JP4101012B2

JP4101012B2 - Thermal property evaluation method and apparatus for laminated material having thermal resistance

Info

Publication number: JP4101012B2
Application number: JP2002296280A
Authority: JP
Inventors: 和也細野; 芳明石本; 昭彦大塚; 久男田中
Original assignee: Japan Ultra High Temperature Materials Research Institute JUTEM
Current assignee: Japan Ultra High Temperature Materials Research Institute JUTEM
Priority date: 2002-10-09
Filing date: 2002-10-09
Publication date: 2008-06-11
Anticipated expiration: 2022-10-09
Also published as: JP2004132778A

Description

【０００１】
【発明の属する技術分野】
本発明は、積層材の層間熱抵抗と層の熱物性及び層厚を非定常状態の下で、例えば、レーザフラッシュ法を用いて同時に測定する熱抵抗を有する積層材の熱特性評価方法及びその装置に関する。
【０００２】
【従来の技術】
構造材料の耐酸化性向上、遮熱性能向上あるいは耐摩耗性向上等を目的として構造材料の表面に被覆膜を形成した積層材、あるいは半導体素子に見られる半導体の表面に機能性膜を形成した積層材の熱特性を評価することは、積層材の性能を確認するために必要となる。
従来、これらの積層材の熱特性評価は、次のような方法により行なわれていた。例えば、構造材料あるいは半導体といった基材とその上に形成した膜との間の層間熱抵抗が無視でき、しかも基材と膜を分離することができる場合は、それぞれの熱物性を個別に測定し、その値をもとに積層材としての熱特性を計算により求めていた。また、基材と膜との間の層間熱抵抗が無視でき、しかも基材と膜を分離することができない場合は、基材のみの熱物性を先に測定し、次いで、例えばレーザフラッシュ法を用いた多層材解析法により膜の熱物性を測定して、得られた基材と膜の各熱物性を用いて積層材の熱特性を計算で求めていた。更に、基材と膜との間の層間熱抵抗が無視できない場合は、基材及び膜の各熱物性を先に測定し、次いで積層材をレーザフラッシュ法で測定して解析により層間熱抵抗を求めて、基材及び膜の熱物性と層間熱抵抗から計算により積層材の熱特性を求めていた。
【０００３】
【発明が解決しようとする課題】
しかしながら、基材と膜との間の層間熱抵抗が無視できず、更に基材と膜を分離することができない積層材の場合、従来の積層材の熱特性評価方法を適用することができず、積層材の熱特性評価を行なうことは不可能であった。また、基材と膜を分離して熱物性の測定を行なうことができる場合でも、積層材の形態で熱特性の測定を行なうことができれば、積層材の熱特性評価の効率化を図ることが可能となる。
本発明はかかる事情に鑑みてなされたもので、層間熱抵抗が無視できない積層材の層間熱抵抗及び層の熱物性を非定常状態の下で同時に測定することが可能な熱抵抗を有する積層材の熱特性評価方法及びその装置を提供することを目的とする。
【０００４】
【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熱抵抗を有する積層材の熱特性評価方法は、第１層と第２層を備え、該第１層と該第２層との層間部に熱抵抗が存在する板状の積層材の熱特性を求める積層材の熱特性評価方法であって、前記積層材の一側の表面を瞬間的に加熱したときの前記積層材の他側の表面の実測表面温度を求める第１工程と、前記積層材の一側の表面を瞬間的に加熱したときの前記積層材の他側の表面の理論表面温度を、境界条件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、前記積層材を構成する各層の熱物性及び層厚の中の一部が未知数であるとして、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、ビオ数、及び該未知数の値を求める第３工程とを有する。
【０００５】
積層材の一側の表面を瞬間的に加熱し、そのときの他側の表面の温度を非定常状態で測定する。このため、測定に要する時間を非常に短くすることができ、その結果、周囲の外乱の影響を受けずに積層材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、積層材の一側の表面を瞬間的に加熱したときの他側の表面の温度を、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、ビオ数、各層の熱物性（例えば、熱拡散率、熱伝導率、比熱容量）及び層厚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できる。
このため、積層材を構成する各層の熱物性及び層厚の中の一部が未知数であると、熱抵抗、ビオ数、及びこの未知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できる。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、ビオ数、及び未知数の各値が、積層材の層間部が有する熱抵抗、積層材のビオ数、及びこの積層材で求める未知数の値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、ビオ数、及び未知数をパラメータとした繰り返し計算から、それぞれ熱抵抗、ビオ数、及び未知数の値を決定することができる。
【０００６】
本発明に係る熱抵抗を有する積層材の熱特性評価方法において、前記未知数を一方の層の熱物性及び層厚、あるいは、一方の層の熱物性及び層厚の中の一部とすることができる。
未知数が一方の層の熱物性及び層厚である場合、既知である他方の層の熱物性及び層厚の各値を用いて、熱抵抗、ビオ数、一方の層の熱物性及び層厚を決定することができる。また、未知数が一方の層の熱物性及び層厚の中の一部である場合、既知である他方の層の熱物性及び層厚の各値と、一方の層の熱物性及び層厚の中の既知である各値を用いて、一方の層の熱物性及び層厚の中で未知数であるものの値、熱抵抗、ビオ数を決定することができる。
【０００７】
本発明に係る熱抵抗を有する積層材の熱特性評価方法において、前記理論表面温度は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って、前記偏差が前記実測表面温度をラプラス変換したラプラス変換温度と前記計算値の２乗偏差とすることが好ましい。
【０００８】
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できる。なお、非定常熱伝導方程式の解はラプラス空間で得られるため、２乗偏差が計算できるように、他面側の表面の実測表面温度をラプラス変換してラプラス変換温度とする。また、２乗偏差を最小とする条件から熱抵抗、ビオ数、及び未知数の値の決定を行うため、熱抵抗、ビオ数、及び未知数の値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。
【０００９】
積層材の第１層側の表面に瞬間的に熱エネルギーＱ（ｔ）を供給した場合、積層材の第２層側の表面のラプラス空間における理論表面温度Ｔ₂ （Ｌ₂ ，ｐ）は（１）式で表される。ここで、α₁ は第１層の熱拡散率、ｃ₁ は第１層の比熱容量、ρ₁ は第１層の密度、ｋ₁ は第１層の熱伝導率（＝ρ₁ ｃ₁ α₁ ）、ΔＬ₁ は第１層の層厚、α₂ は第２層の熱拡散率、ｃ₂ は第２層の比熱容量、ρ₂ は第２層の密度、ｋ₂ は第２層の熱伝導率（＝ρ₂ ｃ₂ α₂ ）、ΔＬ₂ は第２層の層厚、ｈ₀ は第１層側の表面のビオ数、ｈ₁ は第２層側の表面のビオ数、Ｌ₂ は積層材の厚さ（＝ΔＬ₁ ＋ΔＬ₂ ）、Ｒは層間熱抵抗、ｐはラプラス変数、ｒ＝（ｐ／α）^1/2 である。
【００１０】
【数１】

【００１１】
ここで、第２層の熱拡散率α₂ 、第２層の比熱容量ｃ₂ 、第２層の密度ρ₂ 、第２層の熱伝導率ｋ₂ 、及び２層の層厚ΔＬ₂ が既知であるとすると、積層材の第２層側の表面の理論表面温度Ｔ₂ （Ｌ₂ ，ｐ）を与える（１）式は（２）式と考えてよく、理論表面温度Ｔ₂ （Ｌ₂ ，ｐ）は、第１層の熱拡散率α₁ 、第１層の体積熱容量( ρ₁c₁)、第１層の層厚ΔＬ₁ 、層間熱抵抗Ｒ、ビオ数（ｈ₁ 、ｈ₂)の関数となる。理論表面温度Ｔ₂ （Ｌ₂ ，ｐ）において、各層の比熱容量は常に密度との積である体積熱容量の形で現れるので、以下においては密度を固定し、体積熱容量の代わりに比熱容量を変数として考える。
【００１２】
【数２】

【００１３】
なお、２乗偏差Ｓは（３）式に示すように複数のラプラス変数ｐ_i による和で構成する。ここで、Ｅ_i は第２層側の表面の実測表面温度をラプラス変数ｐ_i でラプラス変換したものである。
【００１４】
【数３】

【００１５】
本発明に係る熱抵抗を有する積層材の熱特性評価方法において、前記２乗偏差を最小とする条件を、前記熱抵抗、前記ビオ数、及び前記未知数を独立変数として、該各独立変数毎に求めることができる。
熱抵抗、ビオ数、及び未知数をそれぞれ独立変数とし、各独立変数毎に２乗偏差の値が最小となるときの独立変数の値を求めて、熱抵抗、ビオ数、及び未知数の各値をそれぞれ決定する。
【００１６】
２乗偏差の最小値を与える変数を求める方法として、例えば、ニュートン法や、２乗偏差値の大小を比較して最小値を与える変数を求める方法が挙げられる。
ニュートン法は、２乗偏差をＳ、独立変数をｘとしたときに、２乗偏差Ｓが小さくなる方向に独立変数ｘを順次変化させながらそのときの２乗偏差の値を計算し、最小値を求めるものである。例えば、図１２に示すように、先ず、独立変数の値として初期値ｘ₀ を設定し（ステップＳ１）、２乗偏差Ｓを計算して（ステップＳ２）、２乗偏差Ｓの値が予め設定した値ε未満となるかを判定する（ステップＳ３）。そして、２乗偏差Ｓの値が予め設定した値ε未満の場合、そのときの独立変数の値を２乗偏差Ｓが最小となる条件として採用する（ステップＳ４）。２乗偏差Ｓの値が予め設定した値ε以上の場合では、初期値ｘ₀ を微少量Δｘだけ変化させ（ステップＳ５）、２乗偏差Ｓを求めて（ステップＳ２）、２乗偏差Ｓの値が予め設定した値ε未満となるかを判定する（ステップＳ３）。そして、２乗偏差Ｓの値が予め設定した値ε未満となるまでＳ２、Ｓ３、Ｓ５の各ステップを繰り返す。
【００１７】
２乗偏差値の大小を比較して最小値を与える変数を求める方法は、独立変数を複数設定し、それぞれに対して２乗偏差Ｓを計算して、その最小値を判定しながら２乗偏差Ｓの最小値を与える独立変数を求めるものである。例えば、図１３に示すように、先ず、独立変数ｘ₀ 〜ｘ_n （ｎは３以上）をそれぞれの差がΔｘ（ただし、Δｘ＞０）となるように設定する（ステップＳ１１）。次いで、各独立変数ｘ₀ 〜ｘ_n に対してそれぞれ２乗偏差Ｓを計算し、最小となる２乗偏差Ｓ_min （ｘ_k ）の値が予め設定した値ε未満となるかを判定する（ステップＳ１２）。そして、２乗偏差Ｓ_min （ｘ_k ）の値が予め設定した値ε未満の場合、２乗偏差Ｓ_min （ｘ_k ）の計算を終了して、そのときの独立変数の値を２乗偏差Ｓが最小となる条件として採用する（ステップＳ１３）。
【００１８】
２乗偏差Ｓ_min （ｘ_k ）がε以上であり、２乗偏差Ｓ_min （ｘ_k ）の最小が独立変数ｘ₀ の場合、このｘ₁ を独立変数の最大値として、それぞれの差がΔｘとなるようにｎ個の独立変数ｙ_i を設定し、このｙ_i を新たにｘ_i とする（ステップＳ１４）。また、２乗偏差Ｓ_min （ｘ_k ）の最小が独立変数ｘ_k （ｘ₀ を超えｘ_n 未満）の場合、ｘ_k-m （ｍは１以上）を独立変数の最小値、ｘ_k+m を独立変数の最大値としてｎ分割して得られる各値ｙ_i を独立変数として設定し、このｙ_i を新たにｘ_i とする（ステップＳ１５）。あるいは、２乗偏差Ｓ_min （ｘ_k ）の最小が独立変数ｘ_n の場合、ｘ_n-1 を独立変数の最小値としてそれぞれの差がΔｘとなるようにｎ個の独立変数ｙ_i を設定し、ｙ_i を新たにｘ_i とする（ステップＳ１６）。
次いで、それぞれ新たに設定されたｘ_i に対して２乗偏差Ｓを計算し、最小となる２乗偏差Ｓ_min （ｘ_k ）の値が予め設定した値ε未満となるかを判定する（ステップＳ１２）。そして、２乗偏差Ｓ_min （ｘ_k ）の値が予め設定した値ε未満となるまでＳ１２、Ｓ１４〜Ｓ１６の各ステップを繰り返す。
【００１９】
本発明に係る熱抵抗を有する積層材の熱特性評価方法において、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てもよい。
付加条件を設けることにより、熱抵抗、ビオ数、及び未知数から構成される独立変数の数を１つ減らすことができ、２乗偏差を最小とする各独立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。
【００２０】
積層材の表面からは熱の散逸が生じているので、裏面温度の変化では最高温度が存在し、最高温度を経てからは徐々に温度は低下する。この減衰領域における実測表面温度Ｔ₂ の変化は、実測減衰時定数をτ、時間をｔとすると、Ｔ₂ ∝ｅｘｐ（−ｔ／τ）となる。従って、実測表面温度Ｔ₂ の測定から実測減衰時定数τを求めることができる。一方、理論減衰時定数τ_thは、（４）式で表される。このため、実測減衰時定数τと理論減衰時定数τ_thを等しいとすることにより、付加条件を作成することができる。
【００２１】
【数４】

【００２２】
前記目的に沿う本発明に係る熱抵抗を有する積層材の熱特性評価装置は、第１層と第２層を備え、該第１層と該第２層との間に層間部が存在する板状の積層材の一側の表面を瞬間的に加熱するパルス加熱手段と、前記積層材の他側の表面の実測表面温度を求める温度測定手段と、前記積層材を構成する各層の熱物性及び層厚の中の一部が未知数であるとして、前記一側の表面が瞬間的に加熱されたときの前記他側の表面の理論表面温度を求め該理論表面温度と前記実測表面温度の偏差を最小とする条件から、前記層間部に存在する熱抵抗、ビオ数、及び該未知数の値を求める演算処理部とを有する。
また、本発明に係る熱抵抗を有する積層材の熱特性評価装置において、前記未知数を一方の層の熱物性及び層厚、あるいは、前記未知数を一方の層の熱物性及び層厚の中の一部とすることができる。
【００２３】
積層材の一側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、積層材の他側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、演算処理部が備えられていることにより、測定された他側の表面の実測温度の記録、理論表面温度の算出、偏差の計算、偏差を最小とする条件の決定を連続的に行なって、熱抵抗、ビオ数、及び未知数の各値をそれぞれ求めることができる。ここで、未知数が一方の層の熱物性及び層厚である場合、既知である他方の層の熱物性及び層厚の各値を用いて、熱抵抗、ビオ数、一方の層の熱物性及び層厚が決定される。また、未知数が一方の層の熱物性及び層厚の中の一部である場合、既知である他方の層の熱物性及び層厚の各値と、一方の層の熱物性及び層厚の中の既知である各値を用いて、一方の層の熱物性及び層厚の中で未知数であるものの値、熱抵抗、ビオ数が決定される。
【００２４】
【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熱抵抗を有する積層材の熱特性評価装置の説明図、図２は熱抵抗と熱拡散率を測定対象としたときの２乗偏差の凹溝の熱抵抗と熱拡散率から構成される平面に対する投影図、図３は熱抵抗と熱拡散率を測定対象としたときの２乗偏差の凹溝の熱拡散率と２乗偏差から構成される平面に対する投影図、図４は熱抵抗と熱拡散率を測定対象としたときの２乗偏差の凹溝の熱抵抗と２乗偏差から構成される平面に対する投影図、図５は熱抵抗、熱拡散率、及びビオ数を測定対象としたときの２乗偏差の最小値のビオ数と２乗偏差から構成される平面に対する投影図、図６は熱抵抗と比熱容量を測定対象としたときの熱抵抗に対する２乗偏差の変化挙動を示す説明図、図７は熱抵抗と比熱容量を測定対象としたときの比熱容量に対する２乗偏差の変化挙動を示す説明図、図８は熱抵抗、比熱容量及びビオ数を測定対象としたときの２乗偏差の最小値のビオ数依存性を示す説明図、図９は熱抵抗と第１層の層厚を測定対象としたときの熱抵抗に対する２乗偏差の変化挙動を示す説明図、図１０は熱抵抗と第１層の層厚を測定対象としたときの第１層の層厚に対する２乗偏差の変化挙動を示す説明図、図１１は熱抵抗、第１層の層厚及びビオ数を測定対象としたときのビオ数に対する２乗偏差の変化挙動を示す説明図である。
【００２５】
図１に示すように、本発明の一実施の形態に係る熱抵抗を有する積層材の熱特性評価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１１を発生させるパルス加熱手段１２と、発生したレーザーパルス１１を、レーザーパルス波形を検出するパルス検出手段１３に向かうレーザーパルス１４及び積層材１５の一側にある第１層１６の表面１７を照射するレーザーパルス１８に分配するハーフミラー１９を有している。また、レーザーフラッシュ装置１０は、レーザーパルス１８が照射された積層材１５の他側にある第２層２０の表面２１の温度を測定する温度測定手段２２と、パルス検出手段１３からの信号と温度測定手段２２からの信号が入力され、例えば、積層材１５の第２層２０の熱物性及び層厚ΔＬ₂ を既知として、積層材１５の熱抵抗及びビオ数並びに第１層１６の熱物性及び層厚ΔＬ₁ を求める演算処理部２３と、演算処理部２３による演算結果を表示する出力手段２４とを有している。以下、これらについて詳細に説明する。
【００２６】
パルス加熱手段１２には、積層材１５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第１層１６側の表面１７に注入することが可能な、例えば、ルビーレーザー発振器を使用することができる。積層材１５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２５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が使用できる。
ハーフミラー１９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となっており、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、パルス加熱手段１２から発生したレーザーがハーフミラー１９により反射しパルス検出手段１３の受光部に到達するようにパルス検出手段１３の受光部の光軸を調整することにより、パルス加熱手段１２から発射されたレーザーパルス１１の一部をパルス検出手段１３に導入してレーザーパルス１１の波形をパルス検出手段１３により測定することができる。また、パルス加熱手段１２から発生しハーフミラー１９を透過したレーザーパルス１８の光軸と積層材１５の中心軸とを一致させることにより、積層材１５の第１層１６側の表面１７をレーザーパルス１８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１５の第１層１６側の表面１７をレーザーパルス１８で照射した場合、積層材１５の第２層２０側の表面２１の温度変化を１次元非定常熱伝導方程式により表すことができる。
【００２７】
温度測定手段２２は、レーザーパルス１８が照射された積層材１５の第２層２０側の表面２１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。
演算処理部２３は、パルス検出手段１３からの信号を読み込んで第２層２０の有する熱物性値及び層厚ΔＬ₂ を用いて、積層材１５の境界条件から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１５の第２層２０側の表面２１の理論表面温度を求める機能を備えた理論表面温度演算手段２６と、温度測定手段２２からの積層材１５の第２層２０側の表面２１の実測表面温度の信号を読み込んで実測表面温度のラプラス変換を行なってラプラス変換温度を求める機能を備えたラプラス変換手段２７を有している。また、演算処理部２３は、第２層２０側の表面２１の実測表面温度のラプラス変換温度及び理論表面温度の２乗偏差を求める機能を備えた２乗偏差演算手段２８と、２乗偏差を最小とする条件から積層材１５の熱抵抗及びビオ数、並びに第１層１６の熱物性及び層厚ΔＬ₁ を求め出力手段２４に伝送する機能を備えた２乗偏差最小化手段２９を有している。そして、演算処理部２３は、例えば、パーソナルコンピュータに上記の各機能を発現するプログラムを搭載させることにより構成することができる。なお、出力手段２４には、例えば、パーソナルコンピュータ用の表示機器、印刷機が使用できる。
【００２８】
なお、レーザーフラッシュ装置１０を用いて、積層材１５の第２層２０の熱物性及び層厚ΔＬ₂ がすべて既知、かつ第１層１６の熱物性及び層厚ΔＬ₁ の中の一部が既知である場合でも、演算処理部２３で積層材１５の熱抵抗とビオ数、並びに第１層１６の熱物性及び層厚ΔＬ₁ の中で未知数であるものの値をそれぞれ求めることができる。
また、レーザーフラッシュ装置１０を用いて、第１層１６の熱物性、層厚ΔＬ₁ がすべて既知である場合に、積層材１５の熱抵抗とビオ数、並びに第２層２０の熱物性及び層厚ΔＬ₂ のすべてを求めることもできる。更に、第１層１６の熱物性、層厚ΔＬ₁ がすべて既知で、かつ第２層２０の熱物性及び層厚ΔＬ₂ の中の一部が既知である場合に、積層材１５の熱抵抗とビオ数、並びに第２層２０の熱物性及び層厚ΔＬ₂ の中で未知数であるものの値を求めることもレーザーフラッシュ装置１０を用いて可能である。
【００２９】
次に、本発明の一実施の形態に係る熱抵抗を有する積層材の熱特性評価方法について詳細に説明する。
例えば、直径が８〜１２ｍｍ、厚さが２〜３ｍｍ程度の円板状の積層材１５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２５上に、例えば第１層１６側を上側にして固定する。なお、第２層２０の熱物性と層厚ΔＬ₂ は既知とする。
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１５が所定の温度に安定した段階でパルス加熱手段１２からレーザーパルス１１をハーフミラー１９に向けて発射する。発射されたレーザーパルス１１はハーフミラー１９に到達し、ハーフミラー１９によってレーザーパルス１１の光量の、例えば５０％は反射されてパルス検出手段１３に到達しレーザーパルス１１の波形が求められ、そのデータは演算処理部２３に転送される。また、ハーフミラー１９を透過したレーザーパルス１８は積層材１５の第１層１６側の表面１７に到達し表面を瞬間的に加熱する。
【００３０】
レーザーパルス１８により積層材１５の第１層１６の表面１７が加熱されると、そのときの熱は第２層２０側に伝導するので、第２層２０側の表面２１の温度は徐々に上昇する。しかし、積層材１５の各表面１７、２１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２２により測定し、測定値は演算処理部２３に転送される。演算処理部２３では、先ず、ラプラス変換手段２７において温度測定手段２２から転送された第２層２０側の表面２１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（以上第１工程）。
次いで、理論表面温度演算手段２６において積層材１５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、パルス検出手段１３からの信号により第１層１６側の表面１７が吸収したパルス波形を記録すると共にパルス波形をラプラス変換し、積層材１５を構成している第１層１６の熱物性値（熱拡散率、比熱容量）及び層厚ΔＬ₁ の中で未知数のものをパラメータとし、第２層２０の熱物性（熱拡散率、比熱容量）と第２層２０の層厚ΔＬ₂ の各値、及び第１層１６の熱物性値と第１層１６の層厚ΔＬ₁ の中で既知のものの各値を用いて、第２層２０側の表面２１のラプラス空間における理論表面温度を求める（以上第２工程）。
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を２乗偏差演算手段２８に転送しラプラス変換温度と理論表面温度との２乗偏差を求める。そして、２乗偏差最小化手段２９で２乗偏差を最小とする条件を求めて、積層材１５の第１層１６と第２層２０の層間部に存在する熱抵抗及びビオ数、並びに第１層１６の熱物性と第１層１６の層厚ΔＬ₁ の中で未知数の値を求め、その結果を、出力手段２４の一例である、例えば、パーソナルコンピュータ用の表示機器、印刷機に出力する（以上第３工程）。
【００３１】
続いて、本実施の形態の熱抵抗を有する積層材の熱特性評価方法により決定される積層材１５の熱抵抗及びビオ数、並びに積層材１５を構成する第１層１６の熱物性（熱拡散率、比熱容量）と層厚ΔＬ₁ の精度について説明する。
先ず、表１に示す熱拡散率、比熱容量、密度、層厚を有する第１層１６及び第２層２０からなる積層材１５の第２層２０側表面２１の温度の時系列理論データを（１）式の逆ラプラス変換により作成する。
【００３２】
【表１】

【００３３】
次に、第１層１６の熱拡散率α₁ 、比熱容量ｃ₁ 、及び層厚ΔＬ₁ を独立変数とし、第２層２０の熱拡散率α₂ 、比熱容量ｃ₂ 、及び層厚ΔＬ₂ を既知とすると、積層材１５の第２層２０側表面２１の温度を与える（１）式は（２）式となり、２乗偏差Ｓは（３）式で示される。ここで、Ｅ_i は、表１に示す物性値を有する層１６、２０から構成される積層材１５の第２層２０側表面２１の温度の時系列理論データをラプラス変数をｐ_i としてラプラス変換したものである。
なお、熱抵抗Ｒと第１層１６の熱物性の同時解析を行なう場合、熱抵抗Ｒと他の測定対象の組み合わせは表２のようになる。
【００３４】
【表２】

【００３５】
（１）測定対象が熱抵抗Ｒと熱拡散率α₁ の場合
第１層１６の比熱容量ｃ₁ 、層厚ΔＬ₁ 、ビオ数ｈ₁ を固定して、熱抵抗Ｒと熱拡散率α₁ を独立変数とした場合、２乗偏差Ｓ、熱拡散率α₁ 、及びと熱抵抗Ｒから構成される空間で、２乗偏差Ｓは熱拡散率α₁ と熱抵抗Ｒからなる平面上に凹状の溝を構成する。この溝を熱拡散率α₁ と熱抵抗Ｒからなる平面上に投影したものを図２に、２乗偏差Ｓと熱拡散率α₁ からなる平面上に投影したものを図３に、２乗偏差Ｓと熱抵抗Ｒからなる平面上に投影を図４にそれぞれ示す。
熱抵抗Ｒと熱拡散率α₁ を変数とした場合、２乗偏差Ｓの最小値を与える熱抵抗Ｒと熱拡散率α₁ は、α₁ ＝１．００５２×１０^-4（ｍ² ／ｓ）、Ｒ＝４．５１７×１０^-3（ｍ² Ｋ／Ｗ）と求まり、理論データとの比較から求まる精度はそれぞれ０．５２％、０．２０％である。
【００３６】
（２）測定対象が熱抵抗Ｒ、熱拡散率α₁ 、及びビオ数ｈの場合
次に、第１層１６側の表面１７のビオ数ｈ₀ と第２層２０側の表面２１のビオ数ｈ₁ を等しいとして、ビオ数ｈを独立変数に追加して、２乗偏差Ｓの熱抵抗Ｒ、熱拡散率α₁ 、及びビオ数ｈ₁ に対する依存性を調べる。なお、ビオ数ｈを０．００５〜０．０３の範囲で変化させ、それぞれのビオ数ｈに対する２乗偏差Ｓの最小値と、その点における熱抵抗Ｒ、熱拡散率α₁ を求めた。各ビオ数ｈに対して求めた２乗偏差Ｓの最小値のビオ数ｈと２乗偏差から構成される平面に投影したものを図５に示す。これより２乗偏差Ｓを最小とする熱抵抗Ｒ、熱拡散率α₁ 、及びビオ数ｈは、α₁ ＝１．０２２０×１０^-4（ｍ² ／ｓ）、Ｒ＝４．７３８５×１０^-3（ｍ² Ｋ／Ｗ）、ｈ＝１．３２×１０^-2と求まり、それぞれの精度は、２．２％、５．１１％、及び３２％である。
【００３７】
（３）測定対象が熱抵抗Ｒと比熱容量ｃ₁ の場合
熱拡散率α₁ を１．０×１０^-4ｍ² ／ｓ、ビオ数ｈを０．０１、第１層１６の層厚ΔＬ₁ を１．０×１０^-3ｍに固定し、熱抵抗Ｒと第１層１６の比熱容量ｃ₁ を独立変数として２乗偏差Ｓの構造を調べた。
熱抵抗Ｒを複数設定し、各熱抵抗Ｒに対して２乗偏差Ｓを最小とする比熱容量ｃ₁ を求めた。２乗偏差Ｓ、熱抵抗Ｒ、及び比熱容量ｃ₁ から構成される空間で、２乗偏差Ｓは熱抵抗Ｒ、比熱容量ｃ₁ からなる平面上に凹状の溝を構成する。この凹溝上の各熱抵抗Ｒに対する２乗偏差Ｓの最小値の変化挙動を図６に、比熱容量ｃ₁ に対する２乗偏差Ｓの最小値の変化挙動を図７に示す。２乗偏差Ｓを最小とする熱抵抗Ｒは５．２４３×１０^-3（ｍ² Ｋ／Ｗ）、比熱容量ｃ₁ は７．６３０３×１０^-1（ｋＪ／ｋｇ／Ｋ）と求まり、それぞれの精度は１６．３％、−２３．７％である。
【００３８】
（４）測定対象が熱抵抗Ｒ、比熱容量ｃ₁ 及びビオ数ｈの場合
熱抵抗Ｒ、比熱容量ｃ₁ にビオ数ｈを加えて独立変数を３変数として、２乗偏差Ｓの構造を調べた。複数のビオ数ｈを設定し、各ビオ数ｈに対して２乗偏差Ｓを最小とする熱抵抗Ｒ、比熱容量ｃ₁ を求める。それぞれのビオ数ｈに対する２乗偏差Ｓの最小値とその点における熱抵抗Ｒ、比熱容量ｃ₁ を求めた。２乗偏差Ｓの最小値のビオ数ｈに対する変化を図８に示す。これより２乗偏差Ｓの最小値を与える熱抵抗Ｒは１．１８２０×１０^-3（ｍ² Ｋ／Ｗ）、比熱容量ｃ₁ は２．５７９１×１０^-1（ｋＪ／ｋｇ／Ｋ）、及びビオ数ｈは１．３２×１０^-2と求まり、熱抵抗Ｒの精度は３２％、比熱容量ｃ₁ の精度は−７４．２％、ビオ数ｈの精度は−１６２％である。
【００３９】
（５）測定対象が熱抵抗Ｒと層厚ΔＬ₁ の場合
第１層１６の熱拡散率α₁ を１．０×１０^-4ｍ² ／ｓ、比熱容量ｃ₁ を１．０（ｋＪ／ｋｇ／Ｋ）、ビオ数ｈを０．０１と固定し、熱抵抗Ｒと第１層１６の層厚ΔＬ₁ を独立変数として２乗偏差Ｓの構造を調べた。
２乗偏差Ｓ、熱抵抗Ｒ、及び第１層１６の層厚ΔＬ₁ から構成される空間で、２乗偏差Ｓは熱抵抗Ｒ、第１層１６の層厚ΔＬ₁ からなる平面上に凹状の溝を構成する。２乗偏差Ｓの最小値の熱抵抗Ｒに対する変化を図９に、２乗偏差Ｓの最小値の第１層１６の層厚ΔＬ₁ に対する変化を図１０に示す。これより２乗偏差Ｓを最小とする熱抵抗Ｒは４．５２６×１０^-3（ｍ² Ｋ／Ｗ）、第１層１６の層厚ΔＬ₁ は９．９７３×１０^-4（ｍ）と求まり、それぞれの精度は０．４０％、０．２７％である。
【００４０】
（６）測定対象が熱抵抗Ｒ、層厚ΔＬ₁ 及びビオ数ｈの場合
熱抵抗Ｒと層厚ΔＬ₁ にビオ数ｈを独立変数として加えた３変数の場合における２乗偏差Ｓの構造を調べる。ビオ数ｈを複数設定し、各ビオ数ｈに対して２乗偏差Ｓを最小とする熱抵抗Ｒ、第１層１６の層厚ΔＬ₁ を求める。それぞれのビオ数ｈに対し２乗偏差Ｓの最小値とその点における熱抵抗Ｒ、第１層１６の層厚ΔＬ₁ を求めた。各ビオ数ｈに対して求めた２乗偏差Ｓの最小値のビオ数ｈに対する依存性を図１１に示す。２乗偏差Ｓを最小とする熱抵抗Ｒは４．７５１×１０^-3（ｍ² Ｋ／Ｗ）、第１層１６の層厚ΔＬ₁ は９．８７９×１０^-4（ｍ）、ビオ数ｈは０．０１３と求まり、熱抵抗Ｒの精度は５．３９％、層厚ΔＬ₁ の精度は−１．２１％、及びビオ数ｈの精度は３０％である。
【００４１】
なお、熱抵抗Ｒと第１層の熱物性の同時解析を行なう際に、熱抵抗Ｒとビオ数ｈを独立変数とする２変数の場合、熱抵抗Ｒと熱拡散率α₁ と比熱容量ｃ₁ 、熱抵抗Ｒと熱拡散率α₁ と第１層１６の層厚ΔＬ₁ 、熱抵抗Ｒと比熱容量ｃ₁ と第１層１６の層厚ΔＬ₁ を独立変数とする３変数の場合についても、同様に精度を調べることができるが詳細な説明は省略する。更に、熱拡散率α₁ 、比熱容量ｃ₁ 、第１層１６の層厚ΔＬ₁ 、及びビオ数ｈの中から任意に選択した３項目と熱抵抗Ｒを独立変数とした４変数の場合、熱抵抗Ｒ、熱拡散率α₁ 、比熱容量ｃ₁ 、第１層１６の層厚ΔＬ₁ 、及びビオ数ｈを独立変数とした５変数の場合にも、同様に精度を調べることができが、これらの場合についても詳細な説明は省略する。
以上は、第２層２０の熱物性値と層厚ΔＬ₂ がすべて既知で、かつ第１層の熱物性値と層厚ΔＬ₁ の一部が既知の場合に、積層材１５の熱抵抗Ｒとビオ数ｈ、及び第１層の未知数の値を求めることに関しての積層材の熱特性評価方法について説明した。この積層材の熱特性評価方法は、第２層２０の熱物性値と層厚ΔＬ₂ がすべて既知で、かつ第１層の熱物性値と層厚ΔＬ₁ がすべて未知数の場合、第１層の熱物性値と層厚ΔＬ₁ がすべて既知で、かつ、第２層の熱物性値と層厚ΔＬ₂ の一部が既知の場合、第１層の熱物性値と層厚ΔＬ₁ がすべて既知で、かつ第２層の熱物性値と層厚ΔＬ₂ がすべて未知数の場合に対しても適用可能である。
【００４２】
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、発明の要旨を変更しない範囲での変更は可能であり、前記したそれぞれの実施の形態や変形例の一部又は全部を組み合わせて本発明の熱抵抗を有する積層材の熱特性評価方法及びその装置を構成する場合も本発明の権利範囲に含まれる。例えば、本実施の形態では板状の積層材について説明したが、円筒状の積層材で１次元熱伝導近似が成立する場合にも適用できる。また、積層材の熱特性評価装置におけるパルス加熱手段としてレーザーパルスを使用したが、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てもよい。
【００４３】
【発明の効果】
請求項１〜６記載の熱抵抗を有する積層材の熱特性評価方法においては、積層材の一側の表面を瞬間的に加熱したときの積層材の他側の表面の実測表面温度を求める第１工程と、積層材の一側の表面を瞬間的に加熱したときの積層材の他側の表面の理論表面温度を、境界条件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、積層材を構成する各層の熱物性及び層厚の中の一部が未知数であるとして、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、ビオ数、及び未知数の値を求める第３工程とを有するので、層間熱抵抗が無視できない積層材の層間熱抵抗と各層の未知数の値を同時にしかも高精度で測定することが可能となる。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。
【００４４】
特に、請求項２記載の熱抵抗を有する積層材の熱特性評価方法においては、未知数が一方の層の熱物性及び層厚であるので、また請求項３記載の熱抵抗を有する積層材の熱特性評価方法においては、未知数が一方の層の熱物性及び層厚の中の一部であるので、積層材を構成する各層の熱物性及び層厚の中で既知であるものを用いて未知数を決定でき、積層材の熱抵抗、ビオ数、並びに未知数の値を精度よく決定することができる。
【００４５】
請求項４記載の熱抵抗を有する積層材の熱特性評価方法においては、理論表面温度は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でき、熱抵抗、ビオ数、未知数の値を高精度で求めることが可能となる。また、偏差が実測表面温度をラプラス変換したラプラス変換温度と計算値の２乗偏差であるので、熱抵抗、ビオ数、未知数の値の決定に必要な計算量を大幅に低下させることができ、短時間で熱抵抗、ビオ数、未知数の値を求めることができる。更に、測定から熱抵抗、ビオ数、未知数の値の決定までを自動化することが可能となる。
【００４６】
請求項５記載の熱抵抗を有する積層材の熱特性評価方法においては、２乗偏差を最小とする条件を、熱抵抗、ビオ数、及び未知数を独立変数として、各独立変数毎に求めるので、熱抵抗、ビオ数、及び未知数の値をそれぞれ直接、高精度で決定することが可能となる。
【００４７】
請求項６記載の熱抵抗を有する積層材の熱特性評価方法においては、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に、熱抵抗、ビオ数、及び未知数を独立変数として、各独立変数毎に求めるので、独立変数の個数が１つ減少して計算量を大幅に減少させることができ、熱抵抗、ビオ数、及び未知数の値を更に短時間に高精度で決定することができる。
【００４８】
請求項７〜９記載の熱抵抗を有する積層材の熱特性評価装置においては、第１層と第２層を備え、第１層と第２層との間に層間部が存在する板状の積層材の一側の表面を瞬間的に加熱するパルス加熱手段と、積層材の他側の表面の実測表面温度を求める温度測定手段と、積層材を構成する各層の熱物性及び層厚の中の一部が未知数であるとして、一側の表面が瞬間的に加熱されたときの他側の表面の理論表面温度を求め理論表面温度と実測表面温度の偏差を最小とする条件から、層間部に存在する熱抵抗、ビオ数、及び未知数の値を求める演算処理部とを有するので、例えば、基材と膜との間の層間熱抵抗が無視できない積層材の膜の熱物性（熱拡散率、比熱容量、熱伝導率）、層間熱抵抗、及びビオ数を同時に、高精度で求めることが可能となる。また、微小サイズの試料を用いて測定を行なうことが可能となる。
【００４９】
特に、請求項８記載の熱抵抗を有する積層材の熱特性評価装置においては、未知数が一方の層の熱物性及び層厚であるので、請求項９記載の熱抵抗を有する積層材の熱特性評価装置においては、未知数が一方の層の熱物性及び層厚の中の一部であるので、積層材を構成する各層の熱物性及び層厚の中で既知であるものを用いるて未知数を決定でき、積層材の熱抵抗、ビオ数、並びに未知数の値を精度よく決定することができる。
【図面の簡単な説明】
【図１】本発明の一実施の形態に係る熱抵抗を有する積層材の熱特性評価装置の説明図である。
【図２】熱抵抗と熱拡散率を測定対象としたときの２乗偏差の凹溝の熱抵抗と熱拡散率から構成される平面に対する投影図である。
【図３】熱抵抗と熱拡散率を測定対象としたときの２乗偏差の凹溝の熱拡散率と２乗偏差から構成される平面に対する投影図である。
【図４】熱抵抗と熱拡散率を測定対象としたときの２乗偏差の凹溝の熱抵抗と２乗偏差から構成される平面に対する投影図である。
【図５】熱抵抗、熱拡散率、及びビオ数を測定対象としたときの２乗偏差の最小値のビオ数と２乗偏差から構成される平面に対する投影図である。
【図６】熱抵抗と比熱容量を測定対象としたときの熱抵抗に対する２乗偏差の変化挙動を示す説明図である。
【図７】熱抵抗と比熱容量を測定対象としたときの比熱容量に対する２乗偏差の変化挙動を示す説明図である。
【図８】熱抵抗、比熱容量及びビオ数を測定対象としたときの２乗偏差の最小値のビオ数依存性を示す説明図である。
【図９】熱抵抗と第１層の層厚を測定対象としたときの熱抵抗に対する２乗偏差の変化挙動を示す説明図である。
【図１０】熱抵抗と第１層の層厚を測定対象としたときの第１層の層厚に対する２乗偏差の変化挙動を示す説明図である。
【図１１】熱抵抗、第１層の層厚及びビオ数を測定対象としたときのビオ数に対する２乗偏差の変化挙動を示す説明図である。
【図１２】ニュートン法における処理フローを示す説明図である。
【図１３】２乗偏差値の大小関係から最小値を求める際の処理フローを示す説明図である。
【符号の説明】
１０：レーザーフラッシュ装置、１１：レーザーパルス、１２：パルス加熱手段、１３：パルス検出手段、１４：レーザーパルス、１５：積層材、１６：第１層、１７：表面、１８：レーザーパルス、１９：ハーフミラー、２０：第２層、２１：表面、２２：温度測定手段、２３：演算処理部、２４：出力手段、２５：試料ホルダー、２６：理論表面温度演算手段、２７：ラプラス変換手段、２８：２乗偏差演算手段、２９：２乗偏差最小化手段[0001]
BACKGROUND OF THE INVENTION
The present invention relates to a method for evaluating the thermal properties of a laminated material having a thermal resistance in which the interlayer thermal resistance of the laminated material, the thermal properties of the layer and the layer thickness are measured simultaneously using, for example, a laser flash method under unsteady conditions, and the method Relates to the device.
[0002]
[Prior art]
Laminate with a coating film formed on the surface of the structural material for the purpose of improving the oxidation resistance, thermal insulation performance or wear resistance of the structural material, or forming the functional film on the semiconductor surface found in semiconductor elements It is necessary to evaluate the thermal properties of the laminated material in order to confirm the performance of the laminated material.
Conventionally, the thermal characteristics of these laminated materials have been evaluated by the following method. For example, if the interlayer thermal resistance between a base material such as a structural material or a semiconductor and a film formed thereon can be ignored and the base material and the film can be separated, the respective thermophysical properties are measured individually. Based on this value, the thermal characteristics of the laminated material were obtained by calculation. If the interlayer thermal resistance between the substrate and the film is negligible and the substrate and the film cannot be separated, the thermal properties of only the substrate are measured first, and then, for example, a laser flash method is performed. The thermal properties of the film were measured by the multilayer material analysis method used, and the thermal properties of the laminate were determined by calculation using the obtained substrate and film thermal properties. Furthermore, when the interlayer thermal resistance between the substrate and the film cannot be ignored, the thermal properties of the substrate and the film are measured first, then the laminated material is measured by the laser flash method, and the interlayer thermal resistance is analyzed. The thermal properties of the laminate were determined by calculation from the thermal properties of the substrate and film and the interlayer thermal resistance.
[0003]
[Problems to be solved by the invention]
However, the interlayer thermal resistance between the base material and the film cannot be ignored, and in the case of a laminated material that cannot separate the base material and the film, the conventional thermal property evaluation method for the laminated material cannot be applied. It was impossible to evaluate the thermal characteristics of the laminated material. Even when the thermal properties can be measured by separating the substrate and the film, if the thermal characteristics can be measured in the form of the laminated material, the thermal characteristics of the laminated material can be efficiently evaluated. It becomes possible.
The present invention has been made in view of such circumstances, and a laminated material having a thermal resistance capable of simultaneously measuring an interlayer thermal resistance of a laminated material in which an interlayer thermal resistance cannot be ignored and a thermal property of the layer under an unsteady state. It is an object of the present invention to provide a thermal property evaluation method and apparatus therefor.
[0004]
[Means for Solving the Problems]
The thermal property evaluation method for a laminated material having thermal resistance according to the present invention in accordance with the above object includes a first layer and a second layer, and thermal resistance exists in an interlayer portion between the first layer and the second layer. A method for evaluating the thermal properties of a laminated material for obtaining thermal properties of a plate-shaped laminated material, wherein the measured surface temperature of the other surface of the laminated material when the surface of one side of the laminated material is instantaneously heated. The first step to be calculated, and the theoretical surface temperature of the other surface of the laminated material when the surface of one side of the laminated material is instantaneously heated is calculated from the solution of the unsteady heat conduction equation considering the boundary conditions From the condition that the deviation between the measured surface temperature and the theoretical surface temperature is minimized, assuming that a part of the thermophysical properties and layer thicknesses of each layer constituting the laminated material is an unknown number. , And a third step of obtaining values of the thermal resistance, the bio number, and the unknown.
[0005]
The surface of one side of the laminated material is instantaneously heated, and the temperature of the other side at that time is measured in an unsteady state. For this reason, the time required for the measurement can be made very short, and as a result, the temperature change reflecting the thermal characteristics of the laminated material can be accurately measured without being influenced by the surrounding disturbance. In addition, when the surface of one side of the laminated material is instantaneously heated, the temperature of the other side is solved by solving the unsteady heat conduction equation considering the heating conditions and boundary conditions. The theoretical surface temperature can be obtained by calculation in a form including the thermal properties (for example, thermal diffusivity, thermal conductivity, specific heat capacity) and layer thickness of each layer as variables.
For this reason, if some of the thermophysical properties and layer thicknesses of each layer constituting the laminated material are unknown, the theoretical surface temperature is calculated by changing the thermal resistance, bionumber, and this unknown, thereby calculating the theoretical surface. The temperature can be matched to the measured surface temperature. Therefore, when the theoretical surface temperature matches the measured surface temperature, the values of the thermal resistance, the number of bioses, and the unknown are the thermal resistance of the interlayer part of the laminated material, the number of bios of the laminated material, and the unknowns obtained from this laminated material. Can be considered as the value of.
Here, since the coincidence between the theoretical surface temperature and the measured surface temperature is determined from the condition where the deviation between the measured surface temperature and the theoretical surface temperature is minimized, the thermal resistance, the number of bioses, and the repeated calculation using the unknowns as parameters, The values of thermal resistance, bio number and unknown can be determined respectively.
[0006]
In the thermal property evaluation method for a laminate having thermal resistance according to the present invention, the unknown may be a thermal property and a layer thickness of one layer, or a part of a thermal property and a layer thickness of one layer. it can.
When the unknown is the thermophysical property and layer thickness of one layer, the thermal resistance, bionumber, thermophysical property and layer thickness of one layer are calculated using the known values of the thermophysical property and layer thickness of the other layer. Can be determined. In addition, when the unknown is a part of the thermophysical property and layer thickness of one layer, the known values of the thermophysical property and layer thickness of the other layer and the thermophysical property and layer thickness of one layer are known. Can be used to determine the value, thermal resistance, and bio number of one of the thermophysical properties and thickness of one layer that are unknown.
[0007]
In the thermal property evaluation method for a laminated material having thermal resistance according to the present invention, the theoretical surface temperature is a calculated value based on an analytical solution obtained by Laplace transforming the unsteady heat conduction equation, and the deviation is the actual measurement. It is preferable to set the Laplace conversion temperature obtained by converting the surface temperature to the Laplace conversion and the square deviation of the calculated value.
[0008]
By performing Laplace transform, an unsteady heat conduction equation having boundary conditions can be easily solved analytically. Since the solution of the unsteady heat conduction equation is obtained in the Laplace space, the measured surface temperature of the surface on the other side is Laplace converted to the Laplace conversion temperature so that the square deviation can be calculated. In addition, since the values of thermal resistance, bio number, and unknown number are determined from the condition that minimizes the square deviation, the amount of calculation required to determine the values of thermal resistance, bio number, and unknown number is greatly reduced. Can do.
[0009]
When thermal energy Q (t) is instantaneously supplied to the surface on the first layer side of the laminated material, the theoretical surface temperature T in the Laplace space on the surface on the second layer side of the laminated material ₂ (L ₂ , P) is expressed by equation (1). Where α ₁ Is the thermal diffusivity of the first layer, c ₁ Is the specific heat capacity of the first layer, ρ ₁ Is the density of the first layer, k ₁ Is the thermal conductivity of the first layer (= ρ ₁ c ₁ α ₁ ), ΔL ₁ Is the thickness of the first layer, α ₂ Is the thermal diffusivity of the second layer, c ₂ Is the specific heat capacity of the second layer, ρ ₂ Is the density of the second layer, k ₂ Is the thermal conductivity of the second layer (= ρ ₂ c ₂ α ₂ ), ΔL ₂ Is the thickness of the second layer, h ₀ Is the number of bios on the surface of the first layer, h ₁ Is the number of bios on the second layer side, L ₂ Is the thickness of the laminate (= ΔL ₁ + ΔL ₂ ), R is the interlayer thermal resistance, p is the Laplace variable, r = (p / α) ^1/2 It is.
[0010]
[Expression 1]

[0011]
Here, the thermal diffusivity α of the second layer ₂ , Specific heat capacity c of the second layer ₂ , Density ρ of the second layer ₂ , Thermal conductivity k of the second layer ₂ , And two-layer thickness ΔL ₂ Is known, the theoretical surface temperature T of the surface on the second layer side of the laminated material ₂ (L ₂ , P), the expression (1) may be considered as the expression (2), and the theoretical surface temperature T ₂ (L ₂ , P) is the thermal diffusivity α of the first layer ₁ , Volumetric heat capacity of the first layer (ρ ₁ c ₁ ), Layer thickness ΔL of the first layer ₁ , Interlayer thermal resistance R, bio number (h ₁ , H ₂ ) Function. Theoretical surface temperature T ₂ (L ₂ , P), the specific heat capacity of each layer always appears in the form of volumetric heat capacity, which is the product of the density. Therefore, in the following, the density is fixed and the specific heat capacity is considered as a variable instead of the volumetric heat capacity.
[0012]
[Expression 2]

[0013]
Note that the square deviation S is a plurality of Laplace variables p as shown in equation (3). _i Consists of the sum of Where E _i Is the measured surface temperature of the surface on the second layer side. _i The Laplace transform.
[0014]
[Equation 3]

[0015]
In the thermal property evaluation method for a laminated material having thermal resistance according to the present invention, the condition for minimizing the square deviation is defined as the thermal resistance, the bio number, and the unknown number as independent variables for each independent variable. Can be sought.
The thermal resistance, the number of bios, and the unknown are each independent variables, and for each independent variable, the value of the independent variable when the value of the square deviation is minimum is obtained. Decide each.
[0016]
Examples of a method for obtaining a variable that gives the minimum value of the square deviation include a Newton method and a method for obtaining a variable that gives the minimum value by comparing the magnitudes of the square deviation values.
In the Newton method, when the square deviation is S and the independent variable is x, the value of the square deviation at that time is calculated while sequentially changing the independent variable x in the direction in which the square deviation S is reduced, and the minimum value Is what you want. For example, as shown in FIG. 12, first, as an independent variable value, an initial value x ₀ (Step S1), a square deviation S is calculated (step S2), and it is determined whether the value of the square deviation S is less than a preset value ε (step S3). If the value of the square deviation S is less than the preset value ε, the value of the independent variable at that time is adopted as a condition for minimizing the square deviation S (step S4). If the value of the square deviation S is greater than or equal to the preset value ε, the initial value x ₀ Is changed by a small amount Δx (step S5), a square deviation S is obtained (step S2), and it is determined whether the value of the square deviation S is less than a preset value ε (step S3). The steps S2, S3, and S5 are repeated until the value of the square deviation S is less than a preset value ε.
[0017]
The method of finding the variable that gives the minimum value by comparing the magnitudes of the square deviation values is to set a plurality of independent variables, calculate the square deviation S for each, and determine the minimum value to determine the square deviation An independent variable that gives the minimum value of S is obtained. For example, as shown in FIG. ₀ ~ X _n (N is 3 or more) is set so that each difference becomes Δx (where Δx> 0) (step S11). Then each independent variable x ₀ ~ X _n Respectively, the square deviation S is calculated, and the minimum square deviation S is calculated. _min (X _k ) Is less than a preset value ε (step S12). And the square deviation S _min (X _k ) Is less than a preset value ε, the square deviation S _min (X _k ) Is terminated, and the value of the independent variable at that time is adopted as a condition for minimizing the square deviation S (step S13).
[0018]
Squared deviation S _min (X _k ) Is greater than or equal to ε, and the square deviation S _min (X _k ) Is the independent variable x ₀ In the case of ₁ Is the maximum value of the independent variables, and n independent variables y so that each difference becomes Δx. _i And set this y _i X _i (Step S14). Also, the square deviation S _min (X _k ) Is the independent variable x _k (X ₀ Over x _n Less than x) _km (M is 1 or more) is the minimum value of the independent variable, x _{k + m} Each value y obtained by dividing n by the maximum value of the independent variable _i Is set as an independent variable, and this y _i X _i (Step S15). Or square deviation S _min (X _k ) Is the independent variable x _n X _n-1 Is the minimum value of the independent variables and n independent variables y so that each difference becomes Δx. _i Set y _i X _i (Step S16).
Then each newly set x _i The square deviation S is calculated for the minimum square deviation S _min (X _k ) Is less than a preset value ε (step S12). And the square deviation S _min (X _k Steps S12 and S14 to S16 are repeated until the value of) becomes less than a preset value ε.
[0019]
In the thermal property evaluation method for a laminated material having thermal resistance 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. Alternatively, it may be obtained under an additional condition in which the theoretical damping time constant is equivalent.
By providing an additional condition, the number of independent variables consisting of thermal resistance, number of bios, and unknowns can be reduced by one, greatly increasing the amount of calculation for finding each independent variable that minimizes the square deviation Can be reduced.
[0020]
Since heat is dissipated from the surface of the laminated material, the maximum temperature exists when the back surface temperature changes, and the temperature gradually decreases after the maximum temperature. Measured surface temperature T in this attenuation region ₂ The change in is represented by T, where τ is the actual decay time constant and t is the time. ₂ ∝exp (−t / τ). Therefore, the measured surface temperature T ₂ The actual decay time constant τ can be obtained from the above measurement. On the other hand, theoretical damping time constant τ _th Is expressed by equation (4). Therefore, the measured decay time constant τ and the theoretical decay time constant τ _th It is possible to create an additional condition by making the values equal.
[0021]
[Expression 4]

[0022]
A thermal property evaluation apparatus for a laminated material having a thermal resistance according to the present invention that meets the above-mentioned object includes a first layer and a second layer, and an interlayer portion exists between the first layer and the second layer. Pulse heating means for instantaneously heating the surface of one side of the laminated material, temperature measuring means for determining the measured surface temperature of the other surface of the laminated material, thermophysical properties of each layer constituting the laminated material, and Assuming that a part of the layer thickness is unknown, the theoretical surface temperature of the surface on the other side when the surface on the one side is heated instantaneously is obtained, and the deviation between the theoretical surface temperature and the measured surface temperature is calculated. And an arithmetic processing unit for obtaining values of the thermal resistance, the bio number, and the unknown number existing in the interlayer portion from the minimum condition.
Further, in the thermal property evaluation apparatus for a laminated material having thermal resistance according to the present invention, the unknown is one of the thermophysical properties and layer thickness of one layer, or the unknown is one of the thermophysical properties and layer thickness of one layer. Part.
[0023]
By providing a pulse heating means for instantaneously heating the surface on one side of the laminated material, measurement in an unsteady state becomes possible. Further, by providing a temperature measuring means for measuring the temperature of the surface on the other side of the laminated material, the surface temperature can be accurately measured. In addition, since an arithmetic processing unit is provided, it is possible to continuously record the measured actual temperature of the measured surface on the other side, calculate the theoretical surface temperature, calculate the deviation, and determine the conditions that minimize the deviation. , Thermal resistance, bio number, and unknown value can be obtained respectively. Here, when the unknown is the thermophysical property and the layer thickness of one layer, the thermal resistance, the bio number, the thermophysical property of one layer and The layer thickness is determined. In addition, when the unknown is a part of the thermophysical property and layer thickness of one layer, the known values of the thermophysical property and layer thickness of the other layer and the thermophysical property and layer thickness of one layer are known. Is used to determine the value, thermal resistance, and bio number of one of the thermophysical properties and thickness of one layer that are unknown.
[0024]
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.
FIG. 1 is an explanatory diagram of a thermal property evaluation apparatus for a laminated material having thermal resistance according to an embodiment of the present invention, and FIG. 2 is a square deviation when measuring thermal resistance and thermal diffusivity. FIG. 3 is a projection diagram of a plane composed of the thermal resistance and thermal diffusivity of the concave groove, and FIG. 3 is composed of the thermal diffusivity and square deviation of the concave groove when the thermal resistance and thermal diffusivity are measured. FIG. 4 is a projection view on a plane composed of the square-shaped deviation groove thermal resistance and the square deviation when the thermal resistance and thermal diffusivity are measured, and FIG. 5 is the thermal resistance. , Thermal diffusivity, and projection number on the plane composed of the squared deviation of the number of squares and the deviation when the number of bios is the measurement target, FIG. 6 is the measurement target thermal resistance and specific heat capacity 7 is an explanatory diagram showing the change behavior of the square deviation with respect to the thermal resistance, and FIG. FIG. 8 is an explanatory diagram showing the dependence of the minimum value of the square deviation on the bio number when the thermal resistance, the specific heat capacity, and the bio number are measured. FIG. 9 is an explanatory diagram showing a change behavior of the square deviation with respect to the thermal resistance when the thermal resistance and the layer thickness of the first layer are measured, and FIG. 10 is a diagram showing the thermal resistance and the layer thickness of the first layer as a measurement target. FIG. 11 is a diagram illustrating the change behavior of the square deviation with respect to the layer thickness of the first layer, and FIG. 11 shows the square deviation with respect to the bio number when the thermal resistance, the layer thickness of the first layer, and the number of bios are measured. It is explanatory drawing which shows a change behavior.
[0025]
As shown in FIG. 1, a laser flash device 10 which is an example of a thermal property evaluation apparatus for a laminated material having thermal resistance according to an embodiment of the present invention includes a pulse heating means 12 for generating a laser pulse 11, and a generation A half mirror 19 for distributing the laser pulse 11 to the laser pulse 14 directed to the pulse detection means 13 for detecting the laser pulse waveform and the laser pulse 18 for irradiating the surface 17 of the first layer 16 on one side of the laminate 15. Have. In addition, the laser flash device 10 includes a temperature measurement unit 22 that measures the temperature of the surface 21 of the second layer 20 on the other side of the laminated material 15 irradiated with the laser pulse 18, and a signal and temperature from the pulse detection unit 13. A signal from the measuring means 22 is input, for example, the thermal properties and the layer thickness ΔL of the second layer 20 of the laminated material 15. ₂ Is known, the thermal resistance and bio number of the laminated material 15, the thermal properties and the layer thickness ΔL of the first layer 16. ₁ And an output means 24 for displaying a calculation result obtained by the calculation processing unit 23. Hereinafter, these will be described in detail.
[0026]
The pulse heating means 12 uses, for example, a ruby laser oscillator that can inject thermal energy exceeding the thermal fluctuation of the atmosphere into the surface 17 on the first layer 16 side even when the laminated material 15 is held in a high temperature atmosphere. can do. The size of the laminated material 15 is determined by the size of the sample holder 25 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 19 has a configuration in which a coating layer that reflects a predetermined amount of light from an incident ruby laser is provided on the surface of a substrate having a material with a very low ruby laser absorptivity and extremely high transmittance. For example, 50% of the amount of incident ruby laser light can be reflected and 50% can be transmitted. Therefore, by adjusting the optical axis of the light receiving portion of the pulse detecting means 13 so that the laser generated from the pulse heating means 12 is reflected by the half mirror 19 and reaches the light receiving portion of the pulse detecting means 13, the pulse heating means 12 A part of the emitted laser pulse 11 can be introduced into the pulse detection means 13 and the waveform of the laser pulse 11 can be measured by the pulse detection means 13. Further, by aligning the optical axis of the laser pulse 18 generated from the pulse heating means 12 and transmitted through the half mirror 19 with the central axis of the laminated material 15, the surface 17 on the first layer 16 side of the laminated material 15 is laser-pulsed. 18 can reliably irradiate. With this configuration, when the surface 17 on the first layer 16 side of the laminated material 15 is irradiated with the laser pulse 18, the temperature change of the surface 21 on the second layer 20 side of the laminated material 15 is one-dimensional unsteady. It can be expressed by a heat conduction equation.
[0027]
The temperature measurement means 22 needs to have a function capable of measuring the temperature change of the surface 21 on the second layer 20 side of the laminated material 15 irradiated with the laser pulse 18 at high speed and with high accuracy, for example, as a temperature detection sensor. A temperature measuring instrument equipped with a vessel can be used.
The arithmetic processing unit 23 reads the signal from the pulse detecting means 13 and reads the thermophysical property value and the layer thickness ΔL of the second layer 20. ₂ Is used to analytically solve the one-dimensional unsteady heat conduction equation from the boundary conditions of the laminated material 15 by Laplace transform to obtain the theoretical surface temperature of the surface 21 on the second layer 20 side of the laminated material 15. The function of calculating the Laplace conversion temperature by reading the signal of the measured surface temperature of the surface 21 on the second layer 20 side of the laminated material 15 from the theoretical surface temperature calculating means 26 and the temperature measuring means 22 and performing Laplace conversion of the measured surface temperature. The Laplace conversion means 27 provided with is provided. The arithmetic processing unit 23 includes a square deviation calculating means 28 having a function of calculating a square deviation of the Laplace conversion temperature and the theoretical surface temperature of the measured surface temperature of the surface 21 on the second layer 20 side, and the square deviation. From the minimum conditions, the thermal resistance and the number of bios of the laminated material 15, the thermal properties of the first layer 16 and the layer thickness ΔL ₁ And a square deviation minimizing means 29 having a function of obtaining and transmitting to the output means 24. And the arithmetic processing part 23 can be comprised by mounting the program which expresses said each function on a personal computer, for example. As the output means 24, for example, a display device for a personal computer or a printing machine can be used.
[0028]
Note that the thermal properties and the layer thickness ΔL of the second layer 20 of the laminated material 15 using the laser flash device 10. ₂ Are all known, and the thermal properties and thickness ΔL of the first layer 16 ₁ Even if a part of them is known, the arithmetic processing unit 23 uses the thermal resistance and the bio number of the laminated material 15 as well as the thermal properties and the layer thickness ΔL of the first layer 16. ₁ Each of the values of the unknowns can be obtained.
Further, using the laser flash device 10, the thermal properties of the first layer 16 and the layer thickness ΔL ₁ Are all known, the thermal resistance of the laminate 15 and the number of bios, as well as the thermal properties and layer thickness ΔL of the second layer 20. ₂ You can also ask for everything. Furthermore, the thermophysical properties of the first layer 16 and the layer thickness ΔL ₁ Are all known, and the thermal properties and layer thickness ΔL of the second layer 20 ₂ In the case where a part of them is known, the thermal resistance and the bio number of the laminated material 15 and the thermal properties and the layer thickness ΔL of the second layer 20 ₂ It is also possible to use the laser flash device 10 to determine the value of an unknown number.
[0029]
Next, the thermal property evaluation method for a laminated material having thermal resistance according to an embodiment of the present invention will be described in detail.
For example, a disk-shaped laminated material 15 having a diameter of 8 to 12 mm and a thickness of about 2 to 3 mm is created, and the first layer 16 is placed on the sample holder 25 provided in the sample chamber of the laser flash device 10, for example. Fix with the side up. The thermophysical properties of the second layer 20 and the layer thickness ΔL ₂ Is known.
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 11 is emitted from the pulse heating unit 12 toward the half mirror 19 when the laminated material 15 is stabilized at the predetermined temperature. To do. The emitted laser pulse 11 reaches the half mirror 19, and, for example, 50% of the light quantity of the laser pulse 11 is reflected by the half mirror 19 and reaches the pulse detection means 13, and the waveform of the laser pulse 11 is obtained. Is transferred to the arithmetic processing unit 23. Further, the laser pulse 18 transmitted through the half mirror 19 reaches the surface 17 on the first layer 16 side of the laminated material 15 and instantaneously heats the surface.
[0030]
When the surface 17 of the first layer 16 of the laminated material 15 is heated by the laser pulse 18, the heat at that time is conducted to the second layer 20 side, so that the temperature of the surface 21 on the second layer 20 side gradually increases. To do. However, since heat dissipation from the

front surfaces

17 and 21 of the laminated material 15 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, temperature measuring means 22 having an infrared detector, and the measured value is transferred to the arithmetic processing unit 23. In the arithmetic processing unit 23, first, the Laplace conversion means 27 records the measured surface temperature signal of the surface 21 on the second layer 20 side transferred from the temperature measuring means 22, and performs Laplace conversion of the measured surface temperature to perform Laplace conversion. Record the temperature (first step).
Next, the one-dimensional unsteady heat conduction equation is analytically solved by Laplace transform from the boundary conditions of the laminated material 15 in the theoretical surface temperature calculation means 26, and the surface 17 on the first layer 16 side is obtained by a signal from the pulse detection means 13. Is recorded, and the Laplacian conversion of the pulse waveform is performed, so that the thermal property values (thermal diffusivity, specific heat capacity) and layer thickness ΔL of the first layer 16 constituting the laminated material 15 are recorded. ₁ Of these, the unknowns are used as parameters, the thermal properties (thermal diffusivity, specific heat capacity) of the second layer 20 and the layer thickness ΔL of the second layer 20. ₂ , The thermophysical value of the first layer 16 and the layer thickness ΔL of the first layer 16 ₁ Among these, the theoretical surface temperature in the Laplace space of the surface 21 on the second layer 20 side is obtained using each of the known values (the second step).
Thereafter, the recorded Laplace conversion temperature of the actually measured surface temperature and the theoretical surface temperature in the Laplace space are transferred to the square deviation calculating means 28 to obtain the square deviation between the Laplace conversion temperature and the theoretical surface temperature. Then, the condition for minimizing the square deviation is obtained by the square deviation minimizing means 29, the thermal resistance and the number of bios existing in the interlayer portion of the first layer 16 and the second layer 20 of the laminated material 15, and the first Thermal properties of layer 16 and layer thickness ΔL of first layer 16 ₁ The unknown value is obtained, and the result is output to a display device for a personal computer or a printing machine, which is an example of the output means 24 (the third step).
[0031]
Subsequently, the thermal resistance and the bio number of the laminated material 15 determined by the thermal property evaluation method for the laminated material having thermal resistance according to the present embodiment, and the thermal properties (thermal diffusion) of the first layer 16 constituting the laminated material 15. Rate, specific heat capacity) and layer thickness ΔL ₁ The accuracy of will be described.
First, the time-series theoretical data of the temperature of the surface 21 on the second layer 20 side of the laminated material 15 composed of the first layer 16 and the second layer 20 having the thermal diffusivity, specific heat capacity, density, and layer thickness shown in Table 1 ( 1) Created by inverse Laplace transform of equation (1).
[0032]
[Table 1]

[0033]
Next, the thermal diffusivity α of the first layer 16 ₁ , Specific heat capacity c ₁ , And layer thickness ΔL ₁ Is the independent variable, and the thermal diffusivity α of the second layer 20 ₂ , Specific heat capacity c ₂ , And layer thickness ΔL ₂ Is known, the formula (1) that gives the temperature of the surface 21 on the second layer 20 side of the laminate 15 becomes the formula (2), and the square deviation S is expressed by the formula (3). Where E _i Is the time series theoretical data of the temperature of the surface 21 on the second layer 20 side of the laminate 15 composed of the

layers

16 and 20 having the physical property values shown in Table 1, and the Laplace variable p _i As Laplace transform.
In addition, when performing simultaneous analysis of the thermal resistance R and the thermophysical properties of the first layer 16, combinations of the thermal resistance R and other measurement objects are as shown in Table 2.
[0034]
[Table 2]

[0035]
(1) Measurement object is thermal resistance R and thermal diffusivity α ₁ in the case of
Specific heat capacity c of the first layer 16 ₁ , Layer thickness ΔL ₁ , Bio number h ₁ , The thermal resistance R and the thermal diffusivity α ₁ Is an independent variable, square deviation S, thermal diffusivity α ₁ , And and the thermal resistance R, the square deviation S is the thermal diffusivity α ₁ And a concave groove on a plane formed by the thermal resistance R. This groove has a thermal diffusivity α ₁ 2 is a projection of a square deviation S and a thermal diffusivity α. ₁ FIG. 3 shows a projection onto a plane made up of, and FIG. 4 shows a projection onto a plane made up of the square deviation S and the thermal resistance R, respectively.
Thermal resistance R and thermal diffusivity α ₁ Is a variable, the thermal resistance R giving the minimum value of the square deviation S and the thermal diffusivity α ₁ Is α ₁ = 1.0052 × 10 ^-Four (M ² / S), R = 4.517 × 10 ^-3 (M ² K / W), and the accuracy obtained from comparison with the theoretical data is 0.52% and 0.20%, respectively.
[0036]
(2) Measurement object is thermal resistance R, thermal diffusivity α ₁ , And when the number of bios is h
Next, the bio number h of the surface 17 on the first layer 16 side ₀ And the bio number h of the surface 21 on the second layer 20 side ₁ Are equal to each other, and the number h of bios is added as an independent variable, and the thermal resistance R of the square deviation S and the thermal diffusivity α ₁ , And bio number h ₁ Investigate the dependency on. The bio number h is changed in the range of 0.005 to 0.03, the minimum value of the square deviation S for each bio number h, the thermal resistance R at that point, and the thermal diffusivity α. ₁ Asked. FIG. 5 shows a projection on a plane composed of the minimum number of biodescriptions h of the square deviation S and the square deviation obtained for each bio number h. From this, the thermal resistance R that minimizes the square deviation S, the thermal diffusivity α ₁ , And the bio number h is α ₁ = 1.0220 × 10 ^-Four (M ² / S), R = 4.7385 × 10 ^-3 (M ² K / W), h = 1.32 × 10 ^-2 The respective accuracies are 2.2%, 5.11%, and 32%.
[0037]
(3) Measurement object is thermal resistance R and specific heat capacity c ₁ in the case of
Thermal diffusivity α ₁ 1.0 × 10 ^-Four m ² / S, bio number h is 0.01, layer thickness ΔL of first layer 16 ₁ 1.0 × 10 ^-3 m, the thermal resistance R and the specific heat capacity c of the first layer 16 ₁ Was used as an independent variable, and the structure of the square deviation S was examined.
Specific heat capacity c that sets a plurality of thermal resistances R and minimizes the square deviation S for each thermal resistance R ₁ Asked. Square deviation S, thermal resistance R, and specific heat capacity c ₁ The square deviation S is the thermal resistance R and the specific heat capacity c. ₁ A concave groove is formed on the plane formed by The change behavior of the minimum value of the square deviation S for each thermal resistance R on the concave groove is shown in FIG. ₁ The change behavior of the minimum value of the square deviation S with respect to is shown in FIG. The thermal resistance R that minimizes the square deviation S is 5.243 × 10. ^-3 (M ² K / W), specific heat capacity c ₁ Is 7.6303 × 10 ^-1 (KJ / kg / K) is obtained, and the respective accuracy is 16.3% and −23.7%.
[0038]
(4) Measurement object is thermal resistance R, specific heat capacity c ₁ And if the number of bios is h
Thermal resistance R, specific heat capacity c ₁ The structure of the square deviation S was examined by adding the bio number h to the three independent variables. A plurality of bio numbers h is set, and a thermal resistance R and a specific heat capacity c that minimize the square deviation S for each bio number h ₁ Ask for. Minimum value of square deviation S for each bio number h, thermal resistance R at that point, specific heat capacity c ₁ Asked. The change of the minimum value of the square deviation S with respect to the bio number h is shown in FIG. Accordingly, the thermal resistance R giving the minimum value of the square deviation S is 1.1820 × 10 ^-3 (M ² K / W), specific heat capacity c ₁ Is 2.5791 × 10 ^-1 (KJ / kg / K) and the bio number h is 1.32 × 10 ^-2 The accuracy of the thermal resistance R is 32% and the specific heat capacity c ₁ The accuracy of is -74.2%, and the accuracy of the bio number h is -162%.
[0039]
(5) Measurement object is thermal resistance R and layer thickness ΔL ₁ in the case of
Thermal diffusivity α of the first layer 16 ₁ 1.0 × 10 ^-Four m ² / S, specific heat capacity c ₁ Is fixed at 1.0 (kJ / kg / K), the bio number h is set at 0.01, the thermal resistance R and the layer thickness ΔL of the first layer 16 ₁ Was used as an independent variable, and the structure of the square deviation S was examined.
Square deviation S, thermal resistance R, and layer thickness ΔL of first layer 16 ₁ The square deviation S is the thermal resistance R and the layer thickness ΔL of the first layer 16. ₁ A concave groove is formed on the plane formed by FIG. 9 shows the change of the minimum value of the square deviation S with respect to the thermal resistance R. FIG. 9 shows the layer thickness ΔL of the first layer 16 of the minimum value of the square deviation S. ₁ The change with respect to is shown in FIG. Therefore, the thermal resistance R that minimizes the square deviation S is 4.526 × 10 6. ^-3 (M ² K / W), the layer thickness ΔL of the first layer 16 ₁ Is 9.973 × 10 ^-Four (M) is obtained, and the respective accuracies are 0.40% and 0.27%.
[0040]
(6) Measurement object is thermal resistance R, layer thickness ΔL ₁ And the number of bios h
Thermal resistance R and layer thickness ΔL ₁ The structure of the square deviation S in the case of three variables obtained by adding the number of bioses h as an independent variable is examined. A plurality of bio numbers h are set, the thermal resistance R that minimizes the square deviation S for each bio number h, and the layer thickness ΔL of the first layer 16 ₁ Ask for. The minimum value of the square deviation S for each bio number h, the thermal resistance R at that point, and the layer thickness ΔL of the first layer 16 ₁ Asked. FIG. 11 shows the dependence of the minimum value of the square deviation S obtained for each bio number h on the bio number h. The thermal resistance R that minimizes the square deviation S is 4.751 × 10. ^-3 (M ² K / W), the layer thickness ΔL of the first layer 16 ₁ Is 9.879 × 10 ^-Four (M), the bio number h is found to be 0.013, the accuracy of the thermal resistance R is 5.39%, and the layer thickness ΔL ₁ The accuracy of -1.21%, and the accuracy of the bio number h is 30%.
[0041]
When performing simultaneous analysis of the thermal resistance R and the thermophysical properties of the first layer, in the case of two variables with the thermal resistance R and the bio number h as independent variables, the thermal resistance R and the thermal diffusivity α ₁ And specific heat capacity c ₁ , Thermal resistance R and thermal diffusivity α ₁ And the layer thickness ΔL of the first layer 16 ₁ , Thermal resistance R and specific heat capacity c ₁ And the layer thickness ΔL of the first layer 16 ₁ In the case of three variables where is an independent variable, the accuracy can be examined in the same manner, but a detailed description is omitted. Furthermore, thermal diffusivity α ₁ , Specific heat capacity c ₁ The layer thickness ΔL of the first layer 16 ₁ , And four variables with three variables arbitrarily selected from the number of bioses and thermal resistance R as independent variables, thermal resistance R, thermal diffusivity α ₁ , Specific heat capacity c ₁ The layer thickness ΔL of the first layer 16 ₁ In the case of five variables with the bio number h as an independent variable, the accuracy can be examined in the same manner, but a detailed description of these cases is also omitted.
The above is the thermophysical value of the second layer 20 and the layer thickness ΔL. ₂ Are all known, the thermophysical value of the first layer and the layer thickness ΔL ₁ The method for evaluating the thermal properties of the laminated material in relation to obtaining the values of the thermal resistance R and the bio number h of the laminated material 15 and the unknown number of the first layer when a part of is known is described. The thermal property evaluation method of this laminated material is the thermophysical value of the second layer 20 and the layer thickness ΔL. ₂ Are all known, the thermophysical value of the first layer and the layer thickness ΔL ₁ Are all unknowns, the thermophysical value of the first layer and the layer thickness ΔL ₁ Are all known, and the thermophysical value of the second layer and the layer thickness ΔL ₂ Is known, the thermophysical value of the first layer and the layer thickness ΔL ₁ Are all known, and the thermophysical value of the second layer and the layer thickness ΔL ₂ This is also applicable to cases where all are unknowns.
[0042]
As mentioned above, although embodiment of this invention was described, this invention is not limited to this embodiment, The change in the range which does not change the summary of invention is possible, Each above-mentioned embodiment is possible. A case where a part or all of the forms and modifications are combined to constitute the thermal property evaluation method and apparatus for a laminated material having thermal resistance according to the present invention is also included in the scope of the present invention. For example, although a plate-shaped laminated material has been described in the present embodiment, the present invention can also be applied to a case where a one-dimensional heat conduction approximation is established with a cylindrical laminated material. Further, although the laser pulse is used as the pulse heating means in the thermal property evaluation apparatus for the laminated material, it is also possible to use pulse heating means using a halogen lamp such as a xenon lamp. Also, the condition for minimizing the square deviation can be obtained under the additional condition in which the measured decay time constant obtained from the change in the measured surface temperature and the theoretical decay time constant obtained from the change in the theoretical surface temperature are equal. Good.
[0043]
【The invention's effect】
In the thermal property evaluation method for a laminated material having thermal resistance according to claims 1 to 6, the measured surface temperature of the other side surface of the laminated material when the surface of one side of the laminated material is instantaneously heated is obtained. The first step and the theoretical surface temperature of the other surface of the laminated material when the surface of one side of the laminated material is instantaneously heated are calculated from the solution of the unsteady heat conduction equation considering the boundary conditions. Assuming that some of the thermophysical properties and layer thicknesses of each layer constituting the laminated material are unknowns, the thermal resistance, the number of bioses, and the conditions that minimize the deviation between the measured surface temperature and the theoretical surface temperature, And the third step for obtaining the unknown value, the interlayer thermal resistance of the laminated material where the interlayer thermal resistance cannot be ignored and the unknown value of each layer can be measured simultaneously and with high accuracy. 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.
[0044]
In particular, in the thermal property evaluation method for a laminated material having thermal resistance according to claim 2, since the unknown is the thermal property and the layer thickness of one layer, the heat of the laminated material having thermal resistance according to claim 3 is also used. In the characteristic evaluation method, since the unknown is a part of the thermophysical property and layer thickness of one layer, the unknown is calculated using the known thermophysical property and layer thickness of each layer constituting the laminated material. It is possible to determine the thermal resistance, the bio number, and the unknown value of the laminated material with high accuracy.
[0045]
In the thermal property evaluation method for a laminated material having thermal resistance according to claim 4, since the theoretical surface temperature is a calculated value based on an analytical solution obtained by Laplace transform of an unsteady heat conduction equation, a strict analytical solution is obtained. Since it is obtained, the theoretical surface temperature can be obtained easily and accurately, and the values of the thermal resistance, bio number, and unknown can be obtained with high accuracy. In addition, since the deviation is the square deviation of the Laplace conversion temperature obtained by Laplace conversion of the measured surface temperature and the calculated value, the amount of calculation required to determine the values of the thermal resistance, the number of bioses, and the unknown can be greatly reduced. The values of thermal resistance, bios and unknowns can be obtained in a short time. Furthermore, it is possible to automate from measurement to determination of thermal resistance, number of bios and unknown values.
[0046]
In the thermal property evaluation method of the laminated material having thermal resistance according to claim 5, because the condition for minimizing the square deviation is determined for each independent variable with the thermal resistance, bio number, and unknown as independent variables, It becomes possible to determine the values of the thermal resistance, the number of bioses, and the unknowns directly and with high accuracy.
[0047]
In the thermal property evaluation method of the laminated material having thermal resistance according to claim 6, 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. Under the additional condition that the theoretical damping time constant is the same value, the thermal resistance, the number of bioses, and the unknowns are determined as independent variables for each independent variable, so the number of independent variables is reduced by one and the amount of calculation is reduced. The value of the thermal resistance, the number of bios, and the unknown can be determined with higher accuracy in a shorter time.
[0048]
In the thermal property evaluation apparatus for a laminated material having thermal resistance according to claim 7 to 9, the apparatus has a plate-like shape including a first layer and a second layer, and an interlayer portion is present between the first layer and the second layer. Pulse heating means for instantaneously heating the surface on one side of the laminated material, temperature measuring means for determining the measured surface temperature of the other surface of the laminated material, and the thermal properties and layer thickness of each layer constituting the laminated material If the surface of one side is heated instantaneously, the theoretical surface temperature of the other surface is obtained and the interlayer part is determined from the condition that minimizes the deviation between the theoretical surface temperature and the measured surface temperature. Therefore, for example, the thermal properties (thermal diffusivity) of the laminated material film in which the interlayer thermal resistance between the substrate and the film cannot be ignored. , Specific heat capacity, thermal conductivity), interlaminar thermal resistance, and number of bios can be determined simultaneously with high accuracy It made. In addition, measurement can be performed using a sample of a minute size.
[0049]
In particular, in the thermal property evaluation apparatus for a laminated material having a thermal resistance according to claim 8, since the unknown is the thermal property and the layer thickness of one layer, the thermal characteristics of the laminated material having a thermal resistance according to claim 9 In the evaluation device, the unknown is a part of the thermophysical property and layer thickness of one layer, so the unknown is determined using the known thermophysical property and layer thickness of each layer constituting the laminate. It is possible to accurately determine the thermal resistance, the bio number, and the unknown value of the laminated material.
[Brief description of the drawings]
FIG. 1 is an explanatory diagram of an apparatus for evaluating thermal characteristics of a laminated material having thermal resistance according to an embodiment of the present invention.
FIG. 2 is a projection view on a plane composed of the thermal resistance and thermal diffusivity of a concave groove with a square deviation when the thermal resistance and thermal diffusivity are measured.
FIG. 3 is a projection view on a plane composed of the thermal diffusivity and the square deviation of the concave groove of the square deviation when the thermal resistance and the thermal diffusivity are measured.
FIG. 4 is a projection view with respect to a plane constituted by the thermal resistance and square deviation of the concave groove of square deviation when the thermal resistance and thermal diffusivity are measured.
FIG. 5 is a projection view on a plane composed of the minimum number of biometric deviations of squared deviation and the squared deviation when measuring thermal resistance, thermal diffusivity, and number of bios.
FIG. 6 is an explanatory diagram showing change behavior of square deviation with respect to thermal resistance when thermal resistance and specific heat capacity are measured.
FIG. 7 is an explanatory diagram showing a change behavior of the square deviation with respect to the specific heat capacity when the thermal resistance and the specific heat capacity are measured.
FIG. 8 is an explanatory diagram showing the bio number dependency of the minimum value of the square deviation when the thermal resistance, specific heat capacity, and bio number are measured.
FIG. 9 is an explanatory diagram showing a change behavior of the square deviation with respect to the thermal resistance when the thermal resistance and the thickness of the first layer are measured.
FIG. 10 is an explanatory diagram showing a change behavior of the square deviation with respect to the layer thickness of the first layer when the thermal resistance and the layer thickness of the first layer are measured.
FIG. 11 is an explanatory diagram showing a change behavior of the square deviation with respect to the bio number when the thermal resistance, the layer thickness of the first layer, and the bio number are measured.
FIG. 12 is an explanatory diagram showing a processing flow in the Newton method.
FIG. 13 is an explanatory diagram showing a processing flow for obtaining a minimum value from the magnitude relation of square deviation values.
[Explanation of symbols]
10: Laser flash device, 11: Laser pulse, 12: Pulse heating means, 13: Pulse detection means, 14: Laser pulse, 15: Laminated material, 16: First layer, 17: Surface, 18: Laser pulse, 19: Half mirror, 20: second layer, 21: surface, 22: temperature measurement means, 23: arithmetic processing unit, 24: output means, 25: sample holder, 26: theoretical surface temperature calculation means, 27: Laplace conversion means, 28 : Square deviation calculation means, 29: square deviation minimization means

Claims

A method for evaluating thermal properties of a laminated material, comprising a first layer and a second layer, and obtaining a thermal property of a plate-shaped laminated material having a thermal resistance in an interlayer portion between the first layer and the second layer,
A first step of obtaining an actually measured surface temperature of the other surface of the laminate when the one surface of the laminate is instantaneously heated;
A second step of calculating a theoretical surface temperature of the other surface of the laminate when the surface of the one side of the laminate is instantaneously heated from a solution of an unsteady heat conduction equation considering boundary conditions When,
Assuming that some of the thermophysical properties and layer thicknesses of each layer constituting the laminated material are unknowns, from the condition that minimizes the deviation between the measured surface temperature and the theoretical surface temperature, the thermal resistance, the number of bioses, And a third step of obtaining the unknown value, and a thermal property evaluation method for a laminated material having thermal resistance.

2. The thermal property evaluation method for a laminated material having thermal resistance according to claim 1, wherein the unknown is the thermal property and the layer thickness of one layer.

The thermal property evaluation method for a laminated material having thermal resistance according to claim 1, wherein the unknown is a part of the thermal properties and the layer thickness of one layer. Characterization method.

In the thermal property evaluation method of the laminated material which has a thermal resistance of any one of Claims 1-3, the said theoretical surface temperature is a calculated value based on the analytical solution calculated | required by carrying out the Laplace transform of the said unsteady heat conduction equation. And the deviation is a square deviation between a Laplace conversion temperature obtained by Laplace conversion of the measured surface temperature and the calculated value, and a thermal property evaluation method for a laminate having thermal resistance.

5. The thermal property evaluation method for a laminated material having thermal resistance according to claim 4, wherein the condition for minimizing the square deviation is defined as the thermal resistance, the bio number, and the unknown as independent variables. A method for evaluating thermal properties of a laminated material having thermal resistance, characterized in that:

5. The thermal property evaluation method for a laminated material having thermal resistance according to claim 4, wherein the condition for minimizing the square deviation is based on a measured decay time constant obtained from a change in the measured surface temperature and a change in the theoretical surface temperature. A method for evaluating thermal characteristics of a laminated material having thermal resistance, characterized in that it is obtained under an additional condition in which the obtained theoretical decay time constant is equivalent.

A pulse heating means comprising a first layer and a second layer, and instantaneously heating a surface of one side of the plate-like laminate having an interlayer portion between the first layer and the second layer;
Temperature measuring means for obtaining an actual surface temperature of the other surface of the laminate;
Assuming that some of the thermophysical properties and layer thicknesses of each layer constituting the laminated material are unknown, the theoretical surface temperature of the other surface when the one surface is instantaneously heated is obtained. A thermal resistance characterized by having an arithmetic processing unit for obtaining a value of the thermal resistance existing in the interlayer portion, the bio number, and the unknown number from a condition that minimizes a deviation between the theoretical surface temperature and the measured surface temperature. An apparatus for evaluating thermal properties of laminated materials.

8. The thermal property evaluation apparatus for a laminated material having thermal resistance according to claim 7, wherein the unknown is the thermal property and the layer thickness of one layer.

The thermal property evaluation apparatus for a laminated material having thermal resistance according to claim 7, wherein the unknown is a part of the thermal properties and thickness of one layer. Characteristic evaluation device.