Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy

ROBUST MULTICRITERIA OPTIMIZATION OF SURFACE LOCATION ERROR
AND MATERIAL REMOVAL RATE IN HIGH-SPEED MILLING UNDER
UNCERTAINTY

By

Mohammad H. Kurdi

August 2005

Chair: Tony L. Schmitz

Cochair: Raphael T. Haftka

Major Department: Mechanical and Aerospace Engineering

High-speed milling (HSM) provides an efficient method for accurate discrete part
fabrication. However, successful implementation requires the selection of appropriate
operating parameters. Balancing the multiple process requirements, including high
material removal rate, maximum part accuracy, chatter avoidance, and adequate surface
finish, to arrive at an optimum solution is difficult without the aid of an optimization
framework.

Despite the attractive gain in productivity that HSM offers, full realization of the
benefits is dependent on the proper selection of cutting parameters. Parameters selected
must achieve the required productivity while maintaining an acceptable accuracy. Milling
models are used to aid in the proper selection of these cutting parameters. They provide
information on whether a cutting condition is stable and/or predict the surface accuracy.
However, this selection is rather tedious, costly and time consuming and might not even
provide an optimum solution. Parameters are selected based on experience until a point is
found that provide the productivity and surface accuracy required. Difficulties
encountered in this selection process include sensitivity of surface accuracy to cutting
parameters, uncertainties in several parameters in the milling model and the
computational effort needed to account for stability and surface accuracy. Therefore,
balancing the multiple requirements, including high material removal rate, minimum
surface location error and chatter avoidance, to arrive at an optimum solution is difficult
without the aid of optimization techniques.

In this dissertation a robust optimization algorithm that accounts for the inherent
process uncertainty and surface location error sensitivity is developed. Two optimization
criteria are considered, namely, surface location error and material removal rate under the
stability constraint. The trade off curve of surface location error versus material removal
rate is calculated for the mean values of input parameters, as well as for a confidence
level in the stability boundary. An experimental validation of the robust optimization
algorithm is also conducted, including an experimental validation of the variation of the
cutting forces as a function of spindle speed. The confidence level in the axial depth limit
and surface location error prediction is found using two methods: 1) sensitivity analysis;
and 2) sampling methods. The sensitivity study highlights the most significant factors
affecting process stability and surface location error. The effect of input parameters
correlation is included in the confidence level predictions using Monte Carlo and Latin
Hyper-Cube sampling methods.