Biomedical Engineering Reference
In-Depth Information
where RS - coupled substructures receptance matrices, R - substructure
matrices.
The tool holder -spindle assembly receptances have been defined trough
beam models:
H
L
41
41
G
41
N
P
41
41
H
L
44
44
G
44
N
P
44
44
where H, L, P and N are different assembly responses. Subassembly
receptance matrices have been developed trough Timoshenko beam models for
substructures I-VI and spindle holder dynamics.
Substructures IV - VI have been rigidly coupled to each other and then
rigidly coupled to the spindle holder base receptances to give the direct
receptance matrix for the subassembly.
In order to combine data and couple the tool to the holder a flexible
connection and a scalar stiffness matrix was used:
xf
xm
Kc
m
where: k's represent stiffness values from displacement (x) and rotation (θ)
due to force (f) and moment (m).
Mascardelli et al. [42] applied receptance coupling to predict the FRF at
the tip of the micro tool and consequently use the FRF for chatter analysis.
The authors have divided the machining system into two subsections in their
research. The dynamics of the first subsystem, the cutter and the taper have
been performed using FE analysis due to the fragile and slender nature of the
tool, while the dynamics of the rest of the structure including the tool and the
tool holder have been defined experimentally. By identifying the rotational
degree of freedom (RDOF) at the joint, these two subsystems were linked.
This way, determination of stability lobes that provides information on the
stability of the system for a given axial depth of cut and spindle speed was
accomplished. In FE analysis, two different models have been used, a perfectly
constrained cantilever beam as well as an imperfectly constrained beam.
Micromilling tests were performed in order to confirm the chatter-stability
analysis based on the receptance coupling (RC) method. Information on high-
