The objective of this Small Grant for Exploratory Research (SGER)/Collaborative Research project is to merge the fields of classical decision theory and high-speed milling in order to study machining optimization in the presence of uncertainty. This will enable the mathematical rigor of decision theory to be applied to milling optimization, while incorporating models used to describe milling operations which naturally include uncertainty. The approach will be to expand prior optimization studies to include limitations imposed by process stability and part errors due to forced vibrations, in addition to the more traditionally considered tool wear, on a profit-based objective function. Probabilistic dependence between the control variables will be incorporated to capture the correlation between them. The uncertainty will then be described using a joint probability distribution for all variables and the expected utility will be maximized over the control variables. The effects of risk aversion on the optimal values of these controls will also be explored. In particular, the hyperbolic absolute risk averse (HARA) utility function, which generalizes both the logarithmic and exponential utility functions, will be used. Sensitivity to risk aversion and variance of the variable distributions on the optimal selection will also be established.
If successful, this research will lead to improved selection of machining parameters at the process planning stage. This will increase machining efficiency and reduce cycle times. Another benefit of this research will be increased awareness of decision theory fundamentals within the manufacturing community (and vice versa). By presenting this research in discipline-specific conferences, the investigators will promote future interactions of this nature.
