For the traditional one-step formulations of using shell elements, the computations of the curvature variation and bending stiffness matrix were simplified by omitting the rotational DOFs （degrees of freedom） on the basis of initial flat blank and fully known final configuration. They were highly efficient but not suitable either for the forming processes with non-flat initial configurations or for one-step forward and multistep analyses. Thus, a one-step formulation based on the rotation-free BST （Basic Shell Triangle） element was presented. In this formulation, the penalty method was adopted to deal with contacts in the forming processes.
A new analytical chip formation model is proposed for micro-end-milling operations. The model calculates an instantaneous uncut chip thickness by considering the combination of exact trochoidal trajectory of the tool tip and tool run-out, while the simplified circular trajectory and the neglected run-out create negligible change in conventional-scale chip formation models. Newton-Raphson iterative method is employed during the calculation to obtain quadratic convergence. The proposed approach allows the calculation of instantaneous uncut chip thickness to be done accurately and rapidly, and the prediction accuracy of this model is also verified by comparing the simulation results to experimental cutting forces.
