CN102879418A - Metal wire expansion coefficient measuring method - Google Patents
Metal wire expansion coefficient measuring method Download PDFInfo
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- CN102879418A CN102879418A CN2012103727856A CN201210372785A CN102879418A CN 102879418 A CN102879418 A CN 102879418A CN 2012103727856 A CN2012103727856 A CN 2012103727856A CN 201210372785 A CN201210372785 A CN 201210372785A CN 102879418 A CN102879418 A CN 102879418A
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Abstract
The invention relates to a metal wire expansion coefficient measuring method which includes steps of engraving grating fringe on a to-be-measured metal surface by means of grating engraving, acquiring a digital image of objective grating, making a reference grating, acquiring a digital image of the expanded objective grating, superposing the digital image of the reference grating and the digital image of the objective grating to obtain a first moire fringe, superposing the digital image of the reference grating and the expanded objective grating to obtain a second moire fringe, refining the first moire fringe and the second moire fringe by Fourier transform, filter treatment and extremum method to obtain a first refined isochromatic fringe and a second refined isochromatic fringe which is generated from the second moire fringe correspondingly, calculating slope and inclination of the corresponding isochromatic fringe by the least square method to obtain the variable of the inclination of the corresponding isochromatic fringe relative to an X-axis of the measuring system due to change of temperature, then calculating the calibrated slope and calculating the dependent variable on the condition that the temperature is equal to T2, and finally calculating expansion coefficient of materials.
Description
Technical field
The present invention relates to a kind of measuring technique, be specifically related to a kind of measuring method for linear expansion coefficient.
Background technology
Present measurement to linear expansion coefficient, existing many ripe theory and methods, such as strain gauge method, manometer method, optical lever method, optical fibre displacement sensor method, interferometric method etc., but all there is certain bottleneck in these measuring methods, at first can not on-line measurement.Because above method must be made into material specific sample and be put in the surveying instrument and measure, and can't carry out on-line monitoring.Be exactly that optical lever method, interferometric method all require the size of measured material can not be too little in addition, and the large sample of size easily is subjected to the impact of extraneous factor, thereby the material of measuring and monitoring the growth of standing timber such as not making is heated evenly the accuracy that affects measurement result.In addition, above method can only measure one-dimensional square to linear expansion coefficient, the requirement that does not reach the linear expansion coefficient of measuring simultaneously two-dimensional directional.
Summary of the invention
The present invention provides a kind of method of utilizing the Moire fringe principle to measure linear expansion coefficient in order to overcome the deficiency of above technology.
This metal linear expansion coefficient measuring method, the method comprises the steps:
(1). scribe by grating at normal temperatures that means depict some its angles in metal surface to be measured and pedal line acute angle angle is the grating fringe of θ;
(2). the digital picture of the thing grating that under normal temperature T1, is formed by some grating fringes by camera CCD shooting, collecting;
(3). the thing Grating Digital image of shooting, collecting is obtained its mirror image by computer software the digital picture of the reference grating of pedal line symmetry relative to the thing grating;
(4). be the digital picture of the thing grating after the expansion that is formed by some grating fringes by camera CCD shooting, collecting under the T2 with METAL HEATING PROCESS to temperature;
(5). the digital picture with reference to grating and thing grating superposes mutually, obtains Moire fringe one;
(6). the digital picture with reference to the thing grating after grating and the expansion superposes mutually, obtains Moire fringe two;
(7). the Moire fringe one and the Moire fringe two that obtain are carried out Fourier transform, filtering processing, obtain the equal difference striped one that is formed by Moire fringe one and the equal difference striped two that is formed by Moire fringe two;
(8). equal difference striped one and equal difference striped two are carried out thinning processing by extremum method, the equal difference striped two after the equal difference striped one after the refinement that obtains being formed by equal difference striped one and the refinement that formed by equal difference striped two;
(9). the equal difference striped one after the refinement and the equal difference striped two after the refinement are calculated respectively slope and the inclination angle of equal difference striped separately by least square method, with the stripe direction of the equal difference striped one after the refinement as the measuring system X-direction, the inclination angle of the equal difference striped two after the refinement and the equal difference striped one after the refinement is subtracted each other, obtain relevant temperature and change the equal difference stripe angle cause with respect to this variable of measuring system X-axis
And the slope after the calibration
(10). according to formula
, namely
Dependent variable when calculating temperature and being T2
(11). according to formula
Calculate the linear expansion coefficient of material
Calculate linear expansion coefficient for fear of taking the dependent variable according to a temperature change amount is obtained
The larger situation of the error that causes occurs, and progressively calculates dependent variable under several condition of different temperatures with identical temperature variation
, and take temperature T as horizontal ordinate, dependent variable
For ordinate obtains a strain-temperature curve, utilize least square method that curve is carried out rate of curve after linear fit is calculated match, according to formula
, this slope is the linear expansion coefficient of material in the relevant temperature scope
The too small meeting in θ angle makes actual measurement be difficult for realizing in the practical application, θ crosses at the angle that inclination angle change amount that conference makes equal difference striped two is too small and so that measurement effect is bad, therefore the angle theta span of above-mentioned grating fringe and pedal line is less than or equal to 10 ° more than or equal to 1 °.
Measure more convenient and smartly in order to make, above-mentioned image with reference to grating and thing grating superposes mutually, carry out thinning processing with reference to the extremum method that the thing grating after grating and the expansion superposes mutually, Moire fringe one and Moire fringe two carry out Fourier transform, filtering processing and equal difference striped one and equal difference striped two can utilize computer software to process.
Above-mentioned computer software is MATLAB software.
The invention has the beneficial effects as follows: compare and measure the method for expansion coefficients of metal wire in the past, deficiency such as manometer method, interferometric method etc., this metal linear expansion coefficient measuring method utilize Moire fringe striped principle by gather the thing grating and expand after the thing grating raster image, make the raster image with reference to grating, will finally calculate the linear expansion coefficient of metal according to equal difference stripe angle change amount by modes such as image stack, Fourier transform, filtering processing, extremum method refinements afterwards.It compares in the past, and the maximum of slotted line expansion coefficient method changes shape and the size that has been to change sample, can adopt small size, sheet sample to scribe grating or directly grating is engraved on the outside surface of required monitoring component, thereby can realize the characteristics such as on-line measurement, two-dimensional measurement and measuring equipment miniaturization.And the metal material smaller volume of using in the measuring process can be beneficial to realize the homogeneous heating of metal material.
Description of drawings
Fig. 1 is that grating constant is the reference grating of d;
Fig. 2 is that grating constant is the thing grating of d;
Fig. 3 is that grating constant is the thing grating after the expansion of d ';
Fig. 4 is the moiré topography of Fig. 1 and the superimposed formation of Fig. 2;
Fig. 5 is the moiré topography of Fig. 1 and the superimposed formation of Fig. 3;
Fig. 6 is the reference grating of copper product;
Fig. 7 is the thing grating of copper product;
Fig. 8 is the thing grating after the expansion of copper product;
Fig. 9 is the moiré topography of Fig. 6 and the superimposed formation of Fig. 7;
Figure 10 is the moiré topography of Fig. 6 and the superimposed formation of Fig. 8;
Figure 11 is the isodiff bar graph of Fig. 9;
Figure 12 is the isodiff bar graph of Figure 10;
Figure 13 is the isodiff bar graph after Figure 11 adopts the extremum method refinement;
Figure 14 is the isodiff bar graph after Figure 12 adopts the extremum method refinement;
Figure 15 is the measurement curve map of the dependent variable-temperature of copper;
Figure 16 is the measurement curve map of the dependent variable-temperature of iron;
Embodiment
The present invention will be further described to accompanying drawing 16 below in conjunction with accompanying drawing 1.
According to the thermal expansion metal principle, be located at temperature and be
The time detected sample length be
, in temperature be
The time detected sample length be
Experiment points out, when range of temperature is little, and the elongation △ of solid
=
-
Variable quantity with temperature
And the initial length of sample
Be directly proportional.That is:
Δ
=
·
·Δ
That is:
=Δ
/
/ Δ
Scale-up factor in the formula
The linear expansion coefficient that is called solid.
Because measuring at present the measuring object of linear expansion coefficient method is the whole expanded by heating amount of material, therefore cause sample and measurement mechanism size larger.According to the principle of thermal expansion metal, in conjunction with the theory of Moire fringe, we reflect the whole expanded by heating amount of material by the variation that material surface adheres to the grating constant of grating, namely can reflect by the measurement of detail section whole variation.As shown in Figure 1, with grating constant be the cosine grating of d as the reference grating, make grating fringe and y axle clamp angle be-θ.As shown in Figure 2, other uses cosine grating with equal-specification as the thing grating, and grating constant also is d, but striped and y axle clamp angle are θ.After the thing grating was because of expanded by heating, grating constant became the grating of d ' as the thing grating after expanding as shown in Figure 3, and its striped and y axle clamp angle still are θ.Sample because of the grating constant swell increment that expanded by heating causes its surperficial thing grating to produce is with this understanding
, according to the thermal expansion metal principle, this grating constant swell increment
Grating constant initial value d and temperature variation during with normal temperature
Also proportional, namely
The present invention that Here it is utilizes the characteristic of grating and Moire fringe to measure the basis of the linear expansion coefficient of material.
According to the principle of expansion of metal, in conjunction with the knowwhy of Moire fringe, we change the thermal expansion amount of material to reflect by the grating constant that material surface adheres to grating.As shown in Figure 1, with grating constant be the cosine grating of d as the reference grating, make grating fringe and y axle clamp angle be-θ.As shown in Figure 2, other uses cosine grating with equal-specification as the thing grating, and grating constant also is d, but striped and y axle clamp angle are θ.After the thing grating was because of expanded by heating, grating constant became the grating of d ' as the thing grating after expanding as shown in Figure 3, and its striped and y axle clamp angle still are θ.
Can write out the grating equation of above three gratings, be respectively:
Superimposed with reference to grating and thing grating, form Moire fringe one as shown in Figure 4.Superimposed with reference to the thing grating after grating and the expansion, form Moire fringe two as shown in Figure 5.
We can draw the isodiff equation of two Moire fringes according to above-mentioned three grating equations and accompanying drawing 4, accompanying drawing 5, are respectively:
Wherein:
,
, q and q ＇ are constant.Can find out by following formula, when the thing grating does not expand, it be one group of parallel stripes parallel with the x axle with reference to the formed isodiff of grating.After the thing grating expands, it and be one group of parallel stripes that tilts with reference to the formed isodiff of grating.Above-mentioned equation is out of shape:
Further aforesaid equation is carried out approximate processing, can obtain:
If the linear expansion coefficient of material is
, then it is in temperature change
The time strain be
So following formula becomes:
As can be seen from the above equation, this moment Moire fringe the slope of isodiff by experiment condition
,
And the linear expansion coefficient of material
The common decision.Derive and to get by above theory, the thermal expansion amount of material is reacted in the variation of grating constant, utilize the grating stack to form Moire fringe, pass through again the measurement to the slope of formed Moire fringe under the different temperatures, thereby can measure the thermal expansion strain of material under series of temperature, and then calculate its corresponding linear expansion coefficient.
According to above theoretical research, we can be that d, inclination angle are that the grating of θ is scribed means by grating and is inscribed in metal sample to be measured surface with grating constant, and can depict the demand that required many groups grating is measured to satisfy the two-dimensional line expansion coefficient according to different directions according to the needs of measuring.Can directly grating be utilized grating to scribe means to be inscribed in the detected materials surface in the situation that needs carry out on-line monitoring, and monitor at any time with camera CCD and just can realize measuring in real time online.
The inclination that might produce when taking the digital figure of each amplitude grating with camera CCD owing to camera CCD position causes the coordinate system of measuring system and the error between the sample surfaces optical-mechanical system coordinate system, so we need to carry out scale operation at this.Namely at room temperature gather raster image (with reference to grating and thing grating) first and carry out overlap-add procedure formation Moire fringe, extract isodiff, with this X-direction as measuring system.Again gather the image add the thing grating after the thermal expansion and form Moire fringe with carry out overlap-add procedure with reference to grating, extract isodiff.Will this moment the isodiff inclination angle deduct isodiff inclination angle under the room temperature, the inclination angle of gained namely is the variable quantity at the isodiff inclination angle that caused by material heat expansion.Calibration herein can reduce the difficulty that we regulate light path and camera CCD collection.By image processing software the Moire fringe after calibrating is processed at last, extracted the slope that the difference frequency striped obtains the equal difference striped, calculate the strain of material under this temperature variation.And then under different temperature, carry out duplicate measurements, then can obtain strain and the temperature change the relationship between quantities of material in certain temperature range, thereby obtain the linear expansion coefficient of material in this temperature range.
For the correctness of verifying above theory and the feasibility of measurement scheme, the copper product that we at first choose under the room temperature is measuring object.Scribing means by grating at first at normal temperatures, depict some its angles and pedal line acute angle angle on the surface of copper product to be measured be 5 ° grating fringe.The digital picture of the thing grating as shown in Figure 7 that is formed by some grating fringes by camera CCD shooting, collecting when being 29 ℃ of room temperatures in the measuring basis temperature.And the thing Grating Digital image of shooting, collecting is obtained its mirror image by computer software the reference grating as shown in Figure 6 of pedal line symmetry relative to the thing grating.Be 79 ℃ of lower digital pictures by the thing grating as shown in Figure 8 after the expansion of camera CCD shooting, collecting in temperature afterwards.In order to raise the efficiency and to be convenient for measuring, can use MATLAB software to the image that collects carry out noise reduction, cut out, be inverted, strengthen, stack, Fourier's variation, filtering, extraction difference frequency, normalized processing.
Reference grating shown in accompanying drawing 6 and the accompanying drawing 7 and thing grating after stack, are obtained Moire fringe one as shown in Figure 9, with the reference grating shown in accompanying drawing 6 and the accompanying drawing 8 and the thing grating after expanding after stack, obtain Moire fringe two as shown in Figure 10.
The Moire fringe one and the Moire fringe two that respectively stack are formed carry out Fourier Tranform again, filtering, extract equal difference striped one shown in the accompanying drawing 11 that obtains being formed by Moire fringe one and the accompanying drawing 12 that formed by Moire fringe two shown in equal difference striped two.Then extract by column the position coordinates of each fringe gray level value maximum point, and the coordinate of this point preserved into other piece image again with gray-scale value, so just can be refined as binary image (the method is referred to as extremum method) with being similar to the equal difference striped that the cosine rule distributes, and the equal difference striped two after the refinement shown in the equal difference striped one after the refinement shown in the accompanying drawing 13 that finally obtains being formed by equal difference striped one and the accompanying drawing 14 that formed by equal difference striped two.
Equal difference striped one and equal difference striped two are calculated respectively slope and the inclination angle of equal difference striped separately by least square method.Learn that according to above-mentioned theory research formula the isodiff of the Moire fringe one that accompanying drawing 6 and accompanying drawing 7 stacks form is as the X-axis of measuring system, namely in measuring system, should be horizontal direction, and the isodiff of the Moire fringe two that accompanying drawing 6 and accompanying drawing 8 stacks form should produce certain inclination angle on the basis of the isodiff of Moire fringe one and changes.We need calibration at this, namely with the stripe direction of the equal difference striped one shown in the accompanying drawing 13 as the measuring system X-direction, the inclination angle of equal difference striped one shown in equal difference striped two shown in the accompanying drawing 14 and the accompanying drawing 13 is subtracted each other, obtain relevant temperature and change the equal difference striped cause with respect to the inclination angle change amount of measuring system X-axis
According to formula
, the slope of equal difference striped after namely calibrating
Dependent variable when calculating temperature and being 79 ℃
Finally according to formula
Calculate the linear expansion coefficient of material
The linear expansion coefficient of the copper product that obtains by said method is because it calculates net result according to a temperature variation, it is larger that this result is affected by extraneous enchancement factor, for the linear expansion coefficient of the copper product that makes final calculating accurate, we are with 79 ℃ of initial temperatures, and temperature increment is 10 ℃ of dependent variables that progressively calculate under several condition of different temperatures
, and take temperature T as horizontal ordinate, dependent variable
For ordinate obtains a strain-temperature curve, utilize least square method that curve is carried out rate of curve after linear fit is calculated match, according to formula
, this slope is the linear expansion coefficient of material in the relevant temperature scope
The data list that records is as follows:
The analogue measurement data of the dependent variable-temperature of table 1 copper
| Temperature T (℃) | Dependent variable △ d/d |
| ?79 | 0.000834642 |
| ?89 | 0.00100262 |
| 99 | 0.001172348 |
| 109 | 0.001342076 |
| 119 | 0.001513554 |
| 129 | 0.001692031 |
| 139 | 0.001842512 |
| 149 | 0.002026238 |
| 159 | 0.002180218 |
| 169 | 0.002362194 |
| 179 | 0.002566918 |
| 189 | 0.002668405 |
| 199 | 0.002846882 |
| 209 | 0.00301136 |
| 219 | 0.003219583 |
| 229 | 0.003377063 |
Finally obtain as shown in Figure 15 strain-temperature curve according to the numerical value of table one, by utilizing least square method that curve is carried out rate of curve after match is calculated in match, the formula that utilizes least square method to carry out curve fitting is: and then the linear expansion coefficient that obtains analogue measurement copper product in this temperature range is: 1.687*10
-5℃
-1
We are 1.7*10-5 ℃-1 according to the linear expansion coefficient that inspection information obtains copper product.Therefore relative error is: n=(1.7-1.687) * 10
-5/ 1.7*10
-5=0.7647%.
In addition, can be used for various materials in order to verify this technology, (its Molded Line expansion coefficient is: 1.2*10 to iron to adopt this measuring technique
-5℃
-1) measurement result as follows.
The analogue measurement data of the dependent variable-temperature of table 2 iron
| Temperature T (℃) | Dependent variable △ d/d |
| 79 | 0.000594923 |
| 89 | 0.000682412 |
| 99 | 0.000804896 |
| 109 | 0.000909882 |
| 119 | 0.001049864 |
| 129 | 0.001154851 |
| 139 | 0.001259837 |
| 149 | 0.001382321 |
| 159 | 0.001504805 |
| 169 | 0.001609792 |
| 179 | 0.001749774 |
| 189 | 0.001837262 |
| 199 | 0.001924751 |
| 209 | 0.002064733 |
| 219 | 0.002204715 |
| 229 | 0.002309701 |
Finally obtain the strain-temperature curve of ferrous metal as shown in Figure 16 according to the numerical value of table two, by utilizing least square method curve is carried out rate of curve after match is calculated in match.The formula that utilizes least square method to carry out curve fitting is: and then obtain that the linear expansion coefficient of analogue measurement iron material is in this temperature range: 1.1495*10
-5℃
-1
Relative error is: n=(1.2-1.1495) * 10
-5/ 1.2*10
-5=4.208%.
We can draw according to above experimental result: this new linear expansion coefficient measuring technique can satisfy the linear expansion coefficient of metal material and measure.
Because this technology adopts and scribes grating on the measured material surface, and with this grating in the different phase of measuring respectively as with reference to the thing grating after grating, thing grating and the expansion, therefore can avoid making on the one hand the error effect that a plurality of gratings bring, can also be by the error of calibration technology removal system coordinate system location.The most important thing is to make the required area of grating very I satisfy the requirement of measuring miniaturization avoiding making the inhomogeneous factor of heating that the large scale sample brings; Can also scribe the grating of different directions to realize the measurement requirement of two-dimensional line expansion coefficient at sample surfaces as required; Upper grating directly can be scribed as sensor in the surface of expanded by heating monitoring component at last, avoid making separately sample, can satisfy the requirement of on-line measurement.
Claims (5)
1. metal material linear expansion coefficient measuring method, the method comprises the steps:
(1). scribe by grating at normal temperatures that means depict some its angles in metal surface to be measured and pedal line acute angle angle is the grating fringe of θ;
(2). the digital picture of the thing grating that under normal temperature T1, is formed by some grating fringes by camera CCD shooting, collecting;
(3). the thing Grating Digital image of shooting, collecting is obtained its mirror image by computer software the digital picture of the reference grating of pedal line symmetry relative to the thing grating;
(4). be the digital picture of the thing grating after the expansion that is formed by some grating fringes by camera CCD shooting, collecting under the T2 with METAL HEATING PROCESS to temperature;
(5). the digital picture with reference to grating and thing grating superposes mutually, obtains Moire fringe one;
(6). the digital picture with reference to the thing grating after grating and the expansion superposes mutually, obtains Moire fringe two;
(7). the Moire fringe one and the Moire fringe two that obtain are carried out Fourier transform, filtering processing, obtain the equal difference striped one that is formed by Moire fringe one and the equal difference striped two that is formed by Moire fringe two;
(8). equal difference striped one and equal difference striped two are carried out thinning processing by extremum method, the equal difference striped two after the equal difference striped one after the refinement that obtains being formed by equal difference striped one and the refinement that formed by equal difference striped two;
(9). the equal difference striped one after the refinement and the equal difference striped two after the refinement are calculated respectively slope and the inclination angle of equal difference striped separately by least square method, with the stripe direction of the equal difference striped one after the refinement as the measuring system X-direction, the inclination angle of the equal difference striped two after the refinement and the equal difference striped one after the refinement is subtracted each other, obtain relevant temperature and change the equal difference stripe angle cause with respect to this variable of measuring system X-axis
And the slope after the calibration
(10). according to formula
, namely
Dependent variable when calculating temperature and being T2
(11). according to formula
Calculate the linear expansion coefficient of material
2. metal material linear expansion coefficient measuring method according to claim 1 is characterized in that: progressively calculate dependent variable under several condition of different temperatures with identical temperature variation
, and take temperature T as horizontal ordinate, dependent variable
For ordinate obtains a strain-temperature curve, utilize least square method that curve is carried out rate of curve after linear fit calculates match, according to formula
, this slope is the linear expansion coefficient of material in the relevant temperature scope
3. metal material linear expansion coefficient measuring method according to claim 1 and 2 is characterized in that: the value of the angle theta of described grating fringe and pedal line more than or equal to 1 ° less than or equal to 10 °.
4. metal material linear expansion coefficient measuring method according to claim 3 is characterized in that: described image with reference to grating and thing grating superposes mutually, with reference to grating with expand after the extremum method that the thing grating superposes mutually, Moire fringe one and Moire fringe two carry out Fourier transform, filtering processing and equal difference striped one and equal difference striped two carry out thinning processing and can utilize computer software to process.
5. metal material linear expansion coefficient measuring method according to claim 4, it is characterized in that: described computer software is MATLAB software.
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| CN106198611A (en) * | 2016-06-24 | 2016-12-07 | 南京航空航天大学 | Composite panel thermal coefficient of expansion computational methods based on fibre strain transition matrix |
| CN106969701A (en) * | 2017-04-10 | 2017-07-21 | 广西交通科学研究院有限公司 | The modification method that temperature influences in strain testing |
| CN112639394A (en) * | 2018-08-21 | 2021-04-09 | 瓦锡兰芬兰有限公司 | Method and device for measuring height of tight allowance of sliding bearing |
| CN114646284A (en) * | 2022-03-16 | 2022-06-21 | 重庆邮电大学 | Temperature compensation method for geometric parameters of precision gear |
| US20230119864A1 (en) * | 2021-10-20 | 2023-04-20 | Industrial Technology Research Institute | Measuring method |
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| JP2009162562A (en) * | 2007-12-28 | 2009-07-23 | National Institute For Materials Science | Thermal expansion coefficient measurement method and apparatus for same |
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Cited By (8)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN106198611A (en) * | 2016-06-24 | 2016-12-07 | 南京航空航天大学 | Composite panel thermal coefficient of expansion computational methods based on fibre strain transition matrix |
| CN106198611B (en) * | 2016-06-24 | 2018-11-09 | 南京航空航天大学 | Composite panel coefficient of thermal expansion computational methods based on fibre strain transition matrix |
| CN106969701A (en) * | 2017-04-10 | 2017-07-21 | 广西交通科学研究院有限公司 | The modification method that temperature influences in strain testing |
| CN112639394A (en) * | 2018-08-21 | 2021-04-09 | 瓦锡兰芬兰有限公司 | Method and device for measuring height of tight allowance of sliding bearing |
| US20230119864A1 (en) * | 2021-10-20 | 2023-04-20 | Industrial Technology Research Institute | Measuring method |
| US11682179B2 (en) * | 2021-10-20 | 2023-06-20 | Industrial Technology Research Institute | Measuring method |
| CN114646284A (en) * | 2022-03-16 | 2022-06-21 | 重庆邮电大学 | Temperature compensation method for geometric parameters of precision gear |
| CN114646284B (en) * | 2022-03-16 | 2023-08-11 | 重庆邮电大学 | Temperature compensation method for geometric parameters of precise gear |
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