CN106345857B - A kind of method that flat section approaches circular arc - Google Patents
A kind of method that flat section approaches circular arc Download PDFInfo
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- CN106345857B CN106345857B CN201610865774.XA CN201610865774A CN106345857B CN 106345857 B CN106345857 B CN 106345857B CN 201610865774 A CN201610865774 A CN 201610865774A CN 106345857 B CN106345857 B CN 106345857B
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B21—MECHANICAL METAL-WORKING WITHOUT ESSENTIALLY REMOVING MATERIAL; PUNCHING METAL
- B21D—WORKING OR PROCESSING OF SHEET METAL OR METAL TUBES, RODS OR PROFILES WITHOUT ESSENTIALLY REMOVING MATERIAL; PUNCHING METAL
- B21D5/00—Bending sheet metal along straight lines, e.g. to form simple curves
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Abstract
The present invention provides a kind of method that flat section approaches circular arc, and it is suitable for the forming paths in the forming techniques such as setting laser sheet material forming, plate part press shaping die.It is the circular arc of given curvature by plane or linear feature piecewise approximation based on sine and cosine theorem and triangle geometrical relationship.The method that flat section provided by the invention approaches circular arc, plane or straight line are segmented in advance, segmented mode uniformly segmentation or arbitrary segmentation, then according to the radius of curvature for the circular arc to be approached, the end and each segmented node of plane or straight line after being bent each segmentation section are calculated based on sine and cosine theorem and triangle geometrical relationship relative to plane or the raised height of straight line initial position, and then bending is carried out to each segmentation section and approaches circular arc, it is finally reached the purpose for approaching the circular arc of given curvature, laser forming technology and mathematical theory model foundation can be contacted, there is good directive significance to forming accuracy is improved.
Description
Technical field
The present invention relates to sheet metal processings, and in particular to a kind of method that flat section approaches circular arc.
Background technique
Metal sheet forming technology is very widely used in modern industry, and drip molding occupation ratio is very big, and plate
There are many kinds of methods, such as age forming, increment press shaping die, contour peening, laser bend forming etc. for forming, in these methods
Middle laser bend forming belongs to local buckling forming, by arranging certain scanning area in plate heating surface, and then to plate
The bending forming for carrying out certain deflection can be shaped as different shapes using different forming parameter control plate bending angle
Shape, and circular shape is one such shaping form.The circular arc that sheet material forming is certain curvature is answered in actual industry
With very extensive, such as in the industry such as space flight, automobile, ship, many plate constructions are all the arc structures of certain curvature, therefore
Grasping has realistic meaning for the forming technique for the circular arc that plate bending is certain curvature.
Laser plate forming technique is a kind of technology that partial plastic forming is typically carried out to plate, laser beam in forming process
With certain spot size irradiation in the plate surface to be shaped, bending forming carried out to scanning area, and many scanning areas
Combination can by sheet material forming be various shapes, the forming mode of exactly this partial sweep cause laser plate at
Shape technology faces the problem of scanning strategy planning.The arrangement of scan line can be arbitrary in laser sheet material forming, this any
Property be embodied in the arbitrariness of scan line quantity, arbitrariness of sweep span etc., and be directed to the arrangement of each different scan line,
Different forming parameters is all corresponded to relative to specific shaping form.It particularly, is the circular arc of certain curvature by sheet material forming
Also countless scan line arrangements is corresponded to, and each arrangement corresponds to different forming parameters.For one kind
Specific scan line arrangement, the size of deflection is the key that forming after the scanning of each scan line, how to calculate one kind
Deflection under scan line arrangement after the scanning of each scan line is the pass of laser plate forming technique forming accuracy control
Key；Therefore it is badly in need of providing a kind of method for improving laser plate forming technique forming accuracy.
In view of the above drawbacks, creator of the present invention obtains the present invention by prolonged research and practice finally.
Summary of the invention
To solve above-mentioned technological deficiency, the technical solution adopted by the present invention is, provides a kind of flat section and approaches circular arc
Method, realized by following steps:
Step 1: plane is split, and obtains the length of each segmentation section；
Step 2: the local inclination angle between adjacent segmentation section is calculated；
Step 3: spliting node and planar ends are calculated according to the local inclination angle and the cosine law of adjacent segmentation section
Portion or remaining angle of spliting node line relative to adjacent segmentation section；
Step 4: spliting node and plane or linear end or remaining spliting node line are calculated using the cosine law
Length；
Step 5: according to Step 3: four calculated result finally calculates flat end or remaining spliting node is relatively flat
The height of face initial position, using this highly as the basis for approaching circular arc.
Preferably, plane to be arbitrarily divided into n parts, every part of length is respectively L in step 11、L2、L3…Ln, every part
Corresponding central angle is respectively α1、α2、α3…αn, then have n-1 spliting node after dividing.
Preferably, calculating the local inclination angle between adjacent segmentation section, i.e. phase using angle of osculation theorem in step 2
The sum of neighbour's segmentation section angle of circumference, divides section L1Relative to segmentation section L2Bending angle be
αrel12--- segmentation section L1Opposite segment section L2Local inclination angle；
Similarly, divide section L2Opposite segment section L3Bending angle be
αrel23--- segmentation section L2Opposite segment section L3Bending angle；
And so on, divide section LnDo not scan segmentation section L relativelyn+1Bending angle be
αreln(n+1)--- segmentation section LnOpposite segment section Ln+1Bending angle；
It enablesThen αrel12=b1+b2、αrel23=b2+b3、αrel34=b3+b4…
αreln(n+1)=bn+bn+1。
Preferably, calculating segmented section according to the local inclination angle and the cosine law of adjacent segmentation section in step 3
Point and flat end or remaining angle of spliting node line relative to adjacent segmentation section；Spliting node 1 and flat end line
Relative to segmentation section L2Angle be
a1=b1+b2
a1--- spliting node 1 and flat end line are relative to segmentation section L2Angle；
Spliting node 2 and flat end line are relative to segmentation L3Angle can be calculated as by the cosine law
C2--- the length of spliting node 2 and flat end line；
Then spliting node n and flat end line are relative to segmentation Ln+1Angle be
Cn--- the length of spliting node n and flat end line.
Preferably, calculating spliting node and flat end in step 4 using the cosine law or remaining spliting node connecting
The length of line；The length of spliting node 1 and flat end line is to divide the length of section L1, i.e.,
C1=L1
Spliting node 2 and the length of flat end line are calculated as by the cosine law
And so on, spliting node n and the length of flat end line are
Preferably, in step 5, according to Step 3: four calculated result finally calculates flat end or remaining segmented section
The height of the opposite plane initial position of point carries out bending at spliting node 1 and forces using this highly as the basis for approaching circular arc
After nearly circular arc, flat end is relative to the raised height of initial position
y1=L1sin(b1+b2)=C1sin(b1+b2)=C1sina1
It is bent at spliting node 1,2 after approaching circular arc, flat end is relative to the raised height of initial position
y2=C2sina2
It is then bent at spliting node 1,2 ... n after approaching circular arc, flat end is relative to the raised height of initial position
yn=Cnsinan
In formula, an--- spliting node n and flat end line are relative to segmentation Ln+1Angle.
Preferably, calculating spliting node 1 relatively just when calculating raised relative to the initial position height of each spliting node
When the raised height in beginning position, the subscript in above-mentioned formula is enabled to increase by one, i.e.,
C2=L2
a2=b2+b3
y2=C2sina2
y3=C3sina3
an=arccos [((Ln)2+(Cn)2-(Cn-1)2)/(2LnCn)]+bn+bn+1
yn=Cnsinan
In formula, Cn--- the length of spliting node n and flat end line；
an--- spliting node n and flat end line are relative to segmentation Ln+1Angle；
yn--- it is bent at spliting node 1,2 ... n after approaching circular arc, flat end is relative to the raised height of initial position
Degree.
Preferably, in laser plate forming technique, when approaching plane or linear feature to give the circular arc of curvature,
One section of circular arc that flat sheet local buckling is become to given curvature, meets the final of the above calculation method in each shaping position
Flat end or spliting node can carry out Accurate Shaping to plate relative to the raised height of initial position.
Compared with the prior art the beneficial effects of the present invention are: 1, analyze plane or beeline approaching using method of geometry and give
Determine the method for curvature circular arc, this partial plastic forming technology of laser sheet material forming can be provided in terms of scanning strategy planning and be referred to
It leads.Based on sine and cosine theorem, triangle geometrical relationship, the relationship of plane or straight line and given curvature circular arc is established, it can be by laser
Forming technique is contacted with mathematical theory model foundation, has good directive significance to forming accuracy is improved；2, this method with
Straight line or flat end carry out approaching circular arc for criterion relative to the displacement of initial position to plane or straight segments, particularly suitable
In solving the problems, such as the shaping policy in the forming techniques such as plate part press shaping die, plate with laser bending forming, mention simultaneously
A kind of more convenient forming effect detection method is supplied, i.e., tactful workpiece end is detected into relative to the displacement of initial position
The effect and precision of shape.
Detailed description of the invention
It, below will be to required in embodiment description in order to illustrate more clearly of the technical solution in various embodiments of the present invention
The attached drawing used is briefly described.
Fig. 1 is the schematic diagram that flat section of the present invention approaches circular arc.
Specific embodiment
Below in conjunction with attached drawing, the forgoing and additional technical features and advantages are described in more detail.
The invention reside in a kind of method that flat section approaches circular arc is provided, it is suitable for laser sheet material forming, plate is arranged
Forming path in the forming techniques such as material part press shaping die.Based on sine and cosine theorem and triangle geometrical relationship by plane or straight line
Feature Segmentation approaches to give the circular arc of curvature.Plane or straight line are segmented by this method in advance, segmented mode or uniformly
Segmentation or arbitrary segmentation then according to the radius of curvature for the circular arc to be approached be based on sine and cosine theorem and triangle geometry
Relationship calculate be bent it is each segmentation section after plane or straight line end and each spliting node it is initial relative to plane or straight line
The raised height in position, and then bending is carried out to each segmentation section and approaches circular arc, it is finally reached the circular arc for approaching given curvature
Purpose.
Embodiment one
The method that flat section as described above approaches circular arc, the present embodiment are different from place and are, this method pair
Plane or straight line carry out any segmentation, and the local inclination angle mathematical modulo between adjacent segmentation section is established using angle of osculation theorem
Then type calculates spliting node with plane or linear end or remaining spliting node line relative to adjacent using the cosine law
Then the angle for dividing section calculates the length of spliting node and plane or linear end or remaining spliting node line, finally
Plane or linear end or remaining spliting node are calculated with respect to plane or the height of straight line initial position, using this height as
Approach the basis of circular arc.
Compared to other circular approximation methods, straight line or flat end phase are utilized an advantage of the invention is that it provides a kind of
The method that displacement is foundation approaches circular arc, this method has very strong realistic meaning, especially suitable for plate office
In the forming techniques such as portion's press shaping die, Laser forming of sheet metal, a kind of convenient and practical method is provided for the detection of forming effect.
Embodiment two
The method that flat section as described above approaches circular arc, the present embodiment are different from place and are, institute of the present invention
The method embodiment that the flat section stated approaches circular arc is realized by following steps:
Step 1: carrying out any segmentation for plane or straight line, obtains the length of each segmentation section；
Step 2: the local inclination angle between adjacent segmentation section is calculated；
Step 3: spliting node and planar ends are calculated according to the local inclination angle and the cosine law of adjacent segmentation section
Portion or remaining angle of spliting node line relative to adjacent segmentation section；
Step 4: spliting node and plane or linear end or remaining spliting node line are calculated using the cosine law
Length；
Step 5: according to Step 3: four calculated result finally calculates plane or linear end or remaining spliting node
The height of opposite plane or straight line initial position, using this highly as the basis for approaching circular arc.
By the calculating of above step, plane or linear end or remaining spliting node are finally calculated with respect to plane or straight
The height of line initial position, plane or linear end are with respect to plane or the raised height of straight line initial position after being bent with division position
Degree and each spliting node is raised with respect to plane or straight line initial position highly matches to carry out approaching circle to plane or straight line
Arc ensure that the precision approached.
In actual application, such as in laser Sheet Metal Forming, for a kind of given scan position arrangement with
And the shaped objects of given curvature circular arc, as long as calculation through the invention calculates plate end and each cutting part
The displacement of position opposite plate initial position after each forming, choose suitable forming parameter can to plate progress accurately at
Shape solves the scanning strategy planning problem in laser plate forming technique, improves the precision of forming.
Embodiment three
The method that flat section as described above approaches circular arc, the present embodiment is different from place and is, of the invention
Implementation is divided into five steps and carries out, the curvature of circular arc for first having to the length of clear plane or straight line and being approached, then
Plane or straight line are split for given partitioning scheme, and then to plane or linear end after each bending and each point
The displacement of cutpoint relative initial position is calculated, as the foundation for approaching circular arc, as shown in Fig. 1.
Step 1: as shown in Fig. 1, plane or straight line are arbitrarily divided into n parts, every part of length is respectively L1、L2、
L3…Ln, central angle corresponding to every part is respectively α1、α2、α3…αn, then have n-1 spliting node after dividing.
Step 2: the local inclination angle between adjacent segmentation section, i.e. adjacent segmentation section are calculated using angle of osculation theorem
The sum of angle of circumference, for example, dividing section L in Fig. 11Relative to segmentation section L2Bending angle be
αrel12--- segmentation section L1Opposite segment section L2Local inclination angle.
Similarly, divide section L2Opposite segment section L3Bending angle be
αrel23--- segmentation section L2Opposite segment section L3Bending angle.
And so on, divide section LnDo not scan segmentation section L relativelyn+1Bending angle be
αreln(n+1)--- segmentation section LnOpposite segment section Ln+1Bending angle.
It enablesThen αrel12=b1+b2、αrel23=b2+b3、αrel34=b3+b4…
αreln(n+1)=bn+bn+1。
Step 3: spliting node and planar ends are calculated according to the local inclination angle and the cosine law of adjacent segmentation section
Portion or remaining angle of spliting node line relative to adjacent segmentation section.As shown in Fig. 1, spliting node 1 and flat end connect
Line is relative to segmentation L2Angle be
a1=b1+b2
a1--- spliting node 1 and flat end line are relative to segmentation section L2Angle.
Spliting node 2 and flat end line are relative to segmentation L3Angle can be calculated as by the cosine law
C2--- the length of spliting node 2 and flat end line.
Then spliting node n and flat end line are relative to segmentation Ln+1Angle be
Cn--- the length of spliting node n and flat end line.
Step 4: spliting node and flat end or the length of remaining spliting node line are calculated using the cosine law.
For example, as shown in Fig. 1, the length of spliting node 1 and flat end line is to divide the length of section L1, i.e.,
C1=L1
Spliting node 2 and the length of flat end line are calculated as by the cosine law
And so on, spliting node n and the length of flat end line are
Step 5: according to Step 3: four calculated result finally calculates flat end or remaining spliting node is relatively flat
The height of face initial position, using this highly as the basis for approaching circular arc, for example, as shown in Fig. 1, at spliting node 1
Carry out bending approach circular arc after, flat end is relative to the raised height of initial position
y1=L1sin(b1+b2)=C1sin(b1+b2)=C1sina1
It is bent at spliting node 1,2 after approaching circular arc, flat end is relative to the raised height of initial position
y2=C2sina2
Then after 1,2,3 ... n of spliting node bending approaches circular arc, flat end is relative to the raised height of initial position
yn=Cnsinan
The above calculating process is relative to the raised height of initial position using plane or linear end as approaching circular arc
Foundation, there is also shortcomings in actual production application for this mode for approaching circular arc, to cooperate each spliting node phase
Height raised for initial position can be only achieved the purpose for accurately approaching circular arc.It is similar with above-mentioned calculating process, it calculates each
As long as slightly changing the parameter in above-mentioned calculating formula when raised relative to the initial position height of spliting node, such as count
When the raised height of 1 relative initial position of point counting cut node, the subscript in above-mentioned formula is enabled to increase by one, i.e.,
C2=L2
a2=b2+b3
y2=C2sina2
y3=C3sina3
an=arccos [((Ln)2+(Cn)2-(Cn-1)2)/(2LnCn)]+bn+bn+1
yn=Cnsinan
In formula, Cn--- the length of spliting node n and flat end line；
an--- spliting node n and flat end line are relative to segmentation Ln+1Angle；
yn--- after 1,2,3 ... n of spliting node bending approaches circular arc, flat end is relative to the raised height of initial position
Degree.
The calculation of remaining raised height of spliting node relative initial position is similar with above-mentioned calculation.
Example IV
The method that flat section as described above approaches circular arc, the present embodiment is different from place and is, actual
In laser plate forming technique, when approaching plane or linear feature to give the circular arc of curvature, such as by flat sheet office
Portion is bent to one section of circular arc of given curvature, as long as meeting the final flat end of the above calculation method in each shaping position
Or spliting node can carry out Accurate Shaping to plate relative to the raised height of initial position.
The foregoing is merely presently preferred embodiments of the present invention, is merely illustrative for the purpose of the present invention, and not restrictive
's.Those skilled in the art understand that in the spirit and scope defined by the claims in the present invention many changes can be carried out to it,
It modifies or even equivalent, but falls in protection scope of the present invention.
Claims (8)
1. a kind of method that flat section approaches circular arc, which is characterized in that realized by following steps:
Step 1: plane is split, and obtains the length of each segmentation section；
Step 2: the local inclination angle between adjacent segmentation section is calculated；
Step 3: according to the local inclination angle and the cosine law of adjacent segmentation section calculate spliting node and flat end or
Remaining angle of spliting node line relative to adjacent segmentation section；
Step 4: spliting node and flat end or the length of remaining spliting node line are calculated using the cosine law；
Step 5: according to Step 3: four calculated result finally calculates flat end or remaining spliting node with respect at the beginning of plane
The height of beginning position, using this highly as the basis for approaching circular arc.
2. the method that flat section as described in claim 1 approaches circular arc, which is characterized in that in step 1, plane is any
N parts are divided into, every part of length is respectively L1、L2、L3…Ln, central angle corresponding to every part is respectively α1、α2、α3…αn, then divide
There is n-1 spliting node after cutting.
3. the method that flat section as claimed in claim 2 approaches circular arc, which is characterized in that in step 2, utilize the angle of osculation
Theorem calculates the local inclination angle between adjacent segmentation section, i.e. the sum of adjacent segmentation section angle of circumference, divides section L1Relative to
Divide section L2Bending angle be
αrel12--- segmentation section L1Opposite segment section L2Local inclination angle；
Similarly, divide section L2Opposite segment section L3Bending angle be
αrel23--- segmentation section L2Opposite segment section L3Bending angle；
And so on, divide section LnDo not scan segmentation section L relativelyn+1Bending angle be
αreln(n+1)--- segmentation section LnOpposite segment section Ln+1Bending angle；
It enablesThenαrel23=b2+b3、αrel34=b3+b4…
αreln(n+1)=bn+bn+1。
4. the method that flat section as claimed in claim 3 approaches circular arc, which is characterized in that in step 3, according to adjacent point
It is opposite with flat end or remaining spliting node line that the local inclination angle and the cosine law for cutting section calculate spliting node
In the angle of adjacent segmentation section；Spliting node 1 and flat end line are relative to segmentation section L2Angle be
a1=b1+b2
a1--- spliting node 1 and flat end line are relative to segmentation section L2Angle；
Spliting node 2 and flat end line are relative to segmentation section L3Angle can be calculated as by the cosine law
C2--- the length of spliting node 2 and flat end line；
Then spliting node n and flat end line are relative to segmentation section Ln+1Angle be
Cn--- the length of spliting node n and flat end line.
5. the method that flat section as claimed in claim 4 approaches circular arc, which is characterized in that fixed using cosine in step 4
Reason calculates spliting node and flat end or the length of remaining spliting node line；Spliting node 1 and flat end line
Length is to divide the length of section L1, i.e.,
C1=L1
Spliting node 2 and the length of flat end line are calculated as by the cosine law
And so on, spliting node n and the length of flat end line are
6. the method that flat section as claimed in claim 5 approaches circular arc, which is characterized in that in step 5, according to Step 3:
Four calculated result finally calculates the height of flat end or remaining spliting node with respect to plane initial position, utilizes this height
As the basis for approaching circular arc, carried out at spliting node 1 after bending approaches circular arc, flat end is increased relative to initial position
Height be
y1=L1sin(b1+b2)=C1sin(b1+b2)=C1sina1
It is bent at spliting node 1,2 after approaching circular arc, flat end is relative to the raised height of initial position
y2=C2sina2
It is then bent at spliting node 1,2 ... n after approaching circular arc, flat end is relative to the raised height of initial position
yn=Cnsinan
In formula, an--- spliting node n and flat end line are relative to segmentation section Ln+1Angle.
7. the method that flat section as claimed in claim 6 approaches circular arc, which is characterized in that it is opposite to calculate each spliting node
When initial position raised height, when calculating the raised height of 1 relative initial position of spliting node, under enabling in above-mentioned formula
Mark increases by one, i.e.,
C2=L2
a2=b2+b3
y2=C2sina2
y3=C3sina3
an=arccos [((Ln)2+(Cn)2-(Cn-1)2)/(2LnCn)]+bn+bn+1
yn=Cnsinan
In formula, Cn--- the wire length of spliting node n and flat end；
an--- spliting node n and flat end line are relative to segmentation section Ln+1Angle；
yn--- it is bent at spliting node 1,2 ... n after approaching circular arc, flat end is relative to the raised height of initial position.
8. the method that flat section as described in claim 1 approaches circular arc, which is characterized in that in laser plate forming technique
In, when approaching plane characteristic to give the circular arc of curvature, flat sheet local buckling is become to a Duan Yuan of given curvature
Arc, each shaping position meet the above calculation method final flat end or spliting node it is raised relative to initial position
Highly, Accurate Shaping can be carried out to plate.
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| CN108994838A (en) * | 2018-08-21 | 2018-12-14 | 智久(厦门)机器人科技有限公司上海分公司 | The relationship calculation method and system of robot location and planning path |
| CN112950627B (en) * | 2021-04-01 | 2023-01-20 | 上海柏楚电子科技股份有限公司 | Detection and control method and system for laser cutting |
| CN113751543A (en) * | 2021-08-13 | 2021-12-07 | 南京蓝昊智能科技有限公司 | Metal plate arc bending method |
| CN114619203B (en) * | 2021-12-24 | 2022-09-20 | 钢一控股集团有限公司 | Forming method of large-diameter stainless steel pipe |
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