Optimization of Machining Parameters in Turning Processes by Dynamic Programming

This paper presents a method for optimizing the machining parameters in rough turning processes to control the vibrations and deformations and minimize the production time per component under practical constraints. The optimization model is formulated, in which piecewise constraints are introduced based on the varying length-to-diameter (L/D ) ratio of the workpiece. The optimization problem is solved in two phases. The first phase is to determine the minimum production time for each cutting pass for preset equal-spaced depths of cut. A hybrid solver of combining a genetic algorithm (GA) and sequential quadratic programming (SQP) technique is adopted. In the second phase, a dynamic programming (DP) technique is employed to achieve the optimal production time per component and sequential subdivision of the total depth of cut. An example illustrates the method in detail. The inclusion relation of the solutions is also discussed. NOMENCLATURE C Coefficient for Taylor’s life equation d Allowable depth of cut for a cutting pass (mm) dt Total depth of cut (mm) dmax , dmin Maximum and minimum depth of cut (mm) D0 Initial workpiece diameter (mm) D1 Final workpiece diameter (mm) f Feedrate of the tool (mm/rev) fmax , fmin Maximum and minimum feedrate (mm/rev) Fmax Maximum cutting force (N) Ft Tangential cutting force (N) K Cutting force coefficient (N/mm) i, j, k Index numbers L Length of workpiece (mm) m, q, s Exponents of speed, feed, and depth of cut for