Implementation of the nonlinear programming algorithm when optimizing the final turning mode

M G Galkin,A S Smagin

doi:10.1088/1757-899x/862/3/032009

M G Galkin, A S Smagin

Open Access

https://doi.org/10.1088/1757-899x/862/3/032009

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Abstract

For computer-aided multi-variant design of machining technologies, it is important to optimize the cutting parameters at the final pass in each technological operation. When carrying out designing procedures, there emerge problems relating to the algorithm of choosing the decision-making method, the objective function, and the regions of feasibility at final machining steps. Linear programming is time-consuming for multi-variant and multi-pass machining, if the algorithm is to be clear. It is known that when simulating the optimal metal-cutting process, the optimization criterion and the system of constraints are non-linear. Therefore, a computational algorithm can be made significantly more efficient if it is a non-linear algorithm based on Lagrange multipliers Such approach to design helps simplify automating the computational algorithm for multi-pass single-tool machining with a precision cutting tool (a reamer) This is the method discussed herein.

Highlights

When carrying out designing procedures, there emerge problems relating to the algorithm of choosing the decision-making method, the objective function, and the regions of feasibility at final machining steps
A computational algorithm can be made significantly more efficient if it is a non-linear algorithm based on Lagrange multipliers Such approach to design helps simplify automating the computational algorithm for multi-pass single-tool machining with a precision cutting tool This is the method discussed
Selecting optimal cutting parameters is crucial for designing the machining process

Summary

Introduction

Selecting optimal cutting parameters is crucial for designing the machining process. It helps develop high-quality technological solutions. 2. Mathematical model of the cutting process This paper proposes optimizing the spindle rotation speed and the reamer feed. Mathematical model of the cutting process This paper proposes optimizing the spindle rotation speed and the reamer feed In this case, the mathematical model is determined by how the parameters to optimize are functionally related to the requirements that condition the constraints imposed by the system at each specific machining stage. If we synthesize a model for elementary passes done by a drilling or a reaming machine, it is rational to analyze six constraints at max These are: minimum spindle rotation speed 1, maximum spindle rotation speed 2, minimum reamer feed 3, actual reamer feed (depends on the hole size and the hardness of the workpiece material) 4, reamer durability 5, and machine engine power 6. The above constraints applicable to machining with a precision cutting tool can be formalized as follows

For the primary-motion engine power constraint:

Conclusion