A Probabilistic Approach to the Determination of the Optimum Cutting Conditions

Abstract

An analytical method applying a chance-constrained programming concept is proposed to determine the optimum cutting conditions considering the probabilistic nature of the objective function and constraints. The proposed analytical method is illustrated through an application to an example. It is shown that the optimum cutting conditions are significantly affected by the probabilistic nature of coefficients in the constraints. The effect of the uncertainty of the predicted tool life in the production cost function on the optimum cutting conditions is also considered. The study further investigates the effects of the cost-time parameter and allowable maximum force on the optimum conditions and the resulting production cost.

Application of mathematical programming to metal cutting

“…Iwata et al [9] suggest that a constraint of the form vaf ~> Y (16) should be used to avoid those v and f values likely to cause chatter vibration, adhesion and built-up-edge formation. 6 and /3 are constants to be estimated.…”

“…We will assume that the constraints (33) to (39) used in Example 1 apply here also. The goals stated in (i) and (ii) are formulated using equations (3) and (9). The goals needed to maximize the production rate are: This solution is obtained using an improved partitioning algorithm developed by Arthur and Ravindran [2] to solve linear goal programming problems.…”

“…Currently there is a great deal of interest in the use of Mathematical Programming techniques for the optimization of machining processes [1,3,4,7,8,9,13,14,15]. Machining is one of the more important manufacturing processes.…”

“…The single-pass, single-tool turning operation has been optimized using differential calculus [1], Lagrange multipliers [3,4], geometric programming [7,14], linear programming [8,13] and chance-constrained programming [9]. In this paper some of these approaches will be reviewed and another approach, that of linear goal programming, will be discussed.…”

Multiple-objective optimisation of machining operations based on neural networks

“…Quantitative methods for optimisation of machining operations based on a single objective such as minimisation of costs and maximisation of profit or production rate have been developed. Many paradigms have been proposed for single-objective optimisation of machining operations using various techniques such as differential calculus [2], regression analysis [3], linear programming [2], geometric programming [2,4,5], stochastic programming [6] and computer simulation [7].…”