CN102539235A - Method for measuring elasticity modulus of papermaking plant fibers - Google Patents

Abstract

The invention discloses a method for measuring the elasticity modulus of papermaking plant fibers. Fibers are symmetrically suspended on a support point of a measurement table board, a measurement model can be established by deformation caused by self weight of the fibers, a coordinate system is built with the support point as a coordinate origin, the horizontal plane direction passing through the support point can be set as the X axis, the vertical plane perpendicular to the support point is set as the Y axis, an image collection device and image processing software are adopted, a bending moment formula of any section of material mechanics bending moment definition, a deflection line formula and a boundary condition are combined to perform two infinitesimal calculus on the X axis through bending moment of all points, flexibility (Flex) is achieved, fiber inertia moment is calculated through an image method, and the elasticity modulus of the fiber can be obtained by calculation according to a rigidity definition formula. The measurement method overcomes limit of an existing measurement device, can measure softness and elasticity modulus of one single fiber, and is not prone to be blocked in measurement processes, free of fixing and strong in operation.

Description

A kind of method of measuring papermaking plant-fiber elastic modulus

Technical field

The present invention relates to the paper making raw material fibre property and measure, particularly relate to a kind of method of measuring papermaking plant-fiber elastic modulus.

Background technology

In field of papermaking, the raw material of page mainly is a vegetable fibre, so the performance of fiber and the performance after the sheet forming have very large correlativity.In the performance of page, the physical property of page such as tensile strength, pop strength, tear strength, dimensional stability, deflection and bulk etc., all directly related with the single fiber elastic performance that forms page.In the elastic performance of single fiber, elastic modulus is the emphasis of a concern.If known the elastic performance of single fiber, just can study physical property, dimensional stability and the deflection etc. of page smoothly.

In traditional material mechanical performance detected, the elastic modulus of fiber-like material all was to calculate through the data of measuring stress and strain with checkout equipments such as tensiometers.But because papermaking vegetable fibre too fine (about conventional long 1.5mm, about width 15 μ m), some present surveying instruments all can not be measured the elastic modulus of single fiber.

Summary of the invention

The objective of the invention is to overcome the deficiency of prior art, a kind of method of measuring papermaking plant-fiber elastic modulus is provided, this method is operated easily, and the result is accurate.

Measure the pliability of single fiber earlier, measure the moment of inertia of fiber again, at last through combining pliability and moment of inertia to calculate the elastic modulus of single fiber.

The object of the invention specifically is achieved through following proposal

(1) fiber is suspended on the fulcrum of measuring table top; With the fulcrum is true origin, will be made as the X axle through the surface level direction of fulcrum, is the Y axle perpendicular to the vertical plane of fulcrum; Set up coordinate system; Said fiber is even, continuous and isotropic platypelloid type material fiber, and the moment of flexure formula of fiber arbitrary section is identical with the moment of flexure formula (1) of the arbitrary section of mechanics of materials moment of flexure definition

$M\left(x\right)=-F(l-x)+\frac{1}{2}q{(l-x)}^2,---\left(1\right)$

The definition of Combining material mechanics deflection curve equation and boundary condition carry out integral operation with the moment of flexure of fiber each point to coordinate X axle again, obtain the pliability Flex numerical value of fiber,

$\mathrm{Flex}=\frac{\mathrm{kd}}{{\mathrm{cL}}^4}---\left(2\right)$

0≤x≤l wherein, l be behind the fiber bending not with measure the monolateral distance that table top contacts, k is a constant 1.176 * 10 ¹⁰, d is for measuring a spot diameter, and c is a fibre coarseness; L be fiber not with the distance of measuring between 2 that table top contacts;

(2) image method calculates the fiber moment of inertia: on the XZ plane fiber is carried out electron-microscope scanning, then in the YZ flat scanning, obtain the image of fibre section; With this image binaryzation, calculate the numerical value of moment of inertia I more then;

(3) according to rigidity definition, fiber flexibility numerical value that aforementioned two steps are obtained and moment of inertia numerical value carry out differentiate again behind the product, promptly obtain the numerical value of fiber isotropic modulus.

Said L obtains the analog image of fiber through image collecting device, by image pick-up card the analog image that collects is converted into digital picture through the A/D transition card then, measures with image measurement software again.

Step distance is set to 0.12 μ m during said electron-microscope scanning.

Said binaryzation process is set to 0 or 255 for the gray-scale value of image slices vegetarian refreshments.

Said image method calculates the fiber moment of inertia and adopts Split Method, enthesis or utilize the position of fibre section related pixel point to calculate.

The concrete computation process that in the coordinate system of having set up, obtains pliability by the moment of flexure integral operation is:

Have according to mechanics of materials line of deflection formula definition:

$\frac{d^2\mathrm{<figure-callout\; id="2"\; label="y\; dx"\; filenames="HDA0000111870670000021.png"\; state="\{\{state\}\}">y</figure-callout>}}{{\mathrm{dx}}^{}}=-\frac{M\left(x\right)}{\mathrm{EI}}=-\frac{-F(l-x)+\frac{1}{2}q{(l-x)}^2}{\mathrm{EI}}---\left(3\right)$

The following formula integration obtains:

$\mathrm{EI}\frac{\mathrm{dy}}{\mathrm{dx}}=-\frac{1}{6}{\mathrm{qx}}^3+\frac{1}{2}(\mathrm{ql}-F)x^2+l(F-\frac{1}{2}\mathrm{ql})x+C---\left(4\right)$

$\mathrm{EIy}=-\frac{1}{24}{\mathrm{<figure-callout\; id="4"\; label="qx"\; filenames="HDA0000111870670000021.png"\; state="\{\{state\}\}">qx</figure-callout>}}^4+\frac{1}{6}(\mathrm{ql}-F)x^3+\frac{1}{2}l(F-\frac{1}{2}\mathrm{ql})x^2+\mathrm{Cx}+D---\left(5\right)$

C, D are integration constant.

$x=0,\frac{\mathrm{Dy}}{\mathrm{Dx}}=0;$ $x=l,\frac{\mathrm{Dy}}{\mathrm{Dx}}=0$ Substitution formula (4) gets C=0; $F=\frac{\mathrm{Ql}}{3};$

X=0; Y=0 substitution formula (5) gets D=0.

Get C=0, D=0,

substitution formula (4)

$y=\frac{q}{72\mathrm{EI}}[-3x^4+8{\mathrm{lx}}^3-6l^2{x}^2]---\left(6\right)$

X=l again, y=-d, substitution formula (6) has $\mathrm{EI}=\frac{{\mathrm{<figure-callout\; id="4"\; label="Ql"\; filenames="HDA0000111870670000021.png"\; state="\{\{state\}\}">Ql</figure-callout>}}^4}{72d}---\left(7\right)$

The pliability of fiber, we refer to object when receiving vertical center line direction load usually, and the crooked situation of center line is represented with the inverse of rigidity EI in the mechanics of materials.Promptly

$\mathrm{Flex}=\frac{1}{\mathrm{EI}}---\left(8\right)$

Wushu (7) substitution (8) has

$\mathrm{Flex}=\frac{72d}{{\mathrm{ql}}^4}---\left(9\right)$

According to the definition of even cloth load q and fibre coarseness c, q is actual can be replaced with c, and fibre length is approximate regards 12 times as, and no matter whether its suspension is that symmetry hangs.

$\mathrm{Flex}=\frac{\mathrm{kd}}{{\mathrm{cL}}^4}---\left(2\right)$

In the formula: Flex---the pliability of fiber, N ^-1m ^-2K---constant 1.176 * 10 ¹⁰D---measure wire diameter, m; C---fibre coarseness, mg/100m; L---fiber and the distance of measuring between 2 that table top contact, m is similar to and thinks L=2l.

Other parameter of computation process is: M---moment of flexure, Nm; EI---rigidity, Nm ²L---the monolateral distance that does not contact behind the fiber bending, m with the measurement table top; X---the fiber each point in the coordinate system set up to the projector distance of initial point distance at the X axle, m; C, D---be integration constant.

Moment of inertia is a physical quantity, is used as an object opposing twisting, the ability of reversing described usually.

Because of fiber cross section is an irregular cross section, fiber moment of inertia of the present invention is to utilize the position of related pixel point to calculate.Computing formula is following:

$I=\mathrm{\&Sigma;}{I}_i=\mathrm{\&Sigma;}(\frac{{\mathrm{ab}}^3}{12}+A_i{x}^2)---\left(10\right)$

A and b are respectively the wide of pixel and long, and Ai is the area of pixel, and x is the distance of pixel i to neutral flexure plane.

Record after the moment of inertia of fiber, the fiber flexibility numerical value of convolution (2) again can obtain the numerical value of fiber isotropic modulus, and its computing formula is suc as formula shown in (11).

$E=\frac{1}{\mathrm{FlexgI}}---\left(11\right)$

Compared with prior art, the present invention has the following advantages:

(1) the present invention is through measuring the pliability of fiber, and the combining image computing method obtains the moment of inertia of fiber again, and combines the rigidity defined formula, and the elastic modulus that obtains fiber of ability scientific quantitative analysis has overcome the limitation that existing instrument is measured single fiber;

(2) the present invention can measure the pliability and the elastic modulus of single fiber, is difficult for blocking, and need not fix;

(3) utilize the inventive method can obtain the elastic mould value of fiber, thereby for the page mechanics property analysis provides foundation, and can be used for result of use evaluation like auxiliary agents such as softening agents;

(4) measuring method of the present invention is simple, and existing measurement mechanism can be accomplished fiber flexibility and measure, easy operating.

Description of drawings

Fig. 1 is suspended on the illustraton of model on the steel wire in the measuring method of the present invention with fiber;

Fig. 2 is the fiber force analysis figure to model shown in Figure 1;

Fig. 3 measures the Experimental equipment of pliability for the present invention;

Fig. 4 is the scintigram of masson pine NBSK fibre section among the embodiment 1.

Embodiment

Below in conjunction with embodiment and accompanying drawing, the present invention is done further detailed description, but embodiment of the present invention is not limited thereto.

The foundation of measuring system

(1) measuring system is formed

For the contact situation of correct display fibers with glass, correct measurement, the present invention makes up measuring system on the basis based on Digital Image Processing, as shown in Figure 3.This system mainly is made up of micro magnifier 4, wave carrier piece 2, filter 3, light source 1, CCD camera 5 and computing machine 6.

(2) measure flow process

The fiber that will measure is diluted with water to about 2%, drips to dropper to be fixed with on the diameter 44 μ m wave carrier piece 2 wiry, and fiber is suspended on the tinsel, is placed in the exsiccator drying at room temperature 7 hours then.

Utilize the deformation of fiber own wt effect to set up analytical model, to observe the correlation parameter in the pliability calculating process intuitively.Set up coordinate system earlier, as shown in Figure 1, be true origin with the fulcrum; To be made as the x axle through the surface level direction of fulcrum, be the Y axle perpendicular to the vertical plane of fulcrum, sets up coordinate system; If the stressed left-right symmetric of fiber distributes, and is true origin with the A point, the axis of orientation that is parallel to glass through the A point is the X axle; Set up coordinate perpendicular to the axis of orientation of glass for the y axle through the A point, the stressing conditions of fiber is as shown in Figure 2.In conjunction with the correlation parameter of fiber in this coordinate system, carry out pliability and calculate.

Utilize the cross section formula $M\left(x\right)=-F(l-x)+\frac{1}{2}q{(l-x)}^2,(0\&le;x\&le;l),$ In conjunction with line of deflection definition and boundary condition, the moment of flexure of fiber each point is carried out integral operation to coordinate X axle, obtain the numerical value of the softness index Flex of fiber, $\mathrm{Flex}=\frac{\mathrm{<figure-callout\; id="4"\; label="Kd\; CL"\; filenames="HDA0000111870670000021.png"\; state="\{\{state\}\}">Kd</figure-callout>}}{{\mathrm{CL}}^{}}.$

Wherein c is a fibre coarseness, and L ' is the fiber length overall; Q is an evenly load, is the deadweight (mg) of fiber and the ratio of length, that is: q=mg/L '; D is a diameter wiry, 44 μ m; F is the reacting force of B point glass to fiber; EI is a bendind rigidity.

After system's adjustment, be placed on ready fiber on the test desk, open light source 1 illumination; Choose suitable zone and best focal length measurement through the display of computing machine 6; Fibre image on the wave carrier piece 2 after filter 3 filters after CCD camera 5 is caught, is gathered analog image by the image pick-up card in the computing machine 6 after micro magnifier 4 amplifies; Again the analog image that collects is passed through the digitizing of A/D transition card; After transferring digital picture to, carry out the L value with image measurement software (the Image Viewer software of OLYMPUS) and measure, to obtain net result.

Embodiment 1

Step 1 is measured pliability

(1) experimental raw

The fiber that experiment is used is the masson pine fiber, takes from the paper mill, Guangzhou.

(2) pliability is measured

Masson pine NBSK fiber is carried out handled by above-mentioned measurement flow process, place on request then on the test desk, start measuring system, the L value that obtains fiber through image software is 468.67 μ m.

The NBSK fibre morphology is: number average length 1.01mm, weight average length 2.01mm, heavy equal length 2.62mm; Width 8.90 μ m; Rugosity 20.10mg/100m.

With the above-mentioned pliability formula of measured data substitution, can obtain the pliability numerical value of fiber.The pliability measurement result is as shown in table 1.

Table 1

Step 2 is measured the moment of inertia of fiber

In order to improve the comparative of measurement, the first red fuel with 0.1% of masson pine NBSK fiber was soaked room temperature 24 hours, use filter paper filtering then.Image scans with Leica TCS confocal laser scanning Electronic Speculum earlier.Scanning is carried out on the XZ plane, and the step distance of scanning is set to 0.12 μ m.Come flat scanning with CLSM, can obtain the image of fibre section YZ, as shown in Figure 4.Image is handled with the Flame Image Process tool box of Matlab 7.0 (Mathworks Inc.) after obtaining.Image elder generation binaryzation is about to gradation of image and is set to 0, and entire image presents tangible black and white effect, and then according to its moment of inertia of related pixel point position calculation of masson pine NBSK fibre section.In CAD2007 with the inquiry in the tool command-face territory/mass property, input masprop order can in the hope of.The moment of inertia computing formula is following

$I=\mathrm{\&Sigma;}{I}_i=\mathrm{\&Sigma;}(\frac{{\mathrm{ab}}^3}{12}+A_i{x}^2)$

A and b are respectively the wide of pixel and long, and Ai is the area of pixel, and x is the distance of pixel i to neutral flexure plane.

The result of calculation of moment of inertia numerical value is as shown in table 2.

Table 2

Step 3 is calculated the elastic modulus of fiber

According to formula (11), calculate the numerical value of fiber isotropic modulus:

$E=\frac{1}{\mathrm{FlexgI}}=1/(1.8743\&times;24.51)=2.17\mathrm{GP}$

As stated, can realize preferably that just the present invention, the foregoing description are merely preferred embodiment of the present invention, be not to be used for limiting practical range of the present invention; Be that all equalizations of doing according to content of the present invention change and modification, all contained by claim of the present invention scope required for protection.

Claims (5)

1. measure the method for paper-making fibre elastic modulus, it is characterized in that step is following:

(1) fiber being suspended on the fulcrum of measuring table top, is true origin with the fulcrum, will be made as the X axle through the surface level direction of fulcrum, is the Y axle perpendicular to the vertical plane of fulcrum, sets up coordinate system; Said fiber is even, continuous and isotropic platypelloid type material fiber,

The definition of Combining material mechanics deflection curve equation and boundary condition carry out integral operation with the moment of flexure of fiber each point to coordinate X axle, obtain fiber flexibility FlexNumerical value,

（1）

Wherein k is a constant 1.176 * 10 ¹⁰, d is for measuring a spot diameter, and c is a fibre coarseness; L be fiber not with the distance of measuring between 2 that table top contacts;

(2) image method calculates the fiber moment of inertia: on the XZ plane fiber is carried out electron-microscope scanning, then in the YZ flat scanning, obtain the image of fibre section; With this image binaryzation, calculate moment of inertia more then INumerical value;

(3) according to rigidity definition, fiber flexibility numerical value that aforementioned two steps are obtained and moment of inertia numerical value carry out differentiate again behind the product, promptly obtain the numerical value of fiber isotropic modulus.

2. method according to claim 1; It is characterized in that said L obtains the analog image of fiber through image collecting device; By image pick-up card the analog image that collects is converted into digital picture through the A/D transition card then, measures with image measurement software again.

3. method according to claim 1, step distance is set to 0.12mm when it is characterized in that said electron-microscope scanning.

4. according to the described method of one of claim 1 to 3, it is characterized in that said binaryzation process is set to 0 or 255 for the gray-scale value of image slices vegetarian refreshments.

5. method according to claim 4 is characterized in that said image method calculates the fiber moment of inertia and adopts Split Method, enthesis or utilize the position of fibre section related pixel point to calculate.

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