The aim of the thesis is to propose active damping as a potential control strategy for chatter instability in machine tools. The regenerative process theory explains chatter as a closed loop interaction between the structural dynamics and the cutting process. This is considered to be the most dominant reason behind machine tool chatter although other instability causing mechanisms exist. The stability lobe diagram provides a quantitative idea of the limits of stable machining in terms of two physical parameters: the width of contact between tool and the workpiece, called the width of cut and the speed of rotation of the spindle. It is found that the minimum value of the stability limit is proportional to the structural damping ratio for turning operations. This important finding provides the motivation of influencing the structural dynamics by active damping to enhance stability limits of a machining operation. A direct implementation of active damping in an industrial environment may be difficult. So an intermediate step of testing the strategy in a laboratory setup, without conducting real cutting is proposed. Two mechatronic "Hardware in the Loop" simulators for chatter in turning and milling are presented, which simulate regenerative chatter experimentally without conducting real cutting tests. A simple cantilever beam, representing the MDOF dynamics of the machine tool structure constitutes the basic hardware part and the cutting process is simulated in real time on a DSP board. The values of the cutting parameters such as spindle speed and the axial width of cut can be changed on the DSP board and the closed loop interaction between the structure and the cutting process can be led to instability. The demonstrators are then used as test beds to investigate the efficiency of active damping, as a potential chatter stabilization strategy. Active damping is easy to implement, robust and does not require a very detailed model of the structure for proper functioning, provided a collocated sensor and actuator configuration is followed. The idea of active damping is currently being implemented in the industry in various metal cutting machines as part of the European Union funded SMARTOOL project (www.smartool.org), intended to propose smart chatter control technologies in machining operations.

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This work is the first 3-D continuum study of the free vibration of skewed and simultaneously skewed and twisted, cantilever parallelepipeds. The purpose of this study is to make available in the literature an enlarged data base of natural frequencies of these practical problems for researchers and design engineers to draw upon. The Ritz method is used to determine approximate natural frequency data. The total potential energy of the parallelepipeds is formulated using the three-dimensional theory of elasticity. The three orthogonal displacement components (u,v,w) are each approximated by finite triple series of simple algebraic polynomials with arbitrary coefficients (which are determined by applying the Ritz method). All terms of the series are constructed to satisfy the geometric boundary conditions at the fixed end of the parallelepiped. No other kinematic constraints are imposed in this analysis. Hence, the finite series of algebraic polynomials are both admissible and "mathematically complete" (75). Several convergence studies of natural frequencies are conducted on cantilever parallelepipeds. Effects of geometrical parameters such as side ratio, thickness ratio, skew angle, and twisted angle are presented in the form of nondimensional tables and graphs. Accuracy of solution method is substantiated through comparison with existing rectangular, skewed, and twisted plate results. The central focus of these comparisons are to verify the correctness and accuracy of free vibration data obtained by investigators using classical plate theories and two- and three-dimensional finite element methods.

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