Abstract

This paper presents a mechatronic model of a powertrain with a half toroidal continuously variable transmission. In this model, the actuator, the load on the output shaft, and the mechanical, electrical, and control dynamics are simultaneously considered. A reduced mathematical model is stated for the half toroidal transmission, where a time-variant transmission ratio is considered to drive different input/output dynamic torques of the powertrain. The dynamic performance of the mechatronic model is shown through three case studies with different inertial/dynamic loads at the output shaft. Simulation results are performed for fixed and automatic transmission ratio changes. The model and simulation results presented in this article extend the options to design, control, and drive mechatronic systems that include a half toroidal continuously variable transmission.

References

1.
Mhenni
,
F.
,
Penas
,
O.
,
Hammadi
,
M.
,
Choley
,
J.-Y.
, and
Hehenberger
,
P.
,
2018
, “
Systems Engineering Approach for the Conjoint Design of Mechatronic Products and Their Manufacturing Systems
,” Annual IEEE International Systems Conference (
SysCon
), Vancouver, BC, Canada Apr. 23–26, pp. 1–8 ,
IEEE
.10.1109/SYSCON.2018.8369560
2.
Cervantes-Culebro
,
H.
,
Chong-Quero
,
J. E.
,
Padilla-Garcia
,
E. A.
, and
Cruz-Villar
,
C. A.
,
2021
, “
Concurrent Design of a 2DOF Five-Bar Parallel Robot a Hybrid Design of Rigid and Flexible Links
,”
IEEE Access
,
9
, pp.
17450
17462
.10.1109/ACCESS.2021.3053250
3.
Ansoategui
,
I.
, and
Campa
,
F. J.
,
2019
, “
Mechatronic Model Based Overshoot Prediction and Reduction in Servodrives With Compliant Load
,”
Mech. Mach. Theory
,
137
, pp.
227
236
.10.1016/j.mechmachtheory.2019.01.034
4.
Badreddine
,
E.
,
Houidi
,
A.
,
Affi
,
Z.
, and
Romdhane
,
L.
,
2013
, “
Application of Multi-Objective Genetic Algorithms to the Mechatronic Design of a Four Bar System With Continuous and Discrete Variables
,”
Mech. Mach. Theory
,
61
, pp.
68
83
.10.1016/j.mechmachtheory.2012.11.002
5.
Padilla-Garcia
,
E. A.
,
Rodriguez-Angeles
,
A.
,
Resendiz
,
J. R.
, and
Cruz-Villar
,
C. A.
,
2018
, “
Concurrent Optimization for Selection and Control of ac Servomotors on the Powetrain of Industrial Robots
,”
IEEE Access
,
6
, pp.
27923
27938
.10.1109/ACCESS.2018.2840537
6.
Cusimano
,
G.
,
2019
, “
Non-Rectangular Dynamic Range of the Drive System: A New Approach for the Choice of Motor and Transmission
,”
Machines
,
7
(
3
), p.
54
.10.3390/machines7030054
7.
Kim
,
J.
,
Park
,
F.
,
Park
,
Y.
, and
Shizuo
,
M.
,
2002
, “
Design and Analysis of a Spherical Continuously Variable Transmission
,”
ASME J. Mech. Des.
,
124
(
1
), pp.
21
29
.10.1115/1.1436487
8.
Srivastava
,
N.
, and
Haque
,
I.
,
2009
, “
A Review on Belt and Chain Continuously Variable Transmissions (CVT): Dynamics and Control
,”
Mech. Mach. Theory
,
44
(
1
), pp.
19
41
.10.1016/j.mechmachtheory.2008.06.007
9.
Spanoudakis
,
P.
, and
Tsourveloudis
,
N. C.
,
2013
, “
On the Efficiency of a Prototype Continuous Variable Transmission System
,”
21st Mediterranean Conference on Control and Automation
,
IEEE
, Platanias-Chania, Crete, Greece, June 25–28, pp.
290
295
.10.1109/MED.2013.6608736
10.
Li
,
Q.
,
Dong
,
L.
,
Liao
,
M.
, and
Liang
,
J.
,
2018
, “
Application of Envelope Theorem to Determine the Shapes of Contact Components in Toroidal Continuously Variable Transmission
,”
Mech. Mach. Theory
,
130
, pp.
491
507
.10.1016/j.mechmachtheory.2018.06.021
11.
Chen
,
S.
, and
Dong
,
Z.
,
2018
, “
Transmission Characteristics and Phase Number Optimization on the Transmission Mechanism of Rod Gear Pulse Continuously Variable Transmission
,”
Adv. Mech. Eng.
,
10
(
1
), pp. 1–8.10.1177/1687814017751966
12.
Afrabandpey
,
A.
, and
Ghariblu
,
H.
,
2018
, “
Performance Evaluation of Ball CVT and Comparison With Half Toroidal Cvt
,”
Int. J. Autom. Technol.
,
19
(
3
), pp.
547
557
.10.1007/s12239-018-0052-x
13.
Mendoza-Trejo
,
O.
,
Padilla-García
,
E. A.
,
Cruz-Villar
,
C. A.
, and
Rodríguez-Angeles
,
A.
,
2019
, “
Free Kinematic Singularity Controller for a Planetary Gear Based Cobot
,”
Int. J. Soc. Rob.
,
11
(
2
), pp.
211
218
.10.1007/s12369-018-0486-3
14.
Akbarzadeh
,
S.
, and
Zohoor
,
H.
,
2005
, “
Optimizing the Geometry of a Half-Toroidal CVT
,”
SAE Trans.
, 114, pp.
1476
1481
.
15.
Yildiz
,
A.
,
Kopmaz
,
O.
, and
Cetin
,
S. T.
,
2015
, “
Dynamic Modeling and Analysis of a Four-Bar Mechanism Coupled With a CVT for Obtaining Variable Input Speeds
,”
J. Mech. Sci. Technol.
,
29
(
3
), pp.
1001
1006
.10.1007/s12206-015-0214-y
16.
Yildiz
,
A.
, and
Kopmaz
,
O.
,
2015
, “
Dynamic Analysis of a Mechanical Press Equipped With a Half–Toroidal Continuously Variable Transmission
,”
Int. J. Mater. Prod. Technol.
,
50
(
1
), pp.
22
36
.10.1504/IJMPT.2015.066864
17.
Verbelen
,
F.
,
Derammelaere
,
S.
,
Sergeant
,
P.
, and
Stockman
,
K.
,
2018
, “
A Comparison of the Full and Half Toroidal Continuously Variable Transmissions in Terms of Dynamics of Ratio Variation and Efficiency
,”
Mech. Mach. Theory
,
121
, pp.
299
316
.10.1016/j.mechmachtheory.2017.10.026
18.
Carbone
,
G.
,
Mangialardi
,
L.
, and
Mantriota
,
G.
,
2004
, “
A Comparison of the Performances of Full and Half Toroidal Traction Drives
,”
Mech. Mach. Theory
,
39
(
9
), pp.
921
942
.10.1016/j.mechmachtheory.2004.04.003
19.
Delkhosh
,
M.
,
Foumani
,
M. S.
,
Boroushaki
,
M.
,
Ekhtiari
,
M.
, and
Dehghani
,
M.
,
2011
, “
Geometrical Optimization of Half Toroidal Continuously Variable Transmission Using Particle Swarm Optimization
,”
Sci. Iran.
,
18
(
5
), pp.
1126
1132
.10.1016/j.scient.2011.08.005
20.
Zou
,
Z.
,
Zhang
,
Y.
,
Zhang
,
X.
, and
Tobler
,
W.
,
2001
, “
Modeling and Simulation of Traction Drive Dynamics and Control
,”
ASME J. Mech. Des.
,
123
(
4
), pp.
556
561
.10.1115/1.1402128
21.
Kawabe
,
T.
,
Joe
,
S.
, and
Mensler
,
M.
,
2002
, “
A Gain Scheduled Non-Linear Servo Controller for a Toroidal Continuously Variable Transmission
,”
Proceedings of the International Conference on Motion and Vibration Control 6.1
, The Japan Society of Mechanical Engineers, Saitama, Kantō, Japan, Aug. 19–23, pp.
367
372
.
22.
Tyreas
,
G. C.
, and
Nikolakopoulos
,
P. G.
,
2016
, “
Development and Friction Estimation of the Half-Toroidal Continuously Variable Transmission: A Wind Generator Application
,”
Simul. Modell. Pract. Theory
,
66
, pp.
63
80
.10.1016/j.simpat.2015.11.007
23.
Verbelen
,
F.
,
Derammelaere
,
S.
,
Sergeant
,
P.
, and
Stockman
,
K.
,
2017
, “
Half Toroidal Continuously Variable Transmission: Trade-Off Between Dynamics of Ratio Variation and Efficiency
,”
Mech. Mach. Theory
,
107
, pp.
183
196
.10.1016/j.mechmachtheory.2016.09.013
24.
Verbelen
,
F.
,
Druant
,
J.
,
Derammelaere
,
S.
,
Vansompel
,
H.
,
De Belie
,
F.
,
Stockman
,
K.
, and
Sergeant
,
P.
,
2017
, “
Benchmarking the Permanent Magnet Electrical Variable Transmission Against the Half Toroidal Continuously Variable Transmission
,”
Mech. Mach. Theory
,
113
, pp.
141
157
.10.1016/j.mechmachtheory.2017.03.005
25.
Tanaka
,
H.
,
2003
, “
Torque Control of a Double Cavity Half-Toroidal CVT
,”
Int. J. Veh. Des.
,
32
(
3/4
), pp.
208
215
.10.1504/IJVD.2003.003561
26.
Tsai
,
L.-W.
,
1999
,
Robot Analysis: The Mechanics of Serial and Parallel Manipulators
,
Wiley
, New York.
27.
Siciliano
,
B.
,
Sciavicco
,
L.
,
Villani
,
L.
, and
Oriolo
,
G.
,
2010
,
Robotics: Modelling, Planning and Control
,
Springer Science & Business Media
, New York.
You do not currently have access to this content.