Modeling the cutting force in ultrasonic-vibration assisted milling and its empirical study

Calculation the cutting force in machining processes is of great importance. In this paper، undeformed chip thickness in one-dimensional ultrasonic vibration assisted milling is calculated and then، a model for determining the cutting force in this process is presented. Analytical relations show that in ultrasonic assisted milling (UAM)، the maximum cutting force is greater than in conventional milling (CM)، but the average cutting force is decreased. To verify the proposed relations، with the aid of a particular experimental setup، one-dimensional vibration in feed direction is applied to workpiece and cutting force in CM and UAM is measured experimentally. Greater maximum cutting force in UAM and decrease of average cutting force in UAM compared to CM is observed experimentally as well. Comparison of average values of cutting force shows that the analytical relations for predicting the cutting force have 16% average error in CM and 40% average error in UAM. Given that the analytical calculation of undeformed chip thickness and cutting force in UAM and also comparison of experimental forces with the modeled ones has been done in this paper for the first time، the accuracy of proposed relations are acceptable.