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 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 actual 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 thereon is pasted onto
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, but not limited to this below
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, the strain partial derivative near at shape mutation is monitored, can intuitively obtain strain intensity at this.
Second, largely existed by comer pieces in building, bridge, plant equipment, the relevant 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 direct measurement arrives;
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
Bigger change often accordingly be present in strain.However, just due to the mutation of geomery so that more difficult placement in general at this
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 laying 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 measured
It should change outside the measurable unilateral piece of energy effective detection surface strain transverse direction local derviation in the sensitive grid of cross direction profiles five of horizontal local derviation
Interdigital metal strain plate is dredged, particularly measures that workpiece corner, edge etc. have size restriction site to foil gauge or other are unsuitable
Arrange the horizontal single order local derviation of foil gauge position.
The technical solution adopted for the present invention to solve the technical problems is:
Interdigital metal strain plate, including base are dredged outside a kind of measurable unilateral piece in the sensitive grid of cross direction profiles five of horizontal local derviation
Bottom, the metal strain plate also include five sensitive grids, and the both ends of each sensitive grid connect a pin, consolidated in the substrate respectively
Fixed five 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, and the sensitive segment axis is straight line section, institute
In stating the diameter parallel of each sensitive segment in five sensitive grids and being generally aligned in the same plane, sensitive segment axis is determined in plane, edge
The sensitive segment axis direction is axially, with axially vertical direction for laterally;Its both sides resistance value be present on each sensitive segment
An equal cross section, take the cross-section centroid position and 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;
Five sensitive grid centers zero deflection in the axial direction, there is deviation in the horizontal;Five sensitive grids press sensitive grid centre bit
The order put, thin first sensitive grid is transversely followed successively by from top to bottom, dredges second sensitive grid, middle first sensitive grid, middle second sensitive grid and close
Sensitive grid, it is Δ x to dredge distance between first sensitive grid center and middle first sensitive grid centerA, middle first sensitive grid center and close sensitive grid
Distance is also Δ y between centerA;It is Δ y to dredge distance between second sensitive grid center and middle second sensitive grid centerB, in middle second sensitive grid
Distance is also Δ y between the heart and close sensitive grid centerB, Δ yA>ΔyB;Dredge first sensitive grid center and thin second sensitive grid center away from
From for 2 Δ y1, the distance at middle first sensitive grid center and middle second sensitive grid center is Δ y1, Δ y1=Δ yA-ΔyB;
Each sensitive segment axis determines in plane that it is in interdigital arrangement between first sensitive grid and thin second sensitive grid that top, which is dredged, in
It is in interdigital arrangement between first sensitive grid and middle second sensitive grid in portion;
The sensitive segment all-in resistance for dredge first sensitive grid, dredging second sensitive grid, middle first sensitive grid, middle second sensitive grid and close sensitive grid is in
5:5:12:12:7 proportionate relationship, dredge first sensitive grid, dredge second sensitive grid, middle first sensitive grid, middle second sensitive grid and close sensitive grid
The all-in resistance changing value of sensitive segment sensitive segment under identical strain is also in 5:5:12:12:7 proportionate relationship.
Further, all shape of cross section sizes of each sensitive segment are consistent, 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 thin first sensitive grid, dredge second sensitivity
Grid, middle first sensitive grid, the sensitive segment total length of middle second sensitive grid and close sensitive grid are in 5:5:12:12:7 proportionate relationship.The party
Case is a kind of scheme that can be selected, as long as the position of nominal particle meets the equal cross section position of form center of its both sides resistance value
Can or other positions.
Among five sensitive grids, except being in interdigital arrangement between above-mentioned two pairs of sensitive grids, without between other sensitive grids
Interdigital arrangement.The interdigital arrangement refers to:Two sensitive grids each sensitive segment axis institute in the plane, vertical with sensitive segment axis
The sensitive segment of two sensitive grids distribution straggly on direction, the order occurred respectively to the sensitive segment of two sensitive grids in this direction and time
Number is not limited.
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 f (x, y) y directions first-order partial derivative is as follows:
Wherein y1=y0+ h, y2=y1+ h, it is (x, y to pay special attention to above formula2+ 2h) position first-order partial derivative value formula, should
The smaller truncated error of formula is o (h2) be step-length square higher order indefinite small.By being generally acknowledged that sensitive grid in formula (2) engineering
Resistance change direct ratio and the strain at sensitive grid center, with reference to each sensitive gate resistance and the resistance change under same strain
Proportionate relationship, dredge the resistance of first sensitive grid and close sensitive grid and subtract the resistance value of middle first sensitive grid, then divided by thin first sensitivity
The distance at grid center and close sensitive grid center is the horizontal single order numerical value local derviation of strain, and according to numerical differentiation theory, this is close sensitivity
Grid center is equal to thin first sensitive grid center to close sensitivity certainly to the horizontal single order numerical value local derviation at the 2h distances of downside, h here
The half of distance between grid center, the horizontal single order local derviation surveyed outside usually foil gauge top edge;Equally, second sensitive grid is dredged
With the resistance of close sensitive grid and subtract the resistance value of middle second sensitive grid, then divided by thin second sensitive grid center and close sensitive grid center
Distance is the horizontal single order numerical value local derviation of strain, is close sensitive grid center at the 2h distances of downside according to theoretical this of numerical differentiation
Horizontal single order numerical value local derviation, h at this moment are equal to thin second sensitive grid center to the half of distance between close sensitive grid center, institute certainly
The horizontal single order local derviation surveyed outside usually foil gauge top edge.The horizontal single order local derviation of position can be by close quick at above-mentioned two
The time-sharing multiplex of sense grid is realized almost to be measured simultaneously.Therefore the advantage of the foil gauge is that its downside can be used for measuring corner of workpiece
Fall, the general foil gauge such as edge due to size limitation can not measuring point two at close positions horizontal single order local derviation.
It should be noted that keeping dredging first sensitive grid, dredging second sensitive grid, middle first sensitive grid, middle second sensitive grid and close sensitivity in technique
The variable quantity of grid changeover portion all-in resistance and changeover portion resistance under external strain is in 5:5:12:12:7 numerical relation is to heighten
Measurement accuracy, if the resistance of changeover portion and the lower resistance change of strain be can not ignore, it can also detected as systematic error
When eliminated.
Further, the metal strain plate also 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.
Five sensitive grid upper, middle and lower 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:By the close sensitive grid of time-sharing multiplex, foil gauge can be detected almost simultaneously
Horizontal single order local derviation under close sensitive grid center at outside two, wherein under close sensitive grid center at outside first axially it is upper with it is close quick
Feel grid centers zero deflection, the upper spacing at this with close sensitive grid center of transverse direction is equal to thin first sensitive grid center and close sensitive grid center
Spacing;It is axially upper with close sensitive grid center zero deflection at outside second under close sensitive grid center, in transverse direction at this and close sensitivity
The spacing at grid center is equal to the spacing for dredging second sensitive grid center and close sensitive grid center.Therefore the measurable workpiece in downside of foil gauge
Corner, edge etc. have close positions transverse direction single order local derviation at the two of size restriction site to foil gauge.
Embodiment
The invention will be further described below in conjunction with the accompanying drawings.
1~Fig. 4 of reference picture, interdigital metal is dredged outside a kind of measurable unilateral piece in the sensitive grid of cross direction profiles five of horizontal local derviation
Foil gauge, including substrate, the metal strain plate also include five sensitive grids, and the both ends of each sensitive grid connect one and drawn respectively
Pin, five sensitive grids are fixed 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, and the sensitive segment axis is straight line section, institute
In stating the diameter parallel of each sensitive segment in five sensitive grids and being generally aligned in the same plane, sensitive segment axis is determined in plane, edge
The sensitive segment axis direction is axially, with axially vertical direction for laterally;Its both sides resistance value be present on each sensitive segment
An equal cross section, take the cross-section centroid position and 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;
Each five sensitive grid centers zero deflection in the axial direction, there is deviation in the horizontal;Five sensitive grids press sensitive grid center
The order of position, be transversely followed successively by from top to bottom thin first sensitive grid, dredge second sensitive grid, middle first sensitive grid, middle second sensitive grid and
Close sensitive grid, it is Δ x to dredge distance between first sensitive grid center and middle first sensitive grid centerA, middle first sensitive grid center and close sensitivity
Distance is also Δ y between grid centerA;It is Δ y to dredge distance between second sensitive grid center and middle second sensitive grid centerB, middle second sensitive grid
Distance is also Δ y between center and close sensitive grid centerB, Δ yA>ΔyB;Dredge first sensitive grid center and thin second sensitive grid center
Distance is 2 Δ y1, the distance at middle first sensitive grid center and middle second sensitive grid center is Δ y1, Δ y1=Δ yA-ΔyB;
Each sensitive segment axis determines in plane that it is in interdigital arrangement between first sensitive grid and thin second sensitive grid that top, which is dredged, in
It is in interdigital arrangement between first sensitive grid and middle second sensitive grid in portion;
The sensitive segment all-in resistance for dredge first sensitive grid, dredging second sensitive grid, middle first sensitive grid, middle second sensitive grid and close sensitive grid is in
5:5:12:12:7 proportionate relationship, dredge first sensitive grid, dredge second sensitive grid, middle first sensitive grid, middle second sensitive grid and close sensitive grid
The all-in resistance changing value of sensitive segment sensitive segment under identical strain is also in 5:5:12:12:7 proportionate relationship.
Further, all shape of cross section sizes of each sensitive segment are consistent, 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 thin first sensitive grid, dredge second sensitivity
Grid, middle first sensitive grid, the sensitive segment total length of middle second sensitive grid and close sensitive grid are in 5:5:12:12:7 proportionate relationship.The party
Case is a kind of scheme that can be selected, as long as the position of nominal particle meets the equal cross section position of form center of its both sides resistance value
Can or other positions.
Among five sensitive grids, except being in interdigital arrangement between above-mentioned two pairs of sensitive grids, without between other sensitive grids
Interdigital arrangement.The interdigital arrangement refers to:Two sensitive grids each sensitive segment axis institute in the plane, vertical with sensitive segment axis
The sensitive segment of two sensitive grids distribution straggly on direction, the order occurred respectively to the sensitive segment of two sensitive grids in this direction and time
Number is not limited.
Interdigital metal strain plate is dredged outside the measurable unilateral piece of the present embodiment in the sensitive grid of cross direction profiles five of horizontal local derviation,
Including substrate 1, the metal strain plate also includes five sensitive grids, and the both ends of each sensitive grid connect a pin respectively, described
Five sensitive grids are fixed in substrate 1.
Thin first sensitive grid 2 can be fixed on substrate 1, dredges second sensitive grid 3, middle first sensitive grid 4, middle second sensitive grid 5 and Mi Min
Grid 6 are felt, for shape, the positions and dimensions for keeping each sensitive grid to fix;Substrate 1 is very thin, so as to which the strain of surface of test piece is accurate
Really it is delivered to thin first sensitive grid 2, dredges second sensitive grid 3, middle first sensitive grid 4, middle second sensitive grid 5 and close sensitive grid 6.Substrate 1 can
To be glued membrane substrate, glass fabric substrates, asbestos base bottom, metallic substrates and temporary substrate.Generally with cohere, weld, ceramics spray
Substrate is fixed on the tested position of test block by the modes such as painting.Some lines for being used for foil gauge positioning can be also printed in substrate 1.
Cover plate is made of materials such as paper or glue, be covered in thin first sensitive grid 2, dredge second sensitive grid 3, middle first sensitive grid 4, in
In second sensitive grid 5, close sensitive grid 6 and substrate 1, play the protective layer of protection against the tide, corrosion protection, loss prevention etc..
Pin 7 is used to connect sensitive grid and measuring circuit, dredge first sensitive grid 2, dredge second sensitive grid 3, middle first sensitive grid 4, in
Second sensitive grid 5 and close sensitive grid 6 respectively have two pins 7, pair with foil and membrane type foil gauge, the thin first that pin 7 is connected with it
Sensitive grid 2, thin second sensitive grid 3, middle first sensitive grid 4, middle second sensitive grid 5 and close sensitive grid 6 combine as a whole.Dredge first sensitive grid 2
Two pins are 7-1 and 7-2, and two pins for dredging second sensitive grid 3 are 7-3 and 7-4, and two pins of middle first sensitive grid 4 are 7-5
And 7-6, two pins of middle second sensitive grid 5 are 7-7 and 7-8, and two pins of close sensitive grid 6 are 7-9 and 7-10.
Dredge first sensitive grid 2, dredge second sensitive grid 3, middle first sensitive grid 4, middle second sensitive grid 5 and close sensitive grid 6 according to its metal
The difference of sensitive material and processing technology, can be wire form, foil, diaphragm type, thick-film type.No matter which kind of is dredged first sensitive grid 2, dredged
Second sensitive grid 3, middle first sensitive grid 4, the equal very little of thickness of middle second sensitive grid 5 and close sensitive grid 6 so that dredge first sensitive grid 2, dredge second
Sensitive grid 3, middle first sensitive grid 4, the axial length of middle second sensitive grid 5 and close sensitive grid 6 depend on the deformation of workpiece with it and become
Change.It is of the invention basic it is critical that dredging first sensitive grid 2, dredging second sensitive grid 3, middle first sensitive grid 4, the middle and of second sensitive grid 5
Cooperation between close sensitive grid 6, there is following main points:
First, five sensitive grids are arranged in substrate, thin first sensitive grid 2 is referred to as, dredges second sensitive grid 3, middle first sensitivity
Grid 4, middle second sensitive grid 5 and close sensitive grid 6.
Second, dredge first sensitive grid 2, thin second sensitive grid 3, middle first sensitive grid 4, middle second sensitive grid 5 and close sensitive grid 6 can divide
For multiple sensitive segments 8 and multiple changeover portions 9, the connection of each sensitive segment 8 is formed sensitive grid by each changeover portion 9.Comparatively, sensitive segment
8 is elongated in shape, and resistance is larger and its resistance is more sensitive to straining;The changeover portion 9 is in tubbiness shape substantially so that the mistake
The resistance very little of section and insensitive to straining is crossed, resistance variations are close to 0 under working condition, therefore the summation of sensitive segment resistance
The all-in resistance of essentially single sensitive grid.Fig. 2 has marked sensitive segment 8 and changeover portion 9 in more detail from apparent angle.
3rd, the sensitive segment 8 of each sensitive grid is in elongated strip, and all cross section centres of form composition of each sensitive segment 8 is quick
Feel section axis, the axis of sensitive segment 8 is straight line section, the diameter parallel of each sensitive segment 8 and is generally aligned in the same plane.Each
Projection of shape of all cross sections of sensitive segment 8 along sensitive segment axis direction is consistent.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, dredge first sensitive grid 2, dredge the sensitivity of second sensitive grid 3, middle first sensitive grid 4, middle second sensitive grid 5 and close sensitive grid 6
Section total length is in 5:5:12:12:7 proportionate relationship, on how to realize that this length ratio relation sees below what is illustrated with reference to Fig. 4
Method;Dredge first sensitive grid 2, dredge the sensitive segment all-in resistance of second sensitive grid 3, middle first sensitive grid 4, middle second sensitive grid 5 and close sensitive grid 6
In 5:5:12:12:7 proportionate relationship;Dredge first sensitive grid 2, dredge second sensitive grid 3, middle first sensitive grid 4, middle second sensitive grid 5 and Mi Min
The all-in resistance changing value for feeling sensitive segment sensitive segment under identical strain of grid 6 is also in 5:5:12:12:7 proportionate relationship.
5th, overlook and dredge first sensitive grid 2, dredge second sensitive grid 3, middle first sensitive grid 4, middle second sensitive grid 5 and close sensitive grid 6,
They respectively have two kinds of length and axial starting point difference, terminal identical sensitive segment, and the two hop count is identical, and both reasonable selections are long
Above-mentioned each sensitive grid center all can be configured in y-axis by degree, and specific method sees below with reference to Fig. 4 explanation.Dredge first sensitive grid
2nd, the center of second sensitive grid 3, middle first sensitive grid 4, middle second sensitive grid 5 and close sensitive grid 6 is dredged on the y axis, in them
The heart has lateral deviation without axial deviation.According to the top view of foil gauge in Fig. 2, dredging the sensitive segment 8 of first sensitive grid 2 has axial direction right
Claim axle xSA, the center of first sensitive grid 2 is dredged in y-axis and xSAThe intersection point of axle, the sensitive segment 8 for dredging second sensitive grid 3 have axially symmetric axle
xSB, the center of second sensitive grid 3 is dredged in y-axis and xSBThe intersection point of axle, the sensitive segment 8 of middle first sensitive grid 4 have axially symmetric axle xMA, in
The center of first sensitive grid 4 is in y-axis and xMAThe intersection point of axle, the sensitive segment 8 of middle second sensitive grid 5 have axially symmetric axle xMB, middle second sensitivity
The center of grid 5 is in y-axis and xMBThe intersection point of axle, the sensitive segment 8 of close sensitive grid 6 have axially symmetric axle xD, the center of close sensitive grid 6 exists
Y-axis and xDThe intersection point of axle.
6th, it is Δ y to dredge distance between the center of first sensitive grid 2 and the center of middle first sensitive grid 4A, middle first sensitive grid 4
Distance is also Δ y between center and the center of close sensitive grid 6A;Dredge the center of second sensitive grid 3 and middle second sensitive grid 5 center it
Between distance be Δ yB, distance is also Δ y between the center of middle second sensitive grid 5 and the center of close sensitive grid 6B, Δ yA> Δs yB;Dredge
The distance at the center of first sensitive grid 2 and the center of thin second sensitive grid 3 is Δ y1, the center of middle first sensitive grid 4 and middle second sensitive grid 5
The distance at center be Δ y1, Δ y1=Δ yA-ΔyB, as shown in Figure 2.As shown in Figure 2, each sensitive segment axis determines plane
On, it be in interdigital arrangement that top, which is dredged between first sensitive grid 2 and thin second sensitive grid 3, in middle part first sensitive grid 4 and middle second sensitive grid 5 it
Between be in interdigital arrangement, without the interdigital arrangement between other sensitive grids.The interdigital arrangement refers to:Each sensitive segment 8 of two sensitive grids
Axis institute in the plane, in the sensitive segment distribution straggly with two sensitive grids in sensitive segment axis vertical direction, in this direction
The order and number that the sensitive segment of two sensitive grids occurs respectively are not limited.Due to dredging first sensitive grid 2, dredging second sensitive grid 3, middle first
The relative position of sensitive grid 4, middle second sensitive grid 5 and close sensitive grid 6 is ensured relatively accurately to be fixed by foil gauge production technology
, this is also one of key that the present invention can detect the horizontal partial derivative of workpiece strain.
In summary, the thin first sensitive grid 2 of the present invention, thin second sensitive grid 3, middle first sensitive grid 4, middle second sensitive grid 5 and Mi Min
The all-in resistance changing value for feeling sensitive segment sensitive segment under identical strain of grid 6 is also in 5:5:12:12:7 proportionate relationship, it is each quick
Feel the central axial zero deflection of grid, laterally there is deviation, dredging distance between the center of first sensitive grid 2 and the center of middle first sensitive grid 4 is
ΔyA, distance is also Δ y between the center of middle first sensitive grid 4 and the center of close sensitive grid 6A;The center of second sensitive grid 3 is dredged with
Distance is Δ y between the center of second sensitive grid 5B, distance is also between the center of middle second sensitive grid 5 and the center of close sensitive grid 6
ΔyB, Δ yA> Δs yB;The distance for dredging the center of first sensitive grid 2 and the center of thin second sensitive grid 3 is Δ y1, middle first sensitive grid 4
The distance at center and the center of middle second sensitive grid 5 is Δ y1, Δ y1=Δ yA-ΔyB。
It is R to make and the resistance of second sensitive grid 3 is dredged under free stateU0, the middle resistance of second sensitive grid 5 is RM0, the close resistance of sensitive grid 6 is
RL0, should there is RU0+RL0=RM0=R0.When the foil gauge of the present invention is placed in into certain surface strain, dredging the resistance of second sensitive grid 3 is
R0+ΔRU, the middle resistance of second sensitive grid 5 is R0+ΔRM0, the close resistance of sensitive grid 6 is R0+ΔRL;On the other hand, dredge second sensitive grid 3 with
And the center of close sensitive grid 6 is located at y-axis and x in Fig. 2 respectivelySBIntersection point and y-axis and xDBIntersection point, at a distance of 2 Δ y in transverse directionB。
Formula using the relation and numerical differentiation of sensitive gate resistance and surface strain has:
WhereinFor 2 Δ y on the downside of the close center of sensitive grid 6BPlace, that is, y-axis and x in Fig. 2OBThe intersection point of axle, εUTo dredge second
Strain at the center of sensitive grid 3, εMFor the strain at the middle center of second sensitive grid 5, εLFor the strain at the close center of sensitive grid 6.This is
It is the principle that the present embodiment measurement surface strains horizontal local derviation.Pay special attention to, the numerical differentiation that above formula is calculated is close sensitive grid 6
The center Δ y of outside 2 on the lower sideBThe strain transverse direction single order local derviation of position, the position is foil gauge lower edge outside, therefore has and be easy to
Measurement workpiece corner, edge etc. have the advantage of the horizontal single order local derviation of size restriction site to foil gauge.Equally, it is quick to dredge first
Sense grid 2, middle first sensitive grid 4 and close sensitive grid 6, which can coordinate, calculates the close center of the sensitive grid 6 Δ y of outside 2 on the lower sideAPosition, that is, scheme
Y-axis and x in 2OAThe intersection point of axle, strain transverse direction first-order partial derivative, the position be foil gauge lower edge on the outside of.Above-mentioned close sensitive grid
The 6 centers Δ y of outside 2 on the lower sideAThe strain transverse direction single order local derviation of position and the center of the close sensitive grid 6 Δ y of outside 2 on the lower sideBThe strain of position
Horizontal first-order partial derivative can almost be measured simultaneously by being realized to the close time-sharing multiplex of sensitive grid 6.
Electric bridge is coordinated to can be used for measuring strain, strain horizontal 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.When without 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 laid on individual 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
Now, 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, (5)
Since first, when meeting condition (5), according to relevant theoretical foil gauge sensitivity highest;Second, measuring strain or
The method that person strains horizontal local derviation is required to condition (5) establishment.When foil gauge also strains with external world's strain, above-mentioned electric bridge
Equilibrium condition is typically no longer set up, now
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, the reasonable selection foil gauge in engineering
Installation position can be realized completely.It is generally available the voltage measurement strain of formula (6) acquisition;Can convolution to straining horizontal local derviation
(3) and formula (6), reasonable design arrange each bridge arm sensitive grid and resistance, such as bridge arm R1Second sensitive grid 5 in arrangement, bridge arm R2String
Connection arranges close sensitive grid 6 and thin second sensitive grid 3, remaining bridge arm configuration substitutional resistance, can obtain on the lower side outer with the close center of sensitive grid 6
The Δ y of side 2BPlace strains the linear magnitude of voltage u of horizontal single order local derviationo, the voltage is that small-signal need to be amplified.
With reference to Fig. 4, each sensitive grid in design drawing 2 is illustrated how.Each sensitive grid is furnished with two kinds of length and axial direction in Fig. 2
Starting point is different, terminal identical sensitive segment, and its main purpose is that the center of two interdigital each other sensitive grids can be configured
In y-axis into Fig. 2, principle is shown in Fig. 4.There are two sensitive grids A and B part in Fig. 4, A there are two kinds of sensitive segments of A1 and A2, and B has
Two kinds of sensitive segments of B1 and B2.Each size is shown in that Fig. 4, wherein d are the size that technique determines, it is believed that is definite value;L=2l-x is A1 and A2
Overall length, in design drawing 2 during each sensitive grid, according to resistance ratio and sensitive segment number, it may be determined that its value, therefore in Fig. 4
Think that L has determined that;In Fig. 4 it needs to be determined that amount be l and x.Because A only has two kinds of sensitive segments of A1 and A2, and the hop count of the two
It is identical, as long as therefore one section of A1 and one section of A2 common center is configured in the y-axis in Fig. 4.With reference to resistance value and length
Linear relationship obviously have equation below group:
Wherein first formula left sideRefer to the distance of A1 off-centring y-axis, the rightThen for A2's
The distance of off-centring y-axis.According to symmetry, the l and x that can be solved from above-mentioned formula are equally applicable to B1 and B2.And then strain
The l and x of each sensitive grid first can first determine that L is tied again by the sensitive gate length, proportionate relationship, the sensitive segment hop count etc. that determine early stage in piece
Close process length d and solved by formula (7).