Ants colony algorithm approach for multi-objective optimisation of surface grinding operations

An ant colony based optimisation procedure has been developed to optimise grinding conditions, viz. wheel speed, workpiece speed, depth of dressing and lead of dressing, using a multi-objective function model with a weighted approach for the surface grinding process. The procedure evaluates the production cost and production rate for the optimum grinding condition, subjected to constraints such as thermal damage, wheel wear parameters, machine tool stiffness and surface finish. The results are compared with Genetic Algorithm (GA) and Quadratic Programming (QP) techniques.Nomenclature a _p down feed of grinding (mm/pass) - a _w total thickness of cut (mm) - A _o initial wear flat-area percentage (%) - b _e empty width of grinding (mm) - b _s width of wheel (mm) - b _w width of workpiece (mm) - B _k positive definite approximation of the Hessian - doc depth of dressing (mm) - c _d cost of dressing ($) - c _s cost of wheel per mm³ ($/mm³) - CT total production cost ($/pc) - CT ^* expected production cost limit ($/pc) - d _g grind size (mm) - D _e diameter of wheel (mm) - f _b cross feed rate (mm/pass) - G grinding ratio - k _a constant dependent on coolant and wheel grind type - k _u wear constant (mm^-1) - k _c cutting stiffness (N/mm) - k _m static machine stiffness (N/mm) - k _s wheel wear stiffness (N/mm) - L lead of dressing (mm/rev) - L _e empty length of grinding (mm) - L _w length of workpiece (mm) - M _c cost per hour labour and administration ($/h) - N _d total number of pieces to be grouped during the life of dressing (pc) - N _t batch size of workpieces (pc) - N _td total number of workpieces to be grouped during the life of dressing (pc) - P number of workpieces loaded on the table (pc) - R _a surface roughness (µm) - R _a* surface finish limit during rough grinding (µm) - R _c workpiece hardness (Rockwell hardness number) - R _em dynamic machine characteristics - S _d distance of wheel idling (mm) - S _p number of spark out grinding (pass) - t _sh time of adjusting machine tool (min) - t _i time of loading and unloading workpiece (min) - T _ave average chip thickness during grinding (µm) - U specific grinding energy (J/mm) - U ^* critical specific grinding energy (J/mm³) - V _r speed of wheel idling (mm/min) - V _s wheel speed (m/min) - V _w workpiece speed (m/min) - VOL wheel bond percentage (%) - WRP workpiece removal parameter (mm³/min-N) - WRP ^* workpiece removal parameter limit (mm³/min-N) - WWP wheel wear parameter (mm³/min-N) - W _i weighting factor, 0W _i1 (W ₁+W ₂+W ₃=1)