energy efficient electromagnetic actuated cvt system

Journal of Mechanical Science and Technology 28 (4) (2014) 1153~1160

www.springerlink.com/content/1738-494x DOI 10.1007/s12206-014-0103-9

Energy efficient electromagnetic actuated CVT system†

Ataur Rahman1,*, Sazzad Bin Sharif1, AKM Mohiuddin1, Mahbubur Rashid2 and Altab Hossain3 1Department of Mechanical Engineering, International Islamic University Malaysia, Malaya, Malaysia

2Department of Mechatronics Engineering, International Islamic University Malaysia, Malaya, Malaysia 3Department of Mechanical Engineering, University Malaya, Malaya, Malaysia

(Manuscript Received April 20, 2012; Revised November 11, 2013; Accepted November 19, 2013)

----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

Abstract A continuously variable transmission (CVT) system transmits the engine/battery power to the car driving wheel smoothly and effi-

ciently. Several types of CVT already been developed to improve the transmission losses while maintaining acceleration time. However, most of the CVT has some constraints in the actuation mechanism which led us to develop an innovative electromagnetic actuator for CVT. Simplified mathematical equations have been developed for the kinematics analysis of clamping forces of the CVT and electro-magnetic forces of EMA. The EMA has been developed for ¼ scale car with two sets of solenoid. Each of the two sets has been equipped with primary and secondary pulleys for pushing and pulling the movable sheave. The solenoid is operated by controlling the supply cur-rent with a fuzzy logic controller. A simulation based fuzzy logic controller has been introduced here for identifying the desired current of the EMA actuation. The experimental results show that the EMA develops electromagnetic forces 301 N for the supply current of 3.37 amp, which makes the acceleration time of the car in the range of 2.5~3.5 sec and electromagnetic actuated CVT system highly energy efficient.

Keywords: EMA-CVT; Clamping force; Electromagnetic force; Travelling time; Acceleration time; Fuzzy logic; Energy efficient ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- 1. Introduction

The continuously variable transmission (CVT) technology transmits power from the engine to the wheels by changing its diameter. It adjusts engine's torque in an infinite number of ways, making it more efficient than traditional gearboxes. The CVT will continue to replace traditional gears in the coming years as more carmakers turn to CVT to increase fuel econ-omy. According to Automotive News, Japanese carmakers appear especially interested in adding CVTs to their line-ups. Honda is widely expected to offer a CVT on its next-generation. Honda Accord, Nissan, and Toyota are already in the market with CVT which helps each of the transports to achieve 38 miles per gallon on the highway. However, CVTs have become an annoyance to many enthusiasts and critics because of a number of undesirable characteristics such as unpleasant 'rubber band' sound and slow response of the mov-able sheaves for fast acceleration time under hard acceleration. Pesgens (2006) and Richer and Hurmuzlu (2000) reported that the performance of CVT can be improved by the hydraulic, pneumatic and electro-mechanical actuation mechanism. Hy-draulic CVT system ensures sufficient pressure; however, the

problem is to keep movable sheave of the pulley to its exact position (Pesgens, 2006). Richer and Hurmuzlu (2000) re-ported that pneumatic actuation can offer a better alternative for certain types of applications. Ang (2002) conducted a study on the performance for a car of 3000 cc by simulation on the manual transmission, automatic transmission and the continuously variable transmission. They reported that time taken to accelerate to 100 km/h is 10.20 sec for manual trans-mission; 0.76 sec for automatic transmission; 7.85 sec for CVT. Compressibility of air makes the pneumatic system unreliable. As a consequence, there is fluctuation in holding the sheave to the exact desired position to deliver actual torque to the final drive. For further improvement of CVT perform-ance, we proposed a fast actuation system, “electromagnetic actuated mechanism for CVT system,” which is the core dis-cussion of this study.

2. Development of EMA for CVT

2.1 EMA-CVT clamping force

In the proposed EMA-CVT, movable sheaves are mainly controlled by developing electromagnetic force by the sole-noid actuator. The EMA gets the mechanical advantage to pull the movable sheave, whereas there are difficulties for pushing the sheave against the rotating belt which is considered as the

*Corresponding author. Tel.: +6 3 6196 4544, Fax.: +6 3 6196 4455 E-mail address: [email protected]

† Recommended by Editor Yeon June Kang © KSME & Springer 2014

1154 A. Rahman et al. / Journal of Mechanical Science and Technology 28 (4) (2014) 1153~1160

clamping force. Two sets of solenoids with common plunger are used in this study to overcome the clamping force with developing the electromagnetic force. Fig. 1 shows the kinet-ics of clamping force.

The clamping force of the EMA-CVT system can be mod-elled by using the equation of Toshie (2006):

cos(90 )

2out b

f

TFR

qm

-= (1)

where, Tout is transmission torque in Nm, θb is the belt angle; µf is belt frictional coefficient of pulley, and R is radius of pulley. It should be noted that electromagnetic force genera-tion must be higher than that of clamping force in order to push the plunger against the clamping force. The slip velocity Δv is incurred in both of pulleys during transferring the power to the driving wheel. The slip velocity for the primary pulley and the secondary pulley can be calculated as p p pv R vwD = - and s s sv v RwD = - , where, v is the speed of the belt, ωpRp and ωsRs is the speed and Δvp and Δvs are the slip velocity of the primary and secondary pulley, respectively. So the exact power transferred from the engine to the primary pulley and from the primary to secondary pulley can be computed as:

( )

( )

pin in

p

sout out

s

v vP T and

R

v vP TR

é ùD += ê úê úë ûé ù- D

= ê úë û

(2)

where, Pin is the power generated by the engine or input power of the primary pulley in Watt and Pout is the output power of the primary pulley in Watt.

2.2 Electromagnetic force

The actuator solenoid has been designed and developed to maximum the electromagnetic force to overcome the maxi-mum clamping force with associating the dynamic behavior of the magnetic flux and density and strength of the magnetic

field as shown in Fig. 2. The total electromagnetic force at the magnetic field of cur-

rent conducting solenoid is given by the general equation:

em wireF BIl= (3)

where, Fem is the electromagnetic force for the total solenoid coil length lwire, B is the magnetic flux density for whole sole-noid, I is the current passing through the conductor wire around which magnetic field generates. The magnetic flux density along the z direction for the segment of wire in a sin-gle winding can be estimated by using the equation of Ataur etal. (2012):

( )

2

1

2

2 2 ( , )

3 2 22 2

2 1

ˆ2.

ˆ sin sin2

solenoid

segment

solenoid

Lh wireS r l

h La z

wind per lengthloop

solenoid

JdS a

B za z

N IzN

L

m

ma a

= =-

æ öæ öç ÷ç ÷

ç ÷ç ÷è ø= ç ÷+ç ÷

ç ÷ç ÷è ø

= -

òòå å

(4)

where, µ is magnetic permeability (degree of magnetization of a material in response to magnetic field), Nwind per length is the number of turns in a single loop, Nloop is the number of loop in solenoid housing, N = Nwind per length . Nloop is the total number of turns in the solenoid.

Therefore, the electromagnetic force:

( )2

2 1 sinsin sin .em glewindingsolenoid

IF N lLm a a= - (5)

If the solenoid length is much larger than its radius, then

2 90a = o% and 1 ( )90a = - o% , Eq. (5) can be rewritten as:

2 2

sin 2 .em glewindingsolenoid solenoid

I IF N l N aL Lm m p= = (6)

Fig. 1. Force on pulley surface.

Fig. 2. Magnetic field in coil.

A. Rahman et al. / Journal of Mechanical Science and Technology 28 (4) (2014) 1153~1160 1155

The traction torque of car is estimated by using the equation as follows:

(i) Maximum (initial) traction force:

( )( )sin .

1

f r

winitial c R R wheel

R

w

l f hLT m g rh

L

m qm

é ù-ê úê ú= +ê ú+ê úë û

(7)

(ii) Traction force during rolling:

21sin2final c R r a f D c wheelT m g f W A C v rq ræ ö= + +ç ÷

è ø (8)

where, Tfinal is the traction torque during motion, mc is the mass of the ¼ scale car which is considered as 155.75 kg, slope of the road (q), fr is the rolling motion resistance coeffi-cient, ra is the air density (12.02 N/m3), Af is the frontal area of the car (0.131 m2), CD is the drag coefficient (0.24), vc is the car travelling speed considered as 11.11 m/s.

3. Development of EMA for CVT

Development of electromagnetic actuator (EMA) for the CVT of ¼ scales Perodua Kancil Car (Malaysian car brand). The EMA has been designed by simulating the desired trac-tion torque of the car for all operating conditions. However, the traction force of the car is taken into account for the esti-mation of clamping force of the CVT pulley. The EMA has been designed and developed in such way that it develops the electromagnetic force, which is more or equivalent to the clamping force of the pulley.

The number of windings, wire diameter and solenoid hous-ing and length are considered to develop the EMA. The EMA has been activated with the power of the (24 volt) alternator. To determine the diameter of the coil, the resistance and cur-rent flow in the coil are optimized. The parameters of the EMA are assumed as: resistivity of conductor (ρ) is equal to

81.62 10-´ Ωm, length of the solenoid (Ls) is equal to 0.2 m, largest diameter of the EMA (h2) is equal to 0.171 m and smallest diameter (h1) is equal to 0.031 m. Fig. 3 shows the parametric study of the EMA.

Figs. 3-5 show the variation electromagnetic force with the changing of current and number of windings. The characteris-tics of EMA hav been simulated by varying the current sup-plied in the range of 1-6 A on developing electromagnetic forces (equivalent of clamping forces) 101.22 N (final or minimum) to 274.82 N (initial or maximum) and electromag-netic field. Fig. 5 shows the values of electromagnetic force, electromagnetic field and electromagnetic energy for the cor-responding current of the EMA. Result shows that electro-magnetic field and electromagnetic force increases with in-creasing the current flow. The electromagnetic field tends to become saturated even with increasing the current flow to the EMA. This is could be due to the hysteresis effect. Beyond the

supply current 6 A, excessive heat energy develops due to the inductance of the coil.

The heat energy that develops in the coil can be defined by using the equation of Rahman et al. (2012).

22

.

12

s seng Li

s

N A BLEL N

mm

æ ö= ç ÷

è ø (9)

Fig. 3. Parametric study of EMA.

Fig. 4. Relationship between the electromagnetic force and current and winding.

Fig. 5. Electromagnetic field, electromagnetic force vs current.


where, N is the total number of windings in the solenoid, J is the current density, I is the supply current, r is the wire radius, Ls is length of a single winding, Vs volume of the solenoid, As is the cross sectional area of the coil, B is the magnetic flux density, σ is the electric conductivity and (t2-t1) is the time interval of the solenoid operation.

Fig. 6 shows a 3D drawing of EMA. The EMA is designed with a combination of different diameters of solenoids to maintain the smooth operation of the movable sheave of the pulleys by generation of electromagnetic force. The number of turns of the EMA has been defined as:

2 12

( )2

solenoid

w

L h hN packingfactord

-= ´

while the other parameters of the solenoid such as length of the coil is defined as:

2 22 12

( )4

solenoidcoil

w

L h hL packingfactord

p -= ´ ;

the volume of the solenoid,

2 22 12

( )4

solenoids

w

L h hV packingfactord

p -= ´ ;

the mass of the solenoid, m

s cum Volr= ´ ; the packing factor

(f), 105( )200( )

actualwindingftheoreticalwinding

= ; the density of cupper coil is

considered 38940 /cu kg mr = at room temperature. The speci-fication of EMA has been shown in Table 1.

Fig. 7 shows the developed EMA for CVT of a small IC engine equipped ¼ scale car.

3.1 Control strategy of EMA: Fuzzy logic approach

Fuzzy logic controller is used in this study for predicting the performance EMA on the CVT system operation over time.

EMA actuation control systems with fuzzy logic controller exercises on developing the desired electromagnetic force with optimizing the power supply to the EMA. The fuzzy logic controller is structured with controlled variable and regu-lated variable. The controlled variable is considered as torque error (TE), rate of change of torque error (RTE) while the regulated variable is considered as power consumption (P) by EMA. Figs. 8 and 9 show the fuzzy variable.

The true values of the TE membership functions from fuzzy logic expert system can be computed by using Eqs. (10)-(12).

( )

( )( ) ( )

( )1

1; 5

26.25( ) ; 5< <26.25

21.250; 26.25

Vlow

TE

TETE i TE

TE

m

ì £ üï ï

-ï ï= í ýï ïï ï³î þ

(10)

( )

( )( ) ( )

( ) ( )

( )

1

0; < 5

5; 5 26.25

21.25( )47.5

; 26.25 47.521.25

0; > 47.5

Low

TE

TETE

TE iTE

TE

TE

m

ì üï ï

-ï ï< £ï ïï ï= í ý-ï ï< <ï ï

ï ïï ïî þ

(11)

Fig. 6. 3D drawing of EMA.

Table 1. Specification of EMA.

Parameters Values

Coil diameter (dw), mm 1.6

Cross sectional area of wire, m2 2.01×10-6

Length of solenoid, m 0.2

Solenoid minimum diameter (h1), m 0.031

Solenoid maximum diameter (h2), m 0.171

Cross-sectional surface of the Solenoid (S), m2 7.5x10-4

Packing factor (f) 0.525

Number of turns (N), turns 2843

Length of coil (Lc), m 902.32

Volume of the solenoid coil (Vm), m3 2.3×10-3

Mass of solenoid (ms), kg 20.65

Fig. 7. Developed quarter scale car with EMA-CVT system.


( )

( )( ) ( )

( ) ( )

( )

2

0; < 1

1; 1 3

2( ) .5

; 3 52

0; > 5

Pos

RTE

RTERTE

RTE iRTE

RTE

RTE

m

ì üï ï

-ï ï< £ï ïï ï= í ý-ï ï< <ï ï

ï ïï ïî þ

(12)

For crisp input, TE (i1) = 20 Nm, and RTE (i2) = 2.5 Nm/s,

the corresponding rules are satisfied to be fired. The firing strength of truth values of membership function for individual rules is obtained as:

( ) ( ){ }3 min ,

26.25 20 2.5 1min 0.294, 0.75 0.29421.25 2

Vlow PosTE RTEa m m=

- -æ ö= = = =ç ÷è ø

( ) ( ){ }6 min ,

20 5 2.5 1min 0.705, 0.75 0.705.21.25 2

Low PosTE RTEa m m=

- -æ ö= = = =ç ÷è ø

Defuzzification operates on the implied fuzzy sets produced

by the inference mechanism and combines their effects to provide the most certain prediction output. This defuzzifica-tion is necessary because of crisp control action, which is re-quired to actuate the solenoid control.

The predicted output needed to operate the solenoid as fol-lows by means of Fig. 14 and the following equation:

87.5 500.294 50 0.294 50

20.705 87.5 0.705 87.5 0.705 87.5

219.98

i ibm -æ ö= ´ + + ´ç ÷è ø

+ ´ + ´ + ´=

å

0.294 0.294 0.705 0.705 0.705 2.703219.98 81.382.703

i

crispP

m = + + + + =

= =

å

where, P crisp is the predicted out in watt and bi is the subinter-val position of ith universe in under membership function.

This calculation shows 94.96% close crisp value for fuzzy output 85.7 watt. However, there is some deviation with the result because of using different method of solution which is center of area (COA) instead of center of gravity (COG) method. Fig. 10 shows the fuzzy control surface which repre-sents the fuzzy logic system dynamic behavior.

4. EMA-CVT equipped ¼ scale car performance in-

vestigations

Performance of the EMA-CVT is investigated with keeping initially the CVT in high gear ratio. Electromagnetic force development by developing solenoid is the core discussion of this study, which not only makes the actuation of CVT smooth, but it also makes the transmission more energy efficient. To develop the electromagnetic forces the current of the alternator has been regulated. However, the electromagnetic force changes with changing the current flow high as shown in Fig. 10. Electromagnetic force of the EMA-CVT system offers the desired gear ratio by placing the pulley sheave to its exact position. The gradual response of the electromagnetic force

Fig. 8. Input fuzzy logic controller.

Fig. 9. Output value of fuzzy logic expert system.

Fig. 10. Electromagnetic force vs current flow.


changes from 108N to 300.82 with increasing the current sup-ply from 1.21 to 3.37A. The highest electromagnetic force is 300.82 N, which is much higher than required maximum elec-tromagnetic force 274.82 N. It is supposed to be a linear change with respect to power followed gear ratio.

Fig. 11 shows the travelling time of EMA plunger with varying power supply. It is noted that the plunger of the EMA is only responsible to push and pull the movable sheave of the pulleys. Furthermore, the actuation of the movable sheave of the pulleys makes the car accelerate. Travelling time of the car decreases drastically with decreasing the gear ratio and power supply to the solenoid of EMA. Result shows that the ¼ model car starts from rest with gear ratio 1.8 due to the power supply 14.52, which time is only 3.1 sec. While, the travelling time of the plunger declined almost steadily with the incre-mental power supply and appeared to level off in 1.77 sec until the power reached to its maximum 121.32 watt. This is the sole contribution of this study, which makes the new transmission system EMA-CVT partially energy efficient by reducing transmission losses. Earlier in this study it was re-ported that time taken to accelerate 100 km/h car is 10.20 sec for manual transmission; 0.76 sec for automatic transmission; 7.85 sec for CVT. It would be more if the car starts from rest.

Fig. 11 shows that travelling time (responding time) of the plunger of EMA for pulling mechanism is found significantly lower than that of pushing counterpart. The result indicates that EMA-CVT plunger takes 3.1 sec to push the movable sheave to make a higher gear ratio and 2.257 sec to pull the movable sheave to make a lower gear ratio at lowest current 1.21 amp. The basic reason on taking more time during push-ing is because the higher load on matching area of the sheaves is higher and the pulling of the sheave is found easier than the pushing. Furthermore, clamping releasing force always tends to pull the movable sheave of the pulley towards the solenoid of the EMA, while clamping force pushes the movable sheave against the rotating belt.

Fig. 13 shows the torque characteristics of the final drive. Transmitted torque to the final drive has only 2.74% of aver-

age deviation with respect to gear ratio because of belt slip-page as well as electromagnetic force. Enhanced electromag-netic force could be a better solution for avoiding belt slip. It is noticed that 108 N electromagnetic force is required in the primary pulley to transmit the initial torque when the gear ratio is 1.8. It is also observed that to keep the car in motion the minimum torque needed 32.6 Nm for this ¼ scale car.

4.1 Verification of fuzzy with experiment

Fig. 14 shows the dynamic torque behavior in between 30-90 Nm, which is observed in both experimental and fuzzy simulation during the motion of the car model. Mathematical models used in fuzzy simulation can be verified by comparing the fuzzy data with experimental data. The results of the de-veloped fuzzy logic model have been compared with the ex-perimental results of the EMA as shown in Fig. 15. The corre-lation coefficient of traction torque or goodness of fit is found as 0.9099. It indicates that the predicted data over the meas-ured data have a closed agreement, and thus, validity of the fuzzy simulation results. Relative error of predicted values is in the acceptable limits of 10% (Carman, 2008). The goodness of fit gives the ability of the developed system and its highest value is 1 according to statistical method (Carman, 2008). In this study, according to evaluation criterions of predicted torque performance of the developed fuzzy logic expert sys-tem the model has been found to be valid.

Fig. 12. Pushing and pulling time vs current.

Fig. 13. Wheel torque vs electromagnetic force.

Fig. 11. Travelling time vs power supply.


5. Conclusion

The developed EMA-CVT has a positive impact on car performance in terms of fast acceleration by fast actuation response and remarkable reduction of transmission loss. Kinematics of EMA is done to obtain the clamping force required to hold the pulley sheave to its required position, which is in the range of 101.22 N-274.82N. On the basis of electromagnetic force of the EMA and clamping force, mathematical equations are established for simulating the EMA-CVT system response followed by a fuzzy logic ex-pert system (FLES). The performance of EMA-CVT is in-vestigated.

Theoretically: (i) The EMA is able to develop electromagnetic forces in

the range of 101.22 N to 274.82N equivalent to the clamping forces by supplying current in the range of 1- 4 amps with 24 volts.

(ii) The EMA-CVT is able to develop the electromagnetic

forces 101.22–274.82 N and dynamic torque 31.38 - 85.19 Nm at transmission gear ration 0.820 - 2.369.

(iii) The fuzzy simulation represents the time required reaching the desired maximum torque 85.19 Nm is 3.75sec.and the corresponding current is 4.5 or the maximum desired torque 85.19 Nm.

Experimentally: (i) The EMA develops electromagnetic force in the range of

108–301 N, which has been maintained with supply current maximum 3.37 A.

(ii) The traction torque has been estimated maximum 90 Nm by using the electromagnetic force 301 N, which has been found with the corresponding supplied current 3.37 A for the maximum gear of 1.8.

The correlation between measured (experimental) and pre-

dicted (FLES) values of traction torque was 90.99%, which closely verifies the fuzzy simulation model.

Acknowledgment

This project was financed by the Research Management Centre, International Islamic University Malaysia. It is in pat-ent under the number PI2011-000260 and it was awarded a Gold medal by the Faculty of Engineering Research and Inno-vation Exhibition.

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Fig. 14. Torque verification with experimental and fuzzy simulation.

Fig. 15. Correlation between actual and predicted value of torque.


Dynamics, 44 (5) (2006) 387-406. [9] Rahman, Ataur, B. S. Sazzad and A. Hossain, Kinematics

and non-linear control of electromagnetic actuated CVT sys-tem, Journal of Mechanical, Science and Technology, 26 (7) (2012) 2189-2196.

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Ataur Rahman, Ph.D. is a Professor in the Department of Mechanical Engi-neering, Faculty of Engineering, Interna-tional Islamic University Malaysia since 1996. His research interests are green transportation system: EV/HEV, hybrid engine, intelligent power train for hybrid and electrical vehicle, intelligent steer-

ing system and traction control system, electromagnetic actu-ated CVT and intelligent air-cushion vehicle for swamp and peat terrain. He has worked in The University of Tokyo, Japan, as a Visiting Fellow on the development of integrated instru-mentation systems for Autonomous Vehicles. He has pub-lished 100 Journal articles including 60 ISI listed journal from his research work.

energy efficient electromagnetic actuated cvt system

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