Background technology
The operation principle of metal resistance strain gauge is resistance strain effect, i.e. wire is in effect strained, electricity
Resistance occurs to change accordingly with the size of mechanically deform occurred (stretch or compress).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 cause gold
Belong to the variation of material resistance value.When metal material is stretched, length increases, and sectional area reduces, and resistance value increases;When compressed
When, length reduces, and sectional area increase, resistance value reduces.Therefore, as long as the variation of resistance value can be measured, it can know wire
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 variation 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 elastic element in sensor or tested machine components are generated strain by active force, foil gauge on it is pasted
Identical mechanically deform occurs therewith, causes strain sheet resistance that corresponding variation 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, such as below there are three types of occasion, but not limited to this
Three, it needs to use workpiece surface strain partial derivative:
First, it is concentrated due to nearby will appear strain at workpiece shapes mutation, often occurs damaging it first as workpiece
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 first-order partial derivative of section turn moment is directly proportional to section shearing strain,
Exactly can section shearing strain be known by the axial first-order partial derivative of surface axial strain, and the shearing strain can not use foil gauge
It is directly measured in workpiece surface;
Third, 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 certain positions of workpiece, such as the positions such as at the shaft shoulder, part edge, due to the mutation of geomery,
Often accordingly there are bigger variations for strain.However, just due to the mutation of geomery so that more difficult placement is general at this
Foil gauge needs the product of a kind of inclined marginal position of energy measuring strain piece rather than center position strain local derviation.
Invention content
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 the measurable central axial local derviation of biasing sensitive grid that can effectively detect surface strain axial direction local derviation should be changed is quick
Feel grid metal foil gauge, particularly measuring workpiece corner, edge etc. has foil gauge the axial single order local derviation of size restriction site.
The technical solution adopted by the present invention to solve the technical problems is:
A kind of three sensitive grid metal strain plates of axial distribution of the measurable biasing central axial local derviation of 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
The axis for stating each sensitive segment in three sensitive grids is parallel and be generally aligned in the same plane, in the determining 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 values 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 formed 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 sequence put is referred to as left sensitive grid, middle sensitive grid and right sensitive grid from left to right in an axial direction;Left sensitive grid center is quick in
The distance for feeling grid center is Δ x1, the distance at middle sensitive grid center and right sensitive grid center is Δ x2, Δ x1=Δ x2, arbitrary two
The high person in the central axial position of sensitive grid among a sensitive grid, the axial position of every bit is higher than another sensitivity on each sensitive segment
The axial position of any point on any sensitive segment of grid;
The sensitive segment all-in resistance of left sensitive grid, middle sensitive grid and right sensitive grid is in 1:4:3 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 1:4:3 ratio is closed
System.
Further, all cross-sectional shape 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 1:4:3 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
The heart is to the distance of 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) about 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 pays special attention to above formula as (x2, y) position first-order partial derivative value formula, the formula
Smaller truncated error is o (h2) be step-length square higher order indefinite small.By being generally acknowledged that sensitive gate resistance in formula (2) engineering
Variable quantity direct ratio and the strain at sensitive grid center, with reference to each sensitive gate resistance and the ratio of the resistance change under same strain
Example 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 right side
The distance at sensitive grid center is the axial single order numerical value local derviation of strain;Particularly, this is axial the one of right sensitive grid center
Exponent number value local derviation, therefore the advantage of the foil gauge is to measure the general foil gauge such as workpiece corner, edge since size limits nothing
The axial single order local derviation at the position that method measures.
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 1 to hinder the variable quantity under external strain:4:3 numerical relation measurement accuracy is turned up, if the resistance of changeover portion and should
Become lower resistance change can not ignore, also can when detecting be eliminated 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 for other arrangements.
Beneficial effects of the present invention are mainly manifested in:The strain axial direction single order that right sensitive grid center can effectively be detected is inclined
Derivative, particularly measuring workpiece corner, edge etc. has foil gauge the axial single order local derviation of size restriction site.
Specific embodiment
The invention will be further described below in conjunction with the accompanying drawings.
With reference to Fig. 1~Fig. 3, a kind of sensitive grid metal of axial distribution three of the measurable biasing central axial local derviation of sensitive grid should
Become piece, including substrate, the metal strain plate further includes three sensitive grids, and 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
The axis for stating each sensitive segment in three sensitive grids is parallel and be generally aligned in the same plane, in the determining 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 values 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 formed 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 sequence put is referred to as left sensitive grid, middle sensitive grid and right sensitive grid from left to right in an axial direction;Left sensitive grid center is quick in
The distance for feeling grid center is Δ x1, the distance at middle sensitive grid center and right sensitive grid center is Δ x2, Δ x1=Δ x2, arbitrary two
The high person in the central axial position of sensitive grid among a sensitive grid, the axial position of every bit is higher than another sensitivity on each sensitive segment
The axial position of any point on any sensitive segment of grid.
The sensitive segment all-in resistance of left sensitive grid, middle sensitive grid and right sensitive grid is in 1:4:3 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 1:4:3 ratio is closed
System.
Further, all cross-sectional shape 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 1:4:3 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
The heart is to the distance of 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 the measurable central axial local derviation of biasing sensitive grid of the present embodiment, packet
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 fixed
Shape, positions and dimensions;Substrate 1 is very thin, so as to which 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 modes such as ceramic spraying.Some use can be also printed in substrate 1
In the lines of foil gauge positioning.
The materials such as cover plate paper or glue are made, and are covered in left sensitive grid 2, middle sensitive grid 3, right sensitive grid 4 and substrate 1
On, rise moisture-proof, corrosion protection, loss prevention the effects that protective layer.
Pin 5 is for connecting sensitive grid and measuring circuit, there are two left sensitive grid 2, middle sensitive grid 3 and right sensitive grid 4 are each
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 connect 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 for 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, middle sensitive grid 3 and right sensitive grid 4 the equal very little of thickness,
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 substantially be in tubbiness shape so that the resistance very little of the changeover portion and to strain not
Sensitivity, resistance variations are close to 0 under working condition, 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.
Third, 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 1:4:3 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 1:4:3 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 1:4:3 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 4 respective sensitive segment 6 of right sensitive grid are all parallel with the symmetry axis, respectively
The sensitive segment 6 of sensitive grid is distributed about 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.The vertical view of middle foil gauge according to fig. 2, the sensitive segment 6 of left sensitive grid 2 have 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 x2, Δ x1=Δ x2, 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 yMThe intersection point of axis, as shown in Figure 2.The forward direction of x-axis as shown in Figure 2, the x of arbitrary point on the arbitrary sensitive segment 6 of left sensitive grid 2
Coordinate be less than middle sensitive grid 3 arbitrary sensitive segment 6 on arbitrary point x coordinate, on the arbitrary sensitive segment 6 of middle sensitive grid 3 arbitrarily
Point x coordinate be less than right sensitive grid 4 arbitrary sensitive segment 6 on arbitrary point x coordinate.Due to left sensitive grid 2, middle sensitive grid 3
It is relatively accurately secured by the guarantee of foil gauge production technology with the relative position of right sensitive grid 4, this is also that the present invention can examine
Survey one of key of the axial partial derivative of workpiece strain.
In conclusion the left sensitive grid 2 of the present invention, middle sensitive grid 3 and right sensitive grid 4 increased resistance value under same strain are in
1:4:3 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 with the distance of middle 3 center of sensitive grid to right sensitive grid 4.
It is R to enable 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.Utilize sensitive grid electricity
Resistance has with the relationship of surface strain and the formula (3) of numerical differentiation:
WhereinFor the center of right sensitive grid 4, εLFor the strain at left 2 center of sensitive grid, εMFor in middle sensitive grid 3
Strain at the heart, εRFor the strain at right 4 center of sensitive grid.This is the original of the axial local derviation of the present embodiment measurement surface strain
Reason.Pay special attention to, strain axial direction single order local derviation of the numerical differentiation that above formula is calculated for the center of right sensitive grid 4, the position
The right side of foil gauge is set to, therefore has and measurement workpiece corner, edge etc. is convenient for 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 sensitive segment 6 of the 6 middle sensitive grid 3 of sensitive segment of right sensitive grid 4 is short (real
Half of 6 length of sensitive segment of right sensitive grid 4 for the sensitive segment 6 of middle sensitive grid 3 in the figure 2 above of border), lateral upper right sensitive grid 4
Sensitive segment 6 arrange it is closeer (in practical figure 2 above the hop count of the sensitive segment 6 of right sensitive grid 4 for middle sensitive grid 3 sensitive segment 6 hop count
3/2 times) and the pin 5-5 and 5-6 of right sensitive grid 4 be arranged in 4 left side of right sensitive grid, purpose is to reduce as possible
Right 4 center of sensitive grid to foil gauge right side edge distance, in order to further play above-mentioned advantage.
The present embodiment cooperation electric bridge be can be used for into the axial single order local derviation of measuring strain, strain, 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
Needle direction is respectively labeled as R1、R2、R3、R4, the also electric bridge where these sign flag resistance in the case where that will not obscure.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 that bridge balance i.e. uo=0, it then must satisfy so-called bridge balance condition R1R3-R2R4=0,
The electric bridge of use further meets
R1=R2=R3=R4, (6) because, first, when meeting condition (6), according to related theory foil gauge sensitivity most
It is high;Second, measuring strain or the method for straining axial local derviation are required to condition (6) establishment.When foil gauge is strained with the external world
When straining, above-mentioned bridge balance 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;To strain, axial local derviation can convolution
(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, remaining bridge arm configuration substitutional resistance can obtain and the strain axis at right 4 center of sensitive grid
The voltage value u in a linear relationship to single order local derviationo, which is that small-signal need to be amplified.