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
The sensitive grid of axial deviation six that axial local derviation outside the measurable bilateral piece of energy effective detection surface strain axial direction local derviation should be changed is complete
Bridge mixes interdigital metal strain plate, particularly measure workpiece corner, edge etc. have to foil gauge size restriction site or other
The axial single order local derviation of foil gauge position should not be arranged.
The technical solution adopted for the present invention to solve the technical problems is:
The sensitive grid full-bridge of axial deviation six of axial local derviation mixes interdigital metal strain plate, bag outside a kind of measurable bilateral piece
Substrate is included, the metal strain plate also includes six sensitive grids, and the both ends of each sensitive grid connect a pin, the base respectively
Six sensitive grids are fixed on bottom;
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 six 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;
Zero deflection in the horizontal between six sensitive grid centers, deviation be present in axial component, six sensitive grids are by sensitivity
The order of grid center, it is left seven sensitive grids and left five sensitive grids first from left to right vertically, followed by middle first sensitive grid
It is finally right five sensitive grids and right seven sensitive grids with middle second sensitive grid;Between left seven sensitive grid centers and left five sensitive grid centers
Distance is 0, and the distance at left seven sensitive grid centers and middle first sensitive grid center is Δ x1, middle first sensitive grid center and middle second sensitive grid
The distance at center is 0, and the distance at middle second sensitive grid center and right seven sensitive grid centers is Δ x1, right seven sensitive grid centers and right five
Distance is 0 between sensitive grid center;
Each sensitive segment axis determines in plane that first sensitive grid and middle second are quick in left seven sensitive grids, left five sensitive grids, middle part
Feel interdigital arrangement each other between grid, between middle first sensitive grid, middle second sensitive grid, right seven sensitive grids in the right and right five sensitive grids each other
Interdigital arrangement;
Left seven sensitive grids, left five sensitive grids, middle first sensitive grid, middle second sensitive grid, right five sensitive grids and right seven sensitive grids
Sensitive segment all-in resistance is in 7:5:12:12:5:7 proportionate relationship, left seven sensitive grids, left five sensitive grids, middle first sensitive grid, middle second are quick
The all-in resistance changing value for feeling sensitive segment sensitive segment under identical strain of grid, right five sensitive grids and right seven sensitive grids is also in 7:5:
12:12:5:7 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, left seven sensitive grid, a left side five are sensitive
Grid, middle first sensitive grid, the sensitive segment total length of seven sensitive grids of middle second sensitive grid, right five sensitive grids and the right side are in 7:5:12:12:5:7
Proportionate relationship.The program is a kind of scheme that can be selected, as long as to meet its both sides resistance value equal for the position of nominal particle
Cross section position of form center can or other positions.
Further, left seven sensitive grids are in interdigital arrangement between right seven sensitive grids, right five sensitive grids, left five sensitive grids
It is in interdigital arrangement between right seven sensitive grids, right five sensitive grids;Can also be without interdigital arrangement.The interdigital arrangement refers to:
Two sensitive grids each sensitive segment axis institute in the plane, straggly with the sensitive segment of two sensitive grids in sensitive segment axis vertical direction
Distribution, the order and number occurred respectively to the sensitive segment of two sensitive grids in this direction are not limited.
Further, the sensitive segment axle of relatively middle first sensitive grid and middle second sensitive grid, right seven sensitive grids and left seven sensitive grids
Can be shorter to length and cross direction profiles can be closeer.Purpose be the distance that reduces left seven sensitive grid centers to foil gauge left side edge with
And right seven sensitive grid centers are to the distance of 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 f (x, y) x directions first-order partial derivative is as follows:
Wherein x1=x0+ h, x2=x1+ h, it is (x to pay special attention to above formula2+ 2h, y) 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, the resistance of left seven sensitive grids and right five sensitive grids and the resistance value for subtracting middle first sensitive grid, then divided by Zuo Qimin
The distance for feeling grid center and right five sensitive grid centers is the axial single order numerical value local derviation of strain, is left according to theoretical this of numerical differentiation
The axial single order numerical value local derviation of seven sensitive grid centers position to the left at 2h distances, h here are equal in left seven sensitive grids certainly
The heart is the distance between to middle first sensitive grid center;Equally, the resistance of right seven sensitive grids and left five sensitive grids and middle second sensitivity is subtracted
The resistance value of grid, then divided by right seven sensitive grid centers and left five sensitive grid centers distance it is inclined for the axial single order numerical value strained
Lead, according to numerical differentiation it is theoretical this be right seven sensitive grid centers to the right at 2h distances position axial single order numerical value local derviation, this
In h be equal to right seven sensitive grid centers certainly the distance between to middle second sensitive grid center.The axial single order of position at above-mentioned two
Local derviation can measure simultaneously.Therefore the advantage of the foil gauge is that its both sides is used equally for measurement workpiece corner, edge etc. typically should
Become the axial single order local derviation at the position that piece can not measure due to size limitation;And it is interdigital be arranged such that step-length h reduce, according to above
Analysis can so reduce measurement error.
It should be noted that keeping left seven sensitive grids, left five sensitive grids, middle first sensitive grid, middle second sensitive grid, the right side five quick in technique
It is in 7 to feel the variable quantity of grid and right seven sensitive grid changeover portion all-in resistances and changeover portion resistance under external strain:5:12:12:5:7
Numerical relation to heighten measurement accuracy, if the resistance of changeover portion and the lower resistance change of strain be can not ignore, can also make
Eliminated for systematic error in detection.
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.
Six 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:It can simultaneously detect at left seven sensitive grid center left-external sides one and the right side seven is quick
Axial single order local derviation at the sense right outside one in grid center, wherein laterally upper at left seven sensitive grid center left-external sides and seven sensitive grids of a left side
Center zero deflection, it is equal to right five sensitive grid centers and left seven sensitive grid centers with the spacing at left seven sensitive grid centers at this on axial direction
Spacing;The right right outside in seven sensitive grid centers is laterally upper with right seven sensitive grid center zero deflections, quick with right seven at this on axial direction
The spacing for feeling grid center is equal to the spacing at left five sensitive grid centers and right seven sensitive grid centers.Therefore the measurable corner of workpiece of the present invention
Fall, edge etc. has size restriction site to foil gauge 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.
1~Fig. 3 of reference picture, the sensitive grid full-bridge of axial deviation six mixing of axial local derviation is interdigital outside a kind of measurable bilateral piece
Metal strain plate, including substrate, the metal strain plate also include six sensitive grids, and the both ends of each sensitive grid connect one respectively
Root pin, six 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 six 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;
Zero deflection in the horizontal between six sensitive grid centers, deviation be present in axial component, six sensitive grids are by sensitivity
The order of grid center, it is left seven sensitive grids and left five sensitive grids first from left to right vertically, followed by middle first sensitive grid
It is finally right five sensitive grids and right seven sensitive grids with middle second sensitive grid;Between left seven sensitive grid centers and left five sensitive grid centers
Distance is 0, and the distance at left seven sensitive grid centers and middle first sensitive grid center is Δ x1, middle first sensitive grid center and middle second sensitive grid
The distance at center is 0, and the distance at middle second sensitive grid center and right seven sensitive grid centers is Δ x1, right seven sensitive grid centers and right five
Distance is 0 between sensitive grid center;
Each sensitive segment axis determines in plane that first sensitive grid and middle second are quick in left seven sensitive grids, left five sensitive grids, middle part
Feel interdigital arrangement each other between grid, between middle first sensitive grid, middle second sensitive grid, right seven sensitive grids in the right and right five sensitive grids each other
Interdigital arrangement;
Left seven sensitive grids, left five sensitive grids, middle first sensitive grid, middle second sensitive grid, right five sensitive grids and right seven sensitive grids
Sensitive segment all-in resistance is in 7:5:12:12:5:7 proportionate relationship, left seven sensitive grids, left five sensitive grids, middle first sensitive grid, middle second are quick
The all-in resistance changing value for feeling sensitive segment sensitive segment under identical strain of grid, right five sensitive grids and right seven sensitive grids is also in 7:5:
12:12:5:7 proportionate relationship.
Accordingly, left seven sensitive grids of series connection and right five sensitive grids, middle first sensitive grid, series connection five sensitive grids of a left side and the right side seven are sensitive
Grid, middle second sensitive grid just form four bridge arms of measuring bridge.
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, left seven sensitive grid, a left side five are sensitive
Grid, middle first sensitive grid, the sensitive segment total length of seven sensitive grids of middle second sensitive grid, right five sensitive grids and the right side are in 7:5:12:12:5:7
Proportionate relationship.The program is a kind of scheme that can be selected, as long as to meet its both sides resistance value equal for the position of nominal particle
Cross section position of form center can or other positions.
Further, left seven sensitive grids, left five sensitive grids and right seven sensitive grids, right five sensitive grids are in interdigital cloth between any two
Put;Can also be without interdigital arrangement.The interdigital arrangement refers to:Two sensitive grids each sensitive segment axis institute in the plane, with
The sensitive segment distribution straggly of two sensitive grids in sensitive segment axis vertical direction, the sensitive segment of two sensitive grids in this direction is distinguished
The order and number of appearance are not limited.
Further, the sensitive segment axle of relatively middle first sensitive grid and middle second sensitive grid, right seven sensitive grids and left seven sensitive grids
Can be shorter to length and cross direction profiles can be closeer.Purpose be the distance that reduces left seven sensitive grid centers to foil gauge left side edge with
And right seven sensitive grid centers are to the distance of foil gauge right side edge.
The sensitive grid full-bridge of axial deviation six of axial local derviation mixes interdigital metal and answered outside the measurable bilateral piece of the present embodiment
Become piece, including substrate 1, the metal strain plate also include six sensitive grids, the both ends of each sensitive grid connect one and drawn respectively
Pin, six sensitive grids are fixed in the substrate 1.
It is quick that left seven sensitive grids 2, left five sensitive grids 3, middle first sensitive grid 4, middle second sensitive grid 5, the right side five can be fixed on substrate 1
Grid 6 and right seven sensitive grids 7 are felt, for shape, the positions and dimensions for keeping each sensitive grid to fix;Substrate 1 is very thin, so as to by test specimen
It is quick that the strain on surface is accurately transfer to left seven sensitive grids 2, left five sensitive grids 3, middle first sensitive grid 4, middle second sensitive grid 5, the right side five
Feel grid 6 and right seven sensitive grids 7.Substrate 1 can be glued membrane substrate, glass fabric substrates, asbestos base bottom, metallic substrates and interim base
Bottom.Generally with cohere, weld, substrate is fixed on the tested position of test block by the mode such as ceramic spraying.It can be also printed in substrate 1
Some are used for the lines of foil gauge positioning.
Cover plate is made of materials such as paper or glue, be covered in left seven sensitive grids 2, left five sensitive grids 3, middle first sensitive grid 4, in
In second sensitive grid 5, right five sensitive grids 6, right seven sensitive grids 7 and substrate 1, play the protective layer of protection against the tide, corrosion protection, loss prevention etc..
Pin 8 is used to connect sensitive grid and measuring circuit, left seven sensitive grids 2, left five sensitive grids 3, middle first sensitive grid 4, in
Second sensitive grid 5, right five sensitive grids 6 and right seven sensitive grids 7 respectively have two pins 8, for foil and membrane type foil gauge, pin 8 with
Its sensitive grid 2 of a left side seven connected, left five sensitive grids 3, middle first sensitive grid 4, middle second sensitive grid 5, right five sensitive grids 6 and the right side seven are quick
Sense grid 7 combine as a whole.Two pins of left seven sensitive grids 2 are 8-1 and 8-2, and two pins of left five sensitive grids 3 are 8-3 and 8-
4, two pins of middle first sensitive grid 4 are 8-5 and 8-6, and two pins of middle second sensitive grid 5 are 8-7 and 8-8, right five sensitive grids 6
Two pins be 8-9 and 8-10, two pins of right seven sensitive grids 7 are 8-11 and 8-12.
Left seven sensitive grids 2, left five sensitive grids 3, middle first sensitive grid 4, middle second sensitive grid 5, right five sensitive grids 6 and the right side seven are sensitive
Grid 7 can be wire form, foil, diaphragm type, thick-film type according to its metal sensitive material and the difference of processing technology.No matter which kind of
Left seven sensitive grids 2, left five sensitive grids 3, middle first sensitive grid 4, the thickness of seven sensitive grids 7 of middle second sensitive grid 5, right five sensitive grids 6 and the right side
Spend equal very little so that left seven sensitive grids 2, left five sensitive grids 3, middle first sensitive grid 4, middle second sensitive grid 5, right five sensitive grids 6 and the right side
The axial length of seven sensitive grids 7 depends on the deformation of workpiece with it and changed.It is of the invention basic it is critical that Zuo Qimin
Feel the cooperation between grid 2, left five sensitive grids 3, middle first sensitive grid 4, middle second sensitive grid 5, right five sensitive grids 6 and right seven sensitive grids 7,
There are following main points:
First, six sensitive grids are arranged in substrate, it is sensitive to be referred to as left seven sensitive grids 2, left five sensitive grids 3, middle first
Grid 4, middle second sensitive grid 5, right five sensitive grids 6 and right seven sensitive grids 7.
Second, left seven sensitive grids 2, left five sensitive grids 3, middle first sensitive grid 4, middle second sensitive grid 5, right five sensitive grids 6 and the right side
Seven sensitive grids 7 can be divided into multiple sensitive segments 9 and multiple changeover portions 10, and each sensitive segment 9 is connected to form sensitivity by each changeover portion 10
Grid.Comparatively, sensitive segment 9 is elongated in shape, resistance is larger and its resistance is more sensitive to straining;The changeover portion 10 is basic
In tubbiness shape so that the resistance very little of the changeover portion and insensitive to straining, under working condition resistance variations close to 0,
Therefore the summation of sensitive segment resistance is essentially the all-in resistance of single sensitive grid.Fig. 2 is marked in more detail from apparent angle
Sensitive segment 9 and changeover portion 10.
3rd, the sensitive segment 9 of each sensitive grid is in elongated strip, and all cross section centres of form composition of each sensitive segment 9 is quick
Feel section axis, the axis of sensitive segment 9 is straight line section, the diameter parallel of each sensitive segment 9 and is generally aligned in the same plane.Each
Projection of shape of all cross sections of sensitive segment 9 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, left seven sensitive grids 2, left five sensitive grids 3, middle first sensitive grid 4, middle second sensitive grid 5, right five sensitive grids 6 and the right side
The sensitive segment total length of seven sensitive grids 7 is in 7:5:12:12:5:7 proportionate relationship.Left seven sensitive grids 2, left five sensitive grids 3, middle first
Sensitive grid 4, the sensitive segment all-in resistance of seven sensitive grids 7 of middle second sensitive grid 5, right five sensitive grids 6 and the right side are in 7:5:12:12:5:7 ratio
Example relation, left seven sensitive grids 2, left five sensitive grids 3, middle first sensitive grid 4, middle second sensitive grid 5, right five sensitive grids 6 and the right side seven are sensitive
The all-in resistance changing value of the sensitive segment of grid 7 sensitive segment under identical strain is also in 7:5:12:12:5:7 proportionate relationship.According to
This, the sensitive grid 2 of a series connection left side seven and right five sensitive grids 6, middle first sensitive grid 4, left five sensitive grids 3 of series connection and right seven sensitive grids 7, middle second
Sensitive grid 5 just forms four bridge arms of measuring bridge.
5th, overlook left seven sensitive grids 2, left five sensitive grids 3, middle first sensitive grid 4, middle second sensitive grid 5, right five sensitive grids 6
With right seven sensitive grids 7, they are respectively provided with symmetry axis and symmetrical overlapping of axles (x-axis in Fig. 2), left seven sensitive grids 2, left five sensitive grids
3rd, middle first sensitive grid 4, middle second sensitive grid 5, right five sensitive grids 6 and 7 respective sensitive segment 9 of right seven sensitive grid all with the symmetry axis
Parallel, the sensitive segment 9 of each sensitive grid is distributed on this axial symmetry.Therefore, it can be said that left seven sensitive grids 2, left five sensitive grids 3,
Middle first sensitive grid 4, middle second sensitive grid 5, right five sensitive grids 6 and the sensitive grid 7 of the right side seven are coaxial, that is, detect equidirectional strain and a left side
Seven sensitive grids 2, left five sensitive grids 3, middle first sensitive grid 4, the center of seven sensitive grids 7 of middle second sensitive grid 5, right five sensitive grids 6 and the right side
Their center zero deflection in the horizontal, deviation in the axial direction partly be present in x-axis in position.According to foil gauge in Fig. 2
The sensitive segment 9 of top view, the sensitive grid 2 of a left side seven and left five sensitive grids 3 has lateral symmetry axle yL, the sensitive grid 2 of a left side seven and a left side five are sensitive
The center of grid 2 is in x-axis and yLThe sensitive segment 9 of the intersection point of axle, middle first sensitive grid 4 and middle second sensitive grid 5 has lateral symmetry axle yM, in
The center of first sensitive grid 4 and middle second sensitive grid 5 is in x-axis and yMThe sensitivity of the intersection point of axle, the sensitive grid 6 of the right side five and right seven sensitive grids 7
Section 9 has lateral symmetry axle yR, the center of seven sensitive grids 7 of right five sensitive grids 6 and the right side is in x-axis and yRThe intersection point of axle.
6th, distance is 0 between the center of left seven sensitive grids 2 and the center of left five sensitive grids 3, in left seven sensitive grids 2
The heart and the distance at the center of middle first sensitive grid 4 are Δ x1, the distance at the center of middle first sensitive grid 4 and the center of middle second sensitive grid 5
For 0, the distance at the center of middle second sensitive grid 5 and the center of right seven sensitive grids 7 is Δ x1, center and the right side five of right seven sensitive grids 7
Distance is 0 between the center of sensitive grid 6, as shown in Figure 2.As shown in Figure 2, the axis of each sensitive segment 9 is determined in plane, a left side seven
Interdigital arrangement each other between sensitive grid 2, left five sensitive grids 3, middle first sensitive grid 4 and middle second sensitive grid 5, right five sensitive grids 6, the right side seven
Interdigital arrangement each other between sensitive grid 7, middle first sensitive grid 4 and middle second sensitive grid 5, left seven sensitive grids 2, left five sensitive grids 3, the right side five
Interdigital arrangement it can may be reversed each other between sensitive grid 6 and right seven sensitive grids 7, such as 4 sensitive grids of this in Fig. 2 do not have shape
Into interdigital, but if the length of 4 sensitive grids tune up can formed it is interdigital.The interdigital arrangement refers to:Two sensitive grids
Each axis of sensitive segment 9 institute in the plane, in the sensitive segment distribution straggly with two sensitive grids in sensitive segment axis vertical direction, to
The order and number that the sensitive segment of two sensitive grids occurs respectively in this direction are not limited.Because left seven sensitive grids 2, a left side five are sensitive
Grid 3, middle first sensitive grid 4, the relative position of seven sensitive grids 7 of middle second sensitive grid 5, right five sensitive grids 6 and the right side produce work by foil gauge
Skill ensures relatively accurately to be secured, and this is also one of key that the present invention can detect the axial partial derivative of workpiece strain.
In summary, left seven sensitive grids 2 of the present invention, left five sensitive grids 3, middle first sensitive grid 4, middle second sensitive grid 5, the right side five are quick
The all-in resistance changing value for feeling sensitive segment sensitive segment under identical strain of grid 6 and right seven sensitive grids 7 is also in 7:5:12:12:5:7
Proportionate relationship, each sensitive grid center zero deflection in the horizontal, deviation, the center of left seven sensitive grids 2 in the axial direction partly be present
Distance is 0 between the center of left five sensitive grids 3, and the distance at the center and the center of middle first sensitive grid 4 of left seven sensitive grids 2 is Δ
x1, the distance at the center of the center of middle first sensitive grid 4 and middle second sensitive grid 5 is 0, and the center of middle second sensitive grid 5 is sensitive with the right side seven
The distance at the center of grid 7 is Δ x1, distance is 0 between the center of right seven sensitive grids 7 and the center of right five sensitive grids 6.
It is R to make the resistance of five sensitive grid of free state bottom left 3L0, the middle resistance of second sensitive grid 5 is RM0, the right resistance of seven sensitive grid 7
For RR0, should there is RL0+RR0=RM0=R0.When the foil gauge of the present invention is placed in into certain surface strain, the left resistance of five sensitive grid 3
For R0+ΔRL, the middle resistance of sensitive grid 4 is R0+ΔRM0, the right resistance of seven sensitive grid 7 is R0+ΔRR;On the other hand, left five sensitive grids 3
And the center of right seven sensitive grids 7 is located at x-axis and y in Fig. 2 respectivelyLIntersection point and x-axis and yRIntersection point, at a distance of 2 Δs on axial direction
x1.IfFor the Δ x of 7 central right of right seven sensitive grid 21Place, that is, x-axis and y in Fig. 2ORIntersection point, using sensitive gate resistance with
The relation of surface strain and the formula (3) of numerical differentiation have:
Wherein εLFor the strain at the left center of five sensitive grid 3, εMFor the strain at the middle center of second sensitive grid 5, εRIt is quick for the right side seven
Feel the strain at the center of grid 7.This is the principle that the present embodiment measurement surface strains axial local derviation.Pay special attention to, above formula is counted
The numerical differentiation of calculation is the right center Δ x of outside 2 to the right of seven sensitive grid 71The strain axial direction single order local derviation of position, the position are strain
Outside the right side edge of piece, therefore have and be 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 sensitive segment 9 of the middle second sensitive grid 4 of sensitive segment 9 of right seven sensitive grids 7
Short, its purpose is to reduce the right center of seven sensitive grid 7 as far as possible to the distance of foil gauge right side edge, in order to further play
Above-mentioned advantage.Equally, left seven sensitive grids 2, middle first sensitive grid 4 and right five sensitive grids 6 can coordinate the left center of seven sensitive grid 2 of calculating inclined
The Δ x of left-external side 21The strain axial direction first-order partial derivative of position, the position are located at x-axis and y in Fig. 2OLIntersection point;By shortening a left side seven
The length of the sensitive segment 9 of sensitive grid 2, the left center of seven sensitive grid 2 is reduced as far as possible to the distance of foil gauge left side edge.Above-mentioned right seven
The center of the sensitive grid 7 Δ x of outside 2 to the right1The strain axial direction single order local derviation of position and the left center Δ x of outside 2 to the left of seven sensitive grid 21Position
The strain axial direction first-order partial derivative put can measure simultaneously.
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.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, (6)
Since first, when meeting condition (6), according to relevant theoretical foil gauge sensitivity highest;Second, measuring strain or strain axis
Condition (6) is required to the method for local derviation to set up.When foil gauge also strains with external world's strain, above-mentioned bridge balance condition
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 (7) acquisition;Can convolution to straining axial local derviation
(4) and formula (7), reasonable design arrange each bridge arm sensitive grid and resistance, such as bridge arm R1Second sensitive grid 5 in arrangement, bridge arm R2String
The sensitive grid 7 of the connection arrangement right side seven and left five sensitive grids 3, remaining bridge arm configuration substitutional resistance, it can obtain inclined with the right center of seven sensitive grid 7
The right Δ x of outside 21Place strains the linear magnitude of voltage u of axial single order local derviationo, the voltage is that small-signal need to be amplified.