Automated Upgraded Generalized
Full-Discretization Method: Application
to the Stability Study of a Thin-Walled
Milling Process
Chigbogu Ozoegwu and Peter Eberhard
1 Introduction
Lumped delayed models are usually used to describe the regenerative vibration of
a flexible milling tool when cutting a rigid workpiece. In this case, the tool is the
compliant body, see Fig. 1a. A few of the elaborate references on modeling and stability analysis of such systems include [1–4]. On the other hand, the tool can act as
a rigid body when milling a thin-walled workpiece with high aspect ratio of length
or width to thickness. This case is illustrated in Fig. 1b. Milling of thin-walled workpieces is encountered in the processing of monolithic parts for the aerospace industry
where high strength-to-weight ratio is a major requirement. In such a milling process, much of the blank material is removed, and this has to be done at the maximum
possible material removal rate for economic viability. Knowledge-based choices of
the process parameters that guarantee optimal productivity and surface quality derive
from modeling and analyzing the structural and regenerative dynamics of the cutting
process. Since a thin-walled workpiece is a distributed elastic system, its regenerative machining is governed by a delayed continuum dynamics which is infinite
dimensional in both spatial and temporal space. The infinite-dimensional response,
which is dependent on the location of tool–workpiece contact, can only be made
computationally feasible through spatial–temporal discretization and reduction.
Based on the finite element (FE) method and experimental modal analysis, a model
for three-dimensional prediction of surface finish and displacements of a flexible Tshaped plate at the tool–workpiece contact zone and cutting forces was presented [5].
C. Ozoegwu
Department of Mechanical Engineering, University of Nigeria, Nsukka, Nsukka, Nigeria
e-mail: chigbogu.ozoegwu@unn.edu.ng
P. Eberhard (B)
Institute of Engineering and Computational Mechanics, University of Stuttgart,
Stuttgart, Germany
e-mail: peter.eberhard@itm.uni-stuttgart.de
© Springer Nature Singapore Pte Ltd. 2021
U. S. Dixit and S. K. Dwivedy (eds.), Mechanical Sciences,
https://doi.org/10.1007/978-981-15-5712-5_4
83
Full-Discretization Method: Application
to the Stability Study of a Thin-Walled
Milling Process
Chigbogu Ozoegwu and Peter Eberhard
1 Introduction
Lumped delayed models are usually used to describe the regenerative vibration of
a flexible milling tool when cutting a rigid workpiece. In this case, the tool is the
compliant body, see Fig. 1a. A few of the elaborate references on modeling and stability analysis of such systems include [1–4]. On the other hand, the tool can act as
a rigid body when milling a thin-walled workpiece with high aspect ratio of length
or width to thickness. This case is illustrated in Fig. 1b. Milling of thin-walled workpieces is encountered in the processing of monolithic parts for the aerospace industry
where high strength-to-weight ratio is a major requirement. In such a milling process, much of the blank material is removed, and this has to be done at the maximum
possible material removal rate for economic viability. Knowledge-based choices of
the process parameters that guarantee optimal productivity and surface quality derive
from modeling and analyzing the structural and regenerative dynamics of the cutting
process. Since a thin-walled workpiece is a distributed elastic system, its regenerative machining is governed by a delayed continuum dynamics which is infinite
dimensional in both spatial and temporal space. The infinite-dimensional response,
which is dependent on the location of tool–workpiece contact, can only be made
computationally feasible through spatial–temporal discretization and reduction.
Based on the finite element (FE) method and experimental modal analysis, a model
for three-dimensional prediction of surface finish and displacements of a flexible Tshaped plate at the tool–workpiece contact zone and cutting forces was presented [5].
C. Ozoegwu
Department of Mechanical Engineering, University of Nigeria, Nsukka, Nsukka, Nigeria
e-mail: chigbogu.ozoegwu@unn.edu.ng
P. Eberhard (B)
Institute of Engineering and Computational Mechanics, University of Stuttgart,
Stuttgart, Germany
e-mail: peter.eberhard@itm.uni-stuttgart.de
© Springer Nature Singapore Pte Ltd. 2021
U. S. Dixit and S. K. Dwivedy (eds.), Mechanical Sciences,
https://doi.org/10.1007/978-981-15-5712-5_4
83