CN103994715A - Device and method for measuring minimum diameter of diameter shrinkage portion of tensile sample after fracture - Google Patents

Abstract

The invention relates to a device and method for measuring the minimum diameter of a diameter shrinkage portion of a tensile sample after fracture. The device comprises a resistance-strain U-shaped sensor with a positioning rod and a measurement clamping tool edge, a U-shaped support, a plurality of standard units of standard cylinders and a data collector provided with measurement software. The sensor is installed on the standard cylinders or the tensile failure sample through cooperation of the positioning rod and the support, a measurement signal containing a standard diameter value or the minimum diameter value of the diameter shrinkage portion of the sample and the contact offset of the measurement clamping tool edge is transmitted to the data collector; a standardization algorithm of the measurement software provides a diameter fitting formula, and contact offset errors caused by different diameters of the standard cylinders are eliminated; a measurement algorithm of the measurement software provides a diameter value of the sample, and the contact offset errors caused by different diameters of the sample are eliminated.

Description

Footpath contracting position minimum diameter measurement mechanism and measuring method after tensile sample fracture

Technical field

The present invention relates to one have no progeny diameter measuring device and method, for measurement, the central authorities' measurement of diameter of section of curve variable cross section fatigue testing specimen and the measurement of the circular shaft-type parts such as axle and the Step Shaft diameter that bus is curve of contracting position, footpath minimum diameter after the metal stretching sample fracture of material mechanical performance test circular section, belong to sensor, mechanical test technology and mechanical measurement technique field.

Background technology

In material during tensile mechanical property test, in order to obtain the reduction of area of material, need to measure the minimum diameter at contracting position, footpath after sample fracture, generally use at present vernier caliper to measure.The resolving power of vernier caliper is generally 0.02 millimeter, and measurement data is easily introduced manual operation error, and its measuring method is not suitable for connecting data collecting instrument.Double cantilever beam formula measuring apparatus of diameter (CN101329159 disclosed " a kind of resistor strain type apparatus for measuring diameter and using method thereof " and " analysis of double cantilever beam diameter measurement sensor performance ", journal of Zhejiang university engineering version, Vol.46, No.6, Jun.2012,1060-1066) there is the resolving power that is less than 0.002 millimeter, can measure the green diameter of material tensile sample and the diameter of other similar uniform cross section circular shaft-type parts, measuring accuracy is not subject to the impact of manual operation factor, is suitable for connecting data collecting instrument.But this measuring instrument is owing to being subject to the restriction of adopted sample localization method, is not suitable for measuring the minimum diameter at contracting position, footpath after metal stretching sample fracture, and has contact offset error.Contact offset error refers to the tested sample for different-diameter, because measuring the inconsistent measuring error causing of contact point of blade and sample.

Summary of the invention

Object of the present invention is the device and method that a kind of contracting position, the rear footpath of the measurement tensile sample fracture minimum diameter that can eliminate contact offset error is provided for material mechanical performance test.

After tensile sample fracture of the present invention, contracting position, footpath minimum diameter measurement mechanism comprises sensor, support, Compress Spring, standard and data collecting instrument;

Sensor has a U-shaped elastic body, two sword pieces, a reference column, a guide rod and four pieces of single shaft strain ga(u)ge R ₁, R ₂, R ₃and R ₄; U-shaped elastomer shape symmetry, its structure comprises pedestal B and is fixed on the left Cantilever Beams of Variable Cross Section B at pedestal B two ends ₁with right Cantilever Beams of Variable Cross Section B ₂, left Cantilever Beams of Variable Cross Section B ₁with right Cantilever Beams of Variable Cross Section B ₂xsect be rectangle, and be divided into two sections of head ac and neck ce from free end a to root e, the cross-sectional area of head ac section is greater than the cross-sectional area of neck ce section, and the middle part of pedestal B is processed with a cylindrical hole along the elastomeric axes O of U-shaped, left Cantilever Beams of Variable Cross Section B ₁with right Cantilever Beams of Variable Cross Section B ₂respectively be processed with a rectangular through-hole near free end a place, these two rectangular through-hole are in coaxial position; The structure of each sword piece is divided into triangular head C ₁with rectangle root C ₂two sections, triangular head C ₁front end be rectilinear edge; The top of reference column is triangle, and leg-of-mutton top is the rectilinear edge perpendicular to mast axis, and the bottom of reference column is by lower surface E ₁rise and be processed with internal thread along mast axis; The structure of guide rod is divided into upper, middle and lower segment, and epimere is processed with screw thread, and stage casing is uniform cross section circular shaft, and hypomere is cylindrical flat cap, and the diameter in stage casing is greater than the diameter of epimere, and stage casing forms the step surface E perpendicular to guide rod axis at the section being connected with epimere ₂; Two sword pieces are by its rectangle root C ₂with left Cantilever Beams of Variable Cross Section B ₁with right Cantilever Beams of Variable Cross Section B ₂the interference fit of rectangular through-hole, be inlaid in respectively left Cantilever Beams of Variable Cross Section B ₁with right Cantilever Beams of Variable Cross Section B ₂upper, and in the elastomeric inner side of U-shaped; On two sword pieces, rectilinear edge is parallel to each other, and forms the measurement clamping cutting edge of sensor; Single shaft strain ga(u)ge R ₁and R ₂stick on respectively left Cantilever Beams of Variable Cross Section B ₁the inside and outside both sides of neck ce, its grid axle and left Cantilever Beams of Variable Cross Section B ₁axis parallel; Single shaft strain ga(u)ge R ₃and R ₄stick on respectively right Cantilever Beams of Variable Cross Section B ₂the inside and outside both sides of neck ce, its grid axle and right Cantilever Beams of Variable Cross Section B ₂axis parallel; Four pieces of strain ga(u)ge R ₁, R ₂, R ₃and R ₄connect into full-bridge circuit by wire;

Support is U-shaped structure, shape symmetry; In the centre of frame bottom, coaxially be processed with a rectangular channel and a cylindrical hole along the axes O of support, rectangular channel is positioned at the inner side of support U-shaped structure, and connect along the direction vertical with the middle face of support, in the upper end of support two arms, be respectively processed with a V-shaped groove, this two V-shaped groove shapes and towards identical, and in coaxial position, its axis is arranged in the face of support;

Guide rod is through the cylindrical hole on cylindrical hole, Compress Spring and the U-shaped elastic body base B of frame bottom, and U-shaped elastic body and support are coaxial, U-shaped elastomeric middle mutually vertical with the middle face of support, guide rod epimere screw thread screws with the internal thread of the reference column bottom that is positioned at U-shaped elastic body inner side, reference column lower surface E ₁upper surface E with U-shaped elastic body base B ₃compression fit, the step surface E in guide rod stage casing ₂lower surface E with U-shaped elastic body base B ₄compression fit, Compress Spring is positioned at the stage casing of guide rod, its two ends contact with support with U-shaped elastic body respectively, the cylindrical flat cap of guide rod hypomere props up frame bottom lower surface, being slidably matched of guide rod stage casing and frame bottom cylindrical hole and being slidably matched of the rectangular channel of U-shaped elastomeric pedestal B two sides and frame bottom, common formation one pair is along the guiding rail mechanism of sensor and support common axis O direction, sensor is had along the one-movement-freedom-degree of the two common axis O direction with respect to support, simultaneously, there is certain tolerance clearance in this guide rail mechanism, make sensor there is the small degree of freedom of rotating around the two common axis O with respect to support, the rectilinear edge of reference column is positioned at sword piece below, and coplanar, vertical with the rectilinear edge of two sword pieces,

Standard is made up of standard cylinder and datum diameter rule of some different-diameters, the diameter value d of datum diameter rule ₀be defined as datum diameter; Quantity n>=4 of standard cylinder; The diameter d of standard cylinder ₁, d ₂..., d _narrange minimum diameter value d wherein by order from small to large ₁be greater than the primary leading s of two sword pieces of sensor; The diameter value d of datum diameter rule ₀meet and be related to d ₁<d ₀<d _n;

Data collecting instrument comprises strain signal collection-modulate circuit and the microcomputer system that Survey Software is housed, and contains calibrating procedure and process of measurement in Survey Software, and calibrating procedure and process of measurement respectively contain a contact offset error modified computing formulae.

Apply the method that above-mentioned contracting position, the rear footpath of tensile sample fracture minimum diameter measurement mechanism is measured, comprise measurement mechanism installation, demarcate and measure, operation steps is as follows:

1) measurement mechanism is installed: by the measurement clamping cutting edge of sensor and the measurement cross section of rectilinear edge registration coupon or the normal diameter section of standard cylinder of reference column, at the both sides of frame bottom cylindrical hole pushing support, the V-shaped groove of support two arms is contacted with the column part of both sides, sample measurement cross section respectively, simultaneously sensor under the elastic pressure effect of Compress Spring against sample, measure clamping cutting edge vertical clamping sample, the rectilinear edge of reference column contacts with sample is vertical, left Cantilever Beams of Variable Cross Section B ₁with right Cantilever Beams of Variable Cross Section B ₂produce certain deflection deformation;

2) measurement mechanism is demarcated: by the strain signal collection-modulate circuit of the full-bridge circuit access data Acquisition Instrument of sensor, on each standard cylinder that measurement mechanism is successively arranged on by standard diameter value order from small to large, write down each reading ε of data collecting instrument _r1, ε _r2..., ε _rn, then draw data collecting instrument reading ε by linear fit method _rwith the functional relation of diameter value d, i.e. fit equation

ε _r＝Ad+B (a)

In formula (a), A and B are constants, press respectively formula (b) and (c) calculating:

$A=\frac{\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}(d_i-\stackrel{\&OverBar;}{d_i})({\mathrm{\&epsiv;}}_{\mathrm{ri}}^{*}-\stackrel{\&OverBar;}{{\mathrm{\&epsiv;}}_{\mathrm{ri}}^{*}})}{\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{(d_i-\stackrel{\&OverBar;}{d_i})}^2}---\left(b\right)$

$B=\stackrel{\&OverBar;}{{\mathrm{\&epsiv;}}_{\mathrm{ri}}^{*}}-A\&times;\stackrel{\&OverBar;}{d_i}---\left(c\right)$

${\mathrm{\&epsiv;}}_{\mathrm{ri}}^{*}=\frac{\frac{{3\mathrm{h\&alpha;}}^3(L_0-e)}{{3\mathrm{\&alpha;}}^3(L_0-m)m^2+{3\mathrm{\&alpha;}}^3{(L_0-m)}^{2}m+{\mathrm{\&alpha;}}^3{m}^3+{(L_0-m)}^3}}{\frac{{3\mathrm{h\&alpha;}}^3(L_0+{\mathrm{\&delta;}}_i-e)}{{3\mathrm{\&alpha;}}^3(L_0+{\mathrm{\&delta;}}_i-m)m^2+{3\mathrm{\&alpha;}}^3{(L_0+{\mathrm{\&delta;}}_i-m)}^{2}m+{\mathrm{\&alpha;}}^3{m}^3+{(L_0+{\mathrm{\&delta;}}_i-m)}^3}}{\mathrm{\&epsiv;}}_{\mathrm{ri}}---\left(d\right)$

${\mathrm{\&delta;}}_i=\frac{d_i-d_0}{2}---\left(e\right)$

Formula (b) and (c) in, n represents the number of standard cylinder, d _irepresent the diameter value of different-diameter standard cylinder, the diameter value d of each standard cylinder _iarithmetical mean, represent that with diameter value be d _idata collecting instrument reading ε corresponding to standard cylinder _rimodified value, each reading ε of data collecting instrument _rimodified value arithmetical mean; In formula (d), h represents left Cantilever Beams of Variable Cross Section B ₁with right Cantilever Beams of Variable Cross Section B ₂the thickness of neck ce section, α represents left Cantilever Beams of Variable Cross Section B ₁with right Cantilever Beams of Variable Cross Section B ₂the ratio of the thickness h of the thickness H of head ac section and neck ce section, L ₀represent datum diameter rule and measure the contact point that clamps cutting edge to left Cantilever Beams of Variable Cross Section B ₁with right Cantilever Beams of Variable Cross Section B ₂the distance of root section e, e represents strain ga(u)ge R ₁, R ₂, R ₃and R ₄central point to left Cantilever Beams of Variable Cross Section B ₁with right Cantilever Beams of Variable Cross Section B ₂the distance of root section e, m represents left Cantilever Beams of Variable Cross Section B ₁with right Cantilever Beams of Variable Cross Section B ₂the length of neck ce section, δ _iexpression diameter value is d _istandard cylinder with measure clamping cutting edge contact point with respect to L ₀the displacement producing, i.e. contact side-play amount;

3) diameter measurement: measurement mechanism is arranged on to fracture (19) upper through the tension failure sample (18) engaging, by the full-bridge circuit access data Acquisition Instrument of sensor (1), the reading strain ε of record data Acquisition Instrument _r, by formula (f), (g) with (h) calculate the diameter d of sample:

$d=d_0+\frac{1}{2}(s-\frac{1}{\mathrm{\&Omega;}}-d_0)-\frac{1}{2}\sqrt{{(s-\frac{1}{\mathrm{\&Omega;}}-d_0)}^2+\frac{4}{\mathrm{\&Omega;}}(\frac{{\mathrm{\&epsiv;}}_r-B}{A}-d_0)}---\left(f\right)$

$\mathrm{\&Omega;}=\frac{{3\mathrm{h\&alpha;}}^3-\mathrm{\&eta;}({3\mathrm{\&alpha;}}^3{m}^2+{6\mathrm{\&alpha;}}^3(L_0-m)m+3{(L_0-m)}^2)}{{6\mathrm{h\&alpha;}}^3(L_0-e)}---\left(g\right)$

$\mathrm{\&eta;}=\frac{{3\mathrm{h\&alpha;}}^3(L_0-e)}{{3\mathrm{\&alpha;}}^3(L_0-m)m^2+{3\mathrm{\&alpha;}}^3{(L_0-m)}^{2}m+{\mathrm{\&alpha;}}^3{m}^3+{(L_0-m)}^3}---\left(h\right).$

In the present invention, described tension failure sample comprises tension failure sample, the variable cross section pure bending fatigue testing specimen of material mechanical performance test, and bus be curve non-uniform shaft and Step Shaft axial workpiece.

Feature of the present invention:

1, use reference column and the U-shaped elastic body mix proportion sensor with rectilinear edge, thereby the measurement clamping blade of sensor can accurately be located in tested sample.

2, be set as datum diameter rule by one in standard cylinder; The contact point that clamps blade using datum diameter rule and sensor measurement is as the reference point of demarcating and measuring.

3, utilizing reference column sensor to be positioned and utilized datum diameter rule determine under the condition of datum mark, by formula (b), (d), (c) and (e) coefficient A and the B in digital simulation equation (a), thereby eliminate because of the different contact offset errors that produce of each standard cylinder diameter in the demarcation link of measuring system.

4, adopt formula (f), (g) and (h) calculate the diameter of sample, thereby eliminating the contact offset errors because of the different generations of specimen finish in measurement links.

5, by the band guide rail detent mechanism forming with V-shaped groove support and flexible member and sensor, can ensure that sensor measurement clamping blade place plane is mutually vertical with the axis of sample, and the installation of measurement mechanism had both been suitable for manual operations, be suitable for again automatic or automanual mechanically actuated mode.

Brief description of the drawings

Fig. 1 is that measurement mechanism is arranged on the three-view diagram on sample, wherein: (a) front view, (b) left view, (c) vertical view;

Fig. 2 is the elastomeric three-view diagram of U-shaped, wherein: (a) front view, (b) left view, (c) vertical view;

Fig. 3 is the three-view diagram of support, wherein: (a) front view, (b) vertical view, (c) vertical view;

Fig. 4 is the three-view diagram of sword piece, wherein: (a) front view, (b) vertical view, (c) vertical view;

Fig. 5 is two views of reference column, wherein: (a) front view, (b) vertical view;

Fig. 6 is the structural drawing of guide rod;

Fig. 7 is the schematic diagram of full-bridge circuit;

Fig. 8 is the organigram of measurement mechanism of the present invention, wherein: (a) front view, (b) right view, (c) vertical view;

In figure: 1. sensor, 2. support, 3. Compress Spring, 4.U shape elastic body, 5. sword piece, 6. reference column, 7. guide rod, the cylindrical hole on 8.U shape elastic body, 9. rectangular through-hole, the 10. rectilinear edge of sword piece, the rectilinear edge of 11. reference columns, 12. internal threads, 13. screw threads, 14. cylindrical flat caps, 15. rectangular channels, the cylindrical hole on 16. supports, 17.V shape groove, 18. samples, 19. fractures, R ₁, R ₂, R ₃and R ₄. be respectively single shaft strain ga(u)ge, B. pedestal, B ₁. left Cantilever Beams of Variable Cross Section, B ₂. right Cantilever Beams of Variable Cross Section, C ₁. triangular head, C ₂. rectangle root, E ₁. lower surface, E ₂. step surface, E ₃. upper surface, E ₄. lower surface.

Embodiment

Below in conjunction with accompanying drawing, the invention will be further described.

With reference to Fig. 1-Fig. 8, after tensile sample fracture of the present invention, contracting position, footpath minimum diameter measurement mechanism comprises sensor 1, support 2, Compress Spring 3, standard and data collecting instrument;

Sensor 1 has a U-shaped elastic body 4, two sword pieces 5, reference column 6, guide rod 7 and four pieces of single shaft strain ga(u)ge R ₁, R ₂, R ₃and R ₄; U-shaped elastic body 4 shape symmetries, its structure comprises pedestal B and is fixed on the left Cantilever Beams of Variable Cross Section B at pedestal B two ends ₁with right Cantilever Beams of Variable Cross Section B ₂, left Cantilever Beams of Variable Cross Section B ₁with right Cantilever Beams of Variable Cross Section B ₂xsect be rectangle, and be divided into two sections of head ac and neck ce from free end a to root e, the cross-sectional area of head ac section is greater than the cross-sectional area of neck ce section, and the middle part of pedestal B is processed with a cylindrical hole 8 along the axes O of U-shaped elastic body 4, left Cantilever Beams of Variable Cross Section B ₁with right Cantilever Beams of Variable Cross Section B ₂respectively be processed with a rectangular through-hole 9 near free end a place, these two rectangular through-hole 9 are in coaxial position; The structure of each sword piece 5 is divided into triangular head C ₁with rectangle root C ₂two sections, triangular head C ₁front end be rectilinear edge 10; The top of reference column 6 is triangle, and leg-of-mutton top is the rectilinear edge 11 perpendicular to mast axis, and the bottom of reference column 6 is by lower surface E ₁rise and be processed with internal thread 12 along mast axis; The structure of guide rod 7 is divided into upper, middle and lower segment, and epimere is processed with screw thread 13, and stage casing is uniform cross section circular shaft, and hypomere is cylindrical flat cap 14, and the diameter in stage casing is greater than the diameter of epimere, and stage casing forms the step surface E perpendicular to guide rod axis at the section being connected with epimere ₂; Two sword pieces 5 are by its rectangle root C ₂with left Cantilever Beams of Variable Cross Section B ₁with right Cantilever Beams of Variable Cross Section B ₂the interference fit of rectangular through-hole 9, be inlaid in respectively left Cantilever Beams of Variable Cross Section B ₁with right Cantilever Beams of Variable Cross Section B ₂above, the inner side and in U-shaped elastic body 4; On two sword pieces 5, rectilinear edge 10 is parallel to each other, and forms the measurement clamping cutting edge of sensor 1; Single shaft strain ga(u)ge R ₁and R ₂stick on respectively left Cantilever Beams of Variable Cross Section B ₁the inside and outside both sides of neck ce, its grid axle and left Cantilever Beams of Variable Cross Section B ₁axis parallel; Single shaft strain ga(u)ge R ₃and R ₄stick on respectively right Cantilever Beams of Variable Cross Section B ₂the inside and outside both sides of neck ce, its grid axle and right Cantilever Beams of Variable Cross Section B ₂axis parallel; Four pieces of strain ga(u)ge R ₁, R ₂, R ₃and R ₄connect into full-bridge circuit by wire;

Support 2 is U-shaped structure, shape symmetry; In the centre of support 2 bottoms, coaxially be processed with a rectangular channel 15 and a cylindrical hole 16 along the axes O of support 2, rectangular channel 15 is positioned at the inner side of support U-shaped structure, and connect along the direction vertical with the middle face of support 2, in the upper end of 2 liang of arms of support, be respectively processed with a V-shaped groove 17, this two V-shaped groove 17 shapes and towards identical, and in coaxial position, its axis is arranged in the face of support 2;

Guide rod 7 is through the cylindrical hole 8 on cylindrical hole 16, Compress Spring 3 and the U-shaped elastic body 4 pedestal B of support 2 bottoms, and U-shaped elastic body 4 is coaxial with support 2, and the middle face of U-shaped elastic body 4 is mutually vertical with the middle face of support 2, guide rod 7 epimere screw threads 13 screw with the internal thread 12 of reference column 6 bottoms that are positioned at U-shaped elastic body 4 inner sides, reference column 6 lower surface E ₁upper surface E with U-shaped elastic body base B ₃compression fit, the step surface E in guide rod 7 stage casings ₂lower surface E with U-shaped elastic body 4 pedestal B ₄compression fit, Compress Spring 3 is positioned at the stage casing of guide rod 7, its two ends contact with support 2 with U-shaped elastic body 4 respectively, the cylindrical flat cap 14 of guide rod 7 hypomere props up support 2 bottom lower surfaces, being slidably matched of guide rod 7 stage casings and support 2 bottom cylindrical holes 16 and being slidably matched of the pedestal B two sides of U-shaped elastic body 4 and the rectangular channel 15 of frame bottom, common formation one pair is along the guiding rail mechanism of sensor 1 and support 2 common axis O directions, sensor 1 is had along the one-movement-freedom-degree of the two common axis O direction with respect to support 2, simultaneously, there is certain tolerance clearance in this guide rail mechanism, make sensor 1 there is the small degree of freedom (being generally advisable with ± 0.5 °) of rotating around the two common axis O with respect to support 2, the rectilinear edge 11 of reference column 6 is positioned at sword piece 5 belows, and coplanar, vertical with the rectilinear edge 10 of two sword pieces 5,

Standard is made up of standard cylinder and datum diameter rule of some different-diameters, the diameter value d of datum diameter rule ₀be defined as datum diameter; Quantity n>=4 of standard cylinder; The diameter d of standard cylinder ₁, d ₂..., d _narrange minimum diameter value d wherein by order from small to large ₁be greater than the primary leading s of 1 two sword pieces 5 of sensor; The diameter value d of datum diameter rule ₀meet and be related to d ₁<d ₀<d _n;

Data collecting instrument comprises strain signal collection-modulate circuit and the microcomputer system that Survey Software is housed, and contains calibrating procedure and process of measurement in Survey Software, and calibrating procedure and process of measurement respectively contain a contact offset error modified computing formulae.

By the measuring method of contracting position, footpath minimum diameter measurement mechanism after tensile sample fracture, comprise measurement mechanism installation, demarcate and measure, operation steps is as follows:

1) measurement mechanism is installed: by the measurement cross section of rectilinear edge 11 registration coupon 18 of the measurement clamping cutting edge of sensor 1 and reference column 6 or the normal diameter section of standard cylinder, both sides at support 2 bottom cylindrical holes 16 push support 2 from bottom to top, the column part that the V-shaped groove 17 that makes 2 liang of arms of support is measured both sides, cross section with sample 18 respectively contacts, simultaneously sensor 1 under the elastic pressure effect of Compress Spring 3 against sample 18, measure clamping cutting edge by sample 18 vertical clampings, the rectilinear edge 11 of reference column 6 contacts with sample 18 is vertical, left Cantilever Beams of Variable Cross Section B ₁with right Cantilever Beams of Variable Cross Section B ₂produce certain deflection deformation;

2) measurement mechanism is demarcated: by the strain signal collection-modulate circuit of the full-bridge circuit access data Acquisition Instrument of sensor 1, on each standard cylinder that measurement mechanism is successively arranged on by standard diameter value order from small to large, write down each reading ε of data collecting instrument _r1, ε _r2..., ε _rn, then draw data collecting instrument reading ε by linear fit method _rwith the functional relation of diameter value d, i.e. fit equation

ε _r＝Ad+B (a)

In formula (a), A and B are constants, press respectively formula (b) and (c) calculating:

$A=\frac{\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}(d_i-\stackrel{\&OverBar;}{d_i})({\mathrm{\&epsiv;}}_{\mathrm{ri}}^{*}-\stackrel{\&OverBar;}{{\mathrm{\&epsiv;}}_{\mathrm{ri}}^{*}})}{\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{(d_i-\stackrel{\&OverBar;}{d_i})}^2}---\left(b\right)$

$B=\stackrel{\&OverBar;}{{\mathrm{\&epsiv;}}_{\mathrm{ri}}^{*}}-A\&times;\stackrel{\&OverBar;}{d_i}---\left(c\right)$

${\mathrm{\&epsiv;}}_{\mathrm{ri}}^{*}=\frac{\frac{{3\mathrm{h\&alpha;}}^3(L_0-e)}{{3\mathrm{\&alpha;}}^3(L_0-m)m^2+{3\mathrm{\&alpha;}}^3{(L_0-m)}^{2}m+{\mathrm{\&alpha;}}^3{m}^3+{(L_0-m)}^3}}{\frac{{3\mathrm{h\&alpha;}}^3(L_0+{\mathrm{\&delta;}}_i-e)}{{3\mathrm{\&alpha;}}^3(L_0+{\mathrm{\&delta;}}_i-m)m^2+{3\mathrm{\&alpha;}}^3{(L_0+{\mathrm{\&delta;}}_i-m)}^{2}m+{\mathrm{\&alpha;}}^3{m}^3+{(L_0+{\mathrm{\&delta;}}_i-m)}^3}}{\mathrm{\&epsiv;}}_{\mathrm{ri}}---\left(d\right)$

${\mathrm{\&delta;}}_i=\frac{d_i-d_0}{2}---\left(e\right)$

Formula (b) and (c) in, n represents the number of standard cylinder, d _irepresent the diameter value of different-diameter standard cylinder, the diameter value d of each standard cylinder _iarithmetical mean, represent that with diameter value be d _idata collecting instrument reading ε corresponding to standard cylinder _rimodified value, each reading ε of data collecting instrument _rimodified value arithmetical mean; In formula (d), h represents left Cantilever Beams of Variable Cross Section B ₁with right Cantilever Beams of Variable Cross Section B ₂the thickness of neck ce section, α represents left Cantilever Beams of Variable Cross Section B ₁with right Cantilever Beams of Variable Cross Section B ₂the ratio of the thickness h of the thickness H of head ac section and neck ce section, L ₀represent datum diameter rule and measure the contact point that clamps cutting edge to left Cantilever Beams of Variable Cross Section B ₁with right Cantilever Beams of Variable Cross Section B ₂the distance of root section e, e represents strain ga(u)ge R ₁, R ₂, R ₃and R ₄central point to left Cantilever Beams of Variable Cross Section B ₁with right Cantilever Beams of Variable Cross Section B ₂the distance of root section e, m represents left Cantilever Beams of Variable Cross Section B ₁with right Cantilever Beams of Variable Cross Section B ₂the length of neck ce section, δ _iexpression diameter value is d _istandard cylinder with measure clamping cutting edge contact point with respect to L ₀the displacement producing, i.e. contact side-play amount;

3) diameter measurement: tension failure sample 18 is engaged at fracture 19 places, measurement mechanism is arranged on tension failure sample 18, need the cross section of measuring in rectilinear edge 11 registration coupon of measurement cutting edge and reference column 6; By the full-bridge circuit access data Acquisition Instrument of sensor 1, the reading strain ε of record data Acquisition Instrument _r, by formula (f), (g) with (h) calculate the diameter d of sample:

$d=d_0+\frac{1}{2}(s-\frac{1}{\mathrm{\&Omega;}}-d_0)-\frac{1}{2}\sqrt{{(s-\frac{1}{\mathrm{\&Omega;}}-d_0)}^2+\frac{4}{\mathrm{\&Omega;}}(\frac{{\mathrm{\&epsiv;}}_r-B}{A}-d_0)}---\left(f\right)$

$\mathrm{\&Omega;}=\frac{{3\mathrm{h\&alpha;}}^3-\mathrm{\&eta;}({3\mathrm{\&alpha;}}^3{m}^2+{6\mathrm{\&alpha;}}^3(L_0-m)m+3{(L_0-m)}^2)}{{6\mathrm{h\&alpha;}}^3(L_0-e)}---\left(g\right)$

$\mathrm{\&eta;}=\frac{{3\mathrm{h\&alpha;}}^3(L_0-e)}{{3\mathrm{\&alpha;}}^3(L_0-m)m^2+{3\mathrm{\&alpha;}}^3{(L_0-m)}^{2}m+{\mathrm{\&alpha;}}^3{m}^3+{(L_0-m)}^3}---\left(h\right).$

Contact offset error corrected Calculation principle:

1. the correction algorithm in calibrating procedure

Theoretical and the strain electrical measurement theory according to beam deflection, when measurement mechanism is arranged on standard cylinder that diameter value is d or sample 18, the reading strain ε of data collecting instrument _rcan show with following formula table

${\mathrm{\&epsiv;}}_r=\frac{{3\mathrm{h\&alpha;}}^3(L-e)}{{3\mathrm{\&alpha;}}^3(L-m)m^2+{3\mathrm{\&alpha;}}^3{(L-m)}^{2}m+{\mathrm{\&alpha;}}^3{m}^3+{(L-m)}^3}(d-s)---\left(1\right)$

In formula (1), L represents that sample 18 and the contact point of measuring clamping cutting edge arrive left Cantilever Beams of Variable Cross Section B ₁with right Cantilever Beams of Variable Cross Section B ₂the distance of root section e, is called contact height; H represents left Cantilever Beams of Variable Cross Section B ₁with right Cantilever Beams of Variable Cross Section B ₂the thickness of neck ce section, α represents left Cantilever Beams of Variable Cross Section B ₁with right Cantilever Beams of Variable Cross Section B ₂the ratio of the thickness h of the thickness H of head ac section and neck ce section, e represents strain ga(u)ge R ₁, R ₂, R ₃and R ₄central point to left Cantilever Beams of Variable Cross Section B ₁with right Cantilever Beams of Variable Cross Section B ₂the distance of root section e, m represents left Cantilever Beams of Variable Cross Section B ₁with right Cantilever Beams of Variable Cross Section B ₂the length of neck ce section, s represents to measure the primary leading of clamping cutting edge.

In standard cylinder, select arbitrarily one and specify that as datum diameter rule its normal diameter value is datum diameter, use d ₀represent.Use L ₀expression datum diameter is advised corresponding contact height, uses expression datum diameter is advised corresponding reading strain, with L ₀relation can be write as

${\mathrm{\&epsiv;}}_r^{*}=\frac{{3\mathrm{h\&alpha;}}^3(L_0-e)}{{3\mathrm{\&alpha;}}^3(L_0-m)m^2+{3\mathrm{\&alpha;}}^3{(L_0-m)}^{2}m+{\mathrm{\&alpha;}}^3{m}^3+{(L_0-m)}^3}(d-s)---\left(2\right)$

Contact height L in formula (1) can be write as

L＝L ₀+ΔL (3)

Form, the Δ L on formula (3) the right represents that diameter value is that the standard cylinder of d or the corresponding contact height L of sample are with respect to L ₀the displacement producing, is called contact skew.The standard cylinder that diameter value is different or sample have different contact side-play amounts, if do not consider the existence of contact shifted by delta L in demarcation and Measurement Algorithm, contact height L are regarded as to constant, the reading strain ε directly being obtained by formula (1) _rdemarcate and measure calculating, can produce certain measuring error, be called contact offset error.Adopt reference column 6 and setting datum diameter rule and datum diameter d ₀condition under, the corresponding contact of each standard cylinder side-play amount is all definite constant, and can unified representation be

${\mathrm{\&Delta;L}}_i=\frac{d_i-d_0}{2},(i=\mathrm{1,2},...,n)---\left(4\right)$

In formula (4), d _ithat sequence number is the diameter value of the standard cylinder of i, Δ L _ithat sequence number is the corresponding contact of the standard cylinder side-play amount of i.By formula (1)～(4), can solve

${\mathrm{\&epsiv;}}_{\mathrm{ri}}^{*}=\frac{\frac{{3\mathrm{h\&alpha;}}^3(L_0-e)}{{3\mathrm{\&alpha;}}^3(L_0-m)m^2+{3\mathrm{\&alpha;}}^3{(L_0-m)}^{2}m+{\mathrm{\&alpha;}}^3{m}^3+{(L_0-m)}^3}}{\frac{{3\mathrm{h\&alpha;}}^3(L_0+{\mathrm{\&Delta;L}}_i-e)}{{3\mathrm{\&alpha;}}^3(L_0+{\mathrm{\&Delta;L}}_i-m)m^2+{3\mathrm{\&alpha;}}^3{(L_0+{\mathrm{\&Delta;L}}_i-m)}^{2}m+{\mathrm{\&alpha;}}^3{m}^3+{(L_0+{\mathrm{\&Delta;L}}_i-m)}^3}}{\mathrm{\&epsiv;}}_{\mathrm{ri}}---\left(5\right)$

Formula (5) left side containing contact skew reading strain ε _ricorrected Calculation result, be called equivalent strain reading.Timing signal, uses set up the fitting formula of calculated diameter value d, formula (a), can eliminate contact offset error.

2. the correction algorithm in process of measurement

When measurement, continue to use datum diameter d ₀.With this understanding, the theoretical and strain electrical measurement theory according to beam deflection, can derive following formula:

$\mathrm{\&Delta;d}=\frac{1}{2}(s-\frac{1}{\mathrm{\&Omega;}}-d_0)-\frac{1}{2}\sqrt{{(s-\frac{1}{\mathrm{\&Omega;}}-d_0)}^2+\frac{4}{\mathrm{\&Omega;}}\mathrm{\&delta;d}*}---\left(6\right)$

$\mathrm{\&Omega;}=\frac{{3\mathrm{h\&alpha;}}^3-\mathrm{\&eta;}({3\mathrm{\&alpha;}}^3{m}^2+{6\mathrm{\&alpha;}}^3(L_0-m)m+3{(L_0-m)}^2)}{{6\mathrm{h\&alpha;}}^3(L_0-e)}---(6-a)$

δd ^*＝d ^*-d ₀ (6-b)

$\mathrm{\&eta;}=\frac{{3\mathrm{h\&alpha;}}^3(L_0-e)}{{3\mathrm{\&alpha;}}^3(L_0-m)m^2+{3\mathrm{\&alpha;}}^3{(L_0-m)}^{2}m+{\mathrm{\&alpha;}}^3{m}^3+{(L_0-m)}^3}---(6-c)$

In formula (6), Δ d is that the diameter d of tested sample is with respect to datum diameter d ₀change amount; d ^*by reading strain ε _rdirectly substitution formula (a) obtains diameter value,

$d^{*}=\frac{{\mathrm{\&epsiv;}}_r-A}{B}---\left(7\right)$

Because there is contact skew while measurement, so d ^*comprising contact offset error.D ^*can be called apparent diameter.The δ d being obtained by formula (6-a) ^*, be apparent diameter δ d ^*with respect to datum diameter d ₀change amount.Formula (6) is passed through δ d ^*make corrected Calculation, eliminate contact offset error, obtain Δ d.Obtain rear Δ d, can obtain the diameter d of tested sample:

d＝d ₀+Δd (8)

Claims (3)

1. contracting position, footpath minimum diameter measurement mechanism after tensile sample fracture, is characterized in that comprising sensor (1), support (2), Compress Spring (3), standard and data collecting instrument;

Sensor (1) has a U-shaped elastic body (4), two sword pieces (5), a reference column (6), a guide rod (7) and four pieces of single shaft strain ga(u)ge R ₁, R ₂, R ₃and R ₄; U-shaped elastic body (4) shape symmetry, its structure comprises pedestal B and is fixed on the left Cantilever Beams of Variable Cross Section B at pedestal B two ends ₁with right Cantilever Beams of Variable Cross Section B ₂, left Cantilever Beams of Variable Cross Section B ₁with right Cantilever Beams of Variable Cross Section B ₂xsect be rectangle, and be divided into two sections of head ac and neck ce from free end a to root e, the cross-sectional area of head ac section is greater than the cross-sectional area of neck ce section, the middle part of pedestal B is processed with a cylindrical hole (8) along the axes O of U-shaped elastic body (4), left Cantilever Beams of Variable Cross Section B ₁with right Cantilever Beams of Variable Cross Section B ₂respectively be processed with a rectangular through-hole (9) near free end a place, these two rectangular through-hole (9) are in coaxial position; The structure of each sword piece (5) is divided into triangular head C ₁with rectangle root C ₂two sections, triangular head C ₁front end be rectilinear edge (10); The top of reference column (6) is triangle, and leg-of-mutton top is the rectilinear edge (11) perpendicular to mast axis, and the bottom of reference column (6) is by lower surface E ₁rise and be processed with internal thread (12) along mast axis; The structure of guide rod (7) is divided into upper, middle and lower segment, epimere is processed with screw thread (13), stage casing is uniform cross section circular shaft, hypomere is cylindrical flat cap (14), the diameter in stage casing is greater than the diameter of epimere, and stage casing forms the step surface E perpendicular to guide rod axis at the section being connected with epimere ₂; Two sword pieces (5) are by its rectangle root C ₂with left Cantilever Beams of Variable Cross Section B ₁with right Cantilever Beams of Variable Cross Section B ₂the interference fit of rectangular through-hole (9), be inlaid in respectively left Cantilever Beams of Variable Cross Section B ₁with right Cantilever Beams of Variable Cross Section B ₂above, the inner side and in U-shaped elastic body (4); The upper rectilinear edge (10) of two sword pieces (5) is parallel to each other, and forms the measurement clamping cutting edge of sensor (1); Single shaft strain ga(u)ge R ₁and R ₂stick on respectively left Cantilever Beams of Variable Cross Section B ₁the inside and outside both sides of neck ce, its grid axle and left Cantilever Beams of Variable Cross Section B ₁axis parallel; Single shaft strain ga(u)ge R ₃and R ₄stick on respectively right Cantilever Beams of Variable Cross Section B ₂the inside and outside both sides of neck ce, its grid axle and right Cantilever Beams of Variable Cross Section B ₂axis parallel; Four pieces of strain ga(u)ge R ₁, R ₂, R ₃and R ₄connect into full-bridge circuit by wire;

Support (2) is U-shaped structure, shape symmetry; In the centre of support (2) bottom, coaxially be processed with a rectangular channel (15) and a cylindrical hole (16) along the axes O of support (2), rectangular channel (15) is positioned at the inner side of support U-shaped structure, and connect along the direction vertical with the middle face of support (2), in the upper end of support (2) two arms, respectively be processed with a V-shaped groove (17), this two V-shaped groove (17) shapes and towards identical, and in coaxial position, its axis is arranged in the face of support (2);

Guide rod (7) is through the cylindrical hole (8) on cylindrical hole (16), Compress Spring (3) and U-shaped elastic body (4) the pedestal B of support (2) bottom, U-shaped elastic body (4) is coaxial with support (2), and the middle face of U-shaped elastic body (4) is mutually vertical with the middle face of support (2), guide rod (7) epimere screw thread (13) screws with the internal thread (12) of reference column (6) bottom that is positioned at U-shaped elastic body (4) inner side, reference column (6) lower surface E ₁upper surface E with U-shaped elastic body base B ₃compression fit, the step surface E in guide rod (7) stage casing ₂lower surface E with U-shaped elastic body (4) pedestal B ₄compression fit, Compress Spring (3) is positioned at the stage casing of guide rod (7), its two ends contact with support (2) with U-shaped elastic body (4) respectively, the cylindrical flat cap of guide rod (7) hypomere (14) props up support (2) bottom lower surface, guide rod (7) stage casing and being slidably matched of support (2) bottom cylindrical hole (16) and being slidably matched of the pedestal B two sides of U-shaped elastic body (4) and rectangular channel (15) of frame bottom, common formation one pair is along the guiding rail mechanism of sensor (1) and support (2) common axis O direction, sensor (1) is had along the one-movement-freedom-degree of the two common axis O direction with respect to support (2), simultaneously, there is certain tolerance clearance in this guide rail mechanism, make sensor (1) there is the small degree of freedom of rotating around the two common axis O with respect to support (2), the rectilinear edge (11) of reference column (6) is positioned at sword piece (5) below, and coplanar, vertical with the rectilinear edge (10) of two sword pieces (5),

Standard is made up of standard cylinder and datum diameter rule of some different-diameters, the diameter value d of datum diameter rule ₀be defined as datum diameter; Quantity n>=4 of standard cylinder; The diameter d of standard cylinder ₁, d ₂..., d _narrange minimum diameter value d wherein by order from small to large ₁be greater than the primary leading s of (1) two sword piece of sensor (5); The diameter value d of datum diameter rule ₀meet and be related to d ₁<d ₀<d _n;

Data collecting instrument comprises strain signal collection-modulate circuit and the microcomputer system that Survey Software is housed, and contains calibrating procedure and process of measurement in Survey Software, and calibrating procedure and process of measurement respectively contain a contact offset error modified computing formulae.

2. application rights requires the measuring method of contracting position, the rear footpath of the tensile sample fracture minimum diameter measurement mechanism described in 1, it is characterized in that comprising measurement mechanism installation, demarcates and measures, and operation steps is as follows:

1) measurement mechanism is installed: by the measurement clamping cutting edge of sensor (1) and the measurement cross section of rectilinear edge (11) registration coupon (18) or the normal diameter section of standard cylinder of reference column (6), at the both sides pushing supports (2) of support (2) bottom cylindrical hole (16), the V-shaped groove (17) of support (2) two arms is contacted with the column part of sample (18) measurement both sides, cross section respectively, simultaneously sensor (1) under the elastic pressure effect of Compress Spring (3) against sample (18), measure clamping cutting edge vertical clamping sample (18), the rectilinear edge (11) of reference column (6) and vertical contact of sample (18), left Cantilever Beams of Variable Cross Section B ₁with right Cantilever Beams of Variable Cross Section B ₂produce certain deflection deformation,

2) measurement mechanism is demarcated: by the strain signal collection-modulate circuit of the full-bridge circuit access data Acquisition Instrument of sensor (1), on each standard cylinder that measurement mechanism is successively arranged on by standard diameter value order from small to large, write down each reading ε of data collecting instrument _r1, ε _r2..., ε _rn, then draw data collecting instrument reading ε by linear fit method _rwith the functional relation of diameter value d, i.e. fit equation

ε _r＝Ad+B (a)

In formula (a), A and B are constants, press respectively formula (b) and (c) calculating:

$A=\frac{\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}(d_i-\stackrel{\&OverBar;}{d_i})({\mathrm{\&epsiv;}}_{\mathrm{ri}}^{*}-\stackrel{\&OverBar;}{{\mathrm{\&epsiv;}}_{\mathrm{ri}}^{*}})}{\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{(d_i-\stackrel{\&OverBar;}{d_i})}^2}---\left(b\right)$

$B=\stackrel{\&OverBar;}{{\mathrm{\&epsiv;}}_{\mathrm{ri}}^{*}}-A\&times;\stackrel{\&OverBar;}{d_i}---\left(c\right)$

${\mathrm{\&epsiv;}}_{\mathrm{ri}}^{*}=\frac{\frac{{3\mathrm{h\&alpha;}}^3(L_0-e)}{{3\mathrm{\&alpha;}}^3(L_0-m)m^2+{3\mathrm{\&alpha;}}^3{(L_0-m)}^{2}m+{\mathrm{\&alpha;}}^3{m}^3+{(L_0-m)}^3}}{\frac{{3\mathrm{h\&alpha;}}^3(L_0+{\mathrm{\&delta;}}_i-e)}{{3\mathrm{\&alpha;}}^3(L_0+{\mathrm{\&delta;}}_i-m)m^2+{3\mathrm{\&alpha;}}^3{(L_0+{\mathrm{\&delta;}}_i-m)}^{2}m+{\mathrm{\&alpha;}}^3{m}^3+{(L_0+{\mathrm{\&delta;}}_i-m)}^3}}{\mathrm{\&epsiv;}}_{\mathrm{ri}}---\left(d\right)$

${\mathrm{\&delta;}}_i=\frac{d_i-d_0}{2}---\left(e\right)$

Formula (b) and (c) in, n represents the number of standard cylinder, d _irepresent the diameter value of different-diameter standard cylinder, the diameter value d of each standard cylinder _iarithmetical mean, represent that with diameter value be d _idata collecting instrument reading ε corresponding to standard cylinder _rimodified value, each reading ε of data collecting instrument _rimodified value arithmetical mean; In formula (d), h represents left Cantilever Beams of Variable Cross Section B ₁with right Cantilever Beams of Variable Cross Section B ₂the thickness of neck ce section, α represents left Cantilever Beams of Variable Cross Section B ₁with right Cantilever Beams of Variable Cross Section B ₂the ratio of the thickness h of the thickness H of head ac section and neck ce section, L ₀represent datum diameter rule and measure the contact point that clamps cutting edge to left Cantilever Beams of Variable Cross Section B ₁with right Cantilever Beams of Variable Cross Section B ₂the distance of root section e, e represents strain ga(u)ge R ₁, R ₂, R ₃and R ₄central point to left Cantilever Beams of Variable Cross Section B ₁with right Cantilever Beams of Variable Cross Section B ₂the distance of root section e, m represents left Cantilever Beams of Variable Cross Section B ₁with right Cantilever Beams of Variable Cross Section B ₂the length of neck ce section, δ _iexpression diameter value is d _istandard cylinder with measure clamping cutting edge contact point with respect to L ₀the displacement producing, i.e. contact side-play amount;

3) diameter measurement: measurement mechanism is arranged on to fracture (19) upper through the tension failure sample (18) engaging, by the full-bridge circuit access data Acquisition Instrument of sensor (1), the reading strain ε of record data Acquisition Instrument _r, by formula (f), (g) with (h) calculate the diameter d of sample:

$d=d_0+\frac{1}{2}(s-\frac{1}{\mathrm{\&Omega;}}-d_0)-\frac{1}{2}\sqrt{{(s-\frac{1}{\mathrm{\&Omega;}}-d_0)}^2+\frac{4}{\mathrm{\&Omega;}}(\frac{{\mathrm{\&epsiv;}}_r-B}{A}-d_0)}---\left(f\right)$

$\mathrm{\&Omega;}=\frac{{3\mathrm{h\&alpha;}}^3-\mathrm{\&eta;}({3\mathrm{\&alpha;}}^3{m}^2+{6\mathrm{\&alpha;}}^3(L_0-m)m+3{(L_0-m)}^2)}{{6\mathrm{h\&alpha;}}^3(L_0-e)}---\left(g\right)$

$\mathrm{\&eta;}=\frac{{3\mathrm{h\&alpha;}}^3(L_0-e)}{{3\mathrm{\&alpha;}}^3(L_0-m)m^2+{3\mathrm{\&alpha;}}^3{(L_0-m)}^{2}m+{\mathrm{\&alpha;}}^3{m}^3+{(L_0-m)}^3}---\left(h\right).$

3. the measuring method of contracting position, footpath minimum diameter measurement mechanism after tensile sample fracture according to claim 2, it is characterized in that described tension failure sample (18) comprises tension failure sample, the variable cross section pure bending fatigue testing specimen of material mechanical performance test, and bus be curve non-uniform shaft and Step Shaft axial workpiece.