CN116484542A - Search type layout method for discharging round piece with single size on rectangular plate - Google Patents
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Abstract
The invention discloses a search type layout method for discharging round pieces with single size on a rectangular plate, which relates to the field of optimized layout and comprises the following steps: step 1, initializing the width W and the length L of a rectangular plate and the radius R of a round piece, and setting the maximum storage quantity K; step 2, placing a first round piece on a rectangular plate to generate a scheme S 1 Saving the results to the schema set P 1 In (a) and (b); step 3, traversing scheme set P i In each existing scheme S ik On the basis of which all the position points at which the next round can be discharged are calculated; step 4, S is ik The generated sample points to be discharged are arranged in descending order according to the utilization rate, and the first two sample discharging positions are selectedSetting points; step 5, summarizing all the new schemes generated in the step 4 into a new set S and arranging the new sets in a descending order; step 6, de-duplicating the S; step 7, selecting the first K schemes in S and adding the schemes to P i+1 In (a) and (b); step 8, repeating the steps 3-7 until the rectangular plate is full; and 9, outputting an optimal scheme.
Description
Technical Field
The invention relates to the field of optimized layout, in particular to a search type layout method for discharging round pieces with single size on a rectangular plate.
Background
The round blank can be widely applied to the mechanical manufacturing industry, for example, silicon steel plates are sheared into round sheets to manufacture a stator and a rotor core of the motor; cutting stainless steel coil plate into round pieces to make pot, bowl, cup, basin, kettle, etc. In actual production, the round blank is obtained by punching, shearing and cutting the raw materials. With the increasing importance of people on resource and energy waste, minimizing waste is a goal pursued by enterprises. A good layout scheme can reduce the production cost of enterprises, improve the processing efficiency, strengthen the competitiveness of the enterprises, save raw materials, is an important component for green production and manufacture, and has economic benefit and theoretical value for the study of the layout problem.
Round blanks are statistically about 60% of the total cost of the final product. Therefore, when a single-size round blank is processed on a rectangular plate with a fixed size by using processing equipment with a limited processing range under the precondition of meeting the processing technology and leaving a certain processing allowance, the round piece is required to be arranged in the rectangular plate to obtain higher plate utilization rate.
The existing pattern layout modes include:
1. by virtue of experience layout, the layout has no certain rule, so that the material utilization rate is low, the manufacturing cost is high, raw materials and enterprise resources are seriously wasted, and the enterprise competitiveness is reduced.
2. And adopting an in-line mode for discharging. The straight line is the simplest and most common method for discharging, and the discharging period is easy to find. During the process, only the first row or rows need to be maintained for repeated processing, as shown in fig. 1. However, the board utilization rate of this layout method is also low, mainly because: 1) The part surrounded by the 4 adjacent circular pieces in the straight row is quadrilateral, and the surrounded area is larger; 2) The distances d1 and d2 between the circular member and the edges of the rectangular plate are larger.
Some new methods of proofing have also emerged.
Guo Weijian et al in China patent application No. (application number: CN 201910340227.3) in a method for processing round parts on coiled materials, the problem that rectangular coiled materials (assuming that the width of the materials is fixed and the length is not constrained) are processed into round parts with a single size is solved, and the inclined pattern arranging method is utilized, so that the material utilization rate is effectively improved, and the production cost is reduced. However, in practical production, most of the plates are rectangular plates with fixed width and length, and the practical applicability of the above technical solution is limited.
Wang Yingcong et al in Chinese patent application "a rectangular plate-oriented heuristic layout method for round pieces" (application number: CN 202010344116.2), propose a method of determining points according to rules and then randomly shifting forward or backward on the basis of an initial random sequence to generate a new discharge sequence. The method comprehensively considers the space with the arranged samples and the space without the arranged samples, improves the utilization rate of the plate, has great randomness, and has different results for each operation.
The circular layout problem belongs to one of the combination optimization problems, is a classical NP-hard problem, and unless p=np, there is no deterministic algorithm to find an exact solution in polynomial time.
Accordingly, those skilled in the art have been working to develop a new method of discharging round pieces of a single size on a rectangular plate material, solving the above-mentioned deficiencies in the prior art, and capable of giving better discharging results within a prescribed time.
Disclosure of Invention
In view of the above-mentioned drawbacks of the prior art, the present invention is to provide an optimal layout method for processing round pieces with a single size on rectangular plates, which overcomes the problems of low material utilization, high manufacturing cost, and serious raw material waste in the existing layout method.
In order to solve the technical problems, the invention establishes a mathematical model for processing the single-size round piece on the rectangular plate, and provides a heuristic round layout rule for discharging the single-size round piece on the rectangular plate and a search layout method based on the layout rule, which restrict the length and the width of the rectangular plate, not only improve the material utilization rate and reduce the manufacturing cost, but also are suitable for rectangular plates with different sizes, and have strong practicability.
Specifically, the present invention provides a search type layout method for discharging round pieces of a single size on a rectangular plate, characterized by comprising the steps of:
step 1, initializing the width W and the length L of a rectangular plate and the radius R of a round piece, and setting a scheme set P i A maximum stored number K of (2);
step 2, placing the first round piece at the lower left corner of the rectangular plate to generate a scheme S 1 And saves the result to the scheme set P 1 In (a) and (b);
step 3, traversing the scheme set P i In each existing scheme S ik On the basis of the above, all position points which can be discharged by the next round piece are calculated according to a layout rule algorithm;
step 4, the scheme S ik The generated sample to be discharged is arranged in descending order according to the utilization rate of the used rectangular area, the first two sample discharging position points are selected to discharge the round piece, and a new scheme is generatedAnd->
Step 5, summarizing all the new schemes generated in the step 4 into new setsAnd arranged in descending order;
step 6, performing de-duplication processing on the new set S, namely deleting one of the circles if the positions of each circle in the two stock solutions are the same;
step 7, selecting the first K schemes in the new set S and adding the schemes to P i+1 In (a) and (b);
step 8, repeating the steps 3-7 until the rectangular plate has no redundant space to discharge the next round piece;
step 9, outputting the optimal scheme, namely the scheme set P i First layout pattern S of (a) i1 。
Further, the layout rule algorithm in the step 3 is: in the existing scheme S ik Based on (1), the edge set formed by the coiled material edges of the rectangular plate is denoted as E, and the (i+1) th round piece is denoted as C i+1 C is then i+1 The placeable locations are of the following type:
(1)C i+1 at least with the existing scheme S ik Is tangential to 2 of said circular members;
(2)C i+1 at least with the existing scheme S ik Is tangential to at least 1 of the circular pieces and is tangential to at least 1 of the edges of the set E;
(3)C i+1 at least tangential to 2 edges of the set E of edges;
calculating C according to the rules in (1) to (3) i+1 All location points that can be discharged.
Further, the coil sides of the rectangular sheet include a left side, a right side, an upper side, and a lower side.
Further, the lower left corner of the rectangular plate is taken as an origin of coordinates, the length direction of the rectangular plate is taken as an X axis, and the width direction of the rectangular plate is taken as a Y axis, and a Cartesian coordinate system is established; setting the center coordinates of the ith round piece as (x) i ，y i ) Let M be the circular quantity of arranging into rectangular panel, then rectangular area utilization ratio of rectangular panel is:
wherein U is the utilization rate of the rectangular area of the rectangular plate.
Further, constraint conditions of the mathematical model for processing the single-size round piece layout problem on the rectangular plate are as follows:
wherein the center coordinates of the ith round piece are (x) i ，y i ) The center coordinates of the j-th round piece are (x) j ，y j ) R is the radius of the round piece, W and L are the width and the length of the rectangular plate respectively, and M is the number of circles discharged into the rectangular plate.
Further, no overlap can occur between the circular members, and the circular members cannot exceed the boundaries of the rectangular plate.
Further, a preset distance d is reserved between the round pieces; in this case, the radius R of the circular member is set to R+d/2.
Further, in the step 7, if the number of schemes in the new set S is smaller than K, directly let P i+1 It is sufficient to=s.
Further, the size of the maximum storage number K affects the quality of the layout result: the larger K, the better the layout result, but the longer the time spent.
Further, the value range of the maximum storage quantity K is more than or equal to 10 and less than or equal to 20.
The search type layout method for discharging the round piece with the single size on the rectangular plate has at least the following technical effects:
1. the specific layout rule is determined by establishing a mathematical model of single-size circular layout on a rectangular plate, and the specific coordinates of the next circular piece discharge can be determined on the basis of the existing layout scheme. The utilization rate of the currently used plate can be calculated according to specific coordinate points, so that the quality of the coordinates can be compared, then K better coordinate points are selected for updating iteration, and round pieces are discharged one by one until the rectangular plate cannot accommodate the next round piece;
2. when a circular piece with a single size is processed on a rectangular plate with a fixed size, the search type layout method provided by the invention can obtain the same solution, and compared with the prior art, the method not only improves the material utilization rate, but also reduces the manufacturing cost, is suitable for rectangular plates with different sizes, and has strong practicability. When the method is applied to actual production, the optimal layout scheme can be obtained in a short time only by inputting the radius of the round piece, the width and the length of the rectangular plate and the maximum storage quantity of the scheme set into a computer, so that the method is convenient and quick, has high degree of automation and greatly improves the production efficiency.
The conception, specific structure, and technical effects of the present invention will be further described with reference to the accompanying drawings to fully understand the objects, features, and effects of the present invention.
Drawings
FIG. 1 is a schematic diagram of an inline sample removal method in the prior art;
FIG. 2 is a schematic diagram of the position of searching for the next round part according to the layout rules;
FIG. 3 is a schematic view of a rectangular area of a currently consumed sheet material;
FIG. 4 is a set of schemes P i Is an iterative schematic of (a);
FIG. 5 is a flow chart of a method implementation of a preferred embodiment of the present invention;
FIG. 6 is a schematic diagram of test case results of the method of FIG. 5.
Detailed Description
The following description of the preferred embodiments of the present invention refers to the accompanying drawings, which make the technical contents thereof more clear and easy to understand. The present invention may be embodied in many different forms of embodiments and the scope of the present invention is not limited to only the embodiments described herein.
In the drawings, like structural elements are referred to by like reference numerals and components having similar structure or function are referred to by like reference numerals. The dimensions and thickness of each component shown in the drawings are arbitrarily shown, and the present invention is not limited to the dimensions and thickness of each component. The thickness of the components is exaggerated in some places in the drawings for clarity of illustration.
The invention establishes a mathematical model for processing a circular piece with a single size on a rectangular plate. Because of the NP-hard nature of the problem, the technical scheme provided by the invention provides heuristic round layout rules and a search type layout method based on the layout rules.
Initializing the width W and length L of the rectangular plate and the radius R of the round piece, and setting a scheme set P i Setting the left lower corner of the rectangular plate as an origin of coordinates, and establishing a Cartesian coordinate system by taking the length direction of the rectangular plate as an X axis and the width direction as a Y axis; let the center coordinates of the ith circular piece be (x) i ，y i ) Let M be the circular quantity of discharging into rectangular panel, then rectangular area utilization ratio of rectangular panel is:
wherein U is the rectangular area utilization rate of the rectangular plate.
The constraint conditions of the mathematical model for processing the layout problem of the round piece with a single size on the rectangular plate are as follows:
wherein the center coordinates of the ith round piece are (x) i ，y i ) The center coordinates of the j-th round piece are (x) j ，y j ) R is the radius of the round piece, W and L are the width and the length of the rectangular plate respectively, and M is the number of circles discharged into the rectangular plate.
The specific layout rule is determined by establishing a mathematical model of single-size circular layout on a rectangular plate, and the specific coordinates of the next circular piece discharge can be determined on the basis of the existing layout scheme. The utilization rate of the currently used plate can be calculated according to specific coordinate points, so that the quality of the coordinates can be compared, then K better coordinate points are selected for updating iteration, circular pieces are discharged one by one until the rectangular plate cannot accommodate the next circular piece.
The invention provides a search type layout method for discharging round pieces with single size on a rectangular plate, which comprises the following steps of:
step 1, initializing the width W and the length L of a rectangular plate and the radius R of a round piece, and setting a scheme set P i A maximum stored number K of (2);
step 2, placing a first round piece at the left lower corner of the rectangular plate to generate a scheme S 1 And saves the result to the scheme set P 1 In (a) and (b);
step 3, traversing scheme set P i In each existing scheme S ik On the basis of the above, all position points which can be discharged by the next round piece are calculated according to a layout rule algorithm;
step 4, scheme S ik The generated sample to be discharged is arranged in descending order according to the utilization rate of the used rectangular area, the first two sample discharging positions are selected to discharge the round piece, and a new scheme is generatedAnd->
Step 5, summarizing all the new schemes generated in the step 4 into a new setAs shown in fig. 4, and arranged in descending order;
step 6, carrying out de-duplication treatment on the new set S, namely deleting one of the circles if the positions of each circle in the two stock solutions are the same;
step 7, selecting the first K schemes in the new set S and adding the schemes to P i+1 In (a) and (b); if the number of schemes in the new set S is smaller than K, directly letting P i+1 It is sufficient that =s;
step 8, repeating the steps 3-7 until the rectangular plate has no redundant space to discharge the next round piece;
step 9, outputting the optimal scheme, namely scheme set P i First layout pattern S of (a) i1 。
The layout rule algorithm in the step 3 is as follows: in the existing scheme S ik Based on (1), the set of edges (left, right, upper and lower) of the coiled material edges of the rectangular plate is denoted as E, and the (i+1) th round piece is denoted as C i+1 C is then i+1 The placeable locations are of the following type:
(1)C i+1 at least with the existing scheme S ik The 2 circular pieces are tangent;
(2)C i+1 at least with the existing scheme S ik Tangent to at least 1 of the circles of the set of edges E;
(3)C i+1 at least tangential to 2 edges in the edge set E;
calculating C according to the rules in (1) to (3) i+1 All location points that can be discharged.
As shown in fig. 2, the existing set is S 2 Then C can be determined according to the rule 3 There are 6 (p 1, p2, p3, p4, p5, p 6) positions.
And defining an evaluation function screening layout point at all the position points which can be discharged.
Assuming that the next round is discharged to a certain point therein, the area utilization of the used sheet material at that time can be calculated. And calculating the utilization rate of the plate area of all the position points, and then discharging the parts at one position point with the highest utilization rate.
As shown in fig. 3, if the third round is discharged at p1, the used sheet area utilization at this time is three round areas divided by the area of the rectangle Rect1, with the result u1≡58.9%; if the third round is discharged at p3, then the used sheet area utilization at this time is three round areas divided by the area of rectangle Rect2, resulting in u3≡78.5%. It is clear that U3 is larger than U1, so it is better to discharge the third circle at position p 3.
In the above-described embodiment of the present invention, the problem of the spacing between the circular members is not considered, but in actual production, it is sometimes required to leave a spacing d between the circular members. Under the condition that a distance D is reserved, the optimal layout method is also suitable for the condition that a distance is reserved between the round pieces, and the radius R of the round pieces is set to be R+D/2 in the step 1.
The size of the maximum storage quantity K influences the quality of the layout result: the larger K, the better the layout result, but the longer the time spent. K is more than or equal to 10 and less than or equal to 20.
Compared with the prior art, the method for processing the single-size round piece search type layout on the rectangular plate improves the material utilization rate, reduces the manufacturing cost, is suitable for rectangular plates with different sizes, and has strong practicability. When the method is applied in actual production, the optimal layout scheme can be obtained in a short time only by inputting the radius of a round piece, the width and the length of a rectangular plate and the maximum storage quantity of the scheme set into a computer, so that the method is convenient and quick, has high automation degree, greatly improves the production efficiency, and is a layout case.
As shown in fig. 6, the rectangular plate has a width w=500 and a length l=500, the radius r=20 of the circle to be processed, and the maximum number k=20 of the plan sets stored. 144 circular pieces can be processed in an in-line mode (the left side of fig. 6, the material utilization rate is 72.38%), 166 circular pieces can be processed in the method of the invention (the right side of fig. 6, the material utilization rate is 83.44%), and the material utilization rate is improved by 11.06%.
The foregoing describes in detail preferred embodiments of the present invention. It should be understood that numerous modifications and variations can be made in accordance with the concepts of the invention without requiring creative effort by one of ordinary skill in the art. Therefore, all technical solutions which can be obtained by logic analysis, reasoning or limited experiments based on the prior art by the person skilled in the art according to the inventive concept shall be within the scope of protection defined by the claims.
Claims (10)
1. A search pattern layout method for discharging round pieces of a single size on a rectangular plate material, the method comprising the steps of:
step 1, initializing the width W and the length L of a rectangular plate and the radius R of a round piece, and setting a scheme set P i A maximum stored number K of (2);
step 2, placing the first round piece at the lower left corner of the rectangular plate to generate a scheme S 1 And saves the result to the scheme set P 1 In (a) and (b);
step 3, traversing the scheme set P i In each existing scheme S ik On the basis of the above, all position points which can be discharged by the next round piece are calculated according to a layout rule algorithm;
step 4, the scheme S ik The generated sample to be discharged is arranged in descending order according to the utilization rate of the used rectangular area, the first two sample discharging position points are selected to discharge the round piece, and a new scheme is generatedAnd->
Step 5, summarizing all the new schemes generated in the step 4 into new setsAnd arranged in descending order;
step 6, performing de-duplication processing on the new set S, namely deleting one of the circles if the positions of each circle in the two stock solutions are the same;
step 7, selecting the first K schemes in the new set S and adding the schemes to P i+1 In (a) and (b);
step 8, repeating the steps 3-7 until the rectangular plate has no redundant space to discharge the next round piece;
step 9, outputting the optimal scheme, namely the scheme set P i First layout pattern S of (a) i1 。
2. The method for searching for a pattern layout for discharging round pieces of a single size on a rectangular plate according to claim 1, wherein the pattern layout rule algorithm in the step 3 is: in the existing scheme S ik Based on (1), the edge set formed by the coiled material edges of the rectangular plate is denoted as E, and the circular piece with the (+ 1) th is denoted as C i+1 C is then i+1 The placeable locations are of the following type:
(1)C i+1 at least with the existing scheme S ik Is tangential to 2 of said circular members;
(2)C i+1 at least with the existing scheme S ik Is tangential to at least 1 of the circular pieces and is tangential to at least 1 of the edges of the set E;
(3)C i+1 at least tangential to 2 edges of the set E of edges;
calculating C according to the rules in (1) to (3) i+1 All location points that can be discharged.
3. The search pattern layout method for discharging round pieces of a single size on a rectangular plate material according to claim 2, wherein said coil sides of said rectangular plate material include left, right, upper and lower sides.
4. The search pattern layout method for discharging round pieces of a single size on a rectangular plate according to claim 1, wherein a lower left corner of the rectangular plate is an origin of coordinates, and a cartesian coordinate system is established with a length direction of the rectangular plate being an X-axis and a width direction of the rectangular plate being a Y-axis; setting the center coordinates of the ith round piece as (x) i ,y i ) Let M be the circular quantity of arranging into rectangular panel, then rectangular area utilization ratio of rectangular panel is:
wherein U is the utilization rate of the rectangular area of the rectangular plate.
5. The search pattern layout method for discharging round pieces of a single size on a rectangular plate according to claim 4, wherein the constraint conditions of the mathematical model for processing round piece of a single size pattern layout problem on the rectangular plate are:
wherein the center coordinates of the ith round piece are (x) i ,y i ) The center coordinates of the j-th round piece are (x) j ,y j ) R is the radius of the round piece, W and L are the width and the length of the rectangular plate respectively, and M is the number of circles discharged into the rectangular plate.
6. The method for searching for a pattern layout for discharging round pieces of a single size on a rectangular plate material according to claim 4, wherein no overlapping between the round pieces occurs and the round pieces cannot exceed the boundary of the rectangular plate material.
7. The search pattern layout method for discharging round pieces of a single size on a rectangular plate as claimed in claim 4, wherein a predetermined interval d is left between said round pieces; in this case, the radius R of the circular member is set to R+d/2.
8. The method for searching for a layout for discharging round pieces of a single size on a rectangular plate according to claim 1, wherein in said step 7, if the number of schemes in said new set S is less than K, then directly let P i+1 It is sufficient to=s.
9. The search pattern layout method for discharging round pieces of a single size on a rectangular plate according to claim 1, wherein the size of the maximum storage number K affects the quality of the pattern layout result: the larger K, the better the layout result, but the longer the time spent.
10. The method for searching for a pattern layout for discharging round pieces of a single size on a rectangular plate according to claim 1, wherein the maximum storage number K has a value ranging from 10.ltoreq.k.ltoreq.20.
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