SCIENTIFIC BULLETIN
o f the "POLITEHNICA" University o f Timisoara Transactions on Mechanics
XIIIth International Symposium
Young People and Multidisciplinary Research
Organizer: Association for Multidisciplinary Research in the West Zone of Romania
Edited by
I. M itelea, Valeria Farbaç, R.A. Ro§u
C O N T E N T S
1 C. B Â R B U L E S C U , N . H E R IÇ A N U , V. B A C R IA - E lectrical phenom ena acoustic investigation
2 L . B Â R N U T IU , I. P O P - Elem entary m athem atical analysis o f an unconventional p ow er transm ission system
3 L .B Â R N U T IU , I. P O P - A lternative construction proposal for an unconventional pow er transm ission system
4 R. M . D O B R A , I. M IT E L E A - The benefit o f duplex surface treatm ents on the m echanical parts w ear
5 I. D U M A , S. T . D U M A , C . L O C O V E I - Studies regarding the acquirem ent o f hardness standard blocks for transm itting the B rinell 10/3000 HB W hardness scales
6 C . G R O Z A , I. M IT E L E A - Incom patibility problem s in obtaining Ti-6A1-4V + X IO C rN iTi 18-10 w elds 7 L. K U N , I. D U M IT R U - R esearch on
critical plane positions and stresses in m aterials subjected to cyclic tension
torsion loading
8 G . M E L C IO IU , V . A. Ç E R B A N , C.
C O D R E A N , D. B U Z D U G A N , F. M . C O R N E A - O btaining solder alloys from the fam ily Sn-C u-N i-P form o f ribbon m ethod m elt spinning
9 L. M O L D O V A N , M . F R IE D M A N N , M . M A G Y A R I - Possibilities to use the A gilent V E E Pro program m ing environm ent in order to perform the test for determ ination o f explosion pressure specific for apparatus w ith the type o f protection flam eproof enclosure "d"
10 V. P Â S C U L E S C U , M . ÇU V A R, D.
P Â S C U L E S C U - The necessity o f im plem enting m odem protection systems into the N ational Energetic System
C U PR IN S
C . B Â R B U L E S C U , N . H E R IÇ A N U , 5 V . B A C R IA - Investigarea acusticä a fenom enelor electrice
L . B Â R N U T IU , I. P O P - A naliza 11 m atem aticä a unui sistem neconvenjional de transm isie a puterii
L .B Â R N U T IU , I. P O P - Propunere de 15 variantä constructiva pentru un sistem neconventional de transm isie a puterii
R. M . D O B R A , I. M IT E L E A Efectul 19 tratam entelor de suprafata D uplex asupra uzurii pieselor
I. D U M A , S. T. D U M A , C . L O C O V E I - 25 Studiu privind obtinerea placutelor étalon pentru transm iterea scarilor de duritate Brinell H B W
C . G R O Z A , I. M IT E L E A - Problem e de 31 incom patibilitate la realizarea Tmbinärilor súdate TÍ-6A 1-4V +X 1 OCrNiTi 18-10
L. K U N , I. D U M IT R U - C ercetäri asupra 37 planelor critice §i a tensiunilor in m ateriale supuse la incercäri ciclice de tracjiune cu torsiune
G . M E L C IO IU , V . A. Y ERBA N , C . 43 C O D R E A N , D. B U Z D U G A N , F . M . C O R N E A - O bjinerea aliajelor de lipire din fam ilia Sn-C u-N i-P sub form ä de benzi prin m etoda m elt spinning
L . M O L D O V A N , M . F R IE D M A N N , M . 49 M A G Y A R I - Posibilitad de utilizare a m ediului de program are A gilent V EE Pro la realizarea incercärii de determ inare a presiunii de explozie specificä aparaturii cu tip de protectie capsulare antideflagrantä "d"
V. P Ä S C U L E S C U , M . §U V A R , D. 55 P Ä S C U L E S C U - N ecesitatea im plem entärii sistem elor m oderne de protectie in Sistem ul Energetic N ational
11 F. P Ä U N , L . L U P U , A. J U R C A , N.
V A T A V U , E . G H IC IO I , M . P Ä R Ä IA N - D evelopm ent o f m ethods for determ ining the safety param eters o f conveyor belts used in potentially explosive atm ospheres
12 F . R Ä D O I, C . L U P U , D. C IO C L E A , I. G H E R G H E , C . B O A N T Ä - Judicious placem ent o f fans along the ventilation colum n at the front Castel A m onte feeding pipe using diagram s in the Q -L system sizing
r _ _ V f
13 M . R IS T IC , M . K O C IC , A. A L IL , O . I L IC , J .IG N J A T O V IC - D istribution o f loads o f cycloid speed reducer
14 M . R IS T IC , M . P R V U L O V IC , M . P R O K O L A B , S. B U D IM IR , M . R A D O S A V L J E V IC , D .JO V A N O V IC , Z . M IL U T IN O V IC - N um erical sim ulation o f the cold-w ater pressure test and operating conditions for air reservoir
15 R. A. R O § U , D. R . P A S C U , S.
D R A G O I - Joining alum inum alloy w ith galvanized steel by C M T process 16 J . S Ä R O S I - Function approxim ation
for the hysteresis o f fluidic m uscles 17 J . S Ä R O S I, Z. S Z A B Ö - D evelopm ent
and investigation o f a balancing system using fluidic m uscles
18 M . S U V A R , V . P Ä S C U L E S C U , D.
C IO C L E A , I. G H E R G H E - M odern m ethod for optim ization o f the ventilation netw orks
19 M .V E L IC K O V IC , D. S T O J A N O V IC , V . B A S A R IC - A n approach to city logistics term inal location problem in N ovi Sad
F . P Ä U N , L . L U P U , A. J U R C A , N . 59 V Ä T A V U , E . G H I C I O I , M . P Ä R Ä IA N D ezvoltarea m etodelor de determ inare a param etrilor de securitate ai benzilor transportoare folosite in atm osfere potential explozive
F. R Ä D O I, C . L U P U , D. C IO C L E A , I. 63 G H E R G H E , C . B O A N T Ä - A m plasarea ju d icio asä a ventilatoarelor pe coloana de aeraj in cadrul aducjiunii front C astel A m onte utilizänd nom ogram ele pentru dim ensionare in sistem Q -L
M . R IS T IC , M . K O C IC , A . A L IL , O . 69 I L IC , J .IG N J A T O V IC - D istrib u y a solicitärilor in reductorul cicloid
M . R IS T IC , M . P R V U L O V IC , M . 73 P R O K O L A B , S. B U D IM IR , M . R A D O S A V L J E V IC , D .J O V A N O V IC , Z . M IL U T IN O V IC - Sim ularea num érica a probei hidraulice §i conditii de functionare ale rezervorului de aer
R. A. R O § U , D. R . P A S C U , S. 77 D R Ä G O I - R ealizarea de im binäri eterogene prin procedeul C M T
J . S Ä R O S I - A proxim area fu n ctionalä 81 pentru histereza m u§chilor fluizi
J . S Ä R O S I, Z . S Z A B Ó - D ezvoltarea §i 85 investigarea unui sistem de echilibrare folosind mu§chi fluizi
M . S U V A R , V. P Ä S C U L E S C U , D . 89 C IO C L E A , I. G H E R G H E - M etodä m oderna pentru optim izarea rejelelo r de aeraj
M . V E L IC K O V IC , D. S T O J A N O V IC , 93 V. B A S A R IC - O abordare a p roblem ei locajiilor term inalelor logistice in Novi Sad
S C I E N T I F I C B U L L E T IN O F
T H E „ P O L I T E H N I C A ” U N IV E R S IT Y O F T IM IS O A R A , R O M A N IA T R A N S A C T IO N S O N M E C H A N IC S
B U L E T IN U L $ T I I N T I F I C A L
U N IV E R S IT A T I I „ P O L I T E H N I C A ” D IN T IM IS O A R A , R O M A N IA S E R IA M E C A N IC A
T o m 5 6 ( 7 0 ) _______________ IS S N 1224 - 6077 F a s c . S I , 2011
FUNCTION APPROXIMATION FOR THE HYSTERESIS OF FLUIDIC MUSCLES
J ó z s e f S Á R O S 1
Technical Institute, Faculty of Engineering, University of Szeged Mars tér 7., Szeged, H-6724, Hungary
e-mail: sarosi@mk.u-szeged.hu
Abstract. Numerous researchers have investigated the relationship of the force, length and pressure to find a good approximation and theoretical approach for the equation of force generated by pneumatic artificial muscles (PAMs).
Some of them report several mathematical models, but significant differences have been noticed between the theoretical and experimental results. Accordingly we have generated and introduced a new model and algorithm that gives us simple yet accurate description of this actuator. This paper presents this new function approximation for the hysteresis of Fluidic Muscles manufactured by Festő.
Keywords: Pneumatic Artificial Muscle, Force Equation, Matlab, Genetic Algorithm
1. Introduction
Many researchers have tried to find an actuator similar to human muscles. The most promising actuator in this field of research is undoubtedly the McKibben pneumatic muscle actuator. The McKibben muscle was invented in the 1950’s by physician Joseph L. McKibben to help the movement of polio patients and to motorize pneumatic arm orthotics. There exist several types of artificial muscles that are based on the use of rubber or some similar elastic materials, such as the McKibben muscle, the Rubbertuator made by Bridgestone company, Air Muscle made by Shadow Robot company, Fluid Muscle made by Festo company, Pleated PAM developed by Vrije University of Brussel, ROM AC (RObotic Muscle ACtuator), Yarlott and Kukolj PAM and some others [1,2].
A pneumatic actuator consists of an internal rubber bladder surrounded by a braided shell with flexible yet nonextensible threads according to a helical weaving that is attached at either ends.
W hen inflated, 'the internal bladder tends to expand, with a consequent increase in the angle between the helical woven fibres of the braid and the axis of the tube and a decrease in axial length [3].
The layout of this paper is as follows.
Section 2 (Materials and Methods) is devoted to demonstrate the model of force as a function of pressure and length (contraction). Section 3 (Experimental Results) presents several experimental results and finally, section 4 (Conclusions and Future Work) gives the investigations we plan.
Fluidic Muscles DMSP-10-250N-RM-RM (with inner diameter of 10 mm and initial length of 250 mm), DMSP-20-200N-RM-RM (with inner diameter of 20 mm and initial length of 200 mm) and DMSP-20-400N-RM-RM (with inner diameter of 20 mm and initial length of 400 mm) produced by Festo company were selected for our study.
2. M a te r ia ls a n d M e th o d s
The general behaviour of PAM with regard to shape, contraction and tensile force when inflated depends on the geometry of the inner elastic part and of the braid at rest (Figure 1), and on the materials used [1].
Figure 1 Geometry parameters o f PAM
On the basis of [4], [5] and Figure 1, the force can be calculated:
P dV
F = - p ---
dl (1)
p • ji • r • 1 ■ dr - p • 7i • r2 • (-dl)- F • (-dl) = 0 (2)
„ , d r o
F = - 2 p - 7 t r 1--- p • 71 • r (3) dl
10 j 1
c o s a n = — and c o s a = — (4)
s in a 0 = ■2 • 7t • r0 ■ n
- a n d s in a = - 7 t r n
(5)
dr _ r0 • 1 ■ c o s2a 0 1 dl 15 -sin a 0
h i 1 T
\ U J
(8)
F(/7, tc) = p • 7i • Tq • (a • (1 — k) 2 — b) (9)
Where a =■tg 2a 0
b = sin2a n
k = l o - l
0 < k < k max f and y the muScle volume, F the pulling force, p the applied pressure, lo, a0the initial inner radius and length of the PAM and the initial angle between the thread and the muscle long axis, r, l, a the inner radius and length of the PAM and angle between the thread and the muscle long axis when the muscle is contracted, h the constant thread length, n the number of turns of thread and kthe contraction.
Equation 9 is based on the admittance o f a continuously cylindrical-shaped muscle. The fact is that the shape of the muscle is not cylindrical on the end, but rather is flattened, accordingly, the more the muscle contracts, the more its active part decreases, so the actual maximum contraction ration is smaller than expected [4].
Tondu and Lopez in [4] consider improving equation 9 with a correction factor (e), on the one hand, it does not pay attention to the material that the muscle is made of, and on the other hand, it predicts for various pressures the same maximal contraction. This new equation is relatively good for higher pressure (p > 2 bar). Kerscher et al. in [5] suggest achieving similar approximation for smaller pressure another correction factor (ju) is needed, so the modified equation is:
F(p,K) = p - p - 7t - r 02 - ( a - O - e - K ) 2 - b ) ( 10) c o s a , r s in a
--- a n d — = ---
c o s a o s in a f (6)
r = r Vl - c o s 2a V*o
■cosa
o' sina o sina o
(7) i'
Where e = ae -e P - b e and p = aK e K'^d - b K . The significant differences between the theoretical and experimental results were analyzed and proved in [6, 7, 8]. Therefore we have introduced a new approximation algorithm:
F(p,ic) = (a p+b) e^cK+i^+ (e p + f) K+g p + h ^ The unknown a, b, c, d, e, f g and h parameters can be found using genetic algorithm.
The accuracy of equation 11 was demonstrated in [6, 7, 8], too.
3. E x p e r im e n ta l R e s u lts
The precise positioning of PAMs requires accurate determination of the dynamic model of pneumatic actuators. Therefore the hysteresis in the tension-length (contraction) cycle of PAMs was analyzed.
Chou and Hannaford in [9] report hysteresis to be substantially due to Coulomb friction, which is caused by the contact between the bladder and the shell, between the braided threads and each other, and the shape changing of the bladder.
Some experiments were made to illustrate the hysteresis (Figure 2).
1000
800
' «10
400
200
DMSP-10-250N-RM-RM Fluids Mmole
, 4
— 5 bar measured (upper)
— 5 bar measured (lower)
ft vv - 3 bar measured (upper)
— 3 bar measured (lower) 1 bar measured (upper) 1 bar measured (lower)
250(1
2000 g 1500
0.1 0.15 Contraction
DMSP-20-200N-RM-RM Fluidic Muscle
-a<
\% |
— 5 bar measured (upper) 5 bar measured (lower)
— 3 bar measured < upper) 3 bar measured (lower)
— 1 bar measured (upper) - 1 bar measured (lower)
V V s 's
\ - c-
_________
1.05 0.1 0.15
Contraction 0.2 0.25
2500
2000
7 1500
£ looo 500-
DMSP-20-400N-RM-RM Fluidic Muscle
—Y ....
• 5 bin measured (upper)
— 5 bar measured (lower) 2500
— 3 bar measured (lower)
1 — 1 bar measured (upper) 2000
\ . — 1 bar measured (lower)
v : : ; , g 1500
■U
■Z looo
500
Contraction 0.2 ).25
Figure 2 Hysteresis in the tension-length (contraction) cycle
Figure 3 Determination o f unknown parameters in Matlab environment
To prove versatility of equation 11, comparisons were done between the measured data and force model. The accurate fitting is demonstrated in Figure 4.
DMSP-l 0-250N-RM-RM Fluidic Muscle
• 5 I >ai m ensi ire« I ft ij <| *ei i
— 5 liar th e o r e tic a l ( u p p e r )
■---5 b a i m e a s ure d < l o w e r ) ---3 b ar th e o r e tic a l ( l o w e r i
■ 3 b a r m e a s u r e d i u p p e r )
— 3 b at th e o r e tic a l (u p p e i i ---3 b a r m e a s u r e d t l o w e r 1 ---3 b a i th e o re tic a l ( k m e i ) :
b a r m e a s u r e d (u p p e r I
—— I b a r th e o re tic a l m p j > e i) l>ar m e a s u r e d ( l o w e r )
— 1 b a r th e o r e tic a l ( l o w e r )
0.1 0.15 Contraction
DMSP-20-400N-RM-RM Fluidic Muscle
! !---1 --- •---
• 5 b ar m e a s ure d ( u p ) 1« ) ---5 l>ai th e o r e tic a l ( u p p e r >
...
\
— 5 b a r tlie o r e tic a l ( l o w e r *
• 3 b a r m e a s u re d t u p p e r ) - 3 b a r tlie o r e tic a l < u p p e i i
• 3 b a r m e a s u re d (.lo w e r )
• 3 Iwtr th e o r e tic a l ( lo w e r i
— 1 b a r m e a s u re d t u p p e r » ---1 b a r th e o r e tic a l ( u p p e r )
—— l b fir m e a s u r e d t l o w e r ) - 1 b a r tlie o r e tic a l ( l o w e r )
-0.05
Contraction 0.2 025 0.3
Figure 4 Approximation o f hysteresis loop The unknown parameters were found using
genetic algorithm in Matlab environment (Figure 3).
M)(.
I '
4. C o n c lu s io n s a n d F u t u r e W o r k
In this work a new equation based on purely statistical approach was shown for the hysteresis in the tension-length (contraction) cycle of PAMs. With the help of it precise curve fitting can be proven for any Fluidic Muscles. Our goal is to develop a new mathematical model for pneumatic artificial muscles on the basis of our approximation model.
R e fe re n c e s
1. Daerden F.: Conception and realization of pleated artificial muscles and their use as compliant actuation elements. PhD Dissertation, Vrije Universiteit Brussel, Faculteit Toegepaste Wetenschappen Vakgroep Werktuigkunde, 1999, p.
5-33
2. Daerden F., Lefeber D.: Pneumatic artificial muscles: actuator for robotics and automation.
European Journal of Mechanical and Environmental Engineering, Vol. 47, 2002, p. 10-21
3. Plettenburg D. H.: Pneumatic actuators: comparison of energy-to-mass ratio’s. Proceedings o f the 2005 IEEE, 9th International Conference on
Rehabilitation Robotics, Chicago, IL, USA, 28 June - 1 July, 2005, p. 545-549
4. Tondu B., Lopez P.: Modeling and control of McKibben artificial muscle robot actuator. IEEE Control System Magazine, Vol. 20, 2000, p. 15-38 5. Kerscher T., Albiez J., Zöllner J. M., Dillmann R.:
FLUMUT - Dynamic Modelling of Fluidic Muscles using Quick-Release. 3rd International Symposium on Adaptive Motion in Animals and Machines, Ilmenau, Germany, 25-30 September, 2005, p. 1-6 6. Sârosi J., Szépe T., Gyeviki J.: New Mathematical
Model for Pneumatic Artificial Muscles. Hungarian Agricultural Engineering, Vol. 22/2009, 2010, p. 49
52, ISSN 0864-7410
7. Sârosi J., Szépe T„ Gyeviki J.: Approximation Algorithm for the Force of Pneumatic Artificial Muscles. Factory Automation 2010, Kecskemét, Hungary, 15-16 April, 2010, p. 101-104, ISBN 978
963-7294-83-9
8. Sârosi J., Szabö G., Gyeviki J.: Investigation and Application o f Pneumatic Artificial Muscles.
Biomechanica Hungarica, Vol. 3, No. 1, 2010, p.
208-214, ISSN 2060-4475
9. Chou C. P., Hannaford B.: Measurement and modeling of McKibben pneumatic artificial muscles.
IEEE Transactions on Robotics and Automation, Vol. 12, No. 1, 1996, p. 90-102
S c ie n tific re v ie w e rs : J á n o s G Y E V I K I, F a c u lty o f E n g in e e r in g , U n iv e rs ity o f S z e g e d I s tv á n B Í R Ó , F a c u lty o f E n g in e e r in g , U n iv e rs ity o f S zeg ed
