CN110241602B - Spiral grating density disc and method for measuring warp and weft density of fabric - Google Patents

Abstract

The invention discloses a spiral grating density disk and a method for measuring the warp and weft density of a fabric, wherein the spiral grating density disk comprises a colorless transparent substrate, and a plurality of inversely proportional spiral grating lines which are all formed by anticlockwise rotating around the same central origin are manufactured on the transparent substrate; in the process of anticlockwise rotation, the radial length of each grating line is gradually reduced; the rotation angle of the grating line positioned at the most center is 360 degrees, and the rotation angle of each other grating line is equal to or less than 360 degrees; the transparent substrate is also provided with a plurality of circles of scale circumferences concentric with the grating lines, and the outer sides of the scale circumferences are marked with linear scale lines vertical to the scale circumferences; when the spiral grating density disc is overlapped with the fabric and rotates relatively, a straight line reading stripe along the radial direction is displayed, and the scale value pointed by the straight line reading stripe on the corresponding scale circumference is the warp yarn density or weft yarn density of the fabric. The invention can quickly and conveniently measure the warp and weft density of the fabric and can ensure higher accuracy.

Description

A spiral grating density disc and a method for measuring the warp and weft density of fabrics

technical field

The invention belongs to the technical field of measuring equipment, and particularly relates to a spiral grating density disc and a method for measuring the warp and weft density of fabrics.

Background technique

The warp and weft density of textiles usually refers to the number of warp or weft yarns per centimeter or per inch of length (width) (the domestic standard is often expressed as the number of yarns within 10cm). The size of the density directly affects the physical and mechanical indicators such as the appearance, feel, thickness, strength, folding resistance, air permeability, wear resistance and thermal insulation performance of the fabric, and it is also related to the cost of the product and the level of production efficiency. The existing main methods for measuring the warp and weft density of fabrics are as follows: (1) Fabric decomposition method: that is, manually count the number of yarns after decomposing a fabric of a specified size. (2) Mobile fabric density mirror method: that is, using a mobile fabric density mirror, after magnifying the fabric in the field of view, count the number of yarns in a certain length, and then convert it to 10cm. (3) Computer software simulation analysis method: The warp and weft density is calculated by simulating the fabric surface structure through computer imaging and image recognition technology. (4) Slanted grating measurement method: Place the slanted grating densitometer (densitometer) on the fabric and turn to the yarn direction to display multiple sets of symmetrical patterns of inversely proportional curves similar to rhombus, and the scale at the position pointed by the sharp corner The number represents the warp (or weft) density number. The first three methods above have high measurement accuracy, but the cost of configuring instruments or labor is high, and the measurement speed is also slow. Although the fourth method has low instrument and labor costs, the scale on the slanted grating is non-uniform, and the moiré fringe distribution that appears is complex and scattered, and it is not easy to align the reading position, so the measurement accuracy is low. That is, there is a great contradiction between the accuracy of the existing measurement methods and the measurement cost.

SUMMARY OF THE INVENTION

Aiming at the defects and deficiencies in the prior art, the present invention provides a spiral grating density disc and a method for measuring the warp and weft density of fabrics, which overcome the defects of low measurement accuracy and high measurement cost in the existing fabric warp and weft density measurement methods.

To achieve the above object, the present invention adopts the following technical scheme:

The invention provides a helical grating density disk, comprising a transparent substrate, on which a plurality of inversely proportional helical grating lines are formed by rotating counterclockwise around the same central origin; during the counterclockwise rotation, The radial vector length of each grating line gradually decreases; the rotation angle of the grating line at the center is 360 degrees, and the rotation angle of the other grating lines is equal to or less than 360 degrees; There is a multi-circle scale circle concentric with the grating line, and a straight line scale line perpendicular to the scale circle is marked on the outside of the scale circle;

When the helical grating density disc overlaps with the fabric and rotates relatively, it will display a linear reading stripe along the radial direction, and the scale value indicated by the linear reading stripe on the corresponding scale circle is the fabric warp density or weft density.

The present invention also includes the following technical features:

其中，ρ为矢径长度，即光栅线上任一点与中心原点连线的长度；n为光栅线序号，从中心原点到边缘依次取值为n＝1，2，3，…；θ为极角，是矢径相对极轴逆时针旋转转过的角度(也即矢径与极轴的夹角)，θ取值在长度为2π的区间[θ₁,θ₂]内，θ₁为最小极角，θ₂＝θ₁+2π为最大极角；a为长度量，决定光栅线上各点矢径长度和相邻光栅线在同一极角方向上对应点矢径长度之差(即相邻光栅线在该极角方向上对应点的距离)，并与最小极角θ₁共同决定螺线光栅密度盘的量程。Specifically, the grating lines satisfy the following equation in the polar coordinate system:

Among them, ρ is the length of the vector radius, that is, the length of the line connecting any point on the grating line and the central origin; n is the serial number of the grating line, which is n=1, 2, 3, ... in order from the central origin to the edge; θ is the polar angle , is the counterclockwise rotation angle _of the vector radius relative to the polar axis (that is, the angle between the _vector radius and the polar axis ₎ . Angle, θ ₂ =θ ₁ +2π is the maximum polar angle; a is the length, which determines the difference between the length of each point on the grating line and the length of the corresponding point on the adjacent grating line in the same polar angle direction (that is, adjacent The distance between the grating lines in the polar angle direction corresponds to the point), and together with the minimum polar angle θ ₁ determines the range of the helical grating density disk.

Specifically, there are two scale circles, which are the inner circle scale circle and the outer circle scale circle, and a concentric circular line is also provided between the inner circle scale circle and the outer circle scale circle;

The radius of the scale circle of the inner ring is R, and the value range of the serial number of the grating line within the scale circle of the inner ring can be obtained according to the R value;

The radius of the scale circle of the outer ring is R ₂ , the radius of the circular line is R ₁ , and between the scale circle of the outer ring and the circular line is a grating line located in the annular zone, according to R ₁ and R ₂ The value can get the range of the serial number of the raster line located in the annular band.

与极角θ成反比，具有空间周期性。Specifically, the radii lengths of the corresponding points of each grating line in the same polar angular direction constitute an arithmetic sequence, that is, the corresponding points of any two adjacent grating lines in the same polar angular direction have the same spacing, both of which are

It is inversely proportional to the polar angle θ and has spatial periodicity.

Specifically, the self-width of the grating lines varies with the polar angle, and the widths in any polar angle direction are equal, which is equal to the corresponding point spacing of adjacent grating lines in the polar angle direction.

其中，D为刻度值；所述刻度值为公制或英制，单位为线数/厘米或线数/英寸；Specifically, the distribution law of the scale lines on the scale circle satisfies the equation:

Wherein, D is the scale value; the scale value is metric or imperial, and the unit is lines/cm or lines/inch;

The minimum scale value of the scale value is D ₁ , and the maximum scale value is D ₂ , respectively corresponding to the minimum polar angle θ ₁ and the maximum polar angle θ ₂ of the grating line; wherein,

的公式推导如下：Specifically, the distribution law equation of the scale lines on the scale circle

The formula is derived as follows:

即该点极坐标为

相邻两条光栅线的矢径长度之差为常量

When θ=θ ₀ is any fixed value, the radial vector length of the corresponding point of the grating line with serial number n in the direction of polar angle θ ₀ is

That is, the polar coordinates of the point are

The difference between the radial lengths of two adjacent raster lines is constant

处的切线，直线L4为与各切线垂直的法线方向的矢径；The curve L1 is the grating line, the straight line L2 is the vector radius in the direction of the polar angle θ ₀ , and the straight line L3 is the corresponding point of each grating line in the direction of the polar angle θ ₀

The tangent at , the straight line L4 is the vector radius of the normal direction perpendicular to each tangent;

The included angle between the straight line L4 and the polar axis is φ, the included angle between the straight line L4 and the straight line L2 is φ-θ ₀ , and the included angle between the straight line L3 and the straight line L2 is α;

处的切线方程为ρcos(θ-φ)＝nd，其中，n为切线序号，也为光栅线序号；A point on the raster line

The tangent equation at is ρcos(θ-φ)=nd, where n is the serial number of the tangent, which is also the serial number of the grating line;

该斜率与n值无关；d为相邻两条切线之间的距离，

螺线光栅密度盘与织物相对转动，直至光栅线的切线与织物的纱线重合时，得到纱线密度

The tangents are all parallel to each other and are equally spaced, and the slopes of the tangents are

The slope is independent of the value of n; d is the distance between two adjacent tangents,

The helical grating density disc rotates relative to the fabric until the tangent of the grating line coincides with the yarn of the fabric to obtain the yarn density

处的切线的间距时，使螺线光栅密度盘与织物相对转动，直至光栅线的切线与织物的纱线重合，则该θ₀方向上莫尔条纹空间频率为零，即莫尔条纹间距无穷大；则此处出现一条沿θ₀方向无限延伸的较宽的明条纹，即直线读数条纹；直线读数条纹在对应刻度圆周上所指刻度值

即为织物经纱或纬纱密度。Specifically, when the warp distance of the fabric is equal to the corresponding point of the grating line in the direction of θ ₀

When the distance between the tangent lines at θ 0 is set, the helical grating density disc and the fabric are rotated relatively until the tangent of the grating line coincides with the yarns of the fabric, then the spatial frequency of the moiré fringes in the θ ₀ direction is zero, that is, the moiré fringe spacing is infinite. ; then there is a wider bright stripe extending infinitely along the direction of θ ₀ , that is, the linear reading stripe; the linear reading stripe refers to the scale value on the corresponding scale circle

That is the fabric warp or weft density.

标定刻度；Specifically, according to the actual range

calibration scale;

上限为

That is, the lower limit of the range is

capped at

θ₁为下限D₁对应极角，θ₁+2π为上限D₂对应极角；根据此a和θ₁能画出光栅线。can be calculated

θ ₁ is the polar angle corresponding to the lower limit D ₁ , and θ ₁ +2π is the polar angle corresponding to the upper limit D ₂ ; according to this a and θ ₁ , the grating line can be drawn.

The present invention also provides a method for measuring the warp and weft density of fabrics. The measuring method adopts the spiral grating density disc to measure, and the steps of the measuring method are as follows:

Step 1: Cover the helical grating density disk on the fabric, and initially there will be a plurality of curved light and dark stripes near the direction approximately perpendicular to the warp (or weft) of the fabric;

Step 2: Then turn the helical grating density disk to gradually reduce the number of curved fringes, until finally only a wider bright fringe along the radial direction is displayed, that is, a straight reading fringe, which is on the scale circle. The scale value referred to is the fabric warp density or weft density.

Compared with the prior art, the present invention has the following beneficial technical effects:

(I) When the helical grating density disc of the present invention overlaps with the fabric and rotates relatively, it will display a linear reading stripe along the radial direction, and the scale value indicated by the linear reading stripe on the scale circle is the fabric warp density or Weft density, which can quickly and easily measure the warp and weft density of fabrics, while also ensuring high accuracy.

(II) The innovatively designed grating line type of the present invention makes the scale representing the density number approximately uniformly distributed with the angle, and the reading stripes present simple linear stripes and are concentrated in the reading area, so that the warp and weft density of the fabric can be read more accurately , which better balances the measurement cost and accuracy, and is a new measurement method that is economical, convenient and at the same time ensures better accuracy.

(III) In the helical grating density disc of the present invention, the angle at which stripes appear is approximately proportional to the latitude and longitude density, which can form a uniform scale, and within a certain range, the angular width of the stripes in all directions is basically the same, and there will be no increase in the latitude and longitude density. Larger, the smaller the stripe width, and the reading stripes are wider bright stripes along the radial direction, which is convenient for observation and improves the measurement accuracy; this spiral is printed or engraved as a grating and then covered on the fabric. A "spiral grating density disc" was made.

(IV) The measuring range of the helical grating density disc of the present invention is only related to the maximum and minimum polar angles, and has nothing to do with the size of the grating itself, so the required helical grating line can be drawn by arbitrarily setting the measuring range according to the actual measurement needs; It overcomes the disadvantage that the larger the range of the traditional oblique grating is, the larger the longitudinal size of the grating is.

(V) Since the grating line of the helical grating density disk of the present invention is an inversely proportional helical curve, the tangent direction of each point changes rapidly with the polar angle. Moiré fringes visible to the human eye. That is, the fringes only appear in the vicinity of the reading position, which avoids the interference fringes that affect the resolution of the reading position commonly existing in the traditional oblique grating densitometer.

Description of drawings

FIG. 1 is a schematic diagram of a grating line of the present invention.

FIG. 2 is a schematic diagram of the helical grating density disk in Embodiment 1 of the present invention.

FIG. 3 is a schematic diagram of a helical grating density disk in Embodiment 2 of the present invention.

4 is a schematic diagram of a helical grating density disk in Embodiment 3 of the present invention.

FIG. 5 is a schematic diagram showing the density of the fabric measured by the helical grating density disc in Example 4 of the present invention.

FIG. 6 is a schematic diagram of the density of the fabric measured by the helical grating density disc in Example 4 of the present invention.

FIG. 7 is a schematic diagram of the density of the fabric measured by the helical grating density disc in Example 5 of the present invention.

FIG. 8 is a schematic diagram of the density of the fabric measured by the helical grating density disc in Example 5 of the present invention.

FIG. 9 is a schematic diagram showing the density of the fabric measured by the helical grating density disc in Example 6 of the present invention.

FIG. 10 is a schematic diagram of the density of the fabric measured by the helical grating density disc in Example 7 of the present invention.

FIG. 11 is a schematic diagram of measuring the density of the fabric by the helical grating density disc in Example 8 of the present invention.

FIG. 12 is a schematic diagram of the density of the fabric measured by the helical grating density disc in Example 9 of the present invention.

The meaning of each symbol in the figure: 1- inner circle scale circumference, 2- outer circle scale circumference, 3-circular line.

Detailed ways

The invention provides a helical grating density disc, comprising a transparent substrate, on which a plurality of inversely proportional helical grating lines are formed by rotating counterclockwise around the same central origin; during the counterclockwise rotation, each The length of the vector radius of each grating line gradually decreases; the rotation angle of the grating line at the center is 360 degrees, and the rotation angle of other grating lines is equal to or less than 360 degrees; there is also a concentric grating line on the transparent substrate. When the helical grating density disc overlaps with the fabric and rotates relatively, it will display a linear reading stripe along the radial direction. The scale value indicated by the linear reading stripe on the scale circle is the fabric warp density or Weft density.

其中，ρ为矢径长度，即光栅线上任一点与中心原点连线的长度；n为光栅线序号，从中心原点到边缘依次取值为n＝1，2，3，…；θ为极角，是矢径相对极轴(X轴)逆时针旋转转过的角度(也即矢径与极轴的夹角)，θ取值在长度为2π的区间[θ₁,θ₂]内，θ₁为最小极角，θ₂＝θ₁+2π为最大极角；a为长度量，决定光栅线上各点矢径长度和相邻光栅线在同一极角方向上对应点矢径长度之差(即相邻光栅线在该极角方向上对应点的距离)，并与极角θ共同决定螺线光栅密度盘的量程；例如当θ取值在[2π,4π]时，对第i条螺旋线，矢径长度ρ的取值范围为

相邻两条光栅线的矢径长度之差为常量

量程为

近似为

Raster lines satisfy the following equations in polar coordinates:

Among them, ρ is the length of the vector radius, that is, the length of the line connecting any point on the grating line and the central origin; n is the serial number of the grating line, which is n=1, 2, 3, ... in order from the central origin to the edge; θ is the polar angle , is the counterclockwise rotation angle _of the vector radius relative to the polar axis (X axis) (that is, the angle between the vector radius and the polar axis ₎ . ₁ is the minimum polar angle, θ ₂ =θ ₁ +2π is the maximum polar angle; a is the length, which determines the difference between the length of each point on the grating line and the length of the corresponding point on the adjacent grating line in the same polar angle direction (that is, the distance between the corresponding points of adjacent grating lines in the polar angle direction), and together with the polar angle θ to determine the range of the helical grating density disk; for example, when the value of θ is [2π, 4π], for the i-th Spiral line, the value range of the length ρ of the vector radius is

The difference between the radial lengths of two adjacent raster lines is constant

The range is

approximately

In this embodiment, the scale circle has two circles, namely the inner circle scale circle and the outer circle scale circle, and a concentric circular line is also provided between the inner circle scale circle and the outer circle scale circle; the radius of the inner circle scale circle is is R, and the value range of the serial number of the grating line within the scale circle of the inner ring can be obtained according to the R value: the value range of the serial number of the grating line within the scale circle of the inner circle is n=1,2,...,n _max ; the serial number n The range of polar angle of the grating line is θ∈[θ _min ,θ _max ];

有

可得

光栅线的序号应为整数，故实际应舍去计算结果中的小数部分，取整为

Let the intersection point of the grating line with the serial number n _max and the inner ring scale circle of radius R be

Have

Available

The serial number of the raster line should be an integer, so the decimal part in the calculation result should be discarded, and the integer should be

有

可得

若θ₁<γ<θ₂，实际相交，则取θ_min＝γ,θ_max＝θ₂；否则实际不相交，取θ_min＝θ₁,θ_max＝θ₂；Let the intersection of the grating line of serial number n and the circle of the inner ring scale of radius R be

Have

Available

If θ ₁ <γ<θ ₂ , the actual intersection, then take θ _min =γ, θ _max =θ ₂ ; otherwise, if they do not actually intersect, take θ _min =θ ₁ ,θ _max =θ ₂ ;

The radius of the outer ring scale circle is R ₂ , the radius of the circular line is R ₁ , and between the outer ring scale circle and the circular line is the grating line located in the annular band, according to the values of R ₁ and R ₂ , the position in the annular band can be obtained. The value range of the serial number of the grating line in the ring zone: the range of the serial number of the grating line in the annular zone is n=n _min , n _min +1...,n _max ; the value range of the polar angle of the grating line of serial number n is θ ∈[θ _min ,θ _max ];

即

得

光栅线的序号应为整数，故实际应舍去计算结果中的小数部分，取整后再加一为

Let the intersection point of the grating line with the serial number n _min and the circular line with the radius R ₁ be

which is

have to

The serial number of the raster line should be an integer, so the decimal part in the calculation result should be rounded off, and then add one to the integer.

有

得

光栅线序号应为整数，故实际应舍去计算结果中的小数部分，取整为

Let the intersection point of the grating line with the serial number n _max and the outer ring scale circle of radius R ₂ be

Have

have to

The serial number of the raster line should be an integer, so the decimal part of the calculation result should be discarded, and the integer should be

有

可得

与半径R₂的外圈刻度圆周交点为

有

可得

显然χ<η；若θ₁<η<θ₂，实际与半径R₁圆形线的的圆周相交，应取θ_max＝η，否则实际不相交，取θ_max＝θ₂，若θ₁<χ<θ₂，实际与半径R₂的外圈刻度圆周相交，应取θ_min＝χ，否则实际不相交，取θ_min＝θ₁。Let the intersection of the grating line with the serial number n and the circular line of radius R ₁ be

Have

Available

The point of intersection with the outer ring scale circumference of radius R ₂ is

Have

Available

Obviously χ<_η; if θ ₁ <η<θ ₂ , it actually intersects with the circumference of the circular line of radius R ₁ , and θ _{max =} η should be taken _; χ<θ ₂ , which actually intersects with the scale circle of the outer ring of radius R ₂ , should take θ _min =χ, otherwise it does not actually intersect, take θ _min =θ ₁ .

极角θ成反比，具有空间周期性。优选的，在本实施方式中，光栅线的自身宽度随极角变化，在任一极角方向上的宽度都相等，等于相邻光栅线在该极角方向上的对应点间距，从而黑白部分宽度相同。The length of the vector radius of the corresponding points of each grating line in the same polar angle direction constitutes an arithmetic sequence, that is, the distance between the corresponding points of any two adjacent grating lines in the same polar angle direction is equal, both are

The polar angle θ is inversely proportional and has spatial periodicity. Preferably, in this embodiment, the width of the grating line itself changes with the polar angle, and the width in any polar angle direction is equal, which is equal to the corresponding point spacing of adjacent grating lines in the polar angle direction, so that the width of the black and white part is equal. same.

其中，D为刻度值，因极角θ的平方一般远大于1，将上述刻度线分布规律公式近似为

均匀刻度；刻度值为公制或英制，单位为线数/厘米或线数/英寸；The distribution law of the tick marks on the scale circle satisfies the equation:

Among them, D is the scale value. Since the square of the polar angle θ is generally much larger than 1, the above-mentioned formula for the distribution law of the scale lines is approximated as

Uniform scale; scale values are metric or imperial, in lines/cm or lines/inch;

Determination of a and θ:

The minimum scale value of the scale value is D ₁ , and the maximum scale value is D ₂ , respectively corresponding to the minimum polar angle θ ₁ and the maximum polar angle θ ₂ of the grating line; among them,

The range of the spiral grating density disc is only related to the minimum polar angle θ ₁ and the maximum polar angle θ ₂ , and has nothing to do with the size of the transparent substrate or the number of grating lines or scale lines, so the measurement range can be arbitrarily set according to the actual measurement. The required helical grating line is obtained; the disadvantage of the traditional oblique grating that the larger the range is, the larger the longitudinal size of the grating is.

的公式推导如下：The distribution law equation of the scale circle

The formula is derived as follows:

即该点极坐标为

相邻两条光栅线的矢径长度之差为常量

When θ=θ ₀ is any fixed value, the radial vector length of the corresponding point of the grating line with serial number n in the direction of polar angle θ ₀ is

That is, the polar coordinates of the point are

The difference between the radial lengths of two adjacent raster lines is constant

处的切线，直线L4为与各切线垂直的法线方向的矢径；As shown in Figure 1, the curve L1 is the grating line, the straight line L2 is the vector radius in the direction of the polar angle θ ₀ , and the straight line L3 is the corresponding point of each grating line in the direction of the polar angle θ ₀

The tangent at , the straight line L4 is the vector radius of the normal direction perpendicular to each tangent;

The angle between the line L4 and the polar axis (X axis) is φ, the angle between the line L4 and the line L2 is φ-θ ₀ , and the angle between the line L3 and the line L2 is α;

处的切线方程为ρcos(θ-φ)＝nd，其中，n为切线序号，也为光栅线序号；A point on the raster line

The tangent equation at is ρcos(θ-φ)=nd, where n is the serial number of the tangent, which is also the serial number of the grating line;

该斜率与n值无关；d为相邻两条切线之间的距离，

螺线光栅密度盘与织物相对转动，直至光栅线的切线与织物的纱线重合时，得到纱线密度

The tangents are all parallel and equally spaced, and the slopes of the tangents are

The slope is independent of the value of n; d is the distance between two adjacent tangents,

The helical grating density disc rotates relative to the fabric until the tangent of the grating line coincides with the yarn of the fabric to obtain the yarn density

When the warp (or weft) of the fabric is parallel to the tangent of the grating line at the corresponding point in the direction of a certain polar angle θ ₀ , and the yarn spacing is similar to the tangent spacing, according to the shadow shading principle or spatial beat frequency that forms moire fringes According to the principle, moire fringes appear near the polar angle direction, and the spatial frequency of the fringes is equal to the difference between the spatial frequency of the yarn and the spatial frequency of the tangent;

即为织物经纱或纬纱密度；由于光栅线为反比例螺旋曲线，各点的切线方向随极角快速变化，在其他极角方向上纱线与螺旋线交角较大，则不会形成人眼可见的莫尔条纹；直线读数条纹只集中出现在读数位置附近，避免了传统斜线光栅中普遍存在的影响分辨读数位置的干扰条纹；When the warp pitch of the fabric is equal to the tangent pitch of the grating line at the corresponding point in the polar angle θ ₀ direction, the spatial frequency of the moiré fringes is zero, that is, the moiré fringe pitch is infinite; then there is a line extending infinitely along the θ ₀ direction. The wider bright stripes, that is, the linear reading stripes; the linear reading stripes refer to the scale value on the scale circle

That is, the density of the warp or weft of the fabric; since the grating line is an inversely proportional helical curve, the tangent direction of each point changes rapidly with the polar angle, and the intersection angle between the yarn and the helix in other polar angles is large, and it will not be visible to the human eye. Moiré fringes; linear reading fringes only appear near the reading position, avoiding the interference fringes that affect the resolution of the reading position commonly found in traditional oblique gratings;

其中，经纱间距为

Specifically, the principle of linear reading stripes appearing in the θ ₀ direction: when the warp distance of the fabric is equal to the tangent spacing of the grating lines in the θ ₀ direction, the helical grating density disc overlapping the fabric shows a linear reading stripe along the radial direction. , the linear reading stripes on the scale circle refer to the scale value of the fabric warp density

Among them, the warp distance is

处的切线重合，根据光栅透过率的空间频率理论可知，经纱视为直线光栅，其透过率的空间频率矢量

沿极角φ方向，大小为

则

沿极角θ₀方向的投影分量为

光栅线沿极角θ₀方向周期为

透过率的空间频率

经纱和光栅线在极角θ₀方向重叠后总透过率的空间频率大小为K＝|K₁-K₂|＝0，则空间周期，即莫尔条纹间距

趋于无穷大，因而在此θ₀方向上，形成的莫尔条纹间距将趋于无穷大；而在此θ₀方向附近，设偏离微小角度δ,|δ|<5°，相应空间频率大小变为：Let the initial warp equation be ρcosθ=nd, n=1, 2,..., that is, the warp is initially parallel to the y-axis and perpendicular to the radial vector in the direction of θ=2π, and the fabric is rotated counterclockwise through the angle φ, and the warp equation becomes ρcos(θ-φ)=nd, then the warp is just the corresponding point in the direction of the grating line θ=θ ₀

The tangents at the position coincide, according to the spatial frequency theory of grating transmittance, the warp is regarded as a linear grating, and the spatial frequency vector of its transmittance

Along the polar angle φ direction, the magnitude is

but

The projected component along the polar angle θ ₀ direction is

The period of the grating line along the polar angle θ ₀ is

Spatial frequency of transmittance

The spatial frequency of the total transmittance after the warp yarn and the grating line overlap in the polar angle θ ₀ direction is K=|K ₁ -K ₂ |=0, then the spatial period, that is, the Moire fringe spacing

tends to infinity, so in the θ ₀ direction, the formed Moiré fringe spacing will tend to be infinite; and in the vicinity of this θ ₀ direction, if the deviation is a small angle δ, |δ|<5°, the corresponding spatial frequency becomes :

很大，即条纹间距亦很大，因此在θ₀方向附近有限距离内将只观察到一条较宽明条纹，即直线读数条纹；The difference between K' ₁ and K' ₂ is very small, so the spatial frequency K' of the total transmittance is very small, and a "beat" phenomenon occurs, and the period

is very large, that is, the fringe spacing is also very large, so only a wide bright fringe, that is, a straight reading fringe, will be observed within a limited distance near the θ ₀ direction;

0近似与极角θ₀成正比；因此把D作为读数在刻度圆周上标注，将形成近似呈均匀分布的刻度，各角度方向上出现的读数条纹角宽度亦基本一致；类似的也可用对应条纹代表纬纱密度。Or it can be explained that among the intersections of warp and grating lines, those intersections with smaller distances form bright fringes, and at θ ₀ the warp is tangent to the grating line, so near θ ₀ , the intersection of the warp and the grating line is farther from the tangent point. The distance between adjacent tangent points is small, and each tangent point is connected to form Moiré fringes; the corresponding angle θ ₀ of the fringes can represent the warp density; the warp density

0 is approximately proportional to the polar angle θ ₀ ; therefore, marking D as the reading on the scale circle will form a scale that is approximately evenly distributed, and the angular width of the reading stripes appearing in each angular direction is basically the same; similar stripes can also be used. Represents the weft density.

标定刻度会有微小误差，相对误差约为

绝对误差约为

例如当θ₀取值在[2π,4π]区间内时，相对误差范围约0.32％至1.27％，若设a＝0.1π厘米，则量程近似为

线/厘米，绝对误差约为0.13至0.25线/厘米，θ₀取值越大，误差越小。The derivation of the polar angle formula: if the warp density is based on the approximate result

There will be a small error in the calibration scale, and the relative error is about

The absolute error is about

For example, when the value of θ ₀ is within the interval of [2π, 4π], the relative error range is about 0.32% to 1.27%. If a=0.1π cm, the range is approximately

Line/cm, the absolute error is about 0.13 to 0.25 line/cm, the larger the value of θ ₀ , the smaller the error.

标定刻度；When calibrating the scale, it can be based on the actual range

calibration scale;

上限

That is, the lower limit of the range is

upper limit

θ₁为与下限D₁对应的最小极角，θ₁+2π＝θ₂为与上限D₂对应的最大极角；根据此a和θ₁能画出光栅线。can be calculated

θ ₁ is the minimum polar angle corresponding to the lower limit D ₁ , and θ ₁ +2π=θ ₂ is the maximum polar angle corresponding to the upper limit D ₂ ; according to this a and θ ₁ can draw grating lines.

在极角θ₀方向标注刻度读数D即可不产生此误差。因为近似值与精确值间误差很小，所以精确标定刻度并不影响刻度基本呈均匀分布，但有利于得到更精确的测量结果。then according to

This error can be avoided by marking the scale reading D in the polar angle θ ₀ direction. Because the error between the approximate value and the exact value is very small, the accurate calibration of the scale does not affect the basic uniform distribution of the scale, but it is beneficial to obtain more accurate measurement results.

The present invention also provides a method for measuring the warp and weft density of fabrics. The measuring method adopts the above-mentioned helical grating density disc to measure, and the steps of the measuring method are as follows:

Step 1: Cover the helical grating density disk on the fabric, and initially there will be a plurality of curved light and dark stripes near the direction approximately perpendicular to the warp (or weft) of the fabric;

Step 2: Then turn the helical grating density disk to gradually reduce the number of curved stripes until finally only a wider bright stripe along the radial direction is displayed, that is, a straight reading stripe, which is on the corresponding scale circle. The scale value indicated above is the fabric warp density or weft density.

The yarn spacing of the fabric is inversely proportional to the warp and weft density. The warp and weft density range of common fabrics is about 10 to 120 threads/cm, that is, the yarn spacing is 1/10 to 1/120 cm. Easy to observe readings.

In this embodiment, the helical grating density disc and the fabric yarn are drawn by MATLAB software, and then the measurement in the following embodiment is performed through the relative rotation between the helical grating density disc and the fabric yarn.

Following the above technical solutions, specific embodiments of the present invention are given below. It should be noted that the present invention is not limited to the following specific embodiments, and all equivalent transformations made on the basis of the technical solutions of the present application all fall into the protection scope of the present invention. . The present invention will be described in further detail below in conjunction with the embodiments.

Example 1:

As shown in FIG. 2, Embodiment 1 of the present invention provides a helical grating density disk with a range of 10-40 lines/cm, a design range of 10-40 lines/cm, and a figure size of 13*13 (cm);

The inner ring grating line has a range of 10 to 25. In order to make the measurement value just near the range boundary to facilitate the observation of the moire fringes formed, the lower and upper limits of the range are expanded by 0.5 respectively during the actual drawing, that is, D ₁ =9.5, D ₂ =25.5 ,but

The outer ring grating line has a range of 25 to 40. In order to make the measurement value just near the range boundary to facilitate the observation of the moire fringes formed, the lower limit and upper limit of the range are expanded by 0.5 respectively during the actual drawing, that is, D ₁ =24.5, D ₂ =40.5 ,but

The grating line of the inner ring is drawn within the scale circle of the inner ring with a radius of R = 3.5 cm, and the grating line of the outer ring is drawn between the scale circle of the outer ring with a radius of R ₂ = 6 cm and a circular line with a radius of R ₁ = 4 cm. inside the ring.

The measurement data for measuring the fabric density using the helical grating density disc in this Example 1 are shown in Tables 1 to 3 below.

Example 2:

As shown in FIG. 3, Embodiment 2 of the present invention provides a helical grating density disk with a range of 40-80 lines/cm, a design range of 40-80 lines/cm, and a figure size of 13*13 (cm);

The inner ring grating line has a range of 40 to 60. In order to make the measurement value just near the range boundary to facilitate the observation of the moire fringes formed, the lower limit and upper limit of the range are expanded by 0.5 respectively during the actual drawing, that is, D ₁ =39.5, D ₂ =60.5 ,but

The outer ring grating line has a range of 60 to 80. In order to make the measurement value just near the range boundary to facilitate the observation of the moire fringes formed, the lower limit and upper limit of the range are expanded by 0.5 respectively during the actual drawing, that is, D ₁ =24.5, D ₂ =40.5 ,but

The grating line of the inner ring is drawn within the scale circle of the inner ring with a radius of R = 3.5 cm, and the grating line of the outer ring is drawn between the scale circle of the outer ring with a radius of R ₂ = 6 cm and a circular line with a radius of R ₁ = 4 cm. inside the ring.

Example 3:

As shown in FIG. 4 , Embodiment 3 of the present invention provides a helical grating density disk with a range of 80-120 lines/cm, a design range of 80-120 lines/cm, and a figure size of 13*13 (cm);

The inner ring grating line has a range of 80 to 100. In order to make the measurement value just near the range boundary to facilitate the observation of the moire fringes formed, the lower limit and upper limit of the range are expanded by 0.5 respectively during the actual drawing, that is, D ₁ =79.5, D ₂ =100.5 ,but

The outer ring grating line has a range of 100 to 120. In order to make the measurement value just near the range boundary to facilitate the observation of the moire fringes formed, the lower limit and upper limit of the range are expanded by 0.5 respectively during the actual drawing, that is, D ₁ =99.5, D ₂ =120.5 ,but

The grating line of the inner ring is drawn within the scale circle of the inner ring with a radius of R = 3.5 cm, and the grating line of the outer ring is drawn between the scale circle of the outer ring with a radius of R ₂ = 6 cm and a circular line with a radius of R ₁ = 4 cm. inside the ring.

Example 4:

As shown in Fig. 5 and Fig. 6, an embodiment of the present invention provides a method for measuring the density of a fabric by using the spiral grating density disc in Embodiment 1, as shown in Fig. 5: the parallel vertical lines represent the warp yarns of the fabric, starting to be parallel In the y-axis direction, the yarn spacing d = 1/18 cm corresponds to a warp density of D = 18 threads/cm, which is now shown as a plurality of curved patterns. As shown in Figure 6: The fabric and the helical grating density plate are rotated relative to each other, and finally there is only one wider bright stripe along the radial direction at the scale 18, that is, the reading indicated by the linear reading stripe is 18 lines/cm .

Example 5:

As shown in FIG. 7 and FIG. 8 , an embodiment of the present invention provides a method for measuring fabric density by using the spiral grating density disc in Embodiment 1, as shown in FIG. 7 : the parallel straight lines represent the warp (weft) of the fabric Yarns, starting parallel to the y-axis direction, have a yarn spacing of d=1/36 cm, corresponding to a density of D=36 threads/cm. As shown in Figure 8, after the relative rotation of the fabric and the helical grating density disc, there is only one wide bright pattern at the scale 36, that is, the reading indicated by the linear reading stripe is 36 lines/cm.

Example 6:

As shown in FIG. 9 , an embodiment of the present invention provides a method for measuring fabric density by using the helical grating density disc in Embodiment 2. As shown in FIG. 9 : after the fabric and the helical grating density disc rotate relative to each other, at the scale 45 There is only one wider bright stripe at the display, that is, the reading indicated by the straight reading stripe is 45 lines/cm.

Example 7:

As shown in FIG. 10 , an embodiment of the present invention provides a method for measuring fabric density by using the helical grating density disc in Embodiment 2. As shown in FIG. 10 : after the fabric and the helical grating density disc rotate relative to each other, at the scale 75 There is only one wider bright stripe at the display, that is, the reading indicated by the straight reading stripe is 75 lines/cm.

Example 8:

As shown in FIG. 11 , an embodiment of the present invention provides a method for measuring fabric density by using the helical grating density disc in Embodiment 3. As shown in FIG. 11 : after the relative rotation of the fabric and the helical grating density disc, the There is only one wider bright stripe, that is, the reading indicated by the straight reading stripe is 95 lines/cm.

Example 9:

As shown in FIG. 12 , an embodiment of the present invention provides a method for measuring fabric density by using the helical grating density disc in Embodiment 3. As shown in FIG. 12 : after the relative rotation of the fabric and the helical grating density disc, the scale 110 There is only one wide bright stripe at the display, that is, the reading indicated by the straight reading stripe is 110 lines/cm.

It can be seen from Examples 1 to 9 that the helical grating density disc of the present invention can quickly, conveniently and accurately measure the warp and weft density of plain weave fabrics.

Comparative Example 1:

In this comparative example, the traditional diagonal grating densitometer is used to measure the fabric density, and the measurement results are shown in Tables 1 to 3. The oblique grating density mirror used in this comparative example is a conventional instrument.

Comparative Example 2:

In this comparative example, the density of the fabric was measured by a reading microscope, and the measurement results are shown in Tables 1 to 3. The reading microscope used in this comparative example is also a conventional instrument.

Table 1 is the raw data of fabric density measured in Example 1, Comparative Example 1 and Comparative Example 2 (unit: thread/cm)

Table 2 is the uncertainty analysis data for the measurement of fabric density in Example 1, Comparative Example 1 and Comparative Example 2

Table 3 is a comparison of the measurement results of the fabric density measured in Example 1, Comparative Example 1 and Comparative Example 2 (unit: thread/cm)

As can be seen from the above Tables 1 to 3, the measurement results of the density disc of the present invention are close to that of the reading microscope. Although the measurement accuracy of the reading microscope is high, the cost of configuring instruments or labor is high, and the measurement speed is also relatively slow. The measurement accuracy of the density disc of the present invention is higher than that of the traditional density mirror. The main reason is that the Moiré fringe distribution displayed by the traditional density mirror is a scattered inverse proportional curve. The lines become denser and denser as the reading value increases, showing a non-uniform scale, so the reading position is not easy to align. The density disc stripes are linear stripes along the radial direction. The stripes at different positions have the same length and little difference in angular width, and the stripes appear concentrated near the reading position. Align the reading position, thereby improving the accuracy of the measurement results.

Claims (9)

1. A helical grating density disc, comprising a transparent substrate, characterized in that, on the transparent substrate, a plurality of inversely proportional helical grating lines formed by rotating counterclockwise around the same center origin; During the process, the radial vector length of each grating line gradually decreases; the rotation angle of the grating line at the center is 360 degrees, and the rotation angle of other grating lines is equal to or less than 360 degrees; in the transparent The base plate is also provided with a multi-circle scale circle concentric with the grating line, and a straight line scale line perpendicular to the scale circle is marked on the outside of the scale circle; When the helical grating density disc overlaps with the fabric and rotates relatively, a linear reading stripe along the radial direction will be displayed, and the scale value indicated by the linear reading stripe on the corresponding scale circle is the fabric warp density or weft density; The raster lines satisfy the following equation in polar coordinates:

Among them, ρ is the length of the vector radius, that is, the length of the line connecting any point on the grating line and the central origin; n is the serial number of the grating line, which is n=1, 2, 3, ..., and θ is the polar angle from the central origin to the edge. , is the _{counterclockwise rotation} angle _of the _{vector radius} relative to the polar axis. angle; a is the length, which determines the difference between the length of each point on the grating line and the length of the corresponding point on the adjacent grating line in the same polar angle direction, and together with the minimum polar angle θ ₁ determines the density of the helical grating. range. 2. helical grating density disc as claimed in claim 1 is characterized in that, there are two scale circles, which are respectively the inner circle scale circle and the outer circle scale circle, the difference between the inner circle scale circle and the outer circle scale circle. There are also concentric circular lines; The radius of the scale circle of the inner ring is R, and the value range of the serial number of the grating line within the scale circle of the inner ring can be obtained according to the R value; The radius of the scale circle of the outer ring is R ₂ , the radius of the circular line is R ₁ , and between the scale circle of the outer ring and the circular line is a grating line located in the annular zone, according to R ₁ and R ₂ The value can get the range of the serial number of the raster line located in the annular band. 3. The helical grating density disk according to claim 1, characterized in that, the length of the vector radius of the corresponding point of each grating line in the same polar angle direction constitutes an arithmetic sequence, that is, any two adjacent grating lines are in the same polar angle direction. Corresponding points in the same polar angle are equally spaced, both are

It is inversely proportional to the polar angle θ and has spatial periodicity. 4. The helical grating density disk of claim 3, wherein the grating line's own width varies with the polar angle, and the width in any polar angle direction is equal, equal to the adjacent grating line in the polar angle. Corresponding point spacing in the angular direction. 5. helical grating density disk as claimed in claim 2, is characterized in that, the distribution law of scale line on described scale circle satisfies equation:

Wherein, D is the scale value; the scale value is metric or imperial, and the unit is lines/cm or lines/inch; The minimum scale value of the scale value is D ₁ , and the maximum scale value is D ₂ , respectively corresponding to the minimum polar angle θ ₁ and the maximum polar angle θ ₂ of the grating line; wherein,

6. The helical grating density disk according to claim 5, wherein the distribution law equation of the scale lines on the scale circle

The formula is derived as follows: When θ=θ ₀ is any fixed value, the radial vector length of the corresponding point of the grating line with serial number n in the direction of polar angle θ ₀ is

That is, the polar coordinates of the point are

The difference between the radial lengths of two adjacent raster lines is constant

The curve L1 is the grating line, the straight line L2 is the vector radius in the direction of the polar angle θ ₀ , and the straight line L3 is the corresponding point of each grating line in the direction of the polar angle θ ₀

The tangent at , the straight line L4 is the vector radius of the normal direction perpendicular to each tangent; The included angle between the straight line L4 and the polar axis is φ, the included angle between the straight line L4 and the straight line L2 is φ-θ ₀ , and the included angle between the straight line L3 and the straight line L2 is α;

A point on the raster line

The tangent equation at is ρcos(θ-φ)=nd, where n is the serial number of the tangent, which is also the serial number of the grating line; The tangents are all parallel to each other and are equally spaced, and the slopes of the tangents are

The slope is independent of the value of n; d is the distance between two adjacent tangents,

The helical grating density disc rotates relative to the fabric until the tangent of the grating line coincides with the yarn of the fabric to obtain the yarn density

7. The helical grating density disc according to claim 6, characterized in that, when the warp pitch of the fabric is equal to the corresponding point of the grating line in the direction of θ ₀

When the distance between the tangent lines at θ 0 is set, the helical grating density disc and the fabric are rotated relatively until the tangent of the grating line coincides with the yarns of the fabric, then the spatial frequency of the moiré fringes in the θ ₀ direction is zero, that is, the moiré fringe spacing is infinite. ; then there is a wider bright stripe extending infinitely along the direction of θ ₀ , that is, the linear reading stripe; the linear reading stripe refers to the scale value on the corresponding scale circle

That is the fabric warp or weft density. 8. The helical grating density disc according to claim 5, characterized in that it can be adjusted according to the actual range

calibration scale; That is, the lower limit of the range is

capped at

can be calculated

θ ₁ is the polar angle corresponding to the lower limit D ₁ , and θ ₁ +2π is the polar angle corresponding to the upper limit D ₂ ; according to this a and θ ₁ , the grating line can be drawn. 9. a measuring method of fabric warp and weft density, is characterized in that, this measuring method adopts the spiral grating density disc described in any one of claim 1 to 8 to measure, and the steps of this measuring method are as follows: Step 1: Cover the helical grating density disk on the fabric, and initially a plurality of curved light and dark stripes will appear near the direction of the warp or weft of the fabric; Step 2: Then turn the helical grating density disk to gradually reduce the number of curved stripes until finally only a wider bright stripe along the radial direction is displayed, that is, a straight reading stripe, which is on the corresponding scale circle. The scale value indicated above is the fabric warp density or weft density.

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