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# Multi-objective optimization of multipass turning processes

• N. R. Abburi
• U. S. Dixit
ORIGINAL ARTICLE

## 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.

## Keywords

Turning process Multi-objective optimization Real-parameter genetic algorithm Sequential quadratic programming Linear programming Lagrange multiplier

## Nomenclature

C

Constant in extended Taylor’s tool life equation

Co

Operating cost ($/min) Ct Tool cost ($)

d

Depth of cut (mm)

dF

Depth of cut for the finishing pass (mm)

dR

Depth of cut for the roughing pass (mm)

Df

Final diameter of the work piece (mm)

D0

Initial work piece diameter (mm)

fF

Feed for the finishing pass (mm/rev)

fR

Feed for the roughing pass (mm/rev)

Fc

Total production cost per piece (\$)

Fmax

Cutting force (kgf)

Ft

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

pc, pm

Crossover and mutation probabilities

Pmax

Maximum power (kW)

ri, ui

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

tc

Tool change time (min)

ts

Tool setting time per pass (min)

tts

Total tool setting time (min)

Tf

Tool life for the finishing pass (min)

TL

Loading/unloading time per component (min)

Tmax, Tmin

Maximum and minimum allowed values of tool life

TP

Total production time per component (min)

Tr

Tool life for the roughing pass (min)

TtF

Total cutting time for finishing pass (min)

TtR

Total cutting time for roughing passes (min)

vF

Cutting speed for the finishing pass (m/min)

vR

Cutting speed for the roughing pass(m/min)

η

Machine efficiency

ηc

Crossover index

ηm

Mutation index

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## Copyright information

© Springer-Verlag London Limited 2006

## Authors and Affiliations

1. 1.Department of Mechanical EngineeringIndian Institute of TechnologyGuwahatiIndia