スポット溶接疲労解析

構造にあるスポット溶接の疲労性能をスタディできるようにします。

現在のところ、応力寿命(SN)に基づくスポット溶接疲労の解析のみがサポートされています。スポット溶接位置は、シート1、シート2、ナゲットの3つの属性で定義します。


図 1. スポット溶接疲労

実装

スポット溶接の疲労解析では、Ruppらの論文に基づき、独立した3つの位置であるシート2か所とナゲットでの溶接を検討します。ナゲットの位置で断面に作用する力とモーメントを求め、それらを使用して、シートとナゲットの位置でそれらによって発生する応力を計算します。つづいて、これらの応力を使用し、レインフローカウントとSN法によって疲労損傷を計算します。

以降の各項では、これらの位置での応力とそれによって発生する損傷を計算する方法を取り上げます。

シート位置(1または2)



図 2. シート位置で計算対象とする力とモーメント
ナゲット位置での力とモーメントを考慮することによって、シートに発生する半径方向応力を計算します。次に示す θ の関数として、荷重時間履歴の各時点で半径方向応力 σ(θ) を計算します。(1)
σ(θ)=σmax(fy)cosθσmax(fz)sinθ+σ(fx)+σmax(my)sinθσmax(mz)cosθ MathType@MTEF@5@5@+=feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=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@78E3@
各値の意味は次のとおりです:(2)
σmax(fy)=fyπDT×Cfyz×Ddefyz×Ttefyz MathType@MTEF@5@5@+=feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4Wdm3aaSbaaSqaaiGac2gacaGGHbGaaiiEaaqabaGccaGGOaGaamOzamaaBaaaleaacaWG5baabeaakiaacMcacqGH9aqpdaWcaaqaaiaadAgadaWgaaWcbaGaamyEaaqabaaakeaacqaHapaCcaWGebGaamivaaaacaaMc8Uaey41aqRaaGPaVlaadoeadaWgaaWcbaGaamOzaiaadMhacaWG6baabeaakiaaykW7cqGHxdaTcaaMc8UaamiramaaCaaaleqabaGaamizaiaadwgacaWGMbGaamyEaiaadQhaaaGccaaMc8Uaey41aqRaaGPaVlaadsfadaahaaWcbeqaaiaadshacaWGLbGaamOzaiaadMhacaWG6baaaaaa @63C6@
(3)
σmax(fz)=fzπDT×Cfyz×Ddefyz×Ttefyz MathType@MTEF@5@5@+=feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4Wdm3aaSbaaSqaaiGac2gacaGGHbGaaiiEaaqabaGccaGGOaGaamOzamaaBaaaleaacaWG6baabeaakiaacMcacqGH9aqpdaWcaaqaaiaadAgadaWgaaWcbaGaamOEaaqabaaakeaacqaHapaCcaWGebGaamivaaaacaaMc8Uaey41aqRaaGPaVlaadoeadaWgaaWcbaGaamOzaiaadMhacaWG6baabeaakiaaykW7cqGHxdaTcaaMc8UaamiramaaCaaaleqabaGaamizaiaadwgacaWGMbGaamyEaiaadQhaaaGccaaMc8Uaey41aqRaaGPaVlaadsfadaahaaWcbeqaaiaadshacaWGLbGaamOzaiaadMhacaWG6baaaaaa @63C8@
(4)
σ(fx)=1.744fxT2×Cfx×Ddefx×Ttefxforfx>0.0 MathType@MTEF@5@5@+=feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=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@6FB5@
(5)
fx = 0.0forfx0.0 MathType@MTEF@5@5@+=feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaeWaaeaaqaaaaaaaaaWdbiaadAgadaWgaaWcbaGaamiEaaqabaaak8aacaGLOaGaayzkaaWdbiaabccacqGH9aqpcaqGGaGaaGimaiaac6cacaaIWaGaaGzbVlaabAgacaqGVbGaaeOCaiaaywW7caWGMbWaaSbaaSqaaiaadIhaaeqaaOGaaGjbVlabgwMiZkaaysW7caaIWaGaaiOlaiaaicdaaaa@4D5B@
(6)
σmax(my)=1.872myDT2×Cmyz×Ddemyz×Ttemyz MathType@MTEF@5@5@+=feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4Wdm3aaSbaaSqaaiGac2gacaGGHbGaaiiEaaqabaGccaGGOaGaamyBamaaBaaaleaacaWG5baabeaakiaacMcacqGH9aqpdaqadaqaamaalaaabaGaaGymaiaac6cacaaI4aGaaG4naiaaikdacaWGTbWaaSbaaSqaaiaadMhaaeqaaaGcbaGaamiraiaadsfadaahaaWcbeqaaiaaikdaaaaaaaGccaGLOaGaayzkaaGaaGPaVlabgEna0kaaykW7caWGdbWaaSbaaSqaaiaad2gacaWG5bGaamOEaaqabaGccaaMc8Uaey41aqRaaGPaVlaadseadaahaaWcbeqaaiaadsgacaWGLbGaamyBaiaadMhacaWG6baaaOGaaGPaVlabgEna0kaaykW7caWGubWaaWbaaSqabeaacaWG0bGaamyzaiaad2gacaWG5bGaamOEaaaaaaa@6854@
(7)
σmax(mz)=1.872mzDT2×Cmyz×Ddemyz×Ttemyz MathType@MTEF@5@5@+=feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=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@6856@
D
溶接要素の直径
T
損傷計算の対象とするシートの厚み
Cfyz MathType@MTEF@5@5@+=feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4qamaaBaaaleaacaWGMbGaamyEaiaadQhaaeqaaaaa@39D0@ Cmyz MathType@MTEF@5@5@+=feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4qamaaBaaaleaacaWGTbGaamyEaiaadQhaaeqaaaaa@39D7@ Cfx MathType@MTEF@5@5@+=feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4qamaaBaaaleaacaWGMbGaamiEaaqabaaaaa@38D0@
スケールファクター
defyz MathType@MTEF@5@5@+=feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaWcbaGaamizaiaadwgacaWGMbGaamyEaiaadQhaaaa@3AB0@ demyz MathType@MTEF@5@5@+=feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaWcbaGaamizaiaadwgacaWGTbGaamyEaiaadQhaaaa@3AB7@ defx MathType@MTEF@5@5@+=feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaWcbaGaamizaiaadwgacaWGMbGaamiEaaaa@39B0@
直径指数
tefyz MathType@MTEF@5@5@+=feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaWcbaGaamiDaiaadwgacaWGMbGaamyEaiaadQhaaaa@3AC0@ temyz MathType@MTEF@5@5@+=feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaWcbaGaamiDaiaadwgacaWGTbGaamyEaiaadQhaaaa@3AC7@ tefx MathType@MTEF@5@5@+=feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaWcbaGaamiDaiaadwgacaWGMbGaamiEaaaa@39C0@
厚み指数

Rupp法と同等にするには:

Cfyz=1,defyz=0,tefyz=0 MathType@MTEF@5@5@+=feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4qamaaBaaaleaacaWGMbGaamyEaiaadQhaaeqaaOGaaGPaVlabg2da9iaaykW7caaIXaGaaiilaiaaykW7caaMf8UaamizaiaadwgacaWGMbGaamyEaiaadQhacaaMc8Uaeyypa0JaaGPaVlaaicdacaGGSaGaaGzbVlaadshacaWGLbGaamOzaiaadMhacaWG6bGaaGPaVlabg2da9iaaykW7caaIWaaaaa@57E9@
Cmyz=0.6,demyz=0,temyz=0.5 MathType@MTEF@5@5@+=feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4qamaaBaaaleaacaWGTbGaamyEaiaadQhaaeqaaOGaaGPaVlabg2da9iaaykW7caaIWaGaaiOlaiaaiAdacaGGSaGaaGPaVlaaywW7caWGKbGaamyzaiaad2gacaWG5bGaamOEaiaaykW7cqGH9aqpcaaMc8UaaGimaiaacYcacaaMf8UaamiDaiaadwgacaWGTbGaamyEaiaadQhacaaMc8Uaeyypa0JaaGPaVlaaicdacaGGUaGaaGynaaaa@5AE0@
Cfx=0.6,defx=0,tefx=0.5 MathType@MTEF@5@5@+=feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4qamaaBaaaleaacaWGMbGaamiEaaqabaGccaaMc8Uaeyypa0JaaGPaVlaaicdacaGGUaGaaGOnaiaacYcacaaMc8UaaGzbVlaadsgacaWGLbGaamOzaiaadIhacaaMc8Uaeyypa0JaaGPaVlaaicdacaGGSaGaaGzbVlaadshacaWGLbGaamOzaiaadIhacaaMc8Uaeyypa0JaaGPaVlaaicdacaGGUaGaaGynaaaa@57CB@

相当半径方向応力を、 θ (デフォルトでは18°)の間隔で計算します。 θ の値は、スポット溶接の解設定でNumber of angles欄を編集することで変更できます。つづいて、レインフロー周期カウントを使用し、角度位置( θ )ごとに疲労寿命と損傷を計算します。出力として最悪の損傷値を抽出します。他方のシートでも同様の手順を実施します。

ナゲット位置



図 3. ナゲット断面で計算対象とする力とモーメント
ビーム要素に作用するせん断応力と曲げ応力を使用して、次のように θ の関数として絶対最大主応力を荷重時間履歴の各時点で計算します。(8)
τ(θ)=τmax(fy)sinθ+τmax(fz)cosθ
(9)
σ(θ)=σ(fx)+σmax(my)sinθσmax(mz)cosθ MathType@MTEF@5@5@+=feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4WdmNaaiikaiabeI7aXjaacMcacqGH9aqpcqaHdpWCcaGGOaGaamOzamaaBaaaleaacaWG4baabeaakiaacMcacqGHRaWkcqaHdpWCdaWgaaWcbaGaciyBaiaacggacaGG4baabeaakiaacIcacaWGTbWaaSbaaSqaaiaadMhaaeqaaOGaaiykaiGacohacaGGPbGaaiOBaiabeI7aXjabgkHiTiabeo8aZnaaBaaaleaaciGGTbGaaiyyaiaacIhaaeqaaOGaaiikaiaad2gadaWgaaWcbaGaamOEaaqabaGccaGGPaGaci4yaiaac+gacaGGZbGaeqiUdehaaa@5C85@
各値の意味は次のとおりです:(10)
τmax(fy)=16fy3πD2
(11)
τmax(fz)=16fz3πD2
(12)
σfx=4fxπD2forfx>0.0 MathType@MTEF@5@5@+=feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4Wdm3aaeWaaeaacaWGMbWaaSbaaSqaaiaadIhaaeqaaaGccaGLOaGaayzkaaGaaGjbVlabg2da9iaaysW7daWcaaqaaiaaisdacaWGMbWaaSbaaSqaaiaadIhaaeqaaaGcbaGaeqiWdaNaamiramaaCaaaleqabaGaaGOmaaaaaaGccaaMf8UaaeOzaiaab+gacaqGYbGaaGzbVlaadAgadaWgaaWcbaGaamiEaaqabaGccaaMc8UaeyOpa4JaaGPaVlaaicdacaGGUaGaaGimaaaa@5430@
(13)
σfx=0.0forfx0.0 MathType@MTEF@5@5@+=feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4Wdm3aaeWaaeaacaWGMbWaaSbaaSqaaiaadIhaaeqaaaGccaGLOaGaayzkaaGaaGjbVlabg2da9iaaysW7caaIWaGaaiOlaiaaicdacaaMf8UaaeOzaiaab+gacaqGYbGaaGzbVlaadAgadaWgaaWcbaGaamiEaaqabaGccaaMc8UaeyizImQaaGPaVlaaicdacaGGUaGaaGimaaaa@509E@
(14)
σmax(my)=32myπD3
(15)
σmax(mz)=32mzπD3
D
溶接要素の直径
T
損傷計算の対象とするシートの厚み

τ(θ) から σ(θ) までの範囲で θ ごとに相当最大絶対主応力を計算します。これらの応力を以降の疲労解析で使用します。レインフロー周期カウントを使用して、角度の θ ごとに疲労寿命と損傷を計算します。出力として最悪の損傷値を抽出します。