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Based on the experiments on milling the carbon structural 45 steel with the flat rake milling insert and the waved-edge milling insert, the analysis and study on single physics field and coupling field are studied. On the basis of the milling force and milling temperature mathematical models, the force density function and heat density function of the waved-edge milling insert are built, the stress fields analysis and temperature fields analysis have been done. In order to discuss the distribution principle of equivalent stress and distortion under coupling condition, the coupling analysis on the stress field and temperature field is done. All these studies provide the theoretic and experimental basis for solving the cutter disrepair and groove optimization technology.

Based on the theoretic analysis and experiments on milling the carbon structural 45 steel with the flat rake milling insert and the waved-edge milling insert with complex 3D grooves which is developed by HarBin University of Science and Technology, we have studied on the impact disrepair mathematic model and groove optimization. On the basis of the milling force mathematic model and force density function of the waved-edge milling insert with complex 3D grooves the author built, we have the finite element analysis and blurry synthetical judgement of the 3D stress field, and forecast that the anti-impact disrepair capability of the waved-edge milling insert is choiceness. We find out the difference of the impact disrepair invalidation types between different grooves milling inserts by the experiments. Based on the plentiful and systemic impact disrepair experiments, as the emphasis in this paper, we build the impact disrepair life cumulating distribution function mathematic model by the mathematics statistic method and have contrast analysis of the impact disrepair average lives between the two types of milling inserts, and prove that the anti-impact disrepair capability of the waved-edge milling insert is choiceness. All these studies provide the theoretic and experimental basis for solving the cutter disrepair which is the key problem in the automatization production and groove optimization.

Based on the von Kármán classical nonlinear plate theory, nonlinear axisymmetric vibrations of a clamped thin circular plate subjected to transverse harmonic load are investigated. Effects of static deformation on the vibration responses are considered. Harmonic motion is assumed. The time variable is eliminated and the partial differential equations are converted into a system of nonlinear ordinary differential equations by employing a Kantorovich time averaging method. The resulting nonlinear ordinary differential boundary-value problem is solved numerically by using shooting method. Effects of static-dynamic load on the transverse deflection, frequencies and amplitudes are examined in details. The resonance phenomenon is discussed emphatically.

Geometrically nonlinear bending and buckling of circular sandwich plates subjected to transversely non-uniform temperature rise is investigated in this paper. On the basis of sandwich plate theory, nonlinear equations governing the large thermal axis-symmetric deformations of circular sandwich plate in terms of the middle plane’s displacements are derived. Numerical solutions of the nonlinear boundary value problem are obtained by using the shooting method. Equilibrium paths and configurations for different boundary conditions and different values of materials and geometry parameters are illustrated. Numerical results show that the boundary conditions and the stiffness greatly effect critical buckling loads.

The counterintuitive phenomena of elastic, perfectly plastic beam, circular plate and square plate are investigated numerically and experimentally. A new unstable slot and asymmetry of dynamic response of beam are revealed. The unsteady areas and uncertainty of response are observed numerically. At the end, the law of thermodynamics and the theorem of Lyapunov instability are employed to state the formation mechanism of counterintuitive behavior.

Based on the milling temperature experiments and researches, we established the milling temperature mathematical model using dimension analytic method,and the heat density function and superficial heat density function of the flat milling insert and the waved-edge milling insert, whose rake face is wave curve plane and created by the authors using the diathermanous theory. We describe the mathematic model of the instantaneous temperature field by the theory of the finite moving planar sources of heat. At last, a program was done to calculate the heat density function and the milling temperature field. According to the calculated results and plotted graph, it is proven that the highest temperature is not on the knifepoint and host edge, in fact, it is offset from the host edge a certain space. So we can make the conclusion that the waved-edge milling insert’s cutting capability is higher than the flat milling insert’s which is consistent with the experimental result. All the studies above are the foundation for accurately describing the 3-D temperature field and optimizing groove.