A model to predict the critical undeformed chip thickness in vibration-assisted machining of brittle materials

• Critical uncut chip thickness in vibration machining of brittle materials is modeled.
• The specific cutting energy in vibration-assisted machining is predicted.
• Critical uncut chip thickness is affected by machining and vibration conditions.
• Nominal cutting speed significantly affects critical undeformed chip thickness.
• The model is validated by ultrasonic vibration-assisted machining of silicon.

Vibration-assisted machining (VAM) of brittle materials has been proved to be useful in improving the machining performance by significantly increasing the critical undeformed chip thickness for ductile–brittle transition. However, until now, there does not exist any viable method or model to predict the critical undeformed chip thickness in VAM of brittle materials. The authors have already presented a specific-cutting-energy based model to predict the ductile–brittle transition in nano-machining of brittle materials. In the current study, the specific-cutting-energy based model is extended for VAM by taking into account the vibration parameters in addition to the work-material intrinsic properties, tool geometry and machining parameters in predicting the critical undeformed chip thickness. A series of cutting tests on single crystal silicon workpiece, using single crystal diamond with varying nominal cutting speeds, are conducted to verify the proposed model. It is found that the predicted results are in good agreement with the experimental results.