The ultimate goal of optimal layout of sheet metal is to realize economical and efficient cutting and blanking. Therefore, the problem of optimal layout of sheet metal is by no means a purely two-dimensional geometric shape combination optimization problem. If you do not consider the actual existence of sheet metal cutting and blanking Processing and manufacturing conditions and process constraints, one-sided pursuit of material utilization, may ultimately affect the process feasibility of blanking and processing economy, so how to convert process constraints into geometric constraints that can be used for optimal layout is the purpose of this chapter The key problem to be solved.
This chapter will first comprehensively analyze some of the main process constraints and common optimization goals that exist in the sheet metal cutting process, study the geometric constraints caused by each process constraint, and give the corresponding solution strategies, combined with the previous chapter The established basic nesting algorithm based on the best matching strategy finally forms a universal automatic optimization nesting technology that can consider the main process constraints of sheet metal blanking.
1.1 Research on the transformation strategy of process constraints in sheet metal optimal layout
Because the process constraints encountered during the layout of parts can only be described by geometric constraints in the layout drawing, this section first studies the conversion strategy from actual blanking process constraints to optimized layout geometric constraints.
In actual production, the cutting equipment and cutting method used for blanking are obviously the decisive factors in determining the optimal nesting algorithm for sheet metal. If the blanking uses equipment such as shears, sawing machines, trolley cutting machines, etc., you can only Consider the rectangular layout plan. If the flame, plasma, laser and other CNC cutting equipment are used, it is mainly used for the layout of irregular parts from the economic point of view. Considering that the layout of rectangular parts is the layout of general parts A special situation, so this section will mainly study the process constraint processing technology for the optimized layout of irregular parts. The main process factors considered in the blanking of sheet metal parts can be summarized as follows:
(1) Cutting and fiber direction
When blanking, the fiber direction of the board is a process factor that must be considered. Since the cold-rolled steel sheet used for bending has directionality after many times of rolling, the shape index of the sheet along the fiber direction is better than that of the vertical direction. When the bending line of the bending part is perpendicular to the fiber direction, the material can reach the smallest relative bending radius, and the part is not easy to tear, as shown in Figure 5-1(a); when the bending line is parallel to the fiber direction, if this time Close to the limit processing, the cracking phenomenon shown in Figure 5-1(b) is easy to appear at the bend. When the bent part is bent on both sides, as shown in Figure 5-1(c), there are multiple bending lines that are perpendicular to each other. When layout, try to ensure that each bending line and the fiber direction of the sheet can be fixed. Angle placement.
The fiber direction constraint can be directly mapped to the placement angle constraint of the parts to be arranged during layout. When the layout algorithm is compiled, a rotation flag can be set for each part. When the flag is zero, the part can rotate freely. When the flag is non-zero, the placement direction of the rectangular piece can only be "orderly placed" or "upside down", and the irregular piece must be limited to its discharge angle range based on the direction of the bending line and the fiber direction. Take Figure 5-2 as an example, record the angle between the bending line of the part and the reference center line as Ang1, and arrange it into the specified plate. The rotation angle Ang2 must meet the following conditions:
(2) Cutting loss and sheet material edge loss
No matter what kind of cutting method is used, material loss will inevitably occur. If the cutting is directly based on the design size of the part without considering the existence of the slit, the outer contour size of the actual cut part will become smaller and the inner hole size will change. Large, resulting in dimensional deviation. In addition, the plate may be lost during storage and transportation, resulting in defects such as burrs and cracks in the corners of the plate. Therefore, when the parts are discharged, keep a certain distance from the edge of the plate to ensure the processing quality of the parts. loss. The schematic diagram of the two kinds of losses is shown in 5-3.
The sheet edge loss actually reduces the arranging area of the parts. Therefore, the sheet size can be corrected by setting the "part to the edge distance" before layout. In order to compensate for the kerf loss, the polygonal equidistant offset can generally be used The algorithm first precompensates the design size of the part, and then offsets the cutting loss.
The equidistant offset of polygons is a fundamental problem in the field of digital design and manufacturing. The three steps of the edge equidistant offset algorithm: first offset each edge of the polygon in an equidistant direction, and use a straight line or arc to disconnect The equidistant edge connection of the polygon; secondly, search and mark the self-intersection point in the closed loop formed by the equidistant line; finally delete the redundant invalid loop to obtain the equidistant offset contour of the polygon. Deal with various solving algorithms when disconnecting equidistant edge connections. The algorithm diagram 5-4 is shown in:
Taking into account that the cutting loss produced by different cutting methods is not the same, it is necessary to set the equidistant offset of the parts according to the actual situation before each optimization layout.
(3) Common edge cutting
In actual production, users of laser cutting machines have realized that if the automatic cutting path cannot guarantee effective cutting of parts, ensure component quality and increase production, then the benefits of layout software in material utilization will be lost. Therefore, the new development trend of nesting software is to fully consider the efficiency of subsequent cutting machine tools, and common edge cutting is currently an important means to improve cutting efficiency and save cutting costs. The so-called co-edge cutting is to arrange suitable matched parts in combination of long side and long side according to certain rules when optimizing layout, so that the cutting command only needs to cut the common side part of the part once to realize the separation of the parts.
The difference between ordinary cutting and coedge cutting can be illustrated by the example in Figure 5-5. The traditional cutting method is realized Figure 5-5
The parts in (1) need to be preheated and perforated twice, the number of cutting edges is 8, and the gaps between the parts need to be reserved; using common edge cutting, see Figure 5-5(2), the two parts are inclined The edges share the same edge, and only need to preheat the perforation once during cutting and eliminate a long cutting edge. The cutting path is greatly reduced. As a slit between the common edges is omitted, the material utilization rate is also improved. It can be seen that in the layout process, reasonable use of the common edge cutting technology, consciously bonding the same or similar straight edges or arcs together, can greatly improve the cutting efficiency and save cutting consumables.
The process requirements of co-edge cutting reflect that the optimal layout is actually a combination of parts, that is, how to combine the parts in a long-side-to-long-side manner during layout. In manual layout, the rules of "straight to straight, diagonal to diagonal, concave to convex" are often used to combine parts. This chapter will study how to transform the above engineering experience into intelligent emission that can be followed when combining parts in digital layout. rule.
In actual production, uniform blanking of multiple identical parts on the same plate is a common processing situation. Therefore, co-edge layout of the same parts is the most common part combination requirement. This section will focus on the study of the same parts. Common edge combination technology between the two. In fact, the combination optimization problem of a single part has been well solved in the field of optimized layout of blanking parts. Commonly used combination methods include four schemes: ordinary single row, ordinary double row, opposite single row and opposite double row. Scholars such as Cao Ju and Zhou Ji of Huazhong University of Science and Technology, and Xie Xiaolong and Zhao Zhen of Shanghai Jiaotong University have conducted in-depth research on the mathematical model of this problem and how to solve it. Figure 5-6 shows the effect diagram of the four layout methods of a certain part, and the algorithm principle of single row and double row is shown in Figure 5-7.
In the single and double row layout methods, the compactness of the part arrangement plan can be calculated by the feed step P and the material width W. As shown in Figure 5-7, in a single row, the step distance and material width are both single-valued functions of the part nesting angle α, while in a double row, the part is formed by abutting the "copy" formed by rotating 180° A new composite part is created. At this time, the step distance and material width of the part are not only affected by the rotation angle α, but also depend on the relative displacement s of the vertical height of the two adjacent parts. Taking the material utilization rate h as the optimization target, then A unified mathematical model of the single and double row problem can be described as:
Among them, n is the number of parts in a single step. Obviously, n=1 for single row, n=2 for double row, A is the area of a single part, and s=0 for single row.
The general process for numerically solving the above optimization problems can be roughly divided into two steps: firstly traverse the nesting angles with a suitable step length in the range of 0-180°, and then search for each nesting angle with a suitable step length. Given the optimal relative misalignment at a given angle, the approximate optimal layout scheme is found according to the algorithm's traversal results in these two "directions".
Although the optimization goal of the part single and double row algorithm is to find the layout plan with the highest part layout rate, in most cases, the four layout methods of the algorithm also include the long-side-to-long-side solution scheme, as shown in Figure 5. -6 as an example, the co-edge layout of the parts is realized when the opposite double row is selected. In fact, the above part combination technology is used in many examples of irregular layout in Chapter 4. For example, in the layout result of the Jakobs2 example shown in Figure 4-20, there are multiple parts realized by the opposite single row technology. Coedge combination, it can be seen that it is feasible to apply the single and double row algorithm to solve most of the coedge combination problems. Considering that the combination problem of the same parts is actually similar to the optimal layout problem of a partial area of blanking parts, the nesting program only needs to select the appropriate single and double row algorithm according to the shape of the part to generate parts with long sides that fit each other. Group blocks, so that the same kind of parts can be arranged in a co-edge mode when optimizing nesting.
In addition to the problem of coedge combination of the same parts, the coedge combination of similar parts is also very valuable engineering experience in nesting. For example, in the Jakobs1 example in Figure 4-20, the triangle pair 3 and 4, and the L shape pair 7 The coedge combination with 10, 8 and 11 simultaneously improves the material utilization rate and cutting efficiency of layout. However, it is very difficult to realize automatic coedge combination of dissimilar parts in large-scale layout problems, because it mainly involves the definition of part similarity and how to formulate aggregation rules for similar parts.
At present, the common combination algorithm of similar parts mainly includes the part classification method: this method divides the shape types of all the parts to be arranged into four types: triangle, L-shape, U-shape and other shapes. Triangular parts can be fitted according to the long side. Two-by-two assembly, while the L-shape and U-shape can be combined in a similar way to row. This type of method can be realized by manual methods in small-scale nesting problems, but how to achieve a completely intelligent and automated co-edge bonding of dissimilar parts Still to be studied.
(4) Parts bridge
Parts bridging is also a technology widely used in actual layout. Many commercial software such as FastCAM and ProNest provide bridging functions. Bridging operation refers to connecting a group of parts in rows or columns together. When cutting, the lead-in line of the previous part naturally becomes the lead-in line of the next part, so that multiple parts can be cut with only one perforation to realize continuous cutting. . The bridging operation can save a lot of preheating and perforating time. The cutting nozzle can complete the steps of ignition, preheating, cutting, flameout, etc., and directly return to the cutting origin, thus greatly reducing the cutting stroke and effectively saving the flame cutting nozzle , Plasma electrodes and other consumables as well as water and electricity consumption.
Take the circular table bridge diagram in Figure 5-8 as an example. If 400 circular tables are cut by traditional cutting methods, 400 perforations are required. If the preheating time for each perforation is 1 minute, it will take at least 400 minutes to preheat the perforation. It means that oxygen and propane will burn in vain for nearly 7 hours. After the parts are bridged, the continuous cutting of 400 parts can be completed in one perforation, and the production efficiency has been greatly improved. According to the statistics provided by the FastCAM website, the use of the above-mentioned bridging technology can reduce perforation by at least 60% compared with traditional methods, reduce cutting paths by 20-30%, increase cutting efficiency by 30%, and reduce consumables consumption by up to 40%.
Similar to the requirement of coedge cutting, the bridge technology is still a part combination problem reflected in the layout, that is, how to arrange a group of small parts in rows or columns and form a whole, so it can also use the single and double row algorithm To solve the problem, for the above-mentioned circular platform bridge, the ordinary single-row algorithm can meet the requirements.
(5) Parts nesting
For parts with large holes or recesses, selecting suitable parts to fill or nest the blank areas of the holes or recesses is also an important means to improve material utilization in actual layout. The problem of part nesting mainly occurs in the following three situations: (1) There is a large hole in the part itself, as shown in Figure 5-9(a); (2) The part has a large concave structure, as shown in Figure 5-9 (b); (3) Large holes are produced after the parts are assembled, as shown in Figure 5-9(c).
The automatic nesting algorithm for parts during optimal layout can be set according to the above three situations. The specific algorithm design is as follows:
In case 1, the solution is to extract the contour of the inner hole, search for the largest part that can be lined into the inner hole before nesting, and then complete the nesting;
In case 2, since the concave part is not closed, the first and the last two ends of the line segment constituting the concave area can be connected and closed, as shown by the red dashed line in Figure 5-9(b). After the closed area is formed, follow Case 1. Nesting. The advantage of this processing method is that the original enveloping rectangle shape of the nested parts is not affected after the nesting is completed, thereby reducing the computational complexity.
Case 3. In this case, the parts cannot be pre-nested before nesting. A feasible method is to fill the holes in the part of the hole by searching for the blank arranging area in the later stage of nesting.
The part nesting problem is essentially a part pre-processing problem before nesting, as long as a nesting pre-processing operation is added before automatic nesting.
(6) The influence of the cutting line on the nesting of the inner hole of the part
When parts are nested, it is also necessary to consider the influence of secant lines. Since the parts are generally pierced when cutting the material, and the piercing is often larger than the cutting gap, so when the flange-type parts or the inner hole size of the part is large, the cutting line and the piercing point should be fully considered The impact on the nesting area.
As shown in Figure 5-10, if the layout is purely geometric, the size of part B can fit into the inner hole of part A, but if you consider the existence of perforations and secant lines in the actual blanking, it is obvious that B cannot Complete the nesting operation with A.
The method to solve the above problems is to regard this type of part and its secant line as a whole, and in addition to the part itself, an additional interference check for its secant line is required when the layout is judged.
(7) Other technological constraints
In addition to some of the above common process constraints, there are often other process constraints due to different process requirements involved in different cutting tasks. For example, in the rectangular layout, the cutting level should be reduced as much as possible for the one-size-fits-all case, that is, the number of steps required to cut the final part from the sheet should be reduced. In one-size-fits-all cutting, the direction of entering the knife when the sheet is first cut and the longest cutting distance should also be considered. For parts with grooves, the groove design of the parts should be completed in advance before layout. These process constraints need to be specifically set based on specific blanking tasks, such as additional bevel design modules for beveled parts, and so on.
Based on the nesting process constraints summarized above and the corresponding transformation strategies, the next section will try to incorporate the above process constraints into the nesting algorithm given in Chapter 4 to form a more practical sheet metal optimization nesting algorithm.
1.2 Sheet metal optimization nesting technology under process constraints
The layout personnel select the corresponding parts and plates according to the blanking plan. It is a standard blanking process to arrange the parts to be arranged on the plates according to the layout process requirements and then cut them uniformly. In the previous section, the workers’ perceptual process knowledge in the actual layout has been converted into the part discharge rules that can be understood by the computer-aided layout through the corresponding conversion strategy. Therefore, this section will be based on the above process conversion strategy and the establishment in the previous chapter. Basic nesting algorithm, research on sheet metal digital optimization nesting technology under technological constraints, the algorithm flow chart can be seen in 5-11, the main algorithm steps are described as follows:
Step1 According to the layout plan, count and determine the quantity and type of the parts to be arranged, and read the size and process information of the plates and parts from the plate database and the parts database respectively;
Step2 Set the process constraints according to the size and process information of the parts and plates: set the discharge angle range of the restricted parts according to the fiber direction; determine the equidistant offset of the parts according to the technical parameters of the cutting equipment and perform the offset, set the plate Leave the distance; according to the shape of the part and the given coedge and bridging requirements, pair the blocks and use them as the input for the subsequent nesting; perform nesting preprocessing operations on the parts with holes and recesses.
Step3 After completing the above-mentioned layout plan preparation, use the general optimized layout algorithm based on best matching in Chapter 4 to automatically optimize the nesting, and quickly generate the initial layout plan.
Step4 Make appropriate manual adjustments to some parts of the initial layout plan, such as arranging small parts at the top into the free area. If you are satisfied with the initial layout plan, the layout ends, calculate the material utilization rate and output the layout drawing .
Compared with the pure geometric nesting algorithm in the previous chapter, the algorithm in this section adds a process constraint setting step before automatic nesting. The nesting personnel sets the relevant process parameters through the manual interface. The essence of the process constraint setting is A process of preprocessing the nested parts. After completing the relevant settings, the computer-aided optimization nesting under the process constraints can be completed through the software automatic nesting and subsequent manual adjustments.
1.3 Instance verification
This section will combine a nesting example in a sheet metal workshop to verify the optimal nesting algorithm proposed in the previous section. As shown in Figure 5-12, the example in this section is a large and medium-sized optimized layout problem with 21 types of parts to be arranged and a total of 111 parts. The selected plate size is 400X400.
According to the traditional manual nesting method, the workers will arrange the parts in order from the largest to the smallest according to their experience, and prioritize the discharge of large-area parts so that small parts can be filled into the previously formed holes during subsequent nesting. To a certain extent, reduce the waste of plates. Since the total number of layout parts this time has reached 111, it is obvious that the manual layout method will drastically increase the labor of the layout workers and reduce the efficiency of the blanking process. At this time, the automatic layout based on process constraints proposed in this article can be used. Processing with sample technology: First, read in the parts to be arranged according to the layout task in Figure 5-12, perform corresponding pre-processing settings for some parts with process constraints, and perform automatic layout after setting. The final layout result obtained after proper manual adjustment is shown in Figure 5-13.
Excluding the time spent manually setting the process parameters, although the total number of nesting parts is as high as 111, the entire automatic nesting process takes no more than 1 second, and the subsequent manual partial adjustment operations can be completed within a few minutes. As can be seen from the layout diagrams 5-13, a large number of parts have achieved common edge combination and bridging arrangement. The nesting operation makes the layout of the parts closer. The final layout height is 293, and the material utilization rate reaches 81.4. %. Obviously, the combined arrangement of co-edge and bridging parts will bring great convenience to the subsequent cutting operation, and the overall layout effect is good.
1.4 Summary of this chapter
This chapter is based on the best matching strategy nesting algorithm obtained in the previous chapter, starting from the practicality of the algorithm, focusing on the process constraints generated by the materials, equipment and other factors on the nested parts during the actual blanking process. the study. Aiming at the main process constraints and common optimization goals in the sheet metal cutting and blanking process, this chapter gives a detailed solution strategy for converting process constraints into nesting geometric constraints. When nesting, you only need to set the process constraints parameters, and the corresponding solutions The strategy can automatically generate a part arrangement method that meets the process requirements. Based on the above technology, combined with the basic nesting algorithm in Chapter 4, this chapter finally forms a plate optimization nesting technology that can integrate the actual nesting process constraints and manual nesting experience. The example verification shows the overall nesting effect of the algorithm in this paper. good.