In this paper, a new model of the harmonic drive transmission is presented. The purpose of this work is to better understand the transmission hysteresis behavior while constructing a new type of comprehensive harmonic drive model. The four dominant aspects of harmonic drive behavior—nonlinear viscous friction, nonlinear stiffness, hysteresis, and kinematic error—are all included in the model. The harmonic drive is taken to be a black box, and a dynamometer is used to observe the input/output relations of the transmission. This phenomenological approach does not require any specific knowledge of the internal kinematics. In a novel application, the Maxwell resistive-capacitor hysteresis model is applied to the harmonic drive. In this model, sets of linear stiffness elements in series with Coulomb friction elements are arranged in parallel to capture the hysteresis behavior of the transmission. The causal hysteresis model is combined with nonlinear viscous friction and spectral kinematic error models to accurately represent the harmonic drive behavior. Empirical measurements are presented to quantify all four aspects of the transmission behavior. These measurements motivate the formulation of the complete model. Simulation results are then compared to additional measurements of the harmonic drive performance.

References

References
1.
Musser
,
C. W.
, 1960, “
Breakthrough in Mechanical Drive Design: Harmonic Drive
,”
Mach. Des.
,
32
(
8
), pp.
160
173
.
2.
Musser
,
C. W.
, 1959, “
Strain Wave Gearing
,” U. S. Patent No. 2906143.
3.
Harmonic Drive LLC.
, 1997,
SHF and SHG Housed Unit: SHF-2AGR and SHG-2UH Series
,
Harmonic Drive LLC
,
Peabody
, MA.
4.
Kircanski
,
N. M.
, and
Goldenberg
,
A. A.
, 1997, “
An Experimental Study of Nonlinear Stiffness, Hysteresis, and Friction Effects in Robot Joints With Harmonic Drives and Torque Sensors
,”
Int. J. Robot. Res.
,
16
(
2
), pp.
214
239
.
5.
Schempf
,
H.
, and
Yoerger
,
D. R.
, 1993, “
Study of Dominant Performance Characteristics in Robot Transmissions
,”
ASME J. Mech. Des.
,
115
(
3
), pp.
472
482
.
6.
Volkov
,
D. P.
, and
Zubkov
,
Y. N.
, 1978, “
Vibrations in a Drive With a Harmonic Gear Transmission
,”
Russ. Eng. J.
,
58
(
5
), pp.
11
15
.
7.
Ivanov
,
M. N.
,
Shuvalov
,
S. A.
, and
Amosova
,
E. P.
, 1971, “
Kinematic Accuracy of Harmonic Gear Drive Measured by Two Methods
,”
Izv. Vyssh. Uchebn. Zaved., Mashinostr
, (
1
), pp.
53
58
.
8.
Shuvalov
,
S. A.
, and
Dudko
,
V. D.
, 1971, “
Interlocking Contours of a Harmonic Gear Drive
,”
Izv. Vyssh. Uchebn. Zaved., Mashinostr
, (
7
), pp.
60
65
.
9.
Likhovetzky
,
Y.
, 1976, “
Harmonic Mechanical Drives With Hard Wheels
,”
Isr. J. Technol.
,
14
(
4–5
), pp.
207
211
.
10.
Shuvalov
,
S. A.
, and
Gorelov
,
V. N.
, 1981, “
Force Interaction between the Members of a Harmonic Gear Drive and a Disc Generator
,”
Sov. Eng. Res.
,
1
(
9
), pp.
5
7
.
11.
Peter
,
J.
, 1982, “
Geometric Conditions of Harmonic Drives
,”
Acta Tech. (Budapest)
,
94
(
1–2
), pp.
63
72
.
12.
Peter
,
J.
, 1982, “
Investigation of the Engagement of Harmonic Drives—Part II
,”
Acta Tech. (Budapest)
,
94
(
3–4
), pp.
223
233
.
13.
Emel’yanov
,
A. F.
, 1983, “
Calculation of the Kinematic Error of a Harmonic Gear Transmission Taking into Account the Compliance of Elements
,”
Sov. Eng. Res.
,
3
(
7
), pp.
7
10
.
14.
Emel’yanov
,
A. F.
, 1983, “
Investigation of an Internal Disturbing Action on a Drive With Harmonic Gear Transmission
,”
Sov. Eng. Res.
,
3
(
8
), pp.
13
15
.
15.
Hitchcox
,
A.
, 1983, “
Close-up of Cycloidal Drives
,”
Power Transm. Des.
,
25
(
10
), pp.
27
29
.
16.
Istomin
,
S. N.
, and
Borisov
,
S. G.
, 1983, “
Method of Nomographic Calculation of the Kinematic Error of a Harmonic Drive
,”
Sov. Eng. Res.
,
3
(
5
), pp.
32
34
.
17.
Tseitlin
,
N. I.
, and
Buchakov
,
Y. V.
, 1983, “
Harmonic Drive With Edgeless Contact of Involute Profile Teeth
,”
Sov. Eng. Res.
,
3
(
11
), pp.
22
25
.
18.
Istomin
,
S. N.
, and
Borisov
,
S. G.
, 1984, “
Kinematic Error of a Loaded Harmonic Gear Transmission
,”
Sov. Eng. Res.
,
4
(
3
), pp.
28
30
.
19.
Ivanshov
,
E. N.
, and
Nekrasov
,
M. I.
, 1984, “
Special Features on Planetary Harmonic Drive Generators
,”
Sov. Eng. Res.
,
4
(
2
), pp.
17
19
.
20.
Xie
,
J.-R.
, and
Sun
,
L.-Z.
, 1984, “
Meshing Analysis Method of Harmonic Gear Drive Using Symmetric Disc Wavegenerator
,”
International Symposium on Design and Synthesis
, Tokyo, Japan, pp.
270
274
.
21.
Zhabin
,
A. I.
, and
Ionak
,
V. F.
, 1984, “
Using the Kinematic Error to Assess the Quality of Assembly of Reduction Gears
,”
Sov. Eng. Res.
,
4
(
11
), pp.
4
5
.
22.
Good
,
M. C.
,
Sweet
,
L. M.
, and
Strobel
,
K. L.
, 1985, “
Dynamic Models for Control System Design of Integrated Robot and Drive Systems
,”
ASME J. Dyn. Syst., Meas., Control
,
107
(
1
), pp.
53
59
.
23.
Kojima
,
H.
,
Taguti
,
K.
, and
Tuji
,
H.
, 1989, “
Robot Vibrations Caused by Torque Ripples in Power Transmission Mechanisms
,”
Nippon Kikai Gakkai Ronbunshu, C Hen/Trans. Jpn. Soc. Mech. Eng., Part C
,
55
(
517
), pp.
2390
2395
.
24.
Marilier
,
T.
, and
Richard
,
J. A.
, 1989, “
Non-Linear Mechanic and Electric Behavior of a Robot Axis With a ‘Harmonic-Drive’ Gear
,”
Rob. Comput.-Integr. Manufact.
,
5
(
2–3
), pp.
129
136
.
25.
Taghirad
,
H. D.
, and
Belanger
,
P. R.
, 1998, “
Modeling and Parameter Identification of Harmonic Drive Systems
,”
ASME J. Dyn. Syst., Meas., Control
,
120
(
4
), pp.
439
444
.
26.
Ghorbel
,
F. H.
,
Gandhi
,
P. S.
, and
Alpeter
,
F.
, 2001, “
On the Kinematic Error in Harmonic Drive Gears
,”
ASME J. Mech. Des.
,
123
(
1
), Part 1, pp.
90
97
.
27.
Dhaouadi
,
R.
,
Ghorbel
,
F. H.
, and
Gandhi
,
P. S.
, 2003, “
A New Dynamic Model of Hysteresis in Harmonic Drives
,”
IEEE Trans. Ind. Electron.
,
50
(
6
), pp.
1165
1171
.
28.
Kennedy
,
C. W.
, and
Desai
,
J. P.
, 2005, “
Modeling and Control of the Mitsubishi Pa-10 Robot Arm Harmonic Drive System
,”
IEEE/ASME Trans. Mechatron.
,
10
(
3
), pp.
263
274
.
29.
Zhu, W.-H.,
Dupuis
,
E.
, and
Doyon
,
M.
, 2007, “
Adaptive Control of Harmonic Drives
,”
ASME J. Dyn. Syst., Meas., Control
,
129
(
2
), pp.
182
193
.
30.
Seyfferth
,
W.
,
Maghzal
,
A. J.
, and
Angeles
,
J.
, 1995, “
Nonlinear Modeling and Parameter Identification of Harmonic Drive Robotic Transmissions
,”
IEEE International Conference on Robotics and Automation
, Nagoya, Japan, pp.
3027
3032
.
31.
Tuttle
,
T. D.
, and
Seering
,
W. P.
, 1996, “
Nonlinear Model of a Harmonic Drive Gear Transmission
,”
IEEE Trans. Rob. Autom.
,
12
(
3
), pp.
368
374
.
32.
Klypin
,
A. V.
,
Popov
,
P. K.
, and
Emel’yanov
,
A. F.
, 1985, “
Calculation of the Kinematic Error of a Harmonic Drive on a Computer
,”
Sov. Eng. Res.
,
5
(
11
), pp.
8
13
.
33.
Gandhi
,
P. S.
, and
Ghorbel
,
F. H.
, 2002, “
Closed-Loop Compensation of Kinematic Error in Harmonic Drives for Precision Control Applications
,”
IEEE Trans. Control Syst. Technol.
,
10
(
6
), pp.
759
768
.
34.
Macki
,
J. W.
,
Nistri
,
P.
, and
Zecca
,
P.
, 1993, “
Mathematical Models for Hysteresis
,”
SIAM Rev.
,
35
(
1
), pp.
94
123
.
35.
Brokate
,
M.
, and
Sprekels
,
J.
, 1996,
Hysteresis and Phase Transitions, Applied Mathematical Sciences
,
Springer
,
New York
.
36.
Krasnosel’skii
,
M. A. P. A. V.
, 1989,
Systems With Hysteresis/Uniform Title: Sistemy S Gisterezisom. English, Universitext
, New York, Berlin.
37.
Mayergoyz
,
I. D. M. I. D.
, 2003,
Mathematical Models of Hysteresis and Their Applications, Elsevier Series in Electromagnetism
, Boston, Elsevier.
38.
Lubarda
,
V. A.
,
Sumarac
,
D.
, and
Krajcinovic
,
D.
, 1993, “
Preisach Model and Hysteretic Behavior of Ductile Materials
,”
Eur. J. Mech. A-Solids
,
12
(
4
), pp.
445
470
.
39.
Royston
,
T. J.
, 2008, “
Leveraging the Equivalence of Hysteresis Models from Different Fields for Analysis and Numerical Simulation of Jointed Structures
,”
ASME J. Comput. Nonlinear Dyn.
,
3
(
3
),
031006
.
40.
Nye
,
T. W.
, and
Kraml
,
R. P.
, 1991, “
Harmonic Drive Gear Error. Characterization and Compensation for Precision Pointing and Tracking
,” NASA Conference Publication 3113, p.
237
.
41.
Preissner
,
C.
,
Shu
,
D.
, and
Royston
,
T. J.
, 2007, “
Experimental Investigation and Model Development for a Harmonic Drive Transmission
,”
Proc. SPIE
,
6665
,
66650P
.
42.
Lee
,
S. H.
, and
Royston
,
T. J.
, 2000, “
Modeling Piezoceramic Transducer Hysteresis in the Structural Vibration Control Problem
,”
J. Acoust. Soc. Am.
,
108
(
6
), pp.
2843
2855
.
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