Integrating Analytical Models with Finite-Element Models: An Application in Micromachining

Problem: The prediction of cutting forces is very important in designing mechanical micromachining to ensure geometrical accuracy of the machined feature and avoid tool breakage. These predictions can be done either via analytical models or finite-element models. The finite-element models are precise but usually time consuming to run. Analytical models, on the other hand, are less accurate but computationally much cheaper. The problem here is to integrate these two types of physics-based models and obtain an easy-to-evaluate statistical model that can approximate the machining forces. Approach: We propose performing a sensitivity analysis using the computationally cheap analytical models prior to conducting the computationally intensive finite-element simulations. With the elicited prior knowledge from the sensitivity analysis, a two-stage strategy is presented for designing the finite-element simulations in which customized number of levels can be assigned for each input factor. The finite-element simulation data can then be integrated with the analytical models in developing the final metamodel. Results: We show that the initial sensitivity analysis can reveal critical information about the underlying system and guide us to more efficiently extract information from the finite-element models. The proposed design for the finite-element simulations is comprised of two subarrays and overall can achieve desirable orthogonality and space-filling properties. Compared with using n different levels for all input factors, as in the traditional space-filling design, the new design is more capable for estimating factor interactions while still maintaining the ability to capture necessary nonlinear effects. By using fewer levels, it can also improve the efficiency of estimating the effects when the simulation is subject to stochastic noise. In model validation, our numerical results indicate that the fitted integrated metamodel can more precisely approximate the machining forces than either using the analytical models or the traditional metamodel based on the finite-element simulations alone.