ORIGINAL ARTICLE Inverse analysis of the cutting force in laser-assisted milling on Inconel 718 Yixuan Feng 1 & Yu-Ting Lu 2 & Yu-Fu Lin 2 & Tsung-Pin Hung 2 & Fu-Chuan Hsu 2 & Chiu-Feng Lin 2 & Ying-Cheng Lu 2 & Steven Y. Liang 1 Received: 21 June 2017 /Accepted: 24 January 2018 /Published online: 1 February 2018 # Springer-Verlag London Ltd., part of Springer Nature 2018 Abstract Inverse analysis is of value identifying viable solutions of process parameters that can achieve specified process performance. In this study, an inverse analysis method is proposed for the cutting force in laser-assisted milling on Inconel 718. The method uses the analytical model to solve the direct problem and applies a variance-based recursive method to guide the inverse analysis. The half-slot milling is simplified as an orthogonal cutting at each instant, forces in cutting and radial directions are calculated under microstructure evolution, and the axial force is predicted according to tool geometry and coordinates transformation. The inverse analysis identifies five process parameters including feed rate, axial depth of milling, laser preheating temperature, spindle speed, and rake angle, and finds the optimal solution for target performance, the resultant cutting force. Four experiments verified the effectiveness of the proposed method because of a maximum error less than 8% between predicted forces and experimental measurements. The proposed method is valuable in terms of providing a reference for the selection of process parameters under certain cutting force requirements. Keywords Inconel 718 . Laser-assisted milling . Inverse analysis 1 Introduction Inconel 718 is a nickel-based super alloy with high hardness of HRC 30-40 and high melting temperature about 1300 °C. Because of these properties, Inconel 718 is a typical hard-to- machine material with large cutting forces. Several thermally enhanced machining technologies such as laser-assisted mill- ing have been developed to enhance the machinability of Inconel 718. To simulate this machining process, the authors have applied analytical model [1] and finite element analysis [2] to predict cutting forces under designed process parame- ters, such as feed rate, axial depth of milling, spindle speed, laser preheating temperature, and rake angle. Under the cir- cumstances in actual laser-assisted milling, the drop of cutting force due to material softening is an important standard. People need to specify the setup of milling machine, geometry of milling tool, and laser power to get target cutting forces, but it is difficult to correctly determine the process parameters to meet the requirements of cutting forces by just guessing the parameters and predicting forces through analytical model or finite element analysis repeatedly. An inverse analysis is pre- ferred in addition to the direct analysis to identify viable solu- tions of process parameters that can achieve specified process performance. The inverse analysis so far has been focusing on determin- ing model coefficients that are hard to be defined in analytical model or material properties that are hard to be measured in experiments. Edouard et al. [3] used inverse analysis to deter- mine nine cutting coefficients for two different cutting force models. Their results were validated under different combina- tions of axial depth of cut, radial depth of cut, feed per tooth, and spindle speed, but these process parameters were not in- volved in the inverse analysis. Solidônio et al. [4] predicted the heat flux in a thermal model of the assembly tool-tool holder under four different inverse analysis methods. The di- rect problem was solved by an irregular finite volume mesh. Marcelo et al. [5] estimated the heat flux and the temperature * Yixuan Feng yfeng82@gatech.edu 1 Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA 2 Metal Industries Research and Development Centre (MIRDC), Kaohsiung, Taiwan The International Journal of Advanced Manufacturing Technology (2018) 96:905–914 https://doi.org/10.1007/s00170-018-1670-1