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This paper studied the rule of micro-hole in electrochemical jet machining (EJM) of TC4 alloy and established the mathematical model of machining process and predicted the machining profile. Considering the influence of machining gap and machining time, orthogonal experiment was designed. This paper established the mathematical model of the electrochemical jet machining process of TC4 alloy based on the response surface analysis (RSA) method. The results indicate that the electrochemical jet can improve the directivity of machining, reducing the machining gap can improve the machining efficiency, but the jet will cause secondary corrosion and abrupt change of current at the edge of inlet. The mathematical model based on response surface analysis is accurate after variance test. The experimental results show that the average error between the established prediction model of machining depth and the actual value is 2.32%, and the average error of the prediction model of inlet radius is 2.18%.

When applying the non-parallel shear zone model to predict the cutting process parameters of carbon steel workpiece, it is found that there is a big error between the prediction results and the experimental values. And also, the former approach to obtain the relevant cutting parameters of the non-parallel shear zone model by applying coordinate transformation to the parallel shear zone model has a theoretical error – it erroneously regards the determinant (|J|) of the Jacobian matrix (J) in the coordinate transformation as a constant. The shape of the shear zone obtained when |J| is not constant is drew and it is found that the two boundaries of the shear zone are two slightly curved surfaces rather than two inclined planes. Also, the error between predicted values and experimental values of cutting force and cutting thrust is slightly smaller than that of constant |J|. A corrected model where |J| is a variable is proposed. Since the specific values of inclination of the shear zone (α, β), the thickness coefficient of the shear zone (as) and the constants related to the material (f0, p) are not given in the former work, a method to obtain the above-mentioned five constants by solving multivariable constrained optimization problem based on experimental data was also proposed; based on the obtained experimental data of AISI 1045 steel workpiece cutting force, cutting thrust, chip thickness, the results of five above-mentioned model constants are obtained. It is found that, compared with prediction from uncorrected model, the cutting force and cutting thrust of AISI 1045 steel predicted by the corrected model with the obtained constants has a better agreement with the experimental values obtained by Ivester.