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04CVT-30

Dynamic Performance Analysis of a Full Toroidal IVT

A Theoretical Approach

Robert Fuchs and Yasuhiko HasudaMechatronic Systems Research Department

Koyo Seiko Co. Ltd.

Nara, Japan

Iain JamesTorotrak (Development) Ltd.

Leyland, UK

Copyright 2004 SAE International

ABSTRACT

The torque controlled full toroidal IVT (Infinitely VariableTransmission) provides significant fuel economy benefitover conventional stepped ratio transmissions. This isachieved, in part, by using high overdrive ratios. Thisbenefit must be provided alongside good driveability,which requires the system to have a fast response whilebeing well damped.

This paper gives a theoretical overview of the dynamicresponse of the IVT focusing on different interactionsbetween the full toroidal variator and hydraulic controlcircuits. The concept of system stability is applied tosub-systems and their interactions to indicate designrequirements of this torque controlled transmission.

INTRODUCTION

Despite their inherently low efficiencies compared toconventional stepped ratio transmissions, IVTs andCVTs (Continuously Variable Transmission) allow amore efficient system operation by shifting the engine

operating points for a certain power demand towardhigher torque and lower speed. High overdrive istherefore required, alongside fast response to delivergood driveability. A torque controlled full toroidal IVToffers many advantages to achieve those requirements.The full toroidal variator has the widest ratio range of allCVTs. It is torque controlled instead of the conventionalratio control, which has a number of benefits includingproviding faster response. Two main interactions affect atorque controlled IVT. They are the variator-hydrauliccontrol circuit interaction and the variator-drivelineinteraction. Both must be fully understood to achieveproper system response. This paper is focused only on

the variator-hydraulic interaction.

By applying the types of analyses outlined in this paper,it is possible to predict behavior and design the systemto ensure optimal response.

APPROACH

This analysis is based on previously published work onvariator and IVT driveline modeling and validation [1][2].Firstly, the full toroidal variator is analyzed. The twomechanisms dictating its behavior are described before

investigation of its frequency response. Two generichydraulic control circuits are introduced and theirinteractions with the variator are discussed. Then, thevariator and hydraulics are considered as a system to beintegrated into a powertrain. Further hydraulicoptimizations and methods of input control areintroduced to obtain appropriate system responsematching driveability requirements. Figure 1 gives anoverview of the interactions in the system.

Figure 1: IVT driveline interactions: variator-hydraulic and variator-

driveline (engine and vehicle).

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CONCEPTS OF STABILITY

The objective of this section is to give an overview of themathematical concepts used to describe stability. TheIVT is composed of nonlinear SISO (Single Input, SingleOutput) and MIMO (Multiple Inputs, Multiple Outputs)

systems. Model validation has shown that only softnonlinearities dominate the behavior of these systems[2]. Hence, classical linear techniques such aslinearization and frequency domain analysis can be used[3].

INTERNAL STABILITY - Internal stability is a conceptrelated to linear SISO and MIMO systems of the form:

(t) = (t)+ (t)

(t) = (t)+ (t)

x Ax Bu

y Cx Du (1)

The state-space representation gives access to internal

variables or states x(t) [4]. The internal stability isdemonstrated by computing the eigenvalues of thematrixA:

The system is internally unstable if at least one ofthe eigenvalues of the matrix A is strictly in theright- half of the complex plane.

The system is internally asymptotically stable if alleigenvalues of the matrix A are strictly in the left-half of the complex plane.

The system is marginally stable if all eigenvalues ofthe matrix A are strictly in the left-half of thecomplex plane but at least one is on the imaginaryaxis. If the state-space model results from thelinearization of a nonlinear model, no conclusioncan be drawn as to the stability of the original model.

BIBO STABILITY - The BIBO (Bounded Input BoundedOutput) stability concept states that a linear timeinvariant (LTI) SISO system is BIBO stable if all boundedinputs generate bounded outputs. The BIBO stability isinherently an external concept where only input andoutput are concerned. LTI SISO systems described byrational transfer functions are BIBO stable if and only if

all poles are strictly in the left half of the complex plane[5].

NYQUIST CRITERION - The Nyquist criterion is basedon the stability of a negative unity-feedback controlsystem with loop transfer function K(s)H(s). If thecompensator (or control law) K(s) is properly designed,the closed-loop system will be stable and the

point ( )1/ 1K s = will not be encircled by the Nyquistcontour of the open-loop transfer function K(s)H(s). Thisdescribes the simplified Nyquist stability criterion. FullNyquist stability criterion states that a closed-loopsystem is stable if the point -1 is encircled in the

anticlockwise Ptimes by the Nyquist contour ofK(s)H(s).Where P is the number of poles in the right-half plane.

The simplified criterion corresponds therefore to thespecial case where P=0.

FREQUENCY RESPONSE OF THE FULL

TOROIDAL VARIATOR

DESCRIPTION OF THE FULL TOROIDAL VARIATOR -The full toroidal variator is the main sub-system of theIVT (Figure 2). It is a traction drive unit that transmitspower between smooth surfaces by low-rate shearing ofthin films of fluid between two sets of two discs andthree rollers. Each roller is mounted on a carriageoriented at a castor angle with a perpendicular line to thevariator centerline for self-alignment. A hydraulic pistonholds the extremity of the carriage through a sphericalbearing providing the necessary degree-of-freedom(Figure 3). Hydraulic pressure applied in the cylindergives a direct control of the traction forces at bothcontacts. The full toroidal variator is therefore torque

controlled. The speed ratio is an effect and isdetermined by the input and output speeds.

Figure 2: Dual cavity full toroidal variator.

TWO MAIN MECHANISMS The dynamics of thevariator results from the combination of two mechanismsaffecting the rollers restrained in the toroidal shape ofthe cavities. These mechanisms are the traction drive,which permits the power to be transmitted throughcontact points and the steering geometryorcastor angle

of the roller carriage, which enables roller self-alignment.

Traction Drive - Traction allows the transmission ofpower through loaded contacts between smoothsurfaces. The traction fluid has a high viscosity pressureindex. When the fluid trapped in the contact area ispressurized, the local fluid viscosity increases so that thefilm supports a substantial load force without permittingthe metal parts to come in contact. Only low shear ratesof about 1% of the roller tangential velocity arenecessary to produce the tangential drive forces

required. A traction coefficient is defined as the ratio oftraction force Ft over load force Fl.

t

l

F =

F(2)

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Figure 3: Full toroidal variator geometry. Only one cavity and one roller

are displayed. The variator is composed of 2 cavities and 6 rollers.

Furthermore, the traction coefficient can be obtainedfrom a traction curve where traction coefficient versus

slip ratio ( ) = f s is plotted (Figure 4). The slip ratio isdefined as the ratio between slip and average contact

speed or entrainment speed = / es v v .

Figure 4: Traction curve plots of continuous and pseudo-linear models.

Operation of the variator requires that the tractioncoefficient never exceed its peak value. Above whichgross slip occurs resulting in failure. Traction control isachieved by appropriate piston force and endload forcesettings. Referring to the variator model [1], the staticcontrol law for the piston and endload force is obtained

using the equation governing the piston motion, insteady state, considering small angle and equivalenttraction forces at both input and output contacts:

( )2

3 cos

p

e

F

F

= (3)

This control law gives a basic requirement for theoperation of the variator and defines one of theconditions that should be fulfilled by the hydraulic controlcircuit.

Roller Self-Alignment - As depicted in Figure 3, the roller

carriage and piston are oriented with a castor angleproviding a self-alignment function. This angle plays thesame role as the castor angle in a steering system. Noposition control is therefore required. The roller motion isstable and depends only on three external forces: atraction force at each input and output contact and thepiston reaction force. To ensure roller steering stability, itis necessary to select the direction of castor anglerelative to the direction of rotation of the discs.

In this section, it has been shown that for appropriateinput settings and rotation directions of discs and rollers,the variator is stable. Input disc speed and output disc

speed should have appropriate directions and remainwithin the limits of acceptable speed ratio. The endloadforce and piston force should satisfy the control law (3).To get a more accurate insight of variator stability, alinearized model is presented in the next section.

LINEARIZATION OF THE VARIATOR MODEL Thevariator is a nonlinear multi-variable system, whichcomprises 4 inputs (input speed, output speed, endloadforce and piston force) and 4 outputs (input torque,output torque, piston position and piston velocity).Linearization of this model has been justified already, asonly soft nonlinearities are dominant. However, further

insight into the variator nonlinearities is carried outbefore developing the linearized model.

Static Response - Only two static relationships betweeninputs and outputs are of interest. The first is the piston

position mostly affected by the speed ratio o/i (Figure5). Piston force has only little effect, which is almostlinear because the roller motion is very small. Itcorresponds physically to the slight change of rollerposition to produce the amount of slip necessary tobalance the piston force. The second major dependencyis the effect of the speed ratio and the piston force onthe torques or, in other words, the torque controlfeature

of the variator (Figure 6). As these three inputs aredecoupled, they have decoupled effect on the variatortorques. Torques vary linearly with piston force (or

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pressure) and nonlinearly with speed ratio as it affectsthe contact position ri,o.

( ) ( ), , ,, ,i o i o i o ti o pT r s F F = G GG

(4)

This is the main property that makes the full toroidalvariator different from other CVTs. Conventional CVTsare ratio controlled with a single variable (pulley position)

function ( )CVT CVT pi i x= and their torque dependsmainly on the speed ratio. In the full toroidal variator, thetorques are directly controlled by both piston reactionforce and speed ratio.

These results show that no hard nonlinearities affect thevariator justifying the application of linear techniquessuch as linearization and frequency analysis.

Figure 5: Static piston position in function of input speed and variator

ratio. Piston and endload pressures set to 2MPa.

Figure 6: Torque control: effect of piston pressure (or force) and speed

ratio on input torque. Input speed set to 2000rpm.

Variator Linear Model Due to the toroidal geometryand the two mechanisms described above, themathematical formulation of the variator model is

complex. Reconsideration of the variator modeldescribed in [1] based on a frame of reference locatedon the contact plane and using a decomposed traction

model in the two directions of slip has permittedsubstantial simplifications. Additional simplificationshave been made before linearization. These comprise ofconsidering small angles or speed ratios close to 1:1.The linearized model can be written

11 11 12

22 21 22

33 33

13 11 12 13

23 21 22 23 24

32 33

0 0 00 0 0

0 0 0 0

0 0 0

0 0

0 0 0 0 0

r r

ir

o

e

m c cm c c

m c

k n n n

k n n n nF

k kF

+ +

+ =

"

"

(5)

where the inertia matrix elements are

11

22

33

z

r t

y

m I

m M R

m I

=

=

=

(6)

The damping matrix elements are

( )

( )

( )

( )

( ) ( )

11 1 1

12 1 2

21 1 2

22 1 1

233 1 1

, ,

, ,

, ,

, ,

cos , ,

r i o

t i o

i o

c i o

r i o

c R f

c R f

c f

c k f

c R f

=

=

=

=

=

(7)

The stiffness matrix elements are

( ) ( )

( ) ( )

( ) ( )

( ) ( ) ( )

13 1 3

23 1 4

32 1 1

33 1 1

cos , ,

cos , ,

cos , ,

sin cos , ,

r i o

i o

r r i o

r r i o

k R f

k f

k R f

k R f

=

=

=

=

(8)

Finally, the input matrix elements are

( )( )

( )

( )

( )

( )

( )

11 1 5

12 1 6

113 7

121 5

122 6

123 8

24

, ,, ,

, ,

, ,

, ,

, ,

cos

i r

o r

i oe

i rr

o rr

i oe

n fn f

n fF

n fR

n fR

n fF

n

= =

=

=

=

=

=

(9)

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where 1 is a function of the variator parameters,

/c t rk R R= is the compactness ratio and f1(i,o,) to

f8(i,o,) are slip dependent functions.

This linearization has been validated against thenonlinear model in time and frequency domains. Figure

7gives an example of Bode diagrams of each input toeach output. The frequency responses feature oneresonance peak at about 30Hzdue to the combination oftraction with the steering geometry. Furtherinterpretation of the variator frequency response can bemade by considering only the 3 diagrams related to theinteractions of variator-hydraulic and variator-driveline.They correspond to the transfer function of input torqueversus input speed, output torque versus output speedand piston speed versus piston force. The general high-pass tendency of the two speed-torque responsescomes from the traction mechanism. At low frequency,disc speed change is too slow to cause significant slip

change. The roller merely follows speed ratio. However,at high frequency, slip increases producing highertraction coefficient and therefore higher torque. Thistendency ends with the input perturbation amplitude as itlimits the slip. For the piston force versus piston speedtransfer function, it is easier to look first at the pistonforce versus piston position. In this case, the tendency isopposite and gives a low-pass characteristic but for the

same physical reason. The piston force versus pistonspeed transfer function is simply obtained by derivation.

Finally, piston force-torque transfer functions giveanother illustration of torque control as their Bodediagrams feature merely constant gains.

Dominant Parameters The equation of roller steer or

tilt permits to identify the dominant parameters andstates. From the variator linear model (5), the tiltequation can be written

( ) ( )cos sin 0rI + + = (10)

where( ) ( )1 1cos , ,

y

r i o

II

R f = .

Hence, it appears that the variator damping depends on

castor angle while the stiffness depends mainly on rollerspeed. Thus, variator damping is defined by design, ascastor angle is a parameter. On the other hand, variatorstiffness is not fixed. It varies with roller speed, which is

a state. Roller tilt and roller center position are coupled

by the term ( )sin , which represents the

geometrical constraint of the toroidal cavity.

Figure 7: Bode diagram of the full toroidal variator. Working point set fori=200rad/s, ratio=-1, Pe=Pp=2MPa.

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Numerically generated Bode diagrams of the nonlinearmodel validate the effect of these two dominantparameter and state (Figure 8and Figure 9).

Figure 8: Damping influence of castor angle. Bode diagram of pistonspeed versus piston force. i=200rad/s, ratio=-1, Pe=Pp=2MPa.

Figure 9: Stiffness influence of roller speed. Bode diagram of piston

speed versus piston force. i=200rad/s, ratio=-1, Pe=Pp=2MPa.

Other main parameters are roller mass or inertia andendload force. Roller mass has an effect on variator

damping. However, this effect can be neglected ifassuming relatively low roller inertia compared to thetraction forces. Endload force is not dominant but affectsvariator response mainly by shifting the gain. Becausethe endload force is an input, it can be controlled inorder to optimize variator performance.

Variator Stability Although variator stability has beenintroduced intuitively with the two basic mechanisms, amore formal demonstration is needed. The internalstability concept is used. Computation of theeigenvalues of the matrix A indicates that all are locatedin the left- half of the complex plane confirming the

internal stability of the variator. For example, in the casewhere i=200rad/s, ratio=-1 and Pe=Pp=2MPa, the

eigenvalues are p1,2=-40206i, p3=-1.36e4, p4=-2.72e4,p5=-4.73e4. The two first conjugate complex eigenvaluesare dominant showing again the under dampedcharacteristic of the variator dynamic. Figure 10showsroot-locus maps of these two eigenvalues with castorangle and roller speed as parameter. For castor angle of

0 and 90, the variator is marginally stable, as the self-alignment effect does not exist. Marginal stability is alsoobtained for roller speed null indicating that if the variatoris not rotating, traction and roller self-alignment are notoperational. Critical damping is obtained for castor angle

of about 61.2. These results were illustrated in the Bodediagram ofFigure 8.

(a)

(b)

Figure 10: Root-locus map of the full toroidal variator with castor angle

(a) and roller speed r (b) as parameters. Only the two dominant

poles are represented.

VARIATOR-HYDRAULIC INTERACTION

Hydraulics are used to generate endload and pistonforces (controlling reaction torque). Basic requirementsof the hydraulic control circuit are to satisfy the controllaw (3) and an actuation (solenoid valve) for pistonpressure control. The analysis of the interaction variator-hydraulics concerns only the piston force or pressure.The endload actuation is assumed ideal.

The mechanism of variator interaction can be viewed asfollows: consider the variator at steady state and aconstant pressure demand is set on hydraulic actuators.If the engine speed suddenly changes, it causes thevariator ratio to change inducing a roller motion. Theassociated piston translation induces a flow and acorresponding pressure perturbation in the hydraulic

circuit. Because of the proportional relationship of pistonpressure to torque, the load on the engine changes

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causing potential engine speed variation and so on. Thehydraulic interaction corresponds to the piston motionproducing a pressure perturbation feedback to thevariator. Figure 11 gives the block diagram of thisclosed-loop system.

Figure 11: Variator-hydraulic interaction.

PRESSURE CONTROL CIRCUIT - Two genericpressure control circuits are considered as they cover awide range of possible solutions for torque controlledvariator actuation. They are based on two different typesof valve: flow control valve (FCV) and pressure-reducingvalve (PRV) (Figure 12). The first features a spoolposition dependent on control current only. The secondhas a spool which position depends on control currentand pressure (pressure feedback).

(a)

(b)

Figure 12: Pressure control circuits based on a flow control valve (a)

and on a pressure-reducing valve (b).

Flow Control Valve Circuit - Using a flow control valvefor pressure control is not conventional. Despite,disadvantages such as nonlinear pressure-control

current relation and spool stiction, flow control valvescan be very simple and spool position or orifice area aredirectly related to the control current. The spool position

is therefore independent from pressure changes. This isan advantage for the hydraulic performance, as pressureperturbation will not cause spool oscillation. Thehydraulic concept, shown in Figure 12(a), uses a pumpdelivering a constant flow to the circuit and a valvedefining the circuit pressure.

The Bode diagram of the transfer function piston force

versus velocity ( / pF x ) shows that the hydraulic circuit

behaves like a low pass filter. The cut-off frequencydepends on system parameters and on the loadpressure (Pp). Figure 13 depicts the frequency responseof the hydraulic circuit for different pressure levels. Itshows that for higher pressure, the static gain increasesand the cut-off frequency decreases. Over the variatorpressure range (0 to 3MPa), the cut-off frequency variesfrom about 90to 500Hz.

BIBO stability of this circuit is straightforward and can be

easily demonstrated algebraically.

Figure 13: Bode diagram of the transfer function piston force-speed of

the flow control valve based hydraulic circuit for different load

pressures

Pressure-Reducing Valve Circuit - Pressure-reducingvalves feature a proportional control of pressure over

solenoid current and low hysteresis. Although thesecharacteristics are better than the flow control valve interms of variator actuation, spool position is sensitive topressure. This means that interaction between variatorand hydraulics will cause spool movement. The circuitconcept shown in Figure 12(b) uses a pump connectedto a relief valve to act like a constant pressure source.The pressure-reducing valve connected between thepressure source and the piston control the load pressure.

The Bode diagram for this system is shown in Figure 14.The fundamental difference compared to the circuitusing flow control valve appears as the pressure-

reducing valve has a resonance peak. Although, theresonance frequency and magnitude depends on thevalve design, the dominant parameter is the load

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compliance. A small volume or high bulk modulus makesthe circuit stiffer and less damped. Furthermore, theresonance frequency appears to be within the frequencyrange of the variator resonance. Although, the oscillatorybehavior of the pressure-reducing valve is not a problemspecific to the IVT, conventional hydraulic techniques

may be used to avoid any possible hydraulic instability.Commonly, a compliance valve would be used to satisfythis requirement.

Figure 14: Bode diagram of the transfer function piston force-speed of

the pressure-reducing valve based hydraulic circuit for different load

compliances.

INTERACTION VARIATOR-HYDRAULIC Simplifiedopen and closed-loop block diagrams of the variator-hydraulic system are given in Figure 15. They show thestructure of the interaction and the variables investigatedin the following paragraphs.

(a)

(b)

Figure 15: Open-loop (a) and closed-loop (b) block diagrams of the

variator-hydraulic system.

Interaction Variator-Flow Control Valve Circuit -Connection of the variator with the flow control valvebased hydraulic circuit shows no concern in terms ofstability. The Nyquist plot of the piston force open-loop

transfer function of the variator-hydraulic systemdemonstrates stability because the point -1 is notencircled (Figure 16).

The hydraulic circuit affects the system primarily in termsof damping. Figure 17shows variator-hydraulic closed-loop responses of piston speed-force transfer function atdifferent disc speeds. If compared to Figure 9, the effectdamping clearly appears. The peak of resonance stillfollows the roller speed but its gain is attenuated and itsphase transition smoothed. The reason is that as thedisc speed increases the variator resonance peak ismoving toward the hydraulic cut-off frequency causingattenuation of the variator response.

Figure 16: Nyquist plot of piston force open-loop transfer function of

variator-hydraulic using flow control valve. The stability isdemonstrated, as the point -1 is not encircled by the Nyquist curve.

i=200rad/s, ratio=-1, Pe=Pp=2MPa.

Figure 17: Bode diagram of piston speed-force closed-loop transfer

function of variator-hydraulic using flow control valve at different disc

speeds illustrating hydraulic damping. Ratio=-1, Pe=Pp=2MPa.

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Interaction Variator-Pressure-Reducing Valve Circuit -Concern about the variator stability when actuated with apressure-reducing valve exists as both variator andhydraulic circuit responses have resonance peaks atsimilar frequencies. Furthermore, stability of the valve isdependent on hydraulic compliance defined by circuit

volume and bulk modulus. Appropriate choices duringsystem design can easily satisfy the requirements forachieving stability and system response. However, thepressure reducing valve case is interesting as ithighlights the importance of every sub-system dynamicon overall system response. Thus, system design shouldsatisfy all dynamic response requirements to offeroptimal system performance. Figure 18 depicts aNyquist plot example of the piston force open-looptransfer function of the variator-hydraulic system. As thepoint -1 is not encircled by the Nyquist contour, thesystem is stable.

The worst-case situation appears when the peaks of thevariator and hydraulics responses are aligned. In thiscase, although both sub-systems are independentlystable, their interaction is not necessarily stable. Asdiscussed previously, appropriate hydraulic design willensure that the system satisfies the requirements forstability and response.

Figure 18: Nyquist plot of piston force open-loop transfer function

illustrating stable variator-hydraulic using pressure-reducing valve

interaction. i=200rad/s, ratio=-1, Pe=Pp=2MPa and V0=1l.

Figure 19: Bode diagram of piston speed-force closed-loop transfer

function of variator-hydraulic using pressure reducing valve at different

disc speeds illustrating hydraulic damping. Ratio=-1, Pe=Pp=2MPa andV0=1l.

This hydraulic circuit also produces a hydraulic dampingeffect. The reason is the same as for the flow controlvalve based circuit. Figure 19 depicts the closed-looppiston speed-force transfer function and clearly showsthe two peaks. The resonance from the hydraulic circuitis fixed at 30Hz while the variator peak is moving from 7

to 100Hz. Worst case appears for a disc speed of about200rad/s where both peaks are aligned rising the gain ofthe open-loop transfer function above 0dB. However,because of the effect of phase shift due to hydrauliccompliance, the interaction remains stable.

VARIATOR SYSTEM DAMPING

When connected to a driveline, the variator system(variator + hydraulic) may need additional tuningcapability of its response to achieve the required level ofdriveability. This concerns mainly damping. Twosolutions related to the hydraulic are presented in thissection.

DIFFERENTIAL HYDRAULIC

Until this point, only single side piston actuation wasconsidered (Figure 12). This is because it was sufficientto describe the dynamics of the hydraulic circuits andtheir interactions with the variator. More accuratedynamic representation should account for thedifferential structure of the hydraulic circuit. Figure 20shows the differential structure of the flow control valveand the pressure-reducing valve based circuits.

(a)

(b)

Figure 20: Differential hydraulic circuits using flow control valve (a) and

pressure-reducing valve (b).

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Operation of the variator consists of using the hydraulicto apply a reaction force against the roller traction forces.

Actuation of this reaction force allows force or torquecontrol of the variator. If assuming single side actuation,

piston force is defined as 1 1p pF F F= + where 1F is

the force working point and 1F the variation of this

force due to piston speed perturbations. The reactionforce is the result of the absolute pressure times thepiston area. The other side of the piston is considered tohave no pressure. When the differential structure isconsidered, the piston force or differential force is

1 2 1 2p p p pF F F F F = + + with the indices p1 and p2

referring to the hydraulic circuit at each side of the piston.It can be seen that for same differential force working

points ( )1 2p pF F , the force variations are summed

( )1 2p pF F + resulting in a modified dynamic behavior.

Figure 21 shows that for the hydraulics using flowcontrol valve, increasing the absolute pressures butkeeping a constant differential pressure increases theresponse gain and reduces its bandwidth. It is the sameeffect of load pressure as illustrated in Figure 13 butdecoupled from the reaction force.

Figure 21: Piston speed-force response of the circuit using flow control

valve for different absolute pressures but with a same differential

pressure 0Pa.

Figure 22shows the variator system piston force-speedresponse using a differential flow control valve circuit.The main effect observed is of a damping nature.Control of an IVT should account for this damping orstabilizing effect of piston motion. Pressures Pp1 and Pp2of an IVT are controlled in a way that the non-active sideis set to a bias pressure while the other varies to controltorque. This has two merits. First, it gives a way to tunethe system response to obtain the required driveability.Second, it offsets the flow control valve pressure

working points away from the saturation of their current-pressure static response. This results in a slightly

linearized response of the valve, which simplifies IVTdriveline control. The damping property is also used atgeared neutral. Normally, no differential pressure shouldbe set except for creep. In this case, instead of settingboth pressures to 0Pa, they are set to certain levelsatisfying the condition of no differential pressure but

increasing damping.

Figure 22: Variator system using flow control valve differential circuit.

Bode diagram of the piston force-speed transfer function for different

absolute pressures but with a same differential pressure

0Pa.i=200rad/s, ratio=-1.

This damping effect is not as obvious for the hydraulicusing pressure-reducing valve because the valveresponse is independent from load pressure.Comparison between single and differential hydrauliccircuit responses shows only a gain offset while thephase remains unchanged.

DAMPING ORIFICE

Another solution to damp the hydraulic circuit is toimplement damping orifices between each cylinderchamber and valve (Figure 20). These orifices avoid thedirect effect of piston speed perturbations on the valves.

Frequency response of a single side hydraulic systemusing pressure-reducing valve and restrictiondemonstrates the pure damping effect as the orifice areadecreases (Figure 23). In the variator system, therestrictions damp the oscillation of piston. This effect isdominant especially when hydraulic and variatorresonance peaks are aligned (Figure 24).

Hydraulic circuits using flow control valves are alsoaffected by damping orifices but in a less obvious wayas those valves are not sensitive to flow perturbations.Damping orifices can be used in this case only for fine-tuning of the transmission response.

Here, circular orifices were used to demonstrate theprinciple of this damping effect. Other shapes or

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arrangement of restrictions can be design specifically toobtain optimized system response.

Figure 23: Bode diagram piston force-speed of the hydraulic using

pressure-reducing valve and a damping orifice. As the area of therestriction decreases, damping increases. Pp0=2MPa.

Figure 24: Variator system using pressure-reducing valve with damping

orifice. Bode Diagram of the piston force-speed transfer function for

different orifice areas. In this case, both variator and hydraulic

resonance peaks are aligned. i=200rad/s, ratio=-1 and Pe=Pp=2MPa.

CONCLUSION

This investigation on the performance and mechanismsof the variator-hydraulic interaction of a full toroidal IVT

driveline is a key step in a theoretical approach ofsystem design. The stability of each sub-system hasbeen demonstrated. This has allowed a more in depthinvestigation of these sub-systems performanceresulting in the identification of the dominant parametersaffecting response. Variator-hydraulic interaction was

investigated. Two generic hydraulic circuits wereconsidered. They have shown to have a damping effecton the variator response. Furthermore, solutions to tunethe IVT response have been introduced. They giveadditional control and design flexibilities to optimize thesystem response and achieve optimal driveability.

Key explanations about the mechanisms affecting theresponse of the full toroidal variator system and itsstability were given relatively to dominant parameters. Ithas also been shown that the use of this analysis at thedesign stage can provide a system optimized for fast butwell damped response. Extension to the complete IVTdriveline (variator + hydraulic + driveline) response andcorrelation of data from these analyses to implicationson driveability is beyond the scope of this paper but willbe detailed in future publications.

REFERENCES

[1] R. D. Fuchs, Y. Hasuda, I. B. James, Full Toroidal

IVT Variator Dynamics, SAE paper 2002-01-0586,

March 2002.

[2] R. Fuchs, Y. Hasuda, I. James, Modeling,

Simulation and Validation for the Control

Development of a Full-Toroidal IVT, CVT2002

Congress, VDI-Berichte 1709, October 2002.[3] J.-J. E. Slotine, W. Li, Applied Nonlinear Control,

Prentice Hall, 1991.

[4] R. Vaccaro, Digital Control: a State-Space

Approach, Mc Graw-Hill, 1995.

[5] R. Longchamp, Commande Numrique de

Systmes Dynamiques, PPUR 1995.

CONTACT

Questions or comments can be written to the followingaddresses: robert_fuchs@koyo.seiko.co.jp (in French orEnglish) or yasuhiko_hasuda@koyo-seiko.co.jp (in

Japanese).