Research modular tool system influence on the dynamic characteristics of the boring machines

. The article presents the analysis of modern modular tooling systems (MTS). The calculations of the stiffness of joints modules compounds «Yartim-Flex» and dynamic research of spindles of machine tools models IR-320PMF30 and 2D450F2, equipped with this modular tool system.

diameters in accordance with each specific processing task. Therefore, the block-modular design principle allows you to order not just a tool of a certain type, but a tool system with the necessary replaceable devices.
Currently, to pair the individual blocks of the modular tool with each other and install the tool in the spindle of the machine, various types of connecting elements are used, which must ensure high rigidity and accuracy of the connection. All these elements can be divided into two groups: connecting elements with rigid links and connecting elements with elastic links.
The most common connecting elements with rigid links is a standard mandrel with taper 7:24, links with a short taper and a flat end face (Novex, Walter, Sandvik Coromant), the connection cylinder and the planar end face (Graflex, Varilok Sandvik Coromant, Hertel, Schmalcalden, Dornag, Polledzi, CO, Krupp Widia, Komet, Mapal,Tizit and others.) Due to the deviations of the profiles of the connecting surfaces of the chain links from the ideal, their contact is not over the entire surface, but only on several points, which strongly reduces the stiffness of the connection. The discrepancy between the angles of the cones inner and outer holes particularly strong influence on the stiffness of the conical connections. The most unfavorable is the case when the taper angle of the hole is greater than the mandrel, as it seems to lengthen the cantilever part of the mandrel [5].
The solution to the problem can be the use of elastic links, which are deformed, reduce the impact of manufacturing errors, thereby increasing the contact area and stiffness of the connection.
The connecting elements with elastic links are a base end and a cylindrical or conical collet, which centers the links relative to each other and, working together with the end, increases the stiffness of the connection. Fundamentally these compounds differ from each other only way fastening, which affects effort tightening [6].
Double basing in such constructions is eliminated due to the fact that 1.
The rigidity of the transition place from the end surface to the cylindrical or conical is reduced due to the annular inner recess 2.
Centering on the cylindrical or conical surface of the joint occurs after basing on the end surface. For release based cylinder use either the internal activity collets (Güring, Aachen, Mapal), or the distribution of the balls (Valenite, Widaflex, Krupp Vidia) or a screw with a conical thread (Sandvik Coromant, Novex NC, Walter, ARTEM-Flex) (Fig. 1). Fig. 1. The ways of connection of modules of modular tool systems: а) using the collet; b) using the unclenched balls; c) with conical thread Torque transmission is carried out either by means of end dowels, or by manufacturing a base cylindrical surface in the form of a RK-profile (Sandvik Coromant) Connection scheme of the YARTIM-Flex system junction is represented in Fig. 2. The collet of the module 4 is inserted into the conical hole of the module 1 with a gap Δ = 1.2...2 mm; the end of the stud 3 sets the modules relative to each other. With further screwing of the screw 2, the force Q increases and the module 4 moves to the full selection of the gap, thus creating pressure on the end and conical surfaces of the module 4.
When the torque on the screw 2 will reach 80 N·m, the gap across the contact surface of conical screw thread 2 and the module 4 is selected, the collet module 4 will turn the radial deformation, selecting the gaps along the reference surfaces of the modules 1 and 4.
The calculation of the stiffness of the joints was carried out according to the method given in [5]. The calculation formula was derived [7], which allowed to obtain the initial data for modeling the elastic system in the basic package of the subroutine SPINCH where j is the angular stiffness of the joint; Q -tightening force, N; D is the outer diameter of boring bars, mm; d -diameter of the collet, mm; L -length of boring bars, mm; c -dimensional factor, N 1/2 mm 2 [5]; k -stiffness of the joint, mm/MPa [5]; E -modulus of elasticity, MPa; C3, C4 are empirical dimensionless coefficients [5].
To simulate the error of processing it is necessary to make a mathematical model of the spindle unit of the machine, equipped with tool adjustment. As an example, select the spindle assembly of machines mod. IR320PMF4 and 2D450F2, a design scheme is presented in Fig.3.   Fig. 3. A design scheme for spindle assembly The most convenient way of modeling is the finite element method (FEM). To compile a resolving system of equations in a dynamic formulation, we use the Lagrange equation: where t is time; qi is the generalized coordinates; n is the number of degrees of freedom; T is the kinetic energy of the system, Qi is the generalized forces.
After performing the transformations we obtain a system of equations: where Thus, we obtain a system of differential equations in matrix form: where [D] is the vector of forces acting on the system. n equation (4) in the stiffness matrix [C] there is a stiffness of the conical spindle connection with the tool, the value of which has a great influence on the overall stiffness of the spindle-tool system.
The rigidity of the conical joint, determined by the contact stiffness of the mating surfaces, largely depends on the accuracy of the joint [16].