Young, Sigmund MaxIn this thesis, dynamics of low immersion milling is explored through analytical and numerical means. Using linear and nonlinear cutting force models, maps are constructed for single degree-of-freedom and two degree-of-freedom systems where the time spent cutting is "small" compared to the spindle rotation period. These maps are used to study the possibilities for different nonlinear instabilities and construct stability charts in the space of cutting depth and spindle speed. The analytical predictions are compared with numerical results as well as prior experimental results. Good agreement amongst analytical, numerical, and experimental results is seen. Limitations of the analytical and numerical approaches are discussed and extensions for future work are suggested.en-USThesisEngineering, Mechanicalmillingmapsdynamicslow immersionmodels