CN105547235B - The measurement method of variable-section beam structure tension and compression and bending composite deformation field - Google Patents
The measurement method of variable-section beam structure tension and compression and bending composite deformation field Download PDFInfo
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- CN105547235B CN105547235B CN201610038345.5A CN201610038345A CN105547235B CN 105547235 B CN105547235 B CN 105547235B CN 201610038345 A CN201610038345 A CN 201610038345A CN 105547235 B CN105547235 B CN 105547235B
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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
- G01B21/00—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant
- G01B21/32—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant for measuring the deformation in a solid
Abstract
The invention discloses the measurement methods of a kind of variable-section beam structure tension and compression and bending composite deformation field, in this method, the simple bending curved strain on structural bending surface to be measured for curved surface a the stretching or compressive deformation in the direction x and the bending deformation in the direction w it is common caused by composite strain and the structure difference of strain that stretches or compress on the neutral line of side b.The strain value according to measured by strain transducer on surface a and side b solves structure in the stretching or compression strain of the simple bending curved strain and side b of strain transducer position upper surface a first, then stretching at two surface strain sensor positions or compressive deformation and bending deformation are acquired according to mathematic integral and displacement theory respectively, the composite deformation fields of structure are finally solved using two kinds of deformations.The method of the present invention, efficiently solve that existing measuring technique occurs is difficult to set up that benchmark, benchmark be easily-deformable and the restricted problem of measurement point.
Description
Technical field
The invention belongs to a kind of measurement method of variable-section beam structure more particularly to a kind of variable-section beam structure tension and compression with it is curved
The measurement method of bent composite deformation field.
Background technique
With the fast development of modern industry science and technology, machine-building process increasingly pursue high quality, high-precision,
High efficiency and high-intelligentization.China at this stage, whether railway construction, power plant construction, shipbuilding, space flight and aviation are built
If or automobile, engineering machinery, military industry, a large amount of high-end lathe is required to support.For status, restrict at present
The principal element that heavy digital control machine tool precision further increases is exactly machine tool structure deformation, caused by deformation includes temperature change
The deformation of power caused by thermal deformation and load change.If structural member deforms in use will excessively seriously affect lathe
Precision, repeatability, even with the service life.Since structural member is in complicated work shape in heavy digital control machine tool use process
Under condition environment, the power load from other component should be born, also the thermal force by various heat sources is influenced, so lathe knot
The deformation of structure is difficult to carry out quantitative calculating and measurement, is always the emphasis of the research of domestic and international machine tool field.
In terms of structural member deformation detection, traditionally mainly passed using current vortex sensor, capacitance sensor and laser displacement
Sensor etc. is displaced detecting instrument, measures the change in location of certain point by measuring instrument come the deformation of monitoring of structures part.In order to mention
High precision measurement, generally requires to arrange multiple displacement sensors, and need good measurement space.There are following several for this kind of method
A problem:
One, such measurement method needs displacement sensor being mounted on a fixed position as measuring basis, and
It is difficult to find a constant fixed reference in real work condition environment, because fixed pedestal all can be by the shadow of all environment
It rings and deforms, to influence the precision of measurement.
Two, may be excessive due to the volume of displacement monitoring instrument in special measurement environment, or measurement insufficient space
And leads to not to treat geodesic structure part and measure.
Three, in terms of deformation measurement, due to the difficulty of layouting of displacement sensor, be only able to detect on structural member certain point or certain
The displacement of several points all can not completely describe the deformation of whole knot component over time and space.In order to detect more points
Change in displacement situation, it is necessary to increase the quantity of displacement sensor, therefore also increase the complexity of measurement.
Summary of the invention
The present invention is directed to the problems of the prior art, provides a kind of variable-section beam structure tension and compression and bending composite deformation field
Measurement method, efficiently solve that existing measuring technique occurs is difficult to set up that benchmark, benchmark are easily-deformable and measurement point is restricted
The problem of.
The technical solution adopted by the present invention to solve the technical problems is: providing a kind of variable-section beam structure tension and compression and bending
The measurement method of composite deformation field, this approach includes the following steps, step 1, builds in the plane that variable-section beam structure bends
Vertical rectangular coordinate system, taking the stretching (or compression) of non-uniform beam, direction is as x-axis direction, in one end of non-uniform beam perpendicular to x
W axis is established in the direction (i.e. bending direction) of axis；Then take the upper surface (or lower surface) when non-uniform beam bending deformation along x-axis side
To several strain transducers are installed, at the same time, installation number is identical on the neutral line corresponding position of non-uniform beam side
Strain transducer is denoted as { a respectively1, a2, ai... anAnd { b1, b2, bi... bn, wherein { a1, a2, ai... anIndicate
{ the x of curved surface a (upper surface or lower surface when non-uniform beam bending deformation)1, x2, xi... xnInstalled on position respectively
N strain transducer, { b1, b2, bi... bnIndicate on the neutral line of non-uniform beam side b with { x1, x2, xi... xn}
N strain transducer at corresponding position；Step 2 is led to after geodesic structure occurs to stretch or compress with bending deformation
It crosses installed each strain transducer and measures strain value at each strain transducer installation point, be denoted as { ε respectivelya(x1), εa
(x2), εa(xi) ... εa(xn) and { εb(x1), εb(x2), εb(xi) ... εb(xn), wherein { εa(x1), εa(x2), εa
(xi) ... εa(xn) represent the n strain transducer { a of curved surface a1, a2, ai... anReading value；{εb(x1), εb
(x2), εb(xi) ... εb(xn) represent n strain transducer { b on the neutral line of non-uniform beam side b1, b2, bi... bn}
Reading value；Step 3 extracts stretching or compression strain and bending strain, according to mechanics of materials knowledge it is found that due to { εb(x1),
εb(x2), εb(xi) ... εb(xn) it is strain on the neutral line of non-uniform beam side b, therefore it strains size by knot to be measured
Structure the direction x stretching or compressive deformation and generate, and { εa(x1), εa(x2), εa(xi) ... εa(xn) be curved surface a by
To geodesic structure in the common caused composite strain of the stretching or compressive deformation in the direction x and the bending deformation institute in the direction w.Therefore,
The simple bending curved strain on structural bending surface to be measured is curved surface a in the curved of stretching (or compression) deformation in the direction x and the direction w
Composite strain caused by song deformation institute is common and the difference for stretching (or compression) on the neutral line of side b to geodesic structure and straining, i.e.,
{εa(x1)-εb(x1), εa(x2)-εb(x2), εa(xi)-εb(xi) ... εa(xn)-εb(xn)}.Enable εc(x1)=εa(x1)-εb
(x1), εc(x2)=εa(x2)-εb(x2), εc(xi)=εa(xi)-εb(xi) ... εc(xn)=εa(xn)-εb(xn)；Step 4 is right
It can directly quadrature in stretching (or compression) strain to obtain the deformation of construction stretch to be measured (or compression), according to displacement theory
Acquire the bending deformation to geodesic structure.Detailed process is to generate for being deformed by the Compression and Expansion to geodesic structure in the direction x
Deformation field can directly quadrature acquisition,Wherein Δ L (x) indicates non-uniform beam in x
The Compression and Expansion in direction deforms, εb(x) it indicates to stretch (or compression) strain.According to K0 displacement theory, the calculating of bending deformation field
The corner side in the direction fixing end tan θ=0, x is determined according to practical situations in conjunction with the corner function tan θ to geodesic structure
Journey(i=1,2,3 ... n), wherein εc
(xi-1)、εc(xi) respectively indicate the bending strain value of adjacent two o'clock in x-axis, ci-1、ciIt then respectively indicates in x-axis in adjacent two o'clock
Property layer thickness, Δ l is the distance of two neighboring strain transducer in the direction of the x axis.In conjunction with corner function tan θi, then each point
Change song displacement function into(i
=1,2,3 ... n)；Step 5 calculates composite deformation field in conjunction with step 4, by the Compression and Expansion of every bit acquired in step 4
Deform Δ L (xi) and bending deformation Δ ω (xi) be combined, form the displacement vector { Δ L (x of the pointi), Δ ω (xi), it
The composite deformation field to geodesic structure is described with every displacement vector afterwards, and draws composite deformation shape graph.
According to the above technical scheme, in the step 1, the upper surface (or lower surface) when non-uniform beam bending deformation is along x-axis
The quantity of the strain transducer of direction installation is at least 2.
According to the above technical scheme, in the step 1, non-uniform beam is determined by the way that modeling analysis will be carried out to geodesic structure
The neutral line of side.
The beneficial effect comprise that: 1, the method for the present invention collected strain data can pass through strain transducer
It obtains.Directly strain transducer is placed in and removes measurement strain data to the surface of geodesic structure, and eliminates displacement sensor
It is more severe or be not suitable for the occasion of installation displacement sensor to be more suitable for working condition for placement.2, applied displacement theory
It is the function being displaced about strain, it is only necessary to the geometry to geodesic structure is considered, without regard to material properties, feelings loaded
The factors such as condition and mounting means, it is convenient, easy-operating to have the characteristics that.3, the method for the present invention is primarily adapted for use in non-uniform beam knot
The case where structure (contain uniform beam) Compression and Expansion, bending composite deformation, and be not limited solely to a Tensile compression or only by
Curved special circumstances, there is general applicability, have widened the fields of measurement using measurement.
Detailed description of the invention
Present invention will be further explained below with reference to the attached drawings and examples, in attached drawing:
Fig. 1 is that the process of the measurement method of the tension and compression of variable-section beam structure of the embodiment of the present invention and bending composite deformation field is illustrated
Figure；
Fig. 2 is the embodiment of the present invention for measuring non-uniform beam strain transducer installation instructions figure；
Fig. 3 is the embodiment of the present invention for measuring uniform beam strain transducer scheme of installation；
Fig. 4 is the deformation pattern when embodiment of the present invention is used to measure uniform beam；
Fig. 5 is to utilize embodiment of the present invention method measurement machine pillar deformation schematic diagram.
Specific embodiment
In order to make the objectives, technical solutions, and advantages of the present invention clearer, with reference to the accompanying drawings and embodiments, right
The present invention is further elaborated.It should be appreciated that described herein, specific examples are only used to explain the present invention, not
For limiting the present invention.
In the embodiment of the present invention, as shown in Figure 1, providing the survey of a kind of variable-section beam structure tension and compression and bending composite deformation field
Amount method, this approach includes the following steps, step 1, establishes rectangular coordinate system in the plane that variable-section beam structure bends,
Stretching (or compression) direction of non-uniform beam is taken as x-axis direction, to establish w perpendicular to the direction of x-axis in one end of non-uniform beam
Axis；Then take upper surface or lower surface when non-uniform beam bending deformation that several strain transducers are installed along the x-axis direction, it is same with this
When, the identical strain transducer of installation number on the neutral line corresponding position of non-uniform beam side；Step 2, to geodesic structure
Occur to stretch or compression is with after bending deformation, each strain transducer is measured by installed each strain transducer and is installed
Strain value at point；Step 3 solves and stretches (or compression) strain and simple bending curved strain, the pure bending on structural bending surface to be measured
It strains and is answered for curved surface a is compound caused by the stretching (or compression) in the direction x deforms and the bending deformation in the direction w institute is common
Become and stretch on the neutral line of side b to geodesic structure the difference of (or compression) strain；Step 4, for stretching (or compression) strain
It can directly quadrature to obtain the deformation of construction stretch to be measured (or compression), the bending to geodesic structure is acquired according to displacement theory
Deformation；Step 5 becomes in conjunction with stretching (or compression) deformation and the bending in the direction w that step 4 is calculated to geodesic structure in the direction x
Composite deformation field caused by shape institute is common will swear shape to the stretching of every bit on geodesic structure (or compression) deformation and bending deformation
At displacement vector, composite deformation field is obtained using displacement vector.
Further, in the step 1, upper surface or lower surface when non-uniform beam bending deformation are installed along the x-axis direction
The quantity of strain transducer be at least 2.
Further, in the step 1, non-uniform beam side is determined by the way that modeling analysis will be carried out to geodesic structure
Neutral line.
In presently preferred embodiments of the present invention, in embodiment one, as shown in figure 4, under external force F and M effect, Tensile compression
With the uniform beam deformation of bending while effect.
Wherein, the first step installs several strain transducers, coordinate system is established in plane of bending, for cross-section rectangle
Cantilever beam, it is assumed that the beam left end is fixed, and takes the horizontal direction of the beam as x-axis direction, w axis is perpendicular to x-axis and starts from fixing end.
Then several strain transducers are installed in the corresponding position in the deflection of beam surface face a and the side face b, are denoted as { a respectively1, α2,
ai... αnAnd { b1, b2, bi... bn), wherein { a1, a2, ai... anIndicate that { x is installed respectively in curved surface a1, x2,
xi..xnN strain transducer on position, and { b1, b2, bi... bnIndicate that neutral line corresponds to { x on the b of side1, x2,
xi... xnN strain transducer on position, as shown in Figure 2.Before strain transducer is installed on the side surface b, first will
Modeling analysis is carried out to geodesic structure to determine neutral line.
Second step measures the strain value of each position, after Compression and Expansion-bending deformation occurs for uniform beam, according to
Mounted strain transducer measures the strain value of each point, is denoted as { ε respectivelya(x1), εa(x2), εa(xi) ... εa(xn) with
{εb(x1), εb(x2), εb(xi) ... εb(xn), wherein { εa(x1), εa(x2), εa(xi) ... εa(xn) represent curved surface a
N strain transducer { a1, α2, ai... anReading value；{εb(x1), εb(x2), εb(xi) ... εb(xn) represent side b
N strain transducer { b1, b2, bi... bnReading value, as shown in Figure 3.
Third step extracts Compression and Expansion strain and bending strain, according to mechanics of materials knowledge it is found that due to { εb(x1), εb
(x2), εb(xi) ... εb(xnBe the surface b neutral line strain, therefore its strain size by structure the stretching pressure in the direction x
Compression deformation generates, and { εa(x1), εa(x2), εa(xi) ... εa(xn) it is Compression and Expansion and the direction w by structure in the direction x
Bending institute it is common caused by composite strain, therefore, the simple bending curved strain on structural member bending tensile surface (i.e. upper surface) is { εa
(x1)-εb(x1), εa(x2)-εb(x2), εa(xi)-εb(xi) ... εa(xn)-εb(xn), enable εc(x1)=εa(x1)-εb(x1), εc
(x2)=εa(x2)-εb(x2), εc(xi)=εa(xi)-εb(xi) ... εc(xn)=εa(xn)-εb(xn)。
4th step solves tension and compression deformation field and bending deformation field respectively, according to mechanics of materials knowledge it is found that pressing for stretching
Shrinkage strain can directly quadrature to obtain the deformation field of compressionWherein Δ L (x) table
Show beam in the tension and compression deformation in the direction x, εb(x) tension and compression strain is indicated.Uniform beam is the special circumstances of non-uniform beam, neutral line
It is of uniform thickness, displacement theory equation is carried out after simplifying, the corner function in the direction x is
(i=1,2,3 ... n), wherein εc(xi-1)、εc(xi) respectively indicate the bending strain value of adjacent two o'clock in x-axis, ciIn then indicating
Property layer thickness, Δ l is the distance of two neighboring strain transducer in the direction of the x axis.In conjunction with corner function tan θi, then each
Point curved displacement function be(i=1,2,
3 ... n), it follows that Compression and Expansion deformation field and bending deformation field.
5th step solves composite deformation field, by the tension and compression deformation Δ L (x of acquired every bit in the 4th stepi) and bending change
Shape Δ ω (xi) be combined, form the displacement vector { Δ L (x of the pointi), Δ ω (xi), later with every displacement vector
It describes the composite deformation field of every bit, and draws composite deformation field, as shown in Figure 4.
In embodiment two, when measuring the deformation of lathe variable cross-section column, it is stretched simultaneously in lathe variable cross-section column
After compressive deformation and bending deformation, the measuring surface of selection is as shown in Figure 5.
Wherein, the first step installs displacement sensor in lathe variable cross-section leg surface, first has to send out in variable-section beam structure
Raw curved plane establishes rectangular coordinate system, takes vertical direction as x-axis, as shown in figure 5, in one end of the beam perpendicular to x-axis
Direction (i.e. bending direction) establish w axis；Then take the wherein one side of the beam deflection that several strain sensings are installed along the x-axis direction
Device corresponds to the identical strain transducer of installation number in the neutral line position of its side, is denoted as { α respectively at the same time1, a2,
ai... αnAnd { b1, b2, bi... bn, wherein { a1, a2, ai... anIndicate that { x is installed respectively in curved surface a1, x2,
xi... xnN strain transducer on position, and { b1, b2, bi... bnIndicate that neutral line corresponds to { x on the b of side1, x2,
xi... xnN strain transducer on position.
Second step measures the strain value of each position, after Compression and Expansion-bending deformation occurs for structure, according to installation
Good strain transducer measures each strain value, is denoted as { ε respectivelya(x1), εa(x2), εa(xi) ... εa(xn) and { εb(x1), εb
(x2), εb(xi) .. εb(xn, wherein { εa(x1), εa(x2), εa(xi) .. εa(xn) represent curved surface a n strain pass
Sensor { a1, a2, ai... anReading value；{εb(x1), εb(x2), εb(xi) ... εb(xn) represent side b n strain pass
Sensor { b1, b2, bi... bnReading value.
Third step extracts Compression and Expansion strain and bending strain, according to mechanics of materials knowledge it is found that due to { εb(x1), εb
(x2), εb(xi) ... εb{xnBe the surface b neutral line strain, therefore its strain size by structure the stretching pressure in the direction x
Compression deformation generates, and { εa(x1), εa(x2), εa(xi) ... εa(xn) it is Compression and Expansion and the direction w by structure in the direction x
Bending institute it is common caused by composite strain, therefore, the simple bending curved strain on structural member bending tensile surface is { εa(x1)-εb
(x2), εa(x2)-εb(x2), εa(xi)-εb(xi) ... εa(xn)-εb(xn), enable εc(x1)=εa(x1)-εb(x1), εc(x2)=
εa(x2)-εb(x2), εc(xi)=εa(xi)-εb(xi) ... εc(xn)=εa(xn)-εb(xn)。
4th step solves Compression and Expansion deformation field and bending deformation field respectively, according to mechanics of materials knowledge it is found that for pressure
Shrinkage strain can directly quadrature to obtain the deformation field of compressionWherein Δ L ((x) table
Show non-uniform beam in the tension and compression deformation in the direction x, εb(x) tension and compression strain is indicated.According to K0 theory, bending deformation is asked to want integrated structure
The corner function tan θ of part, the equations of rotating angle in the direction fixing end tan θ=0, x is determined according to practical situations(i=1,2,3 ... ... n) wherein εc(xi-1)、
εc(xi) respectively indicate the bending strain value of adjacent two o'clock in x-axis, ci-1、ciThen respectively indicate the thickness of the adjacent two o'clock neutral line of x-axis
Degree, Δ l are the distance of two neighboring strain transducer in the direction of the x axis.In conjunction with equations of rotating angle tan θi, then the bending of each point
Displacement function be(i
=1,2,3 ... ... n), it follows that Compression and Expansion deformation field and bending deformation field.
5th step solves composite deformation field, by the tension and compression deformation Δ L (x of acquired every bit in the 4th stepi) and bending change
Shape Δ ω (xi) be combined, form the displacement vector { Δ L (x of the pointi), Δ ω (xi), later with every displacement vector come
The composite deformation field of each point is described, and draws composite deformation field.
It should be understood that for those of ordinary skills, it can be modified or changed according to the above description,
And all these modifications and variations should all belong to the protection domain of appended claims of the present invention.
Claims (3)
1. a kind of variable-section beam structure tension and compression and bending composite deformation field measurement method, which is characterized in that this method include with
Lower step, step 1 establish rectangular coordinate system in the plane that variable-section beam structure bends, take the draw direction of non-uniform beam
As x-axis direction, w axis is established perpendicular to the direction of x-axis in one end of non-uniform beam；When then taking non-uniform beam bending deformation
Several strain transducers are installed in upper surface or lower surface along the x-axis direction, and at the same time, the neutral line in non-uniform beam side is corresponding
The identical strain transducer of installation number on position；Step 2, after geodesic structure occurs to stretch or compression is with bending deformation,
The strain value at each strain transducer installation point is measured by installed each strain transducer；Step 3 is solved and is stretched
Strain and simple bending curved strain, the simple bending curved strain on structural bending surface to be measured be curved surface a in the stretcher strain in the direction x and
The bending deformation in the direction w it is common caused by composite strain and the difference to geodesic structure elongation strain on the neutral line of side b；Step
Rapid four, it can directly quadrature elongation strain to obtain the deformation of construction stretch to be measured, be acquired according to displacement theory to be measured
The bending deformation of structure；Step 5 is calculated to geodesic structure in conjunction with step 4 in the stretcher strain in the direction x and the bending in the direction w
Composite deformation field caused by deformation institute is common, will swear to form displacement to the stretcher strain of every bit on geodesic structure and bending deformation
Vector obtains composite deformation field using displacement vector.
2. the measurement method of variable-section beam structure tension and compression according to claim 1 and bending composite deformation field, feature exist
In, in the step 1, strain transducer that upper surface or lower surface when non-uniform beam bending deformation are installed along the x-axis direction
Quantity is at least 2.
3. the measurement method of variable-section beam structure tension and compression according to claim 1 or 2 and bending composite deformation field, feature
It is, in the step 1, determines the neutral line of non-uniform beam side by the way that modeling analysis will be carried out to geodesic structure.
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| CN107966257A (en) * | 2017-11-20 | 2018-04-27 | 滨州学院 | A kind of variable cross-section airofficer girder construction part bending stiffness computational methods |
| CN110887448B (en) * | 2019-11-28 | 2021-08-20 | 上海航天控制技术研究所 | Beam structure form reconstruction method based on optical fiber strain measurement |
| CN112270052A (en) * | 2020-10-23 | 2021-01-26 | 中车长江车辆有限公司 | Method and device for acquiring bending moment of plate |
| CN114239127B (en) * | 2021-09-29 | 2022-09-02 | 长江三峡通航管理局 | Analysis and calculation method for ship lock floating type mooring post in working state |
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