Investigation of Robust Chatter Stability in Milling
| atmire.migration.oldid | 1180 | |
| dc.contributor.advisor | Park, Simon | |
| dc.contributor.author | Graham, Eldon | |
| dc.date.accessioned | 2013-07-23T15:59:04Z | |
| dc.date.available | 2013-11-12T08:00:16Z | |
| dc.date.issued | 2013-07-23 | |
| dc.date.submitted | 2013 | en |
| dc.description.abstract | In machining operations, self-excited regenerative chatter can develop due to a phase difference between overlapping cutting paths which results in oscillating chip thickness. Machine tool chatter decreases overall productivity and quality of manufactured parts due to excessive vibrations. Analytical models are used to predict the chatter stability lobe diagrams, which illustrate stable and unstable combinations of cutting depths and spindle speeds. The conventional chatter models, however, typically assume that parameters are constant, which leads to inaccuracy. Dynamics, including natural frequencies, damping ratios, and cutting coefficients are the primary parameters that are susceptible to uncertainty and can vary during real milling operations. Especially in micro milling, high spindle speeds can generate centrifugal forces, gyroscopic moments, and thermal effects in the spindle bearings, which can significantly affect tooltip dynamics. Cutting coefficients reflect how the cutting tool interacts with the workpiece material and due to the miniature tool size, material uniformity, tool geometry, and frictional effects, can all affect cutting coefficient values. In addition, cutting coefficients can also be affected by the two different cutting regimes, ploughing or shearing dominant that can exist depending upon the chip thickness with respect to the edge radius of tools. The effects of parameter uncertainty can be directly taken into consideration using the robust stability approaches. The objective of this study is to develop two robust formulations for predicting regenerative chatter stability in micro milling while considering the effects of three uncertain parameters: namely natural frequencies, damping ratios, and cutting coefficients. A frequency domain approach using the Edge theorem can analytically account for time invariant parameter uncertainty directly in the characteristic equation. Combined with the Zero Exclusion principle, computation of stability regions can be efficiently checked graphically. Robust chatter stability can also be detected using Lyapunov stability subjected to linear matrix inequality (LMI) constraints. Experiments are conducted to demonstrate that, while both methods can conservatively predict system stability, the Edge theorem approach predicts the stability lobes faster. From an accuracy and computational time viewpoint, both robust stability approaches are compared for establishing micro milling chatter stability regions. Whereas the LMI approach can be extended to account for time varying parameter uncertainty. | en_US |
| dc.identifier.citation | Graham, E. (2013). Investigation of Robust Chatter Stability in Milling (Master's thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca. doi:10.11575/PRISM/26659 | en_US |
| dc.identifier.doi | http://dx.doi.org/10.11575/PRISM/26659 | |
| dc.identifier.uri | http://hdl.handle.net/11023/845 | |
| dc.language.iso | eng | |
| dc.publisher.faculty | Graduate Studies | |
| dc.publisher.institution | University of Calgary | en |
| dc.publisher.place | Calgary | en |
| dc.rights | University of Calgary graduate students retain copyright ownership and moral rights for their thesis. You may use this material in any way that is permitted by the Copyright Act or through licensing that has been assigned to the document. For uses that are not allowable under copyright legislation or licensing, you are required to seek permission. | |
| dc.subject | Engineering--Mechanical | |
| dc.subject.classification | Chatter | en_US |
| dc.subject.classification | robust stability | en_US |
| dc.subject.classification | Edge Theorem | en_US |
| dc.subject.classification | Linear matrix inequality | en_US |
| dc.title | Investigation of Robust Chatter Stability in Milling | |
| dc.type | master thesis | |
| thesis.degree.discipline | Mechanical and Manufacturing Engineering | |
| thesis.degree.grantor | University of Calgary | |
| thesis.degree.name | Master of Science (MSc) | |
| ucalgary.item.requestcopy | true |