CN105547235A - Method for measuring pull-press and bending composite deformation field of variable cross section beam structure - Google Patents
Method for measuring pull-press and bending composite deformation field of variable cross section beam structure Download PDFInfo
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- CN105547235A CN105547235A CN201610038345.5A CN201610038345A CN105547235A CN 105547235 A CN105547235 A CN 105547235A CN 201610038345 A CN201610038345 A CN 201610038345A CN 105547235 A CN105547235 A CN 105547235A
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- composite
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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 a method for measuring a pull-press and bending composite deformation field of a variable cross section beam structure. In this method, a pure bending strain of a bent surface of a to-be-measured structure is the different between a composite strain, caused by the pulling or pressing of a bent surface a in an x direction and the bending deformation in a w direction, and the pulling or pressing deformation of a neutral layer of the structure on a side surface b. The method comprises the steps: firstly solving the pure bending deformation of the surface a of the structure at the position of a strain sensor and the pulling or pressing strain of the side surface a according to strain values, measured by the strain sensor, of the surface a and the side surface b; secondly respectively solving the pulling or pressing deformation and bending information of the two surfaces at the position of the strain sensor according to the theories of mathematic integration and displacement; and finally solving the composite deformation field of the structure through employing the two types of deformation. The method effectively solves problems in the prior art that a reference is difficult to set, the reference is liable to deform, and a measurement is limited.
Description
Technical field
The invention belongs to a kind of measuring method of variable-section beam structure, particularly relate to the measuring method of a kind of variable-section beam structure tension and compression and bending composite deformation field.
Background technology
Along with the fast development of modern industry science and technology, more and more pursue high-quality, high precision, high-level efficiency and high-intelligentization in machine-building process.In China's present stage, no matter be railway construction, power plant construction, shipbuilding, space flight and aviation construction, or automobile, engineering machinery, military industry, all need a large amount of high-end lathes to support.With regard to present situation, at present restriction heavy digital control machine tool precision improve further principal element be exactly machine tool structure distortion, distortion comprises thermal deformation that temperature variation causes and the force deformation that load change causes.If structural member is in use out of shape precision, the repeatability that excessively will have a strong impact on lathe, or even serviceable life.Due under structural member is in complicated working condition environment in heavy digital control machine tool use procedure, the power load coming from miscellaneous part should be born, also the thermal force impact of various thermal source is subject to, so the distortion of machine tool structure is difficult to quantitatively calculate and measure, it is the emphasis of the research of domestic and international machine tool field always.
Structural member deformation detection aspect, mainly adopts the displacement detecting instruments such as current vortex sensor, capacitive transducer and laser displacement sensor traditionally, measures by surveying instrument the distortion that certain change in location put carrys out monitoring of structures part.In order to improve accurate measurement, often needing to arrange multiple displacement transducer, and needing good measurement space.There is following problem in this kind of method:
One, this type of metering system needs displacement transducer to be arranged on a fixing position as measuring basis, and in real work condition environment, be difficult to find a constant fixed reference, because fixing pedestal all can be subject to the impact of all environment and deform, thus the precision that impact is measured.
Two, in special measurement environment, may be excessive due to the volume of displacement monitoring instrument, or measurement space is not enough and cause treating geodesic structure part and measure.
Three, in deformation measurement, due to the difficulty of layouting of displacement transducer, the displacement of certain point or certain several point can only to be detected on structural member, over time and space all cannot the deformation of complete description total part.In order to detect the change in displacement situation of more points, the quantity of displacement transducer must be increased, therefore also just adding the complexity of measurement.
Summary of the invention
The present invention is directed to the problems of the prior art, provide the measuring method of a kind of variable-section beam structure tension and compression and bending composite deformation field, effectively solving being difficult to that existing measuring technique occurs sets up benchmark, benchmark yielding, and the restricted problem of measurement point.
The technical solution adopted for the present invention to solve the technical problems is: the measuring method providing a kind of variable-section beam structure tension and compression and bending composite deformation field, the method comprises the following steps, step one, the plane bent in variable-section beam structure sets up rectangular coordinate system; direction is as x-axis direction to get the stretching (or compression) of non-uniform beam, and w axle is set up in the direction (i.e. bending direction) in one end of non-uniform beam perpendicular to x-axis; Upper surface (or lower surface) when then getting non-uniform beam flexural deformation installs some strain transducers along the x-axis direction, meanwhile, the neutral line correspondence position of non-uniform beam side is installed the identical strain transducer of quantity, is designated as { a respectively
1, a
2, a
i... a
nand { b
1, b
2, b
i... b
n, wherein { a
1, a
2, a
i... a
nrepresent at { the x of curved surface a (upper surface during non-uniform beam flexural deformation or lower surface)
1, x
2, x
i... x
nn strain transducer that position is installed respectively, { b
1, b
2, b
i... b
nrepresent on the neutral line of non-uniform beam side b and { x
1, x
2, x
i... x
nn strain transducer of corresponding position; Step 2, is treating that geodesic structure occurs to stretch or compress and after flexural deformation, measured the strain value at each strain transducer mounting points place, be designated as { ε respectively by each strain transducer installed
a(x
1), ε
a(x
2), ε
a(x
i) ... ε
a(x
n) and { ε
b(x
1), ε
b(x
2), ε
b(x
i) ... ε
b(x
n), wherein { ε
a(x
1), ε
a(x
2), ε
a(x
i) ... ε
a(x
n) represent n the strain transducer { a of curved surface a
1, a
2, a
i... a
nreading value; { ε
b(x
1), ε
b(x
2), ε
b(x
i) ... ε
b(x
n) represent n strain transducer { b on the neutral line of non-uniform beam side b
1, b
2, b
i... b
nreading value; Step 3, extracts and stretches or compressive strain and bending strain, according to mechanics of materials knowledge, due to { ε
b(x
1), ε
b(x
2), ε
b(x
i) ... ε
b(x
n) be non-uniform beam side b neutral line on strain, therefore its strain size produces by treating the stretching of geodesic structure in x direction or compression deformation, and { ε
a(x
1), ε
a(x
2), ε
a(x
i) ... ε
a(x
n) be curved surface a by treating the composite strain that the flexural deformation of the stretching of geodesic structure in x direction or compression deformation and w direction causes jointly.Therefore, the composite strain that the pure bending strain on structural bending surface to be measured causes in stretching (or the compression) distortion in x direction and the flexural deformation in w direction jointly for curved surface a and treat the difference that geodesic structure stretches on the neutral line of side b (or compression) strains, i.e. { ε
a(x
1)-ε
b(x
1), ε
a(x
2)-ε
b(x
2), ε
a(x
i)-ε
b(x
i) ... ε
a(x
n)-ε
b(x
n).Make ε
c(x
1)=ε
a(x
1)-ε
b(x
1), ε
c(x
2)=ε
a(x
2)-ε
b(x
2), ε
c(x
i)=ε
a(x
i)-ε b (x
i) ... ε
c(x
n)=ε
a(x
n)-ε
b(x
n); Step 4, directly can quadrature to obtain the distortion of construction stretch to be measured (or compression), try to achieve the flexural deformation treating geodesic structure according to displacement theory for (or compression) strain that stretches.Detailed process is, can directly to quadrature acquisition for the deformation field produced by treating the Compression and Expansion of geodesic structure in x direction to be out of shape,
wherein Δ L (x) represents the Compression and Expansion distortion of non-uniform beam in x direction, ε
bx () represents (or compression) strain that stretches.According to KO displacement theory, the calculating of flexural deformation field will in conjunction with the corner function tan θ treating geodesic structure, according to practical situations determination stiff end tan θ=0, and the equations of rotating angle in x direction
Wherein ε
c(x
i-1), ε
c(x
i) represent the bending strain value of in x-axis adjacent 2, c respectively
i-1, c
ithen represent the thickness of adjacent 2 neutral lines in x-axis respectively, Δ l is the distance of adjacent two strain transducers in the direction of the x axis.In conjunction with corner function tan θ
i, then the bending displacement function of each point is
Step 5, integrating step four calculates composite deformation field, by step 4 obtain the Compression and Expansion distortion Δ L (x of every bit
i) and flexural deformation Δ ω (x
i) combine, form the displacement vector { Δ L (x of this point
i), Δ ω (x
i), describe the composite deformation field for the treatment of geodesic structure by the displacement vector of often afterwards, and draw composite deformation shape figure.
By technique scheme, in described step one, the quantity of the strain transducer that the upper surface (or lower surface) during non-uniform beam flexural deformation is installed along the x-axis direction is at least 2.
By technique scheme, in described step one, by treating that geodesic structure carries out the neutral line that modeling analysis determines non-uniform beam side.
The beneficial effect that the present invention produces is: 1, the strain data that gathers of the inventive method, obtains by strain transducer.Directly strain transducer is placed in and treats that monitor strain data are gone on the surface of geodesic structure, and eliminate the arrangement of displacement transducer, be more suitable for working condition comparatively severe or be not suitable for the occasion of installation position displacement sensor.2, the displacement theory applied is displacement about the function of strain, only needs the geometric configuration considering to treat geodesic structure, and without the need to considering material properties, by load condition, and the factor such as mounting means, has conveniently, easy-operating feature.3, the inventive method is mainly applicable to the situation of variable-section beam structure (containing uniform beam) Compression and Expansion, bending composite deformation, and be not only confined to Tensile compression or special circumstances only by bending, there is general applicability, widened the fields of measurement that application is measured.
Accompanying drawing explanation
Below in conjunction with drawings and Examples, the invention will be further described, in accompanying drawing:
Fig. 1 is the schematic flow sheet of the measuring method of the tension and compression of embodiment of the present invention variable-section beam structure and bending composite deformation field;
Fig. 2 is that the embodiment of the present invention is for measuring non-uniform beam strain transducer mounting list figure;
Fig. 3 is that the embodiment of the present invention is for measuring uniform beam strain transducer scheme of installation;
Fig. 4 is that the embodiment of the present invention is for measuring deformation pattern during uniform beam;
Fig. 5 utilizes the inventive method examples measure machine pillar to be out of shape schematic diagram.
Embodiment
In order to make object of the present invention, technical scheme and advantage clearly understand, below in conjunction with drawings and Examples, the present invention is further elaborated.Should be appreciated that specific embodiment described herein only in order to explain the present invention, be not intended to limit the present invention.
In the embodiment of the present invention, as shown in Figure 1, the measuring method of a kind of variable-section beam structure tension and compression and bending composite deformation field is provided, the method comprises the following steps, step one, the plane bent in variable-section beam structure sets up rectangular coordinate system, and direction is as x-axis direction to get the stretching (or compression) of non-uniform beam, and w axle is set up in the direction in one end of non-uniform beam perpendicular to x-axis; Upper surface when then getting non-uniform beam flexural deformation or lower surface install some strain transducers along the x-axis direction, meanwhile, the neutral line correspondence position of non-uniform beam side are installed the identical strain transducer of quantity; Step 2, is treating that geodesic structure occurs stretch or compress and after flexural deformation, measured the strain value at each strain transducer mounting points place by each strain transducer installed; Step 3, solve stretching (or compression) strain and pure bending strain, the pure bending strain on structural bending surface to be measured is for curved surface a is at the composite strain that the stretching (or compression) in x direction is out of shape and the flexural deformation in w direction causes jointly and treat the difference that geodesic structure stretches on the neutral line of side b (or compression) strains; Step 4, directly can quadrature to obtain the distortion of construction stretch to be measured (or compression), try to achieve the flexural deformation treating geodesic structure according to displacement theory for (or compression) strain that stretches; Step 5, integrating step four calculates the composite deformation field for the treatment of that geodesic structure causes jointly in stretching (or compression) distortion in x direction and the flexural deformation in w direction, stretching (or compression) distortion and flexural deformation for the treatment of every bit on geodesic structure are vowed and forms displacement vector, utilize displacement vector to obtain composite deformation field.
Further, in described step one, the quantity of the strain transducer that upper surface during non-uniform beam flexural deformation or lower surface are installed along the x-axis direction is at least 2.
Further, in described step one, by treating that geodesic structure carries out the neutral line that modeling analysis determines non-uniform beam side.
In preferred embodiment of the present invention, in embodiment one, as shown in Figure 4, under external force F and M effect, Tensile compression and the bending uniform beam deformation simultaneously acted on.
Wherein, the first step, installs some strain transducers, in plane of bending, sets up coordinate system, for uniform cross section rectangular cantilever beam, supposes that this beam left end is fixed, gets the horizontal direction of this beam as x-axis direction, and w axle is perpendicular to x-axis and start from stiff end.Then in the relevant position in this deflection of beam a face, surface and b face, side, some strain transducers are installed, are designated as { a respectively
1, a
2, a
i... a
nand { b
1, b
2, b
i... b
n, wherein { a
1, a
2, a
i... a
nrepresent, at curved surface a, { x is installed respectively
1, x
2, x
i... x
nn strain transducer on position, and { b
1, b
2, b
i... b
nrepresent neutral line correspondence { x on the b of side
1, x
2, x
i... x
nn strain transducer on position, as shown in Figure 2.Before strain transducer is installed on b surface in side, first will treat that geodesic structure carries out modeling analysis to determine neutral line.
Second step, measures the strain value of each position, after uniform beam generation Compression and Expansion-flexural deformation, measures the strain value of each point, be designated as { ε respectively according to mounted strain transducer
a(x
1), ε
a(x
2), ε
a(x
i) ... ε
a(x
n) and { ε
b(x
1), ε
b(x
2), ε
b(x
i) ... ε
b(x
n), wherein { ε
a(x
1), ε
a(x
2), ε
a(x
i) ... ε
a(x
n) represent n the strain transducer { a of curved surface a
1, a
2, a
i... a
nreading value; { ε
b(x
1), ε
b(x
2), ε
b(x
i) ... ε
b(x
n) represent n the strain transducer { b of side b
1, b
2, b
i... b
nreading value, as shown in Figure 3.
3rd step, extracts Compression and Expansion strain and bending strain, according to mechanics of materials knowledge, due to { ε
b(x
1), ε
b(x
2), ε
b(x
i) ... ε
b(x
n) be the strain of b surface neutral line, therefore its strain size is out of shape by the Compression and Expansion in x direction of structure and is produced, and { ε
a(x
1), ε
a(x
2), ε
a(x
i) ... ε
a(x
n) be by the Compression and Expansion of structure in x direction and the bending composite strain jointly caused in w direction, therefore, the pure bending strain on structural member bending tensile surface (i.e. upper surface) is { ε
a(x
1)-ε
b(x
1), ε
a(x
2)-ε
b(x
2), ε
a(x
i)-ε
b(x
i) ... ε
a(x
n)-ε
b(x
n), make ε
c(x
1)=ε
a(x
1)-ε
b(x
1), ε
c(x
2)=ε
a(x
2)-ε
b(x
2), ε
c(x
i)=ε
a(x
i)-ε
b(x
i) ... ε
c(x
n)=ε
a(x
n)-ε
b(x
n).
4th step, solves tension and compression deformation field and flexural deformation field respectively, according to mechanics of materials knowledge, can directly quadrature the deformation field obtaining compression for Compression and Expansion strain
wherein Δ L (x) represents the tension and compression deformation of beam in x direction, ε
bx () represents tension and compression strain.Uniform beam is the special circumstances of non-uniform beam, and its neutral layer thickness is the same, and after being simplified by displacement theory equation, the corner function in x direction is
Wherein ε
c(x
i-1), ε
c(x
i) represent the bending strain value of in x-axis adjacent 2, c respectively
ithen represent the thickness of neutral line, Δ l is the distance of adjacent two strain transducers in the direction of the x axis.In conjunction with corner function tan θ
i, then the bending displacement function of each point is
Draw Compression and Expansion deformation field and flexural deformation field thus.
5th step, solves composite deformation field, by the 4th step obtain the tension and compression deformation Δ L (x of every bit
i) and flexural deformation Δ ω (x
i) combine, form the displacement vector { Δ L (x of this point
i), Δ ω (x
i), use the displacement vector of often to describe the composite deformation field of every bit afterwards, and draw composite deformation field, as shown in Figure 4.
In embodiment two, when measuring the distortion of lathe variable cross section column, after lathe variable cross section column is subject to Compression and Expansion distortion and flexural deformation simultaneously, the measuring surface of selection as shown in Figure 5.
Wherein, the first step, at lathe variable cross section leg surface installation position displacement sensor, the plane that first will bend in variable-section beam structure sets up rectangular coordinate system, get vertical direction as x-axis, as shown in Figure 5, w axle is set up in the direction (i.e. bending direction) in one end of this beam perpendicular to x-axis; The wherein one side of then getting this beam deflection installs some strain transducers along the x-axis direction, meanwhile, installs the identical strain transducer of quantity, be designated as { a respectively in the neutral line position correspondence of its side
1, a
2, a
i... a
nand { b
1, b
2, b
i... b
n, wherein { a
1, a
2, a
i... a
nrepresent, at curved surface a, { x is installed respectively
1, x
2, x
i... x
nn strain transducer on position, and { b
1, b
2, b
i... b
nrepresent neutral line correspondence { x on the b of side
1, x
2, x
i... x
nn strain transducer on position.
Second step, measures the strain value of each position, after structure generation Compression and Expansion-flexural deformation, measures each strain value, be designated as { ε respectively according to mounted strain transducer
a(x
1), ε
a(x
2), ε
a(x
i) ... ε
a(x
n) and { ε
b(x
1), ε
b(x
2), ε
b(x
i) ... ε
b(x
n), wherein { ε
a(x
1), ε
a(x
2), ε
a(x
i) ... ε
a(x
n) represent n the strain transducer { a of curved surface a
1, a
2, a
i... a
nreading value; { ε
b(x
1), ε
b(x
2), ε
b(x
i) ... ε
b(x
n) represent n the strain transducer { b of side b
1, b
2, b
i... b
nreading value.
3rd step, extracts Compression and Expansion strain and bending strain, according to mechanics of materials knowledge, due to { ε
b(x
1), ε
b(x
2), ε
b(x
i) ... ε
b(x
n) be the strain of b surface neutral line, therefore its strain size is out of shape by the Compression and Expansion in x direction of structure and is produced, and { ε
a(x
1), ε
a(x
2), ε
a(x
i) ... ε
a(x
n) be by the Compression and Expansion of structure in x direction and the bending composite strain jointly caused in w direction, therefore, the pure bending strain on structural member bending tensile surface is { ε
a(x
1)-ε
b(x
1), ε
a(x
2)-ε
b(x
2), ε
a(x
i)-ε
b(x
i) ... ε
a(x
n)-ε
b(x
n), make ε
c(x
1)=ε
a(x
1)-ε
b(x
1), ε
c(x
2)=ε
a(x
2)-ε
b(x
2), ε
c(x
i)=ε
a(x
i)-ε
b(x
i) ... ε
c(x
n)=ε
a(x
n)-ε
b(x
n).
4th step, solves Compression and Expansion deformation field and flexural deformation field respectively, according to mechanics of materials knowledge, can directly quadrature the deformation field obtaining compression for compressive strain
wherein Δ L (x) represents the tension and compression deformation of non-uniform beam in x direction, ε
bx () represents tension and compression strain.Theoretical according to KO, ask flexural deformation to want the corner function tan θ of integrated structure part, according to practical situations determination stiff end tan θ=0, the equations of rotating angle in x direction
Wherein ε
c(x
i-1), ε
c(x
i) represent the bending strain value of in x-axis adjacent 2, c respectively
i-1, c
ithen represent the thickness of adjacent 2 neutral lines of x-axis respectively, Δ l is the distance of adjacent two strain transducers in the direction of the x axis.In conjunction with equations of rotating angle tan θ
i, then the bending displacement function of each point is
draw Compression and Expansion deformation field and flexural deformation field thus.
5th step, solves composite deformation field, by the 4th step obtain the tension and compression deformation Δ L (x of every bit
i) and flexural deformation Δ ω (x
i) combine, form the displacement vector { Δ L (x of this point
i), Δ ω (x
i), use the displacement vector of often to describe the composite deformation field of each point afterwards, and draw composite deformation field.
Should be understood that, for those of ordinary skills, can be improved according to the above description or convert, and all these improve and convert the protection domain that all should belong to claims of the present invention.
Claims (3)
1. the measuring method of variable-section beam structure tension and compression and bending composite deformation field, it is characterized in that, the method comprises the following steps, step one, the plane bent in variable-section beam structure sets up rectangular coordinate system; direction is as x-axis direction to get the stretching (or compression) of non-uniform beam, and w axle is set up in the direction in one end of non-uniform beam perpendicular to x-axis; Upper surface when then getting non-uniform beam flexural deformation or lower surface install some strain transducers along the x-axis direction, meanwhile, the neutral line correspondence position of non-uniform beam side are installed the identical strain transducer of quantity; Step 2, is treating that geodesic structure occurs stretch or compress and after flexural deformation, measured the strain value at each strain transducer mounting points place by each strain transducer installed; Step 3, solve stretching (or compression) strain and pure bending strain, the pure bending strain on structural bending surface to be measured is for curved surface a is at the composite strain that the stretching (or compression) in x direction is out of shape and the flexural deformation in w direction causes jointly and treat the difference that geodesic structure stretches on the neutral line of side b (or compression) strains; Step 4, directly can quadrature to obtain the distortion of construction stretch to be measured (or compression), try to achieve the flexural deformation treating geodesic structure according to displacement theory for (or compression) strain that stretches; Step 5, integrating step four calculates the composite deformation field for the treatment of that geodesic structure causes jointly in stretching (or compression) distortion in x direction and the flexural deformation in w direction, stretching (or compression) distortion and flexural deformation for the treatment of every bit on geodesic structure are vowed and forms displacement vector, utilize displacement vector to obtain composite deformation field.
2. the measuring method of variable-section beam structure tension and compression according to claim 1 and bending composite deformation field, it is characterized in that, in described step one, the quantity of the strain transducer that upper surface during non-uniform beam flexural deformation or lower surface are installed along the x-axis direction is at least 2.
3. the measuring method of variable-section beam structure tension and compression according to claim 1 and 2 and bending composite deformation field, is characterized in that, in described step one, by treating that geodesic structure carries out the neutral line that modeling analysis determines non-uniform beam side.
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| CN110887448A (en) * | 2019-11-28 | 2020-03-17 | 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 |
| CN114239127A (en) * | 2021-09-29 | 2022-03-25 | 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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