Abstract
Parametric expressions of equivalent stiffnesses of a ball-screw shaft are obtained by derivation of its geometric parameters, the finite element method (FEM), and data fitting based on a modified probability density function of log-normal distribution. A dynamic model of a ball-screw drive that considers effects of bearing stiffnesses, the mass of the nut, and the axial pretension is established based on equivalent stiffnesses of its shaft. With the dynamic model and modal experimental results obtained by Bayesian operational modal analysis (BOMA), installation parameters of the ball-screw drive are identified by a genetic algorithm (GA) with a new comprehensive objective function that considers natural frequencies, mode shapes, and flexibility of the ball-screw drive. The effectiveness of the methodology is experimentally validated.
Issue Section:
Research Papers
References
1.
Jarosch
,
P.
, 2008
, Zur Lebensdauerprognose Zyklisch Hoch Belasteter Kugelgewindetriebe
,
Shaker
.2.
Dadalau
,
A.
,
Mottahedi
,
M.
,
Groh
,
K.
, and
Verl
,
A.
, 2010
, “
Parametric Modeling of Ball-Screw Shafts
,” Prod. Eng.
,
4
(6
), pp. 625
–631
.10.1007/s11740-010-0264-z3.
Vicente
,
D. A.
,
Hecker
,
R. L.
,
Villegas
,
F. J.
, and
Flores
,
G. M.
, 2012
, “
Modeling and Vibration Mode Analysis of a Ball Screw Drive
,” Int. J. Adv. Manuf. Technol.
,
58
(1–4
), pp. 257
–265
.10.1007/s00170-011-3375-64.
Okwudire
,
C. E.
, and
Altintas
,
Y.
, 2009
, “
Hybrid Modeling of Ball Screw Drives With Coupled Axial, Torsional, and Lateral Dynamics
,” ASME J. Mech. Des.
,
131
(7
), p. 071002
.10.1115/1.31258875.
Zhang
,
H.
,
Zhang
,
J.
,
Liu
,
H.
,
Liang
,
T.
, and
Zhao
,
W.
, 2015
, “
Dynamic Modeling and Analysis of the High-Speed Ball Screw Feed System
,” Proc. Inst. Mech. Eng., Part B
,
229
(5
), pp. 870
–877
.10.1177/09544054145346416.
Lin
,
C. Y.
,
Hung
,
J. P.
, and
Lo
,
T. L.
, 2010
, “
Effect of Preload of Linear Guides on Dynamic Characteristics of a Vertical Column–Shaft System
,” Int. J. Mach. Tool Manuf.
,
50
(8
), pp. 741
–746
.10.1016/j.ijmachtools.2010.04.0027.
Rouvas
,
C.
, and
Childs
,
D. W.
, 1993
, “
A Parameter Identification Method for the Rotordynamic Coefficients of a High Reynolds Number Hydrostatic Bearing
,” ASME J. Vib. Acoust.
,
115
(3
), pp. 264
–270
.10.1115/1.29303438.
Tiwari
,
R.
,
Lees
,
A. W.
, and
Friswell
,
M. I.
, 2002
, “
Identification of Speed-Dependent Bearing Parameters
,” J Sound Vib.
,
254
(5
), pp. 967
–986
.10.1006/jsvi.2001.41409.
Wang
,
J. H.
, and
Liou
,
C. M.
, 1991
, “
Experimental Identification of Mechanical Joint Parameters
,” ASME J. Vib. Acoust.
,
113
(1
), pp. 28
–36
.10.1115/1.293015110.
Guo
,
Y.
, and
Parker
,
R. G.
, 2012
, “
Stiffness Matrix Calculation of Rolling Element Bearings Using a Finite Element/Contact Mechanics Model
,” Mech. Mach. Theory
,
51
, pp. 32
–45
.10.1016/j.mechmachtheory.2011.12.00611.
Gunduz
,
A.
, and
Singh
,
R.
, 2013
, “
Stiffness Matrix Formulation for Double Row Angular Contact Ball Bearings: Analytical Development and Validation
,” J. Sound Vib.
,
332
(22
), pp. 5898
–5916
.10.1016/j.jsv.2013.04.04912.
Hua
,
G. F.
, and
Lu
,
Y. P.
, 2012
, “
Investigation of Ball Screw Preload Variation Based on Dynamic Modeling of a Preload Adjustable Feed-Drive System and Spectrum Analysis of Ball-Nuts Sensed Vibration Signals
,” Int. J. Mach. Tool Manuf.
,
52
(1
), pp. 85
–96
.10.1016/j.ijmachtools.2011.09.00813.
Altintas
,
Y.
,
Verl
,
A.
,
Brecher
,
C.
,
Uriarte
,
L.
, and
Pritschow
,
G.
, 2011
, “
Machine Tool Feed Drives
,” CIRP Ann.
,
60
(2
), pp. 779
–796
.10.1016/j.cirp.2011.05.01014.
Aitchison
,
J.
, and
James
,
A. C. B.
, 1957
, The Log-Normal Distribution
, Cambridge University Press
, Cambridge, UK
.15.
Yuen
,
K. V.
, and
Katafygiotis
,
L. S.
, 2003
, “
Bayesian Fast Fourier Transform Approach for Modal Updating Using Ambient Data
,” Adv. Struct. Eng.
,
6
(2
), pp. 81
–95
.10.1260/13694330376901318316.
Au
,
S. K.
, 2011
, “
Fast Bayesian FFT Method for Ambient Modal Identification With Separated Modes
,” J. Eng. Mech.
,
137
(3
), pp. 214
–226
.10.1061/(ASCE)EM.1943-7889.000021317.
Au
,
S. K.
, 2011
, “
Assembling Mode Shapes by Least Squares
,” Mech. Syst. Signal Process.
,
25
(1
), pp. 163
–179
.10.1016/j.ymssp.2010.08.00218.
Au
,
S. K.
, and
Zhang
,
F. L.
, 2012
, “
Fast Bayesian Ambient Modal Identification Incorporating Multiple Setups
,” J. Eng. Mech.
,
138
(7
), pp. 800
–815
.10.1061/(ASCE)EM.1943-7889.000038519.
Hu
,
Y. J.
,
Guo
,
W. G.
,
Zhu
,
W. D.
, and
Xu
,
Y. F.
, 2019
, “
Local Damage Detection of Membranes Based on Bayesian Operational Modal Analysis and Three-Dimensional Digital Image Correlation
,” Mech. Syst. Signal Process.
,
131
, pp. 633
–648
.10.1016/j.ymssp.2019.04.05120.
THK
, 2015
, “Official Catalog No. 330-2E,” pp. 9
–10
.Copyright © 2021 by ASME
You do not currently have access to this content.
