Andrew Honeycutt

A Numerical and Experimental Investigation of Period-n Bifurcations in Milling

Numerical and experimental analyses of milling bifurcations, or instabilities, are detailed. The time-delay equations of motions that describe milling behavior are solved numerically and once-per-tooth period sampling is used to generate Poincar e maps. These maps are subsequently used to study the stability behavior, including period-n bifurcations. Once-per-tooth period sampling is also used to generate bifurcation diagrams and stability maps. The numerical studies are combined with experiments, where milling vibration amplitudes are measured for both stable and unstable conditions. The vibration signals are sampled once-per-tooth period to construct experimental Poincar e maps and bifurcation diagrams. The results are compared to numerical stability predictions. The sensitivity of milling bifurcations to changes in natural frequency and damping is also predicted and observed. [DOI: 10.1115/1.4034138]

A New Metric for Automated Stability Identification in Time Domain Milling Simulation

A new metric is presented to automatically establish the stability limit for time domain milling simulation signals. It is based on periodically sampled data. Because stable cuts exhibit forced vibration, the sampled points repeat over time. Periodically sampled points for unstable cuts, on the other hand, do not repeat with each tooth passage. The metric leverages this difference to define a numerical value of nominally zero for a stable cut and a value greater than zero for an unstable cut. The metric is described and is applied to numerical and experimental results. [DOI: 10.1115/1.4032586]

Surface Location Error and Surface Roughness for Period-N Milling Bifurcations

This paper provides time domain simulation and experimental results for surface location error (SLE) and surface roughness when machining under both stable (forced vibration) and unstable (period-2 bifurcation) conditions. It is shown that the surface location error follows similar trends observed for forced vibration, so zero or low error conditions may be selected even for period-2 bifurcation behavior. The surface roughness for the period2 instability is larger than for stable conditions because the surface is defined by every other tooth passage and the apparent feed per tooth is increased. Good agreement is observed between simulation and experiment for stability, surface location error, and surface roughness results. [DOI: 10.1115/1.4035371]

Milling Stability Interrogation by Subharmonic Sampling

This paper describes the use of subharmonic sampling to distinguish between different instability types in milling. It is demonstrated that sampling time-domain milling signals at integer multiples of the tooth period enables secondary Hopf and period-n bifurcations to be automatically differentiated. A numerical metric is applied, where the normalized sum of the absolute values of the differences between successively sampled points is used to distinguish between the potential bifurcation types. A new stability map that individually identifies stable and individual bifurcation zones is presented. The map is constructed using time-domain simulation and the new subharmonic sampling metric. [DOI: 10.1115/1.4034894]

Milling Bifurcations: A Review of Literature and Experiment

This review paper presents a comprehensive analysis of period-n (i.e., motion that repeats every n tooth periods) bifurcations in milling. Although period-n bifurcations in milling were only first reported experimentally in 1998, multiple researchers have since used both simulation and experiment to study their unique behavior in milling. To complement this work, the authors of this paper completed a three year study to answer the fundamental question “Is all chatter bad?”, where time-domain simulation and experiments were combined to: predict and verify the presence of period-2 to period-15 bifurcations; apply subharmonic (periodic) sampling strategies to the automated identification of bifurcation type; establish the sensitivity of bifurcation behavior to the system dynamics, including natural frequency and damping; and predict and verify surface location error (SLE) and surface roughness under both stable and period-2 bifurcation conditions. These results are summarized. To aid in parameter selection that yields period-n behavior, graphical tools including Poincar e maps, bifurcation diagrams, and stability maps are presented. [DOI: 10.1115/1.4041325]