Background technology
The operation principle of metal resistance strain gauge is resistance strain effect, i.e. wire is in effect strained, its electricity
Resistance occurs to change accordingly with the size of mechanically deform occurred (stretching or compression).The theoretical formula of resistance strain effect
It is as follows:
Wherein R is its resistance value, and ρ is metal material resistivity, and L is metal material length, and S is metal material sectional area.
Wire is bearing to strain during mechanically deform occurs, and ρ, L, S three will change, so as to will necessarily cause gold
Belong to the change of material resistance value.When metal material is stretched, length increase, sectional area reduces, resistance value increase;When compressed
When, length reduces, and sectional area increase, resistance value reduces.Therefore, as long as the change of resistance value can be measured, wire can be known
Strained situation.Metal material resistance change rate formula can be exported by relevant knowledges such as formula (1) and the mechanics of materials
Wherein Δ R is resistance variation amount, and Δ L is the change of metal material length on pulling force or pressure action direction
Amount, ε are that the strain in same direction is usually referred to as axial strain, and K is metal material ga(u)ge factor.
In practical applications, metal resistance strain gauge is pasted onto to the table of Sensor Elastic Element or tested machine components
Face.When the flexible member in sensor or tested machine components are produced strain by active force, foil gauge on it is pasted
Identical mechanically deform occurs therewith, causes strain sheet resistance that corresponding change occurs.At this moment, resistance strain gage is just by mechanical quantity
Be converted to the variable quantity output of resistance.
But we are also required to understand the partial derivative of workpiece strain sometimes, for example there are three kinds of occasions below, but not limited to this
Three, it is necessary to use workpiece surface strain partial derivative:
First, due to nearby occurring that strain is concentrated, and often occurs damaging it first as workpiece at workpiece shapes mutation
Place, monitors the strain partial derivative near at shape mutation, can intuitively obtain strain intensity at this.
Second, largely existed by comer pieces in building, bridge, mechanical equipment, the related knowledge of the mechanics of materials is taught that, bending
The axial strain of beam surface is directly proportional to section turn moment, and the axial partial derivative of section turn moment is directly proportional to section shearing strain, that is,
Section shearing strain can be known by the axial partial derivative of surface axial strain, and the shearing strain can not use foil gauge in workpiece table
Face directly measures;
3rd, when applied elasticity research workpiece strains, internal strain is decided by partial differential equation, and equation solution needs
Boundary condition, and workpiece surface strain partial derivative is exactly one of boundary condition, this is that general foil gauge can not provide.
In addition, to some positions of workpiece, such as the position such as at the shaft shoulder, part edge, due to the mutation of geomery, its
Often accordingly there are bigger change for strain.However, just due to the mutation of geomery so that more difficult at this to dispose generally
Foil gauge is, it is necessary to the production of a kind of energy inclined edge of measuring strain piece even edge outer fix rather than center position strain local derviation
Product.It so just may be implemented in and avoid arranging foil gauge at a certain distance from the more difficult target measured point for placing foil gauge, and finally survey
Measure the strain local derviation at the target measured point.
The content of the invention
In order to overcome the shortcomings of that existing metal strain plate can not detect strain local derviation, the present invention provides one kind and can measure
The axial distribution three that axial local derviation on the outside of the measurable biasing sensitive grid that can effectively detect surface strain axial direction local derviation should be changed is quick
Feel grid metal foil gauge, particularly measure workpiece corner, edge etc. have to foil gauge size restriction site or other should not cloth
Put the axial single order local derviation of foil gauge position.
The technical solution adopted by the present invention to solve the technical problems is:
The three sensitive grid metal strain plates of axial distribution of axial local derviation on the outside of a kind of measurable biasing sensitive grid, including base
Bottom, the metal strain plate further include three sensitive grids, and the both ends of each sensitive grid connect a pin respectively, in the substrate
Fixed three sensitive grids;
Each sensitive grid includes sensitive segment and changeover portion, and the both ends of the sensitive segment are changeover portion, and the sensitive segment is in thin
Strip, the changeover portion are in tubbiness shape, and the resistance of the sensitive segment is much larger than the resistance of the changeover portion, same strain state
Under the increased resistance value of the sensitive segment be much larger than the increased resistance value of the changeover portion, the increased resistance value of the changeover portion connects
It is bordering on 0;
All cross section centres of form of each sensitive segment form sensitive segment axis, which is straight line section, institute
It is parallel and be generally aligned in the same plane to state the axis of each sensitive segment in three sensitive grids, in the definite plane of sensitive segment axis institute, edge
The sensitive segment axis direction is axial, with axially vertical direction for laterally;There are its both sides resistance value on each sensitive segment
An equal cross section, takes the cross-section centroid position and is formed place sensitive segment by nominal mass of the sensitive segment resistance value
Nominal particle, the centroid position that the nominal particle of each sensitive segment is collectively forming are the center of sensitive grid;
There is deviation at three sensitive grid centers in the axial direction, in the horizontal zero deflection;Three sensitive grids press sensitive grid centre bit
The order put, is referred to as left sensitive grid, middle sensitive grid and right sensitive grid from left to right vertically;Left sensitive grid center is quick with
The distance for feeling grid center is Δ x1, the distance at middle sensitive grid center and right sensitive grid center is Δ x1, among any two sensitive grid
The high person in the central axial position of sensitive grid, the axial location of every bit is higher than any sensitive segment of another sensitive grid on its each sensitive segment
The axial location of upper any point;
The sensitive segment all-in resistance of left sensitive grid, middle sensitive grid and right sensitive grid is in 3:8:5 proportionate relationship, left sensitive grid,
The all-in resistance changing value of the sensitive segment of middle sensitive grid and right sensitive grid sensitive segment under identical strain is also in 3:8:5 ratio is closed
System.
Further, all shape of cross section sizes of each sensitive segment are consistent, take the axis point midway of each sensitive segment
And using the sensitive segment resistance value as nominal mass formed where sensitive segment nominal particle, the left sensitive grid, middle sensitive grid and
The sensitive segment total length of right sensitive grid is in 3:8:5 proportionate relationship.The program is a kind of scheme that can be selected, nominal particle
As long as position meet the equal cross section position of form center of its both sides resistance value can or other positions.
Further, two pins of right sensitive grid are respectively positioned on the left side of right sensitive grid.Purpose is reduced in right sensitive grid
Distance of the heart to foil gauge right side edge.
Further, relatively middle sensitive grid, the sensitive segment axial length of right sensitive grid can be shorter and cross direction profiles can be closeer.
Purpose is the distance for reducing right sensitive grid center to foil gauge right side edge.
Using the linear relationship between metal material increased resistance value and strain, this foil gauge is as common foil gauge
It can be used for measuring strain.On the other hand, according in numerical differentiation theory, (such as Yi Fengkang is compiled, National Defense Industry Press 1978
December in year publishes《Numerical computation method》Page 21 (1.4.11)-(1.4.14) formulas make equidistant interpolation analysis) on single order local derviation
Circular, the numerical computation method of the x directions first-order partial derivative of f (x, y) is as follows:
Wherein x1=x0+ h, x2=x1+ h, it is (x to pay special attention to above formula2+ h, y) position first-order partial derivative value formula, the formula
Truncated error it is smaller be o (h2) be step-length square higher order indefinite small.By being generally acknowledged that sensitive grid electricity in formula (2) engineering
The strain at variable quantity direct ratio and sensitive grid center is hindered, with reference to each sensitive gate resistance and the resistance change under same strain
Proportionate relationship, the resistance of left sensitive grid and right sensitive grid and the resistance value for subtracting middle sensitive grid, then divided by left sensitive grid center and
The distance at right sensitive grid center is the axial single order numerical value local derviation of strain;Particularly, this is right sensitive grid center h distances to the right
The axial single order numerical value local derviation at place, h here should be answered certainly equal to the distance between right sensitive grid center to middle sensitive grid
Become piece advantage be to measure workpiece corner, edge etc. have to foil gauge size restriction site or other should not arrange foil gauge
The axial single order local derviation of position.
It should be noted that keeping left sensitive grid, middle sensitive grid and right sensitive grid changeover portion all-in resistance and changeover portion electricity in technique
It is in 3 to hinder the variable quantity under external strain:8:5 numerical relation to heighten measurement accuracy, if the resistance of changeover portion and should
Become lower resistance change can not ignore, can also be eliminated when detecting as systematic error.
Further, the metal strain plate further includes cover plate, and the cover plate is covered in the sensitive grid and substrate.
Further, the sensitive grid is wire form, foil, diaphragm type or thick-film type sensitive grid.
Further, the substrate is glued membrane substrate, glass fabric substrates, asbestos base bottom, metallic substrates or temporary substrate.
Three sensitive grid left, center, right are arranged in substrate.It is of course also possible to it is other arrangements.
Beneficial effects of the present invention are mainly manifested in:The strain axial direction single order at the right right outside one in sensitive grid center can be detected
Local derviation, with right sensitive grid center zero deflection at this in transverse direction, the spacing at this and right sensitive grid center is equal to middle sensitivity in axial direction
The spacing at grid center and right sensitive grid center.Therefore there is foil gauge at the measurable workpiece corner of the present invention, edge etc. size limitation
Position or other should not arrange the axial single order local derviation of foil gauge position.
Embodiment
The invention will be further described below in conjunction with the accompanying drawings.
With reference to Fig. 1~Fig. 3, the sensitive grid metal of axial distribution three of axial local derviation should on the outside of a kind of measurable biasing sensitive grid
Become piece, including substrate, the metal strain plate further include three sensitive grids, the both ends of each sensitive grid connect one and draw respectively
Foot, fixes three sensitive grids in the substrate;
Each sensitive grid includes sensitive segment and changeover portion, and the both ends of the sensitive segment are changeover portion, and the sensitive segment is in thin
Strip, the changeover portion are in tubbiness shape, and the resistance of the sensitive segment is much larger than the resistance of the changeover portion, same strain state
Under the increased resistance value of the sensitive segment be much larger than the increased resistance value of the changeover portion, the increased resistance value of the changeover portion connects
It is bordering on 0;
All cross section centres of form of each sensitive segment form sensitive segment axis, which is straight line section, institute
It is parallel and be generally aligned in the same plane to state the axis of each sensitive segment in three sensitive grids, in the definite plane of sensitive segment axis institute, edge
The sensitive segment axis direction is axial, with axially vertical direction for laterally;There are its both sides resistance value on each sensitive segment
An equal cross section, takes the cross-section centroid position and is formed place sensitive segment by nominal mass of the sensitive segment resistance value
Nominal particle, the centroid position that the nominal particle of each sensitive segment is collectively forming are the center of sensitive grid;
There is deviation at three sensitive grid centers in the axial direction, in the horizontal zero deflection;Three sensitive grids press sensitive grid centre bit
The order put, is referred to as left sensitive grid, middle sensitive grid and right sensitive grid from left to right vertically;Left sensitive grid center is quick with
The distance for feeling grid center is Δ x1, the distance at middle sensitive grid center and right sensitive grid center is Δ x1, among any two sensitive grid
The high person in the central axial position of sensitive grid, the axial location of every bit is higher than any sensitive segment of another sensitive grid on its each sensitive segment
The axial location of upper any point.
The sensitive segment all-in resistance of left sensitive grid, middle sensitive grid and right sensitive grid is in 3:8:5 proportionate relationship, left sensitive grid,
The all-in resistance changing value of the sensitive segment of middle sensitive grid and right sensitive grid sensitive segment under identical strain is also in 3:8:5 ratio is closed
System.
Further, all shape of cross section sizes of each sensitive segment are consistent, take the axis point midway of each sensitive segment
And using the sensitive segment resistance value as nominal mass formed where sensitive segment nominal particle, the left sensitive grid, middle sensitive grid and
The sensitive segment total length of right sensitive grid is in 3:8:5 proportionate relationship.The program is a kind of scheme that can be selected, nominal particle
As long as position meet the equal cross section position of form center of its both sides resistance value can or other positions.
Further, two pins of right sensitive grid are respectively positioned on the left side of right sensitive grid, it is therefore an objective to reduce in right sensitive grid
Distance of the heart to foil gauge right side edge.
Further, relatively middle sensitive grid, the sensitive segment axial length of right sensitive grid can be shorter and cross direction profiles can be closeer,
Purpose is the distance for reducing right sensitive grid center to foil gauge right side edge.
The three sensitive grid metal strain plates of axial distribution of axial local derviation, bag on the outside of the measurable biasing sensitive grid of the present embodiment
Substrate 1 is included, the metal strain plate further includes three sensitive grids, and the both ends of each sensitive grid connect a pin respectively, described
Three sensitive grids are fixed in substrate 1.
Left sensitive grid 2, middle sensitive grid 3 and right sensitive grid 4 can be fixed on substrate 1, for keeping each sensitive grid fixation
Shape, positions and dimensions;Substrate 1 is very thin, so that the strain of surface of test piece is accurately transfer to left sensitive grid 2, middle sensitive grid 3
With right sensitive grid 4.Substrate 1 can be glued membrane substrate, glass fabric substrates, asbestos base bottom, metallic substrates and temporary substrate.Usually
With cohere, weld, substrate is fixed on the tested position of test block by the mode such as ceramic spraying.Some use can be also printed in substrate 1
In the lines of foil gauge positioning.
Cover plate is made of materials such as paper or glue, is covered in left sensitive grid 2, middle sensitive grid 3, right sensitive grid 4 and substrate 1
On, play the protective layer of moisture-proof, corrosion protection, loss prevention etc..
Pin 5 is used to connect sensitive grid and measuring circuit, and left sensitive grid 2, middle sensitive grid 3 and right sensitive grid 4 respectively have two
Pin 5, pair with foil and membrane type foil gauge, left sensitive grid 2, middle sensitive grid 3 and the right sensitive grid 4 that pin 5 is connected with it
It is integrated.Two pins of left sensitive grid 2 are 5-1 and 5-2, and two pins of middle sensitive grid 3 are 5-3 and 5-4, right sensitive grid 4
Two pins be 5-5 and 5-6, pin 5-5 and 5-6 are respectively positioned on the left side of right sensitive grid 4, it is therefore an objective to reduce right sensitive grid 4 and arrive
The distance of foil gauge right side edge.
Left sensitive grid 2, middle sensitive grid 3 and right sensitive grid 4, can be with according to its metal sensitive material and the difference of processing technology
For wire form, foil, diaphragm type, thick-film type.No matter which kind of left sensitive grid 2, the equal very little of the thickness of middle sensitive grid 3 and right sensitive grid 4,
So that the axial length of left sensitive grid 2, middle sensitive grid 3 and right sensitive grid 4 depends on the deformation of workpiece with it and changes.The present invention
It is basic it is critical that cooperation between left sensitive grid 2, middle sensitive grid 3 and right sensitive grid 4, there is following main points:
First, three sensitive grids are arranged in substrate, are referred to as left sensitive grid 2, middle sensitive grid 3 and right sensitive grid 4.
Second, left sensitive grid 2, middle sensitive grid 3 and right sensitive grid 4 can be divided into multiple sensitive segments 6 and multiple changeover portions 7,
The connection of each sensitive segment 6 is formed sensitive grid by each changeover portion 7.Comparatively, sensitive segment 6 is elongated in shape, resistance is larger and it is hindered
Value is more sensitive to straining;The changeover portion 7 is in tubbiness shape substantially so that the resistance very little of the changeover portion and to strain not
Sensitivity, resistance variations are close to 0 under working status, therefore the summation of sensitive segment resistance is essentially the all-in resistance of single sensitive grid.
Fig. 2 has marked sensitive segment 6 and changeover portion 7 in more detail from clearer angle.
3rd, the sensitive segment 6 of each sensitive grid is in elongated strip, and all cross section centres of form composition of each sensitive segment 6 is quick
Feel section axis, which is straight line section, and the axis of each sensitive segment 6 is parallel and is generally aligned in the same plane.Each
All cross sections of sensitive segment 6 are consistent along the projection of shape of sensitive segment axis direction.Take the axis point midway of each sensitive segment
And the nominal particle of place sensitive segment is formed using the sensitive segment resistance value as nominal mass, the nominal particle of each sensitive segment is common
The centroid position of formation is the center of sensitive grid.
4th, 6 total length of sensitive segment of left sensitive grid 2, middle sensitive grid 3 and right sensitive grid 4 is in 3:8:5 proportionate relationship,
6 all-in resistance of sensitive segment of left sensitive grid 2, middle sensitive grid 3 and right sensitive grid 4 is in 3:8:5 proportionate relationship, left sensitive grid 2, in it is quick
The all-in resistance changing value for feeling the sensitive segment under identical strain of sensitive segment 6 of grid 3 and right sensitive grid 4 is also in 3:8:5 ratio is closed
System.
5th, left sensitive grid 2, middle sensitive grid 3 and right sensitive grid 4 are overlooked, they are respectively provided with symmetry axis and symmetrical overlapping of axles
(x-axis in Fig. 2), left sensitive grid 2, middle sensitive grid 3 and the respective sensitive segment 6 of right sensitive grid 4 are all parallel with the symmetry axis, respectively
The sensitive segment 6 of sensitive grid is distributed on this axial symmetry.Therefore, it can be said that left sensitive grid 2, middle sensitive grid 3 and right sensitive grid 4 are same
Axis, that is, detect it is equidirectional strain and left sensitive grid 2, middle sensitive grid 3 and right sensitive grid 4 center in x-axis, it
Center have axial deviation without lateral deviation.According to the top view of foil gauge in Fig. 2, the sensitive segment 6 of left sensitive grid 2 has transverse direction
Symmetry axis yL, the center of left sensitive grid 2 is in x-axis and yLThe intersection point of axis, the sensitive segment 6 of middle sensitive grid 3 have lateral symmetry axis yM, in
The center of sensitive grid 3 is in x-axis and yMThe intersection point of axis, the sensitive segment 6 of right sensitive grid 4 have lateral symmetry axis yR, in right sensitive grid 4
The heart is in x-axis and yRThe intersection point of axis.
6th, the distance at left 2 center of sensitive grid and middle 3 center of sensitive grid is Δ x1, middle 3 center of sensitive grid and right sensitive grid
The distance at 4 centers is Δ x1, i.e., the center of left sensitive grid 2 and the line midpoint at the center of right sensitive grid 4 are also x-axis and yMAxis
Intersection point, as shown in Figure 2.The forward direction of x-axis as shown in Figure 2, during the x coordinate of arbitrary point is less than on any sensitive segment 6 of left sensitive grid 2
Sensitive grid 3 any sensitive segment 6 on arbitrary point x coordinate, the x coordinate of arbitrary point is small on any sensitive segment 6 of middle sensitive grid 3
In right sensitive grid 4 any sensitive segment 6 on arbitrary point x coordinate.Due to left sensitive grid 2, middle sensitive grid 3 and right sensitive grid 4
Relative position by foil gauge production technology ensure relatively accurately secured, this is also that the present invention can detect workpiece strain axis
One of key to partial derivative.
In conclusion left sensitive grid 2, middle sensitive grid 3 and right sensitive grid 4 increased resistance value under same strain of the present invention is in
3:8:5 proportionate relationship, each sensitive grid central cross zero deflection axially have deviation, 2 center of left sensitive grid to middle 3 center of sensitive grid
Distance it is equal to the distance of right sensitive grid 4 with middle 3 center of sensitive grid.
It is R to make 2 resistance of free state bottom left sensitive gridL0, middle 3 resistance of sensitive grid is RM0, right 4 resistance of sensitive grid is RR0, should
There is RL0+RR0=RM0=R0.When the foil gauge placement Mr. Yu of the present invention is had surface strain, left 2 resistance of sensitive grid is R0+ΔRL,
Middle 3 resistance of sensitive grid is R0+ΔRM0, right 4 resistance of sensitive grid is R0+ΔRR;On the other hand, left sensitive grid 2 and right sensitive grid 4
Center respectively be located at Fig. 2 in x-axis and yLIntersection point and x-axis and yRIntersection point, at a distance of 2 Δ x in axial direction1.IfFor right sensitivity
4 central right Δ x of grid1Place, that is, x-axis and y in Fig. 2OIntersection point, using sensitive gate resistance and surface strain relation and
The formula (3) of numerical differentiation has:
Wherein εLFor the strain at left 2 center of sensitive grid, εMFor the strain at middle 3 center of sensitive grid, εRFor right sensitive grid 4
Strain at center.This is the principle of the axial local derviation of the present embodiment measurement surface strain.Pay special attention to, the number that above formula is calculated
Value differential is right 4 center of sensitive grid Δ x in outside to the right1The strain axial direction single order local derviation of position, the position are the right side of foil gauge
Edge has even on the outside of edge and is easy to measurement workpiece corner, edge etc. to have size restriction site to foil gauge
The advantage of axial single order local derviation.With reference to Fig. 2, it is noted that the pin 5-5 and 5-6 of right sensitive grid 4 are arranged in the right left side of sensitive grid 4,
Its purpose is to reduce right 4 center of sensitive grid as far as possible to the distance of foil gauge right side edge, above-mentioned in order to further play
Advantage.
Electric bridge is coordinated to can be used for measuring strain, strain axial single order local derviation the present embodiment, it is assumed that bridge input voltage is
ui, output voltage uo, the schematic diagram of measuring bridge is shown in Fig. 3.In no workpiece effects of strain, each arm resistance of electric bridge is according to up time
Pin direction is respectively labeled as R1、R2、R3、R4, in the also electric bridge where these sign flag resistance in the case of will not obscuring.Often
The sensitive grid or resistance of foil gauge can be placed on a electric bridge.It is identical with general foil gauge arrangement, if in multiple bridge arms
Upper placement sensitive grid, the requirement of order, strain difinite quality to each installation position.During without workpiece effects of strain, the output of electric bridge
Voltage equation is
At this time, it is desirable to bridge balance i.e. uo=0, then it must is fulfilled for so-called bridge balance condition R1R3-R2R4=0,
The electric bridge of use further meets
R1=R2=R3=R4, (6)
Since first, when meeting condition (6), according to related theoretical foil gauge sensitivity highest;Second, measuring strain or
The method that person strains axial local derviation is required to condition (6) establishment.When foil gauge is also strained with external world's strain, above-mentioned electric bridge
Equilibrium condition is generally no longer set up, at this time
Due to Δ Ri< < RiFirst ≈ of (i=1,2,3,4) event is set up, and second ≈ works as Δ R1-ΔR2With Δ R3-ΔR4
Jack per line or contrary sign but | Δ R1-ΔR2| with | Δ R3-ΔR4| not in close proximity to when set up, foil gauge is reasonably selected in engineering
Installation position can be realized completely.It is generally available the voltage measurement strain of formula (7) acquisition;Can convolution to the axial local derviation of strain
(4) and formula (7), reasonable design arrange each bridge arm sensitive grid and resistance, such as bridge arm R1Sensitive grid 3 in arrangement, bridge arm R2Series connection
Arrange left sensitive grid 2 and right sensitive grid 4, the configuration of remaining bridge arm and bridge arm R1Equivalent resistance, can obtain and right 4 center of sensitive grid
Δ x in outside to the right1The axial single order local derviation of position strain magnitude of voltage u in a linear relationshipo, which is that small-signal need to be put
Greatly.