CN111208312A - Method for monitoring rotating speed and strain of high-speed rotating tubular structure based on waves - Google Patents

Method for monitoring rotating speed and strain of high-speed rotating tubular structure based on waves Download PDF

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CN111208312A
CN111208312A CN201911405520.XA CN201911405520A CN111208312A CN 111208312 A CN111208312 A CN 111208312A CN 201911405520 A CN201911405520 A CN 201911405520A CN 111208312 A CN111208312 A CN 111208312A
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tubular structure
waves
excitation
strain
speed
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CN111208312B (en
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吕朝锋
张殷楠
张鹤
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Zhejiang University ZJU
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01P—MEASURING LINEAR OR ANGULAR SPEED, ACCELERATION, DECELERATION, OR SHOCK; INDICATING PRESENCE, ABSENCE, OR DIRECTION, OF MOVEMENT
    • G01P3/00—Measuring linear or angular speed; Measuring differences of linear or angular speeds
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
    • G01B15/00—Measuring arrangements characterised by the use of electromagnetic waves or particle radiation, e.g. by the use of microwaves, X-rays, gamma rays or electrons
    • G01B15/06—Measuring arrangements characterised by the use of electromagnetic waves or particle radiation, e.g. by the use of microwaves, X-rays, gamma rays or electrons for measuring the deformation in a solid
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/11—Complex mathematical operations for solving equations, e.g. nonlinear equations, general mathematical optimization problems

Abstract

The invention discloses a method for monitoring the rotating speed and strain of a high-speed rotating tubular structure based on waves, which comprises the steps of giving wave excitation to the outer surface of the tubular structure, receiving excitation waves at a receiving position, enabling the receiving position and the position for applying the wave excitation to be on the same cross section of the tubular structure and on the outer surface opposite to the rotating direction of the tubular structure, enabling an included angle between the two positions to be smaller than 180 degrees, enabling the wavelength of the excitation waves to be the same as the perimeter of the outer boundary of the tubular structure, controlling the frequency of the excitation waves to continuously increase from zero, analyzing the frequency of the receiving waves, stopping excitation when the first maximum resonant frequency occurs, enabling the value of the obtained resonant frequency to be the angular speed of the rotation of the tubular structure, and obtaining the strain condition of one point in a rotating body according to the relationship. The non-contact monitoring method based on the waves does not need to implant equipment, has small interference on an original structure and low requirement on space conditions, and is suitable for rotating tubular structures with any sizes and used already.

Description

Method for monitoring rotating speed and strain of high-speed rotating tubular structure based on waves
Technical Field
The invention relates to the field of structure dynamic monitoring, in particular to a method for monitoring the rotating speed and strain of a high-speed rotating tubular structure based on waves.
Background
The high-speed rotating tubular structure is widely applied to industrial structures such as various rotors, flywheels and the like, and in the application process, the rotating speed and the strain condition of the tubular structure are generally required to be monitored, so that the structural damage caused by overhigh rotating speed and overlarge strain is avoided. According to the existing rotating speed monitoring method for the high-speed rotating structure, the implanted equipment is difficult to repair after being damaged, but the non-implanted equipment needs to be externally connected to a rotating shaft or a sensor is shielded through the structure rotating process, so that the method is not suitable for the situation that the rotating shaft cannot provide an external space and the tubular structure cannot realize periodic shielding. According to the strain monitoring method, the traditional strain gauge needs an external circuit and monitoring equipment, the arrangement is complicated, and the strain monitoring mode of carrying out signal acquisition through implanted equipment and wirelessly transmitting the acquired signal to the monitoring equipment also faces the problem that the strain gauge is difficult to repair after being damaged.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention provides a method for monitoring the rotating speed and the strain of a high-speed rotating tubular structure based on waves, which has the following specific technical scheme:
a method for monitoring the rotating speed and strain of a high-speed rotating tubular structure based on waves comprises the following steps:
giving wave excitation on the outer surface of the tubular structure, receiving excitation waves at a receiving position, wherein the receiving position and the position for applying the wave excitation are on the same cross section of the rotary tubular structure, the receiving position is positioned on the outer surface opposite to the rotation direction of the tubular structure, the included angle between the two positions is less than 180 degrees, the wavelength of the excitation waves is the same as the perimeter of the outer boundary of the tubular structure, the frequency of the excitation waves is controlled to be increased continuously from zero, the frequency of the receiving waves is analyzed while the excitation frequency is increased, the excitation is stopped when the first maximum resonance frequency occurs, the obtained value of the resonance frequency is the angular speed of the rotation of the tubular structure, and the radial strain epsilon of one point in the rotary body is obtained according to the relation between the rotation speed of the tubular structure and the strainrAnd hoop strain epsilonθ。
Further, the radial strain εrAnd hoop strain epsilonθThe size is obtained by the following formula,
Figure BDA0002348525410000011
Figure BDA0002348525410000012
Figure BDA0002348525410000021
Figure BDA0002348525410000022
Figure BDA0002348525410000023
Figure BDA0002348525410000024
r∈[a,b],θ∈[0,2π)
wherein u isrThe method is characterized in that the method is the radial displacement of any point in a tubular structure, r is a radial coordinate, theta is an annular coordinate, omega is the rotation angular velocity of the tubular structure, a is the inner diameter of the tubular structure, b is the outer diameter of the tubular structure, rho is the mass density of a structural material, E is the Young modulus of the structural material, v is the Poisson's ratio, pi is the circumferential ratio, and the coefficient C is1And C2The values of (a) are related to the boundary conditions of the tubular structure:
if the inner and outer boundaries of the rotating tubular body are free boundaries, the coefficients satisfy:
Figure BDA0002348525410000025
and is established on the inner and outer boundaries, so as to obtain the value of the coefficient,
if the inner boundary of the tubular structure is fixed and the outer boundary is free, the coefficients satisfy:
at the outer boundary
Figure BDA0002348525410000026
On the inner boundary urAnd (5) obtaining a coefficient value when the coefficient value is 0.
The invention has the advantages that the invention obtains the rotating speed of the high-speed rotating tubular structure by exciting the wave on the outer surface of the high-speed rotating tubular structure and analyzing the frequency of the received wave, obtains the strain of one point in the rotating body according to the corresponding relation between the rotating speed and the strain, eliminates the defect that the traditional implanted equipment is difficult to repair after being damaged by a non-contact monitoring mode, can excite and receive the wave on any cross section vertical to the symmetrical axis of the tubular structure, eliminates the limit value of external equipment on the rotating shaft with specific requirements on space, can be suitable for tubular structures with various sizes by monitoring the rotating speed and the strain by the exciting wave, and eliminates the defect that the sensor is not suitable for the structure which can not realize periodic shielding by the sensor in the rotating process of the structure. According to the invention, the strain condition of any point in the tubular structure can be obtained by utilizing the relation between the rotating speed and the strain, strain gauges do not need to be arranged at a plurality of positions of the tubular structure, the equipment arrangement is simple, and the interference to the original structure is small. Meanwhile, the wave-based monitoring mode provided by the invention is suitable for monitoring the used rotating structure because the equipment does not need to be implanted into the rotating body.
Drawings
The invention is further illustrated with reference to the following figures and examples.
FIG. 1 is a schematic flow chart of an embodiment of the present invention;
FIG. 2 is a schematic diagram of the method of the present invention;
in the figure, 1 is a tubular structure, 2 is an excitation, 3 is a receiving, and 4 is a tubular structure rotating shaft.
Detailed Description
The present invention will be described in detail below with reference to the accompanying drawings and preferred embodiments, and the objects and effects of the present invention will become more apparent, it being understood that the specific embodiments described herein are merely illustrative of the present invention and are not intended to limit the present invention.
As shown in fig. 1, the method for monitoring the rotational speed and strain of the high-speed rotating tubular structure based on waves of the present invention specifically comprises the following steps:
giving wave excitation 2 to the outer surface of the tubular structure 1, receiving the excitation 2 wave at a receiving 3 position, wherein the receiving 3 position and the position for applying the wave excitation 2 are on the same cross section of the rotary tubular structure 1, the receiving 3 position is positioned on the outer surface opposite to the rotation direction of the tubular structure 1, an included angle between the two positions is less than 180 degrees, the wavelength of the excitation 2 wave is the same as the peripheral length of the outer boundary of the tubular structure 1, controlling the frequency of the excitation 2 wave to continuously increase from zero, analyzing the frequency of the receiving 3 wave while increasing the frequency of the excitation 2, stopping the excitation 2 when the first maximum resonant frequency occurs, and obtaining the value of the resonant frequency which is the angular speed of the rotation of the tubular structure;
as shown in fig. 2, the deformation of a tubular structure rotating at high speed at an angular velocity Ω can be regarded as a uniform expansion deformation with an inner diameter a and an outer diameter b of the tubular structure. And setting a radial coordinate r, a circumferential coordinate theta and an axial coordinate z, wherein the strain does not change along with the axial coordinate z for a point in the tubular structure for determining the radial coordinate r and the circumferential coordinate theta. Therefore, only radial and hoop strain levels are required. According to the relation between the rotating speed and the strain of the tubular structure, the radial strain epsilon of one point in the rotating body can be obtainedrAnd hoop strain epsilonθThe size of the capsule is determined by the size of the capsule,
Figure BDA0002348525410000031
wherein u isrIs the radial displacement of a point inside the tubular structure, which can be expressed as an equation for the rotational speed,
Figure BDA0002348525410000032
in the formula (I), the compound is shown in the specification,
Figure BDA0002348525410000041
Figure BDA0002348525410000042
Figure BDA0002348525410000044
r∈[a,b],θ∈[0,2π)
wherein rho is the mass density of the structural material, E is the Young modulus of the structural material, v is the Poisson's ratio, pi is the circumference ratio, and the coefficient C1And C2The values of (a) are related to the boundary conditions of the tubular structure:
if the inner and outer boundaries of the rotating tubular structure are free boundaries, the coefficients satisfy:
Figure BDA0002348525410000045
and is established on the inner and outer boundaries, so as to obtain the value of the coefficient,
if the inner boundary of the tubular structure is fixed and the outer boundary is free, the coefficients satisfy:
at the outer boundary
Figure BDA0002348525410000046
On the inner boundary urAnd (5) obtaining a coefficient value when the coefficient value is 0.
It will be understood by those skilled in the art that the foregoing is only a preferred embodiment of the present invention, and is not intended to limit the invention, and although the invention has been described in detail with reference to the foregoing examples, it will be apparent to those skilled in the art that various changes in the form and details of the embodiments may be made and equivalents may be substituted for elements thereof. All modifications, equivalents and the like which come within the spirit and principle of the invention are intended to be included within the scope of the invention.

Claims (2)

1. A method for monitoring the rotating speed and strain of a high-speed rotating tubular structure based on waves is characterized by comprising the following steps:
giving wave excitation on the outer surface of the tubular structure, receiving excitation waves at a receiving position, wherein the receiving position and the position for applying the wave excitation are on the same cross section of the rotary tubular structure, the receiving position is positioned on the outer surface opposite to the rotation direction of the tubular structure, the included angle between the two positions is less than 180 degrees, the wavelength of the excitation waves is the same as the perimeter of the outer boundary of the tubular structure, the frequency of the excitation waves is controlled to be increased continuously from zero, the frequency of the receiving waves is analyzed while the excitation frequency is increased, the excitation is stopped when the first maximum resonance frequency occurs, the obtained value of the resonance frequency is the angular speed of the rotation of the tubular structure, and the radial strain epsilon of one point in the rotary body is obtained according to the relation between the rotation speed of the tubular structure and the strainrAnd hoop strain epsilonθ。
2. Method for rotational speed and strain monitoring of a wave-based high speed rotating tubular structure according to claim 1, characterized in that the radial strain ∈ isrAnd hoop strain epsilonθThe size is obtained by the following formula,
Figure FDA0002348525400000011
Figure FDA0002348525400000012
Figure FDA0002348525400000013
Figure FDA0002348525400000014
Figure FDA0002348525400000015
Figure FDA0002348525400000016
r∈[a,b],θ∈[0,2π)
wherein u isrThe method is characterized in that the method is the radial displacement of any point in a tubular structure, r is a radial coordinate, theta is an annular coordinate, omega is the rotation angular velocity of the tubular structure, a is the inner diameter of the tubular structure, b is the outer diameter of the tubular structure, rho is the mass density of a structural material, E is the Young modulus of the structural material, v is the Poisson's ratio, pi is the circumferential ratio, and the coefficient C is1And C2The values of (a) are related to the boundary conditions of the tubular structure:
if the inner and outer boundaries of the tubular structure are free boundaries, the coefficients satisfy:
Figure FDA0002348525400000021
and is established on the inner and outer boundaries, so as to obtain the value of the coefficient,
if the inner boundary of the tubular structure is fixed and the outer boundary is free, the coefficients satisfy:
at the outer boundary
Figure FDA0002348525400000022
On the inner boundary urAnd (5) obtaining a coefficient value when the coefficient value is 0.
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