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 first-order partial derivative of section turn moment is directly proportional to section shearing strain,
Exactly section shearing strain can be known by the axial first-order partial derivative of surface axial strain, and the shearing strain can not use foil gauge
Arrived in workpiece surface direct measurement;
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 product of a kind of inclined marginal position of energy measuring strain piece rather than center position strain local derviation.
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 cross direction profiles three that the measurable biasing sensitive grid central cross local derviation of energy effective detection surface strain transverse direction local derviation should be changed are quick
Feel grid metal foil gauge, particularly measuring workpiece corner, edge etc. has the horizontal single order local derviation of size restriction site to foil gauge.
The technical solution adopted for the present invention to solve the technical problems is:
A kind of sensitive grid metal strain plate of cross direction profiles three of measurable biasing sensitive grid central cross local derviation, including base
Bottom, the metal strain plate also 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, and the sensitive segment axis is straight line section, institute
In stating the diameter parallel of each sensitive segment in three 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;
Three sensitive grid centers zero deflection in the axial direction, there is deviation in the horizontal;Three sensitive grids press sensitive grid centre bit
The order put, sensitive grid, middle sensitive grid and lower sensitive grid are transversely referred to as from top to bottom;Upper sensitive grid center is quick with
The distance for feeling grid center is Δ y1, the distance at middle sensitive grid center and lower sensitive grid center is Δ y1, among any two sensitive grid
The high person in sensitive grid central cross position, the lateral attitude of every bit is higher than any sensitive segment of another sensitive grid on its each sensitive segment
The lateral attitude of upper any point;
The sensitive segment all-in resistance of upper sensitive grid, middle sensitive grid and lower sensitive grid is in 1:4:3 proportionate relationship, upper sensitive grid,
The all-in resistance changing value of the sensitive segment of middle sensitive grid and lower sensitive grid sensitive segment under identical strain is also in 1:4:3 ratio is closed
System.
Further, all shape of cross section sizes of each sensitive segment are consistent, take the axis point midway of each sensitive segment
And using the sensitive segment resistance value as nominal mass formed where sensitive segment nominal particle, the upper sensitive grid, middle sensitive grid and
The sensitive segment total length of lower 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, the lateral separation very little of the lower edge of the pin of lower sensitive grid and lower sensitive grid bottom sensitive segment or
Even pin lower edge is located at the top of lower sensitive grid bottom sensitive segment.Purpose is to reduce lower sensitive grid center to foil gauge downside
The distance at 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) 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) 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
The resistance of example relation, upper sensitive grid and lower sensitive grid and the resistance value for subtracting middle sensitive grid, then except above sensitive grid center is with
The distance at sensitive grid center is the horizontal single order local derviation of strain, and particularly, according to numerical differentiation theory, this is lower sensitive grid center
The horizontal single order numerical value local derviation of position, rather than the horizontal single order local derviation in the middle part of foil gauge, therefore the advantage of the foil gauge is
The horizontal single order local derviation at the position that the general foil gauge such as measurement workpiece corner, edge can not be measured due to size limitation.
It should be noted that sensitive grid, middle sensitive grid and lower sensitive grid changeover portion all-in resistance and changeover portion are electric on keeping in technique
It is in 1 to hinder the variable quantity under external strain:4:3 numerical relation to heighten measurement accuracy, if the resistance of changeover portion and should
Become lower resistance change can not ignore, also systematic error can be used as to be eliminated 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.
Three 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:The horizontal single order numerical value of sensitive grid center is inclined under energy effective detection
Lead, particularly measuring workpiece corner, edge etc. has the horizontal single order local derviation of size restriction site to foil gauge.
Embodiment
The invention will be further described below in conjunction with the accompanying drawings.
1~Fig. 3 of reference picture, a kind of three sensitive grid metal of cross direction profiles of measurable biasing sensitive grid central cross local derviation should
Become piece, including substrate, the metal strain plate also include three sensitive grids, the both ends of each sensitive grid connect one and drawn respectively
Pin, three 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 three 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;
Three sensitive grid centers zero deflection in the axial direction, there is deviation in the horizontal;Three sensitive grids press sensitive grid centre bit
The order put, sensitive grid, middle sensitive grid and lower sensitive grid are transversely referred to as from top to bottom;Upper sensitive grid center is quick with
The distance for feeling grid center is Δ y1, the distance at middle sensitive grid center and lower sensitive grid center is Δ y1, among any two sensitive grid
The high person in sensitive grid central cross position, the lateral attitude of every bit is higher than any sensitive segment of another sensitive grid on its each sensitive segment
The lateral attitude of upper any point;
The sensitive segment all-in resistance of upper sensitive grid, middle sensitive grid and lower sensitive grid is in 1:4:3 proportionate relationship, upper sensitive grid,
The all-in resistance changing value of the sensitive segment of middle sensitive grid and lower sensitive grid sensitive segment under identical strain is also in 1:4:3 ratio is closed
System.
Further, all shape of cross section sizes of each sensitive segment are consistent, take the axis point midway of each sensitive segment
And using the sensitive segment resistance value as nominal mass formed where sensitive segment nominal particle, the upper sensitive grid, middle sensitive grid and
The sensitive segment total length of lower 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, the lateral separation very little of the lower edge of the pin of lower sensitive grid and lower sensitive grid bottom sensitive segment or
Even pin lower edge is located at the top of lower sensitive grid bottom sensitive segment.Purpose is to reduce lower sensitive grid center to foil gauge downside
The distance at edge.
The sensitive grid metal strain plate of cross direction profiles three of the measurable biasing sensitive grid central cross local derviation of the present embodiment, bag
Substrate 1 is included, the metal strain plate also 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.
Sensitive grid 2, middle sensitive grid 3 and lower sensitive grid 4 can be fixed on substrate 1, for keeping each sensitive grid fixation
Shape, positions and dimensions;Substrate 1 is very thin, so as to which the strain of surface of test piece is accurately transfer into upper sensitive grid 2, middle sensitive grid 3
With lower sensitive grid 4.Substrate 1 can be glued membrane substrate, glass fabric substrates, asbestos base bottom, metallic substrates and temporary substrate.Generally
With cohere, weld, substrate is fixed on the tested position of test block by the mode such as ceramic spraying.Some use can be also printed in substrate 1
In the lines of foil gauge positioning.
Cover plate is made of materials such as paper or glue, is covered in sensitive grid 2, middle sensitive grid 3, lower sensitive grid 4 and substrate 1
On, play the protective layer of protection against the tide, corrosion protection, loss prevention etc..
Pin 5 is used to connect sensitive grid and measuring circuit, and upper sensitive grid 2, middle sensitive grid 3 and lower sensitive grid 4 respectively have two
Pin 5, pair with foil and membrane type foil gauge, upper sensitive grid 2, middle sensitive grid 3 and the lower sensitive grid 4 that pin 5 is connected with it
It is integrated.Two pins of upper sensitive grid 2 are 5-1 and 5-2, and two pins of middle sensitive grid 3 are 5-3 and 5-4, lower sensitive grid 4
Two pins be 5-5 and 5-6, the lateral separation very little of pin 5-5 and 5-6 lower edge and the lower bottom sensitive segment of sensitive grid 4
Or even the two pins lower edge is located at the top of the lower bottom sensitive segment of sensitive grid 4, it is therefore an objective to reduces the lower center of sensitive grid 4 and arrives
The distance of foil gauge lower edge.
Upper sensitive grid 2, middle sensitive grid 3 and lower 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 the equal very little of thickness of which kind of upper sensitive grid 2, middle sensitive grid 3 and lower sensitive grid 4,
So that the axial length of upper sensitive grid 2, middle sensitive grid 3 and lower sensitive grid 4 depends on the deformation of workpiece with it and changed.The present invention
It is basic it is critical that cooperation between upper sensitive grid 2, middle sensitive grid 3 and lower sensitive grid 4, there is following main points:
First, three sensitive grids are arranged in substrate, are referred to as sensitive grid 2, middle sensitive grid 3 and lower sensitive grid 4.
Second, upper sensitive grid 2, middle sensitive grid 3 and lower sensitive grid 4 can be divided into sensitive segment 6 and changeover portion 7, each changeover portion 7
The connection of each sensitive segment 6 is formed into sensitive grid.Comparatively, sensitive segment 6 is elongated in shape, resistance is larger and its resistance to strain compared with
For sensitivity;The changeover portion 7 is in tubbiness shape substantially so that the resistance very little of the changeover portion and, work insensitive to straining
Resistance variations are close to 0 under state, therefore the summation of sensitive segment resistance is essentially the all-in resistance of single sensitive grid.Fig. 2 is from more clear
Clear angle has marked sensitive segment 6 and changeover portion 7 in more detail.
3rd, the sensitive segment 6 of each sensitive grid is in elongated strip, and all cross section centres of form composition of each sensitive segment 6 is quick
Feel section axis, the axis of sensitive segment 6 is straight line section, the diameter parallel of each sensitive segment 6 and is generally aligned in the same plane.Each
Projection of shape of all cross sections of sensitive segment 6 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, the total length of sensitive segment 6 of upper sensitive grid 2, middle sensitive grid 3 and lower sensitive grid 4 is in 1:4:3 proportionate relationship,
The all-in resistance of sensitive segment 6 of upper sensitive grid 2, middle sensitive grid 3 and lower sensitive grid 4 is in 1:4:3 proportionate relationship, upper 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 lower sensitive grid 4 is also in 1:4:3 ratio is closed
System.
5th, sensitive grid 2, middle sensitive grid 3 and lower sensitive grid 4 in vertical view, they are respectively provided with symmetry axis and symmetrical overlapping of axles
(y-axis in Fig. 2), upper sensitive grid 2, middle sensitive grid 3 and the respective sensitive segment 6 of lower sensitive grid 4 are all vertical with the symmetry axis, and
And the sensitive segment 6 of each sensitive grid is distributed on this axial symmetry.Therefore, it can be said that upper sensitive grid 2, middle sensitive grid 3 and lower sensitivity
On the y axis, there is lateral deviation at their center to the center of grid 4 without axial deviation.According to the top view of foil gauge in Fig. 2,
The sensitive segment 6 of upper sensitive grid 2 has axially symmetric axle xU, the center of upper sensitive grid 2 is in y-axis and xUThe intersection point of axle, middle sensitive grid 3
Sensitive segment 6 has axially symmetric axle xM, the center of middle sensitive grid 3 is in y-axis and xMThe intersection point of axle, the sensitive segment 6 of lower sensitive grid 4 have axle
To symmetry axis xL, the center of lower sensitive grid 4 is in y-axis and xLThe intersection point of axle.
6th, the distance at upper sensitive grid center and middle sensitive grid center is Δ y1, in middle sensitive grid center and lower sensitive grid
The distance of the heart is Δ y1, i.e., the line midpoint at the center and the center of lower sensitive grid 4 of upper sensitive grid 2 is also y-axis and xMThe friendship of axle
Point, as shown in Figure 2.The forward direction of y-axis as shown in Figure 2, the y-coordinate of arbitrfary point is quick in being more than on any sensitive segment 6 of upper sensitive grid 2
Feel grid 3 any sensitive segment 6 on arbitrfary point y-coordinate, the y-coordinate of arbitrfary point is more than on any sensitive segment 6 of middle sensitive grid 3
Lower sensitive grid 4 any sensitive segment 6 on arbitrfary point y-coordinate.Due to upper sensitive grid 2, middle sensitive grid 3 and lower sensitive grid 4
Relative position is ensured relatively accurately to be secured by foil gauge production technology, and this is also that the present invention can detect workpiece strain laterally
One of key of partial derivative.
In summary, sensitive grid 2, middle sensitive grid 3 and lower sensitive grid 4 increased resistance value under same strain are in the present invention
1:4:3 proportionate relationship, each central axial zero deflection of sensitive grid laterally have deviation, the center of upper sensitive grid 2 to the middle center of sensitive grid 3
Distance it is equal with the distance of the middle center of sensitive grid 3 to lower sensitive grid 4.
It is R to make the upper resistance of sensitive grid 2 under free stateU0, the middle resistance of sensitive grid 3 is RM0, the lower resistance of sensitive grid 4 is RL0, should
There is RU0+RL0=RM0=R0.When the foil gauge of the present invention is placed in into certain surface strain, the upper resistance of sensitive grid 2 is R0+ΔRU,
The middle resistance of sensitive grid 3 is R0+ΔRM, the lower resistance of sensitive grid 4 is R0+ΔRL;On the other hand, upper sensitive grid 2 and lower sensitive grid 4
Center respectively be located at Fig. 2 in y-axis and xUIntersection point and y-axis and xLIntersection point, at a distance of 2 Δ y in transverse direction1.Utilize sensitive grid electricity
Resistance has with the relation of surface strain and the formula (3) of numerical differentiation:
WhereinFor the center of lower sensitive grid 4, εUFor the strain at the upper center of sensitive grid 2, εMFor in middle sensitive grid 3
Strain at the heart, εLFor the strain at the lower center of sensitive grid 4.This is the original that the present embodiment measurement surface strains horizontal local derviation
Reason.Pay special attention to, the numerical differentiation that above formula is calculated for lower sensitive grid 4 center strain transverse direction single order local derviation, the position
The downside of foil gauge is set to, therefore has and is easy to measurement workpiece corner, edge etc. to have size restriction site to foil gauge
The advantage of horizontal single order local derviation.With reference to Fig. 2, the pin 5-5 and 5-6 of lower sensitive grid 4 lower edge are sensitive with lower sensitive grid bottom
Section lateral separation very little or even pin lower edge is located at the top of lower sensitive grid bottom sensitive segment, it is therefore an objective to it is quick under reduction
Grid center is felt to the distance of foil gauge lower edge, in order to further play above-mentioned advantage.
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, (6)
Since first, when meeting condition (6), according to relevant theoretical foil gauge sensitivity highest;Second, measuring strain or
The method that person strains horizontal local derviation is required to condition (6) 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 (7) acquisition;Can convolution to straining horizontal local derviation
(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
Sensitive grid 2 and lower sensitive grid 4 in arrangement, remaining bridge arm configuration substitutional resistance, can be obtained with being strained laterally at the lower center of sensitive grid 4
The linear magnitude of voltage u of single order local derviationo, the voltage is that small-signal need to be amplified.