Vibrations of micro-scale cutting-tools and ultra-high-speed-spindles---modeling and experimentation

Applications such as consumer products, medical micro-devices, miniature fluidic devices, aerospace components and miniature energy storage/conversion systems continuously demand micro-scale parts for using the advantages of miniaturization. Being capable of fabricating three-dimensional micro-scale features on a wide variety of materials, mechanical micro-machining is a viable micro-manufacturing technique for addressing this demand. A critical challenge in successful application of micro-machining is deterioration of output quality (geometric accuracy and surface finish) and process efficiency (material removal rate, tool life) due to the vibrations stemming from machining forces and high-speed-rotations. The objective of this Ph.D. thesis is to address this challenge by developing novel, accurate and efficient models that can be used for prediction, control and minimization of vibrations during micro-machining processes.;Various modeling approaches are used for modeling the micro-scale cutting-tool dynamics. First, a model that predicts the bending vibrations of micro-endmills by assuming the cross-section as circular is presented. A more accurate bending model is derived by including the actual fluted cross-section and the pretwisted geometry. The extended Hamilton's principle is used for deriving the models. For capturing the rotary inertia and shear deformation effects, Timoshenko beam model is used. The models include the setup errors and the gyroscopic effects due to high-speed rotation.;A one-dimensional/three-dimensional model is used for predicting the dynamics of micro-drills. The model can accurately predict the bending, torsional and axial vibrations of the micro- and macro-scale cutting tools. The three-dimensional linear-elasticity based model is utilized for modeling the dynamics of the fluted section of the micro-drills. The sections with circular cross-sections (such as the shank, tapers and extension sections) are modeled with beam models to increase the efficiency without compromising the accuracy. A component mode synthesis technique is used to assemble the global system matrices from the section system matrices. The fluted section is represented in the model on a rectangular domain after a polynomial mapping is applied on the cross-section and the pretwist is captured with a coordinate transformation. Using the model, three-dimensional mode-shapes of the cutting-tools can be obtained.;The models lead to boundary value problems (BVPs) with coupled partial differential equations and boundary conditions. The BVPs are numerically solved using a newly developed spectral technique utilizing orthogonal Tchebychev polynomials. The accuracy, efficiency, and robustness of the spectral-Tchebychev solution is demonstrated by solving beam (1D) and solid (3D) problems with different boundary conditions.;The dynamics of micro-machining processes has two components, the mechanics of micro-machining, which governs the machining forces as a result of the material removal, and the dynamics of the cutting-tool/machine-tool parts. This thesis focuses on developing analytical models for dynamics of micro-scale cutting-tools and experimental models for an ultra-high-speed spindle.;The model predictions are experimentally validated using modal analysis setups. Specially designed experimental setups are designed since the traditional modal analysis equipment cannot be used due to the small size of the cutting tools. The cutting-tools are suspended freely with elastic bands to minimize the boundary effects, excitation is supplied with miniature piezoelectric elements attached on the tools such that high-frequency excitation can be supplied without corrupting the dynamic measurements, and measurements are performed with laser Doppler vibrometers coupled through a microscope. From the experimentally obtained frequency response functions, natural frequencies and mode-shapes are acquired, which are compared to the model predictions. Using the models, parametric studies are performed to investigate the effect of geometric parameters on the dynamics of the micro-scale cutting tools.;In the last chapter of the thesis, dynamics of an ultra-high-speed spindle is experimentally modeled. The excitation is supplied with a miniature impact hammer on a precision gage pin rotating in the spindle, and the response of the spindle is measured on the gage pin using laser Doppler vibrometers. The experimental model for dynamics of the spindle is obtained by fitting transfer functions to the experimental FRFs through curve fitting with orthogonal Forsythe polynomials. The modal parameters are extracted for different spindle speeds and compared. (Abstract shortened by UMI.)...