Biomedical Engineering Reference
In-Depth Information
The FRF of the substructure A can be defined as:
H
H
X
F
1
A
,11
A
,12
1
X
H
H
F
A
,2
A
,21
A
,22
2
The FRF of the substructure B can be defined as:
X
H
F
B
,2
B
,22
B
,2
where: X, F - displacement and force vectors applied on the structure. H
A,ij
vectors - FRFs between points i and j.
Boundary conditions used for coupling substructures A (free - free model
of the end mill) and B (spindle) can be defined as:
F
F
F
2
A
,2
B
,2
X
X
X
2
A
,2
B
,2
The displacements X
1
and X
2
can be expressed in a matrix form as:
(
H
H
H
H
)
(
H
H
H
H
)
X
X
A
,11
A
,12
2
A
,21
A
,12
A
,12
2
A
,22
1
(
H
H
H
H
)
(
H
H
H
H
)
2
A
,21
A
,22
2
A
,21
A
,22
A
,22
2
A
,22
The direct and cross receptances at the tool tip can be expressed as:
X
1
1
H
H
H
H
H
H
A
,11
A
,12
A
,22
B
,22
A
,21
11
F
X
1
1
1
H
H
H
H
H
H
A
,12
A
,12
A
,22
B
,22
A
,22
12
F
2
Since each FRF contains translational and rotational displacements, the
FRF expressed earlier needs to be expanded as:
11,
ff
11,
fM
X
H
F
1
11
1
h
h
M
1
11,
Mf
11,
MM
1
12,
ff
12,
fM
X
H
F
1
12
2
h
h
M
1
12,
Mf
12,
MM
2
