1. Field of the Invention
The present invention relates to a vibration type measuring instrument for measuring at least one of density and mass flow rate of a fluid flowed in a straight measurement pipe by vibrating the straight measurement pipe.
2. Description of the Related Art
FIG. 1A shows the configuration of an example of a vibration type measurement instrument. FIG. 1B is a top view of the detecting unit of the vibration type measuring instrument.
The vibration type measuring instrument comprises a detecting unit 1, a driving circuit 8, and a signal processing circuit 9 as shown in FIG. 1A. The detecting unit 1 comprises a hollow straight measurement pipe 2, fixtures 3a and 3b for fixing both ends of the straight measurement pipe 2, supporters 4a and 4b for connecting the fixtures 3a and 3b, a driver 5 for vibrating the straight measurement pipe 2, sensors 6a and 6b for detecting the vibration of the straight measurement pipe 2, and adapters 7a, 7b, and 7c for respectively fixing the driver 5 sensors 6a and 6b as shown in FIGS. 1A and 1B. The straight measurement pipe 2 is provided with a temperature sensor 10 for detecting the temperature of the measurement pipe.
The straight measurement pipe 2 is connected to external pipes not shown in FIG. 1A in such a way that the fluid to be measured can flow through the straight measurement pipe 2. Both ends of the straight measurement pipe 2 are fixed with wax or welded to the fixtures 3a and 3b respectively so that the end portions can be vibration nodes. The supporters 4a and 4b stably support the driver 5, and sensors 6a and 6b. They have greater rigidity than the straight measurement pipe 2, and are connected to the fixtures 3a and 3b through soldering, welding, etc. The sensors 6a and 6b can be speed detecting sensors, displacement sensors, acceleration sensors, etc.
The driver 5 is mounted at the center of the straight measurement pipe 2. The sensors 6a and 6b are mounted symmetrically about the driver 5 in contact with the measurement pipe. When the vibration type measuring instrument is used as a Coriolis mass flow meter, the density of the fluid is measured using at least one of the sensors 6a and 6b by the method described below. Simultaneously, the mass flow rate of the fluid is measured based on the phase difference (time difference) of the fluid vibration between the two sensors 6a and 6b mounted up stream and down stream of the driver 5. When the vibration type measuring instrument is used as a density meter for only measuring the density of a fluid, only one of the sensors 6a and 6b may be mounted (for example, the sensor 6a only) as a sensor for measuring the density.
The straight measurement pipe 2 is vibrated at its resonant frequency by the driver 5 operated according to the drive signal from the driving circuit 8. The detection signals from the sensors 6a and 6b and the temperature detection signal from the temperature sensor 10 are transmitted to the signal processing circuit 9. The signal processing circuit 9 obtains the resonant frequency of the straight measurement pipe 2 according to the detection signals from the sensors 6a and 6b, and calculates the density of the fluid by the operation described below, according to the resultant resonant frequency and the temperature of the straight measurement pipe 2.
The following differential equation (1) is expressed relating to the straight measurement pipe 2 having uniform cross-section, where E indicates the Young's modulus of the straight measurement pipe 2; I indicates the cross-sectional secondary moment of the straight measurement pipe 2; x indicates a position on the straight measurement pipe 2 in the axial direction (x=0 at one end of the measurement pipe 2, and x=L at the other end of the measurement pipe 2); y indicates the vibration amplitude of the straight measurement pipe 2 at the position x (a function with the variable x); .rho.w indicates the density of the fluid; Si indicates the cross-sectional area of the hollow portion of the straight measurement pipe 2; .rho.t indicates the density of the straight measurement pipe 2; St indicates the cross-sectional area of the straight measurement pipe 2; and t indicates time. EQU EI(.differential..sup.4 /.differential.x.sup.4)+(.rho.wSi+.rho.tSt)(.differential..sup.2 y/.differential.t.sup.2)=0 (1)
Solving the equation (1) using given boundary conditions, the resonant frequency f of the horizontal vibration of the straight measurement pipe 2 is obtained by the following equation (2). EQU f=.lambda..sup.2 {EI/(.rho.wSi+.rho.tSt)}.sup.1/2 /(2.pi.L.sup.2)(2)
(.lambda. indicates the constant determined by the boundary conditions and vibration mode of the straight measurement pipe 2; and L indicates the length of the straight measurement pipe 2 in the axial direction)
The above described equation (2) is solved for .rho.w as indicated below. EQU .rho.w{(.lambda..sup.4 EI/4.pi..sup.2 L.sup.4 f.sup.2)-.rho.tSt}/Si(3)
The density .rho.w of the fluid can be obtained by substituting the detected resonant frequency f of the straight measurement pipe 2 in the above equation (3), and further substituting the Young's modulus E after a temperature amendment is performed based on the temperature of the straight measurement pipe 2 measured by the temperature sensor 10, the secondary cross-sectional moment I obtained by amending the thermal expansion according to the temperature, length L of the measurement pipe, and the cross-sectional areas St and Si.
However, in the case of the device using the straight measurement pipe 2 as shown in FIG. 1, a temperature difference arises between the straight measurement pipe 2 and the supporters 4a and 4b by a change in temperature of, for example, the fluid, surrounding atmosphere, etc., thereby generating a force (axial force) in the straight measurement pipe 2 in the axial direction. The axial force changes, as is well-known, the resonant frequency f of the straight measurement pipe 2, and generates an error in the density .rho.w calculated by the above described equation (3).
The conventional countermeasures to the above problems are to prevent the influence of the axial force by providing a curved measurement pipe, applying a bellows or diaphragm structure at both ends of the measurement pipe, etc., or to limit the difference in temperature between the fluid and the surrounding atmosphere. However, a curved measurement pipe raises hygienic problems such as corrosions caused by the puddles of the fluid, which is hard to clean, and can create a large pressure loss in the fluid, thereby making problems for the user. There are additional problems with the bellows and diaphragm structures in that they are complicated in configuration, they are weak against shock when transported because of their mechanical fragility, and they cannot completely eliminate the axial force. Additionally, the method of limiting the temperature difference between the fluid and the surrounding atmosphere imposes large limitations on field online measurements. This is not a desired phenomenon in measurement technology.
Another method of solving the problem due to axial force changes, is to amend a measured density value based on the measured axial force by measuring the axial force working on the measurement pipe by measuring the temperature difference between the measurement pipe and a supporter, measuring the distortion of the measurement pipe using a strain gauge, etc. However, this method also has the following problems.
That is, the above described differential equation (1) is expressed as follows when the axial force (tension) T is present. EQU EI(.differential..sup.4 y/.differential.x.sup.4)-T(.differential..sup.2 y/.differential.x.sup.2)+(.rho.wSi+.rho.tSt)(.differential..sup.2 y/.differential.t.sup.2)=0 (4)
Solving the differential equation (4) under the given boundary conditions, the equations (2) and (3) for obtaining the density values, which are expressed as follows, are obtained. EQU g (f, .rho.w, T, E, I, Si, .rho.t, St)=0 (5)
This is an extremely complicated function not explicitly containing the density .rho.w. Therefore, in this case, the density .rho.w cannot be directly obtained as shown by equation (3), and a numerical analysis such as a successive approximation cannot be applied in practical use because of the complicated equation.
In addition to the above described problems, the mass of the components in contact with or added to the measurement pipe, such as the driver 5, sensors 6a and 6b, and temperature sensor 10, can be a factor in lowering the density measurement precision. The inertial force of such an added mass functions as a shearing force for the measurement pipe, and furthermore complicates the differential equation (4) and function (5), thereby making the computation of the density .rho.w more difficult.
In the method of obtaining the axial force based on the temperature difference between a measurement pipe and a supporter, the temperature distribution of the supporter changes with the thermal conductivity of the supporter and the temperature of the fluid and the surrounding atmosphere, therefore the axial force cannot be correctly measured. The method of fixing a strain gauge to a measurement pipe has problems in the fixing technology and long-term reliability. Therefore, it is difficult to use this method for mass production.