Abstract
In this paper, a methodology is proposed for the multi-objective optimization of a multipass turning process. A real-parameter genetic algorithm (RGA) is used for minimizing the production time, which provides a nearly optimum solution. This solution is taken as the initial guess for a sequential quadratic programming (SQP) code, which further improves the solution. Thereafter, the Pareto-optimal solutions are generated without using the cost data. For any Pareto-optimal solution, the cost of production can be calculated at a higher level for known cost data. An objective method based on the linear programming model is proposed for choosing the best among the Pareto-optimal solutions. The entire methodology is demonstrated with the help of an example. The optimization is carried out with equal depths of cut for roughing passes. A simple numerical method has been suggested for estimating the expected improvement in the optimum solution if an unequal depth of cut strategy would have been employed.
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Abbreviations
- C :
-
Constant in extended Taylor’s tool life equation
- C o :
-
Operating cost ($/min)
- C t :
-
Tool cost ($)
- d :
-
Depth of cut (mm)
- d F :
-
Depth of cut for the finishing pass (mm)
- d R :
-
Depth of cut for the roughing pass (mm)
- D f :
-
Final diameter of the work piece (mm)
- D 0 :
-
Initial work piece diameter (mm)
- f F :
-
Feed for the finishing pass (mm/rev)
- f R :
-
Feed for the roughing pass (mm/rev)
- F c :
-
Total production cost per piece ($)
- F max :
-
Cutting force (kgf)
- F t :
-
Fraction of tool consumed per piece
- k, α, β :
-
Constants used in the empirical relation for cutting force
- L :
-
Length of machining (mm)
- m :
-
Number of roughing passes
- n :
-
Exponent of extended Taylor’s tool life equation
- p, q, r :
-
Exponents of speed, feed, and depth of cut in tool life equation
- p c, p m :
-
Crossover and mutation probabilities
- P max :
-
Maximum power (kW)
- r i , u i :
-
Random numbers between 0 and 1
- R :
-
Nose radius of cutting tool (mm)
- \(R_{{t_{{\max }} }} \) :
-
Peak-to-valley height of surface roughness for finishing pass
- t c :
-
Tool change time (min)
- t s :
-
Tool setting time per pass (min)
- t ts :
-
Total tool setting time (min)
- T f :
-
Tool life for the finishing pass (min)
- T L :
-
Loading/unloading time per component (min)
- T max, T min :
-
Maximum and minimum allowed values of tool life
- T P :
-
Total production time per component (min)
- T r :
-
Tool life for the roughing pass (min)
- T tF :
-
Total cutting time for finishing pass (min)
- T tR :
-
Total cutting time for roughing passes (min)
- v F :
-
Cutting speed for the finishing pass (m/min)
- v R :
-
Cutting speed for the roughing pass(m/min)
- η :
-
Machine efficiency
- η c :
-
Crossover index
- η m :
-
Mutation index
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Abburi, N.R., Dixit, U.S. Multi-objective optimization of multipass turning processes. Int J Adv Manuf Technol 32, 902–910 (2007). https://doi.org/10.1007/s00170-006-0425-6
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DOI: https://doi.org/10.1007/s00170-006-0425-6