Milling dynamic model based on rotatory Euler–Bernoulli beam model under distributed load

The precise description of dynamic milling system has been the core for process quality promotion for a long time. The conventional models simplify the milling system into a two-degree of freedom dynamic model to describe the cutter vibration. However, cutting forces are distributed along the cutting edges in milling process with large axial depth of cut, which cannot be treated as concentrated force. To this end, this paper presents a theoretical modeling method with boundary conditions of cutter-holder-spindle system simplified. Firstly, the cutter is modeled with a continuous rotatory Euler–Bernoulli beam, it is then discretized by the Finite Difference Method. Secondly, the discretized dynamic equations are synthesized with dynamic cutting force model to describe the dynamic behavior of the milling system. Cutting forces in the milling process are predicted as vectors in a distributed way. To evaluate the developed model, the model shape analysis and cutting tests are implemented. The simulation and cutting test results indicate that the developed model can improve the simulation precision in some simulations by taking structural flexibility into consideration. This model generally improves the simulation precision for cutting forces, and the developed model shows smaller stiffness under large axial depth of cut. Furthermore, the developed methods can be applied for situations where the modal test can be avoided or the modal test conditions cannot be satisfied.