Modeling and optimization of cycles of internal grinding in the conditions of the automated machine-building productions

Despite emergence of new high-productive metal working machines with CNC in the national engineering industry, the problem connected with the existing low-productivity of the operations carried out on these machines isn’t solved yet. The reason for that is the lack of normative and reference literature, CAD and the engineering techniques allowing to design cycles for CNC machine tools which would satisfy the requirements of modern automated production. In practice, this problem is solved in two ways: 1) purchasing of the cutting modes from equipment manufacturers; 2) using the method of cutting modes choice by processing of a number of test billets. Both ways require considerable additional expenses which are imposed on the final cost of the products and don't solve a problem of increasing the productivity of operations carried out on CNC machine tools in general, throughout the domestic engineering industry. The solution of this problem is the methodology of designing of optimal internal grinding cycles considered in this article which is based on two fundamental models: the model of the cutting force components and the model of metal removal. The power model of internal grinding process connects the cutting forces with processing regimes and covers most of the basic technological parameters. The model of metal removal reflects interrelation of the program and the actual values of the radial feed with elastic deformations of the technological system, and also allows calculating the value of the actually removed allowance, the current values of radiuses of the treated holes, cutting force, removal time for the specified grinding cycle, etc. As a mathematical optimization method of grinding cycles the dynamic programming method is used. Application of this method is caused by the fact that it doesn't require pre-construction of the boundaries of acceptable restrictions and isn't sensitive to properties of model controls and limitations. The methodology of designing of optimal internal grinding cycles allows calculating mathematically optimal values of radial and axial feeds at all steps of a cycle, optimal allocation of removal allowance on cycle steps for radial and axial feeds in case of which the minimal cycle time considering the specified technological limitations of criterion function is provided.