Abstract

Hydrostatic worm-rack-drive has obvious advantages on large-sized machine tools, and its performance is significantly affected by pitch errors. This paper theoretically researches the axial static and dynamic characteristics of hydrostatic worm-rack-drive, including the effects of the amplitude, period, and phase of pitch errors. Based on the expanded view of the helicoid of threads, a numerical calculation method is implemented where the Reynolds’ equation and flow continuity equation are solved simultaneously. The influence rule of pitch errors on pocket pressure, flow, axial fluid-film force, axial stiffness coefficient, and axial damping coefficient are discussed in detail, for providing beneficial guidance for the design and performance optimization of hydrostatic worm-rack-drive.

References

1.
Uriarte
,
L.
,
Zatarain
,
M.
,
Axinte
,
D.
,
Yagüe-Fabra
,
J.
,
Ihlenfeldt
,
S.
,
Eguia
,
J.
, and
Olarra
,
A.
,
2013
, “
Machine Tools for Large Parts
,”
CIRP Ann.
,
62
(
2
), pp.
731
750
. 10.1016/j.cirp.2013.05.009
2.
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.2011.05.010
3.
Whalley
,
R.
,
Ebrahimi
,
M.
, and
Abdul-Ameer
,
A. A.
,
2005
, “
Hybrid Modelling of Machine Tool Axis Drives
,”
Int. J. Mach. Tools Manuf.
,
45
(
14
), pp.
1560
1576
. 10.1016/j.ijmachtools.2005.03.002
4.
Robert
,
S.
, and
Jochen
,
S.
,
2010
, “
Hydrostatic Lead Screw in Compare to Linear Motor and Ball Screw
,”
J. Mechatron. Ind.
,
324
, pp.
18
24
.
5.
Jiang
,
W. P.
,
1984
, “
The Static and Dynamic Characteristics of Hydrostatic Worm and Rack
,”
Mach. Tool Hydraul.
,
5
, pp.
34
40
.
6.
El-Sayed
,
H. R.
, and
Khatan
,
H.
,
1974
, “
The Exact Performance of Externally Pressurized Power Screws
,”
Wear
,
30
(
2
), pp.
237
247
. 10.1016/0043-1648(74)90178-1
7.
El-Sayed
,
H. R.
, and
Khatan
,
H.
,
1975
, “
A Suggested New Profile for Externally Pressurized Power Screws
,”
Wear
,
31
(
1
), pp.
141
156
. 10.1016/0043-1648(75)90127-1
8.
Liang
,
P.
,
Lu
,
C. H.
,
Ding
,
J.
, and
Chen
,
S. J.
,
2013
, “
A Method for Measuring the Hydrodynamic Effect on the Bearing Land
,”
Tribol. Int.
,
67
, pp.
146
153
. 10.1016/j.triboint.2013.07.020
9.
Rajput
,
A. K.
,
Yadav
,
S. K.
, and
Sharma
,
S. C.
,
2017
, “
Effect of Geometrical Irregularities on the Performance of a Misaligned Hybrid Journal Bearing Compensated With Membrane Restrictor
,”
Tribol. Int.
,
115
, pp.
619
627
. 10.1016/j.triboint.2017.06.012
10.
Hanawa
,
N.
,
Kuniyoshi
,
M.
,
Miyatake
,
M.
, and
Yoshimoto
,
S.
,
2017
, “
Static Characteristics of a Water-Lubricated Hydrostatic Thrust Bearing With a Porous Land Region and a Capillary Restrictor
,”
Precis. Eng.
,
50
, pp.
293
307
. 10.1016/j.precisioneng.2017.06.002
11.
Gohara
,
M.
,
Somaya
,
K.
,
Miyatake
,
M.
, and
Yoshimoto
,
S.
,
2014
, “
Static Characteristics of a Water-Lubricated Hydrostatic Thrust Bearing Using a Membrane Restrictor
,”
Tribol. Int.
,
75
, pp.
111
116
. 10.1016/j.triboint.2014.03.016
12.
Sinhasan
,
R.
, and
Sah
,
P. L.
,
1996
, “
Static and Dynamic Performance Characteristics of an Orifice Compensated Hydrostatic Journal Bearing With Non-Newtonian Lubricants
,”
Tribol. Int.
,
29
(
6
), pp.
515
526
. 10.1016/0301-679X(95)00115-K
13.
Shi
,
J.
,
Cao
,
H.
, and
Jin
,
X.
,
2019
, “
Investigation on the Static and Dynamic Characteristics of 3-DOF Aerostatic Thrust Bearings With Orifice Restrictor
,”
Tribol. Int.
,
138
, pp.
435
449
. 10.1016/j.triboint.2019.06.026
14.
Kong
,
S.
,
Sharif
,
K.
,
Evans
,
H. P.
, and
Snidle
,
R. W.
,
2001
, “
Elastohydrodynamics of a Worm Gear Contact
,”
ASME J. Tribol.
,
123
(
2
), pp.
268
275
. 10.1115/1.1308003
15.
Sharif
,
K. J.
,
Kong
,
S.
,
Evans
,
H. P.
, and
Snidle
,
R. W.
,
2001
, “
Contact and Elastohydrodynamic Analysis of Worm Gears Part 1: Theoretical Formulation
,”
Proc. Inst. Mech. Eng., Part C
,
215
(
7
), pp.
817
830
. 10.1243/0954406011524171
16.
Simon
,
V.
,
1997
, “
EHD Lubrication Characteristics of a New Type of Ground Cylindrical Worm Gearing
,”
ASME J. Mech. Des.
,
119
(
1
), pp.
101
107
. 10.1115/1.2828770
17.
Liu
,
Z.
,
Zhan
,
C.
,
Cheng
,
Q.
,
Zhao
,
Y. S.
, and
Li
,
X. Y.
,
2016
, “
Thermal and Tilt Effects on Bearing Characteristics of Hydrostatic Oil Pad in Rotary Table
,”
J. Hydrodyn.
,
28
(
4
), pp.
585
595
. 10.1016/S1001-6058(16)60662-5
18.
Zoupas
,
L.
,
Wodtke
,
M.
,
Papadopoulos
,
C. I.
, and
Wasilczuk
,
M.
,
2019
, “
Effect of Manufacturing Errors of the Pad Sliding Surface on the Performance of the Hydrodynamic Thrust Bearing
,”
Tribol. Int.
,
134
, pp.
211
220
. 10.1016/j.triboint.2019.01.046
19.
Zhang
,
P.
,
Chen
,
Y.
, and
Liu
,
X.
,
2018
, “
Relationship Between Roundness Errors of Shaft and Radial Error Motions of Hydrostatic Journal Bearings Under Quasi-static Condition
,”
Precis. Eng.
,
51
, pp.
564
576
. 10.1016/j.precisioneng.2017.10.012
20.
Zhang
,
P.
,
Chen
,
Y.
, and
Zha
,
J.
,
2017
, “
Relationship Between Geometric Errors of Thrust Plates and Error Motions of Hydrostatic Thrust Bearings Under Quasi-Static Condition
,”
Precis. Eng.
,
50
, pp.
119
131
. 10.1016/j.precisioneng.2017.04.020
21.
Fukada
,
S.
,
1999
, “
Friction of Sliding Leadscrews Under Hydrodynamic Lubrication: 1st Report, Establishment of Clearance Shape Model and Its Analysis Based on Infinitely Short Bearing Theory
,”
JSME Int. J., Ser. C
,
42
(
4
), pp.
1003
1011
. 10.1299/jsmec.42.1003
22.
Fukada
,
S.
, and
Otsuka
,
J.
,
1999
, “
Friction of Sliding Leadscrews Under Hydrodynamic Lubrication: 2nd Report, Verification of Drunkenness-Model Theory and Consideration of Appropriate Driving Condition
,”
JSME Int. J., Ser. C
,
42
(
4
), pp.
1012
1020
. 10.1299/jsmec.42.1012
23.
Zhang
,
Y.
,
Chen
,
S.
,
Lu
,
C.
, and
Liu
,
Z.
,
2017
, “
Performance Analysis of Capillary-Compensated Hydrostatic Lead Screws With Discontinuous Helical Recesses Including Influence of Pitch Errors in Nut
,”
Tribol. Trans.
,
60
(
6
), pp.
974
987
. 10.1080/10402004.2016.1240839
24.
Rowe
,
W. B.
, and
Chong
,
F. S.
,
1986
, “
Computation of Dynamic Force Coefficients for Hybrid (Hydrostatic/Hydrodynamic) Journal Bearings by the Finite Disturbance and Perturbation Techniques
,”
Tribol. Int.
,
19
(
5
), pp.
260
271
. 10.1016/0301-679X(86)90005-8
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