SU1619044A1 - Method of measuring mass flow rate - Google Patents

Description

oscillations on the second natural form of oscillations under the action of Coriolis inertia forces (line 20, Figures 1 and 3).

The equation of motion of the resonator on the first natural waveform has the form

Y - | - (1 - cos ax) sintOt, (I)

where A is the amplitude of the forced oscillations; 2fr

one

a-g-;

where R, L, M, N are constant integrations;

The Ab QMCOs "t a

The constant integrations are found from the boundary conditions determined by the pinning conditions. For rigid fastening of the ends of the resonator have

x Oh

 0; x L

Y (x)

15

1 - the length of the resonator; (0 2 H f - circular oscillation frequency,

Ј - oscillation frequency. On the area of the resonator having a length dx and containing inside a controlled liquid with linear mass m (fig.Z), the Coriolis inertia force dFy acts:

F to 2mV

. &.

dxdt

(2)

where V is the velocity of the medium;

t is time; mV Q j mass flow rate of the medium;

x is the tube length coordinate. Substituting the value of Y from equation (1) into expression (2), we obtain

db AQCOQ sinaxcosCOtdx.

(3)

TO

For small deformations, the equation of the elastic line under the action of Coriolis inertia forces has the form

Gt d 1

LUI -jrj

dFK dx

where E is the modulus of elasticity of the material

resonator; L,

I 77 (D -d) - the moment of inertia ce och

cheni resonator;

D and d are the outer and inner diameters of the resonator, respectively.

3, by solving equation (4),

 -, {- -, - sb

 x + mx + s,

R 3 ah + -g- x +

(five)

x Oh

dlM dx

 0

x L

th cable and

what)

e ner4)

20 Then the constant integrations N 0;

and - -J-,.

25 L - -

L aL

2B

R gza

30 Substituting the obtained values of the constant integration in equation (5), have

, ACOQM G 2 3

Y ggf -G sinax - --- 2 to +

35, -1

+ - x - x cosOt. (6)

Since oscillations under the action of Coriolis inertia forces occur in resonance, their amplitude increases Q times, where Q is the value of the mechanical goodness of the resonator.

Then equation (6) takes the form

"--Gglr- 4-

sinax 2332

-.- v-4- ---- v -

50 x cosGJt,

(7)

Thus, the output signal U of the receiver 16 oscillations can be represented (FIG. 2) as the sum of two components shifted in phase by if

2

6 to U2 U2 + U

g

(3)

, &

where U is the output signal of the receiver 16 as a result of oscillations of the resonator 2 under the action of the exciting force;

and - the output signal of the receiver 16 as a result of oscillations of the resonator 2 under the action of Coriolis inertia forces. Taking into account expressions (1) and (7),

write equation (3) in the form

(9)

U2 bsinCOt + ccostjt,

Aqj 2 arctg

2GJQQM (sinax - --- x3 + --- x 2 - x)

Ela (1 - cosax)

I

From expression (10), a value of 20 is obtained or for small phase shifts of the mass flow rate.

0KtAO FM - 2Ј

QM T8 T (11)

,

TO(

Ela (I - cosax)

12

4 / iTO (sinax - -aL

In the case of the installation of receivers 16 and 17 in the antinodes of the second natural mode of oscillation of the resonator 2,

L

those. for x -Ј

to,

QL (16 - 3fr)

X13)

If we measure the time interval A t between the momentum of reaching the output signals U and Uj of a certain amplitude value (for example, zero), then taking into account the fact that Alp G) u, t receive

(bt. (14)

Claims (2)

1. A method for measuring the mass flow rate of a medium flowing through a tubular mechanical resonator, consisting in the excitation of forced where b is - (1 - cosax);  QACOQM I-Ela 2 L a sin ax X3 L2 X - .. Then the phase shift VJЈ and Uj of the receivers 16 NII is defined as  ( ten) scarlet phase shifts World Cup - 2Ј , (12) g to + -r (12) - x) 0 five 0 five 0 five oscillations of the resonator in the direction perpendicular to the flow rate of the controlled medium, on the first natural mode of oscillation with a frequency equal to the resonant frequency of the second natural mode of oscillation, and measuring the parameters of these oscillations, which is the fact that, in order to improve the accuracy measurements, excite self-oscillations of the second identical resonator through which the controlled medium flows, determine the resonant frequency of the second natural form of the second resonator on any natural mode of oscillations a, adjust the frequency of the forced oscillations of the first resonator in accordance with the change in the resonant frequency of the second resonator, and the mass flow rate of the medium is judged by the time interval between the moments of passage of the fixed position of two points of the first resonator located in the antinodes of the second natural mode. „I; 2. The method according to claim 1, characterized in that the mass flow rate of the medium 9.61904410 judging by the phase shift of the oscillatory waveform, divided by two points of the first resonator, by the frequency of oscillations of the first resonator, located in the antinodes of the second collector. i 4A and k- 1 & ./f // &. "I ;; CHЈR ) S, PS W / Vxv d CHA VA7 Editor A. Bobkova Compiled by V.Yarych Tehred A. Kravchuk Order 1134 Circulation 427 VNIIPI State Committee for Inventions and Discoveries at the State Committee on Science and Technology of the USSR 113035, Moscow, Zh-35, Raushsk nab. 4/5 Production and Publishing Combine Patent, Uzhgorod, st. Gagarin, 101 Proofreader S. Shekmar Subscription