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.
Issue Section:
Research Papers
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.pdf11.
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
.Copyright © 2017 by ASME
You do not currently have access to this content.
