Browsing by Subject "Instantaneous Frequency"
Now showing 1 - 2 of 2
Results Per Page
Sort Options
Item Nonlinear Time-Frequency Control Theory with Applications(2012-10-04) Liu, Mengkun 1978-Nonlinear control is an important subject drawing much attention. When a nonlinear system undergoes route-to-chaos, its response is naturally bounded in the time-domain while in the meantime becoming unstably broadband in the frequency-domain. Control scheme facilitated either in the time- or frequency-domain alone is insufficient in controlling route-to-chaos, where the corresponding response deteriorates in the time and frequency domains simultaneously. It is necessary to facilitate nonlinear control in both the time and frequency domains without obscuring or misinterpreting the true dynamics. The objective of the dissertation is to formulate a novel nonlinear control theory that addresses the fundamental characteristics inherent of all nonlinear systems undergoing route-to-chaos, one that requires no linearization or closed-form solution so that the genuine underlying features of the system being considered are preserved. The theory developed herein is able to identify the dynamic state of the system in real-time and restrain time-varying spectrum from becoming broadband. Applications of the theory are demonstrated using several engineering examples including the control of a non-stationary Duffing oscillator, a 1-DOF time-delayed milling model, a 2-DOF micro-milling system, unsynchronized chaotic circuits, and a friction-excited vibrating disk. Not subject to all the mathematical constraint conditions and assumptions upon which common nonlinear control theories are based and derived, the novel theory has its philosophical basis established in the simultaneous time-frequency control, on-line system identification, and feedforward adaptive control. It adopts multi-rate control, hence enabling control over nonstationary, nonlinear response with increasing bandwidth ? a physical condition oftentimes fails the contemporary control theories. The applicability of the theory to complex multi-input-multi-output (MIMO) systems without resorting to mathematical manipulation and extensive computation is demonstrated through the multi-variable control of a micro-milling system. The research is of a broad impact on the control of a wide range of nonlinear and chaotic systems. The implications of the nonlinear time-frequency control theory in cutting, micro-machining, communication security, and the mitigation of friction-induced vibrations are both significant and immediate.Item On the Machining Dynamics of Turning and Micro-milling Processes(2012-10-19) Halfmann, EricExcessive vibrations continue to be a major hurdle in improving machining efficiency and achieving stable high speed cutting. To overcome detrimental vibrations, an enhanced understanding of the underlying nonlinear dynamics is required. Cutting instability is commonly studied through modeling and analysis which incorporates linearization that obscures the true nonlinear characteristics of the system which are prominent at high speeds. Thus to enhance cutting dynamics knowledge, a comprehensive nonlinear turning model that includes tool-workpiece interaction is experimentally validated using a commercial laser vibrometer to capture tool and workpiece vibrations. A procedure is developed to use instantaneous frequency for experimental time-frequency analysis and is shown to thoroughly characterize the underlying dynamics and identify chatter. For the tests performed, chatter is associated with changing spectral components and bifurcations which provides a view of the underlying dynamics not experimentally observed before. Validation of the turning model revealed that the underlying dynamics observed experimentally are accurately captured, and the coupled tool-workpiece chatter vibrations are simulated. The stability diagram shows an increase in the chatter-free limit as the spindle speed increases until 1500rpm where it begins to level out. At high speeds the workpiece dominates the dynamics, and excessive workpiece vibrations create another stability limit to consider. Thus, workpiece dynamics should not be neglected in analyses for the design of machine tools and robust control laws. The chip formation mechanisms and high speeds make micro-milling highly non-linear and capable of producing broadband frequencies that negatively affect the tool. A nonlinear dynamic micro-milling model is developed to study the effect of parameters on tool performance through spectral analysis using instantaneous frequency. A lumped mass-spring-damper system is assumed for modeling the tool, and a slip-line force mechanism is adopted. The effective rake angle, helical angle, and instantaneous chip thickness are accounted for. The model produced the high frequency force components seen experimentally in literature. It is found that increasing the helical angle decreased the forces, and an increase in system stiffness improved the dynamic response. Also, dynamic instability had the largest effect on tool performance with the spindle speed being the most critical parameter.