Automated Upgraded Generalized Full-Discretization Method …
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analysis and regenerative chatter stability analysis in the frequency domain of milling
thin-walled structures. Methods based on thin plate theory, mode superposition principle, and updated Rayleigh–Ritz solutions were used to prepare the regenerative
dynamics of milling of thin-walled workpiece for stability analysis in the frequency
domain [15, 16].
Application of time-domain methods to the stability analysis of milling of flexible workpieces is more recent and less extensively investigated than the frequencydomain methods. The simultaneous effect of tool position and material removal on
the regenerative chatter stability of milling of thin-walled workpiece was studied with
the semi-discretization method [17, 18]. A semi-discrete time-domain method based
on Simpson Rules was applied in the stability analysis of milling of flexible workpiece considering process damping and non-uniform pitch effects [19]. This method
of stability analysis was recently applied in identifying the enhanced stability boundaries of milling of thin-walled workpieces connected to appropriate additional masses
[20]. Using the full-discretization method (FDM) based on the third-order Newton
interpolation of the milling current state and first-order interpolation of the delayed
state and considering process damping and helix angle, three-dimensional stability
lobes which give the boundary axial depths of cut as a function of spindle speed and
tool location were constructed [21]. The FDM based on numerical integration was
used in [22] to construct the stability boundaries of milling of a thin-walled workpiece
while submerged in a viscous fluid. The first-order semi-discretization was used in
the stability analysis of a reduced order model of milling of a thin-walled workpiece
[23]. The parametric model order reduction, which was based on modal truncation
of location-dependent modal matrices and cubic spline interpolation of the individual reduced modes was utilized. An efficient decomposition-condensation method
for chatter stability analysis of large-scale thin-walled structures has been proposed
[24] by condensing and coupling the FE models of the machined workpiece and the
initially removed material using the component mode synthesis method and subsequently integrating the reduced system to the discrete time-domain chatter prediction method [19]. Considering tool helix and mode coupling, the semi-discretization
method is reconstructed based on the Shannon interpolation function for stability
analysis of thin-walled workpieces [25]. A second-order polynomial tensor has been
used to approximate both the current and delayed regenerative states for the stability
analysis of a flexible workpiece milling [26].
Few works used a lumped parameter model of the flexible workpiece system. The flexible workpiece was considered as a lumped single-degree-of-freedom
(1DOF) oscillator in [27] for maximization of milling material removal rate. The
three-dimensional stability lobe diagrams, calculated using the frequency-domain
approach, were presented on axial depth, radial depth, and spindle speed axes. In
[28], the stability lobes of a 120 × 100 × 6 mm thin-walled workpiece, partitioned
into four zones, were determined from MATLAB time-domain simulations and statistical error analyses. The zone-dependent modal parameters, which determine the
dynamics of the 2DOF lumped models of flexible workpiece–tool system in [28],
were extracted from impact tests in each zone. A procedure based on operational
modal analysis, which uses the cutting force model for scaling modal residues, and a
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analysis and regenerative chatter stability analysis in the frequency domain of milling
thin-walled structures. Methods based on thin plate theory, mode superposition principle, and updated Rayleigh–Ritz solutions were used to prepare the regenerative
dynamics of milling of thin-walled workpiece for stability analysis in the frequency
domain [15, 16].
Application of time-domain methods to the stability analysis of milling of flexible workpieces is more recent and less extensively investigated than the frequencydomain methods. The simultaneous effect of tool position and material removal on
the regenerative chatter stability of milling of thin-walled workpiece was studied with
the semi-discretization method [17, 18]. A semi-discrete time-domain method based
on Simpson Rules was applied in the stability analysis of milling of flexible workpiece considering process damping and non-uniform pitch effects [19]. This method
of stability analysis was recently applied in identifying the enhanced stability boundaries of milling of thin-walled workpieces connected to appropriate additional masses
[20]. Using the full-discretization method (FDM) based on the third-order Newton
interpolation of the milling current state and first-order interpolation of the delayed
state and considering process damping and helix angle, three-dimensional stability
lobes which give the boundary axial depths of cut as a function of spindle speed and
tool location were constructed [21]. The FDM based on numerical integration was
used in [22] to construct the stability boundaries of milling of a thin-walled workpiece
while submerged in a viscous fluid. The first-order semi-discretization was used in
the stability analysis of a reduced order model of milling of a thin-walled workpiece
[23]. The parametric model order reduction, which was based on modal truncation
of location-dependent modal matrices and cubic spline interpolation of the individual reduced modes was utilized. An efficient decomposition-condensation method
for chatter stability analysis of large-scale thin-walled structures has been proposed
[24] by condensing and coupling the FE models of the machined workpiece and the
initially removed material using the component mode synthesis method and subsequently integrating the reduced system to the discrete time-domain chatter prediction method [19]. Considering tool helix and mode coupling, the semi-discretization
method is reconstructed based on the Shannon interpolation function for stability
analysis of thin-walled workpieces [25]. A second-order polynomial tensor has been
used to approximate both the current and delayed regenerative states for the stability
analysis of a flexible workpiece milling [26].
Few works used a lumped parameter model of the flexible workpiece system. The flexible workpiece was considered as a lumped single-degree-of-freedom
(1DOF) oscillator in [27] for maximization of milling material removal rate. The
three-dimensional stability lobe diagrams, calculated using the frequency-domain
approach, were presented on axial depth, radial depth, and spindle speed axes. In
[28], the stability lobes of a 120 × 100 × 6 mm thin-walled workpiece, partitioned
into four zones, were determined from MATLAB time-domain simulations and statistical error analyses. The zone-dependent modal parameters, which determine the
dynamics of the 2DOF lumped models of flexible workpiece–tool system in [28],
were extracted from impact tests in each zone. A procedure based on operational
modal analysis, which uses the cutting force model for scaling modal residues, and a