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Methods of designing spline broaches of optimal structure according to smallest length of body are described. Multitude of broach designs may be explained by summation of geometric, structural and operating parameters of working and tail parts. In order to evaluate the efficiency of spline broaches, a system of functions characterizing length of broach, round and chamfer parts in accordance with the cutting pattern is introduced. A system of structural and technological limitations over basic features of broaches is supported. Mathematical optimization model of a broach consisting of a sum of target functions and constraint system is put together. Choice of optimal solution is based on implementation of linear programming algorithms. Optimal methods of designing spline broaches are determined using MS Excel. The developed design method is applicable for comparative evaluation of spline broaches of various designs with various cutting and cut-off patterns and allows to form the entire sum of broach designs according to set input parameters and to choose the most efficient one which would correspond to minimal length of the tool.

The paper studies a comparative evaluation method for the modular cutting tools stress-strain state under the cutting forces loading with the help of the finite element numerical method. The method allows forecasting the modular cutting tool the position of the tip of the cutting edge with identification of the confidence bounds for its exploitation in compliance with its intended use and reference operating conditions. The conducted modeling describes the modular cutting tool structure as a ranked set of structural components, such as the frame, cutting insert, shim, etc., oriented towards a certain direction with some surfaces being contiguous and thus making contact interactions. The research examined different tool structural component layout options, including those equipped/not equipped with a shim, having a radial/tangential location type of cutting components. Regression models were obtained for calculating the total displacements of tips the cutting edges of the cutting inserts, as well as maximum equivalent stresses in the cutting inserts, depending on the attachment and cutting forces for various clamping patterns and positioning cutting plates in the form of linear polynomials. The authors developed recommendations for the most efficient application of the modular cutting tool structural component layout options under specific production conditions.

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The description of the semi-empirical models developed on the basis of results of theoretical and pilot studies is provided in article, for calculation of thermal offsets of spindle blocks at the most characteristic modes of operation of lathes.