JP3645855B2 - Arcuate Coriolis Meter and Shape Determination Method - Google Patents

Description

【００３１】
を満たすように、距離ｄを選ぶとｄは(2) 式で表される。
【００３２】
【数２】

【００３３】
まず最初に、温度突変によるｘ方向の膨張による弾性歪エネルギーＵ_x を考える。ｓ：アーチ（弓形）の任意位置での長さ、ｄｓ：アーチの任意位置での微小長さ、U ：弾性歪エネルギー、Mx:X軸方向のモーメント、My：Y 軸方向のモーメント、N ：チューブの圧縮力、α：チューブ材料の温度膨張係数、ｔ：チューブの温度または温度差とし、弾性中心（Ｏ点）における水平方向の力である圧縮力Ｈ_o と弾性中心（Ｏ点）における曲げモーメントＭ_o を不静定量に取るとカステリアーノの第２定理から、
【００３４】
【数３】

【００３５】
【数４】

【００３６】
が成り立つ。ここに
【００３７】
【数５】

【００３８】
弾性中心の条件によりＭ_o ＝０であるから
【００３９】
【数６】

【００４０】
が得られる。(5) 、(6) 式によって弓形チューブの任意断面の曲げモーメントと圧縮力が求められる。図２に示すような円弧と直線による弓形チューブの諸元を入れて(2) 式のｄを解くと
【００４１】
【数７】

【００４２】
ここで、R ：アーチ型チューブの円弧部分の円弧半径である。
従って頂点A から弾性中心までの距離は
【００４３】
【数８】

【００４４】
と表される。
同様にして(6) 式を解くと
【００４５】
【数９】

【００４６】
となる。ここで
【００４７】
【数１０】

【００４８】
【数１１】

【００４９】
(5),(9),(10),(11) 式より任意チューブ断面の曲げモーメント及び圧縮力N が求まる。ここで、A ：チューブの断面積＝π・（Do² −Di² ）/4 、Do：チューブ外径、Di：チューブ内径である。
【００５０】
次に熱膨張による垂直方向に関しては図４のように、不静定力をＨ1 、不静定モーメントをＭ1 とすると次式が成り立つ。
【００５１】
【数１２】

【００５２】
カステリアーノの第２定理から、弾性歪エネルギーをＵy とすると、
【００５３】
【数１３】

【００５４】
また、
【００５５】
【数１４】

【００５６】
これより
【００５７】
【数１５】

【００５８】
が得られる。ここで
【００５９】
【数１６】

【００６０】
【数１７】

【００６１】
【数１８】

【００６２】
MxもMyも同じ向きなので加算され合成モーメントM は
【００６３】
【数１９】

【００６４】
となる。また最大モーメントは固定端C における値でこれをM max とすると
最大曲げ応力は
【００６５】
【数２０】

【００６６】
となる。ここでZ ：アーチの断面係数＝（π／３２）・ （Do⁴ −Di⁴ ） ／Doである。またC 点の圧縮応力は
【００６７】
【数２１】

【００６８】
従って合応力は
【００６９】
【数２２】

【００７０】
なお、計算の結果、σC はσMmaxの2 〜3 ％と小さく無視できることが分かった。即ち、
【００７１】
【数２３】

【００７２】
としてよい。従って最大応力は固定端に発生し
【００７３】
【数２４】

【００７４】
と表される。
例えば口径25mmでチューブ材料にステンレス製を用い、諸元をチューブ内径Di＝15mm、チューブ肉厚0.75mmとし突変温度110 ℃とした時、図２の幾何学的寸法形状から、
【００７５】
【数２５】

【００７６】
の関係があるので、L=371.4 ｍｍ＝一定とし、φ1=φ0=40°とした場合、寸法比ｈ／Ｌを変えた時の最大応力σmax 及びチューブ高さｈをグラフに示すと図５のようになる。図から分かるように、寸法比ｈ／Ｌ≧０．３１で最大応力σmax は最小値( 約125N/mm2) に収斂する。しかし寸法比ｈ／Ｌを大きく取るとｈが増大するので寸法比ｈ／Ｌ＝０．３１に取ると最大応力も少なく、寸法もコンパクトになる（図５における白抜きのマークがそのポイントである)。また、このポイントに決定したものを、図９及び図１０において「実施例」として示している。このように、このポイントは最適のものではあるが、図５に見られるように、寸法比ｈ／Ｌ＝１／４〜１／３の範囲であれば、最大応力σmax は事実上最小値に近い一方、チューブ高さｈについても十分に低く、コンパクトに構成することが可能となる。寸法比ｈ／Ｌを小さくすると、最大応力は増加するが、h/L＝1/3の時の応力値をσminとすると、h/L≧1/4であれば1.3σmin以下に抑えることができる。
【００７７】
図９は、本発明の実施例（Ｌ１＝１３０ｍｍ、ｈ＝１１５ｍｍ、ｈ／Ｌ＝０．３１）の形状を中央より右側に、そして本発明の範囲外の比較例（Ｌ１＝２０ｍｍ、ｈ＝７５ｍｍ、ｈ／Ｌ＝1/5）を左側に対比して示す図である。
【００７８】
図１０は、上記実施例と比較例についての「温度突変後の密度精度の変化」を示す図である。これは、流体温度を、グラフ横軸に示す温度差に急激に変化させた（突変）後、再度常温に戻して密度精度を測定した結果を示している。図示したように、実施例は、大きな温度差に急激に変化しても、測定した密度精度にエラーは生じないのに対して、比較例は、突変温度が大きくなるにつれて、密度表示エラーが増加している。
【００７９】
図１１は、寸法比を変えたときの温度突変後の器差変化を示す図である。図中、右側欄外に示すような寸法を有する流量計について、実測により求めたデータである。流量計を使用する際に温度突変が行われる状況として、洗浄（スチーム洗浄）時にフローチューブ温度が130℃程度まで急激に上昇し、常温を20℃とすると最大110℃の温度差の温度突変が考えられる。以上を想定し110℃温度差を負荷する実験をおこなった。実験の結果としては、1/4≦ｈ/L≦1/3の範囲において製作されたものは、温度突変後の器差変化はほとんどなく、1/4≦ｈ/L≦1/3の範囲外であるh/L＝1/5で製作されたものは-0.2%以上の器差変化が見られた。コリオリ流量計として-0.2％の器差変化は大きく、流量計の保証精度から外れてしまう（一般的なコリオリ質量流量計の器差精度は±0.2%程度）。
【００８０】
図１２は、図１１の「器差変化」に代えて、「密度表示変化」を表す同様な実測結果を示す図である。図１１と同様な傾向が得られている。h/L＝1/5で製作されたものは、密度表示値においても変化量が大きく保証精度から外れる（密度計としての一般的な保証精度は±0.002g/ml程度）。
【００８１】
図１１及び図１２に示すような実測結果によって、h/Lが1/4以下になると器差変化および密度表示値が、急激に変化することが確認できた。h/L=1/5のものは、温度突変によりフローチューブ応力が弾性限界を超え塑性変形を引き起こし、フローチューブの機械的特性の変化によりフローチューブ周期が変化したことで、器差変化及び密度表示値変化が発生したものと推定ができる。
【００８２】
【発明の効果】
本発明によれば、計測流体が温度突変を起こしたときに、応力を所定の値に低く抑え、かつ、最もコンパクトになるようにチューブ形状を決定することが可能になる。
【００８３】
また、本発明は、フローチューブを円弧セグメントと直線セグメントから構成した並列２本の弓形管式であるために、応力分散、耐震性に優れているという効果を有している。
【図面の簡単な説明】
【図１】本発明を適用するコリオリメータを例示する図であり、入口配管及び出口配管を水平にして取り付けたと仮定して、その正面から見た部分的断面図（左側図）と、中央部で切断した側面図（右側図）である。
【図２】弓形チューブの諸元図である。
【図３】固定アーチを示す図である。
【図４】垂直方向の熱膨張によるモーメント図である。
【図５】直線長さL1を変えた時の最大応力σmax 及びチューブ高さｈを示すグラフである。
【図６】中央の円弧部とその両側の直線部により構成される弓形構成のフローチューブを説明するための図である。
【図７】従来の弓形構成のフローチューブを有するコリオリメータの動作を説明するための概念図である。
【図８】従来の円弧構成のフローチューブを説明するための図である。
【図９】本発明の実施例の形状を中央より右側に、そして本発明の範囲外の比較例を左側に対比して示す図である。
【図１０】実施例と比較例についての「温度突変後の密度精度の変化」を示す図である。
【図１１】寸法比を変えたときの温度突変後の器差変化を示す図である。
【図１２】図１１の「器差変化」に代えて、「密度表示変化」を表す同様な実測結果を示す図である。
【符号の説明】
１ フローチューブ
２ フローチューブ
１２ フレキシブルプリント板
１５ 駆動装置
１６，１７ 振動検出センサ
１８，１９ フランジ
２５ マニフォールド
２６ 鍔部
２８ 基板
３０ 基部
３１ カバー
３４ 配線取出部[0001]
BACKGROUND OF THE INVENTION
The present invention relates to an arcuate tube type coriolis meter of a type using two parallel arcuate flow tubes and a method for determining the shape thereof.
[0002]
[Prior art]
When both ends of the flow tube through which the fluid to be measured flows are supported and the flow tube is vibrated in a direction perpendicular to the flow direction of the flow tube around the support point, the flow tube (hereinafter referred to as the flow tube to be vibrated) A mass flow meter (Coriolis meter) utilizing the fact that the Coriolis force acting on the flow tube is proportional to the mass flow rate is well known.
[0003]
Further, such a flow tube is formed as two tubes in parallel, and the two flow tubes are resonantly driven in opposite phases to each other, and the measurement fluid is caused to flow equally through the two flow tubes, thereby allowing the types of fluids to flow. Even if the temperature changes or the temperature fluctuates, the natural frequency of the two flow tubes is always equalized, which enables efficient and stable driving, and is free from external vibration and temperature effects. It is known that can be configured.
[0004]
Such a conventional flow tube of two parallel Coriolis meters drives the two flow tubes to resonate in phases opposite to each other by a driving device composed of a coil and a magnet at the center. In addition, a pair of vibration detection sensors composed of a coil and a magnet are installed at symmetrical positions on both the left and right sides with respect to the mounting position of the drive device, and detect a phase difference proportional to the Coriolis force.
[0005]
The measurement fluid flows in from an external flow pipe connected via a flange on the inlet side, and is equally branched into two flow tubes. And it merges in the exit side of a flow tube, and flows out into the external flow pipe connected via the flange of an exit side. As such two parallel Coriolis meters, a curved tube type and a straight tube type are known.
[0006]
Since the two curved tube parallel Coriolis meters use and measure the vibration of the flow tube leg extending in the lateral direction from the main body, it is necessary to secure the necessary length for the lateral leg. is there. That is, there is a problem that the size increases in shape.
[0007]
On the other hand, a straight tube type Coriolis meter has a flow tube with a straight tube configuration in the direction of the external flow tube line, and vibrates in a direction perpendicular to the straight tube axis at the center of the straight tube supported at both ends. When detecting the mass flow rate as a phase difference signal, the displacement difference of the straight pipe due to the Coriolis force between the support part and the central part of the straight pipe, such a straight pipe type Coriolis meter is A simple, compact and robust configuration can be achieved.
[0008]
However, the flow tube of the straight tube type Coriolis meter is affected by temperature because it needs to be fixedly supported on both sides thereof. That is, when the temperature of the measurement fluid changes, the flow tube immediately follows and changes in temperature, whereas the temperature fluctuation of the fixed structure such as the outer casing that fixes the flow tube is delayed. For this reason, the flow tube and the fixed structure cause a difference in elongation, and stress is generated in the longitudinal direction, and the natural frequency of the tube changes due to the change in the spring constant caused thereby. For this reason, the straight pipe type Coriolis meter requires a separate stress absorbing means such as a diaphragm or a bellows.
[0009]
The problem of longitudinal elongation due to such temperature fluctuations can be solved by configuring the flow tube in an arcuate shape. US Pat. No. 5,796,011 discloses such an arcuate flow tube. FIG. 7 is a conceptual diagram for explaining the operation of a conventional Coriolis meter having a flow tube having an arcuate configuration. The flow tube having an arcuate configuration can disperse stress and has excellent earthquake resistance. However, in the conventional arcuate tube, the connection between the manifold and the flow tube is in the tube axis direction. Therefore, as shown by the center R and the two r on both sides in the upper diagram of FIG. 7, the number of man-hours for bending the flow tube is required three times or more, and in particular, a double tube that requires symmetry. It was disadvantageous. The lower diagram in FIG. 7 shows the two states of the flow tube during vertical vibration. As shown in FIG. 7, the vibration node itself fixed by the substrate is subjected to vibration. Therefore, accurate measurement could not be performed.
[0010]
U.S. Pat. No. 5,796,011 also discloses a flow tube having an arc configuration as shown in FIG. However, such a simple arc-shaped flow tube cannot make a smooth connection in line with the inlet or outlet conduit.
[0011]
[Problems to be solved by the invention]
The present invention, in view of the above, requires that the arcuate configuration flow tube not only be a simple bending configuration in one direction, but also be smoothly connected in a straight line with the inlet and outlet conduits. For that purpose, as shown in FIG. 6, the flow tube having an arcuate configuration is configured by a central arc portion and straight portions on both sides thereof, and the inlet conduit and the outlet conduit are set to have a predetermined rising angle and are the same as the flow tube. It is desirable to bond in the direction. However, in that case, it is necessary not only to design the flow tube compactly but also to have a shape that also takes into account the thermal effects.
[0012]
In view of the above, the present invention provides a parallel two arched tube Coriolis meter in which the flow tube is composed of an arc segment and a straight segment and has excellent stress dispersion and earthquake resistance. The purpose is to determine the tube shape so that the stress is kept low to a predetermined value and the most compact when a sudden change occurs.
[0013]
[Means for Solving the Problems]
An arcuate tube type coriolis meter and a method for determining the shape of the present invention include two flow tubes in parallel, an inlet manifold that branches into two flow tubes from a measurement fluid inlet, and a measurement that flows through the two flow tubes. An outlet side manifold that joins fluids and flows out from the measurement fluid outlet, a drive device that resonates one flow tube with respect to the other flow tube in mutually opposite phases, and left and right relative to the mounting position of the drive device And a pair of vibration detection sensors that are installed at symmetrical positions on both sides and detect a phase difference proportional to the Coriolis force. Each of the two flow tubes is formed in an arcuate shape including a central arc portion and straight portions on both sides thereof. Based on the target pressure loss including the manifold and arcuate flow tube at the maximum flow rate, the target time phase difference of the sine wave output from the vibration detection sensor at the maximum flow rate, and the tube natural diameter and the tube end point based on the target natural frequency of the tube Determine the straight line length. The flow tube shape is such that the dimensional ratio (h / L) between the straight line length (L) between the tube end points and the vertical height (h) of the flow tube is between 1/4 and 1/3. To decide.
[0014]
DETAILED DESCRIPTION OF THE INVENTION
Hereinafter, an arcuate tube type Coriolis meter using two parallel arcuate flow tubes of the present invention will be described based on an example. FIG. 1 is a diagram illustrating a Coriolis meter to which the present invention is applied. Assuming that an inlet pipe and an outlet pipe are mounted horizontally, a partial sectional view (left side view) viewed from the front, It is the side view cut | disconnected by (right view). The Coriolis meter shown in the figure can be mounted either in the horizontal direction or in the vertical direction when it is used, and when it is mounted in the horizontal direction, as shown in FIG. It is possible to mount with the top facing up or with the bottom facing down. However, in the case of gas measurement, it is desirable to have the curved convex part upward as shown in the figure so that the liquid does not stay on the curved convex part in the center of the flow tube. In order to prevent bubbles from staying, it is desirable to attach the curved convex portion downward.
[0015]
The flow tubes 1 and 2 of the illustrated Coriolis meter are flow tubes of the same shape curved in an arcuate shape, and both ends of each are connected to the inlet side and outlet side manifolds 25 by welding or the like. In the following description, it is assumed that the measurement fluid flows in from the left side of FIG. 1 and flows out to the right side. The measurement fluid flows in from the external flow pipe connected via the flange 18 and is equally branched into the two flow tubes 1 and 2 at the inlet side manifold. Then, at the outlet side of the flow tubes 1 and 2, they merge at the outlet side manifold 25 and flow out to the external flow pipe connected via the flange 19.
[0016]
Since the inflow side and the outflow side are configured symmetrically, the illustrated outflow side will be described. The manifold 25 smoothly draws an arc from its outflow port (connecting portion with the flange 19) in a predetermined upper angle direction. It turns and reaches the connection port with the flow tubes 1 and 2. In this way, by setting the tube connection port of the manifold to the tube rising angle, the flow tube itself can be simply bent in one direction, and the connected flow tube and manifold form a smooth arcuate shape as a whole. To do. The manifold forms two flow paths so as to branch into two flow tubes 1 and 2 from one outlet.
[0017]
Thus, the flow tubes 1 and 2 themselves that perform an important function for vibration measurement have only a simple curved configuration in one direction, and the flow path is connected to the external piping from the two flow tubes. Complex flow path changes in the direction are handled by the manifold. The flow tubes 1 and 2 can be fixed to the manifold by welding or the like, do not need a flexible portion, absorb the heat stress by making the flow tube into an arcuate shape, and have a structure strong against piping stress.
[0018]
Also, a substrate 28 is provided near both ends of the flow tubes 1 and 2 to form a vibration node when driven, and this is secured to the flow tubes 1 and 2 so that the flow tubes 1 and 2 are maintained in parallel. doing. When this substrate 28 is provided, the fixing point by the substrate 28 becomes the first fulcrum of vibration, and the coupling end of the flow tubes 1 and 2 and the upper ends of the inlet side and outlet side manifolds 25 is the second fulcrum. And vibrate.
[0019]
In the central portion of the arcuate flow tube, the drive device 15 has a drive device coil attached to one flow tube 1 and a drive device magnet attached to the other flow tube 2 via attachments. Wiring to the driving device coil is connected to the outside of the Coriolis meter through the flexible printed board 12 and the wiring extraction unit 34. The wiring extraction portion 34 is supported by and penetrates the base 30 having a semicircular cross section. A cover 31 is integrally joined to the base portion 30 and cooperates with the flange portion 26 of the manifold portion to form an airtight space therein. In the pair of vibration detection sensors 16 and 17, on both sides of the driving device 15, a detection sensor magnet is attached to one flow tube 1 and a detection sensor coil is attached to the other flow tube 2 via attachments.
[0020]
In operation, the driving device 15 resonates and drives the two flow tubes 1 and 2 in mutually opposite phases at the center of the two parallel flow tubes 1 and 2. The pair of vibration detection sensors 16 and 17 are installed at left and right symmetrical positions with respect to the mounting position of the driving device 15 to detect a phase difference proportional to the Coriolis force. The illustrated driving device 15 and the pair of vibration detection sensors 16 and 17 are both disposed between the tube axes between the flow tube 1 and the flow tube 2. In other words, as shown in FIG. 1, when the two flow tubes are viewed in the overlapping direction, the drive device 15 and the pair of vibration detection sensors 16 and 17 are respectively connected between the flow tubes and the flow of both. The tube is arranged around the line connecting the central axes of the tubes. As a result, a driving force can be applied on the line connecting the central axes of both flow tubes, and a Coriolis force based on this driving force can be detected, so that an inertia moment due to a vibration inertia force does not occur.
[0021]
As shown, temperature sensors are provided at two locations. Variations in the distance between the fixed ends on both sides of the flow tube affect the vibration frequency and need to be corrected. The illustrated apparatus performs this correction by measuring the representative temperature of the base 30 and estimating the elongation. In addition, a sensor is provided for measuring temperature near the manifold coupling end of the flow tube. This is to correct the change in rigidity due to the change in the temperature of the flow tube.
[0022]
The flow tube having an arcuate configuration shown in FIG. 1 is composed of a central arc portion and straight portions on both sides thereof, and an inlet conduit and an outlet conduit are connected in the same direction as the flow tube at a predetermined rising angle. Yes. The shape of such a flow tube is not only designed to be compact, but also needs to be determined to be optimal in consideration of thermal effects.
[0023]
Hereinafter, a method of determining the tube shape so as to suppress the stress to a predetermined value and to be the most compact when the measurement fluid undergoes a temperature sudden change will be described with reference to FIGS.
[0024]
In FIG. 2, the connection points between the inlet and outlet manifolds of the flow tube are the points C ′ and C, respectively, the top vertex on the intermediate flow tube is the point A, and the connection point between the central arc and the straight line part. Is indicated as B point. Point A is the coordinate origin, and from there, the right direction is the x-axis positive direction, and the downward direction is the y-axis positive direction. Using the line connecting the arc center of the arc portion and point A as a reference, the angle to the arc-shaped arbitrary point is indicated as φ, the angle to the end point of the arc portion (ie B point) is indicated as φ0, and the radius of the arc portion is indicated as R. Yes. Furthermore, the height of the flow tube is indicated as h, the half of the straight line length connecting the points C ′ and C (the straight line distance between the end points) is L / 2, and the angle formed by this straight line and the straight line portion of the flow tube is indicated as φ1. doing.
[0025]
As a procedure for determining the shape of the flow tube, the ratio h / L = 1/3 to 1/4 (0.33 to 0.25) of the linear distance L between the end points of the flow tube and the vertical height h of the flow tube To do. In view of the above, the present invention is premised on two parallel arcuate collimators that are excellent in stress dispersion and earthquake resistance. Normally, a conventional curved tube type flow tube is configured to satisfy h / L> 1.3, and a straight tube type flow tube is naturally configured such that h = 0 and h / L = 0.
[0026]
Furthermore, as a precondition for determining the shape, the target is to reduce the pressure loss including the manifold and the arcuate tube at the maximum flow rate to 1 bar or less. (Total of pressure loss due to the restriction effect of the inlet side manifold and the expansion effect of the outlet side manifold and the pressure loss with the total length of the arcuate tube as the equivalent straight pipe length). The target is to set the time phase difference of the sine wave output from the two tube sensor coils at the maximum flow rate to 6 μs or more. Set the natural frequency of the tube to 250-400Hz higher than the commercial frequency.
[0027]
From the above assumptions, the tube inner diameter Di and the end point linear distance L are determined. Next, details of the shape of the arcuate tube roughly determined in this manner are obtained with less stress due to the sudden change temperature of the measurement fluid. In conclusion, the maximum stress generated at the fixed end can be obtained as shown in the following equation (24). Since the maximum stress can be obtained in association with the length L1 of the straight line portion, the vertical height h of the tube can be obtained together with the length L1 where the maximum stress is reduced. This will be described in detail below.
[0028]
As shown in Fig. 2, point A is the top of the arcuate tube, arc tube (half) between A and B, straight tube between B and C, and points C and C 'are fixed. ing. From the tube continuation condition, φ0 = φ1. The thermal stress generated in the tube when the temperature of the liquid flowing inside the tube suddenly changes (suddenly) from t1 to t2 is obtained, but the point moved by d in the y-axis direction from point A, that is, the elastic center ( Analyze the moment 0) due to thermal expansion as the origin. The coordinates with this elastic center as the origin are represented by (x1, y1). That is, x1 = x and y1 = y-d.
[0029]
According to Timoshenko, the origin of the coordinates is moved from point A to point O with a fixed arch as shown in FIG. 3, the longitudinal elastic modulus of the tube material is E, and the secondary moment of inertia of the tube = π / 64 (Do ⁴ -Di ⁴ ) If I is I, the new ordinate y1 = y−d is
[Expression 1]

[0031]
When the distance d is selected so as to satisfy the above, d is expressed by equation (2).
[0032]
[Expression 2]

[0033]
First, the elastic strain energy U _x due to expansion in the x direction due to temperature change is considered. s: length of the arch (bow) at an arbitrary position, ds: minute length at an arbitrary position of the arch, U: elastic strain energy, Mx: moment in the X-axis direction, My: moment in the Y-axis direction, N: compression of the tube, alpha: temperature expansion coefficient of the tube material, t: a temperature or temperature difference of the tube, bending the compressive force is a horizontal force in the elastic center (O point) H _o and the elastic center (O point) If we take the moment M _o as a static quantity, from the second theorem of Casteriano,
[0034]
[Equation 3]

[0035]
[Expression 4]

[0036]
Holds. Here [0037]
[Equation 5]

[0038]
Because M _o = 0 due to the condition of the elastic center
[Formula 6]

[0040]
Is obtained. The bending moment and compressive force of the arbitrary cross section of the arcuate tube can be obtained from equations (5) and (6). Entering the specifications of the arcuate tube with arcs and straight lines as shown in FIG.
[Expression 7]

[0042]
Where R is the arc radius of the arc portion of the arched tube.
Therefore, the distance from the vertex A to the elastic center is [0043]
[Equation 8]

[0044]
It is expressed.
Similarly, solving equation (6):
[Equation 9]

[0046]
It becomes. Where [0047]
[Expression 10]

[0048]
[Expression 11]

[0049]
From the equations (5), (9), (10), and (11), the bending moment and compressive force N of the arbitrary tube cross section can be obtained. Here, A: the cross-sectional area of the tube = π · (Do ² −Di ² ) / 4, Do: the outer diameter of the tube, and Di: the inner diameter of the tube.
[0050]
Next, with respect to the vertical direction due to thermal expansion, as shown in FIG. 4, the following equation is established, where H1 is the static force and M1 is the static moment.
[0051]
[Expression 12]

[0052]
From Casteriano's second theorem, if the elastic strain energy is Uy,
[0053]
[Formula 13]

[0054]
Also,
[0055]
[Expression 14]

[0056]
From this [0057]
[Expression 15]

[0058]
Is obtained. Where [0059]
[Expression 16]

[0060]
[Expression 17]

[0061]
[Expression 18]

[0062]
Since Mx and My are in the same direction, the combined moment M is
[Equation 19]

[0064]
It becomes. The maximum moment is the value at the fixed end C. If this is M max, the maximum bending stress is [0065]
[Expression 20]

[0066]
It becomes. Here, Z: section modulus of the arch = (π / 32) · (Do ⁴ −Di ⁴ ) / Do. The compressive stress at point C is [0067]
[Expression 21]

[0068]
Therefore, the resultant stress is [0069]
[Expression 22]

[0070]
As a result of calculation, it was found that σC is as small as 2-3% of σMmax and can be ignored. That is,
[0071]
[Expression 23]

[0072]
As good as Therefore, the maximum stress is generated at the fixed end.
[Expression 24]

[0074]
It is expressed.
For example, when the diameter of the tube is 25mm and stainless steel is used, the dimensions are the tube inner diameter Di = 15mm, the tube wall thickness is 0.75mm, and the sudden change temperature is 110 ° C.
[0075]
[Expression 25]

[0076]
When L = 371.4 mm = constant and φ1 = φ0 = 40 °, the maximum stress σmax and the tube height h when the dimension ratio h / L is changed are shown in the graph of FIG. It becomes like this. As can be seen from the figure, the maximum stress σmax converges to the minimum value (about 125 N / mm 2) at the dimensional ratio h / L ≧ 0.31. However, if the dimension ratio h / L is increased, h increases. Therefore, if the dimension ratio h / L = 0.31, the maximum stress is small and the dimension is compact (the white mark in FIG. 5 is the point). ). Further, what is determined as this point is shown as “Example” in FIGS. 9 and 10. Thus, although this point is optimal, as shown in FIG. 5, the maximum stress σmax is practically the minimum value within the range of the dimensional ratio h / L = 1/4 to ３. On the other hand, the tube height h is also sufficiently low and can be configured compactly. If the dimensional ratio h / L is reduced, the maximum stress increases. However, if the stress value when h / L = 1/3 is σmin, it can be suppressed to 1.3σmin or less if h / L ≧ 1/4. it can.
[0077]
FIG. 9 shows the shape of an embodiment of the present invention (L1 = 130 mm, h = 115 mm, h / L = 0.31) on the right side from the center, and a comparative example (L1 = 20 mm, h = out of the scope of the present invention). 75 mm, h / L = 1/5) is shown in comparison with the left side.
[0078]
FIG. 10 is a diagram showing “change in density accuracy after temperature change” for the above-described example and comparative example. This shows the result of measuring the density accuracy by rapidly changing the fluid temperature to the temperature difference shown on the horizontal axis of the graph (abrupt change) and then returning it to room temperature again. As shown in the figure, the example does not cause an error in the measured density accuracy even if it suddenly changes to a large temperature difference, whereas in the comparative example, the density display error increases as the sudden change temperature increases. It has increased.
[0079]
FIG. 11 is a diagram showing a change in vessel difference after a sudden temperature change when the dimensional ratio is changed. It is the data calculated | required by actual measurement about the flowmeter which has a dimension as shown in the right margin in the figure. When using a flow meter, the temperature suddenly changes when the flow tube temperature rapidly rises to about 130 ° C during cleaning (steam cleaning). Strange things are possible. Assuming the above, an experiment was conducted to load a temperature difference of 110 ° C. As a result of the experiment, those manufactured in the range of 1/4 ≤ h / L ≤ 1/3 have almost no change in the instrumental error after sudden temperature change, and 1/4 ≤ h / L ≤ 1/3. Those produced with h / L = 1/5, which is out of the range, showed a difference of -0.2% or more. As the Coriolis flowmeter, -0.2% instrumental change is large and deviates from the guaranteed accuracy of the flowmeter (the instrumental accuracy of a general Coriolis mass flowmeter is about ± 0.2%).
[0080]
FIG. 12 is a diagram showing a similar measurement result representing “density display change” instead of “vessel difference change” in FIG. The same tendency as in FIG. 11 is obtained. Those manufactured with h / L = 1/5 have a large variation in density display value and deviate from the guaranteed accuracy (generally guaranteed accuracy as a density meter is about ± 0.002 g / ml).
[0081]
From the actual measurement results as shown in FIGS. 11 and 12, it was confirmed that when h / L was 1/4 or less, the instrumental difference change and the density display value changed rapidly. For h / L = 1/5, the flow tube stress exceeds the elastic limit due to temperature change and causes plastic deformation, and the flow tube cycle changes due to the change in mechanical properties of the flow tube. It can be estimated that the density display value has changed.
[0082]
【The invention's effect】
According to the present invention, when the measurement fluid undergoes a sudden temperature change, it is possible to determine the tube shape so that the stress is kept at a predetermined value and the most compact.
[0083]
In addition, the present invention has an effect of being excellent in stress dispersion and earthquake resistance because the flow tube is a parallel two arched tube type composed of an arc segment and a straight segment.
[Brief description of the drawings]
FIG. 1 is a diagram illustrating a Coriolis meter to which the present invention is applied, assuming that an inlet pipe and an outlet pipe are mounted horizontally, a partial sectional view (left side view) viewed from the front, and a central portion It is the side view cut | disconnected by (right view).
FIG. 2 is a specification diagram of an arcuate tube.
FIG. 3 shows a fixed arch.
FIG. 4 is a moment diagram due to thermal expansion in the vertical direction.
FIG. 5 is a graph showing the maximum stress σmax and the tube height h when the straight line length L1 is changed.
FIG. 6 is a diagram for explaining a flow tube having an arcuate configuration constituted by a central arc portion and straight portions on both sides thereof.
FIG. 7 is a conceptual diagram for explaining the operation of a Coriolis meter having a conventional flow tube having an arcuate configuration.
FIG. 8 is a view for explaining a conventional flow tube having an arc configuration.
FIG. 9 is a diagram showing the shape of an example of the present invention on the right side from the center and a comparative example outside the range of the present invention in comparison with the left side.
FIG. 10 is a diagram showing “change in density accuracy after temperature change” for an example and a comparative example.
FIG. 11 is a diagram showing a change in vessel difference after a temperature sudden change when the dimensional ratio is changed.
12 is a diagram showing a similar actual measurement result representing “density display change” instead of “vessel difference change” in FIG. 11; FIG.
[Explanation of symbols]
DESCRIPTION OF SYMBOLS 1 Flow tube 2 Flow tube 12 Flexible printed board 15 Driving device 16, 17 Vibration detection sensor 18, 19 Flange 25 Manifold 26 Gutter part 28 Substrate 30 Base part 31 Cover 34 Wiring extraction part

Claims (3)

Two flow tubes in parallel, an inlet side manifold that branches from the measurement fluid inlet to the two flow tubes, and an outlet side manifold that joins the measurement fluid flowing through the two flow tubes and flows out from the measurement fluid outlet And a driving device that resonates and drives one flow tube in opposite phases with respect to the other flow tube, and is installed at symmetrical positions on both the left and right sides with respect to the mounting position of the driving device and is proportional to the Coriolis force. In a bow-shaped tube Coriolis meter provided with a pair of vibration detection sensors for detecting a phase difference,
Each of the two flow tubes is formed into an arcuate shape comprising a central arc portion and straight portions on both sides thereof,
Based on the target pressure loss including the manifold and arcuate flow tube at the maximum flow rate, the target time phase difference of the sine wave output from the vibration detection sensor at the maximum flow rate, and the tube natural diameter and the tube end point based on the target natural frequency of the tube Determine the linear length of
The flow tube shape is determined so that the dimensional ratio (h / L) between the straight line length (L) between the tube end points and the vertical height (h) of the flow tube is between 1/4 and 1/3. An arcuate tube type Coriolis meter characterized by The length of the straight portion is selected so that the thermal stress due to the sudden change temperature of the measurement fluid is reduced, and the flow tube is within the range where the thermal stress is substantially constant even if the length of the straight portion is changed. The arcuate tubular coriolis according to claim 1, wherein the shape of the flow tube is determined so as to reduce the height in the direction. Two flow tubes in parallel, an inlet side manifold that branches from the measurement fluid inlet to the two flow tubes, and an outlet side manifold that joins the measurement fluid flowing through the two flow tubes and flows out from the measurement fluid outlet And a driving device that resonates and drives one flow tube in opposite phases with respect to the other flow tube, and is installed at symmetrical positions on both the left and right sides with respect to the mounting position of the driving device and is proportional to the Coriolis force. In a method for determining the shape of an arcuate tubular coriolis meter comprising a pair of vibration detection sensors for detecting a phase difference,
Each of the two flow tubes is formed into an arcuate shape comprising a central arc portion and straight portions on both sides thereof,
Based on the target pressure loss including the manifold and arcuate flow tube at the maximum flow rate, the target time phase difference of the sine wave output from the vibration detection sensor at the maximum flow rate, and the tube natural diameter and the tube end point based on the target natural frequency of the tube Determine the linear length of
The flow tube shape is determined so that the dimensional ratio (h / L) between the straight line length (L) between the tube end points and the vertical height (h) of the flow tube is between 1/4 and 1/3. A method for determining the shape of an arched tube type coriolis meter.

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