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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.

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Reduction of cutting force in a machining process offers several advantages including increase in tool life, and improvement in the quality of the machined surface. One the new techniques for reducing cutting force relates to ultrasonic vibration assisted machining. In the present paper, one-dimensional ultrasonic vibration-assisted side milling process of Al7022 aluminum alloy has been studied. In order to investigate the effect of cutting speed, feed rate, radial depth of cut, and vibration amplitude on three cutting force components and their resultant, a special experimental setup has been designed and established which applies one dimensional ultrasonic vibration to work piece. Applying the ultrasonic vibrations on milling process, affects mostly on feed component of cutting force which is unidirectional with the work piece vibration, and decreases it by 33.5% in average. Decrease in cutting speed and increase in vibration amplitude, results to increase the separation of tool and work piece from each other in a portion of each vibration cycle, and larger decrease of the feed force. The average decrease of the resultant cutting force in ultrasonic-assisted milling process is 10.8%.