CN105335961B - A kind of filter bag pastes clamp method automatically - Google Patents

A kind of filter bag pastes clamp method automatically Download PDF

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Publication number
CN105335961B
CN105335961B CN201510449765.8A CN201510449765A CN105335961B CN 105335961 B CN105335961 B CN 105335961B CN 201510449765 A CN201510449765 A CN 201510449765A CN 105335961 B CN105335961 B CN 105335961B
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msub
mrow
filter bag
msup
edge
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CN105335961A (en
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孙成磊
王宪保
臧济文
吴国良
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Zhejiang Clean Environmental Protection Technology Co Ltd
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Zhejiang Clean Environmental Protection Technology Co Ltd
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    • GPHYSICS
    • G06COMPUTING; CALCULATING OR COUNTING
    • G06TIMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T7/00Image analysis
    • G06T7/0002Inspection of images, e.g. flaw detection
    • G06T7/0004Industrial image inspection
    • GPHYSICS
    • G06COMPUTING; CALCULATING OR COUNTING
    • G06TIMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T2207/00Indexing scheme for image analysis or image enhancement
    • G06T2207/10Image acquisition modality
    • G06T2207/10016Video; Image sequence
    • GPHYSICS
    • G06COMPUTING; CALCULATING OR COUNTING
    • G06TIMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T2207/00Indexing scheme for image analysis or image enhancement
    • G06T2207/30Subject of image; Context of image processing
    • G06T2207/30108Industrial image inspection

Abstract

A kind of filter bag pastes clamp method and comprised the following steps automatically:First by the integral projection for the longitudinal first derivative for calculating image overall, longitudinal rough position of leading edge is obtained, the integral projection of the horizontal first derivative by calculating image overall, obtain the horizontal rough position at left and right edge;Then by calculating longitudinal first derivative local at two near leading edge, 2 points on leading edge of exact position is obtained;By calculating horizontal first derivative local at two near left hand edge, 2 points on left hand edge of exact position is obtained;By the way that the accurate mark of filter bag paste position in the picture is calculated;Finally provide the deflection angle of filter bag.This method makes full use of the advantage that computer quickly calculates, and obtains the exact position of filter bag in real time by vision imaging system, then drives robot crawl clamp and moves to relevant position, so as to realize the Rapid pasting on filter bag.

Description

A kind of filter bag pastes clamp method automatically
Technical field
The present invention relates to automatic measurement and control field, more particularly to a kind of filter bag is in patch clamp method.
Background technology
With the enhancing of people's environmental consciousness, the various filtering products for materials such as empty gas and waters are more and more, are used as it In core component, filter bag fast and automatically metaplasia production as enterprise active demand.But in existing production line balance mistake Cheng Zhong, the characteristics of due to filter bag flexibility, it is difficult to be accurately positioned with the mode of machinery, filter bag is caused to paste the life of clamp Production. art needs to be accomplished manually, and production efficiency is low, with high costs, can not meet the quick, production requirement of high quality.Therefore, Develop a kind of filter bag fast and automatically and paste the active demand that clamp method is current filter bag manufacturing enterprise.
At present, with the development of computer vision and robot technology, the product based on vision robot is examined automatically Survey and be gradually developed and apply with production.The present invention is to realize being accurately positioned for filter bag by computer vision technique, Then control machine people, the automatic stickup of clamp is completed.
The content of the invention
To solve the problems, such as that prior art is low to filter bag production efficiency, unstable product quality, there is provided one kind is based on The filter bag of vision robot pastes clamp method automatically, and this method makes full use of the advantage that computer quickly calculates, by regarding Feel that image system obtains the exact position of filter bag in real time, then drive robot crawl clamp and move to relevant position, from And realize the Rapid pasting on filter bag.
To achieve the above object, the present invention uses following technical scheme:
A kind of filter bag pastes clamp method automatically, comprises the following steps:
Step 1:Obtain the realtime graphic G of filter bag;
Step 2:Longitudinal rough position of filter bag leading edge is calculated, detailed process is as follows:
(2.1) integral projection of longitudinal first derivative of image is calculated, calculation formula is
Wherein j is ordinate, and N is the height of image, and i is abscissa, and M is the width of image, II, jRepresent to sit in image G Mark the pixel value at (i, j) place;
(2.2) maximum of longitudinal integral projection is calculated, calculation formula is
SMax=Max ({ Sj), 0 < j < N
Then SMaxCorresponding j values are longitudinal rough position H of filter bag leading edge,
Max({Sj) it is to ask for sequence { SjMaximum;
Step 3:The horizontal rough position at the left and right edge of filter bag is calculated, detailed process is as follows:
(3.1) integral projection of the horizontal first derivative of image is calculated, calculation formula is
Wherein j is ordinate, and N is the height of image, and i is abscissa, and M is the width of image;
(3.2) maximum of horizontal integral projection is calculated, calculation formula is
WL=Max ({ Ti), 0 < i < M
Then WLCorresponding i values are the horizontal rough position of filter bag left hand edge;
(3.3) minimum value of horizontal integral projection is calculated, calculation formula is
WR=Min ({ Ti), 0 < i < M
Then WRThe horizontal rough position of corresponding i values as filter bag right hand edge, Min ({ Ti) it is to ask for sequence { Ti} Minimum value;
Step 4:Two points are found in the right and left of longitudinal rough position of filter bag leading edge, before filter bag The exact position at edge, calculating process are:
(4.1) the horizontal rough position W at filter bag leading edge center is calculatedC, formula is
WC=(WR+WL)/2
(4.2) respectively with coordinate (WC+k1, H) and (WC-k1, H) centered on, in the range of 2 × L+1 of longitudinal direction, calculate vertical To first derivative, calculation formula is
Wherein i is abscissa, and j is ordinate, k1It is according to filter bag size and the ginseng for allowing angle of inclination to set with L Number;
(4.3) calculate the maximum of longitudinal first derivative sequence, and its position is arranged on leading edge 2 points accurate Position.Calculation formula is
ThenCorresponding j values are the ordinate H of point on the right of leading edgeQR,Corresponding j values are front The ordinate H of edge left side pointQL
Step 5:Two points are found on the both sides up and down of the horizontal rough position of filter bag left hand edge, it is left as filter bag The exact position at edge, calculating process are:
(5.1) two reference points are set at filter bag left hand edge rough position, and its coordinate is respectively (WL, H+k2)、(WL, H+ k3), wherein k2、k3For according to filter bag size and the parameter for allowing angle of inclination to set;
(5.2) respectively with coordinate (WL, H+k2) and (WL, H+k3) centered on, in the range of laterally 2 × L+1, calculate horizontal To first derivative, calculation formula is
(5.3) calculate the maximum of horizontal first derivative sequence, and its position is arranged on left hand edge 2 points accurate Position, calculation formula are
ThenCorresponding i values are the abscissa W of edge point on left hand edgeLA,Corresponding i values are the left side The abscissa W of edge point under edgeLB
Step 6:If product requirement paste clamp center to the distance of leading edge be V1, to the distance of left hand edge For V2, then the calculation formula of its position coordinates (X, Y) be:
Wherein
Step 7:The deflection angle θ of filter bag is:
The principle that filter bag of the present invention pastes clamp method automatically is as follows:Using the realtime graphic of filter bag, pass through computer The method of visual processes realizes that automatic and accurate positions:First by the integral projection for the longitudinal first derivative for calculating image overall, Longitudinal rough position of leading edge is obtained, the integral projection of the horizontal first derivative by calculating image overall, obtains left and right side The horizontal rough position of edge;Then by calculating longitudinal first derivative local at two near leading edge, obtain two on leading edge The exact position of point;By calculating at two near left hand edge local horizontal first derivative, 2 points accurate is obtained on left hand edge Position;By the way that the accurate mark of filter bag paste position in the picture is calculated;Finally provide the deflection angle of filter bag.
Advantages of the present invention is as follows:It is embedded into the real-time control system of filter bag automated production as independent algoritic module In system, realized by positional information and carrying of the robot to pasting boards is controlled, reach the filter bag mesh that fast and automatically metaplasia is produced 's.Calculating speed of the present invention is fast, intelligence degree is high, accurate positioning, and locating effect is unrelated with the size of non-woven bag:This This quickly filter bag vision positioning method is invented, by the calculating to realtime graphic, obtains the position of front end of line and left end line Put, so as to calculate the exact position of paste position, and the deviation angle of filter bag, and provide pasting boards accordingly and need to move The position arrived and angle.This method can obtain image more than 30 frame per second under the auxiliary of high-speed industrial video camera, will Position Positioning Precision Control is in below 1mm.
Brief description of the drawings
Fig. 1 is the workflow block diagram of the present invention;
Fig. 2 is the filter bag image schematic diagram that the present invention collects;
Fig. 3 is the edge line rough position schematic diagram that the present invention asks for;
Fig. 4 is the exact position schematic diagram put on the edge line that the present invention asks for;
Fig. 5 is the filter bag deflection angle schematic diagram that the present invention asks for.
In figure mark for:1st, leading edge, 2, left hand edge, 3, filter bag, 4, right hand edge, 5, clamp paste position center, 6, Leading edge rough position, 7, left hand edge rough position, 8, right hand edge rough position, 9, left hand edge partial lateral first derivative asks for Position, 10, two precise local fixs asking for of left hand edge, 11, locally longitudinal first derivative asks for position to top edge, 12, top Two precise local fixs that edge is asked for, 13, the deflection angle of filter bag.
Embodiment
Embodiment one
Referring to the drawings 1-5, a kind of filter bag pastes clamp method automatically, and step is as follows:
Step 1, the realtime graphic G of filter bag is obtained, width 600, is highly 800:
Step 2, calculates longitudinal rough position of filter bag leading edge, and detailed process is as follows:
2.1 calculate the integral projection of longitudinal first derivative of image, and calculation formula is
Wherein j is ordinate, and i is abscissa, II, jRepresent the pixel value at coordinate (i, j) place in image G.
2.2 calculate the maximum of longitudinal integral projection, and calculation formula is
SMax=Max ({ Sj), 0 < j < 800
If the S tried to achieveMaxValue be 8000, its corresponding j value is 100, then longitudinal rough position H of filter bag leading edge =100.
Step 3, calculates the horizontal rough position at the left and right edge of filter bag, and detailed process is as follows:
3.1 calculate the integral projection of the horizontal first derivative of image, and calculation formula is
Wherein j is ordinate, and i is abscissa.
3.2 calculate the maximum of horizontal integral projection, and calculation formula is
TMax=Max ({ Ti), 0 < i < 600
If the T tried to achieveMaxIt is worth for 6000, corresponding i values are 150, then the horizontal rough position W of filter bag left hand edgeL= 150。
3.3 calculate the minimum value of horizontal integral projection, and calculation formula is
TMin=Min ({ Ti), 0 < i < 600
If the T tried to achieveMinIt is worth for -6000, corresponding i values are 450, then the horizontal rough position W of filter bag right hand edgeR =150.
Step 4, two points are found in the right and left of longitudinal rough position of filter bag leading edge, before filter bag The exact position at edge, calculating process are:
4.1 calculate the horizontal rough position W at filter bag leading edge centerC
WC=(WR+WL)/2=(450+150)/2=300
4.2 assume parameter k1=150, L=100, then respectively centered on coordinate (450,100) and (150,100), vertical To in the range of 201, longitudinal first derivative is calculated, calculation formula is
S450 j=II, j-II, j-1, i=450,0≤j≤200
S150 j=II, j-II, j-1, i=150,0≤j≤200
Wherein i is abscissa, and j is ordinate.
4.3 calculate the maximum of longitudinal first derivative sequence, and its position are arranged to 2 points on leading edge of accurate position Put.Calculation formula is
S450 Max=Max ({ S450 j), 0≤j≤200
S150 Max=Max ({ S150 j), 0≤j≤200
If the S asked for450 MaxFor 800, corresponding j values are 80, then the ordinate of point is H on the right of leading edgeQR=80, ask for S150 MaxFor 900, corresponding j values are 120, then the ordinate of leading edge left side point is HQL=120,.
Step 5, two points are found on the both sides up and down of the horizontal rough position of filter bag left hand edge, it is left as filter bag The exact position at edge, calculating process are:
5.1 assume parameter k2=150, k3=350, then the coordinate of two reference points is distinguished at filter bag left hand edge rough position For (150,250), (150,450).
5.2 respectively centered on coordinate (150,250), (150,450), in the range of laterally 201, calculate horizontal single order Derivative, calculation formula are
S250 i=II, j-II-1, j, 50≤i≤250, j=250
S450 i=II, j-II-1, j, 50≤i≤250, j=450
5.3 calculate the maximum of horizontal first derivative sequence, and its position are arranged to 2 points on left hand edge of accurate position Put.Calculation formula is
S250 Max=Max ({ S250 i), 50≤i≤250
S450 Max=Max ({ S450 i), 50≤i≤250
If the S tried to achieve250 MaxBe worth for 850, corresponding i values are 120, then on left hand edge edge point abscissa WLA=120, ask The S obtained450 MaxBe worth for 860, corresponding i values are 180, then under left hand edge edge point abscissa WLB=180.
Step 6, it is assumed that product requirement pastes the center of clamp to the distance V of leading edge1For 260, left hand edge is arrived Distance V2For 300, then it is as follows to ask for process for its position coordinates (X, Y):
Parameter calculates:
Then
Step 7, the deflection angle θ of filter bag are:

Claims (1)

1. a kind of filter bag pastes clamp method automatically, it is characterised in that the patch clamp method comprises the following steps:
Step 1:Obtain the realtime graphic G of filter bag;
Step 2:Longitudinal rough position of filter bag leading edge is calculated, detailed process is as follows:
(2.1) integral projection of longitudinal first derivative of image is calculated, calculation formula is
<mrow> <msub> <mi>S</mi> <mi>j</mi> </msub> <mo>=</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mi>M</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <mrow> <mo>(</mo> <msub> <mi>I</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>I</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>)</mo> </mrow> <mo>,</mo> <mn>0</mn> <mo>&lt;</mo> <mi>j</mi> <mo>&lt;</mo> <mi>N</mi> </mrow>
Wherein j is ordinate, and N is the height of image, and i is abscissa, and M is the width of image, Ii,jRepresent coordinate in image G (i, J) pixel value at place;
(2.2) maximum of longitudinal integral projection is calculated, calculation formula is
SMax=Max ({ Sj), 0 < j < N
Then SMaxCorresponding j values are longitudinal rough position H of filter bag leading edge,
Max({Sj) it is to ask for sequence { SjMaximum;
Step 3:The horizontal rough position at the left and right edge of filter bag is calculated, detailed process is as follows:
(3.1) integral projection of the horizontal first derivative of image is calculated, calculation formula is
<mrow> <msub> <mi>T</mi> <mi>i</mi> </msub> <mo>=</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>j</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mi>N</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <mrow> <mo>(</mo> <msub> <mi>I</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>I</mi> <mrow> <mi>i</mi> <mo>-</mo> <mn>1</mn> <mo>,</mo> <mi>j</mi> </mrow> </msub> <mo>)</mo> </mrow> <mo>,</mo> <mn>0</mn> <mo>&lt;</mo> <mi>i</mi> <mo>&lt;</mo> <mi>M</mi> </mrow>
Wherein j is ordinate, and N is the height of image, and i is abscissa, and M is the width of image;
(3.2) maximum of horizontal integral projection is calculated, calculation formula is
WL=Max ({ Ti), 0 < i < M
Then WLCorresponding i values are the horizontal rough position of filter bag left hand edge;
(3.3) minimum value of horizontal integral projection is calculated, calculation formula is
WR=Min ({ Ti), 0 < i < M
Then WRThe horizontal rough position of corresponding i values as filter bag right hand edge, Min ({ Ti) it is to ask for sequence { TiMost Small value;
Step 4:Two points are found in the right and left of longitudinal rough position of filter bag leading edge, as filter bag leading edge Exact position, calculating process is:
(4.1) the horizontal rough position W at filter bag leading edge center is calculatedC, formula is
WC=(WR+WL)/2
(4.2) respectively with coordinate (WC+k1, H) and (WC-k1, H) centered on, in the range of 2 × L+1 of longitudinal direction, calculate longitudinal single order Derivative, calculation formula are
<mrow> <msub> <msup> <mi>S</mi> <mrow> <msub> <mi>W</mi> <mi>C</mi> </msub> <mo>+</mo> <msub> <mi>k</mi> <mn>1</mn> </msub> </mrow> </msup> <mi>j</mi> </msub> <mo>=</mo> <msub> <mi>I</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>I</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> <mi>i</mi> <mo>=</mo> <msub> <mi>W</mi> <mi>C</mi> </msub> <mo>+</mo> <msub> <mi>k</mi> <mn>1</mn> </msub> <mo>,</mo> <mi>H</mi> <mo>-</mo> <mi>L</mi> <mo>&amp;le;</mo> <mi>j</mi> <mo>&amp;le;</mo> <mi>H</mi> <mo>+</mo> <mi>L</mi> </mrow>
<mrow> <msub> <msup> <mi>S</mi> <mrow> <msub> <mi>W</mi> <mi>C</mi> </msub> <mo>-</mo> <msub> <mi>k</mi> <mn>1</mn> </msub> </mrow> </msup> <mi>j</mi> </msub> <mo>=</mo> <msub> <mi>I</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>I</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> <mi>i</mi> <mo>=</mo> <msub> <mi>W</mi> <mi>C</mi> </msub> <mo>-</mo> <msub> <mi>k</mi> <mn>1</mn> </msub> <mo>,</mo> <mi>H</mi> <mo>-</mo> <mi>L</mi> <mo>&amp;le;</mo> <mi>j</mi> <mo>&amp;le;</mo> <mi>H</mi> <mo>+</mo> <mi>L</mi> </mrow>
Wherein i is abscissa, and j is ordinate, k1It is according to filter bag size and the parameter for allowing angle of inclination to set with L;
(4.3) maximum of longitudinal first derivative sequence is calculated, and its position is arranged to 2 points on leading edge of exact position, Calculation formula is
<mrow> <msub> <msup> <mi>S</mi> <mrow> <msub> <mi>W</mi> <mi>C</mi> </msub> <mo>+</mo> <msub> <mi>k</mi> <mn>1</mn> </msub> </mrow> </msup> <mrow> <mi>M</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> <mo>=</mo> <mi>M</mi> <mi>a</mi> <mi>x</mi> <mrow> <mo>(</mo> <mo>{</mo> <msub> <msup> <mi>S</mi> <mrow> <msub> <mi>W</mi> <mi>C</mi> </msub> <mo>+</mo> <msub> <mi>k</mi> <mn>1</mn> </msub> </mrow> </msup> <mi>j</mi> </msub> <mo>}</mo> <mo>)</mo> </mrow> <mo>,</mo> <mi>H</mi> <mo>-</mo> <mi>L</mi> <mo>&amp;le;</mo> <mi>j</mi> <mo>&amp;le;</mo> <mi>H</mi> <mo>+</mo> <mi>L</mi> </mrow>
<mrow> <msub> <msup> <mi>S</mi> <mrow> <msub> <mi>W</mi> <mi>C</mi> </msub> <mo>-</mo> <msub> <mi>k</mi> <mn>1</mn> </msub> </mrow> </msup> <mrow> <mi>M</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> <mo>=</mo> <mi>M</mi> <mi>a</mi> <mi>x</mi> <mrow> <mo>(</mo> <mo>{</mo> <msub> <msup> <mi>S</mi> <mrow> <msub> <mi>W</mi> <mi>C</mi> </msub> <mo>-</mo> <msub> <mi>k</mi> <mn>1</mn> </msub> </mrow> </msup> <mi>j</mi> </msub> <mo>}</mo> <mo>)</mo> </mrow> <mo>,</mo> <mi>H</mi> <mo>-</mo> <mi>L</mi> <mo>&amp;le;</mo> <mi>j</mi> <mo>&amp;le;</mo> <mi>H</mi> <mo>+</mo> <mi>L</mi> </mrow>
ThenCorresponding j values are the ordinate H of point on the right of leading edgeQR,Corresponding j values are that leading edge is left The ordinate H of edge pointQL
Step 5:Two points are found on the both sides up and down of the horizontal rough position of filter bag left hand edge, as filter bag left hand edge Exact position, calculating process is:
(5.1) two reference points are set at filter bag left hand edge rough position, and its coordinate is respectively (WL, H+k2)、(WL, H+k3), Wherein k2、k3For according to filter bag size and the parameter for allowing angle of inclination to set;
(5.2) respectively with coordinate (WL, H+k2) and (WL, H+k3) centered on, in the range of laterally 2 × L+1, calculate horizontal single order Derivative, calculation formula are
<mrow> <msub> <msup> <mi>S</mi> <mrow> <mi>H</mi> <mo>+</mo> <msub> <mi>k</mi> <mn>2</mn> </msub> </mrow> </msup> <mi>i</mi> </msub> <mo>=</mo> <msub> <mi>I</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>I</mi> <mrow> <mi>i</mi> <mo>-</mo> <mn>1</mn> <mo>,</mo> <mi>j</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>W</mi> <mi>L</mi> </msub> <mo>-</mo> <mi>L</mi> <mo>&amp;le;</mo> <mi>i</mi> <mo>&amp;le;</mo> <msub> <mi>W</mi> <mi>L</mi> </msub> <mo>+</mo> <mi>L</mi> <mo>,</mo> <mi>j</mi> <mo>=</mo> <mi>H</mi> <mo>+</mo> <msub> <mi>k</mi> <mn>2</mn> </msub> </mrow>
<mrow> <msub> <msup> <mi>S</mi> <mrow> <mi>H</mi> <mo>+</mo> <msub> <mi>k</mi> <mn>3</mn> </msub> </mrow> </msup> <mi>i</mi> </msub> <mo>=</mo> <msub> <mi>I</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>I</mi> <mrow> <mi>i</mi> <mo>-</mo> <mn>1</mn> <mo>,</mo> <mi>j</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>W</mi> <mi>L</mi> </msub> <mo>-</mo> <mi>L</mi> <mo>&amp;le;</mo> <mi>i</mi> <mo>&amp;le;</mo> <msub> <mi>W</mi> <mi>L</mi> </msub> <mo>+</mo> <mi>L</mi> <mo>,</mo> <mi>j</mi> <mo>=</mo> <mi>H</mi> <mo>+</mo> <msub> <mi>k</mi> <mn>3</mn> </msub> </mrow>
(5.3) maximum of horizontal first derivative sequence is calculated, and its position is arranged to 2 points on left hand edge of exact position, Calculation formula is
<mrow> <msub> <msup> <mi>S</mi> <mrow> <mi>H</mi> <mo>+</mo> <msub> <mi>k</mi> <mn>2</mn> </msub> </mrow> </msup> <mrow> <mi>M</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> <mo>=</mo> <mi>M</mi> <mi>a</mi> <mi>x</mi> <mrow> <mo>(</mo> <mo>{</mo> <msub> <msup> <mi>S</mi> <mrow> <mi>H</mi> <mo>+</mo> <msub> <mi>k</mi> <mn>2</mn> </msub> </mrow> </msup> <mi>i</mi> </msub> <mo>}</mo> <mo>)</mo> </mrow> <mo>,</mo> <msub> <mi>W</mi> <mi>L</mi> </msub> <mo>-</mo> <mi>L</mi> <mo>&amp;le;</mo> <mi>i</mi> <mo>&amp;le;</mo> <msub> <mi>W</mi> <mi>L</mi> </msub> <mo>+</mo> <mi>L</mi> </mrow>
<mrow> <msub> <msup> <mi>S</mi> <mrow> <mi>H</mi> <mo>+</mo> <msub> <mi>k</mi> <mn>3</mn> </msub> </mrow> </msup> <mrow> <mi>M</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> <mo>=</mo> <mi>M</mi> <mi>a</mi> <mi>x</mi> <mrow> <mo>(</mo> <mo>{</mo> <msub> <msup> <mi>S</mi> <mrow> <mi>H</mi> <mo>+</mo> <msub> <mi>k</mi> <mn>3</mn> </msub> </mrow> </msup> <mi>i</mi> </msub> <mo>}</mo> <mo>)</mo> </mrow> <mo>,</mo> <msub> <mi>W</mi> <mi>L</mi> </msub> <mo>-</mo> <mi>L</mi> <mo>&amp;le;</mo> <mi>i</mi> <mo>&amp;le;</mo> <msub> <mi>W</mi> <mi>L</mi> </msub> <mo>+</mo> <mi>L</mi> </mrow>
ThenCorresponding i values are the abscissa W of edge point on left hand edgeLA,Corresponding i values are under left hand edge The abscissa W of edge pointLB
Step 6:If product requirement paste clamp center to the distance of leading edge be V1, the distance to left hand edge is V2, Then the calculation formula of its position coordinates (X, Y) is:
<mrow> <mi>X</mi> <mo>=</mo> <msub> <mi>V</mi> <mn>2</mn> </msub> <mo>-</mo> <mfrac> <mrow> <msub> <mi>b</mi> <mn>2</mn> </msub> <mo>-</mo> <msub> <mi>b</mi> <mn>1</mn> </msub> </mrow> <mrow> <msub> <mi>a</mi> <mn>2</mn> </msub> <mo>-</mo> <msub> <mi>a</mi> <mn>1</mn> </msub> </mrow> </mfrac> </mrow>
<mrow> <mi>Y</mi> <mo>=</mo> <msub> <mi>V</mi> <mn>1</mn> </msub> <mo>+</mo> <msub> <mi>a</mi> <mn>1</mn> </msub> <mo>&amp;times;</mo> <mfrac> <mrow> <msub> <mi>b</mi> <mn>2</mn> </msub> <mo>-</mo> <msub> <mi>b</mi> <mn>1</mn> </msub> </mrow> <mrow> <msub> <mi>a</mi> <mn>1</mn> </msub> <mo>-</mo> <msub> <mi>a</mi> <mn>2</mn> </msub> </mrow> </mfrac> <mo>+</mo> <msub> <mi>b</mi> <mn>1</mn> </msub> </mrow>
Wherein
<mrow> <msub> <mi>a</mi> <mn>1</mn> </msub> <mo>=</mo> <mfrac> <mrow> <msub> <mi>H</mi> <mrow> <mi>Q</mi> <mi>R</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>H</mi> <mrow> <mi>Q</mi> <mi>L</mi> </mrow> </msub> </mrow> <mrow> <mn>2</mn> <msub> <mi>k</mi> <mn>1</mn> </msub> </mrow> </mfrac> </mrow>
<mrow> <msub> <mi>b</mi> <mn>1</mn> </msub> <mo>=</mo> <msub> <mi>H</mi> <mrow> <mi>Q</mi> <mi>R</mi> </mrow> </msub> <mo>-</mo> <mfrac> <mrow> <msub> <mi>H</mi> <mrow> <mi>Q</mi> <mi>R</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>H</mi> <mrow> <mi>Q</mi> <mi>L</mi> </mrow> </msub> </mrow> <mrow> <mn>2</mn> <msub> <mi>k</mi> <mn>1</mn> </msub> </mrow> </mfrac> <mo>&amp;times;</mo> <mrow> <mo>(</mo> <msub> <mi>W</mi> <mi>C</mi> </msub> <mo>+</mo> <msub> <mi>k</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> </mrow>
<mrow> <msub> <mi>a</mi> <mn>2</mn> </msub> <mo>=</mo> <mfrac> <mrow> <msub> <mi>k</mi> <mn>3</mn> </msub> <mo>-</mo> <msub> <mi>k</mi> <mn>2</mn> </msub> </mrow> <mrow> <msub> <mi>W</mi> <mrow> <mi>L</mi> <mi>B</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>W</mi> <mrow> <mi>L</mi> <mi>A</mi> </mrow> </msub> </mrow> </mfrac> </mrow>
<mrow> <msub> <mi>b</mi> <mn>2</mn> </msub> <mo>=</mo> <mi>H</mi> <mo>+</mo> <msub> <mi>k</mi> <mn>2</mn> </msub> <mo>-</mo> <msub> <mi>W</mi> <mrow> <mi>L</mi> <mi>A</mi> </mrow> </msub> <mo>&amp;times;</mo> <mfrac> <mrow> <msub> <mi>k</mi> <mn>3</mn> </msub> <mo>-</mo> <msub> <mi>k</mi> <mn>2</mn> </msub> </mrow> <mrow> <msub> <mi>W</mi> <mrow> <mi>L</mi> <mi>B</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>W</mi> <mrow> <mi>L</mi> <mi>A</mi> </mrow> </msub> </mrow> </mfrac> </mrow>
Step 7:The deflection angle θ of filter bag is:
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