Probabilistic multi-objective robust design and its application in metal cutting

Abstract

Introduction/purpose: Cutting is a typical material process. However, an appropriate solution for simultaneous optimization of material machinability and tool life in material cutting processes has not been obtained yet. In this article, probabilistic multi-objective robust design (PMORD) is expounded and the robust design problem in the simultaneous optimization of material machinability and tool life is analyzed by taking the machining of ferrite-bainite dual-phase steel as an example. Methods: According to PMORD, the arithmetic mean and its deviation of various performance and utility indexes of alternative schemes are evaluated as twin independent responses, which respectively contribute a part of the partial preferable probability to the performance indexes. In the evaluation, the arithmetic average of the utility index is taken as the representative of the utility attribute, and the evaluation is made in accordance with the function or preference of the utility index. However, the deviation term is generally used as an unbeneficial type of the index (that is, the smaller the better) to participate in the evaluation. The product of the two parts of partial preferable probability is the actual partial preferable probability of the corresponding performance index. The product of the partial preferable probability of all performance utility indexes gives the total preferable probability of the corresponding scheme, which is the only index for each scheme to participate in the competition in robust design. Results: The optimization result of this example is that the tool life is 1297.3333 s (standard deviation is 2.0817 s) and the surface roughness is 2.22mm (standard deviation is 0.2mm), while the corresponding working conditions are that the heat treatment temperature of the material is 790°C, the cutting speed is 150m/min, the feed speed is 0.15mm/rev, and the cutting depth is 0.2mm. Conclusion: The example of the parameter optimization of cutting of ferrite-bainite dual-phase steel by means of PMORD indicates the rationality of the appropriate solution.

Keywords

• multi-objective optimization
• robust design
• simultaneous optimization
• probability-based method
• preferable probability