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Abstract

Machining thin-walled, flexible parts is challenging due to significant static deflections and forced vibrations. The static component of the cutting force induces deflections, while dynamic components at the Tooth Passing Frequency (TPF) and its harmonics can excite the natural frequencies of these highly compliant structures. Excessive deflections can lead to violations of tight dimensional tolerances, which are critical in aerospace manufacturing. In industrial settings, clamps are used to secure the workpiece to the machine tool table. However, clamp locations and applied forces are often determined intuitively. This heuristic approach is typically suboptimal, as the dynamics of flexible workpieces are highly sensitive to the stiffness and placement of the clamps. This thesis presents a computationally efficient methodology for optimizing both clamp locations and clamping forces to minimize static deflections and forced vibrations at the tool–workpiece interface. The method includes modeling the clamping contact stiffness as a function of the applied force and contact materials, and efficiently estimating dynamic compliance across the frequency range excited by milling forces. A fractal contact mechanics model is introduced to represent clamping stiffness. The clamping force is distributed over the contact surface between the clamp and a cantilevered beam. Finite Element (FE) simulations are used to determine contact stiffness from beam deflections, enabling the estimation of fractal surface parameters. These parameters are then used to analytically estimate contact stiffness as a function of applied load. Alternatively, an experimental approach is proposed for directly estimating contact stiffness under static loading conditions. An optimization algorithm is developed to identify optimal clamp positions and forces that minimize deflections and vibrations induced by milling forces at the TPF and its harmonics. The static and dynamic deflections at the tool–workpiece interface are computed by analytically reduced FE model. The effects of clamping forces - and resulting stiffness - are incorporated. Simulation results demonstrate that optimal clamping reduces static deflections and vibrations significantly. In a representative application, deflection is reduced by 72.76%. Computational efficiency is improved thirtyfold by accounting for mass and stiffness changes due to material removal. The proposed models are validated through both simulations and experimental measurements.