In this paper, a special type of beam element is developed with three nodes and with only translational degrees-of-freedom (DOFs) at each node. This element can be used effectively to build low degree-of-freedom models of rotors. The initial model from the Bernoulli theory is fitted to experimental results by nonlinear optimization. This way, we can avoid the complex modeling of contact problems between the parts of squirrel cage rotors. The procedure is demonstrated on the modeling of a machine tool spindle.

References

References
1.
Abele
,
E.
,
Altintas
,
Y.
, and
Brecher
,
C.
,
2010
, “
Machine Tool Spindle Units
,”
CIRP Ann. Manuf. Technol.
,
59
(
2
), pp.
781
802
.
2.
Nelson
,
H. D.
, and
McVaugh
,
J. M.
,
1976
, “
The Dynamics of Rotor-Bearing Systems Using Finite Elements
,”
ASME J. Eng. Ind.
,
98
(
2
), pp.
593
600
.
3.
Cao
,
Y.
, and
Altintas
,
Y.
,
2004
, “
A General Method for the Modeling of Spindle-Bearing Systems
,”
ASME J. Mech. Des.
,
126
(
6
), pp.
1089
1104
.
4.
Gagnol
,
V.
,
Bouzgarrou
,
B. C.
,
Ray
,
P.
, and
Barra
,
C.
,
2007
, “
Stability-Based Spindle Design Optimization
,”
ASME J. Manuf. Sci. Eng.
,
129
(
2
), pp.
407
415
.
5.
Rantatalo
,
M.
,
Aidanpää
,
J.-O.
,
Göransson
,
B.
, and
Norman
,
P.
,
2007
, “
Milling Machine Spindle Analysis Using FEM and Non-Contact Spindle Excitation and Response Measurement
,”
Int. J. Mach. Tools Manuf.
,
47
(
7–8
), pp.
1034
1045
.
6.
Thomas
,
D.
,
Wilson
,
J.
, and
Wilson
,
R.
,
1973
, “
Timoshenko Beam Finite Elements
,”
J. Sound Vib.
,
31
(
3
), pp.
315
330
.
7.
Nelson
,
H. D.
,
Meacham
,
W. L.
,
Fleming
,
D. P.
, and
Kascak
,
A. F.
,
1983
, “
Nonlinear Analysis of Rotor-Bearing Systems Using Component Mode Synthesis
,”
ASME J. Eng. Power
,
105
(
3
), pp.
604
614
.
8.
Wang
,
W.
, and
Kirkhope
,
J.
,
1995
, “
Complex Component Mode Synthesis for Damped Systems
,”
J. Sound Vib.
,
181
(
5
), pp.
781
800
.
9.
Shanmugam
,
A.
, and
Padmanabhan
,
C.
,
2006
, “
A Fixed-Free Interface Component Mode Synthesis Method for Rotordynamic Analysis
,”
J. Sound Vib.
,
297
(
3–5
), pp.
664
679
.
10.
Kolar
,
P.
, and
Holkup
,
T.
,
2010
, “
Prediction of Machine Tool Spindle's Dynamics Based on a Thermo-Mechanical Model
,”
Mod. Mach. Sci. J.
,
3
(
1
), pp.
167
171
.http://www.mmscience.eu/archives/MM_Science_201002.pdf
11.
Kolar
,
P.
,
Sulitka
,
M.
, and
Janota
,
M.
,
2011
, “
Simulation of Dynamic Properties of a Spindle and Tool System Coupled With a Machine Tool Frame
,”
Int. J. Adv. Manuf. Technol.
,
54
(
1–4
), pp.
11
20
.
12.
Klerk
,
D. D.
,
Rixen
,
D. J.
, and
Voormeeren
,
S. N.
,
2008
, “
General Framework for Dynamic Substructuring: History, Review and Classification of Techniques
,”
Am. Inst. Aeronaut. Astronaut.
,
46
(
5
), pp.
1169
1181
.
13.
Augarde
,
C. E.
,
1998
, “
Generation of Shape Functions for Straight Beam Elements
,”
Comput. Struct.
,
68
(
6
), pp.
555
560
.
14.
Jian
,
L.
,
Shenjie
,
Z.
,
Meiling
,
D.
, and
Yuqin
,
Y.
,
2012
, “
Three-Node Euler-Bernoulli Beam Element Based on Positional FEM
,”
Procedia Eng.
,
29
, pp.
3703
3707
.
15.
Louca
,
L. S.
,
2015
, “
Finite Segment Model Bomplexity of an Euler-Bernoulli Beam
,”
IFAC-PapersOnLine
,
48
(
1
), pp.
334
340
.
16.
Dwivedy
,
S. K.
, and
Eberhard
,
P.
,
2006
, “
Dynamic Analysis of Flexible Manipulators, a Literature Review
,”
Mechanism Mach. Theory
,
41
(7), pp.
749
777
.
17.
Narasiah
,
G. L.
,
2008
,
Finite Element Analysis
,
BS Publications
,
New Delhi, India
.
18.
Kohnke
,
P.
, ed.,
2009
, “
Theory Reference for the Mechanical APDL and Mechanical Applications
,”
ANSYS, Inc.
,
Canonsburg, PA
.
19.
Nocedal
,
J.
, and
Wright
,
S.
,
2006
,
Numerical Optimization
,
Springer-Verlag
,
New York
.
20.
Tseytlin
,
Y. M.
,
2006
,
Structural Synthesis in Precision Elasticity
,
Springer-Verlag
,
New York
.
21.
Stepan
,
G.
,
Munoa
,
J.
,
Insperger
,
T.
,
Suricoc
,
M.
,
Bachrathy
,
D.
, and
Dombovari
,
Z.
,
2014
, “
Cylindrical Milling Tools: Comparative Real Case Study for Process Stability
,”
CIRP Ann. Manuf. Technol.
,
63
(
1
), pp.
385
388
.
22.
Denkena
,
B.
,
Krueger
,
M.
,
Bachrathy
,
D.
, and
Stepan
,
G.
,
2012
, “
Model Based Reconstruction of Milled Surface Topography From Measured Cutting Forces
,”
Int. J. Mach. Tools Manuf.
,
54–55
, pp.
25
33
.
You do not currently have access to this content.