A bespoke version of SECANT was developed for Lionweld Kennedy, Middlesbrough to create plans for the production of cut to size pieces of a gridded material. This is a particular example of planning for a material that is featured in such a way that a piece may only be cut from certain positions of the stock material. Other examples that could be handled in a similar manner are patterned material where a piece must be aligned with a pattern feature or damaged material where part of the stock sheet is unusable.   

The Requirement

The stock material is a framed metal grid. The outer frame is thicker than the cross members of the grid. The cells of 

the grid may or may not be square.

The pieces to be cut are defined by their length and width and by the form of each of the four edges. The possible types are;

  • This edge must coincide with the frame.
  • This edge must coincide with the grid member.
  • This edge must be a fixed distance from a grid member (this is termed a fixed leg).
  • This edge can be positioned anywhere on the sheet.

The positioning of a piece on a pattern can be very restricted. If the material is not symmetric then a piece that is frame edged on adjacent sides may only be cut from the top left-hand corner or the bottom right-hand corner of the stock sheet.

The sheet is cut into a number of vertical strips which are then cross cut into the finished pieces. A cut may not coincide with a grid member. 

A significant factor in cut planning is the need to clamp the material on both sides before any cut can be made.   

 

The impact of clamping is illustrated above. We wish to cut the material at position A and create a trailing leg T.  This leaves a leading leg for the next piece of L (T+kerf+L equals the grid cell width G). If the next piece requires a leading leg of L then no further cut need be made. However, if the next piece has a leading leg that is not equal to L then we need to ensure that the next cut can be clamped on both sides and that this may mean that the cut must be moved to position B with the consequential waste of material. Clamping applies both to the cutting of strips from the sheet and the cutting down of the strips into the finished pieces. The cut planner must also be aware that cutting is a time-consuming operation and that the number of cuts should be minimized as far as is possible.

The Development

At the heart of the SECANT pattern generation engine is a search for combinations of pieces that when cut together contribute to low wastage patterns. The search is intelligent and will abandon the building of a pattern as soon as it is able to recognize that it cannot improve on the best pattern found so far. It is this intelligence that allows it to effectively search through vast numbers of patterns in a practical amount of computing time. Two major additions were made to handle this application. SECANT was modified to perform a pattern search on an approximate problem that incorporated many of the new constraints as to which pieces were compatible for cutting from the same strip but ignored precise positioning of the pieces on the pattern. When the engine believed it had found an improved pattern then a second search was used to position pieces and check clamping. This second search would then report the validity and efficiency of the pattern back to the main engine. If the pattern remained an improvement after checking then it was accepted as the best so far and used to direct the future search.

This approach proved highly effective in producing high yield and entirely implementable patterns in a few minutes of computer time.

The Result

The company manufactures many different types of gridded product in addition to the metal mesh described above. Each product has its own restrictions on piece placement. The bespoke SECANT application was found to be versatile enough to manage all the required variants and is delivering time and cost savings across the entire product range.