Title:
Analysis of Milling Forces via Angular Convolution
Analysis of Milling Forces via Angular Convolution
Author(s)
Wang, J. - J. Junz
Liang, Steven Y.
Book, Wayne J.
Liang, Steven Y.
Book, Wayne J.
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Abstract
The measurement of cutting force systems is one of the most frequently used techniques for the monitoring of machining processes. Its wide spread application ranges from tool condition
identification, feedback control, cutting system design, to process optimization. To gain fundamental
understanding of the force system in machining, this paper presents the work of establishing a closed
form expression for the cutting force in end milling as an explicit function of cutting parameters and tool/workpiece geometry. Based on the theoretical local cutting force model, the generation of total
cutting forces is formulated as the angular convolution of three uncorrelated cutting process component
functions, namely the elemental cutting force function, the chip width density function, and the tooth
sequence function. The elemental cutting force function is related to the chip formation process in an
elemental cutting area and it is characterized by the chip thickness variation, specific cutting pressure
constants, and entry/exit angles. The chip width density function defines the chip width per unit cutter
rotation along a cutter flute within the range of axial depth of cut as the function of the angular position
of each cutting point. The tooth sequence function represents the spacing between flutes as well as
their cutting sequence as the cutter rotates. The analysis of cutting forces is extended into the Fourier
domain by taking the frequency multiplication of the transforms of the three component functions.
Fourier series coefficients of the cutting forces are shown to be algebraic functions of various tool
parameters and cutting conditions. Simulation results are presented in the frequency domain to
illustrate the effects of process parameters. A series of end milling experiments are performed and
their results discussed to validate the analytical model.
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Date Issued
1991
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Text
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Proceedings