A Theory of Nonlinear Regenerative Chatter

Cheng

Int J Adv Manuf Technol

et al. 2005

Abstract:In this paper, the authors propose the generic concept of machining instability based on the analysis of all kinds of machining instable behaviors and their features. The investigation covers all aspects of the machining process, including the machine tool structural response, cutting process variables, tooling geometry and workpiece material property in a full dynamic scenario. The paper presents a novel approach for coping with the sophisticated machining instability and enabling better understanding of its effect on the surface generation through a combination of the numerical method with the characteristic equations and using block diagrams/functions to represent implicit equations and nonlinear factors. It therefore avoids the lengthy algebraic manipulations in deriving the outcome and the solution scheme is thus simple, robust and intuitive. Several machining case studies and their simulation results demonstrate the proposed approach is feasible for shop floor CNC machining optimisation in particular. The results also indicate the proposed approach is *Correspondence to Professor Kai Cheng, Email: K.Cheng@lmu.ac.uk +Currently working as a visiting scholar at Leeds Metropolitan University, Professor Xueke Luo is with North China University of Technology 2 useful to monitor the machining instability and surface topography and to be potentially applied in adaptive control of the instability in real time.

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%

A simulated investigation on the machining instability and dynamic surface generation

Cheng

Int J Adv Manuf Technol

et al. 2005

International Journal of Mechanical Sciences

“…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%

Improvement of chatter stability in boring operations with passive vibration absorbers

Miguélez

Rubio

Loya

et al. 2010

115

This paper is focused on the behavior of boring bars with a passive dynamic vibration absorber (DVA) for chatter suppression. The boring bar was modeled as a cantilever Euler-Bernoulli beam and only its first mode of vibration was considered. The stability of the two-degree-of-freedom model was analyzed constructing the stability diagram, dependent on the bar characteristics and on the absorber parameters (mass, stiffness, damping, and position). Two analytical approaches for tuning the absorber parameters were compared. The selection criterion consisted on the maximization of the minimum values of the stability-lobes diagram. Subsequent analysis performed in this work, allowed formulating of new analytical expressions for the tuning frequency improving the behavior of the system against chatter.

“…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%

Experimental Investigation of Evolution Process of Nonlinear Characteristics from Chatter Free to Chatter

Kong¹,

Liu²,

Wang³

2011

JMP

The vibration acceleration time history of the cutter holder was separated into three parts; namely, chatter free, transition and chatter processes. The reconstructed attractor and probability distribution of vibration acceleration time series were studied in order to observe the system's behavior. The Lyapunov exponent andKolmogorov entropy were used to help judge the cutting state. Meanwhile, the relation curves of the Lyapunov exponent and entropy versus machining parameters were plotted and discussed. The research shows that Lyapunov exponent and Kolmogorov entropy are toned up when vibration acceleration time history goes from chatter free, transition to chatter. When cutting state transited from chatter free to chatter, the Lyapunov exponent and Kolmogorov entropy increase with increasing amplitude. In addition, the relation curves looks like stability lobes. The experimental study allow us to select optimal machining parameters for decreasing the uncertainty of cutting vibration.