Abstract
Methodology, that allows to use the transfer matrices method for the static calculation of spindle unit as elastic system, which consists of a few associate subsystems, has been developed. Restrictions of the dynamic compliances method use for static calculations of «spindle unit» system decomposing has been stated. For such calculations it is suggested to conduct the decoupling of the system with the use of mixed method of indefinable beam systems static calculation. The elastically-deformation model of the «Spindle unit» system, that consist of subsystems: tool, spindle, spindle housing elastically mounted on the machine-tool bed, is being presented. The scheme of decoupling of this system for static calculations has been developed. The analytical solution of task of the elastic displacements calculation in the characteristic points of subsystems has been obtained. The algorithm of static calculation of the «Spindle unit» elastic system has been developed. Offered approach allows applying an identical methodological base for the static and dynamic characteristics simulation of the «Spindle unit» elastic system.
Highlights
Accuracy of machining on metal-cutting machine tools is determined by mutual position of tool and workpiece during machining and first of all depends on the size of their elastic displacements
It is related to measuring complication of axis displacement of the rotating element: tool at milling or workpiece at turning. As a rule, such displacements are determined by indirect methods, for example, by results of measuring of supports deformations in spindle unit or displacement of spindle pin, with fixed tool or workpiece [1]. It means for determination of elastic displacement of the rotating element in the cutting zone this approach assume the use of calculation elastic-deformation model of spindle unit
Use of transfer matrices method (TMM) in combination with the method of dynamic compliances [7] allow to carry out the calculation of dynamic characteristics of spindle unit as an elastic system consisting of a few associate subsystems [4]
Summary
Accuracy of machining on metal-cutting machine tools is determined by mutual position of tool and workpiece during machining and first of all depends on the size of their elastic displacements. Joint of tool (workpiece) with spindle and joint of spindle unit housing with the bed of machine-tool - simulated by elastic connections [1, 2] Such model allows calculation static and dynamic characteristics of the «Spindle unit» system [2]. The use of FEM allows obtaining the most exact results of simulation, but procedure of model development differs in considerable labour intensiveness and complication Among another ways of the elastic system description of spindle unit it should be noted the use of the method of initial parameters in matrix formulation, more known as a transfer matrices method (TMM)[3], [4]. As a result, solving of these equations (taking into account obtained values of reactions of throw-away connections) displacements are determined in the characteristic points of subsystems. Where for every subsystem: Gi – mass-inertia matrix of the concentrated load; Ri – matrix of elastic-dissipative linear and angular support; Ui – matrix of the beam section with distributed mass; i – number of the subsystem section; u – general number of subsystem sections
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