This paper develops the dynamic equations of motion for the planetary roller screw mechanism (PRSM) accounting for the screw, rollers, and nut bodies. First, the linear and angular velocities and accelerations of the components are derived. Then, their angular momentums are presented. Next, the slip velocities at the contacts are derived in order to determine the direction of the forces of friction. The equations of motion are derived through the use of Lagrange's Method with viscous friction. The steady-state angular velocities and screw/roller slip velocities are also derived. An example demonstrates the magnitude of the slip velocity of the PRSM as a function of both the screw lead and the screw and nut contact angles. By allowing full dynamic simulation, the developed analysis can be used for much improved PRSM system design.

Issue Section:
Technical Brief
Keywords:
Actuators, Dynamics, Mechanism design, Transmissions
Topics:
Rollers, Screws, Dynamics (Mechanics), Friction, Steady state

References

1.
Strandgren
,
C. B.
,
1954
, “
Screw-Threaded Mechanism
,” U.S. Patent No. 2,683,379.
2.
Velinsky
,
S. A.
,
Chu
,
B.
, and
Lasky
,
T. A.
,
2009
, “
Kinematics and Efficiency Analysis of the Planetary Roller Screw Mechanism
,”
ASME J. Mech. Des.
,
131
(
1
), p.
011016
.
Google Scholar
Crossref
Search ADS
 
3.
Sokolov
,
P. A.
,
Ryakhovsky
,
O. A.
,
Blinov
,
D. S.
, and
Laptev
,
A.
,
2005
, “
Кинематика Планетарных Роликовинтовых Механизмов (Kinematics of Planetary Roller–Screw Mechanisms)
,”
Vestn. MGTU, Mashinostr.
,
1
, pp.
3
–
14
.
4.
Ryakhovsky
,
O.
,
Blinov
,
D.
, and
Sokolov
,
P.
,
2002
, “
Анализ Работы Планетарной Роликовинтовой Передачи (Analysis of the Operation of a Planetary Roller–Screw Mechanism)
,”
Vestn. MGTU, Mashinostr.
,
4
, pp.
52
–
57
.
5.
Jones
,
M. H.
, and
Velinsky
,
S. A.
,
2013
, “
Contact Kinematics in the Roller Screw Mechanism
,”
ASME J. Mech. Des.
,
135
(
5
), p.
051003
.
Google Scholar
Crossref
Search ADS
 
6.
Jones
,
M. H.
, and
Velinsky
,
S. A.
,
2012
, “
Kinematics of Roller Migration in the Planetary Roller Screw Mechanism
,”
ASME J. Mech. Des.
,
134
(
6
), p.
061006
.
Google Scholar
Crossref
Search ADS
 
7.
Jones
,
M. H.
, and
Velinsky
,
S. A.
,
2014
, “
Stiffness of the Roller Screw Mechanism by the Direct Method
,”
Mech. Based Des. Struct. Mach.
,
42
(
1
), pp.
17
–
34
.
Google Scholar
Crossref
Search ADS
 
8.
Lemor
,
P.
,
1996
, “
The Roller Screw: An Efficient and Reliable Mechanical Component of Electro-Mechanical Actuators
,”
31st Intersociety Energy Conversion Engineering Conference
(
IECEC 96
),
Washington, DC
, Aug. 11–16, pp.
215
–
220
.
9.
Schinstock
,
D.
, and
Haskew
,
T.
,
1996
, “
Dynamic Load Testing of Roller Screw EMAs
,”
31st Intersociety Energy Conversion Engineering Conference
(
IECEC 96
),
Washington, DC
, Aug. 11–16, pp.
221
–
226
.
10.
Hojjat
,
Y.
, and
Mahdi Agheli
,
M.
,
2009
, “
A Comprehensive Study on Capabilities and Limitations of Roller–Screw With Emphasis on Slip Tendency
,”
Mech. Mach. Theory
,
44
(
10
), pp.
1887
–
1899
.
Google Scholar
Crossref
Search ADS
 
11.
Tselishchev
,
A. S.
, and
Zharov
,
I. S.
,
2008
, “
Elastic Elements in Roller–Screw Mechanisms
,”
Russ. Eng. Res.
,
28
(
11
), pp.
1040
–
1043
.
Google Scholar
Crossref
Search ADS
 
12.
Sokolov
,
P.
,
Blinov
,
D.
,
Ryakhovskii
,
O.
,
Ochkasov
,
E.
, and
Drobizheva
,
A. Y.
,
2008
, “
Promising Rotation–Translation Converters
,”
Russ. Eng. Res.
,
28
(
10
), pp.
949
–
956
.
Google Scholar
Crossref
Search ADS
 
13.
Falkner
,
M.
,
Nitschko
,
T.
,
Supper
,
L.
,
Traxler
,
G.
,
Zemann
,
J.
, and
Roberts
,
E.
,
2003
, “
Roller Screw Lifetime Under Oscillatory Motion: From Dry to Liquid Lubrication
,”
10th European Space Mechanisms and Tribology Symposium
(ESMATS), San Sebastian, Spain, Sept. 24–26, pp.
297
–
301
.
14.
Yang
,
J.
,
Wei
,
Z.
,
Zhu
,
J.
, and
Du
,
W.
,
2011
, “
Calculation of Load Distribution of Planetary Roller Screws and Static Rigidity
,”
J. Huazhong Univ. Sci. Technol.,
39
(
4
), pp.
1
–
4
.
15.
Ma
,
S.
,
Liu
,
G.
,
Tong
,
R.
, and
Fu
,
X.
,
2015
, “
A Frictional Heat Model of Planetary Roller Screw Mechanism Considering Load Distribution
,”
Mech. Based Des. Struct. Mach.
,
43
(
2
), pp.
164
–
182
.
Google Scholar
Crossref
Search ADS
 
16.
Crandall
,
S.
,
Karnopp
,
D.
,
Kurtz
,
E. F.
, Jr., and
Pridmore-Brown
,
D.
,
1982
,
Dynamics of Mechanical and Electromechanical Systems
,
Krieger Publishing Company
,
Malabar, FL
.
17.
Jones
,
M. H.
,
2013
, “
Mechanics Based Design of the Planetary Roller Screw Mechanism
,” Ph.D., thesis, Mechanical and Aerospace Engineering, University of California, Davis, CA, p. 124.
Copyright © 2016 by ASME
You do not currently have access to this content.