CN105004309B - A kind of wedge angle detecting method - Google Patents
A kind of wedge angle detecting method Download PDFInfo
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- CN105004309B CN105004309B CN201510243214.6A CN201510243214A CN105004309B CN 105004309 B CN105004309 B CN 105004309B CN 201510243214 A CN201510243214 A CN 201510243214A CN 105004309 B CN105004309 B CN 105004309B
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
- G01B11/00—Measuring arrangements characterised by the use of optical techniques
- G01B11/26—Measuring arrangements characterised by the use of optical techniques for measuring angles or tapers; for testing the alignment of axes
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- Testing Of Devices, Machine Parts, Or Other Structures Thereof (AREA)
- Measurement Of Mechanical Vibrations Or Ultrasonic Waves (AREA)
Abstract
The invention discloses a kind of wedge angle detecting methods, including：According to principle of elasticity, the stress and wedge wave displacement relation of linear type wedge are obtained；According to wave equation, the dispersion equation that wedge wave is propagated is obtained in conjunction with boundary condition；Dispersion equation is solved using secondary extrapolation and five step iterative methods, and draws the theoretical dispersion curve of wedge wave propagation；Wedge point excitation using laser action in wedge generates wedge wave, and is optically acquired to wedge wave signal；The actual measurement dispersion curve that wedge wave is propagated is drawn according to the wedge wave signal of acquisition；The same order wedge wave mode frequency dispersion of theoretical dispersion curve and actual measurement dispersion curve is compared, by changing wedge angle so that theoretical dispersion curve and actual measurement dispersion curve coincide, to which inverting obtains wedge angle.The present invention provides a kind of reliable method to measure the angle of wedge, to realize that the on-line checking of angle provides guidance foundation.
Description
Technical field
The present invention relates to ultrasonic detecting technology field more particularly to a kind of wedge angle detecting methods.
Background technology
Wedge design material is a kind of very common structural material.The metal plate-like structure of non-uniform thickness, especially
Metal tapered member is widely used in industrial materials and its parts.Angle is an important parameter of wedge.And angle
Degree and angle measurement technique play an important role in economy and industrial development, and High-precision angle measuring technique is industrial production
With a vital step in quality control.Therefore, find a kind of be detected to wedge angle has weight with the method assessed
The meaning wanted.
All there is traditional detection method certain limitation, common detection method to have：
1) mechanical angle measurement technique：Mechanical angle measurement technique is mainly using end tooth indexing as representative.Multiple tooth indexing is machine
A kind of most common method in tool formula angle-measuring method, it be it is a kind of using a pair of of number of teeth and the identical end-toothed disc of modulus with different phases
Position is engaged, is positioned to realize indexing function.Since complicated fluted disc rises and falls structure, it is difficult to ensure between each layer
The reasons such as concentricity, therefore be difficult to segment, precision is limited.
2) Electro-magnetic Graduation angle measurement technique：Electro-magnetic Graduation angle measurement technique mainly has round magnetic grid angle measurement and inductosyn angle measurement two
Kind.The disadvantage is that being mostly hand dipping, it is not easy to realize that automation, measurement accuracy are restricted.
3) laser interference angle-measuring method：Laser interference small angle measurement method is using Michelson's interferometer as substantially former mostly
The variation of angle is converted into length variation to measure by reason.The advantages of angle interferometer based on the principle is accuracy
Height, the disadvantage is that measuring device is complicated, it is more difficult to use, this point improves to some extent with the development of laser interferometry instrument.
4) laser auto-collimation method：Using optical autocollimating method, angular metric is converted linear amount, reflection is measured with mircrometer gauge
The small linear change in face and the method that angular metric detected indirectly.It is primarily adapted for use in low-angle and accurate measurement
Work.
By can be seen that mechanical and electromagnetic type angle measurement technique due to grinding to the introduction of common angle-measuring method in recent years
Study carefully relatively early, technology is highly developed.And optics angle-measuring method is due to having the characteristics that accuracy of measurement height and non-cpntact measurement,
It is more and more widely used in angle measurement, and is gradually replacing mechanical and electromagnetic type in some cases and surveys
Amount method.But optical means is since light path adjusts that cumbersome, optical device needs the dynamic range of Precision Machining and measurement small,
Therefore be not suitable for the large batch of production of commercialization.
But there is presently no utilize the research in terms of acoustic method measurement angle.Wedge wave is one kind along wedge top
The guided wave of propagation, it can form energy concentration, Dispersion Characteristics in communication process.Dispersion Characteristics are assessed wedge design
With the major criterion of detection, therefore wedge angle can be detected using it.
Invention content
Technical problem to be solved by the present invention lies in provided a kind of wedge angle detecting method, surveyed using acoustic method
Measure wedge angle.
In order to solve the above technical problem, the present invention provides a kind of wedge angle detecting methods, including：
According to principle of elasticity, the stress and wedge wave displacement relation of linear type wedge are obtained, is propagated to establish wedge wave
Theoretical model；
According to the theoretical model that wave equation and the wedge wave are propagated, the frequency dispersion side that wedge wave is propagated is obtained in conjunction with boundary condition
Journey；
The dispersion equation is solved using secondary extrapolation and five step iterative methods, and draws the theoretical dispersion of wedge wave propagation
Curve；
Wedge point excitation using laser action in wedge generates wedge wave, and is optically adopted to wedge wave signal
Collection；
The actual measurement dispersion curve that wedge wave is propagated is drawn according to the wedge wave signal of acquisition；
The same order wedge wave mode frequency dispersion of the theoretical dispersion curve and the actual measurement dispersion curve is compared, by changing
Become wedge angle so that the theoretical dispersion curve and the actual measurement dispersion curve coincide, to which inverting obtains wedge angle.
Further, described that the stress and wedge wave displacement relation of linear type wedge are obtained according to principle of elasticity, to
The theoretical model for establishing the propagation of wedge wave, specifically includes：
According to principle of elasticity, upper surface stress and the relationship of wedge wave displacement in linear type wedge of obtaining are
To establish the theoretical model of wedge wave propagation, wherein σ3'、τ′31、τ'32For the upper surface components of stress, λ, μ in wedge
It is the Lame constants of material, θ indicates wedge angle, u1、u2、u3Indicate that wedge is applied in the wedge wave generated when external force along x respectively1、
x2、x3The displacement in direction, x1、x2、x3For three orthogonal directions of linear type wedge, x2It is parallel to wedge top line direction, x1、x3Vertically
In wedge top line.
Further, the theoretical model propagated according to wave equation and the wedge wave, wedge is obtained in conjunction with boundary condition
The dispersion equation that wave is propagated, specifically includes：
According to wave equation, wedge wave displacement components u is calculatedjSolution, wherein
In formula, j=1,2,3, αjIndicate that amplitude, k indicate sound wave along x2The wave number that direction is propagated, τ and b indicate phase, v tables
Show sound wave along x2The phase velocity that direction is propagated, t is the time；
In conjunction with the zero stress boundary condition σ ' of free wedge3=τ '32=0 and x3=x1Tan θ/2=0, by wedge wave displacement components uj
Solution substitute into upper surface stress in the wedge and obtain one group of nonlinear equation with displacement relation；
It is zero to make the determinant of the nonlinear equation, to obtain the symmetric and anti-symmetric mould for the wedge wave propagated along wedge top
The dispersion equation of state.
Further, described that the dispersion equation is solved using secondary extrapolation and five step iterative methods, and draw wedge wave
The theoretical dispersion curve of propagation, specifically includes：
The root that wedge wave dispersion equation is searched using five step iterative methods, by changing wave number, linear deduction sum number value meter
It calculates, obtains adjacent thereto several；
When asking the 7th, the estimated value of root is determined using secondary extrapolation, further according to formula cn+1=cn-5-3cn-3+
3cn-1, the exact value of root is calculated, repeats this step, you can obtain a series of of a pattern, wherein cn+1Indicate n-th
+ 1 estimated value；
Two steps of repetition front obtain several serial roots of the different modalities of wedge wave, and according to the several of different modalities
Serial root draws the theoretical dispersion curve that wedge wave is propagated.
Further, the wedge point excitation using laser action in wedge generates wedge wave, and optically to wedge
Wave signal is acquired, and is specifically included：
Wedge point excitation using laser action in wedge generates wedge wave, and waits space intervals 64 or 128 groups of wedge waves of acquisition
Time-domain signal.
Further, described that the actual measurement dispersion curve that wedge wave is propagated is drawn according to the wedge wave signal of acquisition, it specifically includes：
According to the wedge wave signal of acquisition, dispersion curve is converted to by two-dimensional Fourier transform method or phase spectrometry.
Implement the present invention, has the advantages that：Since the wedge wave propagated along straight line wedge contains angled information, adopt
With subwave method, obtained and the relevant characteristic equation of angle in conjunction with suitable boundary condition.Survey obtained Dispersion curve
With the comparison of theoretical Dispersion curve, optimization algorithm, inverting obtains the angle of wedge.This method being capable of preferable measuring wedge
The angle of body improves measurement accuracy, can be used for the on-line monitoring of industry.
Description of the drawings
In order to more clearly explain the embodiment of the invention or the technical proposal in the existing technology, to embodiment or will show below
There is attached drawing needed in technology description to be briefly described, it should be apparent that, the accompanying drawings in the following description is only this
Some embodiments of invention for those of ordinary skill in the art without creative efforts, can be with
Obtain other attached drawings according to these attached drawings.
Fig. 1 is the flow diagram of one embodiment of wedge angle detecting method provided by the invention；
Fig. 2 is the description schematic diagram of wedge internal stress；
Fig. 3 is the description schematic diagram of secondary extrapolation.
Specific implementation mode
Following will be combined with the drawings in the embodiments of the present invention, and technical solution in the embodiment of the present invention carries out clear, complete
Site preparation describes, it is clear that described embodiments are only a part of the embodiments of the present invention, instead of all the embodiments.It is based on
Embodiment in the present invention, those of ordinary skill in the art are obtained every other without creative efforts
Embodiment shall fall within the protection scope of the present invention.
Fig. 1 is the flow diagram of one embodiment of wedge angle detecting method provided by the invention, as shown in Figure 1,
Including：
S101, according to principle of elasticity, the stress and wedge wave displacement relation of linear type wedge are obtained, to establish wedge wave
The theoretical model of propagation
Specifically, step S101 includes：According to principle of elasticity, upper surface stress and wedge wave in linear type wedge are obtained
The relationship of displacement is
To establish the theoretical model of wedge wave propagation, wherein σ3'、τ'31、τ'32For the upper surface components of stress, λ, μ in wedge
It is the Lame constants of material, θ indicates wedge angle, u1、u2、u3Indicate that wedge is applied in the wedge wave generated when external force along x respectively1、
x2、x3The displacement in direction, x1、x2、x3For three orthogonal directions of linear type wedge, x2It is parallel to wedge top line direction, x1、x3Vertically
In wedge top line.
Specifically, upper surface stress and the calculating process of the relationship of wedge wave displacement are in wedge：
For the description schematic diagram of wedge internal stress as shown in Fig. 2, in the theoretical model that wedge wave is propagated, wedge wave includes three directions
Vibration, and close to wedge point, nearby, edge is parallel to wedge top line direction (x together for three direction vibration couplings of wedge wave2Side
To) propagate, along two orthogonal direction x perpendicular to wedge top line1、x3Direction has certain distribution form.It is obtained according to Elasticity
Certain stress put is on upper surface in wedge：
In formula 2, σ1,σ2,σ3,τ12,τ13,τ21,τ23,τ31,τ32For the element of the stress tensor at the point.
The stress of wedge and the relationship of displacement are again
Formula 3 is substituted into formula 2, you can obtain the relationship of upper surface stress and wedge wave displacement in wedge.
S102, the theoretical model propagated according to wave equation and the wedge wave obtain what wedge wave was propagated in conjunction with boundary condition
Dispersion equation.
Specifically, step S102 includes step：
S1021, according to wave equation, wedge wave displacement components u is calculatedjSolution, wherein
In formula, j=1,2,3, αjIndicate that amplitude, k indicate sound wave along x2The wave number that direction is propagated, τ and b indicate phase, v tables
Show sound wave along x2The phase velocity that direction is propagated, t are time
Wherein, S1021 specifically includes following steps：
Assuming that uj=αjexp(ikτx1)exp(ikbx2)exp(ik(x2- vt)) (j=1,2,3), formula 5,
In formula, ρ is the mass density of material, and f indicates the external power applied,Indicate xiThe displacement component in direction is to the time
Two subdifferentials of t, ui,jiIndicate uiTo xi、xjDifferential, uj,jiIndicate ujTo xi、xjDifferential.
Formula 5 is substituted into formula 6, obtains a gram sharp Stoffel equation：
In formula, Γ11=(+2 μ of λ) τ2+μ(b2+1)-ρv2, Γ12=(λ+μ) τ b, Γ13=(λ+μ) τ, Γ22=(+2 μ of λ) b2
+μ(τ2+1)-ρv2, Γ23=(λ+μ) b, Γ33=(+2 μ of λ)+μ (τ2+b2)-ρv2。
Formula 7 is that its determinant of coefficient is made to be zero there are the condition of untrivialo solution.Three met the requirements are solved to it
The relationship of a τ and b brings τ and b into formula 7, obtains three effectively α values.The solution of wave equation in wedge can be expressed as three
The linear superposition of a subwave:
S1022, the zero stress boundary condition σ ' in conjunction with free wedge3=τ '32=0 and x3=x1Tan θ/2=0, by wedge wave
Displacement components ujSolution substitute into upper surface stress in the wedge and obtain one group of nonlinear equation with displacement relation.
S1023, make the determinant of the nonlinear equation be zero, to obtain the wedge wave propagated along wedge top it is symmetrical with it is anti-
The dispersion equation of symmetrical mode.
S103, the dispersion equation is solved using secondary extrapolation and five step iterative methods, and draws the reason of wedge wave propagation
By dispersion curve.
Specifically, step S103 includes step：
S1031, the root that wedge wave dispersion equation is searched using five step iterative methods, by change wave number, it is linear infer and
Numerical computations obtain adjacent thereto several.
Wherein, the root of dispersion equation is phase velocity.
S1032, when asking the 7th, the estimated value of root is determined using secondary extrapolation, further according to formula cn+1=cn-5-
3cn-3+3cn-1, the exact value of root is calculated, repeats this step, you can obtain a series of of a pattern, wherein cn+1Table
Show (n+1)th estimated value.
Wherein, secondary extrapolation is referring in particular to Fig. 3.
S1033, two steps for repeating front obtain several serial roots of the different modalities of wedge wave, and according to different modalities
Several serial roots draw the theoretical dispersion curve that wedge waves are propagated.
Wherein, in its solution procedure, consider the feature of wedge wave and its in x1The decaying in direction, according to the imaginary part of solution into
Row is accepted or rejected.
S104, using laser action wedge wedge point excitation generate wedge wave, and optically to wedge wave signal into
Row acquisition.
Specifically, step S104 includes：Wedge point excitation using laser action in wedge generates wedge wave, and waits space intervals
Acquire the time-domain signal of 64 or 128 groups of wedge waves.
Wherein, excitation light source is fixed on precise electric control translation stage, and computer control precise electronic control translation stage to excite
Light source is moved along wedge point direction, to 64 or 128 groups of data of space intervals such as measuring.
S105, the actual measurement dispersion curve that wedge wave is propagated is drawn according to the wedge wave signal of acquisition.
Specifically, step S15 includes：According to the wedge wave signal of acquisition, pass through two-dimensional Fourier transform method or phase
Spectrometry is converted to dispersion curve.
S106, the same order wedge wave mode frequency dispersion of the theoretical dispersion curve and the actual measurement dispersion curve is compared,
By changing wedge angle so that the theoretical dispersion curve and the actual measurement dispersion curve coincide, to which inverting obtains wedge
Angle.
Implement the present invention, has the advantages that：Since the wedge wave propagated along straight line wedge contains angled information, adopt
With subwave method, obtained and the relevant characteristic equation of angle in conjunction with suitable boundary condition.Survey obtained Dispersion curve
With the comparison of theoretical Dispersion curve, optimization algorithm, inverting obtains the angle of wedge.This method being capable of preferable measuring wedge
The angle of body improves measurement accuracy, can be used for the on-line monitoring of industry.
It should be noted that herein, the terms "include", "comprise" or its any other variant are intended to non-row
His property includes, so that process, method, article or device including a series of elements include not only those elements, and
And further include other elements that are not explicitly listed, or further include for this process, method, article or device institute it is intrinsic
Element.In the absence of more restrictions, the element limited by sentence "including a ...", it is not excluded that including this
There is also other identical elements in the process of element, method, article or device.
In embodiment provided herein, it should be understood that disclosed method can be real by another way
It is existing.
Professional further appreciates that, unit described in conjunction with the examples disclosed in the embodiments of the present disclosure
And algorithm steps, can be realized with electronic hardware, computer software, or a combination of the two, in order to clearly demonstrate hardware and
The interchangeability of software generally describes each exemplary composition and step according to function in the above description.These
Function is implemented in hardware or software actually, depends on the specific application and design constraint of technical solution.Profession
Technical staff can use different methods to achieve the described function each specific application, but this realization is not answered
Think beyond the scope of this invention.
The step of method described in conjunction with the examples disclosed in this document or algorithm, can directly be held with hardware, processor
The combination of capable software module or the two is implemented.Software module can be placed in random access memory (RAM), memory, read-only deposit
Reservoir (ROM), electrically programmable ROM, electrically erasable ROM, register, hard disk, moveable magnetic disc, CD-ROM or technology
In any other form of storage medium well known in field.
The foregoing description of the disclosed embodiments enables those skilled in the art to implement or use the present invention.
Various modifications to these embodiments will be apparent to those skilled in the art, as defined herein
General Principle can be realized in other embodiments without departing from the spirit or scope of the present invention.Therefore, of the invention
It is not intended to be limited to the embodiments shown herein, and is to fit to and the principles and novel features disclosed herein phase one
The widest range caused.
Claims (6)
1. a kind of wedge angle detecting method, which is characterized in that including：
According to principle of elasticity, the stress and wedge wave displacement relation of linear type wedge are obtained, to establish the reason of wedge wave propagation
By model；
According to the theoretical model that wave equation and the wedge wave are propagated, the dispersion equation that wedge wave is propagated is obtained in conjunction with boundary condition；
The dispersion equation is solved using secondary extrapolation and five step iterative methods, and the theoretical dispersion for drawing the propagation of wedge wave is bent
Line；
Wedge point excitation using laser action in wedge generates wedge wave, and is optically acquired to wedge wave signal；
The actual measurement dispersion curve that wedge wave is propagated is drawn according to the wedge wave signal of acquisition；
The same order wedge wave mode frequency dispersion of the theoretical dispersion curve and the actual measurement dispersion curve is compared, by changing wedge
Body angle so that the theoretical dispersion curve and the actual measurement dispersion curve coincide, to which inverting obtains wedge angle.
2. wedge angle detecting method as described in claim 1, which is characterized in that it is described according to principle of elasticity, it obtains
The stress of linear type wedge and wedge wave displacement relation specifically include to establish the theoretical model of wedge wave propagation：
According to principle of elasticity, upper surface stress and the relationship of wedge wave displacement in linear type wedge of obtaining are
To establish the theoretical model of wedge wave propagation, wherein σ3'、τ'31、τ'32For the upper surface components of stress in wedge, λ, μ are materials
The Lame constants of material, θ indicate wedge angle, u1、u2、u3Indicate that wedge is applied in the wedge wave generated when external force along x respectively1、x2、x3
The displacement in direction, x1、x2、x3For three orthogonal directions of linear type wedge, x2It is parallel to wedge top line direction, x1、x3Perpendicular to wedge
Top line.
3. wedge angle detecting method as claimed in claim 2, which is characterized in that described according to wave equation and the wedge wave
The theoretical model of propagation obtains the dispersion equation that wedge wave is propagated in conjunction with boundary condition, specifically includes：
According to wave equation, wedge wave displacement components u is calculatedjSolution, wherein
In formula, j=1,2,3, αjIndicate that amplitude, k indicate sound wave along x2The wave number that direction is propagated, τ and b indicate phase, v expression sound
Wave is along x2The phase velocity that direction is propagated, t is the time；
In conjunction with the zero stress boundary condition σ ' of free wedge3=τ '32=0 and x3=x1Tan θ/2=0, by wedge wave displacement components ujSolution
It substitutes into upper surface stress in the wedge and obtains one group of nonlinear equation with displacement relation；
It is zero to make the determinant of the nonlinear equation, to obtain the symmetric and anti-symmetric mode of the wedge wave propagated along wedge top
Dispersion equation.
4. wedge angle detecting method as described in claim 1, which is characterized in that described to be changed using secondary extrapolation and five steps
The dispersion equation is solved for method, and draws the theoretical dispersion curve of wedge wave propagation, is specifically included：
The root that wedge wave dispersion equation is searched using five step iterative methods, by changing wave number, linear deduction sum number value calculates, and obtains
To adjacent thereto several；
When asking the 7th, the estimated value of root is determined using secondary extrapolation, further according to formula cn+1=cn-5-3cn-3+3cn-1,
The exact value of root is calculated, repeats this step, you can obtain a series of of a pattern, wherein cn+1Indicate (n+1)th
Estimated value；
Two steps of repetition front obtain several serial roots of the different modalities of wedge wave, and according to several series of different modalities
Root draws the theoretical dispersion curve that wedge wave is propagated.
5. wedge angle detecting method as described in claim 1, which is characterized in that it is described using laser action wedge wedge
Point excitation generates wedge wave, and is optically acquired to wedge wave signal, specifically includes：
Wedge point excitation using laser action in wedge generates wedge wave, and waits the time domain of space intervals 64 or 128 groups of wedge waves of acquisition
Signal.
6. wedge angle detecting method as described in claim 1, which is characterized in that described to be drawn according to the wedge wave signal of acquisition
The actual measurement dispersion curve that wedge wave is propagated, specifically includes：
According to the wedge wave signal of acquisition, dispersion curve is converted to by two-dimensional Fourier transform method or phase spectrometry.
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| CN110726456B (en) * | 2019-11-28 | 2020-11-17 | 河海大学常州校区 | Method for detecting liquid level position based on wedge wave frequency dispersion |
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| CN103995053A (en) * | 2014-03-13 | 2014-08-20 | 天津大学 | Method for detecting isotropic material surface Young modulus by using surface acoustic wave technology |
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| CN102183212A (en) * | 2010-12-28 | 2011-09-14 | 睿励科学仪器（上海）有限公司 | Method and device for rapidly determining topography parameters of microperiodic structure |
| CN103995053A (en) * | 2014-03-13 | 2014-08-20 | 天津大学 | Method for detecting isotropic material surface Young modulus by using surface acoustic wave technology |
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