Mathematical simulation of vibration cutting process for food materials
Annotation
The purpose of the paper is to develop a complex of mathematical models for vibration cutting process of food materials. An analysis of the research papers on vibration cutting of food products has been performed. A scheme for knife penetration with a straight cutting edge into a viscoelastic material during vibration is considered. The effect of kinematic transformation of an elementary knife when applying longitudinal vibrations is analyzed. Mathematical models for determining the vibration velocity of an elementary knife and the vibration cutting angle have been developed. The main dependences of the vibration cutting angle on the vibration frequency, amplitude, and feed speed of the knife have been calculated. Mathematical models for determining the dimensional and dimensionless resistance forces of the knife shape, which change during vibration cutting according to the harmonic law, have been developed. The main dependences of these forces on the vibration frequency, amplitude, and blade feed speed have been calculated. Mathematical models for determining the average vibration cutting angle and the average dimensionless shape resistance force have been developed; the main dependencies on the vibration frequency, amplitude and feed rate of the knife have been determined. The process of vibration cutting with the imposition of polyharmonic vibrations, including the fundamental and higher harmonics, is considered. Mathematical models for determining the vibration cutting angle and dimensionless shape resistance force have been developed. The main dependences of the indicated angle and dimensionless force on the number of the highest harmonic and the knife feed speed have been calculated. Mathematical models for determining the average vibration cutting angle and the average dimensionless shape resistance force when polyharmonic vibrations with two harmonics are applied are proposed. The main dependences of the indicated angle and dimensionless force on the number of the highest harmonic and the knife feed speed have been calculated. The average values of the vibration cutting angle and dimensionless force are significantly reduced with the imposition of vibrations with higher harmonics on the cutting body at a constant total vibration frequency, which leads to a noticeable reduction in energy costs for cutting and an improvement in the quality of the cut surface.
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