4 th International DAAAM Conference “INDUSTRIAL ENGINEERING-INNOVATION AS COMPETITIVE EDGE FOR SME” 29-30 th April 2004, Tallinn, Estonia ANALYSIS OF LATHE VIBRATION INFLUENCE ON BLANK ROUGHNESS Ph.D Gennady Aryassov*, M. Sc. Tauno Otto**, M. Sc. Svetlana Gromova* Department of Mechatronics*, Department of Machinery** Tallinn University of Technology Abstract: The effect of lathe vibrations to the roughness of machined surface was investigated in this article. The calculation schemes involve systems with one and two degrees of freedom representing the vibration of the blank as a rigid body hinged in the spindle and elastically supported in the tailstock of the lathe. Experimental measurements were performed on lathes of type 1K62 at different cutting speeds, feeds and depths of cut. Processing of the roughness measurements data confirmed the precision of the calculation model. Surface roughness parameters of the blank corresponded quite satisfactory to the corresponding data of the theoretical investigation. For research of influence of gyroscopic forces to the surface roughness was used a calculation model with two degrees of freedom. The results of experimental and theoretical investigations confirmed the theoretical hypothesis. Key words: Lathe, vibration, calculation model, natural frequency, blank roughness. 1. INTRODUCTION In the turning operations, tool vibrations influence both product quality and productivity and may also have a negative influence on the working environment (Hakansson, 1999). The effect of lathe vibration to the roughness of machined surface is considered in this article. Dynamical phenomena’s concerned with the vibration are caused from external factors on the strained system of the lathe. During the machining of material all disturbances finally lead to relative displacements of cutter and blank. It allows to link parameters of the surface roughness with the relative vibrodisplacements of the cutter and the blank (Gaponkin, 1995). On calculation of dynamics characteristics the real elastic system of the lathe was replaced by a system with finite degrees of freedom. Use of complicated calculation schemes can lead in case of insufficient accuracy of the underlying data to significant error of the calculation (Arshanski, 1998). Therefore simplified schemes were used which composite on the basis of experimental investigations. The fundamental calculation scheme is a system with one degree of freedom representing the vibration of the blank as a rigid body hinged in the spindle and elastically supported in the tailstock of the lathe. Exact solution for continuous system having infinite number of degrees of freedom showed that the first natural frequency of the continuous model is keeping with the natural frequency of the accepted model. It makes possible to use this calculation model for analysis of the vibrations in case of the metal cutting. Experimental measuring was performed on lathes of type 1K62 by different cutting speeds, feeds and depths of cut. The experimental results satisfactory coincided with the similar theoretical results in adequate frequency range. With growth of frequency number a divergence between the theoretical and the experimental results increased gradually. As a result the limits of use of the proposed mathematical model of the blank on lathe vibration were considered. After every cutting the surface roughness was measured by profilograph ‘Surftronic 3+’. The processing of the roughness measurements data confirmed precision of the calculation model. Surface roughness parameters of the blank quite satisfactory agreed with the corresponding data of the theoretical investigation. For research of influence of gyroscopic forces to the surface roughness was used calculation model with two degrees of freedom. Until now in such formulation this problem has not been researched. The results of experimental and theoretical investigations confirmed the theoretical hypothesis. This knowledge gives the possibility to increase the accuracy of processing on different conditions of cutting. Calculation models with four degrees of freedom are assumed to use in future. Question of stability of the blank in the action of the moving cutting force was remained without investigation. It is necessary to derivate theoretical expressions enabling to determine the roughness more precisely. It gives the possibility to control and adjust the surface roughness of processing details. But for that is necessary to conduct a large number of experiments with good equipment. 2. THEORETICAL INVESTIGATION Treatment of the dynamic calculation model started from a formulation of research problem. For selection of this model was used data received from workable experiments. In order to simplify the dynamic model were not taken into account factors which have a little effect on results of solution. Of course these models have unlimited area of use (Aryassov, 2003). In current work the dynamic models with one and two degrees of freedom are considered (Fig.1) Fig.1. Calculation dynamical models. 2.1. Calculation scheme with one degree of freedom (Fig.1a). On idling of the lathe the differential equation of forced vibrations induced by the foundation vibrations t p M l k J y o sin 0 2 .. = + ϕ ϕ (1) ϕ y a) with one degree of freedom y y=y 0 sinpt x l b) with two degress of freedom y x z z=z 0 sinpt y=y 0 sinpt y γ β z l 113