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Proceedings of ASME-IMECE’07 2007 ASME International Mechanical Engineering Congress and RD&D Expo November 11-15, 2007, Seattle, Washington USA IMECE2007-42559 HIGH SPEED ROTARY PULSE WIDTH MODULATED ON/OFF VALVE Haink C. Tu, Michael B. Rannow, James D. Van de Ven, Meng Wang, Perry Y. Li and Thomas R. Chase Center for Compact and Efficient Fluid Power Department of Mechanical Engineering University of Minnesota 111 Church St. SE Minneapolis, MN 55455 Email: {tuxxx021,rann0018,vandeven,wang134,pli,trchase}@me.umn.edu ABSTRACT A key enabling technology to effective on/off valve based control of hydraulic systems is the high speed on/off valve. High speed valves improve system efficiency, offer faster control band- width, and produce smaller output pressure ripples. Current valves rely on the linear translation of a spool or poppet to meter flow. The valve spool must reverse direction twice per PWM cy- cle. This constant acceleration and deceleration of the spool re- quires a power input proportional to the PWM frequency cubed. As a result, current linear valves are severely limited in their switching frequencies. In this paper, we present a novel PWM on/off valve design that is based on a unidirectional rotary spool. The on/off functionality of our design is achieved via helical bar- riers that protrude from the surface of a cylindrical spool. As the spool rotates, the helical barriers selectively channel the flow to the application (on) or to tank (off). The duty ratio is con- trolled by altering the axial position of the spool. Since the spool no longer accelerates or decelerates during operation, the power input to drive the valve must only compensate for viscous fric- tion, which is proportional to the PWM frequency squared. We predict that our current design, sized for a nominal flow rate of 40l /m, can achieve a PWM frequency of 84Hz. This is roughly a 400% improvement over current designs. This paper presents our valve concept, design equations, and an analysis of predicted performance. A simulation of our design is also presented. 1 Introduction On/off (or digital) valve based control of hydraulic systems is an energy efficient alternative to control via throttling valves. In either the on or the off state, energy loss is minimized since either the pressure drop across the valve is small or the flow through it is zero. When the on/off valve is pulse width mod- ulated, the average pressure or flow can be controlled. Our pre- vious papers [7] and [6] have proposed and modeled the use of a PWM on/off valve with a fixed displacement pump to achieve the functionality of a variable displacement pump. A critical require- ment for practical on/off valve based control is the availability of high speed on/off valves. High speed valves improve system ef- ficiency, increase control bandwidth, and reduce output pressure ripple. Commercial on/off valves typically have transition times on the order of 20ms for flow rates of 5l /m-40l /m. Digital valve control with current valves demonstrate a noticeable decrease in system efficiency when operating at PWM frequencies greater than 10Hz [6]. A limitation in conventional valve designs based on linear spool or poppet movement is that the spool/poppet must be started and stopped during each on/off cycle. The power re- quired to actuate the valve is proportional to the 3rd power of the PWM frequency. In this paper, we present a novel fluid driven unidirectional rotary PWM on/off valve design. Our valve spool achieves rotary motion by capturing momentum from the fluid that it meters. Since the spool rotates at a near constant veloc- ity, the power required drive the valve only needs to overcome viscous friction, which is proportional to the frequency squared. A number of high speed hydraulic solenoid or piezo-electric 1 Copyright c 2007 by ASME
Transcript
Page 1: D:/research/PWM/ss3way/ASME paper/IMECE2007 …lixxx099/papers/IMECE2007-42559 Rotary.pdfJune 22, 2007 14:31 Proceedings of ASME-IMECE’07 2007 ASME International Mechanical Engineering

June 22, 2007 14:31

Proceedings of ASME-IMECE’072007 ASME International Mechanical Engineering Congress and RD&D Expo

November 11-15, 2007, Seattle, Washington USA

IMECE2007-42559

HIGH SPEED ROTARY PULSE WIDTH MODULATED ON/OFF VALVE ∗

Haink C. Tu, Michael B. Rannow, James D. Van de Ven, Meng Wang, Perry Y. Li†and Thomas R. ChaseCenter for Compact and Efficient Fluid Power

Department of Mechanical EngineeringUniversity of Minnesota

111 Church St. SEMinneapolis, MN 55455

Email: {tuxxx021,rann0018,vandeven,wang134,pli,trchase}@me.umn.edu

ABSTRACT

A key enabling technology to effective on/off valve basedcontrol of hydraulic systems is the high speed on/off valve.Highspeed valves improve system efficiency, offer faster control band-width, and produce smaller output pressure ripples. Currentvalves rely on the linear translation of a spool or poppet to meterflow. The valve spool must reverse direction twice per PWM cy-cle. This constant acceleration and deceleration of the spool re-quires a power input proportional to the PWM frequency cubed.As a result, current linear valves are severely limited in theirswitching frequencies. In this paper, we present a novel PWMon/off valve design that is based on a unidirectional rotaryspool.The on/off functionality of our design is achieved via helical bar-riers that protrude from the surface of a cylindrical spool.Asthe spool rotates, the helical barriers selectively channel the flowto the application (on) or to tank (off). The duty ratio is con-trolled by altering the axial position of the spool. Since the spoolno longer accelerates or decelerates during operation, thepowerinput to drive the valve must only compensate for viscous fric-tion, which is proportional to the PWM frequency squared. Wepredict that our current design, sized for a nominal flow rateof40l/m, can achieve a PWM frequency of 84Hz. This is roughlya 400% improvement over current designs. This paper presentsour valve concept, design equations, and an analysis of predictedperformance. A simulation of our design is also presented.

1 Introduction

On/off (or digital) valve based control of hydraulic systemsis an energy efficient alternative to control via throttlingvalves.In either the on or the off state, energy loss is minimized sinceeither the pressure drop across the valve is small or the flowthrough it is zero. When the on/off valve is pulse width mod-ulated, the average pressure or flow can be controlled. Our pre-vious papers [7] and [6] have proposed and modeled the use of aPWM on/off valve with a fixed displacement pump to achieve thefunctionality of a variable displacement pump. A critical require-ment for practical on/off valve based control is the availability ofhigh speed on/off valves. High speed valves improve system ef-ficiency, increase control bandwidth, and reduce output pressureripple. Commercial on/off valves typically have transition timeson the order of 20msfor flow rates of 5l/m-40l/m. Digital valvecontrol with current valves demonstrate a noticeable decrease insystem efficiency when operating at PWM frequencies greaterthan 10Hz [6]. A limitation in conventional valve designs basedon linear spool or poppet movement is that the spool/poppet mustbe started and stopped during each on/off cycle. The power re-quired to actuate the valve is proportional to the 3rd power of thePWM frequency. In this paper, we present a novel fluid drivenunidirectional rotary PWM on/off valve design. Our valve spoolachieves rotary motion by capturing momentum from the fluidthat it meters. Since the spool rotates at a near constant veloc-ity, the power required drive the valve only needs to overcomeviscous friction, which is proportional to the frequency squared.

A number of high speed hydraulic solenoid or piezo-electric

1 Copyright c© 2007 by ASME

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Figure 1. Diagram of 3-way rotary spool

actuated linear on/off valves have been proposed since the early1990’s. Yokota et al. [8] and Lu et al. [10] achieved quick end-to-end spool/poppet movement using piezo-electric materials, whileKajima et al. [9] investigated the development of a high speed lin-ear solenoid valve for control in diesel engines. A unidirectionalrotary spool valve was proposed by Cyphelly et al. [11] in 1980for use with hydraulic applications, while Royston et al. [12] pro-posed a unidirectional rotary PWM control valve to improve theresponse of pneumatic systems in high speed automation. In theearly 1990’s, Cui et al. [13] investigated the use of a high speedsingle stage rotary based valve.

This paper presents the concept and design of a fluid drivenrotary on/off valve. Section 2 introduces the functionality anddesign features of our concept. Section 3 provides an analysisof our design including calculations for performance and effi-ciency. A complete system simulation is presented in Section 4,and some concluding remarks are discussed in Section 5.

2 Self-spinning, 3-way Rotary on/off Valve ConceptOur self-spinning, 3-way rotary on/off valve concept is pre-

sented in Fig. 1. The valve spool consists of a central PWMsection sandwiched by two outlet turbines. The central sectioncontains alternating helical barriers overlayed onto the spool sur-face. The helical barriers partition the spool into regionswhereflow is directed to the application (on, red) or to tank (off, blue).As the spool rotates, the inlet nozzles, which are stationary on thevalve sleeve, transition across the barriers and alternatethe flow

Figure 2. Diagram of internal geometry

path between application and tank. The duty ratio, or propor-tion per PWM cycle that the flow is directed to the application,iscontrolled by changing the axial position of the spool. By trans-lating the spool upward relative to the inlet, the inlet willremainconnected to the tank region for a greater portion per rotation ofthe spool. This decreases the duty ratio. The opposite effect willoccur if the spool is translated downwards relative to the inlet.

The rotary motion of our valve spool is achieved by extract-ing momentum from the fluid itself as the valve apportions flowto the application and to tank. The sleeve contains an internalpressure rail (see Fig. 4) that feeds tangential inlet nozzles, whichcreate the fluid momentum. As the high speed fluid is transferredfrom the inlet nozzles to the valve spool, the helical barriers actas turbine blades to capture momentum from the fluid and directit inward toward the center of the spool. As the fluid is directedinward, the momentum in the fluid is transferred to angular mo-mentum in the spool. Once the fluid is at the center of the spool,it is forced to flow axially through an internal axial passagewaythat leads to the outlet stage turbine (see Fig. 2). The outlet stageturbine, similar in functionality to a lawn sprinkler, re-acceleratesthe flow outward and tangential to the spool. The outlet stagere-verses the direction of the fluid relative to the inlet stage,whichresults in a reaction torque on the spool. By utilizing the fluidthat must already pass through the valve for actuation, our self-spinning concept does not require an additional power source foroperation. The self-spinning design is further enhanced bythe3-way configuration of our valve. The 3-way design continu-ously feeds fluid through the valve spool regardless of whetherthe flow is directed to application or tank. This allows the spoolto rotate regardless of duty ratio. When combined with a 4-waydirectional valve, the 3-way functionality of our spool allows thesystem to operate as both a pump and as a motor.

Our valve is packaged as an integrated pump cover/sleevethat can be bolted directly onto existing fixed displacementpumps. This integrated packaging allows us to minimize the inletvolume between the pump and valve (see Fig. 8), thus reducing

2 Copyright c© 2007 by ASME

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Figure 3. Cutaway rendering of rotary spool/sleeve assembly

Figure 4. Detailed rendering of rotary spool/sleeve assembly

energy loss due to fluid compressibility [6]. A diagram of ourvalve assembly is presented in Figs. 3 and 4. Figure 4 revealsa closer look at the interior geometry of our design as well asillustrates many of the design features.

Figure 5. Diagram of unwrapped spool

2.1 Spool Geometry and Design ParametersThe geometry of our spool is presented in Fig. 5, which il-

lustrates the central PWM section of our spool unwrapped fromthe spool surface. The helical barriers unfold into a triangularsawtooth partition. As the spool rotates, the helical barriers trans-late across the inlets and fluid is directed from one branch (appli-cation or tank) to the other. Note that the central PWM sectionofthe spool is divided intoN triangular sections corresponding toN inlets. Each triangular section performs one complete on/offcycle. Therefore, there areN PWM cycles per revolution of thespool and the PWM frequency of the valve isN times the spoolfrequency. A description of the relevant design parametersforthe spool geometry is given in Table 1.

The inlet orifice of our design is shaped as a rhombus withsides of lengthRs that are parallel to the helical barriers, as shownin Fig. 5. A rhombus shaped inlet provides a faster rate of changein area (dA

dθ ) than a circular orifice of equal size during the initialand final stages of transition, which can be seen in Fig. 6. Theseare the regions where quick transitions are desirable sincemostthrottling losses occur when the inlet orifice is just beginning toopen or close. Note that the area gradientdA

dθ is constant for arhombus shaped inlet.

Four transition events occur every PWM cycle in our 3-waydesign: opening and closing of the inlet to the load branch, andopening and closing to the tank branch. The proportion of timethat the valve is in transition is dependent on the width of therhombus inlet,Rw, thickness of the helical barriers,Ht , and thenumber of PWM sections on the spool surface,N. Thus, theproportion of time that the valve is in transition is:

κ =2·N ·

(

Rw + Htsin(β)

)

π ·D(1)

3 Copyright c© 2007 by ASME

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Parameter Description

D Spool diameter

R Spool radius,R= D2

Ls Spool length

L PWM section length

Le Exit section length

Rh Rhombus height

Rw Rhombus width

Rs Rhombus side length,Rs = 12

R2w +R2

h

β Helix angle

Hh Helix height

Hw Helix width

Ht Helix thickness

N Number of helices

Table 1. Definition of parameters

0 0.1 0.2 0.3 0.4 0.50

0.2

0.4

0.6

0.8

1

1.2

1.4x 10

−5

θ (rad)

Ope

n O

rific

e A

rea

(m2 )

CircleRhombus

Figure 6. Open orifice area during transition

0 ≤ κ ≤ 1. Physically,Rw is constrained such that 0≤ κ ≤ 1while Rh is constrained by the length of the PWM section of thespool, orRh < L. Ideally, κ must be small to minimize the pro-portion of each PWM cycle that the valve is in transition. Sinceour valve is least efficient during transition, decreasingκ will in-crease the efficiency of our valve.κ can be decreased by settingRw to be small, orD to be large. Both cases, however, increasethe surface area of the spool, which increases viscous friction anddecreases the spool velocity.

The sizing of the rhombus shaped inlet orifice areaAin and

outlet turbine exit areaAout (see Fig. 16) represent a direct trade-off between the spool rotational velocity, valve transition time,and fully-open throttling losses. We define∆Popento be the pres-sure drop across the rhombus inlet when it is fully open, and∆Pexit to be the pressure drop across the outlet turbine exit. When∆Popenor ∆Pexit is large, more kinetic energy is transferred to thefluid resulting in a higher spool velocity. This speed, however,is attained at the cost of greater throttling losses.Ain andAout

are sized in our current design such that the fully open throttlinglosses do not exceed some maximum acceptable value. Sincethe flow rateQ of the system is constant, the maximum throttlingloss requirement limits the pressure drop across the inlet and out-let stages, which determinesAin andAout. The maximum fullyopen throttling loss is given byPower= (∆Popen+ ∆Pexit) ·Q.Ain andAout can be calculated using the orifice equation, whichis defined as:

∆P =ρ2

(

QCd ·A·N

)2

(2)

ρ is the density of hydraulic oil,Cd is the orifice discharge coef-ficient, andA is the cross-sectional area of interest. The height,Rh, and width,Rw, of the rhombus are constrained by the inletarea according toAin = .5·Rw ·Rh.

2.2 Linear Actuation and SensingThe axial position of the spool is actuated hydro-statically

using an electro-hydraulic gerotor pump that is hydraulicallyconnected to both ends of the valve sleeve. A schematic of thehydraulic axial position system is presented in Fig. 7. The DCmotor is powered by a PWM controller H-bridge electrical cir-cuit. By pumping fluid from one end of the sleeve to the other,the axial position of the spool can be varied. The gerotor pumpflow rate is statically related to the input to the DC motor driv-ing circuit. The hydraulic axial control system was chosen for itselegance as well as its simplicity.

The axial position of the spool is measured using a non-contact optical method. A sensor plate with two LEDs and aphotodiode is mounted to one end of the valve sleeve. The lightemitted from the LEDs is reflected off of the surface of the valvespool and sensed by a photodiode in the sensor plate. The lightintensity detected by the photodiode decreases as the distance be-tween the photodiode and spool surface increases. Therefore theposition of the spool can be measured from the output voltageofthe photodiode.

2.3 Rotary SensingThe rotary sensing of the spool is achieved similarly to the

linear sensing. The rotary position and angular velocity ofthespool are measured using a 32 sector code wheel that is attached

4 Copyright c© 2007 by ASME

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Figure 7. Diagram of linear actuation and rotary sensing system

Figure 8. Circuit diagram of PWM variable displacement pump

to one end of the spool. A low-power diode laser module and aphotodiode are mounted on a sensor plate, which is attached toone end of the sleeve. The intensity of the reflected light variessignificantly with the position of the code wheel. This lightin-tensity is detected by the photodiode and is transformed into aproportional voltage signal. A counter is used to store the volt-age information, from which the spool velocity can be calculated.A reference is added to one sector to reset the counter for deter-mining the spool’s axial position.

3 Throttling Loss and Flow AnalysisThe analysis presented in this section is based upon the sys-

tem shown in Fig. 8. The system consists of an ideal flow sourcewith flow rateQ, relief valve set atPrelie f , and a constant applica-tion or load pressure ofPload. An orifice load will be consideredin the simulation discussed in Section 4.Pin is defined as thepressure in the inlet volume, which is the volume upstream of

Figure 9. Change in rhombus area during transition

0 0.5 1 1.5 2 2.50

0.2

0.4

0.6

0.8

1

1.2

1.4x 10

−5

θ (rad)

Ope

n O

rific

e A

rea

(m2 )

Load BranchTank Branch

Figure 10. Open orifice area for 1 PWM period

the valve.This section is organized as follows: Section 3.1 provides an

analysis of the throttling losses experienced by our valve,whileSection 3.2 presents the relationship between the spools’saxialposition and flow. Section 3.3 contains a method of estimatingthe spool velocity and Section 3.4 provides an analysis on theeffect bearing surface area on viscous friction. A preliminaryleakage analysis is presented in Section 3.5, and a summary ofour design is given in Section 3.6.

3.1 Valve Throttling LossesOur valve experiences two types of throttling losses: con-

stant (or fully open) losses that occur across the rhombus in-lets and outlet turbine exits, and transition losses that occur asthe valve opens and closes to application and tank. The regionswhere these two losses occur during each PWM cycle is illus-trated in Fig. 11, which corresponds to the area plots shown inFig. 10. Figures 13 and 12 illustrate the pressure drop across theinlet and flow profiles corresponding to Fig. 10. The total throt-tling power loss for one PWM cycle can be found by multiplyingthe curves in Figs. 12 and 13 together. The result is shown inFig. 14, which reveals that a majority of the energy loss occursduring transition when the relief valve opens and during thetwo

5 Copyright c© 2007 by ASME

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0 0.5 1 1.5 2 2.50

1

2

3

4

5

6

7

8x 10

6

θ (rad)

Inle

t Pre

ssur

e (P

a)

Pload

Pload

Pload

+Popen

Prelief

Popen

Fully open losses

Transition losses

Figure 11. Inlet pressure for 1 PWM period

0 0.5 1 1.5 2 2.50

5

x 10−4

Load

bra

nch

Flow Rate (m3/s)

0 0.5 1 1.5 2 2.50

5

x 10−4

Tan

k br

anch

0 0.5 1 1.5 2 2.50

5

x 10−4

Rel

ief v

alve

θ (rad)

Figure 12. Flow rate through valve for 1 PWM period

0 0.5 1 1.5 2 2.50

2

4

6

8x 10

6

Load

bra

nch

Pressure Drop Across Orifice (Pa)

0 0.5 1 1.5 2 2.50

2

4

6

8x 10

6

Tan

k B

ranc

h

θ (rad)

Figure 13. Pressure drop across inlet orifice for 1 PWM period

0 0.5 1 1.5 2 2.50

5000

Load

Power Loss (W)

0 0.5 1 1.5 2 2.50

5000

Tan

k

0 0.5 1 1.5 2 2.50

5000

Rel

ief

0 0.5 1 1.5 2 2.50

5000

Tot

al

θ (rad)

Figure 14. Transition power loss for 1 PWM period

tank transition events.The first type of loss, the fully open loss, is determined by

the sizing ofAin andAout as described in Section 2.1. The fullyopen loss is estimated by assuming that the full system flowQen-ters and exits the valve throughout the entire PWM cycle whenthe valve is not in transition. As shown in Fig. 11, we only con-sider the fully open losses to occur when the valve is not transi-tioning. The losses that occur acrossAin andAout during transi-tion will be included in the transition losses. Thus, the fully openlosses can be estimated by considering∆Popen, ∆Pexit, Q, andκ:

Poweropen= (1−κ) · (∆Popen+∆Pexit) ·Q (3)

During transition, throttling losses occur because the valvecannot open and close instantaneously. As a result the inletori-fice is partially open during transition, which induces a largepressure drop across the orifice. To estimate the throttlinglossesof our valve during transition, we neglect the short period dur-ing the transition when the inlet orifice is simultaneously opento both load and tank. Assuming that the spool rotates at a con-stant angular velocityω, we expect the transition time for eachtransition event to be equal and given by:

ttrans = 2·

(

Rw + Htsin(β)

D ·ω

)

(4)

Sincettrans is constant, we expect the energy lost during the twotransition events involving the load branch (opening and closing)to be equal, and similarly for the two events involving the tankbranch. We define∆Pon andQload to be the pressure drop andflow though the open orifice areaAopen when the valve is con-nected to the load branch, and similarly define∆Po f f andQtank

6 Copyright c© 2007 by ASME

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for when the valve is connected to tank.Aopen is a function ofthe spool’s angular positionθ, and is determined from geometryto be:

Aopen(θ) = Rs ·R·sin(β) ·θ (5)

We now consider the throttling losses during the two transi-tions to tank. When the inlet orifice is opening, the initial inletpressure is high and the relief valve is open. As the open orificearea increases, the pressure begins to decrease until the reliefvalve closes and the full flowQ is sent through the valve to tank.Initially, when the relief valve is open, the inlet pressureis fixedat Prelie f and flow is being throttled across both the relief valveand inlet orifice areaAopen. During this period, flow is throttledacross both the relief valve andAopenat a pressure drop ofPrelie f .Thus, the energy lost while the relief valve is open is:

Etrans,1 =∫ t=tR

t=0Q·Prelie fdt (6)

tR is the time when the pressure at the inlet is equal toPrelie f

and the relief valve is on the verge of closing. We now use thedefinition ofω = dθ

dt to integrate Eq. 6 with respect toθ:

Etrans,1 =1ω

∫ θ=θR

θ=0Q·Prelie f ·dθ

=Q·Rw

ω ·R·√

Popen·Prelie f (7)

θR is the angular displacement corresponding to the orifice areathat producesPrelie f . At θR, the relief valve closes as the inletpressure just begins to fall belowPrelie f . θR can be calculatedusing the orifice equation, Eq. 2, and Eq. 5.

Once the inlet pressure drops belowPrelie f and the reliefvalve closes, the flow throughAopenis Q and remains constant forthe remainder of the transition.∆Po f f , the pressure drop acrossthe orifice, is calculated using the orifice equation. The energyloss for the remainder of the transition with the relief valve closedis:

Etrans,2 =1ω

∫ θ= RwR

θ=θR

Q·∆Po f f ·dθ

=Q·Rw

ω ·R·√

Popen· (Prelie f −Popen) (8)

The total energy lost during the transition from fully closedto fully open to tank is the sum of Eq. 7 and Eq. 8.

The energy loss during the two transitions involving the loadbranch are calculated in a similar manner. The main difference is

that the inlet pressure is now the pressure drop across the orifice∆Pon plus the load pressure. When the relief valve is open, flowis throttled acrossPrelie f through the relief valve, but only across(Prelie f −Pload) throughAopen. We now consider the transitionwhen the orifice is beginning to open to the load branch. The en-ergy lost during the initial stage of the transition when thereliefvalve is open is:

Etrans,3 =1ω

∫ θ=θR

θ=0(Q−Qload) ·Prelie f ·dθ

+1ω

∫ θ=θR

θ=0Qload · (Prelie f −Pload) ·dθ

=Q·Rw

ω ·R·

Popen

(Prelie f −Pload)·

(

Prelie f −12

Pload

)

(9)

Once the relief valve closes, the remaining energy loss dur-ing the transition is:

Etrans,4 =1ω

∫ θ= RwR

θ=θR

Q·Pon ·dθ

=Q·Rw

ω ·R·Popen·

(√

(Prelie f −Pload)

Popen−1

)

(10)

The total energy lost during the transition from fully closedto fully open to the load branch is the sum of Eq. 9 and Eq.10. The total energy lost for all four transition events, or for onecomplete PWM cycle, is:

Etrans,total = 2· (Etrans,1 +Etrans,2 +Etrans,3 +Etrans,4) (11)

The total power loss due to fully open and transition throt-tling is:

Powertotal = Poweropen+Etrans,total ·N ·ω

2·π(12)

3.2 Output Flow vs. Axial PositionThe relationship between flow to the load and tank branches

with respect to the axial displacement was determined numeri-cally using the Matlab model presented in Section 4. The resultsare shown in Fig. 15. The central portion of Fig. 15 is linear,which is expected given the linear nature of the helical barriershown in Fig. 5. Toward the two extremes of the axial travel theflow levels off. This is when the full flow is directed to eitherload or tank and the inlet does not overlap the barriers at all. Inbetween the linear and level portions of the curve exist nonlinear-ities, which occur due to the junctions where the barriers inter-sect. Note thatQload + Qtank 6= Q due to flow through the relief

7 Copyright c© 2007 by ASME

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0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

1.2

1.4

Normalized Axial Travel

Nor

mal

ized

Flo

w

Load BranchTank BranchLoad+Tank

Pload

=6.9 × 106 Pa

Pload

=2.1 × 106 Pa

Figure 15. Relationship between flow and axial position

valve during transition. Also note thatQload decreases asPload

increases, which is expected since the relief valve opens for agreater proportion of transition for a higher load pressure. This isbecausePin = ∆Pon+Pload≤Prelie f . The total flow,Qload+Qtank,in the linear range of the axial travel between 20%−80%, is es-pecially low (about 90%) due to the relief valve opening duringtransition, which indicates a significant source of energy loss.Methods to reduce or eliminate the energy lost through the reliefvalve must be investigated.

3.3 Spool Velocity AnalysisThe spool rotational velocity was calculated by considering

an angular momentum balance on the spool. The analysis as-sumes incompressible flow and one-dimensional inlets and out-lets. The momentum balance yields:

J · θ = τin + τout− τ f (13)

J is the mass moment of inertia of the spool andθ is the angularacceleration of the spool.τin is the torque generated by the inletstage turbine, andτout by the outlet stage. In the steady state,θ =0 and the angular momentum generated by the inlet and outletstages of the spool are balanced by viscous friction.

The resistive torque due to viscous friction was assumed toobey Petroff’s Law. Petroff’s Law presumes that the torque dueto friction is proportional to the bearing surface area, shear stress,and the moment arm where the shear stress acts on the system[3]. Thus, the torque due to friction is given by:

τ f = Ae f f ·µc·R2 ·ω (14)

R is the spool radius,µ is the dynamic viscosity of hydraulic oil,c is the radial clearance between the spool and sleeve, andAe f f

Figure 16. Sketches of the inlet and outlet turbine stages

is the effective surface area of the spool. TheAe f f is estimatednumerically in Section 3.4 using a simple CFD analysis.

In our current design, the inlet stage of the valve spool hasthe functionality of an impulse turbine, and the outlet stage areaction turbine [4]. A sketch of the inlet and outlet stagesof thevalve as well as the control volumes that were used is shown inFig. 16. The inlet stage of the valve consists ofN stationary inletnozzles located on the valve sleeve tangential to the spool.Theinlets are offset a distanceRin from the center of the spool. In theinlet stage analysis, we consider a stationary control volume thatsurrounds the spool and inlets. This control volume hasN inletsand one outlet, although for simplicity, only one inlet is shown inFig. 16. At the inlets, angular momentum is generated in the fluidas it enters the control volume tangentially. Since the fluidexitsthe control volume through an internal axial passage, we assumethat the fluid exits with no angular momentum, and that all of theangular momentum generated by the inlets is transferred to thespool. Using this control volume approach, the torque generatedby the inlet stage is:

τin =N

∑1

(Rin ×v)in · min =ρ ·Rin

Ain ·N·Q2 (15)

ρ is the density of hydraulic oil,v is the mean velocity of the fluidas it exits the inlet nozzle, and ˙m is the mass flow rate throughthe nozzle.

By equatingτin = τ f , the velocity of the spool generated by

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the inlet stage alone is:

ω =ρ ·Q2

N ·R2 ·Ae f f ·µc

·Rin

Ain(16)

The outlet stage of the valve consists ofN curved bladesthat turn the flow as is travels outward. In the outlet stage tur-bine analysis, we consider a control volume that rotates with thespool. This control volume consists of one inlet, andN rotat-ing outlets, although only one is shown for simplicity in Fig. 16.Fluid enters the outlet stage axially through the internal axial pas-sage which connects the inlet stage to the outlet stage. Since thefluid enters the stage axially, it is assumed to have no angular mo-mentum as it enters the control volume. As the fluid is directedoutward and tangential to the spool surface, a reaction torque isexperienced by the spool as it turns the flow. The outlet stageisassumed to be ideal such that the fluid is completely turned bythe blades. With this assumption, the outlet stage can be thoughtof as a rotating tangential outlet nozzle with areaAout = cout ·Le

offset a distanceRout from the center of the spool. The torquegenerated by the outlet stage is:

τout =N

∑1

(Rout×(v−vCV))out ·mout =ρ ·Rout

Aout ·N·Q2−R2

out ·ρ ·ω ·Q

(17)vCV = Rout ·ω is the velocity of the control volume.

Equating the inlet and outlet torque to the friction torque inthe steady state produces the equation forω, the angular velocityof the spool generated by both stages:

ω =ρ ·Q2

N ·R2 · (Ae f f ·µc +

R2outR2 ·ρ ·Q)

·Rin

A(18)

From Eq. 18, we see that the combined inlet and outlet effectscan be normalized such that the system resembles an inlet onlyconfiguration.A is defined as the equivalent area, and is givenby:

1

A=

1Ain

+Rout

Rin ·Aout(19)

Note that settingRout = 0 reduces Eq. 18 to the inlet turbine onlycase.

Eq. 18 illustrates the dual effects of the outlet stage tur-bine on the spool velocity. Rout

Rin·Aoutcorresponds to the angular

momentum generated by the tangential outlet. Either increasingthe moment armRout or decreasing the outlet nozzle areaAout

(and thereby imparting more kinetic energy to the fluid at the

Figure 17. Bearing surface area of valve spool

expense of pressure drop) will increase the spool velocity.Themomentum generated by the outlet, however, is counteractedby

the additionalR2outR2 ·ρ ·Q term, which corresponds to the angular

momentum which must be transferred to the fluid as it is forcedtorotate with the same circumferential velocity as the outletblades.As the fluid flows radially outward, more momentum must betransferred to the fluid as the circumferential velocity of the out-let blades increases proportionally withRout. Therefore, increas-ing the outlet moment armRout also has the effect of decreasingthe spool speed.

The greatest benefit from the addition of the outlet stage tur-bine is that the effects of the inlet geometry on the PWM func-tionality of the valve can be decoupled from the spool velocity.By using the outlet stage to provide a majority of the momentumto rotate the spool, the inlet orifice area and thickness of the heli-cal barriers can be optimized for PWM. The only potential issueis whether or not the outlet stage can be designed as effectivelyas the inlet stage, which resembles the more traditional inflowturbine geometry.

3.4 Effective Bearing Surface AnalysisA simple CFD analysis was performed to calculate the effec-

tive bearing surface area of the spool. The effective surface areaaccounts for the contribution of the non-bearing surface area tothe friction torque. The non-bearing surface area is definedtobe the total surface areaπ ·D ·L minus the bearing surface area,which is shown in Fig. 17.Ae f f is given by:

Ae f f = Abearing+α · (π ·D ·Ls−Abearing) (20)

α is defined to be the ratio of non-bearing shear stress to bear-ing surface shear, orα =

σnon−bearingσbearing

. The objective of our CFD

analysis is to determineα.In our current design, the radial bearing surface area clear-

ance is 2.54×10−5mwhile the radial clearance for the remainingsurface area is 3.175×10−3m. Petroff’s Law, which assumes aNewtonian fluid where shear stress is inversely proportional to

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Figure 18. Schematic of pocketed non-bearing surface

clearance, would predict that the effect of the non-bearingareais negligible. Our previous experiments with a.0323m diame-ter rotary valve, however, revealed otherwise. This is becausethe fluid in contact with the non-bearing surface area is trappedin a pocketed area between the helical barriers. The fluid in thepocket will recirculate due to the no-slip conditions at theouterstationary sleeve wall as the spool rotates. These vorticeswillincrease the frictional force in the pocketed area.

In our current design, however, the fluid is not completelytrapped between the helical barriers. The inlets between the bar-riers direct fluid toward the center of the spool. Therefore,weexpect less circulation and vorticity in our current design, whichshould correspond to less friction in the non-bearing surface area.Thus the following analysis is a conservative prediction ofwhatthe non-bearing friction will be. A diagram of a simplified modelof the pocketed area is shown in Fig. 18.

Although the actual upper boundary of the domain is curved(sleeve ID) as shown in Fig. 18, we will approximate the uppersurface as flat to simplify the analysis. As a further simplifica-tion, the system is inverted. Instead of rotating the spool in thesimulation, we rotate the sleeve. In the computational domain,this equates to a moving upper boundary. The CFD analysis as-sumes two-dimensional, steady, incompressible Newtonianflow.The pocket was modeled as a rectangular chamber with a mov-ing upper boundary. The upper boundary was given a velocitythat corresponded with our previous valve, a.0323m diameterspool rotating at 27Hz. Both the depth and width of the pock-eted area were explored. A plot of the streamlines generatedby the CFD code illustrating the primary vortex of the flow isshown in Fig. 19. The primary vortex accounts for the circu-lation occurring within the pocket between the helical barriers.The numerical results of the analysis are presented in Figs.20and 21. These figures show that the width of the pocket hasa negligible effect on the shear stress, while the depth of thepocket is crucial. Therefore, in our current design, we willdesignthe pocket depth, or clearance of the non-bearing area, to beaslarge as possible while still maintaining adequate wall thicknessfor the internal axial passage between the inlet and outlet stages.From Fig. 20, for a depth of 3.175×10−3m, the corresponding

Pocket width (m)

Poc

ket d

epth

(m

)

1 2 3 4 5 6 7 8 9

x 10−3

−2

−1

0

1

2

3

4

5

x 10−3

Figure 19. Streamlines within pocket

2 4 6 8 10 12 14

x 10−3

400

450

500

550

600

650

700

750

800

850

Pocket Depth (m)

She

ar S

tres

s (N

/m2 )

Pocket Width = 9.525 × 10−3 m

Figure 20. Effect of pocket depth on shear stress

shear stress is predicted to be roughly 820N/m2 = σnon−bearing.The shear stress for the bearing surface of a.0323m diameterspool rotating at a frequency of 27Hz with a radial clearanceof 2.54× 10−5m results inσbearing = 4169N/m2. Therefore,α =

σnon−bearingσbearing

= 19.7%.

3.5 Leakage Analysis

A preliminary analysis of the internal leakage of the valvewas conducted by assuming laminar leakage flow. Since the onlyfeature of the valve that separates high pressure fluid from lowpressure fluid is the helical barrier, the valve leakage is assumedto be the flow across this area. The following equation was used

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2 4 6 8 10 12 14

x 10−3

400

450

500

550

600

650

700

750

800

850

Pocket Width (m)

She

ar S

tres

s (N

/m2 )

Pocket Depth = 3.175 × 10−3 m

Figure 21. Effect of pocket width on shear stress

to estimate the leakage [5]:

Qleak =Per·c3 · (Pload−Popen)

(12·µ·Ht)(21)

Per is the perimeter of the leakage surface. This equation indi-cates a strong relationship between the leakage and the clearance.A small clearance is desirable to reduce leakage, however a smallclearance increases the viscous friction drag on the spool and re-duces the spool velocity.

3.6 Design SummarySeveral trade offs exist in the design of our self-spinning,

3-way rotary valve concept. By specifyingL and D, the opti-mal rhombus inlet area becomes constrained byAin

κ2 = π·D·L48·N . By

decreasingAin, κ must decrease as well, which indicates that thevalve is in transition for a smaller proportion of each PWM cycle.This equates to higher efficiency since our valve is least efficientduring transition. Additionally, from Eq. 18, the rotational speedof our valveω also increases with a smallerAin. DecreasingAin,however, increases the fully open throttling losses acrossthe in-let, which is a constant loss throughout each rotation of thespool.If we wish to decrease the transition losses at the inlet by manipu-latingAin, ω can be maintained by appropriately specifyingAout.Another trade off in our design exists between leakage across thehelical barriers andω. A smaller radial clearancec significantlydecreases leakage, however the penalty in spool velocity issig-nificant as well.

The PWM frequency of our design is proportional to thespool velocity by a factorN. By increasingN, the PWM fre-quency of our valve can be increased for a givenω. However,N is limited by leakage, as the thickness of the barriersHt mustdecrease withN.

Parameter SI English Description

N 3 − Number of inlets

D .0254m 1.0in Spool diameter

L .0856m 3.37in Spool length

c 2.54×10−5m .001in Radial clearance

α .197 - Ratio of shear

Abearing .0015m2 2.39in2 Bearing area

Ain 1.22×10−5m2 .0189in2 Inlet rhombus area

Aout 4.68×10−5m2 .0726in2 Turbine exit area

Rh .0065m .2558in2 Rhombus height

Rw .0037m .1476in2 Rhombus width

β 1.05rad 60deg Helix angle

Ht .003m .1181in Helix thickness

Cd .6 - Orifice coefficient

Q 6.3×10−4m3/s 10gpm Flow rate

Pload 6.89×106Pa 1000psi Load pressure

Prelie f 7.58×106Pa 1100psi Relief pressure

Table 2. Current system design parameters

Our current prototype is sized for a nominal flow rate of40l/m at a maximum operating pressure of 7Mpa. The designgoals for our valve are to maximize the spool velocity, and mini-mize losses and physical size. Based on the analysis presented inthis paper as well as considering manufacturing constraints, thefinal parameters chosen for our first prototype are summarized inTable 2.

From our current design parameters, we predict that ourspool can achieve a rotational velocity of 28Hz, which corre-sponds to a PWM frequency of 84Hz. This is a conservativeestimate since we believe our estimate ofα from the CFD anal-ysis is an over prediction.κ, the proportion of time per revo-lution that the valve is in transition, is 54.2%. The resistingtorque due to viscous friction is estimated to be 0.1116N/m.From this we estimate that an input power of 19.6W is neededto overcome viscous friction. The pressure drop across the fullyopen rhombus inlet and outlet turbine exit are 3.6275× 105Paand 2.4541× 104Pa respectively. The leakage flow across thehelical barriers is 1.2618× 10−5m3/s and the total energy lostper PWM cycle due to transition throttling is 13.6J. Therefore,the total power loss attributed to our valve, which consistsoftransition and fully open throttling, is 1256W. The total powerloss can be expressed as an equivalent pressure drop, which is

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equal to 1.99×106Pa. Compared to the maximum output powerof our system,Powerout = Q ·Pload = 4350W, the system effi-ciency is 71.1%. This estimated system efficiency includes theenergy required to drive the valve; no additional power source isrequired.

From the analysis presented in this paper, the majority ofpower loss is due to throttling during transition. In our 3-wayvalve configuration, the transition losses are especially high sincethe number of transition events is doubled in comparison to a2-way valve. The additional transition losses incurred by the3-waydesign, however, are offset by the enhanced self-spinning capa-bility. A 2-way valve requires an auxiliary power source to spinthe valve during the portion of the PWM cycle when there isno flow through the valve. Additional complications arise whencoupling an outside power source to the valve spool. Further-more, transition throttling losses are not unique to our rotaryvalve, and exist for any on/off valve. Additional investigationinto the role of the inlet geometry on the transition loss canpo-tentially decrease losses as our current inlet was designedby con-sidering the fully open losses only.

4 Rotary Valve SimulationA dynamic model of the system shown in Fig. 8 was simu-

lated in Matlab. The system consists of an ideal flow source witha constant flow rate of 6.31×10−4m3/sand an ideal relief valveset at 7.58×106Pa. The accumulator is assumed to be adiabaticwith a pre-charge pressure of 6.89×105Pa and a pre-charge gasvolume of.16L. An orifice load described by Eq. 2 with a diam-eter of 0.0025m and discharge coefficient of.7 was used in themodel. The current model assumes no fluid compressibility.

The complete system is controlled using a pressure controlalgorithm proposed by Li et al. [7] of the form:

s(t) = K f f ·√

Pre f +K f b · (Pre f −Pout(t)) (22)

s(t) is the desired duty ratio andPre f is the desired referenceoutput pressure.K f b, the feedback gain, was chosen to be.01,which provided a good compromise between responsiveness andovershoot. K f f , the feedforward gain, was calculated to be2.69×10−4 based on an orifice load.

The relationship between duty ratio,s(t), and the axial posi-tion of the spool,l , is given in Fig. 15. Inverting the load branchcurve in Fig. 15 produces the relationship for calculating the ax-ial position as a function of duty ratio. The axial position of thespool corresponding to the desired duty ratio is regulated by con-trolling the input to a DC motor PWM driving circuit. The inputis given by:

l =f (u)

Aend(23)

0 0.5 1 1.5 2 2.5 30

1

2

3

4

5

6

7x 10

6

Time (s)

Pre

ssur

e (P

a)

ReferenceOutput

Figure 22. Simulated output pressure

u is the input to the DC motor PWM driving circuit,l is the axialposition of the spool, andAend = π

4 ·D2 is the area of one end of

the spool.A PI controller with feedforward is used to trackl to a ref-

erence signal. The system poles were placed at−10rad/s and−15rad/s. Simulations of the axial position controller predictthat the controller can reposition the spool from full on to full offin less than.15s.

A step reference pressure from 1.3789× 106Pa to 5.52×106Pa with a second step to 3.45×106Pa was simulated. Thisinput corresponds to a step in flow from 1.99× 10−4m3/s to3.97× 10−4m3/s to 3.15× 10−4m3/s. The system was able tocomplete the first step in.19s and the second step in.054s. Theaverage pressure ripple was 6.67%. The results of the simulationare presented in Figs. 22 and 23, and show that our 3-way rotaryvalve with hydro-static linear actuation can work effectively tomodulate flow.

The response of the simulated system is currently limited bythe accumulator. The speed of the system can be increased byeither decreasing the pre-charge pressure, or decreasing the pre-charge volume of the accumulator. Either of these modifications,however, will increase the magnitude of the output pressurerip-ple. Another alternative is to increase the PWM frequency ofthe system. This can further improve the response without thepenalty in ripple size.

5 ConclusionA novel 3-way self-spinning rotary on/off valve concept has

been presented that is potentially more efficient than a compa-rable linear valve of equal switching frequency and flow rating.The analysis in this paper predicts that a rotary valve sizedfora nominal flow rate of 40l/m can achieve a PWM frequency of84Hz, roughly a 400% improvement over current linear valve de-

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0 0.5 1 1.5 2 2.5 31.5

2

2.5

3

3.5

4

4.5

5x 10

−4

Time (s)

Out

put F

low

(m

3 /s)

Figure 23. Simulated output flow

signs. This frequency is attained by harvesting waste throttlingenergy from the system flow. No external actuation is needed torotate the spool in this design.

A complete system model of a PWM variable displacementpump utilizing our 3-way rotary valve has been simulated withpromising results. The simulation shows that the hydro-static lin-ear control scheme is effective in controlling the axial position ofthe spool. The simulation also shows that variable displacementpump functionality utilizing the rotary valve can be achieved byadding closed-loop control to the system.

A number of trade offs between performance and efficiencyexist in the design of our rotary on/off valve. The equationspre-sented in this paper provide a means for sizing and optimizing thedesign based upon physical constraints and efficiency require-ments. An analysis of the various modes of power loss in thesystem reveal that throttling during transition accounts for a ma-jority of the loss in our valve. An opportunity exists to reducetransition losses by optimizing the valve geometry to transitionmore effectively. κ, the proportion of time that the valve is intransition, needs to be reduced to improve efficiency. This canbe achieved by decreasingRw, increasingD, or by having thevalve spin selectively faster during transition. Reducingor elim-inating the flow throttled across the relief valve during transi-tion will improve efficiency significantly as well. Our design canalso be improved by investigating methods of decreasing viscousfriction, increasing the number of helical barriers (N), as well asdeveloping a more effective outlet stage turbine.

AcknowledgmentThis material is based upon work supported by the National

Science Foundation under grant numbers ENG/CMS-0409832and EEC-0540834.

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1967.[2] F. White,Fluid Mechanics. McGraw-Hill, 5th ed., 2003.[3] A. Cameron,Basic Lubrication Theory. John Wiley and

Sons, 3rd ed., 1981.[4] S.L. Dixon, Fluid Mechanics and Thermodynamics of Tur-

bomachinery. Elsevier Butterworth-Heinemann, 5th ed.,2005.

[5] J. Cundiff, Fluid Power Circuits and Controls. CRC Press,2002.

[6] M. Rannow, H. Tu, P. Li and T. Chase, “Software EnabledVariable Displacement Pumps - Experimental Studies”Pro-ceedings of the 2006 ASME-IMECE, no. IMECE2006-14973,2006.

[7] P. Li, C. Li and T. Chase, “Software Enabled Variable Dis-placement Pumps”Proceedings of the 2005 ASME-IMECE,no. IMECE2005-81376, 2005.

[8] S. Yokota, Y. Kondou and K. Akutu, “Ultra fast-actingelectro-hydraulic digital valve by making use of a multilay-ered piezo-electric device (PZT),”Proceedings of Flucome’91, pp. 379–384, 1991.

[9] T. Kajima, S. Satoh and R. Sagawa, “Development of a highspeed solenoid valve,”Transactions of the Japan Society ofMechanical Engineering: Part C, vol. 60, no. 576, pp. 2744–2751, 1994.

[10] H. Lu, C. Zhu, S. Zeng, Y. Huang, M. Zhou and Y. He,“Study on the new kind of electro-hydraulic high speed on-off valve driven by PZT components and its powerful andspeedy technique,”Chinese Journal of Mechanical Engineer-ing, vol. 38, no. 8, pp. 118–121, 2002.

[11] I. Cyphelly and J. Langen, “Ein neues energiesparendesKonzept der Volumenstromdosierung mit Konstantpumpen”Aachener Fluidtechnisches Kolloquium, 1980.

[12] T. Royston and R. Singh, “Development of a Pulse-WidthModulated Pneumatic Rotary Valve for Actuator PositionControl” Journal of Dynamic Systems, Measurement, andControl-Transactions of the ASME, vol. 115, pp. 495–505,1993.

[13] P. Cui, R. Burton and P. Ukrainetz, “Development of a highspeed on/off valve,”Transactions of the SAE, vol. 100, no. 2,pp. 312–316, 1991.

[14] Industrial Hydraulics Manual. Eaton Corporation, 4th ed.,2001.

13 Copyright c© 2007 by ASME


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