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UBC Theses and Dissertations

Dynamic modeling of single and multi point turning operations Suren, Muharrem Gokhan

Abstract

The thesis presents the dynamic modeling of single point cutting operations like turning and boring operations. Single point cutting operations such as turning and boring, are widely used in the industry. Turning operation is used to create axisymmetric surfaces whereas the boring is a machining operation used to enlarge the inner diameters of existing holes. A frequency domain stability solution for the oblique turning is introduced. The model takes all the flexibilities in three directions into account for the stability analysis. The vibrations are projected in the direction of chip thickness which is perpendicular to the cutting edge so that the system is oriented in one direction. By scanning the chatter frequencies around the dominant modes of the system, the stability lobes are created. Stability lobes are used to select stable cutting conditions for a particular machining operation, tool, workpiece and machine tool. Dynamics of boring operation are also investigated in the thesis. The vibrations in the process are shown to be in the radial direction which is different from other machining operations. The uncut chip area variation in the boring also brings complexity to the operation. This is caused by the corner radius of the insert used in the operation. The uncut chip area is a nonlinear function of tool geometry, feed rate and vibrations at the current and previous revolutions. A linear chip area formulation based on the least squares method is used for the linear stability solution. A recently developed method, Time Finite Element Analysis, is implemented to boring operation. The time in cut is divided into finite elements and with the help of boundary conditions, and a set of linear equations are obtained. The delay differential equation is transformed into a linear discrete dynamical system. The eigenvalues of the discrete dynamical equation determine the stability of the system. Turning of long shafts has been a problem for the manufacturers. Bearing supports have been used widely to increase the dynamic stiffness of the shafts during machining to prevent chatter. However, the supports should be placed to the most flexible regions of the shaft so that the dynamic stiffness is increased. The aim of increasing the dynamic stiffness is related to increasing the width of cut in turning of long shafts. The dynamic stiffness is proportional to the limiting width of cut in the chatter stability analysis. An algorithm is presented in the thesis which optimizes the bearing support locations according to the predicted Frequency Response Function (FRF) of the system in the cutting region. FRF of the system is calculated using Finite Element Method. The bearing support optimization is verified analytically. Multiple inserted boring operation is generally preferred instead of single inserted boring operation when high material removal rates are desired. The main advantage of using a multiple inserted boring bar is that the workpiece can be machined with a high feed rate, which is the number of inserts times the desirable feed rate per insert. An analytical three dimensional chatter stability approach is introduced for the multiple inserted boring heads which have regular pitch cutters. The simulation results are compared with the available experimental results. The method is further extended to variable pitch cutters. Variable pitch cutters are specially designed tools for preventing chatter vibrations for a desired spindle speed. The stability problem is solved analytically, and a method for selecting optimum pitch angles is presented. The method finds the optimum pitch angles in such a way that the depth of cut is maximized for a given spindle speed. The depth of cut is increased considerably against the regular pitch cutter for the desired spindle speed.

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