A Finite Element Model for Ultrasonic Cutting of Toffee


Article Preview

The performance of an ultrasonic cutting device critically relies on the interaction of the cutting tool and the material to be cut. A finite element (FE) model of ultrasonic cutting is developed to enable the design of the cutting blade to be influenced by the requirements of the toolmaterial interaction and to allow cutting parameters to be estimated as an integral part of designing the cutting blade. In this paper, an application in food processing is considered and FE models of cutting are demonstrated for toffee; a food product which is typically sticky, highly temperature dependent, and difficult to cut. Two different 2D coupled thermal stress FE models are considered, to simulate ultrasonic cutting. The first model utilises the debond option in ABAQUS standard and the second uses the element erosion model in ABAQUS explicit. Both models represent a single blade ultrasonic cutting device tuned to a longitudinal mode of vibration cutting a specimen of toffee. The model allows blade tip geometry, ultrasonic amplitude, cutting speed, frequency and cutting force to be adjusted, in particular to assess the effects of different cutting blade profiles. The validity of the model is highly dependent on the accuracy of the material data input and on the accuracy of the friction and temperature boundary condition at the blade-material interface. Uniaxial tensile tests are conducted on specimens of toffee for a range of temperatures. This provides temperature dependent stress-strain data, which characterises the material behaviour, to be included in the FE models. Due to the difficulty in gripping the tensile specimens in the test machine, special grips were manufactured to allow the material to be pulled without initiating cracks or causing the specimen to break at the grips. A Coulomb friction condition at the bladematerial interface is estimated from experiments, which study the change in the friction coefficient due to ultrasonic excitation of a surface, made from the same material as the blade, in contact with a specimen of toffee. A model of heat generation at the blade-toffee interface is also included to characterise contact during ultrasonic cutting. The failure criterion for the debond model assumes crack propagation will occur when the stress normal to the crack surface reaches the tensile failure stress of toffee and the element erosion model uses a shear failure criterion to initiate element removal. The validity of the models is discussed, providing some insights into the estimation of contact conditions and it is shown how these models can improve design of ultrasonic cutting devices.



Edited by:

Patrick Sean Keogh




E. McCulloch et al., "A Finite Element Model for Ultrasonic Cutting of Toffee", Applied Mechanics and Materials, Vols. 5-6, pp. 519-526, 2006

Online since:

October 2006




[1] M. Lucas, A. MacBeath, E. McCulloch and A. Cardoni: A Finite Element Model for Ultrasonic Cutting, World Congress on Ultrasonics, Beijing, China (2005).

DOI: https://doi.org/10.1016/j.ultras.2006.05.115

[2] M. Lucas, J.N. Petzing, A. Cardoni and L.J. Smith: Design and Characterisation of Ultrasonic Cutting Tools, Annals of CIRP, 50/1 (2001).

DOI: https://doi.org/10.1016/s0007-8506(07)62092-7

[3] T. Mason and M.J. Povey: Ultrasound in Food Processing, Blackie Academic (1998).

[4] L. Smith and M. Lucas: Fracture Model of Ultrasonically Assisted Osteotomy, 9th International Congress on Experimental Mechanics, Orlando, USA (2000).

[5] A. Smith, A. Nurse, G. Graham and M. Lucas: Ultrasonic Cutting - A Fracture Mechanics Model, Ultrasonics, 34 (1996).

DOI: https://doi.org/10.1016/0041-624x(95)00078-h

[6] M.N. Charalambides, S.M. Goh, S.L. Lim and J.G. Williams: The Analysis of the Frictional Effect on Stress-Strain Data from Uniaxial Compression of Cheese, Journal of Materials Science, 36 (2001).

[7] Y.A. Çengel: Heat Transfer a Practical Approach, McGraw-Hill Higher Education (2003).

[8] W. Littmann, H. Storck, and J. Wallaschek: Sliding Friction in the Presence of Ultrasonic Oscillations: Superposition of Longitudinal Oscillations, Archive of Applied Mechanics, 71 (2001).

DOI: https://doi.org/10.1007/s004190100160

[9] Hibbitt, Karlsson, Sorensen: Abaqus User Manual version 6. 4.

[10] M. Lucas, A. Cardoni and A. MacBeath: Temperature Effects in Ultrasonic Cutting of Natural Materials, Annals of CIRP, 54/1 (2005).

DOI: https://doi.org/10.1016/s0007-8506(07)60082-1