The optimal equivalent method of dynamics model for endmills

In order to rapidly analyze the dynamics in free boundary condition, endmills were divided into two parts, tool shank and fluted portion. Their frequency response functions were calculated respectively and then coupled. For the fluted portion, three equivalent models based on the principle of equal area of cross-section (EAC), equal area moment of inertia (EAMI) and equal average area moment of inertia (EAAMI) were proposed. The results show EAAMI can achieve the best accuracy. Based on this result, three factors such as percent of fluted portion length to tool length, ratio of tool length to diameter and helix angle are analyzed to identify the influence on equivalent model of actual cutting tools. An orthogonal design scheme was established with three factors and four levels. The results obtained from range analysis and variance analysis show that percent of fluted portion length to tool length and helix angle are the main affecting factors on equivalent diameter, and a correction model is established between the three factors and equivalent diameter according to the multivariable regression method. Finally, three endmills were used to do the verification and the results show the method proposed in this paper work best.