵ᱱᮥ᜽ᔍ⦽݅. ⦽⠙ᯕ᪡۵ၹݡಽ, ᝅᱽၽ⩥ࡹ۵

ࢱ⢽໕᮹ษₑĥᙹaᗭ⍴ᖅĥ᜽ᨱaᱶ⧩޹ษₑĥᙹᨱእ⦹ᩍ

᯲ᮡĞᬑ, ᗭ⍴ᱥ໕ᇡᨱ۵ᖅĥݚ᜽ᨱ۵Łಅࡹḡ༜⦽ŝࠥ⦽

᮲ಆḲᵲᯕၽᔾࢁᙹࠥᯩᮭᮥӹ┡ԕ۵äᯕ݅. ঑௝ᕽᗭ⍴

ᖅĥᨱᯩᨕᕽᗭ⍴ԕᄞŝᵝ᯦⧊ɩᰍ᮹⢽໕ษₑĥᙹ۵ๅᬑ

ᵲ᫵⦽ᖅĥᄡᙹ௝⧁ᙹᯩᮝ໑, ᝅᱽၽ⩥ࡹ۵ࢱ⢽໕᮹ษₑĥᙹ aᗭ⍴ᖅĥݚ᜽Łಅ⧩޹ษₑĥᙹ(0.2) ᅕ᯲݅݅Ł❱݉ࡹ۵

Ğᬑᨱ۵ၹऽ᜽ᗭ⍴ᱥ໕ᇡ᮹ᨥၡ⦽᮲ಆ⧕ᕾᮥ☖⦹ᩍᗭ⍴᮹

ᦩᱶᖒᮥ á☁⦹ᩍ᧝ ⦽݅.

5.2 ࣫෍୍߹ߦࡦ܄ࠫܤச଺෍୍ׁଭଦߚंඑ ᗭ⍴᮹Ğᬑ᪡ษ₍aḡಽษₑĥᙹᨱ঑ෙᵝ᯦⧊ɩᰍ᮹᮲ಆ

ᇥ⡍ෝ ᳑ᔍ⦹Ł đŝෝ ᇥᕾ⦹ᩡ݅. ᅙ םྙᨱᕽ ᗭ⍴ ԕᇡ᮹

ᵝ᯦⧊ɩᇡᇥᮡ}ᄥvᖁŝᵝ᯦⧊ɩᰍ᮹ྜྷᖒᮥ༉ࢱŁಅ⦽

ḢƱᯕႊᖒᅖ⧊ᰍഭಽ༉ߙยࡹᨩ݅. ᗭ⍴᮹᮲ಆᇥ⡍ᨱᕽᔍᬊ

ࡹᨩ޹ᮁ⬉᮲ಆ(Von-Mises stress)᮹}ֱᮡ॒ႊᖒᰍഭᨱݡ⧕

ᕽอᱢᬊᯕa܆⦹ʑভྙᨱ, ḢƱᯕႊᖒᰍഭಽ༉ߙยࡽᅖ⧊ᰍ ഭ᮹ၽᔾ᮲ಆᮡᮁ⬉᮲ಆᯕᦥܭ↽ᗭᵝ᮲ಆ(↽ݡᦶ⇶ၽᔾ)ᮝಽ

ݡℕ⦹ᩍ ӹ┡ԕᨩ݅.

Fig. 12᪡Fig. 13ᮡᗭ⍴ᱥ໕ᮝಽᇡ░᮹Ñญᨱ঑ෙᗭ⍴

ԕᇡᅖ⧊ᰍഭ᮹↽ᗭᵝ᮲ಆ᮹ᄡ⪵᪡, ษₑĥᙹ᮹ᄡ⪵ᨱ঑ෙ

↽ᗭᵝ᮲ಆ᮹ᄡ⪵ෝӹ┡ԙäᯕ݅. ᗭ⍴᮹᮲ಆᇥ⡍Ğ⨆ŝ

ษ₍aḡಽᡱʑ⬉ŝᨱ᮹⦹ᩍᗭ⍴᮹༊ᇡᇥᨱᕽaᰆⓑᵝ᮲ಆ ᯕၽᔾ⧉ᮥ᦭ᙹᯩᮝ໑, ᗭ⍴ԕ໕ŝᵝ᯦⧊ɩ⢽໕ᔍᯕ᮹

ษₑĥᙹa᷾a⧉ᨱ঑௝ᅖ⧊ᰍᨱၽᔾ⦹۵↽ᗭᵝ᮲ಆ᮹ᱩݡ sᮡɪĊ⯩qᗭ⦹ᩡ݅. ঑௝ᕽ, ᗭ⍴ԕ໕ŝᵝ᯦⧊ɩᰍ⢽໕

ᔍᯕ᮹ษₑᮡ ᗭ⍴᮹ ᮁ⬉᮲ಆᐱ ᦥܩ௝ ᵝ᯦⧊ɩᰍ᮹ ᮲ಆ

᪥⪵ᨱࠥʑᩍ⦹Łᯩᮭᮥ᦭ᙹᯩ݅. đŝᱢᮝಽᗭ⍴ԕ/᫙ᄞ᮹

(11)

Fig. 13. Variation of the minimum principal stress of casting alloy with respect to fictional coefficients

(a)ł^=0.0 ^(b)ł^=0.7

Fig. 14. Contact stresses on the internal surface of a socket and the surface of casting alloy ᮲ಆᇥ⡍᪡ษ₍aḡಽษₑĥᙹ۵ᗭ⍴ԕᇡᅖ⧊ᰍഭ᮹᮲ಆ

ᇥ⡍ᨱⓑᩢ⨆ᮥᵝ۵ᯙᯱ௝⧁ᙹᯩᮝ໑, ᗭ⍴ᖅĥݚ᜽ᨱ

Łಅ⧩޹ษₑĥᙹᨱእ⦹ᩍᝅᱽၽ⩥ࡹ۵ษₑĥᙹ᮹sᯕ᯲ᮡ

Ğᬑ, ᗭ⍴ԕᇡᅖ⧊ᰍഭ᮹ᦩᱶᖒᨱݡ⦽ᇡaᱢᯙ᮲ಆá☁a

⦥᫵⧉ᮥ ᦭ ᙹ ᯩ݅.

5.3 ୦ోଦߚंඑ

᜾(6)᮹Column friction ༉ߙᨱᕽᗭ⍴ԕ໕ŝᵝ᯦⧊ɩᰍ

⢽໕ᨱᕽษₑ᮲ಆᮥᮁၽ⦹۵ᙹḢ᮲ಆᮡᱲⅪ᮲ಆƎಽᱶ᮹ࡽ݅.

⦽⠙, 2.2ᱩᨱᕽᨙɪࡽၵᯩ۵ᗭ⍴᮹ᖅĥჶᨱᕽ۵ᙹḢ᮲ಆᨱ

ᗭ⍴᮹ᖅĥჶᨱᕽᙹḢ᮲ಆᮥᱶ᮹⦽᜾(1)᮹sࠥFig. 14ᨱ

እƱ⦹ᩍ zᯕ ӹ┡ԕᨩ݅.

ᗭ⍴ԕ໕ŝᵝ᯦⧊ɩᰍ⢽໕ᨱᕽၽᔾ⦹۵ᱲⅪᨱ᮹⦽ᙹḢ᮲ ಆᮡᕽಽ᯲ᬊ-ၹ᯲ᬊ᮹šĥᨱᯩʑভྙᨱFig. 14ᨱᕽᅕ۵

ၵ᪡zᯕࢱ⢽໕᮹ᙹḢ᮲ಆᮡᗭ⍴⇶ႊ⨆ᨱ঑௝Ñ᮹࠺ᯝ⧉ᮥ

᦭ᙹᯩ݅. ੱ⦽, Fig. 14۵ᗭ⍴ᱥ໕ᇡᨱᕽๅᬑⓑᙹḢ᮲ಆᯕ

ၽᔾ⦹Łᗭ⍴⬥໕ᇡᨱᕽ۵ᙹḢ᮲ಆᯕɪĊ⯩qᗭ⦹۵ᱥ⩶ᱢ ᯙ ᡱʑ ⬉ŝෝ ᯹ ᅕᩍᵝŁ ᯩ݅. Fig. 14(a)᪡ Fig. 14(b)ෝ

እƱ⦹໕, ᗭ⍴ŝᵝ᯦⧊ɩᰍ᮹ᇥ⡍᮲ಆŝษ₍aḡಽᱲⅪᨱ

᮹⦽ᙹḢ᮲ಆᩎ᜽ࢱ⢽໕ᔍᯕ᮹ษₑᨱ᮹⦹ᩍᔢݚపqᘥ⦹Ł

ᯩᮭᮥ ᦭ ᙹ ᯩ݅.

⦽⠙, ᗭ⍴ᖅĥჶᨱᕽ᜾(1)ᨱ᮹⦹ᩍᱶ᮹ࡽᙹḢ᮲ಆᮡᗭ⍴

ԕᄞ Ğᔍbŝ ⢽໕ ษₑĥᙹᨱ ᮹⦹ᩍ đᱶࡹ۵ sᮝಽ ᗭ⍴

⇶ႊ⨆ᨱÙℱᯝᱶ⦹݅Łaᱶࡹᨩʑভྙᨱ, ᗭ⍴Ǎ᳑ᨱᕽၽᔾ

⦹۵ᡱʑ⬉ŝ۵ၹᩢ⦹ḡ༜⦽݅. ᩩᔢ⦽ၵݡಽ᜾(1)ಽĥᔑࡽ

⢽໕᮹ᙹḢ᮲ಆᮡᮁ⦽᫵ᗭ⧕ᕾᨱᕽĥᔑࡽ↽ݡᱲⅪ᮲ಆŝ۵

(12)

Fig. 15. Variation on the contact stress with respect to frictional coefficients

ๅᬑⓑ₉ᯕaᯩ݅. ə్ӹ᜾(1)ᯕᮁ⬉ᵝ᯦⧊ɩᇡᨱᕽอ

᯲ᬊ⦹۵ äᮝಽ aᱶࡹᨩ݅۵ ᱱᮥ qᦩ⦹໕, ᮁ⬉ Ǎe(ᖒʕ

ᱱᖁᮝಽ⢽᜽)ᨱᕽ᜾(1)ᨱ᮹⦹ᩍĥᔑࡽᙹḢ᮲ಆᮡݡఖᮁ⦽

᫵ᗭ ⧕ᕾᨱᕽ ᔑᱶࡽ ↽ݡ᪡ ↽ᗭ ⢽໕ ᱲⅪ᮲ಆ᮹ ⠪Ɂsᮥ

ݡ⢽⦹Ł ᯩ݅Ł ᅕᯙ݅.

᜾(1)ŝᮁ⦽᫵ᗭ⧕ᕾᨱᕽᔑᱶࡽᱲⅪᨱ᮹⦽ᙹḢ᮲ಆ᮹

šĥෝ ᅕ݅ ᯱᖙ⯩ Łₑ⦹ʑ ᭥⧕ᕽ ᮁ⦽᫵ᗭ ⧕ᕾᨱᕽ ᗭ⍴

⇶ႊ⨆ᮝಽ ĥᔑࡽ ᱲⅪ᮲ಆ᮹ ᇥ⡍ෝ ᔢᯱᙹᩝࠥ(Box and whisker plot)ෝᯕᬊ⦹ᩍFig. 15ᨱӹ┡ԕᨩ݅. ੱ⦽, ษₑĥᙹᨱ

঑௝᜾(1)ಽĥᔑࡽᖅĥჶᨱᕽ᮹ᙹḢ᮲ಆࠥFig. 15ᨱእƱ⦹ᩍ

ӹ┡ԕᨩ݅. Fig. 15ᨱ ӹ┡ӽݡಽ ᔢᯱᙹᩝࠥᨱᕽ۵ ᇥ⡍s᮹

↽ݡsŝ↽ᗭsᯕə௹⥥᮹↽ᔢ݉ŝ↽⦹݉ᨱᙹᩝᮝಽ⢽⩥ࡹ

໑, ᇥ⡍s᮹ᔢᇡၰ⦹ᇡᔍᇥ᭥s(25%)ᮡᔢᯱ᮹ᔢ݉ŝ⦹݉ᨱ

⢽⩥ࡽ݅. ੱ⦽, ᔢᯱ᮹ᵲeᨱ᭥⊹⦽ᝅᖁᮡᇥ⡍sᵲᨱᕽ᮹

ᵲesᮥ ᮹ၙ⦽݅.

ᯕ᪡zᮡᔢᯱᙹᩝࠥ᮹ᱶ᮹ෝʑၹᮝಽFig. 15ෝᔕ⠕ᅕ໕, ᔢ݉ŝ⦹݉ᔍᇥ᭥sᮡᇥ⡍᮲ಆ᮹↽ݡsŝ۵ⓑ₉ᯕෝᅕᯕ໑, ᇥ⡍᮲ಆ᮹↽ᗭsɝ⃹ಽ⊹ᬑℱᯩᮭᮥ᦭ᙹᯩ݅. ᔢᯱ᮹ᔢ݉

ᔍᇥ᭥sᮡ᮲ಆᇥ⡍s᮹75%ෝݡᄡ⦹۵äᯕʑভྙᨱ, ᮁ⦽᫵

ᗭ⧕ᕾᨱᕽᔑᱶࡽᗭ⍴ԕᄞ᮹ᱲⅪ᮲ಆᮡᡱʑ⬉ŝᨱ᮹⦹ᩍ

Ḳᵲࡹ۵ ᗭ⍴ ᱥ໕ᇡ᮹ ᯝᇡ Ḳᵲ ᮲ಆᮥ ᱽ᫙⦹Ł۵ ݡᇡᇥ

ᔢᇡᔍᇥ᭥sᦥ௹ᨱᇥ⡍⧕ᯩ۵äᯕ݅. ᗭ⍴ᖅĥჶᨱᕽ᜾

(1)ಽĥᔑࡽᙹḢ᮲ಆᮡFig. 15ᨱᕽᅕ۵ၵݡಽᮁ⦽᫵ᗭ⧕ᕾᨱ ᕽ ᨜ᮡ ᱲⅪᨱ ᮹⦽ ᙹḢ᮲ಆ᮹ ᔢ⦹ᇡ ᔍᇥ᭥s᮹ ⠪Ɂsᮥ

ݡ⢽⦹Łᯩᮭᮥ᦭ᙹᯩ݅. ᷪ, ᖅĥ᜾(1)ᮡᗭ⍴ŝᵝ᯦⧊ɩᰍᨱ ᕽၽᔾ⦹۵ᡱʑ⬉ŝᨱ᮹⦽᮲ಆᇥ⡍sᮡ႑ᱽ⦹Ł, ӹນḡ

ᇡᇥᨱݡ⦽ᱲⅪᙹḢ᮲ಆᮥݡ⢽⧁ᙹᯩ۵⠪Ɂsᮝಽᱶ᮹ࡽ

äᯕ௝Ł ⧁ ᙹ ᯩ݅.

đುᱢᮝಽᗭ⍴ᖅĥ᜾(1)ᮡᗭ⍴᮹ᮁ⬉ʙᯕԕᨱᇥ⡍⦹۵

ᱲⅪᨱ᮹⦽ᙹḢ᮲ಆ᮹ݡᇡᇥᮥ᯹ݡᄡ⦹Łᯩᮝ໑ᖅĥ༊ᱢᮝ ಽ ᱢᬊࡹ۵ äᮡ ┡ݚ⦹݅Ł ❱݉ࡽ݅. ᪽Ա⦹໕ ᗭ⍴ ԕᄞŝ

ᵝ᯦⧊ɩᰍ᮹ษₑᨱ᮹⦹ᩍᗭ⍴ᖅĥ᜾(1)ᨱᕽŁಅࡹḡ༜⦽

ᗭ⍴ᱥ໕ᇡ᮹Ḳᵲ᮲ಆᯕᔢݚపqᘥࢁᙹᯩʑভྙᯕ݅(5.1ᱩ

ၰ5.2ᱩₙ᳑). ᯕ్⦽ᱱᮥŁಅ⦹ḡᦫŁᗭ⍴ᱥ໕ᇡᯝᇡᨱ

ŝࠥ⦹íḲᵲࡹ۵ᙹḢ᮲ಆᮥᖅĥ᜾ᨱ⡍⧉⦹۵Ğᬑ, ᗭ⍴᮹

ŝ݅ᖅĥෝⅩ௹⧁ᙹᯩ݅. ə్ӹ, ᱥᱩᨱᕽᨙɪࡽၵ᪡zᯕ

ᗭ⍴ԕᄞŝᵝ᯦⧊ɩᰍ⢽໕ᔍᯕ᮹ษₑᨱᯩᨕᕽᖅĥݚ᜽

Łಅ⧩޹ษₑĥᙹᨱእ⦹ᩍᝅᱽၽ⩥ࡹ۵ ษₑĥᙹa᯲݅Ł

❱݉ࡹ۵Ğᬑᨱ۵ᖅĥđŝᨱݡ⧕ᕽၹऽ᜽ᨥၡ⦽᮲ಆ⧕ᕾᮥ

☖⦹ᩍ ᗭ⍴ Ǎ᳑᮹ ᦩᱶᖒᮥ á☁⦹ᩍ᧝อ ⦽݅.

6. đು

ᅙ םྙᨱᕽ۵ ᗭ⍴ Ǎ᳑᮹ Ñ࠺ᮥ ᨥၡ⦹í ⧕ᕾ⦹ʑ ᭥⦽

ᮁ⦽᫵ᗭ⧕ᕾႊჶᮥᱽᦩ⦹ᩡŁ, ษₑĥᙹᨱ঑ෙᗭ⍴ၰᵝ᯦

⧊ɩᰍ᮹Ñ࠺ᮥᇥᕾ⦹ᩡ݅. ᗭ⍴ԕ໕ŝᵝ᯦⧊ɩᰍ⢽໕ᔍᯕ᮹

ษₑᮥŁಅ⦹ʑ᭥⦹ᩍCoulomb frictionᮥʑၹᮝಽ⦽ᱲⅪ

༉ߙᮥᱢᬊ⦹ᩡŁ, ࢱ⢽໕᮹ᱲⅪᮥ༉ᔍ⦹ʑ᭥⦹ᩍ⢽໕ᱲⅪ

༉ߙᮥ᯦ࠥ⦹ᩡ݅. ᗭ⍴Ǎ᳑᮹ᰍഭᱢ✚ᖒᮥᱶ⪶⯩ၹᩢ⦹ʑ

᭥⦹ᩍ┥ᗭvᵝv⣩ᮝಽᱽ᯲ࡽᗭ⍴ᮡ॒ႊᖒᰍഭಽ༉ߙย

⦹ᩡŁ, ᵝ᯦⧊ɩᰍ۵}ᄥvᖁ᮹ᩢ⨆ᮥŁಅ⦹ᩍḢƱᯕႊᖒ

ᅖ⧊ᰍഭಽ༉ߙย⦹ᩡ݅. ᯙᰆᝅ⨹ᨱᕽ⊂ᱶࡽᗭ⍴᫙⢽໕᮹

ᄡ⩶ශŝᮁ⦽᫵ᗭ⧕ᕾđŝෝእƱ⦹ᩍ, ᯲ᖒࡽᮁ⦽᫵ᗭ⧕ᕾ

༉ߙ᮹┡ݚᖒᮥá᷾⦹ᩡ݅. ᯲ᖒࡽᙹ⊹༉ߙᮥݡᔢᮝಽ⦹ᩍ

ᗭ⍴ ԕ໕ŝ ᵝ᯦ ⧊ɩᰍ ⢽໕ᔍᯕ᮹ ษₑĥᙹᨱ ঑ෙ ᗭ⍴ŝ

ᵝ᯦⧊ɩᅖ⧊ᰍ᮹᮲ಆᇥ⡍ෝ᳑ᔍ⦹ᩡŁ, ᗭ⍴ԕ໕ŝᵝ᯦

⧊ɩᰍ᮹ᱲⅪ᮲ಆᮥᙹ⊹ᱢᮝಽᔑᱶ⦹ᩡ݅. ੱ⦽, ᖅĥჶᨱᕽ

ᱢᬊ⦹Łᯩ۵ᙹḢ᮲ಆ᜾ŝᮁ⦽᫵ᗭ⧕ᕾᨱᕽ᨜ᮡđŝෝእƱ

⦹ᩍ ᖅĥ᜾᮹ ᮹ၙෝ ᰍŁₑ⦹ᩡ݅. ᩑǍ đŝಽ ᨜ᮡ đುᮥ

ᱶญ⦹໕ ݅ᮭŝ z݅.

(1) ᅙםྙᨱᕽ᯦ࠥ⦽ḢƱᯕႊᖒᅖ⧊ᰍഭ༉ߙŝ, Coulomb friction ၰ⢽໕ᱲⅪ༉ߙᮥ⪽ᬊ⦹ᩍ᯲ᖒࡽᗭ⍴᮹ᮁ⦽᫵ᗭ

⧕ᕾ༉ߙᮡᗭ⍴᮹ᝅᱽÑ࠺ᮥ᯹ၹᩢ⦹ᩡ݅. ᯙᰆᝅ⨹ᨱᕽ

᨜ᮡᗭ⍴᫙⢽໕᮹ᄡ⩶ශᮡᱽᦩࡽ༉ߙᮥᔍᬊ⦽ᮁ⦽᫵ᗭ

⧕ᕾᨱᕽᔑᱶࡽᄡ⩶ᮉŝ᯹ᯝ⊹⦹۵äᮝಽӹ┡ԍ݅. ੱ⦽, ᱽᦩࡽ ༉ߙᮡ ᬱ⇵⩶ ᗭ⍴ᨱᕽ ၽᔾ⦹۵ ᗭ⍴ ᱥ໕ᇡᨱᕽ

᮲ಆᯕ ḲᵲࡹŁ ⬥໕ᇡᨱᕽ ɪĊ⯩ qᗭࡹ۵ ᡱʑ ⩥ᔢᮥ

ᩩ⊂⧁ ᙹ ᯩᨩ݅.

(13)

ษₑĥᙹᨱእ⦹ᩍᝅᱽၽ⩥ࡹ۵ษₑĥᙹa᯲݅Ł❱݉ࡹ۵

Ğᬑᨱ۵ᖅĥđŝᨱݡ⧕ᕽၹऽ᜽ᨥၡ⦽᮲ಆ⧕ᕾᮥ☖⦹

ᩍ ᗭ⍴ Ǎ᳑᮹ ᦩᱶᖒᮥ ᄥࠥಽ á☁⦹ᩍ᧝อ ⦽݅.

qᔍ᮹ɡ

ᅙᩑǍ۵ǎ☁⧕᧲ᇡÕᖅʑᚁ⩢ᝁᔍᨦⅩᰆݡƱపᔍᨦ݉ᱽ2

⧖ᝍŝᱽ᮹ᩑǍእḡᬱ(ŝᱽჩ⪙: 08ʑᚁ⩢ᝁE01-ⅩᰆݡƱపᔍ ᨦ݉)ᨱ ᮹⦹ᩍ ᙹ⧪ࡹᨩ᜖ܩ݅. ᩑǍእ ḡᬱᨱ qᔍऽพܩ݅.

References

Brandon, J. E., Chaplin C. R. and Ridge, I. M. L. (2001). “Analysis of a resin socket termination for a wire rope.” J. of Strain Anal.

Eng., Vol. 36, No. 1, pp. 71-88.

Brandon, J. E. and Ridge, I. M. L. (2003). “Comparison of white metal and resin socket terminations for wire ropes.” J. of Strain Anal. Eng., Vol. 38, No. 2, pp. 149-160.

Feyrer, K. (2010). Wire ropes - tension, endurance, reliability, Springer, Germany.

Flory, J. F., McKenna, H. A. and Gibson, P. T. (1995). “Improvement in potted socket terminations.” OCEANS ’95. MTS/IEEE. Challenges of Our Changing Global Environment. Conference Proceedings, Vol. 2, pp. 1345-1353.

HSBA-Honshu Shikoku Bridge Autority (1989). HBS 3503 Prefabricated

cable-stayed bridges, Wiley.

Seo, J. W., Jung, W., Cho, E. K. and Yoo, H. (2010). “Parametric analysis to determine optimum geometries of PPWS sockets in cable-suspension bridges.” 2010 Annual Conference of Korean Society of Steel Construction, pp. 35-36 (in Korean).

Simulia (2010). ABAQUS Analysis user's manual.

Verreet, R. (1999). Wire rope end connections, CASAR, Germany.

Waisman, H., Montoya, A., Betti, R. and Noyan, L. C. (2011).

“Load transfer and recovery length in parallel wires of suspension bridge cables.” J. of Eng. Mech., ASCE, Vol. 137, No. 4, pp.

227-237.

Wire Rope Technical Board (2005). Wire rope users manual, 4th edition. USA.

Yoo, H., Jung, W. and Seo, J. W. (2010a). “Design and verification of safety factor for PPWS sockets of suspension bridges.” 2010 Annual Conference of Korean Society of Civil Engineers, p. 2517 (in Korean).

Yoo, H., Lee, S. H. and Seo, J. W. (2013). “Effect of the tapered angle on the ultimate load factors of PPWS sockets in main cables of suspension bridges.” J. of Civil Eng., KSCE, Vol. 33, No. 1, pp.

47-59 (in Korean).

Yoo, H., Seo, J. W. and Lee, S. H. (2011). “Applicability verification of high-strength parallel wire strands by tensile tests.” J.

of Civil Eng., KSCE, Vol. 31, No. 6A, pp. 435-447 (in Korean).

Yoo, H., Seo, J. W., Jung, W. and Lee, S. H. (2010b). “Parametric study of optimum design variables of PPWS socket and stability analysis.” 2010 COSEIK Annual Conference, Computational Structural Engineering Institute of Korea.

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