| Milling is one of the most important subtractive manufacturing processes. Cutting force predictions in milling are useful for the structural design of machine tools, selection of optimum cutting parameters, design of workholding fixtures, tool stress analysis, spindle bearing design, and the real time monitoring of tool wear and breakage. Force models are also used in predicting the stability of the milling process, surface location error predictions, as well as surface finish predictions.;In this dissertation, closed form analytical mechanistic cutting force models, using linearized lumped parameter cutting coefficients, are considered. Existing analytical mechanistic force models of helical peripheral milling, which use linearized cutting coefficients, either utilize four different sets of analytical expressions to describe the forces for one complete cutter rotation, or do not have closed form solutions. Numerical models are computationally-intensive, fail to provide the insights that analytical models do, and do not permit symbolic manipulation. In this work, two equivalent versions of closed form analytical expressions for chip thickness and chip width are developed using Heaviside unit step function and Fourier series approaches. The distinguishing feature is that single expressions describe the chip thickness and chip width during the entire cutter rotation. These expressions are then applied to develop single, analytical closed form expressions for each of the three orthogonal components of the cutting force, in a fixed coordinate frame, for helical peripheral milling. The model can be calibrated using partial radial immersion experiments.;A procedure has been developed to calculate the variances in measured model input parameters. The propagation of uncertainties through the model is determined by Type A and Type B evaluations to develop an overall expanded uncertainty for placement of confidence intervals on cutting force predictions. The availability of single expressions for force components permits the derivation of compact expressions for sensitivity coefficients for use in the uncertainty analysis.;Extensive experimental tests, as well as comparisons with established numerical models, verify the fidelity of the predictions. The model is extended to be able to predict cutting forces in cases of runout or differential pitch cutters. A refined formulation using instantaneous cutting coefficients, instead of the usual method of average coefficients, has also been developed, further increasing the accuracy of force predictions. Experiments show that the refined model is able to predict the force patterns and magnitudes very accurately for the entire range of radial immersions. |
