JP4252207B2

JP4252207B2 - Measuring method and measuring device for thermal resistance and biot number of laminated material

Info

Publication number: JP4252207B2
Application number: JP2000306534A
Authority: JP
Inventors: 和也細野; 文徳森山
Original assignee: Japan Ultra High Temperature Materials Research Institute JUTEM
Current assignee: Japan Ultra High Temperature Materials Research Institute JUTEM
Priority date: 2000-10-05
Filing date: 2000-10-05
Publication date: 2009-04-08
Anticipated expiration: 2020-10-05
Also published as: JP2002116166A

Description

【０００１】
【発明の属する技術分野】
本発明は、第１層と第２層とを有する積層材料の層間に存在する熱抵抗と積層材料のビオー数の測定方法及びその測定装置に係り、更に詳しくは層間厚さが明確に定義できない層間を有する積層材料の熱抵抗とそのときの積層材料のビオー数の測定方法及びその測定装置に関する。
【０００２】
【従来の技術】
耐熱金属や非酸化物系材料の耐酸化性を向上させるための耐酸化皮膜の形成、材料の耐熱性を向上させるための遮熱コーティング層の形成等、材料の適用範囲を拡大するために、母材となる材料の表面に他の材料を積層させて材料の特性を向上させる材料の多層化が広く検討されている。特に、高温下で使用される多層材料においては、熱伝導特性が材料設計における重要な物性値となり、その中でも多層材料の層間に生じる熱抵抗は、高温材料の材料設計において特に重要な因子となる。そのため、従来、例えば、母材表面に耐酸化皮膜や遮熱コーティング層が形成されている積層材料において、母材表面上の形成層との間に生成される層間の厚さが明確に定義できてこの部分を中間層として考慮することができる場合には、この層間に存在する熱抵抗は、例えばレーザーフラッシュ法を用いた多層材解析法により求めることができる。
【０００３】
レーザーフラッシュ法を用いた多層材解析法では、始めに、積層材料の一方の表面にレーザー光を照射して瞬間加熱し、そのときの熱が伝導することによる他方の面の温度の変化を、例えば赤外線検出器で測定し、実測表面温度を求める。また、積層材料の一方の面をレーザー光で照射したときの他方の面の温度変化を熱伝導方程式を解いて求め、この解析解に積層材料の各層が有する密度、厚さ、熱物性などのデータを代入し、更に層間に形成された中間層の熱抵抗を仮定し、計算機を用いて数値計算し、他方の表面の理論表面温度を求める。次いで、実測表面温度と数値計算で得られた理論表面温度との２乗偏差が最小となる条件から中間層の有する熱抵抗を決定し、この値を中間層の熱抵抗としていた。
【０００４】
例えば、第１層と第３層の厚さが共に１ｍｍ、第１層と第３層の間に形成された中間層である第２層の厚さを０．００５〜１ｍｍとした試料を用いて、パルス幅１ｍｓでパルス波形が三角波形のレーザー光を一方の表面に照射し、他方の表面の温度変化に基づいて熱抵抗を決定する場合、決定した熱抵抗の精度と熱抵抗が生じている中間層の厚さの関係を求めると、図４、図５に示す結果となる。図４、図５では、横軸は中間層である第２層の厚さ（ΔＬ₂ ）と積層材料の厚さ（Ｌ₃ ）との比として表記している。また、レーザーフラッシュ法の測定においては温度測定は１０μｓ、パルス波形の測定は１μｓのサンプリング速度で行い、数値計算においては熱拡散率は第１層が１．０×１０^-4ｍ² ／ｓ、第２層が１．１×１０^-4ｍ² ／ｓ、第３層が１．２×１０^-4ｍ² ／ｓ、比熱は第１層が１．０ｋＪ／ｋｇ／Ｋ、第２層が１．１ｋＪ／ｋｇ／Ｋ、第３層が１．２ｋＪ／ｋｇ／Ｋ、密度は第１層が１０００ｋｇ／ｍ³ 、第２層が１１００ｋｇ／ｍ³ 、第３層が１２００ｋｇ／ｍ³ として、放射損失を示すビオー数は第１層及び第３層共に０．０１とした。なお、図４はレーザーのパルス波形を考慮した場合における中間層である第２層の厚さ（ΔＬ₂ ）と積層材料の厚さ（Ｌ₃ ）との比をパラメータとしたときの決定した熱抵抗の精度の変化を、図５はパルス波形をデルタ関数近似した重心法の場合における中間層である第２層の厚さ（ΔＬ₂ ）と積層材料の厚さ（Ｌ₃ ）との比をパラメータとしたときの決定した熱抵抗の精度の変化をそれぞれ示している。
【０００５】
【発明が解決しようとする課題】
図４及び図５に示されているように、中間層である第２層の厚さ（ΔＬ₂ ）と積層材料の厚さ（Ｌ₃ ）の比が小さくなるにつれて、すなわち中間層である第２層の厚さ（ΔＬ₂ ）が薄くなるにつれて、決定した熱抵抗の精度は徐々に低下する。例えば、図４のレーザーのパルス波形を考慮した場合では、中間層である第２層の厚さ（ΔＬ₂ ）と積層材料の厚さ（Ｌ₃ ）の比が０．０５未満になると誤差が急激に増加し、図５のパルス波形をデルタ関数近似した重心法の場合では、中間層である第２層の厚さ（ΔＬ₂ ）と積層材料の厚さ（Ｌ₃ ）の比が０．１未満になると誤差が急激に増加するようになる。このように、中間層である第２層の厚さ（ΔＬ₂ ）が積層材料の厚さ（Ｌ₃ ）に比較して薄くなると、レーザーフラッシュ法を用いた多層材解析法により決定した熱抵抗の精度が低下してくるため、部分的に第１層と第３層とが接触して層間厚さが消失して層間厚さが明確に定義できない層間の有する熱抵抗を、レーザーフラッシュ法を用いた多層材解析法から精度よく求めることは不可能となる。
【０００６】
本発明はかかる事情に鑑みてなされたもので、第１層と第２層とを有する積層材料の層間に厚さが明確に定義できない層間が存在する場合の層間部の有する熱抵抗を精度よく決定できると共に積層材料のビオー数を決定できる積層材料の熱抵抗とビオー数の測定方法及び測定装置を提供することを目的とする。
【０００７】
【課題を解決するための手段】
前記目的に沿う本発明に係る積層材料の熱抵抗とビオー数の測定方法は、第１層と第２層を有する板状の積層材料で該第１層と該第２層との間に厚さが明確に定義できない層間部が存在する場合の該層間部が有する熱抵抗及び該積層材料の熱放射損失の程度を示すビオー数を測定する積層材料の熱抵抗とビオー数の測定方法であって、前記積層材料の第１層の表面を瞬間的に加熱したときの前記積層材料の第２層の表面の実測表面温度を求める第１工程と、前記積層材料の第１層の表面を瞬間的に加熱したときの前記積層材料の第２層の表面の理論表面温度を、境界条件Ｔ _１（Ｌ _１，ｔ）−Ｔ _２（Ｌ _１，ｔ）＝−Ｒｋ _１ ∂Ｔ _１（Ｌ _１，ｔ）／∂ｘを考慮した非定常熱伝導方程式の解から計算して求める第２工程と、前記実測表面温度と前記理論表面温度との偏差を最小とする条件から前記熱抵抗と前記ビオー数を決定する第３工程とを有する。
ここに、Ｔ _１、Ｔ _２：前記第１層、前記第２層の温度、ｘ：前記第１層表面を基準として該表面から積層材料内部に進入した距離、ｔ：時間、Ｌ _１：前記第１層の厚さ、Ｒ：前記層間部が有する熱抵抗、ｋ _１：前記第１層の熱伝導率
【０００８】
積層材料の第１層の表面を瞬間的に加熱し、そのときの第２層の表面の温度を非定常状態で測定するため、測定に要する時間を非常に短くすることができ、周囲の外乱の影響を受けずに積層材料の熱特性を反映した温度変化を正確に測定することができる。また、積層材料の第１層の表面を瞬間的に加熱したときの第２層の表面の温度を、加熱条件と境界条件を考慮した非定常の熱伝導方程式を解くことにより、熱抵抗とビオー数を変数として含む形で理論表面温度を計算により求めることが可能となる。このため、熱抵抗とビオー数を変化させながら理論表面温度を計算することにより、理論表面温度を実測表面温度に一致させることが可能となる。従って、理論表面温度が実測表面温度に一致するときの熱抵抗とビオー数の値が、積層材料の層間部が有する熱抵抗、積層材料のビオー数であると考えることができる。ここで、理論表面温度と実測表面温度との一致を、実測表面温度と理論表面温度の偏差が最小になる条件から判定するので、熱抵抗とビオー数をパラメータとした繰り返し計算から熱抵抗とビオー数を決定することができる。
【０００９】
本発明に係る積層材料の熱抵抗とビオー数の測定方法において、前記実測表面温度が前記第２層の表面の実測表面温度をラプラス変換したラプラス変換温度、前記理論表面温度が前記非定常熱伝導方程式をラプラス変換して求めた解析解に基づく計算値であり、前記偏差が前記ラプラス変換温度と前記計算値の２乗偏差とすることもできる。
ラプラス変換することにより、境界条件を有する非定常熱伝導方程式を容易に解析的に解くことが可能となる。また、ラプラス変換温度と解析解に基づく計算値との２乗偏差が最小となる条件から熱抵抗とビオー数の決定を行うため、熱抵抗とビオー数の決定に必要な計算量を大幅に低下させることができる。
【００１０】
本発明に係る積層材料の熱抵抗とビオー数の測定方法において、前記実測表面温度が前記第２層の表面の実測表面温度をラプラス変換したラプラス変換温度、前記理論表面温度が前記非定常熱伝導方程式をラプラス変換して求めた解析解に基づく計算値であり、前記偏差が前記ラプラス変換温度の逆数と前記計算値の逆数の２乗偏差とすることが好ましい。
解析解に基づく計算値が分数形式であり、分母が求める熱抵抗とビオー数を含む形式で構成されている場合、計算値の逆数を採用することで、求める熱抵抗とビオー数が分母から分子に移行する。従って、ラプラス変換温度の逆数と計算値の逆数との２乗偏差を採用すると、２乗偏差の計算式の中では分数式に関する計算部分がなくなり、煩雑な計算処理を避けて熱抵抗とビオー数を決定することができる。
【００１１】
本発明に係る積層材料の熱抵抗とビオー数の測定方法において、前記２乗偏差を最小とする条件を、前記実測表面温度の変化から求めた実測減衰時定数と前記理論表面温度の変化から求めた理論減衰時定数とを同値とする付加条件のもとで求めることもできる。
付加条件を設けることにより、熱抵抗とビオー数という２つの独立変数を熱抵抗又はビオー数の１つの独立変数にすることができ、変数を求めるための計算量を大幅に減少させることができる。
【００１２】
続いて、第１層と第２層とを有する積層材料の熱抵抗とビオー数の測定方法について、更に詳しく説明する。
第１層と第２層の層間に熱抵抗Ｒが存在する板状の積層材料の第１層表面を瞬間的に加熱し、そのときの熱が第１層表面から第２層表面（積層材料の裏面）にのみ移動すると近似できる場合、熱の伝導状態は、温度Ｔに関する１次元の非定常熱伝導方程式と境界条件を示す（１）〜（８）式により記述できる。ここで、ｔは時間、ｘは第１層表面を基準として表面から積層材料内部に進入した距離、α₁、α₂はそれぞれ第１層、第２層の熱拡散率、ｋ₁、ｋ₂はそれぞれ第１層、第２層の熱伝導率、Ｌ₁、Ｌ₂はそれぞれ第１層、積層材料の厚さ、ｈ₀、ｈ₁はそれぞれ第１層、第２層のビオー数、Ｑは第１層表面をパルス加熱した際の最大吸収エネルギー、ｆ（ｔ）は第１層表面をパルス加熱する際のパルス波形の時間変化を示す。
【００１３】
【数１】

【００１４】
上記の１次元の非定常熱伝導方程式と境界条件を示す（１）〜（８）式をラプラス変換すると、（９）〜（１６）式となる。
【００１５】
【数２】

【００１６】
微分方程式（９）の一般解は、Ａ_i 、Ｂ_i を定数として次式（１７）、（１８）で与えられる。ここで、ｒ_i ＝（ｐ／α_i ）^1/2 であり、ｉ＝１は第１層、ｉ＝２は第２層を示す。
【００１７】
【数３】

【００１８】
次に、境界条件を示す（１１）、（１２）、（１３）、及び（１６）に一般解を代入し整理すると、（１９）〜（２２）式となる。
【００１９】
【数４】

【００２０】
更に、（１９）、（２２）式を整理すると（２３）、（２４）式となる。
【００２１】
【数５】

【００２２】
次に、（２０）、（２１）式より、定数Ａ₁ 、Ｂ₁ 、とＡ₂ 、Ｂ₂ の関係を求める。（２０）、（２１）式をＡ₁ 、Ｂ₁ 、Ａ₂ 、Ｂ₂ を用いて整理して示すと、（２５）、（２６）式となり、この関係は（２７）式の形にまとめられる。
【００２３】
【数６】

【００２４】
更に、（２４）、（２７）式より、Ａ₁ 、Ｂ₁ とＡ₂ の関係を導くと（２８）、（２９）式となる。
【００２５】
【数７】

【００２６】
また、（２８）、（２９）式を（２３）式に代入してＡ₂ を導くと（３０）式となる。
【００２７】
【数８】

【００２８】
これより積層材料の裏面の温度は（３１）式で表される。
【００２９】
【数９】

【００３０】
（３１）式において、分子の大括弧（［］）内を変形すると（３２）式となる。
【００３１】
【数１０】

【００３２】
また、（３１）式において、分母の大括弧（［］）内を変形する。先ず、ｃ＋ｄγ、ａ＋ｂγを変形すると、それぞれ（３３）、（３４）式となる。
【００３３】
【数１１】

【００３４】
（３３）、（３４）を用いて、更に分子の大括弧内の変形により生じたｒ₂ −ｈ₁ ／Ｌ₂ を考慮して、（３１）式の分母の大括弧内を変形し整理すると、（３５）となる。
【００３５】
【数１２】

【００３６】
従って、（３１）、（３２）、（３５）式を用いて、積層材料の裏面の温度を求めると（３６）式となる。
【００３７】
【数１３】

【００３８】
続いて、第１層及び第２層の熱物性値が判明している場合の層間部に発生している熱抵抗を求める方法について説明する。
積層材料の裏面の実測表面温度と理論表面温度を表す理論式を用いて２乗偏差を構成し、この２乗偏差を最小とするものとして熱抵抗Ｒ及びビオー数ｈを求めるが、その方法には直接法と時定数法がある。直接法は熱抵抗Ｒ及びビオー数ｈを共に独立変数として、２乗偏差が小さくなる方向に両変数を順次移動して２乗偏差を最小とする熱抵抗Ｒとビオー数ｈを求めるものである。一方、時定数法は、時間空間における積層材料の裏面の実測表面温度の減衰領域において減衰時定数τを測定し、この測定した減衰時定数τと積層材料の裏面の理論表面温度を表す理論式より計算される理論減衰時定数とを同値とする付加条件の下に２乗偏差の最小値を求めるものである。この時定数に関する付加条件式は、熱抵抗Ｒとビオー数ｈの関係を表す式である。ここで、第１層表面と第２層表面のビオー数が等しいと仮定する。ｈ₀ ＝ｈ₁ ＝ｈとして、（３６）式を変形すると（３７）式となる。
【００３９】
【数１４】

【００４０】
（３７）式をパルス波形の時間変化部分のラプラス変換式ｆ（ｐ）で除して整理すると（３８）式となる。
【００４１】
【数１５】

【００４２】
続いて、積層材料の裏面の実測表面温度と理論表面温度を表す理論式を用いて２乗偏差を構成し、この２乗偏差を最小とする熱抵抗Ｒとビオー数ｈを求めることになるが、２乗偏差は、実測表面温度と理論表面温度の理論式を用いた通常の２乗偏差でもよし、それぞれの逆数を用いた２乗偏差でもよい。ここでは、理論表面温度を与える式中で求める熱抵抗Ｒとビオー数ｈが分母に存在しているため、逆数を用いた２乗偏差を採用する。積層材料の裏面である第２層表面の実測表面温度の逆数と（３７）で得られる理論表面温度の逆数との２乗偏差は、（３９）式として与えられる。ここで、第２層表面の実測表面温度をラプラス変換したものをＥ_j 、その逆数をｖ_j としている。ここで、ｎはラプラス変数の個数である。
【００４３】
【数１６】

【００４４】
先ず、最大吸収エネルギーＱを（４０）式より求める。
【００４５】
【数１７】

【００４６】
次に、熱抵抗Ｒは、２乗偏差Ｓを最小とするＲの値として決定できるので、Ｒで偏微分したものを０とすることにより、（４１）式に示す２乗偏差ＳのＲによる偏微分式が得られる。
【００４７】
【数１８】

【００４８】
従って、（４２）式より熱抵抗Ｒが決定される。
【００４９】
【数１９】

【００５０】
ビオー数が小さく無視できる場合、（４２）式のａ_j 、ｂ_j に、ａ_0j、ｂ_0jを代入することにより熱抵抗Ｒが決定される。また、ビオー数ｈが無視できない場合の熱抵抗Ｒは、直接法の場合には熱抵抗Ｒ及びビオー数ｈを２乗偏差が小さくなる方向に順次移動して最終的に２乗偏差の最小値を与える熱抵抗Ｒとビオー数ｈを求めることができる。また、時定数法の場合には、２乗偏差を最小とする条件から熱抵抗Ｒとビオー数ｈを決定する際に、実測された積層材料の裏面である第２層表面の温度の減衰過程から計算される時定数が熱抵抗Ｒとビオー数ｈの関数であるという付加条件を設けるため、熱抵抗Ｒとビオー数ｈの２つの独立変数が熱抵抗Ｒ又はビオー数ｈのいずれか１つの独立変数となり、計算が容易となる。従って、ここでは、時定数法を用いた場合について説明する。そこで、（３６）式を用いて理論時定数を計算する。先ず、（３６）式の分母の括弧内を（ｐ）^1/2 ＝ｘとして３次項まで展開すると（４３）式となる。
【００５１】
【数２０】

【００５２】
これより第２層表面の温度減衰の時定数τは（４４）式で与えられる。
【００５３】
【数２１】

【００５４】
この時定数τをビオー数及び熱抵抗Ｒに対して整理すると（４４）式の分母及び分子はそれぞれ（４５）、（４６）式となる。
【００５５】
【数２２】

【００５６】
従って、（４５）、（４６）式を用いて時定数τは（４７）式で表される。ここで、ビオー数が小さい場合では（４７）式よりビオー数は（４８）式として求まる。
【００５７】
【数２３】

【００５８】
また、熱抵抗Ｒは（４９）式として求まる。
【００５９】
【数２４】

【００６０】
以上のことから、実測表面温度の減衰過程から時定数τを具体的に求め、（４２）式と（４９）式を同値とすることにより、ビオー数を具体的に決定できる。決定したビオー数を（４２）に代入することにより熱抵抗Ｒが求まる。更に、（４２）式の近似式を使用して熱抵抗Ｒを求めることも可能である。（４２）式の近似式は、（４２）式の各項を展開しビオー数の関数として表した（５０）式を用いて得られる。
【００６１】
【数２５】

【００６２】
すなわち、（５０）式を（４２）式に代入して、（４５）式の分母、分子ともビオー数の１次項までとして整理すると（５１）式となり、（５１）式を用いて熱抵抗Ｒが決定できる。
【００６３】
【数２６】

【００６４】
前記目的に沿う本発明に係る積層材料の熱抵抗とビオー数の測定装置は、第１層と第２層とを有し該第１層と該第２層との間に厚さが明確に定義できない層間部が存在する板状の積層材料の第１層の表面を瞬間的に加熱するパルス加熱手段と、前記積層材料の第２層の表面の実測表面温度を求める温度測定手段と、前記第１層の表面が瞬間的に加熱されたときの前記第２層の表面の理論表面温度を、境界条件Ｔ _１（Ｌ _１，ｔ）−Ｔ _２（Ｌ _１，ｔ）＝−Ｒｋ _１ ∂Ｔ _１（Ｌ _１，ｔ）／∂ｘを考慮した非定常熱伝導方程式の解から求め、該理論表面温度を前記実測表面温度に一致させることにより前記積層材料の前記層間部の有する熱抵抗と前記積層材料のビオー数を決定する演算処理手段とを有する。
ここに、Ｔ _１、Ｔ _２：前記第１層、前記第２層の温度、ｘ：前記第１層表面を基準として該表面から積層材料内部に進入した距離、ｔ：時間、Ｌ _１：前記第１層の厚さ、Ｒ：前記層間部が有する熱抵抗、ｋ _１：前記第１層の熱伝導率
積層材料の第１層の表面を瞬間的に加熱するパルス加熱手段を備えることにより、非定常状態における測定が可能となる。また、積層材料の第２層の表面の温度を測定する温度測定手段を備えることにより、正確な表面の温度測定が可能となる。更に、演算処理手段が備えられていることにより、測定された第２層の表面の温度の記録と、理論表面温度の算出、及び熱抵抗と積層材料のビオー数を決定を連続的に行うことができる。
【００６５】
【発明の実施の形態】
続いて、添付した図面を参照しつつ、本発明を具体化した実施の形態につき説明し、本発明の理解に供する。
ここに、図１は本発明の一実施の形態に係る積層材料の熱抵抗とビオー数の測定装置の構成図、図２は本発明の一実施の形態に係る積層材料の熱抵抗とビオー数の測定方法を適用して決定した熱抵抗値の精度を示す説明図、図３は同積層材料の熱抵抗とビオー数の測定方法を中間層が熱抵抗層として作用する３層積層材料に適用して決定した熱抵抗の精度を示す説明図である。
【００６６】
図１に示すように、本発明の一実施の形態に係る積層材料の熱抵抗とビオー数の測定装置の一例であるレーザーフラッシュ装置１０は、レーザーパルスを発生させることが可能なパルス加熱手段の一例であるレーザーパルス発生手段１１と、発生したレーザーパルスを、レーザーパルスの波形を検出するレーザーパルス検出手段１２に向かうレーザーパルス及び積層材料１３を照射するレーザーパルスに分配するハーフミラー１４と、レーザーパルスが照射された積層材料１３の裏面の温度を測定する温度測定手段１５と、レーザーパルス検出手段１２からの信号と温度測定手段１５からの信号を入力信号として積層材料の熱抵抗とビオー数の解析を行う演算処理手段１６と、演算処理手段１６による解析結果を表示する出力手段１７とを有している。以下、これらについて詳細に説明する。
【００６７】
レーザーパルス発生手段１１には、試料を高温雰囲気に保持した場合でも雰囲気の熱変動を超える熱エネルギーを積層材料１３表面に注入することが可能な、例えば、ルビーレーザー発振機を使用することができる。積層材料１３の大きさは、レーザーフラッシュ装置１０に設けられた試料ホルダー１８のサイズにより決定され、例えば、直径が８〜１２ｍｍ、厚さが２〜３ｍｍ程度の円板状の積層材料が使用できる。ハーフミラー１４は、ルビーレーザーの吸収率が極めて小さく、かつ透過性が極めて高い材質を有した基板の表面に入射したルビーレーザーから所定量の光を反射するコーティング層を設けた構成を有し、入射したルビーレーザーの光量の、例えば５０％を反射し、５０％を通過させることができる。従って、レーザーパルス発生手段１１から発生したレーザーがハーフミラー１４により反射しレーザーパルス検出手段１２の受光部に到達するようにレーザーパルス検出手段１２の受光部の光軸を調整することにより、レーザーパルス発生手段１１から発射されたレーザー光の一部をレーザーパルス検出手段１２に導入してレーザーパルスの波形をレーザーパルス検出手段１２により測定することができる。また、レーザーパルス発生手段１１から発生しハーフミラー１４を透過したレーザーの光軸と積層材料１３の中心軸とを一致させることにより、積層材料１３の表面をレーザーパルスで確実に照射することができる。このような構成とすることにより、積層材料１３の一方の表面をルビーレーザーパルスで照射した場合、積層材料１３の温度変化を１次元非定常熱伝導方程式により記述することができる。
【００６８】
温度測定手段１５は、レーザーパルスが照射された積層材料１３の裏面の温度変化を高速で精度よく測定できる機能を有する必要があり、例えば、温度検知センサーとして赤外線検出器を備えた温度計測器が使用できる。演算処理手段１６は、例えば、１）レーザーパルス検出手段１２からの信号を記録すると共に該パルス波形をラプラス変換する機能、２）温度測定手段１５からの積層材料１３の裏面の実測表面温度の信号を記録すると共に、実測表面温度のラプラス変換を行う機能、３）積層材料１３を構成している第１層及び第２層の有する各種物性値、積層材料１３の寸法を用いて、積層材料１３の有する境界条件から１次元の非定常熱伝導方程式をラプラス変換により解析的に解いて積層材料１３の裏面の理論表面温度を求める機能、４）実測表面温度のラプラス変換と理論表面温度の２乗偏差を求めて、２乗偏差を最小とする条件から熱抵抗とビオー数を決定する機能、５）決定された熱抵抗とビオー数を表示手段に表示する機能とを備えている。演算処理手段１６には、例えば、パーソナルコンピュータが使用できる。出力手段１７は決定された熱抵抗とビオー数を表示する機能を有するもので、例えば、パーソナルコンピュータ用の表示機器が使用できる。
【００６９】
次に、本発明の一実施の形態に係る積層材料の熱抵抗とビオー数の測定方法について詳細に説明する。
例えば、第１層と第２層とを圧着して形成した素材から直径が１０ｍｍで第１層と第２層の境界を中心に第１層と第２層の厚さが各１ｍｍで全体の厚さが２ｍｍとなる円板形状の積層材料１３を作成し、レーザーフラッシュ装置１０の試料室に設けられている試料ホルダー１８上に、例えば第１層側を上側にして固定する。続いて、試料室を真空等の所定雰囲気にし、試料室内の温度を制御して、積層材料１３が所定の温度に安定した段階でレーザーパルス発生手段１１からレーザーパルスをハーフミラー１４に向けて発射する。発射されたレーザーパルスはハーフミラー１４に到達し、ハーフミラー１４によってレーザーパルスの光量の、例えば５０％は反射されてレーザーパルス検出手段１２に到達しレーザーパルスの波形が求められ、そのデータは演算処理手段１６に転送される。また、ハーフミラー１４を透過したレーザーパルスは積層材料１３の第１層表面に到達し表面を瞬間的に加熱する。
【００７０】
レーザーパルスにより積層材料１３の第１層表面が加熱されると、そのときの熱は第２層側に伝導するので、第２層表面（積層材料１３の裏面）の温度は徐々にに上昇する。しかし、積層材料１３の表面からの熱の散逸も同時に生じているので、裏面温度は最高温度を経てから次に徐々に低下する。このときの温度変化を、例えば赤外線検出器を備えた温度測定手段１５により測定し、測定値は演算処理手段１６に転送される。演算処理手段１６では、先ず、温度測定手段１５から転送された積層材料１３の裏面の実測表面温度の信号を記録すると共に、実測表面温度のラプラス変換を行いラプラス変換温度を記録する。次いで、積層材料１３の有する境界条件から１次元の非定常熱伝導方程式をラプラス変換により解析的に解き、レーザーパルス検出手段１２からの信号により積層材料１３の表面が吸収したパルス波形を記録すると共に該パルス波形をラプラス変換し、積層材料１３を構成している第１層及び第２層の有する各種物性値、第１層及び第２層の寸法を用いて、積層材料１３の裏面のラプラス空間における理論表面温度を求める。その後、記録している実測表面温度のラプラス変換温度とラプラス空間における理論表面温度の２乗偏差を求め、２乗偏差を最小とする条件から熱抵抗とビオー数を決定する。最後に、決定した熱抵抗とビオー数、測定データ等の指定された内容を、例えばパーソナルコンピュータ用の表示機器に表示する。
【００７１】
続いて、本発明の積層材料の熱抵抗とビオー数の測定方法により決定される熱抵抗とビオー数の精度について説明する。
先ず、積層材料１３の第１層と第２層の有する熱物性値を含む各種物性値、試料寸法、ビオー数、及び第１層と第２層の層間に生じている熱抵抗を設定して、レーザーパルスを用いて第１層表面を加熱したときの第２層表面（裏面）の温度を、境界条件を考慮した１次元非定常熱伝導方程式から解析的に求める。ここで、設定する熱抵抗の値は妥当な範囲内の数値であることを条件として任意に数種類設定し、ビオー数も第１層と第２層で同一として妥当な値に設定した。次に、解析的に求めた裏面の温度を仮想実測表面温度とし、レーザーパルスによる加熱条件を同一として、積層材料１３の第１層と第２層の有する熱物性値を含む各種物性値、試料寸法を用いて、（３６）式によりラプラス空間における理論表面温度を求める。続いて、仮想実測表面温度のラプラス変換値と理論表面温度の２乗偏差を求め、２乗偏差を最小とする条件から熱抵抗とビオー数を決定する。決定された熱抵抗とビオー数を仮想実測表面温度を求める際に設定した熱抵抗とビオー数の値と比較することにより、その一致の程度から（３６）式を用いた、すなわち本発明の積層材料の熱抵抗とビオー数の測定方法により決定された熱抵抗とビオー数の精度が評価できる。
【００７２】
例えば、第１層を密度：１０００ｋｇ／ｍ³ 、比熱：１．００ｋＪ／ｋｇ／Ｋ、熱拡散率：１．０×１０^-4ｍ² ／ｓ、層厚さ：１．０ｍｍとし、第２層を密度：１２００ｋｇ／ｍ³ 、比熱：１．２０ｋＪ／ｋｇ／Ｋ、熱拡散率：１．２×１０^-4ｍ² ／ｓ、層厚さ：１．０ｍｍとし、ビオー数を０．０１、設定熱抵抗値（Ｒ₀ ）を表１に示す１１種類の値にして、仮想実測表面温度を求め仮想実測表面温度のラプラス変換値を求めた。更に、仮想実測表面温度に対して、積層材料１３の第１層と第２層の有する熱物性値を含む各種物性値、試料寸法を用いて（３６）式により理論表面温度を求めて、仮想実測表面温度のラプラス変換値と理論表面温度との２乗偏差を最小とする条件から熱抵抗とビオー数を決定した。決定した熱抵抗の値を熱抵抗解析値（Ｒ）として設定熱抵抗値（Ｒ₀ ）と共に表１に記載する。なお、（３６）式を用いて熱抵抗とビオー数を決定する際、第１層の表面が吸収したレーザーパルス波形を重心近似した場合（重心法）と、パルス波形を考慮した場合（パルス補正法）の２種類の方法を採用した。
【００７３】
【表１】

【００７４】
また、図２に示すように、縦軸を設定熱抵抗値（Ｒ₀ ）と２乗偏差を最小とするものとして求めた熱抵抗解析値（Ｒ）との比とし、横軸を設定熱抵抗値（Ｒ₀ ）と第１層及び第２層の熱抵抗の和（Ｒ₁ ＋Ｒ₂ ）との比として表示し、熱抵抗解析値（Ｒ）の特性を検討した。ここで、Ｒ₁ 、Ｒ₂ は第１層及び第２層の厚さを各層の熱伝導率で割ったものである。表１及び図２から、２乗偏差を用いた積層材料の熱抵抗とビオー数の測定方法により、第１層と第２層の層間に厚さが明確に定義できない層間部が存在する場合の層間部の有する熱抵抗を精度よく決定することが可能となることが判明した。更に、熱抵抗を精度よく決定するには、決定される熱抵抗と、第１層及び第２層の熱抵抗の和との比が、０．０５以上であることが必要であることも判明した。更に、パルス波形を考慮するパルス補正法（●）は、パルス重心法（〇）に比較して、高い精度で熱抵抗を決定することが可能であることも判った。なお、２乗偏差を用いて決定される熱抵抗とビオー数の精度の検討は、熱抵抗の場合について具体的に示したが、仮想実測表面温度のラプラス変換値と理論表面温度との２乗偏差を最小とする条件から熱抵抗とビオー数を決定しているため、決定したビオー数の精度も熱抵抗と同様の精度を有している。
【００７５】
本発明に係る積層材料の熱抵抗の測定方法は、第１層、第２層、及び第３層を有する積層材料で第２層の熱拡散率が第１層及び第３層の熱拡散率と比較して小さく熱抵抗層として作用するときの熱抵抗の決定にも適用できることが判明している。例えば、第１層を密度：１１００ｋｇ／ｍ³ 、比熱：１．００ｋＪ／ｋｇ／Ｋ、熱拡散率：１．０×１０^-4ｍ² ／ｓ、層厚さ：１．０ｍｍとし、第３層を密度：１２００ｋｇ／ｍ³ 、比熱：１．２０ｋＪ／ｋｇ／Ｋ、熱拡散率：１．２×１０^-4ｍ² ／ｓ、層厚さ：１．０ｍｍとし、第２層を熱拡散率：１．１×１０^-6ｍ² ／ｓ、比熱：１．１０ｋＪ／ｋｇ／Ｋとし、ビオー数を０．０１、第２層の層厚さを変更することにより熱抵抗を５種類の値に設定して、３層材裏面温度の理論式より理論表面温度を求めて、この仮想実測表面温度に対して本発明に係る積層材料の熱抵抗の測定方法を適用して第２層の熱抵抗を決定した。その結果を、図２と同じ要領で表した図３に示す。図３から判るように、第２層の熱拡散率が第１層及び第３層の熱拡散率の１／１００以下であれば、パルス補正法を採用すると、決定される熱抵抗（Ｒ₂ ）と第１層及び第３層の熱抵抗の和（Ｒ₁ ＋Ｒ₃ ）との比が０．０５以上であれば５％以内の精度で第２層の有する熱抵抗を決定することができる。
【００７６】
以上、本発明の実施の形態を説明したが、本発明は、この実施の形態に限定されるものではなく、例えば、積層材料の熱抵抗とビオー数の測定装置におけるパルス加熱手段としてレーザーパルス発生手段を使用したが、キセノンランプ等のハロゲンランプを使用したパルス加熱手段を使用することも可能である。また、実測表面温度のラプラス変換値と理論表面温度との２乗偏差として、各逆数の偏差を２乗して求めた２乗偏差を例として求めたが、実測表面温度のラプラス変換値と理論表面温度の偏差を２乗して求める２乗偏差を使用することも可能である。
【００７７】
【発明の効果】
請求項１〜４記載の積層材料の熱抵抗とビオー数の測定方法においては、積層材料の第１層の表面を瞬間的に加熱したときの積層材料の第２層の表面の実測表面温度を求める第１工程と、積層材料の第１層の表面を瞬間的に加熱したときの積層材料の第２層の表面の理論表面温度を、境界条件Ｔ _１（Ｌ _１，ｔ）−Ｔ _２（Ｌ _１，ｔ）＝−Ｒｋ _１ ∂Ｔ _１（Ｌ _１，ｔ）／∂ｘを考慮した非定常熱伝導方程式の解から計算して求める第２工程と、実測表面温度と理論表面温度との偏差を最小とする条件から熱抵抗と前記ビオー数を決定する第３工程とを有するので、熱抵抗とビオー数の決定を測定に熟練を要することなく高精度に行うことができる。更に、非定常状態での測定であるため、低温から高温までの広い温度範囲で測定を容易に行うことが可能となる。
【００７８】
特に、請求項２記載の積層材料の熱抵抗とビオー数の測定方法においては、実測表面温度が第２層の表面の実測表面温度をラプラス変換したラプラス変換温度、理論表面温度が非定常熱伝導方程式をラプラス変換して求めた解析解に基づく計算値であり、偏差がラプラス変換温度と計算値の２乗偏差であるので、厳密な解析解が得られることから理論表面温度を容易に正確に求めることが可能となり、更に２乗偏差を最小とする条件から熱抵抗とビオー数を求めるため、測定から熱抵抗とビオー数の決定までが自動化でき熱抵抗とビオー数を短時間に高精度で決定することができる。
【００７９】
請求項３記載の積層材料の熱抵抗とビオー数の測定方法においては、実測表面温度が第２層の表面の実測表面温度をラプラス変換したラプラス変換温度、理論表面温度が非定常熱伝導方程式をラプラス変換して求めた解析解に基づく計算値であり、偏差がラプラス変換温度と計算値の逆数の２乗偏差であるので、２乗偏差を最小とする条件から熱抵抗とビオー数を決定するに際して、分数式の煩雑な計算を避けることができ、熱抵抗とビオー数をより短時間に高精度で決定することができる。
【００８０】
請求項４記載の積層材料の熱抵抗とビオー数の測定方法においては、２乗偏差を最小とする条件を、実測表面温度の変化から求めた実測減衰時定数と理論表面温度の変化から求めた理論減衰時定数とを同値とする付加条件のもとで求めるので、２つの独立変数を１つの独立変数にすることで計算量を大幅に減少させることができ、熱抵抗とビオー数を更に短時間に高精度で決定することができる。
【００８１】
請求項５記載の積層材料の熱抵抗とビオー数の測定装置においては、第１層と第２層とを有し第１層と第２層との間に厚さが明確に定義できない層間部が存在する板状の積層材料の第１層の表面を瞬間的に加熱するパルス加熱手段と、積層材料の第２層の表面の実測表面温度を求める温度測定手段と、第１層の表面が瞬間的に加熱されたときの第２層の表面の理論表面温度を、境界条件Ｔ _１（Ｌ _１，ｔ）−Ｔ _２（Ｌ _１，ｔ）＝−Ｒｋ _１ ∂Ｔ _１（Ｌ _１，ｔ）／∂ｘを考慮した非定常熱伝導方程式の解から求め、理論表面温度を実測表面温度に一致させることにより積層材料の層間部の有する熱抵抗と積層材料のビオー数を決定する演算処理手段とを有するので、測定に熟練していない者でも測定を行うことが可能で、高精度に熱抵抗とビオー数を決定することができる。また、測定には微小サイズの試料でも可能となる。
【図面の簡単な説明】
【図１】本発明の一実施の形態に係る積層材料の熱抵抗とビオー数の測定装置の構成図である。
【図２】本発明の一実施の形態に係る積層材料の熱抵抗とビオー数の測定方法を適用して決定した熱抵抗値の精度を示す説明図である。
【図３】同積層材料の熱抵抗とビオー数の測定方法を中間層が熱抵抗層として作用する３層積層材料に適用して決定した熱抵抗の精度を示す説明図である。
【図４】レーザーパルス波形を考慮した場合の、中間層が熱抵抗層として作用する３層積層材料における多層材解析法により決定した熱抵抗の精度の中間層厚さとの関係を示すグラフである。
【図５】レーザーパルス波形を重心法で近似した場合の、中間層が熱抵抗層として作用する３層積層材料における多層材解析法により決定した熱抵抗の精度の中間層厚さとの関係を示すグラフである。
【符号の説明】
１０：レーザーフラッシュ装置（積層材料の熱抵抗とビオー数の測定装置）、１１：レーザーパルス発生手段（パルス加熱手段）、１２：レーザーパルス検出手段、１３：積層材料、１４：ハーフミラー、１５：温度測定手段、１６：演算処理手段、１７：出力手段、１８：試料ホルダー[0001]
BACKGROUND OF THE INVENTION
The present invention relates to a method of measuring a thermal resistance and a biot number of a laminated material between layers of a laminated material having a first layer and a second layer, and a measuring apparatus therefor, and more specifically, the interlayer thickness cannot be clearly defined. The present invention relates to a method for measuring the thermal resistance of a laminated material having layers and the number of bios of the laminated material at that time, and a measuring apparatus therefor.
[0002]
[Prior art]
In order to expand the application range of materials, such as the formation of an oxidation-resistant film to improve the oxidation resistance of refractory metals and non-oxide materials, the formation of a thermal barrier coating layer to improve the heat resistance of materials, Multilayering of materials that improve the characteristics of materials by laminating other materials on the surface of a base material has been widely studied. In particular, in multilayer materials used at high temperatures, thermal conductivity is an important physical property value in material design, and thermal resistance generated between the layers of multilayer materials is a particularly important factor in material design of high temperature materials. . Therefore, conventionally, for example, in a laminated material in which an oxidation-resistant film or a thermal barrier coating layer is formed on the surface of the base material, the thickness between the layers formed with the formation layer on the surface of the base material can be clearly defined. When this portion can be considered as an intermediate layer, the thermal resistance existing between the layers can be obtained by a multilayer material analysis method using, for example, a laser flash method.
[0003]
In the multilayer material analysis method using the laser flash method, first, one surface of the laminated material is irradiated with laser light and heated instantaneously, and the change in temperature on the other surface due to conduction of the heat at that time, For example, measurement is performed with an infrared detector, and an actual surface temperature is obtained. Also, the temperature change of the other surface when one surface of the laminated material is irradiated with laser light is obtained by solving the heat conduction equation, and the density, thickness, thermophysical properties, etc. of each layer of the laminated material are found in this analytical solution Substituting the data, further assuming the thermal resistance of the intermediate layer formed between the layers, numerical calculation is performed using a computer, and the theoretical surface temperature of the other surface is obtained. Next, the thermal resistance of the intermediate layer was determined from the condition that the square deviation between the measured surface temperature and the theoretical surface temperature obtained by numerical calculation was minimized, and this value was used as the thermal resistance of the intermediate layer.
[0004]
For example, a sample is used in which the thickness of both the first layer and the third layer is 1 mm, and the thickness of the second layer, which is an intermediate layer formed between the first layer and the third layer, is 0.005 to 1 mm. Thus, when laser light having a pulse width of 1 ms and a triangular pulse waveform is irradiated on one surface and the thermal resistance is determined based on the temperature change of the other surface, the accuracy and thermal resistance of the determined thermal resistance are generated. When the relationship of the thickness of the intermediate layer is obtained, the results shown in FIGS. 4 and 5 are obtained. 4 and 5, the horizontal axis represents the thickness of the second layer, which is an intermediate layer (ΔL₂ ) And the thickness of the laminated material (L_Three ) And the ratio. In laser flash measurement, temperature measurement is performed at a sampling rate of 10 μs and pulse waveform measurement is performed at a sampling rate of 1 μs. In numerical calculation, the thermal diffusivity is 1.0 × 10 × 10 for the first layer.^-Fourm² / S, second layer 1.1 × 10^-Fourm² / S, the third layer is 1.2 × 10^-Fourm² / S, specific heat is 1.0 kJ / kg / K for the first layer, 1.1 kJ / kg / K for the second layer, 1.2 kJ / kg / K for the third layer, and 1000 kg / m for the first layer.^Three , The second layer is 1100kg / m^Three The third layer is 1200kg / m^Three As for the number of bioses indicating the radiation loss, the first layer and the third layer are both 0.01. Note that FIG. 4 shows the thickness (ΔL) of the second layer, which is an intermediate layer, in consideration of the pulse waveform of the laser.₂ ) And the thickness of the laminated material (L_Three FIG. 5 shows the change in the accuracy of the thermal resistance determined when the ratio to the thickness of the second layer as the intermediate layer in the case of the centroid method approximating the pulse waveform to the delta function (ΔL).₂ ) And the thickness of the laminated material (L_Three ) And the change in the accuracy of the thermal resistance determined when the ratio is used as a parameter.
[0005]
[Problems to be solved by the invention]
As shown in FIGS. 4 and 5, the thickness (ΔL₂ ) And the thickness of the laminated material (L_Three ) Ratio, that is, the thickness (ΔL) of the second layer as the intermediate layer₂ ) Becomes thinner, the accuracy of the determined thermal resistance gradually decreases. For example, when the pulse waveform of the laser in FIG. 4 is considered, the thickness (ΔL₂ ) And the thickness of the laminated material (L_Three ) Ratio is less than 0.05, the error increases rapidly. In the case of the centroid method in which the pulse waveform of FIG. 5 is approximated by a delta function, the thickness of the second layer (ΔL)₂ ) And the thickness of the laminated material (L_Three ) Becomes less than 0.1, the error increases rapidly. In this way, the thickness (ΔL₂ ) Is the thickness of the laminated material (L_Three ), The accuracy of the thermal resistance determined by the multilayer material analysis method using the laser flash method is lowered, so that the first layer and the third layer are partially in contact with each other and the interlayer thickness It is impossible to accurately obtain the thermal resistance between the layers whose thickness cannot be clearly defined due to disappearance of the layer from the multilayer material analysis method using the laser flash method.
[0006]
The present invention has been made in view of such circumstances, and the thermal resistance of the interlayer portion when there is an interlayer whose thickness cannot be clearly defined between the layers of the laminated material having the first layer and the second layer is accurately determined. It is an object of the present invention to provide a method and a measuring apparatus for measuring the thermal resistance and bior number of a laminated material that can be determined and the number of bios of the laminated material can be determined.
[0007]
[Means for Solving the Problems]
The method for measuring the thermal resistance and the number of bioses of the laminated material according to the present invention in accordance with the above object is a plate-like laminated material having a first layer and a second layer, and is between the first layer and the second layer.If there is an interlayer part where the thickness cannot be clearly defined,A method of measuring a thermal resistance and a bio-number of a laminated material for measuring a thermal resistance of an interlayer part and a biot number indicating a degree of thermal radiation loss of the laminated material,1st layerOf the laminated material when the surface ofSecond layerA first step of determining the measured surface temperature of the surface of the laminated material;1st layerOf the laminated material when the surface ofSecond layerThe theoretical surface temperature of the surface of the boundary conditionT ₁ (L ₁ , T) -T ₂ (L ₁ , T) = − Rk ₁ ∂T ₁ (L ₁ , T) / ∂xThe second step of determining the thermal resistance and the number of bioses from the second step obtained by calculating from the solution of the unsteady heat conduction equation in consideration of the above and the condition for minimizing the deviation between the measured surface temperature and the theoretical surface temperature Process.
Where T ₁ , T ₂ : Temperature of the first layer and the second layer, x: distance entering the laminated material from the surface with reference to the surface of the first layer, t: time, L ₁ : Thickness of the first layer, R: thermal resistance of the interlayer, k ₁ : Thermal conductivity of the first layer
[0008]
Laminated material1st layerThe surface of theSecond layerThe temperature of the surface of the material is measured in an unsteady state, so the time required for the measurement can be greatly shortened, and the temperature change that reflects the thermal characteristics of the laminated material is accurately measured without being affected by the surrounding disturbance. be able to. Also, the laminated material1st layerWhen the surface of theSecond layerBy solving the unsteady heat conduction equation considering the heating conditions and boundary conditions, the theoretical surface temperature can be calculated by including the thermal resistance and the number of bioses as variables. For this reason, it is possible to make the theoretical surface temperature coincide with the measured surface temperature by calculating the theoretical surface temperature while changing the thermal resistance and the number of bioses. Therefore, it can be considered that the values of the thermal resistance and the number of bioses when the theoretical surface temperature coincides with the measured surface temperature are the thermal resistance and the number of bioses of the laminated material of the interlayer material. Here, the agreement between the theoretical surface temperature and the measured surface temperature is determined from the condition that the deviation between the measured surface temperature and the theoretical surface temperature is minimized. The number can be determined.
[0009]
In the method for measuring the thermal resistance and the biot number of the laminated material according to the present invention, the measured surface temperature is the above-described surface temperature.Second layerThe Laplace conversion temperature obtained by performing Laplace conversion on the measured surface temperature of the surface, the theoretical surface temperature is a calculated value based on an analytical solution obtained by Laplace conversion of the unsteady heat conduction equation, and the deviation is the Laplace conversion temperature and the above The square deviation of the calculated value can also be used.
By performing Laplace transform, it becomes possible to analytically solve unsteady heat conduction equations having boundary conditions. In addition, since the thermal resistance and biot number are determined from the condition that the square deviation between the Laplace conversion temperature and the calculated value based on the analytical solution is minimized, the amount of calculation required to determine the thermal resistance and biot number is greatly reduced. Can be made.
[0010]
In the method for measuring the thermal resistance and the biot number of the laminated material according to the present invention, the measured surface temperature is the above-described surface temperature.Second layerThe Laplace conversion temperature obtained by converting the measured surface temperature of the surface to Laplace, the theoretical surface temperature is a calculated value based on the analytical solution obtained by Laplace conversion of the unsteady heat conduction equation, and the deviation is the reciprocal of the Laplace conversion temperature. And the square deviation of the reciprocal of the calculated value.
If the calculated value based on the analytical solution is in a fractional format and is configured in a format that includes the thermal resistance and bior number obtained by the denominator, the reciprocal of the calculated value is used to obtain the desired thermal resistance and bior number from the denominator. Migrate to Therefore, when the square deviation between the inverse of the Laplace conversion temperature and the inverse of the calculated value is adopted, there is no calculation part related to the fractional expression in the calculation formula of the square deviation, and it is possible to avoid the complicated calculation processing and the thermal resistance and the bio number. Can be determined.
[0011]
In the method for measuring the thermal resistance and the number of bioses of the laminated material according to the present invention, the condition for minimizing the square deviation is obtained from the measured decay time constant obtained from the change in the measured surface temperature and the change in the theoretical surface temperature. It can also be obtained under the additional condition that makes the theoretical damping time constant equal.
By providing an additional condition, the two independent variables of thermal resistance and bior number can be made one independent variable of thermal resistance or bior number, and the amount of calculation for obtaining the variable can be significantly reduced.
[0012]
Next, a method for measuring the thermal resistance and the number of bioses of the laminated material having the first layer and the second layer will be described in more detail.
The surface of the first layer of the plate-shaped laminated material having a thermal resistance R between the first layer and the second layer is instantaneously heated, and the heat at that time is changed from the surface of the first layer to the surface of the second layer (laminated material). If it can be approximated to move only to the back surface of (1), the heat conduction state can be described by the one-dimensional unsteady heat conduction equation relating to the temperature T and the equations (1) to (8) showing the boundary conditions. Where t is time, x is the distance from the surface to the inside of the laminated material with respect to the surface of the first layer, α₁, Α₂Are the thermal diffusivities of the first and second layers, respectively, k₁, K₂Are the thermal conductivity of the first and second layers, respectively, L₁, L₂Are the first layer,Laminate materialThickness, h₀, H₁Is the number of bios in the first layer and the second layer, Q is the maximum absorption energy when the surface of the first layer is pulse-heated, and f (t) is the time change of the pulse waveform when the surface of the first layer is pulse-heated. Show.
[0013]
[Expression 1]

[0014]
When the above-described one-dimensional unsteady heat conduction equation and the equations (1) to (8) showing the boundary conditions are Laplace transformed, equations (9) to (16) are obtained.
[0015]
[Expression 2]

[0016]
The general solution of the differential equation (9) is A_i , B_i Is given by the following equations (17) and (18). Where r_i = (P / α_i )^1/2 I = 1 indicates the first layer and i = 2 indicates the second layer.
[0017]
[Equation 3]

[0018]
Next, when general solutions are substituted into (11), (12), (13), and (16) indicating boundary conditions, the equations (19) to (22) are obtained.
[0019]
[Expression 4]

[0020]
Further, when formulas (19) and (22) are arranged, formulas (23) and (24) are obtained.
[0021]
[Equation 5]

[0022]
Next, from the expressions (20) and (21), a constant A₁ , B₁ , And A₂ , B₂ Seeking the relationship. Equations (20) and (21)₁ , B₁ , A₂ , B₂ Using (), the expressions (25) and (26) are obtained, and this relationship is summarized in the form of the expression (27).
[0023]
[Formula 6]

[0024]
Furthermore, from equations (24) and (27), A₁ , B₁ And A₂ When the relationship is derived, equations (28) and (29) are obtained.
[0025]
[Expression 7]

[0026]
Also, by substituting equations (28) and (29) into equation (23), A₂ Is derived, the equation (30) is obtained.
[0027]
[Equation 8]

[0028]
Accordingly, the temperature of the back surface of the laminated material is expressed by the equation (31).
[0029]
[Equation 9]

[0030]
In the equation (31), when the inside of the brackets ([]) of the molecule is deformed, the equation (32) is obtained.
[0031]
[Expression 10]

[0032]
Further, in the equation (31), the inside of the denominator bracket ([]) is transformed. First, when c + dγ and a + bγ are transformed, equations (33) and (34) are obtained, respectively.
[0033]
## EQU11 ##

[0034]
Using (33) and (34), r generated by deformation within the brackets of the molecule₂ -H₁ / L₂ In consideration of the above, if the brackets in the denominator of equation (31) are transformed and arranged, (35) is obtained.
[0035]
[Expression 12]

[0036]
Therefore, when the temperature of the back surface of the laminated material is determined using the equations (31), (32), and (35), the equation (36) is obtained.
[0037]
[Formula 13]

[0038]
Next, a method for obtaining the thermal resistance generated in the interlayer portion when the thermophysical values of the first layer and the second layer are known will be described.
A square deviation is constructed using a theoretical expression representing the measured surface temperature and the theoretical surface temperature of the back surface of the laminated material, and the thermal resistance R and the biot number h are obtained with this square deviation as a minimum. There are direct method and time constant method. In the direct method, both the thermal resistance R and the biot number h are independent variables, and both variables are sequentially moved in the direction in which the squared deviation is reduced to obtain the thermal resistance R and the biot number h that minimize the squared deviation. . On the other hand, the time constant method measures the decay time constant τ in the attenuation region of the measured surface temperature of the back surface of the laminated material in time space, and expresses the measured decay time constant τ and the theoretical surface temperature of the back surface of the laminated material. The minimum value of the square deviation is obtained under the additional condition that the theoretical damping time constant calculated from the above is equivalent. The additional conditional expression relating to this time constant is an expression representing the relationship between the thermal resistance R and the bior number h. Here, it is assumed that the number of bioses on the surface of the first layer and the surface of the second layer is equal. h₀ = H₁ When (36) is transformed with = h, the following formula (37) is obtained.
[0039]
[Expression 14]

[0040]
When formula (37) is divided by the Laplace transform formula f (p) of the time-varying portion of the pulse waveform, formula (38) is obtained.
[0041]
[Expression 15]

[0042]
Subsequently, a square deviation is constructed using a theoretical formula representing the measured surface temperature and the theoretical surface temperature of the back surface of the laminated material, and the thermal resistance R and the bioh number h that minimize this square deviation are obtained. The square deviation may be a normal square deviation using a theoretical formula of the actually measured surface temperature and the theoretical surface temperature, or may be a square deviation using their reciprocal numbers. Here, since the thermal resistance R and the biot number h obtained in the formula for giving the theoretical surface temperature exist in the denominator, the square deviation using the reciprocal is adopted. The square deviation between the reciprocal of the measured surface temperature of the second layer surface, which is the back surface of the laminated material, and the reciprocal of the theoretical surface temperature obtained in (37) is given as equation (39). Here, the measured surface temperature on the surface of the second layer is converted to Laplace._j , And vice versa_j It is said. Here, n is the number of Laplace variables.
[0043]
[Expression 16]

[0044]
First, the maximum absorbed energy Q is obtained from the equation (40).
[0045]
[Expression 17]

[0046]
Next, since the thermal resistance R can be determined as a value of R that minimizes the square deviation S, by substituting 0 for the partial differential of R, the R of the square deviation S shown in the equation (41) A partial differential equation is obtained.
[0047]
[Formula 18]

[0048]
Therefore, the thermal resistance R is determined from the equation (42).
[0049]
[Equation 19]

[0050]
If the number of bioses is small and can be ignored, a in equation (42)_j , B_j A_0j, B_0jIs substituted for the thermal resistance R. In the case of the direct method, the thermal resistance R when the biot number h cannot be ignored is the minimum value of the squared deviation by sequentially moving the thermal resistance R and the biot number h in the direction in which the squared deviation becomes smaller. Can be obtained. Further, in the case of the time constant method, when determining the thermal resistance R and the biot number h from the condition that minimizes the square deviation, the temperature decay process of the surface of the second layer, which is the back surface of the laminated material actually measured. In order to provide an additional condition that the time constant calculated from is a function of the thermal resistance R and the Bioh number h, two independent variables of the thermal resistance R and the Bioh number h are either one of the thermal resistance R or the Bioh number h. It becomes an independent variable and calculation is easy. Therefore, here, a case where the time constant method is used will be described. Therefore, the theoretical time constant is calculated using equation (36). First, the parenthesis in the denominator of equation (36) is (p)^1/2 When x is expanded to the third order term, equation (43) is obtained.
[0051]
[Expression 20]

[0052]
Thus, the time constant τ of temperature decay on the second layer surface is given by the equation (44).
[0053]
[Expression 21]

[0054]
When this time constant τ is arranged with respect to the biot number and the thermal resistance R, the denominator and the numerator of the equation (44) become the equations (45) and (46), respectively.
[0055]
[Expression 22]

[0056]
Therefore, the time constant τ is expressed by the equation (47) using the equations (45) and (46). Here, when the number of bioses is small, the number of bioses can be obtained from equation (47) as equation (48).
[0057]
[Expression 23]

[0058]
Further, the thermal resistance R is obtained as the equation (49).
[0059]
[Expression 24]

[0060]
From the above, the Biot number can be specifically determined by specifically obtaining the time constant τ from the decay process of the actually measured surface temperature and setting the equations (42) and (49) to the same value. The thermal resistance R is obtained by substituting the determined number of bios into (42). Furthermore, it is also possible to obtain the thermal resistance R using the approximate expression (42). The approximate expression of the expression (42) is obtained by using the expression (50) in which each term of the expression (42) is expanded and expressed as a function of the number of bioses.
[0061]
[Expression 25]

[0062]
That is, substituting the equation (50) into the equation (42) and arranging both the denominator and the numerator of the equation (45) up to the first order term of the Biot number, the equation (51) is obtained, and the thermal resistance R using the equation (51) Can be determined.
[0063]
[Equation 26]

[0064]
An apparatus for measuring a thermal resistance and a biot number of a laminated material according to the present invention that meets the above-described object has a first layer and a second layer, and is between the first layer and the second layer.Thickness cannot be clearly definedOf plate-like laminated material with an interlayer1st layerPulse heating means for instantaneously heating the surface of the laminated material, andSecond layerTemperature measuring means for determining the actual surface temperature of the surface of the surface, and1st layerWhen the surface of the is instantaneously heatedSecond layerThe theoretical surface temperature of the surface of, Boundary condition T ₁ (L ₁ , T) -T ₂ (L ₁ , T) = − Rk ₁ ∂T ₁ (L ₁ , T) / From the solution of the unsteady heat conduction equation considering ∂xSeeking,Arithmetic processing means for determining the thermal resistance of the interlayer portion of the laminated material and the number of bios of the laminated material by making the theoretical surface temperature coincide with the measured surface temperature.
Where T ₁ , T ₂ : Temperature of the first layer and the second layer, x: distance entering the laminated material from the surface with reference to the surface of the first layer, t: time, L ₁ : Thickness of the first layer, R: thermal resistance of the interlayer, k ₁ : Thermal conductivity of the first layer
Laminated material1st layerBy providing pulse heating means for instantaneously heating the surface of the film, measurement in an unsteady state can be performed. Also, the laminated materialSecond layerBy providing a temperature measuring means for measuring the surface temperature of the surface, it is possible to accurately measure the surface temperature. Furthermore, it was measured by being provided with arithmetic processing means.Second layerIt is possible to continuously record the temperature of the surface, calculate the theoretical surface temperature, and determine the thermal resistance and the number of biores in the laminated material.
[0065]
DETAILED DESCRIPTION OF THE INVENTION
Next, embodiments of the present invention will be described with reference to the accompanying drawings for understanding of the present invention.
Here, FIG. 1 is a configuration diagram of a thermal resistance and bior number measuring device of a laminated material according to an embodiment of the present invention, and FIG. 2 is a thermal resistance and bior number of the laminated material according to an embodiment of the present invention. FIG. 3 is an explanatory diagram showing the accuracy of the thermal resistance value determined by applying the measuring method of FIG. 3, and FIG. 3 shows the application of the measuring method of the thermal resistance and the number of bios of the same laminated material to a three-layer laminated material in which the intermediate layer acts as a thermal resistance layer It is explanatory drawing which shows the precision of the thermal resistance determined by doing.
[0066]
As shown in FIG. 1, a laser flash device 10, which is an example of an apparatus for measuring the thermal resistance and biot number of a laminated material according to an embodiment of the present invention, is a pulse heating means capable of generating a laser pulse. Laser pulse generating means 11 which is an example, a half mirror 14 which distributes the generated laser pulse to a laser pulse directed to the laser pulse detecting means 12 for detecting the laser pulse waveform and a laser pulse for irradiating the laminated material 13, a laser The temperature measuring means 15 for measuring the temperature of the back surface of the laminated material 13 irradiated with the pulse, the signal from the laser pulse detecting means 12 and the signal from the temperature measuring means 15 as input signals are used to determine the thermal resistance and the number of bios of the laminated material. An arithmetic processing means 16 for performing analysis and an output means 17 for displaying the analysis result by the arithmetic processing means 16 are provided. To have. Hereinafter, these will be described in detail.
[0067]
For the laser pulse generating means 11, for example, a ruby laser oscillator capable of injecting thermal energy exceeding the thermal fluctuation of the atmosphere into the surface of the laminated material 13 even when the sample is held in a high temperature atmosphere can be used. . The size of the laminated material 13 is determined by the size of the sample holder 18 provided in the laser flash device 10, and for example, a disk-shaped laminated material having a diameter of about 8 to 12 mm and a thickness of about 2 to 3 mm can be used. . The half mirror 14 has a configuration in which a coating layer for reflecting a predetermined amount of light from a ruby laser incident on the surface of a substrate having a material with a very low ruby laser absorptivity and extremely high transmittance is provided. For example, 50% of the amount of incident ruby laser light can be reflected and 50% can be transmitted. Therefore, the laser pulse is adjusted by adjusting the optical axis of the light receiving portion of the laser pulse detecting means 12 so that the laser generated from the laser pulse generating means 11 is reflected by the half mirror 14 and reaches the light receiving portion of the laser pulse detecting means 12. A part of the laser light emitted from the generating means 11 can be introduced into the laser pulse detecting means 12 and the laser pulse waveform can be measured by the laser pulse detecting means 12. Further, by matching the optical axis of the laser generated from the laser pulse generating means 11 and transmitted through the half mirror 14 with the central axis of the laminated material 13, the surface of the laminated material 13 can be reliably irradiated with the laser pulse. . With such a configuration, when one surface of the laminated material 13 is irradiated with a ruby laser pulse, the temperature change of the laminated material 13 can be described by a one-dimensional unsteady heat conduction equation.
[0068]
The temperature measuring means 15 needs to have a function capable of measuring the temperature change of the back surface of the laminated material 13 irradiated with the laser pulse at high speed and with high accuracy. For example, a temperature measuring device including an infrared detector as a temperature detection sensor is used. Can be used. The arithmetic processing means 16 is, for example, 1) a function for recording a signal from the laser pulse detection means 12 and a Laplace transform of the pulse waveform, and 2) a signal of the measured surface temperature of the back surface of the laminated material 13 from the temperature measurement means 15. 3) a function of performing Laplace conversion of the measured surface temperature, and 3) using the various physical property values of the first layer and the second layer constituting the laminated material 13 and the dimensions of the laminated material 13, the laminated material 13 A function that analytically solves a one-dimensional unsteady heat conduction equation by Laplace transform from boundary conditions possessed by 4) Laplace transform of measured surface temperature and square of theoretical surface temperature A function for obtaining the deviation and determining the thermal resistance and the number of bioses from the condition that minimizes the square deviation is provided. 5) A function for displaying the determined thermal resistance and the number of bioses on the display means. For the arithmetic processing means 16, for example, a personal computer can be used. The output means 17 has a function of displaying the determined thermal resistance and the number of bioses. For example, a display device for a personal computer can be used.
[0069]
Next, a method for measuring the thermal resistance and the number of bioses of a laminated material according to an embodiment of the present invention will be described in detail.
For example, from a material formed by pressure bonding the first layer and the second layer, the diameter is 10 mm, the thickness of the first layer and the second layer is 1 mm each centering on the boundary between the first layer and the second layer, and the whole A disc-shaped laminated material 13 having a thickness of 2 mm is prepared and fixed on a sample holder 18 provided in a sample chamber of the laser flash device 10 with the first layer side facing upward, for example. Subsequently, the sample chamber is set to a predetermined atmosphere such as a vacuum, the temperature in the sample chamber is controlled, and the laser pulse is emitted from the laser pulse generating means 11 toward the half mirror 14 when the laminated material 13 is stabilized at the predetermined temperature. To do. The emitted laser pulse reaches the half mirror 14, and, for example, 50% of the amount of the laser pulse is reflected by the half mirror 14 and reaches the laser pulse detection means 12 to obtain the laser pulse waveform, and the data is calculated. It is transferred to the processing means 16. Further, the laser pulse transmitted through the half mirror 14 reaches the surface of the first layer of the laminated material 13 and instantaneously heats the surface.
[0070]
When the first layer surface of the laminated material 13 is heated by the laser pulse, the heat at that time is conducted to the second layer side, so that the temperature of the second layer surface (the back surface of the laminated material 13) gradually increases. . However, since heat dissipation from the surface of the laminated material 13 also occurs at the same time, the back surface temperature gradually decreases after passing through the maximum temperature. The temperature change at this time is measured by, for example, the temperature measuring means 15 provided with an infrared detector, and the measured value is transferred to the arithmetic processing means 16. The arithmetic processing means 16 first records the measured surface temperature signal on the back surface of the laminated material 13 transferred from the temperature measuring means 15, performs Laplace conversion of the measured surface temperature, and records the Laplace conversion temperature. Next, a one-dimensional unsteady heat conduction equation is analytically solved from the boundary conditions of the laminated material 13 by Laplace transform, and a pulse waveform absorbed by the surface of the laminated material 13 is recorded by a signal from the laser pulse detecting means 12. The Laplace space on the back surface of the laminated material 13 is obtained by performing Laplace transform on the pulse waveform and using various physical property values of the first and second layers constituting the laminated material 13 and the dimensions of the first and second layers. Obtain the theoretical surface temperature at. Thereafter, the Laplace conversion temperature of the recorded actual surface temperature and the square deviation of the theoretical surface temperature in the Laplace space are obtained, and the thermal resistance and the number of bioses are determined from the conditions that minimize the square deviation. Finally, designated contents such as the determined thermal resistance, the number of bioses, and measurement data are displayed on a display device for a personal computer, for example.
[0071]
Subsequently, the accuracy of the thermal resistance and the bio number determined by the method for measuring the thermal resistance and the bio number of the laminated material of the present invention will be described.
First, various physical property values including the thermophysical property values of the first layer and the second layer of the laminated material 13, the sample dimensions, the number of bioses, and the thermal resistance generated between the first layer and the second layer are set. Then, the temperature of the second layer surface (back surface) when the first layer surface is heated using a laser pulse is analytically obtained from a one-dimensional unsteady heat conduction equation considering boundary conditions. Here, several kinds of thermal resistance values to be set are arbitrarily set on the condition that the values are within a reasonable range, and the number of bioses is also set to a reasonable value as the same in the first layer and the second layer. Next, the back surface temperature obtained analytically is set as the virtual measured surface temperature, the heating conditions by the laser pulse are the same, and various physical property values including the thermophysical values of the first layer and the second layer of the laminated material 13 and the sample Using the dimensions, the theoretical surface temperature in the Laplace space is determined by equation (36). Subsequently, the Laplace transform value of the virtual measured surface temperature and the square deviation of the theoretical surface temperature are obtained, and the thermal resistance and the number of bioses are determined from the conditions that minimize the square deviation. By comparing the determined thermal resistance and bior number with the values of the thermal resistance and bior number set when obtaining the virtual measured surface temperature, the equation (36) is used from the degree of coincidence, that is, the lamination of the present invention The accuracy of the thermal resistance and bior number determined by the method of measuring the thermal resistance and biot number of the material can be evaluated.
[0072]
For example, the density of the first layer is 1000 kg / m^Three Specific heat: 1.00 kJ / kg / K, Thermal diffusivity: 1.0 × 10^-Fourm² / S, layer thickness: 1.0 mm, density of second layer: 1200 kg / m^Three Specific heat: 1.20 kJ / kg / K, Thermal diffusivity: 1.2 × 10^-Fourm² / S, layer thickness: 1.0 mm, biore number 0.01, set thermal resistance value (R₀ ) Was set to 11 types of values shown in Table 1, and a virtual measured surface temperature was obtained to obtain a Laplace transform value of the virtual measured surface temperature. Furthermore, with respect to the virtual measured surface temperature, the theoretical surface temperature is calculated by the equation (36) using various physical property values including the thermophysical property values of the first layer and the second layer of the laminated material 13 and the sample dimensions, and the virtual surface temperature is calculated. The thermal resistance and the number of bioses were determined from the conditions that minimize the square deviation between the measured surface temperature Laplace transform value and the theoretical surface temperature. The determined thermal resistance value is set as the thermal resistance analysis value (R) and the set thermal resistance value (R₀ ) And listed in Table 1. When the thermal resistance and the number of bioses are determined using equation (36), the laser pulse waveform absorbed by the surface of the first layer is approximated by the center of gravity (center of gravity method), and the pulse waveform is considered (pulse correction). Two types of methods were adopted.
[0073]
[Table 1]

[0074]
Also, as shown in FIG. 2, the vertical axis represents the set thermal resistance value (R₀ ) And the thermal resistance analysis value (R) determined to minimize the square deviation, and the horizontal axis represents the set thermal resistance value (R₀ ) And the sum of the thermal resistance of the first and second layers (R₁ + R₂ ) And the characteristics of the thermal resistance analysis value (R) were examined. Where R₁ , R₂ Is the thickness of the first and second layers divided by the thermal conductivity of each layer. From Table 1 and FIG. 2, when there is an interlayer part where the thickness cannot be clearly defined between the first layer and the second layer by the method of measuring the thermal resistance and the biot number of the laminated material using the square deviation It has been found that the thermal resistance of the interlayer part can be determined with high accuracy. Furthermore, it has been found that, in order to accurately determine the thermal resistance, the ratio of the determined thermal resistance to the sum of the thermal resistances of the first layer and the second layer needs to be 0.05 or more. did. Furthermore, it was also found that the pulse correction method (●) considering the pulse waveform can determine the thermal resistance with higher accuracy than the pulse centroid method (◯). In addition, although the examination of the accuracy of the thermal resistance and the biot number determined using the square deviation is specifically shown for the case of thermal resistance, the square of the Laplace transform value of the virtual measured surface temperature and the theoretical surface temperature is shown. Since the thermal resistance and the number of bioses are determined from the condition that minimizes the deviation, the accuracy of the determined number of bioses has the same accuracy as the thermal resistance.
[0075]
The method for measuring the thermal resistance of a laminated material according to the present invention is a laminated material having a first layer, a second layer, and a third layer. The thermal diffusivity of the second layer is the thermal diffusivity of the first layer and the third layer. It can be applied to the determination of thermal resistance when acting as a thermal resistance layer. For example, the density of the first layer is 1100 kg / m^Three Specific heat: 1.00 kJ / kg / K, Thermal diffusivity: 1.0 × 10^-Fourm² / S, layer thickness: 1.0 mm, density of third layer: 1200 kg / m^Three Specific heat: 1.20 kJ / kg / K, Thermal diffusivity: 1.2 × 10^-Fourm² / S, layer thickness: 1.0 mm, second layer thermal diffusivity: 1.1 × 10^-6m² / S, specific heat: 1.10 kJ / kg / K, the number of bioses is 0.01, the thermal resistance is set to five values by changing the layer thickness of the second layer, and the three-layer material back surface temperature The theoretical surface temperature was obtained from the above theoretical formula, and the thermal resistance of the second layer was determined by applying the method for measuring the thermal resistance of the laminated material according to the present invention to the virtual measured surface temperature. The result is shown in FIG. 3 expressed in the same manner as FIG. As can be seen from FIG. 3, when the thermal diffusivity of the second layer is 1/100 or less of the thermal diffusivity of the first layer and the third layer, the thermal resistance (R₂ ) And the sum of the thermal resistance of the first and third layers (R₁ + R_Three )) Is 0.05 or more, the thermal resistance of the second layer can be determined with an accuracy within 5%.
[0076]
The embodiment of the present invention has been described above. However, the present invention is not limited to this embodiment. For example, laser pulse generation is performed as a pulse heating unit in a measurement device for the thermal resistance and biot number of a laminated material. However, it is also possible to use pulse heating means using a halogen lamp such as a xenon lamp. In addition, as a square deviation between the Laplace conversion value of the measured surface temperature and the theoretical surface temperature, a square deviation obtained by squaring the deviation of each reciprocal was taken as an example. It is also possible to use a square deviation obtained by squaring the deviation of the surface temperature.
[0077]
【The invention's effect】
In the measurement method of the thermal resistance and bio-number of the laminated material according to claim 1,1st layerOf the laminated material when the surface ofSecond layerThe first step of determining the measured surface temperature of the surface of the laminated material1st layerOf the laminated material when the surface ofSecond layerThe theoretical surface temperature of the surface of the boundary conditionT ₁ (L ₁ , T) -T ₂ (L ₁ , T) = − Rk ₁ ∂T ₁ (L ₁ , T) / ∂xA second step that is calculated from the solution of the unsteady heat conduction equation in consideration of the above, and a third step that determines the thermal resistance and the biot number from the condition that minimizes the deviation between the measured surface temperature and the theoretical surface temperature. Therefore, the determination of the thermal resistance and the number of bioses can be performed with high accuracy without requiring skill in measurement. Furthermore, since the measurement is performed in an unsteady state, the measurement can be easily performed in a wide temperature range from a low temperature to a high temperature.
[0078]
In particular, in the method for measuring the thermal resistance and the number of bioses of the laminated material according to claim 2, the measured surface temperature isSecond layerLaplace conversion temperature obtained by Laplace conversion of the measured surface temperature of the surface, theoretical surface temperature is a calculated value based on the analytical solution obtained by Laplace conversion of the unsteady heat conduction equation, and the deviation is the square of the Laplace conversion temperature and the calculated value Since it is a deviation, a precise analytical solution can be obtained, so that the theoretical surface temperature can be obtained easily and accurately, and further, the thermal resistance and biot number are obtained from the conditions that minimize the square deviation. It is possible to automate the determination of the resistance and the number of bioses, and to determine the thermal resistance and the number of bioses in a short time with high accuracy.
[0079]
In the method of measuring the thermal resistance and biot number of the laminated material according to claim 3, the measured surface temperature isSecond layerThe Laplace conversion temperature obtained by Laplace conversion of the measured surface temperature of the surface, the theoretical surface temperature is a calculated value based on the analytical solution obtained by Laplace conversion of the unsteady heat conduction equation, and the deviation is the reciprocal of the Laplace conversion temperature and the calculated value. Since it is a square deviation, it is possible to avoid complicated calculations of fractional expressions when determining the thermal resistance and the number of bioses from the condition that minimizes the square deviation, and the thermal resistance and the number of bioses can be accurately obtained in a shorter time. Can be determined.
[0080]
In the method of measuring the thermal resistance and the biot number of the laminated material according to claim 4, the condition for minimizing the square deviation is obtained from the measured decay time constant obtained from the change in the measured surface temperature and the change in the theoretical surface temperature. Since it is calculated under the additional condition that the theoretical damping time constant is equivalent, the calculation amount can be greatly reduced by making two independent variables into one independent variable, and the thermal resistance and the number of bioses are further reduced. The time can be determined with high accuracy.
[0081]
In the thermal resistance of the laminated material of Claim 5, and the bio-number measuring apparatus, it has the 1st layer and the 2nd layer, and it is between the 1st layer and the 2nd layer.Thickness cannot be clearly definedOf plate-like laminated material with an interlayer1st layerPulse heating means for instantaneously heating the surface ofSecond layerTemperature measuring means for determining the actual surface temperature of the surface of1st layerWhen the surface of the is heated instantaneouslySecond layerThe theoretical surface temperature of the surface of, Boundary condition T ₁ (L ₁ , T) -T ₂ (L ₁ , T) = − Rk ₁ ∂T ₁ (L ₁ , T) / From the solution of the unsteady heat conduction equation considering ∂xSeeking,Since the theoretical surface temperature matches the measured surface temperature, it has an arithmetic processing means that determines the thermal resistance of the interlayer part of the laminated material and the number of bioses of the laminated material, so even those who are not skilled in measurement can make measurements It is possible to determine the thermal resistance and the number of bioses with high accuracy. In addition, the measurement can be performed even with a minute sample.
[Brief description of the drawings]
FIG. 1 is a configuration diagram of an apparatus for measuring the thermal resistance and the number of bioses of a laminated material according to an embodiment of the present invention.
FIG. 2 is an explanatory diagram showing the accuracy of the thermal resistance value determined by applying the method for measuring the thermal resistance and the number of bioses of a laminated material according to an embodiment of the present invention.
FIG. 3 is an explanatory diagram showing the accuracy of thermal resistance determined by applying the method for measuring the thermal resistance and biot number of the same laminated material to a three-layer laminated material in which an intermediate layer acts as a thermal resistance layer.
FIG. 4 is a graph showing a relationship between thermal resistance accuracy and intermediate layer thickness determined by a multilayer analysis method in a three-layer laminated material in which an intermediate layer acts as a thermal resistance layer in consideration of a laser pulse waveform. .
FIG. 5 shows the relationship between the thermal resistance accuracy determined by the multilayer analysis method and the intermediate layer thickness in a three-layer laminated material in which the intermediate layer acts as a thermal resistance layer when the laser pulse waveform is approximated by the center of gravity method. It is a graph.
[Explanation of symbols]
10: Laser flash device (measurement device of thermal resistance and biot number of laminated material), 11: Laser pulse generating means (pulse heating means), 12: Laser pulse detecting means, 13: Laminated material, 14: Half mirror, 15: Temperature measuring means, 16: arithmetic processing means, 17: output means, 18: sample holder

Claims

Thermal resistance possessed by the interlayer unit when the interlayer unit that is not clearly defined thickness between the first layer and the first layer and the second layer in the plate-shaped laminate material having a second layer is present, And a method of measuring the thermal resistance and biot number of the laminated material for measuring the biot number indicating the degree of thermal radiation loss of the laminated material,
A first step of determining an actual surface temperature of the surface of the second layer of the laminated material when the surface of the first layer of the laminated material is instantaneously heated;
The theoretical surface temperature of the surface of the second layer of the laminated material when the surface of the first layer of the laminated material is instantaneously heated is defined as a boundary condition T ₁ (L ₁ , t) −T ₂ (L ₁ , t ) =-Rk ₁ ∂T ₁ (L ₁ , t) / second step calculated from the solution of the unsteady heat conduction equation considering 考慮 x ;
A method for measuring the thermal resistance and bionumber of a laminated material, comprising: a third step of determining the thermal resistance and the biot number from a condition that minimizes a deviation between the measured surface temperature and the theoretical surface temperature. .
Where, T ₁ , T ₂ : temperature of the first layer and the second layer, x: distance entering the laminated material from the surface with reference to the surface of the first layer, t: time, L ₁ : the above Thickness of the first layer, R: thermal resistance of the interlayer part, k ₁ : thermal conductivity of the first layer

2. The method for measuring the thermal resistance and biot number of a laminated material according to claim 1, wherein the measured surface temperature is a Laplace conversion temperature obtained by Laplace conversion of the measured surface temperature of the surface of the second layer , and the theoretical surface temperature is the unsteady heat. It is a calculated value based on an analytical solution obtained by Laplace transform of a conduction equation, and the deviation is a square deviation of the Laplace transform temperature and the calculated value. Method.

2. The method for measuring the thermal resistance and biot number of a laminated material according to claim 1, wherein the measured surface temperature is a Laplace conversion temperature obtained by Laplace conversion of the measured surface temperature of the surface of the second layer , and the theoretical surface temperature is the unsteady heat. A thermal resistance of the laminated material, wherein the deviation is a square deviation of the reciprocal of the Laplace conversion temperature and the reciprocal of the calculated value. How to measure the biot number.

4. The method for measuring the thermal resistance and bior number of a laminated material according to claim 2 or 3, wherein the conditions for minimizing the square deviation are the measured decay time constant obtained from the change in the measured surface temperature and the theoretical surface temperature. A method for measuring a thermal resistance and a biot number of a laminated material, characterized in that it is obtained under an additional condition in which a theoretical decay time constant obtained from a change is equivalent.

The surface of the first layer of the plate-like laminated material having the first layer and the second layer and having an interlayer portion whose thickness cannot be clearly defined between the first layer and the second layer is instantaneously applied. Pulse heating means for heating to
Temperature measuring means for determining an actual surface temperature of the surface of the second layer of the laminated material;
The theoretical surface temperature of the surface of the second layer when the surface of the first layer is instantaneously heated is defined as a boundary condition T ₁ (L ₁ , t) −T ₂ (L ₁ , t) = − Rk ₁ determined from the solution of _{_{∂T 1 (L 1, t)}} / unsteady heat conduction equation in consideration of ∂x, thermal resistance possessed by the interlayer of the laminated material by matching the該理theory surface temperature on the measured surface temperature And an arithmetic processing means for determining the number of bios of the laminated material. The apparatus for measuring the thermal resistance and the number of bios of the laminated material.
Where, T ₁ , T ₂ : temperature of the first layer and the second layer, x: distance entering the laminated material from the surface with reference to the surface of the first layer, t: time, L ₁ : the above Thickness of the first layer, R: thermal resistance of the interlayer part, k ₁ : thermal conductivity of the first layer