Abstract
One of the complex optimization problems arising in technical applications is the cutting path problem for CNC sheet metal cutting machines. This problem is to optimize the tool path for the CNC technological equipment when cutting a fixed set of parts allocated on sheet metal. The time of cutting process is one of objective functions for the optimization problem. This objective function depends on six parameters of cutting process: 1) cutting speed; 2) lengths of the cutting tool path; 3) speed of idling motion of tool; 4) length of idling motion; 5) number of piercings; 6) time of one piercing. When programming NC program, speed of cutting is defined by the user of the CAM (Computer-Aided-Manufacturing) system and considered as a constant. However, this is actually not the case. Consequently, the problem of exact calculation of objective function is arisen. In order to solve this problem, the correction coefficients for the cutting speed value defined by the user must been calculated. Obviously, these coefficients will vary for different thicknesses and grades of metal. The paper presents the results of investigates, which made it possible to find the functional dependences of the cutting speed for the CNC laser cutting machine (CO2) on the number of NC program commands for the following metal grades: 1.0114 (thickness Δ = 1-10 mm) and AWAIMg3 (Δ = 1-5 mm).The statistical materials of experiments were processed by using software “Mathcad”. The received results show that the actual average value of cutting speed is monotonically decreasing function depended on number of NC program commands. In addition, the calculation of the actual cutting speed provides not only an accurate calculation of the value of the objective function, but also, as a result, the correct finding of the optimal tool path
Highlights
Tool path problem for CNC sheet cutting machines that belongs to the class of NP-hard problems of continuous-discrete optimization is one of the most complex optimization problems in development of NC programs by using Computer Aided Manufacturing (CAM)
One of the complex optimization problems arising in technical applications is the cutting path problem for CNC sheet metal cutting machines
The paper presents the results of investigates, which made it possible to find the functional dependences of the cutting speed for the CNC laser cutting machine (CO2) on the number of NC program commands for the following metal grades: 1.0114 and AWAIMg3 (Δ = 1-5 mm).The statistical materials of experiments were processed by using software “Mathcad”
Summary
Tool path problem for CNC sheet cutting machines that belongs to the class of NP-hard problems of continuous-discrete optimization is one of the most complex optimization problems in development of NC programs by using Computer Aided Manufacturing (CAM). The considering problem is to optimize the tool path for the CNC equipment when cutting a fixed set of parts allocated on sheet metal. Problem of exact objective function calculation As we noted above when programming NC program, is defined by the user of the CAM system and considered as a constant This is not the case (see, in particular, [13]). In order to determine what kind of factors affects on changing of tool speed during thermal cutting on CNC equipment the following hypotheses are tested: Hypothesis 1: The working speed depends on temperature change of sheet metal during.
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