A New Theoretical Approach for the Prediction of Machine Tool Chatter in Milling

Abstract

A new method for the prediction of chatter in milling is presented. The dynamics of the milling process are described by a set of differential-difference equations with time varying periodic coefficients. The stability of this system is examined using Fourier analysis and basic properties of the parametric transfer functions of linear periodic systems. The resulting characteristic equation is of infinite order and has constant coefficients. Its truncated version is used to determine the limit of stability employing standard techniques of control theory. The proposed method is applied to a theoretical example and a practical milling system.

Hardware reduction of vibration in milling of complex-shaped surfaces

“…Если общая длина наладки от торца шпинделя до край-ней точки режущей кромки превышает по размеру 8 диаметров концевой фрезы, рекоменду-ется производить обработку с использованием антивибрационной оснастки [8,9]. При изго-товлении деталей из труднообрабатываемых материалов, когда диапазон режимов резания ограничен, применение демпферов способствует значительному повышению производитель-ности обработки и обеспечению требуемой точности [10].…”

Tool stiffness influence on the chosen physical parameters of the milling process

“…Generally speaking about the rigidity, we usually have in mind the complete MCWT system, so we take into account the relative displacement, which occurs in the place of the tool contact with the object, in result of elastic deformation of the MCWT system by the resultant force F [7][8][9][10]. We can also separately consider the rigidity of the individual elements included in the MCWT system.…”

Non-linear oscillations of milling

“…This provided a basis for the work of Sridhar et al [8] who numerically computed the fundamental matrix and the eigenvalues of this matrix. In the study of Minis and Yanushevsky [10], as in previous studies [8,11], milling operations with straight fluted cutters are considered. They used Floquet theory to determine the stability of the zero solution of a linear, homogeneous delay-differential system.…”

“…These approximations deal with consideration of non-linearities, the timeperiodic nature of the cutting-force coefficients, and the feed terms. For example, if one does not consider multiple regenerative effects, loss-of-contact dynamics, friction, structural non-linearities, and other sources of non-linearities, then the resulting system of equations is linear [5,7,8,10,11]. In the work of Hanna and Tobias [9], face milling processes were considered and it was modelled with structural non-linearities and cutting-force non-linearities.…”