JP3790873B2 - Acoustic surface area meter - Google Patents

Description

【数２】

【０００８】
４は蓋であって、その上に内部体積Ｖ₁ の基準容器１がつけられている。蓋４の上面の容器１と２の間の隔壁を成す部分には連通管５がつけられていて、容器１と２の内部を連通している。またこの隔壁の部分には音源のスピーカ６もとりつけられている。７はスピーカの振動板である。スピーカ６には端子８および９を通して導線１８および１９がつながっており、これらの導線を通して信号発生器１６より角周波数ωの正弦波駆動信号が供給され、振動板７の表裏によって測定容器２と基準容器１に交番的体積変化を差動的に与える。その結果、測定容器２および基準容器１の内部に圧力変化、すなわち音圧、を生ずる。１１は基準容器１の内部の音圧を検出するマイクロホンで、その出力は増幅器１３で増幅されて音圧信号ｅ₁ となり信号処理装置１５にとりこまれる。１２は測定容器２内部の音圧を検出するマイクロホンで、その出力は端子１０を通って増幅器１４に至りここで増幅されて音圧信号ｅ₂ となり信号処理装置１５にとり込まれる。
【０００９】
図２は信号処理装置１５の構成の一例を示すものである。音圧信号ｅ₁ とｅ₂ はそれぞれアナログディジタル変換器１５１および１５２によってディジタル量に変換され、ディジタル計算機１５０にとり込まれる。１５５は周波数逓倍器で、信号発生器１６から導線１７を通して供給される同期信号を周波数逓倍してサンプリングパルスとし、このサンプリングパルスに同期してアナログディジタル変換が行なわれる。しかし、信号処理装置１５の内部にクロックパルス発生器を設け、アナログディジタル変換は、信号発生器１６とは独立に、この内部クロックパルスに同期して行なうようにしてもよい。この場合には、周波数逓倍器１５５および導線１７は不要となる。なお、アナログディジタル変換の開始は、ディジタル計算機１５０から導線１５３および１５４によって送られるスタートパルスによって制御される。
【００１０】
ディジタル計算機１５０は音圧信号ｅ₁ とｅ₂ のフーリエ変換を行ない、ｅ₂ のｅ₁ に対する位相差θを測定し、また、物体の体積の測定も必要な場合には、信号ｅ₁ とｅ₂ のそれぞれの振幅Ｅ₁ とＥ₂ も測定する。すなわち、ディジタル計算機１５０では、時間をｔで表わすとして、音圧信号ｅ₁(t)とｅ₂(t)の波形をｔ＝ｔ₀ からｔ＝ｔ₀ ＋Ｔまでの間とり込んで、それらのとり込んだ波形と sinωｔ、 cosωｔとの積のｔに関する積分を行なってフーリエ変換をするが、ｅ₁(t) sinωｔの積分値をＥ_1S、ｅ₁(t) cosωｔの積分値をＥ_1C、ｅ₂(t) sinωｔの積分値をＥ_2S、ｅ₂(t) cosωｔの積分値をＥ_2Cとすると、これらの値からｅ₂(t)のｅ₁(t)に対する位相差θ、ｅ₁(t)の振幅Ｅ₁ 、ｅ₂(t)の振幅Ｅ₂ はそれぞれ下記の式により求められる。
【数３】

【数４】

【数５】

【００１１】
上記の式において、Ｇ₁ 、Ｇ₂ はアナログディジタル変換器のゲインや積分時間Ｔ等を含む定数である。なお、位相差と振幅の測定には、上記のフーリエ変換による方法に限らず、他の既知の種々の方法が適用できる。
【００１２】
連通管５は基準容器１と測定容器２の内部の静圧を平衡させるとともに、両者の中の気体の成分を均一化する働きをするが、作動気体が空気の場合には、湿度などの成分は両者の容器の間でほとんど違いがない。したがって連通管５に替えて静圧を平衡させるためだけの毛細管を用いることもできる。また、特に容器のシールを厳重に行なわないかぎり、容器１と２の内部の静圧は、組み立てられた装置の部品の間のすき間を通じて外部の大気圧と等しくなっているのが普通であるから、連通管や毛細管は必須なものではない。
【００１３】
スピーカ６から測定容器２の内部空間をみたときの音響インピーダンスをＺ₂ とすると、測定容器の大きさが音の波長にくらべて十分小さい場合、Ｚ₂ は近似的につぎのように表わされる。
【数６】

【数７】

【数８】

【００１４】
これらの式において、ｊは単位虚数、γは気体の比熱比（空気の場合は約１．４）、Ｐ₀ は容器内の気体の静圧、κは気体の熱伝導度、ρは気体の密度、ｃ_p は気体の定圧比熱である。δ_t は熱境界層の厚さを意味するが、標準状態の空気の場合、ｆ＝ω／２π＝２５Ｈｚでδ_t は約０．５ｍｍである。
【００１５】
式（６）の音響インピーダンスＺ₂ の偏角をαｒａｄとすると、それはつぎのようになる。
【数９】

【００１６】
εは１にくらべて非常に小さいから、上式は近似的につぎのようになる。
【数１０】

【００１７】
音響インピーダンスの偏角αの変化は測定容器２内部の音圧の位相変化として現われるが、式（７）に示したように、εは表面積Ｓ₂ に比例して変化するから、容器２に中に被測定物体３を入れたことでＳ₂ が変わると偏角αが変化し、それに応じて容器２内部の音圧の位相が変化する。したがって、この音圧の位相変化により被測定物体３の表面積Ｓを知ることができる。これが本発明の表面積計の基本原理である。
【００１８】
前述したように、この実施例装置において測定されるのは、測定容器２の中に体積がＶで表面積がＳの物体３を入れたときの信号ｅ₂ の信号ｅ₁ に対する位相差θであるが、容器２を空にしたときのθをθ₀ とすると、式（１）、（２）、（７）、（１０）より次式が導き出される。
【数１１】

【数１２】

【００１９】
式（１１）は表面積の測定式で、図３はそのグラフであるが、測定容器２の内部寸法の測定によってその空容積Ｖ₀ が求められており、また、容器２が空のときの位相差θ₀ が予め測定されていれば、体積と表面積が既知の２個の標準物体を用いた較正で、式（１１）の係数を定めることができる。すなわち、体積Ｖ_A で表面積Ｓ_A の第１の標準物体を容器２の中に入れてそのときの位相差θ_A を測定して図３のグラフのＡ点を定め、つぎに、体積Ｖ_B で表面積Ｓ_B の第２の標準物体を容器２の中に入れてそのときの位相差θ_B を測定してグラフのＢ点を定めれば、Ａ、Ｂの２点を結ぶ直線が係数が定められた測定式を表わす。この式はディジタル計算機１５０の中で生成され記憶される。被測定物体３の体積Ｖが既知でその表面積Ｓが未知の場合、物体３を測定容器２の中に入れてそのときの位相差θを測定し、その値と体積Ｖの値を上記の記憶されている測定式に当てはめればＳ／Ｖがわかり、したがって表面積Ｓの値が求められる。
【００２０】
以上の説明では、測定容器２の内部体積Ｖ₀ や被測定物体３の体積Ｖは、寸法測定やアルキメデスの原理による水中重量法など、他の方法により測定され予めわかっているものとしたが、本発明の表面積計には、任意の形状の物体の体積を音響的手段により測定する体積計としての機能を併せもたせることができ、この機能を使って求められた物体の体積の値を表示するとともに、その値を物体の表面積の測定に利用することができる。以下に、この体積測定の機能を説明する。
【００２１】
信号発生器１６からの信号によってスピーカ６が駆動され、ある瞬間において振動板７が押し出されて測定容器２の内部空間の体積Ｖ₂ がΔＶ_S なる微小体積だけ圧縮されると、基準容器１の内部体積Ｖ₁ はΔＶ_S だけ膨張する。また連通管５を通して測定容器２の中にΔＶ_P なる微小体積の気体が流入すると、基準容器１からはΔＶ_P なる体積の気体が連通管５を通して流出する。このとき基準容器１および測定容器２の内部に生ずる圧力変化をそれぞれ−ΔＰ₁ 、ΔＰ₂ とし、また
【数１３】

【００２２】
とおくと、気体の断熱変化の関係式よりつぎのようになる。
【数１４】

【数１５】

【００２３】
上記２つの式より次式の関係がえられる。
【数１６】

【００２４】
式（１）と式（１６）より被測定物体の体積Ｖはつぎのように表わされる。
【数１７】

【００２５】
上式において、Ｖ₀ とＶ₁ は一定値であるから、物体の体積Ｖは圧力変化の大きさの比ΔＰ₁ ／ΔＰ₂ から求められることになる。
【００２６】
ディジタル計算機１５０においては、上式におけるΔＰ₁ ／ΔＰ₂ に対応する量としてフーリエ変換によって測定された音圧信号の振幅比Ｅ₁ ／Ｅ₂ を用い、つぎの体積測定式によって物体の体積Ｖを算出する。
【数１８】

【００２７】
図４は上式のグラフであるが、この式の係数Ｖ₀ とＶ₁ は体積既知の標準物体を用いた較正により定めることができる。まず、測定容器２を空にしてＶ＝０の状態とし、そのときの振幅比Ｅ₁ ／Ｅ₂ の値Ｒ₀ によりＥ₁ ／Ｅ₂ 軸上のＲ₀ 点を定め、つぎに体積Ｖ_C の標準物体を容器２の中に入れてそのときの振幅比の値Ｒ_C によりＣ点を定めれば、Ｒ₀ 、Ｃの２点を結ぶ直線が係数が定められた測定式を表わし、この直線が縦座標軸をよぎる点がＶ₀ の値を表わす。被測定物体３の体積Ｖと表面積Ｓがともに未知の場合、被測定物体３を測定容器２の中に入れ、そのときの信号ｅ₁ 、ｅ₂ の振幅の比Ｅ₁ ／Ｅ₂ から上記の体積測定式によってまずＶを求め、つぎにｅ₁ とｅ₂ の位相差θを測定し、その値と求められた体積Ｖの値を用いて式（１１）の表面積測定式により表面積Ｓを算出し、その値を表示する。
【００２８】
以上に説明した体積測定の方法は、スピーカ６から測定容器２の内部をみたときの音響インピーダンスの絶対値｜Ｚ₂ ｜を測ることと等価である。式（６）により明らかなように、｜Ｚ₂ ｜は表面積Ｓ₂ の影響を少し受け、その結果、測定容器２の中の被測定物体３の体積Ｖは、その表面積Ｓに比例して、（γ−１）δ_t Ｓ／２だけ真の体積より小さく測定される。したがって、前述した方法で求められた物体表面積の値を用いてこの誤差を補正してより正確な体積測定値を得て、この補正された体積測定値を用いてもう一段正確な表面積の測定値を得るようにすることもできる。
【００２９】
【第２実施例】
図５は本発明を容器の内部表面積測定に適用した例である。基準容器１とそれにつけられたスピーカ６、マイクロホン１１、１２、連通管５、信号発生器１６および信号処理装置１５は図１の場合と同じである。図５の装置では、基準容器１の下に内部体積Ｖ₀ のアダプタ２２が固定されてつけられている。そして、基準容器１は、内部体積Ｖの被測定容器２３の上にアダプタ２２を下にして載せることにより２３と結合される。ここで、アダプタ２２の内部空間と被測定容器２３の内部空間は断面積Ｓ_H の測定孔２１によって通じ、内部体積Ｖ₀ ＋Ｖの音響的に閉じた一つの空間を構成する。
【００３０】
以上に説明した状況は、図１において測定容器２の中の物体３が−Ｖなる負の体積を有することと等価である。したがって、図５の装置の表面積測定式は、式（１１）においてＶの替わりに−Ｖを代入することにより得られる。すなわち、被測定容器２３の内部表面積Ｓは下記の式により測定される。
【数１９】

【数２０】

【００３１】
上記において、Ｓ₀ は、被測定容器２３をとって測定孔２１を平板で閉じたときのアダプタ２２の内部表面積で、θ₀ はこのときの信号ｅ₂ の信号ｅ₁ に対する位相差である。Ｓ_X は上記の平板をとって被測定容器２３を結合したときの内部表面積の増加分で、２３の内部表面積Ｓは、式（２０）に示すように、このＳ_X に、別途測定することにより求められた測定孔２１の断面積Ｓ_H を加えたものになる。また、式（１１）の場合と同様に、アダプタ２２の内部体積Ｖ₀ が知れており、θ₀ が予め測定されていれば、被測定容器２３の替わりに内部体積と内部表面積が既知の２個の標準容器を順次に結合して較正を行なうことにより、式（１９）が定められる。そして、内部体積Ｖがわかっている被測定容器２３を結合してそのときの位相差θを測定し、その値とＶの値を上記の定められた測定式に当てはめてＳ_X を算出し、それから式（２０）により被測定容器２３の内部表面積Ｓを求める。
【００３２】
図１の装置の場合と同様に、図５の装置によってアダプタ２２の内部体積Ｖ₀ や被測定容器２３の内部体積Ｖを求めることもできる。このときの体積測定式は、式（１８）においてＶの替わりに−Ｖを代入して得られる次式である。
【数２１】

【００３３】
式（１８）の場合と同様に、内部体積既知の標準容器を用いた較正により上記の測定式は定められる。そして、被測定容器２３を結合したときの信号ｅ₁ とｅ₂ の振幅の比Ｅ₁ ／Ｅ₂ をこの定められた体積測定式に当てはめることにより、２３の内部体積Ｖが測定され表示され、また、その値は２３の内部表面積Ｓの算出に用いられる。
【図面の簡単な説明】
【図１】本発明の一実施例の表面積計である。
【図２】図１における信号処理装置の構成の一例である。
【図３】表面積測定式のグラフである。
【図４】体積測定式のグラフである。
【図５】容器の内部表面積測定に対する本発明の適用例である。
【符号の説明】
１ 内部体積Ｖ₁ の基準容器
２ 空のときの内部体積がＶ₀ で内部表面積がＳ₀ の測定容器
３ 体積がＶで表面積がＳの被測定物体
４ 蓋
５ 連通管
６ スピーカ
７ スピーカの振動板
８、９、１０ 端子
１１、１２ マイクロホン
１３、１４ 増幅器
１５ 信号処理装置
１６ 信号発生器
１７、１８、１９ 導線
２１ 断面積がＳ_H の測定孔
２２ 内部体積がＶ₀ で内部表面積がＳ₀ のアダプタ
２３ 内部体積がＶで内部表面積がＳの被測定容器[0001]
[Industrial application fields]
The present invention relates to an apparatus for measuring the surface area of an arbitrarily shaped object or the internal surface area of an arbitrarily shaped container by acoustic means.
[0002]
[Prior art]
Conventionally, a so-called gas adsorption method has been used as a method for measuring the surface area of an object having an arbitrary shape. This is because an object is put in a measurement container and vacuumed, then the object is heated to release the gas adsorbed on its surface, and the gas released from the pressure increase in the measurement container at that time. This is a method of determining the surface area by determining the amount of the amount.
[0003]
[Problems to be solved by the invention]
The above gas adsorption method not only takes time and labor for measurement, but also evacuates the measurement container or heats the object to be measured, so it cannot be applied to a living body such as a human being. There is also.
[0004]
[Means for Solving the Problems]
According to the present invention, when an object to be measured is placed in a measurement container and the inside of the container is acoustically driven, the gas in the thermal boundary layer in contact with the surface of the object exchanges heat with the object, thereby losing acoustic energy. As a result, the real part of the acoustic impedance viewed from the mouth of the container changes in proportion to the surface area of the object, and this real part change is detected as the phase change of the sound pressure inside the container. The surface area of an object is obtained.
[0005]
That is, one form of the surface area meter of the present invention includes a reference container, a measurement container, a speaker that differentially changes an alternating volume to these two containers, and two pressure detectors that detect pressure changes inside each of these two containers. It consists of two microphones, a signal processing device that captures and processes the outputs of these microphones, the phase difference between the outputs of the two microphones measured in the signal processing device, and the phase difference when an object is put in the measurement container To calculate the surface area of the object.
[0006]
【The invention's effect】
In the surface area meter of the present invention as described above, the surface area can be obtained within a few seconds after putting an object in a measurement container. Moreover, since it is not necessary to evacuate the inside of the measurement container or to heat the object, it can be applied to a living body. Furthermore, since the main components used are acoustic components such as speakers and microphones, the manufacturing cost is low, and the size of the device is smaller than that of conventional products. The operation principle of the present invention will be described below with reference to examples.
[0007]
[First embodiment]
In FIG. 1, reference numeral 2 denotes a measurement container having an internal volume V ₀ and an internal surface area S ₀ when empty, and a measured object 3 having a volume V and a surface area S is placed therein. If the volume of the space between 2 and 3 is V ₂ and the internal surface area of the space is S ₂ , they are expressed as follows.
[Expression 1]

[Expression 2]

[0008]
4 is a lid, reference container 1 of the internal volume V ₁ is being attached thereon. A communication pipe 5 is attached to a portion forming a partition wall between the containers 1 and 2 on the upper surface of the lid 4 so as to communicate the interiors of the containers 1 and 2. A sound source speaker 6 is also attached to the partition wall. Reference numeral 7 denotes a speaker diaphragm. Conductors 18 and 19 are connected to the speaker 6 through terminals 8 and 9, and a sinusoidal drive signal having an angular frequency ω is supplied from the signal generator 16 through these conductors. An alternating volume change is applied to the container 1 differentially. As a result, a pressure change, that is, a sound pressure is generated inside the measurement container 2 and the reference container 1. Reference numeral 11 denotes a microphone for detecting the sound pressure inside the reference container 1, and its output is amplified by an amplifier 13 to be a sound pressure signal e ₁ and is taken into the signal processing device 15. Reference numeral 12 denotes a microphone for detecting the sound pressure inside the measurement container 2, and its output reaches the amplifier 14 through the terminal 10, where it is amplified and becomes a sound pressure signal e ₂ , which is taken into the signal processing device 15.
[0009]
FIG. 2 shows an example of the configuration of the signal processing device 15. The sound pressure signals e ₁ and e ₂ are converted into digital quantities by analog-digital converters 151 and 152, respectively, and taken into the digital computer 150. A frequency multiplier 155 frequency-multiplies the synchronizing signal supplied from the signal generator 16 through the conductor 17 to obtain a sampling pulse, and performs analog-digital conversion in synchronization with the sampling pulse. However, a clock pulse generator may be provided inside the signal processing device 15, and the analog-digital conversion may be performed in synchronization with the internal clock pulse independently of the signal generator 16. In this case, the frequency multiplier 155 and the conducting wire 17 are not necessary. The start of the analog-digital conversion is controlled by a start pulse sent from the digital computer 150 through the conductors 153 and 154.
[0010]
Digital computer 150 performs a Fourier transform of the sound pressure signal e ₁ and e _2, the phase difference θ as measured against e ₁ of e _2, also when the measured object volume also required, the signal e ₁ and e respective amplitudes E _{1 2} and E ₂ is also measured. That is, in the digital computer 150, the time is represented by t, and the waveforms of the sound pressure signals e ₁ (t) and e ₂ (t) are acquired from t = t ₀ to t = t ₀ + T, elaborate taken waveform and sin .omega.t, although the Fourier transform by performing integration over t of the product of the cosωt, e ₁ (t) sinωt integral value E _1S, e ₁ (t) the integral value of cos .omega.t E _1C, If the integral value of e ₂ (t) sinωt is E _2S and the integral value of e ₂ (t) cosωt is E _2C , the phase difference θ, e _{1 of} e ₂ (t) with respect to e ₁ (t) is calculated from these values. The amplitude E ₁ of (t) and the amplitude E ₂ of e ₂ (t) are obtained by the following equations, respectively.
[Equation 3]

[Expression 4]

[Equation 5]

[0011]
In the above formula, G ₁ and G ₂ are constants including the gain of the analog-digital converter, the integration time T, and the like. Note that the phase difference and the amplitude are not limited to the above-described Fourier transform, and various other known methods can be applied.
[0012]
The communication pipe 5 functions to balance the static pressure inside the reference container 1 and the measurement container 2 and to equalize the gas components in both, but when the working gas is air, components such as humidity are used. There is little difference between the two containers. Therefore, it is possible to use a capillary tube only for balancing the static pressure instead of the communication tube 5. Also, unless the container is tightly sealed, the static pressure inside the containers 1 and 2 is usually equal to the external atmospheric pressure through the gap between the assembled device parts. Communicating tubes and capillaries are not essential.
[0013]
Assuming that the acoustic impedance when the internal space of the measurement container 2 is viewed from the speaker 6 is Z ₂ , if the size of the measurement container is sufficiently smaller than the wavelength of sound, Z ₂ is approximately expressed as follows.
[Formula 6]

[Expression 7]

[Equation 8]

[0014]
In these equations, j is the unit imaginary number, γ is the specific heat ratio of the gas (about 1.4 for air), P ₀ is the static pressure of the gas in the container, κ is the thermal conductivity of the gas, and ρ is the gas The density, c _p, is the constant pressure specific heat of the gas. [delta] _t is mean thickness of the thermal boundary layer, the standard state of the air, f = ω / 2π = 25Hz at [delta] _t is about 0.5 mm.
[0015]
Assuming that the angle of deviation of the acoustic impedance Z _{2 in} equation (6) is α rad, it is as follows.
[Equation 9]

[0016]
Since ε is very small compared to 1, the above equation is approximately as follows.
[Expression 10]

[0017]
The change in the deflection angle α of the acoustic impedance appears as a phase change of the sound pressure inside the measurement container 2, but as shown in the equation (7), ε changes in proportion to the surface area S _2. When S ₂ is changed by inserting the object 3 to be measured, the declination α changes, and the phase of the sound pressure inside the container 2 changes accordingly. Therefore, the surface area S of the measured object 3 can be known from the phase change of the sound pressure. This is the basic principle of the surface area meter of the present invention.
[0018]
As described above, what is measured in the apparatus of this embodiment is the phase difference θ of the signal e ₂ with respect to the signal e ₁ when the object 3 having the volume V and the surface area S is placed in the measurement container 2. However, when θ when the container 2 is emptied is θ ₀ , the following equation is derived from the equations (1), (2), (7), and (10).
[Expression 11]

[Expression 12]

[0019]
Formula (11) is a measurement formula for the surface area, and FIG. 3 is a graph thereof. The empty volume V ₀ is obtained by measuring the internal dimensions of the measurement container 2, and the position when the container 2 is empty is shown. If the phase difference θ ₀ has been measured in advance, the coefficient of equation (11) can be determined by calibration using two standard objects with known volumes and surface areas. That is, defining a point A in the graph of FIG. 3 by measuring the phase difference theta _A at that time put first standard object surface area S _A in the container 2 by volume V _A, then the volume V _B If the second standard object having the surface area S _B is put into the container 2 and the phase difference θ _B at that time is measured to determine the point B of the graph, the straight line connecting the two points A and B has a coefficient. Represents a defined measurement formula. This equation is generated and stored in the digital computer 150. When the volume V of the object 3 to be measured is known and its surface area S is unknown, the object 3 is placed in the measurement container 2 and the phase difference θ is measured at that time, and the value and the value of the volume V are stored in the above memory. S / V can be obtained by applying the measurement formula, and the value of the surface area S can be obtained.
[0020]
In the above description, the internal volume V ₀ of the measurement container 2 and the volume V of the object 3 to be measured are measured and known in advance by other methods such as dimensional measurement and underwater weight method based on Archimedes' principle. The surface area meter of the present invention can be combined with a function as a volume meter for measuring the volume of an object of any shape by acoustic means, and the volume value of the object obtained using this function is displayed. In addition, the value can be used to measure the surface area of the object. The function of volume measurement will be described below.
[0021]
When the speaker 6 is driven by a signal from the signal generator 16 and the diaphragm 7 is pushed out at a certain moment and the volume V ₂ of the internal space of the measurement container 2 is compressed by a minute volume of ΔV _S , The internal volume V ₁ expands by ΔV _S. Also, if [Delta] V _P becomes very small volume of gas into the measurement vessel 2 through the communicating pipe 5 flows, [Delta] V _P becomes the volume of gas flowing through the communicating pipe 5 from the reference container 1. At this time, the pressure changes generated in the reference container 1 and the measuring container 2 are set to −ΔP ₁ and ΔP ₂ , respectively, and

[0022]
Then, from the relational expression of the adiabatic change of gas, it becomes as follows.
[Expression 14]

[Expression 15]

[0023]
From the above two formulas, the following formula is obtained.
[Expression 16]

[0024]
From the equations (1) and (16), the volume V of the object to be measured is expressed as follows.
[Expression 17]

[0025]
In the above equation, V ₀ and V ₁ are constant values, so the volume V of the object is obtained from the ratio ΔP ₁ / ΔP ₂ of the magnitude of pressure change.
[0026]
In the digital computer 150, the amplitude ratio E ₁ / E ₂ of the sound pressure signal measured by Fourier transform is used as an amount corresponding to ΔP ₁ / ΔP ₂ in the above equation, and the volume V of the object is calculated by the following volume measurement equation. calculate.
[Formula 18]

[0027]
FIG. 4 is a graph of the above equation, and the coefficients V ₀ and V ₁ of this equation can be determined by calibration using a standard object with a known volume. First, the measuring container 2 is emptied and V = 0 is set, the R ₀ point on the E ₁ / E ₂ axis is determined by the value R ₀ of the amplitude ratio E ₁ / E ₂ at that time, and then the volume V _C is set. Is placed in the container 2 and the point C is determined by the value R _C of the amplitude ratio at that time, a straight line connecting the two points R ₀ and C represents the measurement formula in which the coefficient is determined. The point where the straight line crosses the ordinate axis represents the value of V ₀ . When both the volume V and the surface area S of the object to be measured 3 are unknown, the object to be measured 3 is put into the measurement container 2 and the above-described amplitude ratio E ₁ / E ₂ of the signals e ₁ and e _{2 is used} as described above. First, V is obtained by the volume measurement formula, then the phase difference θ between e ₁ and e ₂ is measured, and the surface area S is calculated by the surface area measurement formula of Formula (11) using the value and the value of the obtained volume V. And display the value.
[0028]
The volume measurement method described above is equivalent to measuring the absolute value | Z ₂ | of the acoustic impedance when the inside of the measurement container 2 is viewed from the speaker 6. As apparent from the equation (6), | Z ₂ | is slightly affected by the surface area S ₂ , and as a result, the volume V of the measured object 3 in the measurement container 2 is proportional to the surface area S, It is measured smaller than the true volume by (γ−1) δ _t S / 2. Therefore, this error is corrected by using the object surface area value obtained by the above-described method to obtain a more accurate volume measurement value, and this corrected volume measurement value is used to obtain another more accurate surface area measurement value. Can also be obtained.
[0029]
[Second embodiment]
FIG. 5 shows an example in which the present invention is applied to the measurement of the internal surface area of a container. The reference container 1, the speaker 6, the microphones 11 and 12, the communication pipe 5, the signal generator 16, and the signal processing device 15 attached thereto are the same as those in FIG. In the apparatus of FIG. 5, an adapter 22 having an internal volume V ₀ is fixed and attached under the reference container 1. The reference container 1 is coupled to the reference container 1 by placing the adapter 22 on the container to be measured 23 having the internal volume V. Here, the internal space and the internal space of the container to be measured 23 of the adapter 22 through the measurement hole 21 of the cross-sectional area S _H, constituting the acoustically closed one space inside the volume V ₀ + V.
[0030]
The situation described above is equivalent to the fact that the object 3 in the measurement container 2 in FIG. 1 has a negative volume of −V. Therefore, the surface area measurement formula of the apparatus of FIG. 5 is obtained by substituting -V for V instead of V in formula (11). That is, the internal surface area S of the container 23 to be measured is measured by the following formula.
[Equation 19]

[Expression 20]

[0031]
In the above, S ₀ is the internal surface area of the adapter 22 when the container to be measured 23 is taken and the measurement hole 21 is closed with a flat plate, and θ ₀ is the phase difference of the signal e _{2 from} the signal e _{1 at} this time. S _X is an increase in the internal surface area when the measurement container 23 is bonded by taking the flat plate, and the internal surface area S of 23 should be separately measured as S _X as shown in the equation (20). It becomes plus the cross-sectional area S _H of the measurement hole 21 obtained by. Similarly to the case of the expression (11), if the internal volume V ₀ of the adapter 22 is known and θ ₀ is measured in advance, the internal volume and the internal surface area are known 2 instead of the container 23 to be measured. Equation (19) is determined by combining the standard containers in sequence and performing calibration. Then, the container 23 to be measured whose internal volume V is known is combined, the phase difference θ at that time is measured, and the value and the value of V are applied to the above defined measurement formula to calculate S _X. Then, the internal surface area S of the container 23 to be measured is obtained by the equation (20).
[0032]
As in the case of the apparatus of FIG. 1, the internal volume V _{0 of the} adapter 22 and the internal volume V of the measured container 23 can be obtained by the apparatus of FIG. The volume measurement formula at this time is the following formula obtained by substituting -V for V instead of V in formula (18).
[Expression 21]

[0033]
As in the case of equation (18), the above measurement equation is determined by calibration using a standard container with a known internal volume. Then, the internal volume V of 23 is measured and displayed by applying the ratio E ₁ / E ₂ of the amplitudes of the signals e ₁ and e ₂ when the container to be measured 23 is coupled to the determined volume measurement equation, The value is used to calculate the internal surface area S of 23.
[Brief description of the drawings]
FIG. 1 is a surface area meter according to an embodiment of the present invention.
FIG. 2 is an example of a configuration of a signal processing device in FIG. 1;
FIG. 3 is a graph of a surface area measurement formula.
FIG. 4 is a volume measurement type graph.
FIG. 5 is an application example of the present invention for measuring the internal surface area of a container.
[Explanation of symbols]
Vibration measurement vessel 3 surface area volume in V internal volume internal surface area V ₀ S ₀ is the measured object 4 lid 5 communicating tube 6 speaker 7 speaker S when the first internal volume V ₁ of the reference vessel 2 empty plate 8,9,10 terminals 11 and 12 microphones 13, 14 amplifier 15 signals measurement hole 22 inside the volume of the processing unit 16 the signal generator 17, 18, 19 lead 21 sectional area S _H is the internal surface area V ₀ S ₀ Adapter 23 The container to be measured whose internal volume is V and whose internal surface area is S

Claims (2)

A reference container, a measurement container, a means for differentially applying an alternating volume change to the two containers, a means for detecting a pressure change inside each of the two containers, and the two detected pressures A surface area meter comprising means for measuring a phase difference between change signals, and determining a surface area of the object to be measured based on the phase difference when the object to be measured is placed in the measurement container. A reference container coupled to the container to be measured, a means for differentially applying an alternating volume change to the two containers, a means for detecting a pressure change inside each of the two containers, and the detected Means for measuring a phase difference between two pressure change signals, and determining an internal surface area of the measured container by the phase difference when the reference container is coupled to the measured container. Surface area meter.

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