1974
DOI: 10.1115/1.3438305
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Abstract: A mathematical theory of nonlinear chatter is developed. In this, the structure is represented by an equivalent single degree of freedom system with nonlinear stiffness characteristics and the cutting force by a third degree polynomial of the chip thickness. This model leads to a second order differential equation with nonlinear stiffness and nonlinear time delay terms from which the conditions of steady state chatter are derived. These are then discussed by applying them to an equivalent system derived from e… Show more

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Cited by 208 publications
(119 citation statements)
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“…Since the cutting force is proportional to the chip thickness, the structural modes in the overall machining system are self-excited and lead to unstable vibrations [1]. Since 1960s, many researchers including Tobias and Tlusty had developed the basic theory of machining chatter [2][3].…”
Section: Introductionmentioning
confidence: 99%
See 1 more Smart Citation
“…Since the cutting force is proportional to the chip thickness, the structural modes in the overall machining system are self-excited and lead to unstable vibrations [1]. Since 1960s, many researchers including Tobias and Tlusty had developed the basic theory of machining chatter [2][3].…”
Section: Introductionmentioning
confidence: 99%
“…Hanna and Tobias carried out a study of face-milling and turning processes in 1970s [1], in which both structural nonlinearities and cutting force nolinearities were taken into account. Quadratic and cubic nonlineraities were included in a differential equation with constant coefficients and the stability of the zero solution was studied.…”
Section: Introductionmentioning
confidence: 99%
“…In the 1970s in a reference work, Hanna and Tobias [8] proposed a single-degree-of-freedom time-delay differential equation including non-linear terms, due to structural stiffness and cutting force.…”
Section: Introductionmentioning
confidence: 99%
“…His formulation was latter adopted by many investigators and led to major advances towards the understanding and prediction of the chatter phenomenon. Hanna [4], Shi and Tobias [5], Tlusty [6] and others carried out theoretical and experimental researches on cutting chatter, explained the mechanism of stabilization of chatter amplitudes and the phenomenon of finite amplitude instability, and presented a non-linear theory of machine tool chatter. Chaos cutting is an important phenomenon which is related to the non-linear theory of machine tool chatter.…”
Section: Introductionmentioning
confidence: 99%