# Mathematical model for cutting force in ultrasonic-assisted milling of soda-lime glass

• Yasmine El-Taybany
• Hassan El-Hofy
ORIGINAL ARTICLE

## Abstract

Ultrasonic-assisted milling (UAM) has an outstanding performance in machining hard and brittle materials, such as glass. The cutting force which has been investigated both experimentally and theoretically is the key factor that affects the machined surface quality. This paper presents a mechanistic mathematical model for the axial cutting force in UAM of soda-lime glass. This model is based on the process mechanism of material removal and can be used to predict the cutting force without the need of performing actual experiments. The mathematical model is proposed taking into consideration two different material removal mechanisms, that directly affect the final material removed volume for the brittle material. The first model is the ductile model which is described by the ductile mechanism where the material is removed by the plastic flow, while the other is the brittle model described by the brittle mechanism where the material is removed due to the crack formation that cause material fracture. In the present models, the effects of both the rotation and ultrasonic vibration motion of the cutting tool were taken into consideration through their effects on the indentation volume, by each diamond grain, into the workpiece. The development of the model started by the analysis of the behaviour of a single diamond grain and obtaining the cutting force for an individual diamond grain first. The total cutting force then was derived by summing up the forces caused by all diamond grains taking part in the cutting process. From the developed models results, the trends of the predicted results from the ductile model agree well with the results determined experimentally at low feed rates and low depths of cut. However, the predicted results from the brittle model agree well with the results determined experimentally at high feed rates and high depths of cut. These results explain that the ductile mode of the material removal is occurring at low feed rates and low depths of cut. Then it changes to the brittle mode of material removal by further increasing of the feed rate and depth of cut.

## Keywords

Ultrasonic-assisted milling Cutting force Glass mathematical model Ductile Brittle Material removal mechanism

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© Springer-Verlag London Ltd., part of Springer Nature 2019

## Authors and Affiliations

1. 1.Industrial Engineering and Systems Management Department, School of Innovative Design EngineeringEgypt-Japan University of Science and TechnologyAlexandriaEgypt
2. 2.Production Engineering and Mechanical Design Department, Faculty of EngineeringPort Said UniversityPort SaidEgypt
3. 3.Production Engineering Department, Faculty of EngineeringAlexandria UniversityAlexandriaEgypt