The closed-loop performance of a lead-screw drive is usually limited by a resonance in which the carriage oscillates in the direction of motion as the screw undergoes longitudinal and torsional deformation. In this paper, we develop a model of lead-screw system dynamics that accounts for the distributed inertia of the screw and the compliance and damping of the thrust bearings, nut, and coupling. The distributed-parameter model of the lead-screw drive system is reduced to a low-order model using a Galerkin procedure and verified by experiments performed on a pair of ball-screw systems. The model is found to accurately predict the presence of a finite right-half plane zero in the transfer function from motor torque to carriage position. A viscoelastic damper incorporated into one of the lead-screw support bearings is shown to give rise to significant, deterministic damping in the system transfer functions.

Issue Section:
Technical Papers
Keywords:
closed loop systems, deformation, distributed parameter systems, compliance control, Galerkin method, fasteners, transfer functions, viscoelasticity, damping, motor drives, elastic constants, machine bearings
Topics:
Damping, Motors, Railroad passenger cars, Screws, Transfer functions, Engines, Bearings, Resonance, Stiffness
1.
Chen
,
Y.
, and
Tlusty
,
J.
,
1995
, “
Effect of Low-Friction Guideways and Lead-Screw Flexibility on Dynamics of High-Speed Machines
,”
Annals of the CIRP
,
44
, pp.
353
–
356
.
2.
Tlusty, J., 2000, Manufacturing Processes and Equipment, Prentice Hall, Upper Saddle River, New Jersey.
3.
Smith, D. A., 1999, “Wide Bandwidth Control of High-Speed Milling Machine Feed Drives,” Ph.D. thesis, University of Florida, Gainesville, Florida.
4.
Smith
,
M. H.
,
Annaswamy
,
A. M.
, and
Slocum
,
A. H.
,
1995
, “
Adaptive Control Strategies for a Precision Machine Tool Axis
,”
Precision Engineering
,
17
(
3
), pp.
192
–
206
.
5.
Lim, H., Seo, J-W., Choi, C-H., 2000, “Position Control of XY Table in CNC Machining Center with Non-rigid Ballscrew,” Proceedings of the American Control Conference, pp. 1542–1546, Chicago, Illinois.
6.
Nayfeh, S. A., 1998, “Design and Application of Damped Machine Elements,” Ph.D. thesis, Massachusetts Institute of Technology, Cambridge, Massachusetts.
7.
Nayfeh, S. A., and Slocum, A. H., 1998, “Enhancing Ball-screw Axial Dynamics,” Proceedings of the ASPE 13th Annual Meeting, St. Louis, Missouri.
8.
Book
,
W. J.
,
1993
, “
Controlled Motion in an Elastic World
,”
ASME J. Dyn. Syst., Meas., Control
,
115
, pp.
252
–
261
.
9.
Meirovitch, L., 1980, Computational Methods in Structural Dynamics, Sijthoff & Noordhoff, Rockville, Maryland.
10.
Lowenfeld, K., 1959, “Zusatzda¨mpfung von Werkzeugmaschinen durch Lamellenpakete,” Maschinenmarkt No. 19.
11.
Koenigsberger, F., and Tlusty, J., 1970, Machine Tool Structures, Pergammon Press, London.
12.
Nashif, A. D., Jones, D. I. G., and Henderson, J. P., 1985, Vibration Damping, John Wiley, New York.
13.
Crandall
,
S. H.
,
1991
, “
The Hysteretic Damping Model in Vibration Theory
,”
Rep. Sci. Res. Inst.
,
25
, pp.
23
–
28
.
14.
Freudenberg
,
J. S.
, and
Looze
,
D. P.
,
1985
, “
Right Half Plane Poles and Zeros and Design Tradeoffs in Feedback Systems
,”
IEEE Trans. Autom. Control
,
30
(
6
), pp.
555
–
565
.
15.
Spector
,
V. A.
, and
Flashner
,
H.
,
1990
, “
Modeling and Design Implications of Noncollocated Control in Flexible Systems
,”
ASME J. Dyn. Syst., Meas., Control
,
112
, pp.
186
–
193
.
16.
Hochmuth, C. A., 1990, “Design and Construction of a Machine Tool Axis Prototype for Evaluation of Adaptive and Learning Control Systems,” S. M. thesis, Massachusetts Institute of Technology, Cambridge, Massachusetts.
17.
Aerotech Inc., Pittsburgh, Pennsylvania.
18.
Renbrandt Flexible Couplings Inc., Boston, Massachusetts.
19.
dSPACE Inc., Novi, Michigan.
20.
Varanasi, K. K., 2002, “On the Design of a Precision Machine for Closed-Loop Performance,” S. M. thesis, Massachusetts Institute of Technology, Cambridge, Massachusetts.
21.
Schneeberger Inc., Bedford, Massachusetts.
22.
Gam Servo Couplings, Harwood Heights, Illinois.
23.
E-A-R Speciality Composites, Indianapolis, Indiana.
24.
PCB Piezotronics, Depew, New York.
25.
Varanasi, K. K., and Nayfeh, S. A., 2001, “Modeling, Identification, and Control of Ballscrew Drives,” Proceedings of the ASPE 16th Annual Meeting, Crystal City, Virginia.
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