Haink C. Tue-mail: tuxxx021@umn.edu

Michael B. Rannowe-mail: rann0018@umn.edu

Meng Wange-mail: wangx833@umn.edu

Perry Y. Li1e-mail: perry-li@umn.edu

Thomas R. Chasee-mail: trchase@umn.edu

James D. Van de Vene-mail: vandeven@umn.edu

Center for Compact and Efficient Fluid Power,

Department of Mechanical Engineering,

University of Minnesota,

111 Church Street SE,

Minneapolis, MN 55455

Design, Modeling,and Validation of a High-SpeedRotary Pulse-Width-ModulationOn/Off Hydraulic ValveEfficient high-speed on/off valves are an enabling technology for applying digital controltechniques such as pulse-width-modulation (PWM) to hydraulic systems. Virtually vari-able displacement pumps (VVDPs) are one application where variable displacementfunctionality is attained using a fixed-displacement pump paired with an on/off valve andan accumulator. High-speed valves increase system bandwidth and reduce output pres-sure ripple by enabling higher switching frequencies. In addition to fast switching, on/offvalves should also have small pressure drop and low actuation power to be effective inthese applications. In this paper, a new unidirectional rotary valve designed for PWM isproposed. The valve is unique in utilizing the hydraulic fluid flowing through it as apower source for rotation. An unoptimized prototype capable of high flow rate (40 lpm),high speed (2.8 ms transition time at 100 Hz PWM frequency), and low pressure drop(0.62 MPa), while consuming little actuation power (<0.5% full power or 30 W, scav-enged from fluid stream), has been constructed and experimentally validated. This paperdescribes the valve design, analyzes its performance and losses, and develops mathematicalmodels that can be used for design and simulation. The models are validated using experi-mental data from a proof-of-concept prototype. The valve efficiency is quantified and sugges-tions for improving the efficiency in future valves are provided. [DOI: 10.1115/1.4006621]

1 Introduction

Traditional means of controlling fluid power systems such asproportional valves and variable displacement pumps (VDPs)have their limitations. Valve controlled systems (for example, thebleed off circuit in Fig. 1) are typically compact, inexpensive, andprovide good control bandwidth. However, these traits come atthe cost of efficiency since all excess flow is throttled by the pro-portional valve. In contrast, VDPs offer better efficiency since thedisplacement of the pump can be tuned to the load, thus producingonly the required flow. The disadvantage of VDPs is that conven-tional electronic displacement control (EDC) piston pumps typi-cally require 3–4 times the volume and weight of a fixed-displacement gear pump of equal displacement [1]. The addedcomplexity of the EDC unit also increases the cost of VDPs, andthe bandwidth is typically lower due to the moving mass of thedisplacement varying mechanism (for example, a swash plate).

An efficient alternative that retains the simplicity of valve con-trol is the VVDP concept (see Fig. 2) [1,2]. This approach, whichis the hydromechanical analogue of a switched-mode dc–dc con-verter, attains flow control with a fixed-displacement pump byquickly switching the output flow between a high pressure (load)branch and a low pressure (tank) branch instead of restricting theflow using an orifice. If the switching between the load and thetank is pulse-width-modulated, the mean output flow of the pump/valve system is controlled by varying the PWM duty ratio, or frac-tion of each period that the on/off valve is open to load (hence theuse of “virtually variable” to describe the system’s displacement).This approach is efficient relative to throttling because the valveloss in either the fully on or fully off state is small.

The VVDP is an example of the emerging field of digitalhydraulics that necessitates advancements in on/off valve technol-

ogy. Other examples include (but are not limited to) piston-by-pis-ton digital-displacement pumps, where one or more active valvesare used to control each piston [3]. Binary sequencing has alsobeen explored, whether applied to the orifice area of a parallelarray of on/off valves for approximating the function of a propor-tional valve (with reduced cost) [4] or to a stepped area piston(with each step activated by an on/off valve) to enable variablearea pistons that can be used as transformers [5].

Operating VVDPs at high frequencies is desirable because out-put ripple is reduced and system bandwidth is improved [1,2].This requires high-speed valves which have low pressure drop,high flow capacity, and low actuation power. Conventional on/offvalves rely on the alternating linear motion of a spool or poppet.Therefore, increasing their flow capacity and speed requireshigher actuation power. The actuation power required to over-come the inertial forces alone is proportional to the cube of thePWM frequency and to the square of the valve travel (i.e., orificeopening). High switching speeds (0.1–1.5 ms transitions) havebeen achieved using piezo-electric actuators [6,7], although thesevalves typically have limited flow capacity (8 lpm) or exhibit highpressure drop (up to 10 MPa). Solenoid based valves have beenproposed which exhibit similar characteristics [8].

To overcome the fundamental trade off between valve speed,flow area, and actuation power in PWM applications, a rotarythree-way on/off valve is proposed such that the on/off sequenceis embedded in the continuous unidirectional rotary motion of thespool. The PWM frequency is proportional to the spool’s rota-tional speed. This eliminates the need for the valve to start andstop so that actuation power needs only to overcome friction, whichis proportional to the square of the frequency. In addition, the valvetransition time as a proportion of the PWM period is fixed so thattransition losses do not increase as PWM frequency increases.Since the spool has a helical shaped land on its surface, the duty ra-tio of the valve is determined by the axial motion of the spool inrelation to fixed ports on the valve sleeve. The valve is also self-spinning: it scavenges power from the fluid flow to achieve its ro-tary motion so that an external rotary actuator is not needed.

1Corresponding author.Contributed by the Dynamic Systems Division of ASME for publication in the

JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript receivedDecember 31, 2009; final manuscript received April 11, 2012; published onlineSeptember 13, 2012. Editor: J. Karl Hedrick.

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A review of the prior art has revealed several other high-speedvalve designs based on rotary motion. Cui et al. [9] developed abidirectional two-stage rotary spool valve. This valve is not con-tinuously rotating as in the present paper. Instead, a step rotarymotion of the pilot is used to create an axial pressure imbalancethat causes linear sliding motion of a second stage poppet. Thisvalve achieved a fast transition time of 2.5 ms with a pressuredrop of 9 MPa at 18 lpm of flow due to a relatively small valveopening.

Continuous rotational motion, which is exploited by the valveproposed in the present paper, has been used by other researchgroups as well [10–14]. Royston and Singh [12] developed apneumatic rotary PWM valve capable of 80 Hz based on a contin-uously rotating inner shaft with supply and return ports on a fixedouter stator. The duty ratio is set by the angular position of theload port relative to the stator. Brown et al. [10] proposed a designcapable of 500 Hz PWM frequency, consisting of a concentriccontrol shaft, hollow rotor, and stator. The rotor sets the PWM fre-quency while the angle between the control shaft and the statordetermines the duty ratio. Recently, Van de Ven and Katz [13]proposed a design based on two tiers of continuously rotatingdisks designed for a PWM frequency of 100 Hz with the duty ratiodetermined by the phase difference between the disks. The two-way valve proposed by Cyphelly and Langen [14] uses a continu-ously rotating spool and a helical land that alternately opens andcloses the valve, similar to what is proposed in the present paper,but it is motor driven rather than self-spinning.

The present paper is unique, however, in that it is a three-waydesign that alternately sends flow to either tank or the application.More importantly, it scavenges power from the fluid flow itself forrotating the spool. An unoptimized prototype capable of high flowrate (40 lpm), high speed (100 Hz PWM frequency or 2.8 ms tran-sition time when self-spinning), and low pressure drop (0.62 MPa)has been constructed and experimentally tested. The valve con-sumes relatively little actuation power (30 W or less than0.5% full power) that is scavenged from the fluid flow. This paperdescribes the design and also develops design equations that char-acterize the primary valve losses and operating characteristics. Adetailed simulation and experimental study of the efficiency char-acteristics of the valve when used in a VVDP is also provided.

Section 2 describes the three-way self-spinning rotary valveconcept. The operating principle of the VVDP is outlined in Sec.3. Design equations and loss analysis of the valve are presented inSec. 4. A dynamic model of the VVDP is developed in Sec. 5 andan overview of the test bench is given in Sec. 6. Experimentaldata from an unoptimized proof-of-concept prototype are used tovalidate the model in Sec. 7. The validated model is thenemployed to predict the VVDP efficiency for an optimized valveand to compare it with a similar proportional valve controlled sys-tem. Conclusions are summarized in Sec. 8.

2 Rotary Valve Concept

The three-way rotary valve concept is illustrated in Figs. 3 and4. The design consists of a stationary sleeve and a rotating/trans-lating spool. The sleeve (Fig. 3) is designed to replace part of thepump housing in order to minimize the dead volume between thepump outlet and the spool. The outlet flow of the pump is directedto tangential nozzles that port fluid to the inner diameter of thesleeve bore and into the inlet section of the spool. The cross sec-tions of the nozzles are rhombic shaped to match the helical landas this minimizes the on/off transition time for a given flow area(Fig. 5).

The spool, shown in Fig. 4, rotates and translates within thesleeve bore. The inlet (center) section of the spool is partitionedinto two flow paths (highlighted in dark and light gray in Fig. 4)by overlapping helical lands. Internal pathways along the axis ofthe spool direct flow from the inlet section to one of the two adja-cent outlet turbines. The dark gray region of the inlet section con-nects to the load outlet turbine (also in dark gray), and the lightgray region connects to the tank outlet turbine (also in light gray).

Fig. 2 Two VVDP implementations. Qvol and Qacc represent the net flows into the inlet volumeand accumulator.

Fig. 3 Rotary valve spool/sleeve assembly. The spool rotatesand translates within the sleeve bore.

Fig. 1 Bleed off circuit

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Flow is directed from the outlet of the pump to load or tank depend-ing on which region of the spool is connected to the ports on thesleeve. As the spool rotates, fluid is alternately ported between loadand tank, thereby achieving PWM. The inlet section of the spool isdivided into N sections coinciding with N inlets (see Fig. 5). Eachsection performs one complete on/off cycle and the PWM fre-quency of the valve is N times the spool’s rotational frequency.

The duty ratio of the valve, s, is dependent on the spool’s axialposition and controls the output flow fraction of the VVDP. Ats¼ 0 or the zero duty ratio position (as shown in Fig. 4), flow isbypassed to tank during the entire revolution, thus sending noflow to load (i.e., no VVDP output flow). The opposite occurs ats¼ 1 or full duty ratio position when the VVDP flow equals thefull pump flow. Because of the spool’s helical structure, the dutyratio and normalized output flow of the VVDP vary linearly withaxial position. The spool’s axial position is controlled using anelectrohydraulic gerotor pump in a hydrostatic configuration,although other actuation methods are possible. The gerotor portsfluid to either side of the spool using the axial positioning portsshown in Fig. 3. Sensing of the axial and angular positions of thespool is accomplished using noncontact optical sensors [15,16].

Self-spinning of the spool is accomplished by designing boththe inlet and outlet sections of the spool as turbines to capturethrottling energy and fluid momentum. The inlet section acts as animpulse turbine, where fluid is accelerated via nozzles tangentialto the rotor (i.e., valve spool) [17]. As the fluid impinges on theturbine blades, angular momentum is transferred to the spool as itredirects flow to the center of the spool. Fluid then exits the inletsection axially with no angular momentum. In contrast, the outletsection is designed as a reaction turbine. Blades on the outlet sec-tion guide the fluid from the center of the spool outwardly and tan-gentially, thus imparting a reaction torque on the spool.

3 VVDP Overview

Figure 2 illustrates two possible VVDP implementations usinga three-way on/off valve. The systems differ in how the inlet pres-sure (Pin) is limited when the on/off valve is transitioning. A reliefvalve set to Prelief is used in Fig. 2(a), and a check valve in parallelwith the on/off valve with cracking pressure Pcheck is used in Fig.2(b). The check valve circuit is potentially more efficient byreducing losses during transition in two ways: (1) limiting throt-tling losses to Pcheck above Pload in comparison to a fixed reliefpressure which needs to be higher than any conceivable Pload and(2) porting the high pressure bypassed flow to load instead ofdumping the fluid to tank. The latter achieves a soft-switchingfunction that reduces losses when the on/off valve is switching[18,19].

Figure 6 illustrates the inlet pressure profile of the VVDP overone PWM cycle along with the corresponding nozzle open areaprofiles to tank (solid) or to load (dotted). Because the rhombicorifice is designed to match the helical land geometry, the orificeopening varies linearly with the spool rotation until the orifice iscompletely open or closed. The full pump flow, Qin, is supplied tothe inlet volume Vin (Fig. 2) throughout the entire PWM cycle.The pressure drop across the rotary valve consists of the pressuredrop across the rhombic orifices and the pressure drop across therest of the spool. Let Popen denote the fully open orifice pressuredrop and Pspool denote the pressure drop for the rest of the spool,both with the full pump flow Qin through the valve. Assume thatPtank¼ 0 for simplicity.

Interval a in Fig. 6 represents the VVDP in the off state withthe rotary valve completely open to tank. Since the pump isunloaded, Pin is low (¼PopenþPspool). The accumulator suppliesflow to the load and Qin is returned to tank.

Interval b is when the valve transitions from being open to tankto being open to load. First, the rhombic nozzle orifice closes totank, causing Pin to rise (interval b1). Once Pin reaches Prelief

Fig. 4 Three-way helical spool concept. Internal passagesconnect the center section (responsible for PWM) to one of thetwo adjacent outlet turbines. The dark gray portions of thespool are hydraulically connected and permit flow from the inletto the load. Similarly, the light gray sections connect the inlet totank.

Fig. 5 2D representation of the rotary valve’s geometry includ-ing variable definitions used in Sec. 4

Fig. 6 Top: Inlet pressure (Pin) profile over one PWM cycle2pN rad spool rotation� �

for the two circuits in Fig. 2. Bottom: Cor-responding profiles of the valve inlet nozzle open areas (A(h))to load or to tank.

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(in Fig. 2(a)) or PcheckþPload (in Fig. 2(b)), the relief or checkvalve opens to regulate Pin at these levels. Since the valve is criticallylapped (i.e., the helical lands and the rhombic orifices have equalwidths), the instant the orifice closes completely to tank, it begins toopen to load (interval b2). The relief or check valve will close oncethe orifice is sufficiently open, thus causing Pin to decrease.

Interval c represents the period when the valve is completelyopen to load. The system is in the on state and the pressure dropacross the rotary valve (Pin�Pload) becomes PopenþPspool. Qin

from the pump is supplied to the accumulator and the load.Interval d is when the valve transitions from being open to load

to being open to tank. As the orifice closes to load (interval d1),Pin rises until the relief or check valve opens. As the orifice isfully closed to load, it begins to open to tank (interval d2). Therelief or check valve closes once the orifice is sufficiently open.As the valve becomes fully open to tank, Pin¼PopenþPspool andthe system returns to the off state.

4 Design and Performance Analysis

An analysis and design equations for the rotary valve and thetwo VVDP configurations shown in Fig. 2 are presented in thissection. Variables used in the analysis are defined in Fig. 5. Sev-eral simplifying assumptions are applied: (1) The fixed-displacement pump is assumed to be an ideal flow source withconstant output flow Qin. (2) The system pressure is assumed to becapped at Prelief for the relief circuit and PcheckþPload for thecheck circuit when the relief valve or check valve is activated. (3)Variation of Pload (load/accumulator pressure) is assumed to beslow such that it can be considered a constant. (4) Tank pressure,Ptank, is assumed to be zero. Dynamic effects of the inlet and ac-cumulator pressure will be discussed later in Sec. 5.

Section 4.1 investigates throttling losses. Section 4.2 examinescompressibility losses. Valve leakage is explored in Sec. 4.3. Thespool’s self-spinning velocity is analyzed in Sec. 4.4 and the rela-tionship between its axial position and the VVDP’s output flow isstudied in Sec. 4.5. Various design trade offs and a summary ofthe design are discussed in Sec. 4.6.

4.1 Valve Throttling Losses. Throttling losses through therotary valve include sleeve losses from the variable rhombic noz-zle orifices, losses through the spool itself, and losses due to therelief valve or check valve. Section 4.1.1 considers the losseswhen the rhombic orifices are fully open and Sec. 4.1.2 considersthe losses when the valve is in transition.

Let the fraction of time that the valve is in transition or fullyopen be j and (1� j), respectively. Assuming that the duty ratio sand the spool angular frequency x are constant while the valve istransitioning, the helical land traverses the width of the rhombusRw (Fig. 5) during each transition. The corresponding duration ofeach of the four transitions is

Ttran ¼ 2Rw=ðDxÞ (1)

and the PWM period is 2p/(xN).Thus

j ¼ 4NRw

pD(2)

4.1.1 Full Open Orifice Losses. When the rotary valve isfully open, the pressure drop across the N rhombic orifices isdescribed by the orifice equation [20]

Popen ¼q2

Qin

CdNAin

� �2

(3)

q is the density of hydraulic oil, Cd is the orifice discharge coeffi-cient (assumed constant), and Ain¼ 0.5RwRh is the cross-sectionalarea of one inlet with Rw and Rh being the rhombus width andheight (see Fig. 5).

The pressure drop across the spool itself, Pspool, is estimatedusing a computational fluid dynamics (CFD) generated semi-empirical formula [21] based on a scaled version of the proto-type’s geometry. For a given diameter (D) and flow rate (Qin),Pspool is assumed to be constant regardless of whether the valve isconnected to load or tank due to the symmetry of the flow paths.Thus, the rotary valve’s full open power loss is

Popen ¼ ð1� jÞðPopen þ PspoolÞQin (4)

4.1.2 Transition Losses. The transition throttling lossesderived in this section include losses from blocking the inletrhombic orifices, losses through the relief valve (Fig. 2(a)) orcheck valve (Fig. 2(b)), and losses through the spool. During eachPWM cycle, the rotary valve undergoes four transitions: openingand closing to tank with equal energy losses (Etank) and openingand closing to load also with equal energy losses (Eload).

For the relief circuit in Fig. 2(a), consider first the opening totank transition (interval d2 in Fig. 6). At the beginning of the tran-sition, the rhombic inlet orifice is blocked and all flow goesthrough the relief valve to tank and Pin¼Prelief. As the rhombicorifice opens to tank (with the relief valve still open), flow passesthrough both the relief and the on/off valve to tank with a pressuredrop of Prelief. When the valve is sufficiently open, Pin falls belowPrelief and all flow goes through the on/off valve to tank causing apressure drop of Pspool across the spool.

Considering the problem in angle coordinates with H¼xtwhere H¼ 0 corresponds to the start of transition, let Pi(H) be theinstantaneous pressure drop across the orifice with varying orificearea if the full flow Qin passes through it

PiðHÞ ¼q2

Qin

CdNAðHÞ

� �2

¼ Popen

Htran

H

� �2

(5)

where the definition in Eq. (3) has been employed and A(H) is theinstantaneous open area of one rhombic inlet and Htran is the totalrotational angle for each transition

AðHÞ ¼ RhD

4H ¼ Ain

HHtran

ð0 � H � HtranÞ (6)

Htran ¼ 2Rw=D (7)

Let Hcrit be the critical angle when the relief valve just begins toopen or close coinciding with Pi(Hcrit)¼Prelief. From Eqs. (5) and(6), the relationship between them is as follows

Hcrit

Htran

¼ffiffiffiffiffiffiffiffiffiffiffiPopen

Prelief

r(8)

Therefore, considering whether the relief valve is open or closedand utilizing Eqs. (5)–(8), the resulting energy loss during eachtank transition is

Etank ¼Qin

x

ðHcrit

0

PreliefdH

�|fflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflffl}

relief open

þðHtran

Hcrit

ðPiðHÞ þ PspoolÞdH

|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}

relief closed

(9)

¼ Qin

xPreliefHcrit þ PopenHtran

Htran

Hcrit

� 1

� ��þ PspoolðHtran �HcritÞ�

(10)

¼ 2QinRw

xD

ffiffiffiffiffiffiffiffiffiffiPopen

p2ffiffiffiffiffiffiffiffiffiffiffiPrelief

p�

ffiffiffiffiffiffiffiffiffiffiPopen

pþ Pspool

1ffiffiffiffiffiffiffiffiffiffiPopen

p � 1ffiffiffiffiffiffiffiffiffiffiffiPrelief

p !#

(11)

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The energy lost when opening the inlet to load (interval b2) iscalculated similarly. The main difference is that when the reliefvalve is open, the flow through the relief valve is throttled acrossPrelief, whereas the flow through the rotary valve is throttled acrossPrelief�Pload. In angle coordinates, the instantaneous flow throughthe rotary valve (Qi) with varying orifice area when the reliefvalve is open is

QiðHÞ ¼ Qin

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiPrelief � Pload

Popen

sH

Htran

(12)

The critical angle for the load transitions, H0crit, occurs whenQiðH0critÞ ¼ Qin. Thus,

H0crit

Htran

¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

Popen

Prelief � Pload

r(13)

The resulting energy loss during each load transition is

Eload ¼1

x

ðH0crit

0

fðQin � QiðHÞÞPrelief þ QiðHÞ"

� ðPrelief � PloadÞgdHþðHtran

H0crit

QinðPiðHÞ þ PspoolÞdH

(14)

¼ 2QinRw

xD

ffiffiffiffiffiffiffiffiffiffiPopen

p 2Prelief � 1:5Pload � PspoolffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiPrelief � Pload

p�

þ Pspool � PopenffiffiffiffiffiffiffiffiffiffiPopen

p#

(15)

The average transition power loss is derived from the total energyloss per cycle (four transitions) and the PWM frequencyðfPWM ¼ N � x=2 � pÞ

Ptrans ¼ ð2Eload þ 2EtankÞfPWM

2p(16)

Using the definition in Eq. (16), the loss for the relief circuit is

Ptrans;relief ¼ jffiffiffiffiffiffiffiffiffiffiPopen

p|fflfflfflfflffl{zfflfflfflfflffl}optimizable

Qin

2

2Prelief � 1:5Pload � PspoolffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiPrelief � Pload

p�

þ 2ðPspool � PopenÞffiffiffiffiffiffiffiffiffiffiPopen

p þ 2Prelief � PspoolffiffiffiffiffiffiffiffiffiffiffiPrelief

p#

(17)

The loss for the check circuit is calculated similarly. The maindifference is that the critical angle when the check valve firstbegins to open or close corresponds to a pressure of(PcheckþPload) for the tank transitions and Pcheck for the load tran-sitions. The resulting loss is

Ptrans;check ¼ jffiffiffiffiffiffiffiffiffiffiPopen

p|fflfflfflfflffl{zfflfflfflfflffl}optimizable

Qin

2

2Pcheck þ 1:5Pload � PspoolffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiPcheck þ Pload

p�

þ 2ðPspool � PopenÞffiffiffiffiffiffiffiffiffiffiPopen

p þ 2Pcheck � PspoolffiffiffiffiffiffiffiffiffiffiffiffiPcheck

p#

(18)

Remarks.

(1) Equations (17) and (18) reveal that the average transitionloss of the rotary valve is independent of PWM frequency.This is unlike linear valves with fixed transition time wheretransition losses increase with frequency.

(2) Separating these equations into two parts reveals that thetransition loss is dependent only on geometric and systemparameters: j

ffiffiffiffiffiffiffiffiffiffiPopen

pconsists of rotary valve design param-

eters that can be optimized to reduce losses, while theremaining terms consist mostly of system operating condi-tions and check and relief valve settings.

(3) The last term in Eqs. (17) and (18) highlights the loss sav-ing advantage of the check circuit. In Eq. (17), Prelief is con-strained by the load pressure and is typically � Pspool. Incontrast, the last term of Eq. (18) is independent of loadpressure, and Pcheck can be sized just slightly larger thanPopenþPspool. A comparison of how the transition lossescompare between the two circuits is presented in Fig. 7when Pload<Prelief.

4.2 Compressibility Losses. Compressibility loss consists ofthe energy per cycle that is required to compress the fluid in theinlet volume, Vin (see Fig. 2), from tank to load pressure. Thisenergy is lost when the valve reopens to tank and is characterizedby [2]

Ecomp ¼ Vin

ðPload

Ptank

Pin

bðPinÞdPin (19)

Pin is the inlet volume pressure and b(Pin) is the pressure depend-ent bulk modulus of oil (used because of the substantial variationof bulk modulus with pressure between Ptank and Pload). Themodel used here, plotted in the top of Fig. 8, is the one proposedby Yu et al. [22] with the effect of air dissolving into oilneglected. This produces a more compressible model which yieldsconservative results. The power lost due to compressibility isfound using the energy per unit volume needed to compress theoil (shown in the bottom of Fig. 8)

Pcomp ¼ EcompfPWM (20)

4.3 Leakage. Leakage paths exist in two locations (refer toFig. 5): (1) across the helical land separating load pressure fromtank and (2) across the spool ends (L1) separating working fluidfrom the hydrostatic axial control chambers.

Because the outlet sections of the spool are always connectedto load and tank pressure, the pressure differential across the heli-cal land is nominally constant and equal to Pload�Ptank. Assum-ing laminar leakage flow [23], the leakage across the helical landis

Fig. 7 Comparison of transition losses for relief and checkcircuits

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Qleak ¼Lpc3

r ðPload � PtankÞ12lRw sin /

(21)

l is the dynamic viscosity of hydraulic oil, cr is the radial clear-ance between the spool and sleeve, Rw sin/ is the thickness of theland normal to its edge, / is the angle of the rhombus, and Lp isthe perimeter of the leakage path parallel to the land edges

Lp ¼ N2L� Rh

sin /

� �(22)

L ¼ pDRh

2NRwis the total axial travel. The resultant power loss is

Pleak ¼Lpc3

r ðPload � PtankÞ2

12lRw sin /(23)

Similarly, the power loss due to leakage across the spool endland assuming laminar leakage flow is

Pleak;L1 ¼pDc3

r ðPload � PaxialÞ2

12lL1

(24)

Paxial is the pressure in the axial control chamber acting on thespool end adjacent to the load side. This pressure is used for axialpositioning and is dependent on the method used.

4.4 Self-Spinning Velocity Analysis. The dynamics of thespool rotation can be determined by summing torques on thespool

J €h ¼ sin þ sout � sf (25)

where J is the mass moment of inertia of the spool, €h is the angu-lar acceleration, sin and sout are the torques contributed by theinlet and outlet turbines, respectively, and sf is the resisting torquedue to viscous friction. sf is estimated using Petroff’s law [24]which assumes Newtonian shear stress between concentric cylin-ders with relative rotary motion

sf ¼1

4Aeff

lcr

D2x (26)

Aeff is the effective bearing surface area of the spool which is dis-cussed in more detail in Sec. 4.4.1.

A diagram of the inlet and outlet turbines and their correspond-ing control volumes (CV) is shown in Fig. 9. The inlet turbine ismodeled as a stationary CV that surrounds the spool and tangen-tial rhombic sleeve ports (offset Rin from the axis of rotation). Thetangential sleeve ports serve as the inlet to the CV and generateangular momentum in the fluid. The fluid exits the inlet turbineaxially (with no angular momentum) through an internal channelwith cross-sectional area Aaxial that leads to the outlet turbine.Thus, all angular momentum generated by the inlets is transferredto the spool. Assuming steady incompressible flow and onedimensional inlets/outlets, the inlet turbine torque is

sin ¼XN

1

ðRin � vÞIN _min ¼qRin

AinNQ2

in (27)

q is the density of hydraulic oil, v is the mean velocity of the fluidas it exits the inlet and enters the spool, _m is the correspondingmass flow rate, and ð� � �ÞIN refers to the conditions at the inlet ofthe CV.

The outlet turbine is modeled as a CV that rotates with thespool (Fig. 9). Sleeve effects on the fluid are assumed small sincethe sleeve/turbine interface allows the fluid to exit the turbineunguided before accumulating the fluid at the outlet port down-stream. Fluid enters the CV axially from the inlet turbine with noangular momentum. As the fluid is turned by the curved turbineblades (n blades with n¼N in the current design for simplicity), areaction torque is generated on the spool. Assuming Aout, the flowarea through the blades (see Figs. 5 and 9), is constant and offsetby Rout from the axis of rotation, the outlet turbine torque is

sout ¼XN

1

ðRout � ðv� vCVÞÞOUT _mout

¼ RoutqQin

Qin

AoutN� Routx

� � (28)

vCV¼Routx is the velocity of the CV at the tip of the blades wherethe fluid exits. Equating the inlet and outlet torques to the frictiontorque at steady state (Eq. (25)) produces the steady state angularspool velocity

x ¼ 4q

ND2 Aeff

lcrþ 4R2

out

D2qQin

� �Rin

�AQ2

in (29)

where �A is an equivalent combined flow area

Fig. 9 Inlet and outlet turbines with their control volumes

Fig. 8 Top: Yu pressure dependent bulk modulus for variousfractions (r) of air entrainment and no dissolved air. Bottom:Unit compression energy required to compress fluid from Ptank

to Pload.

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1�A¼ 1

Ain

þ Rout

RinAout

(30)

Remarks.

(1) Equation (28) illustrates competing effects in the outlet tur-bine. Qin=ðAoutNÞ corresponds to the angular momentum gen-erated by the fluid flow as it is turned by the turbine blades.However, this momentum is counteracted by the Routx termwhich reflects the angular momentum that must be trans-ferred to the fluid as it is forced to rotate with the same cir-cumferential velocity as the blades. Consequently, when thetip velocity of the outlet turbine exceeds the mean velocityof the fluid ði:e:; Routx > Qin=ðAoutNÞÞ, the turbine will actas a pump and require torque to maintain its velocity.

(2) For applications where low throttling is desired and aslower PWM frequency is acceptable, the inlet turbinealone can be used for self-spinning and the outlet sectioncan be designed to minimize pressure drop. Equation (29)can be simplified to this case by setting Rout¼ 0 whichreduces Eq. (25) to sin¼ sf (both designs will be verifiedexperimentally in Sec. 7.2)

x ¼ 4q

ND2Aeff

lcr

Rin

Ain

Q2in (31)

4.4.1 Effective Bearing Surface and Friction Analysis. Amethod is developed in this section for estimating the total frictioneffects on the valve spool. This is done by finding an equivalentspool bearing surface area Aeff that can be used in Eq. (26). Thefirst type of friction present is the journal bearing friction which isdue to the helical land and L1/L2 sealing lands which have a com-bined surface area of

Ab ¼ pD Rh þ 2ðL1 þ L2Þ½ � (32)

The second type of friction is due to fluid recirculation in thepockets between the helical lands and the outlet turbine bladeswith surface areas pDL and 2pDLout, respectively (refer to Fig. 5).By using CFD to characterize the friction in the pockets, the effectof this friction can be combined with Ab to form an effective bear-ing surface area

Aeff ¼ Ab þ k ainpDLþ aout2pDLout½ �¼ pD Rh þ 2ðL1 þ L2Þ þ kðainLþ 2aoutLoutÞ½ �

(33)

ain and aout are the ratios of shear stress due to fluid recirculation(rp) to the bearing surface shear (rb), and k is a correction factorused to match the predicted self-spinning velocity to experimentaldata. rp is estimated from a CFD code that assumes steady two-dimensional incompressible Newtonian flow. The spool geometryis approximated by a rectangular chamber with moving upperboundary (Fig. 10). The CFD analysis shows that a single trendline (Fig. 11) is able to capture the dependence of normalizedshear rp=ðqV2Þ

� �on aspect ratio n ¼ w=hð Þ and Reynolds num-

ber Re ¼ qVh=lð Þ

rp

qV2¼ 10bnK (34)

b is a function of Re and is defined at the bottom of Fig. 11 andK¼�0.653. w is the chamber width, h is the chamber depth, andV¼Rx is the sliding velocity of the upper boundary correspond-ing to the spool’s rotational velocity x.

Equation (34) is used to quantify the shear stress due to recircu-lation in the fluid pockets of the nonbearing surface area. Becausethe aspect ratio of the pocket between the helical lands of the inletturbine varies with respect to the spool’s axial position, an averageshear stress is defined for the inlet turbine. Integrating the differ-ential shear stress along the length of the pocket and then dividingby the total surface area (0:5 �wL, where �w ¼ pD=N is the widestportion of the pocket) and knowing that the aspect ratio varies lin-early according to nðlÞ ¼ �w=ðLhÞl for 0 � l � L produces

rp;avg ¼

ðl¼L

l¼0

rpwdl

0:5 �wL¼

ðl¼L

l¼0

10bqV2nðlÞKnðlÞhdl

0:5 �wL

¼ 2

K þ 2qV210b �n

K

(35)

�n ¼ �w=h is the largest aspect ratio corresponding to the widestportion of the pocket. Using Eq. (35), ain ¼ rp;avg=rb. Conversely,because the aspect ratio of the fluid pocket between the outlet tur-bine blades is constant, the shear stress is calculated directly fromEq. (34) and aout ¼ rp=rb.

The journal bearing shear rb is estimated using the shear stressequation for Newtonian flow between two moving plates withconstant relative velocity [25]

rb ¼ lRxcr

(36)

Figure 12 presents the predicted driving power needed to over-come viscous friction. Only 30 W is required to achieve 100 HzPWM frequency with the prototype valve described in Table 1and Sec. 6. ain 0.05 and aout 0.035 for the prototype, and thecorresponding drag torque due to recirculation is about 30% of thetotal friction torque.

4.5 Output Flow Analysis. Due to the rotary valve’s non-zero switching time, flow is bypassed through the relief or checkvalve during transition to limit pressure spikes. Consequently, thevalve’s normalized axial position does not correspond to the trueduty ratio of the valve (i.e., 50% travel does not equal 50% VVDPFig. 10 Pocketed volume and corresponding CFD model

Fig. 11 Normalized pocket shear (K 5 20.653)

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output flow). The two can be correlated by finding the volume offluid bypassed through either the relief (Fig. 2(a)) or check valve(Fig. 2(b)) during transition. Using the approach and definitionsfound in Sec. 4.1.2 and integrating with respect to spool angle, thebypassed fluid volume for a single transition is

Vby ¼1

x

ðH¼Hcrit

H¼0

ðQin � QiðHÞÞdH ¼ QinRw

xD

ffiffiffiffiffiffiffiffiffiffiPopen

DP

r(37)

Qi(H) is the flow through the rotary valve when the relief or checkvalve is open and DP is the critical angle pressure differentialwhen the relief or check valve closes.

For the relief circuit, the volume of fluid bypassed during thetwo load transitions decreases the output flow of the system. Onthe other hand, the two tank transitions have no effect. Accountingfor two load transitions and substituting DP¼Prelief�Pload, jfrom Eq. (2), and multiplying by the PWM frequency, the averageflow bypassed is

Qrelief ¼ jQin

4

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiPopen

Prelief � Pload

r(38)

For the check circuit, the bypassed flow is ported to loadregardless of whether the rotary valve is transitioning to load ortank. Therefore, the bypassed flow during the two tank transitionswill increase the output flow. DP¼PcheckþPload for the tank tran-sitions and the average bypassed flow is

Qcheck ¼ jQin

4

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiPopen

Pcheck þ Pload

r(39)

As with the transition loss, the bypassed flow through the relief orcheck valve is independent of PWM frequency and dependentonly on geometric and system parameters. Using Eqs. (38) and(39), the duty ratio (VVDP output flow fraction) with respect tothe valve’s normalized axial position z is

srelief ¼ z� Qrelief

Qin

(40)

scheck ¼ zþ Qcheck

Qin

(41)

For the prototype described in Table 1 and Sec. 6,Qrelief=Qin ¼ 0:077 and Qcheck=Qin ¼ 0:031 at a load pressure of6.9 MPa.

4.6 Trade Off and Design Summary. Several design tradeoffs exist that can be exploited to improve the rotary valve’s effi-ciency. Using the geometric constraints that the sides of the rhom-bic inlets are parallel to the helical lands and the valve is criticallylapped produces the equality Rh=Rw ¼ L=pD=2N. Using thisequality and substituting in j and Popen from Eqs. (2) and (3) pro-duces the constraint

j2ffiffiffiffiffiffiffiffiffiffiPopen

p¼

ffiffiffiffiffiffiffiffiffiffi128qp

Qin

pCdDL¼ constant (42)

Equation (42) states that Popen and j cannot decrease simultane-ously for a fixed DL. However, since transition losses (Eqs. (17)and (18)) scale with j

ffiffiffiffiffiffiffiffiffiffiPopen

p, Eq. (42) suggests that j should be

increased in order to decrease jffiffiffiffiffiffiffiffiffiffiPopen

p.

Another trade off exists between spool velocity, spool size,leakage, and flow area (pressure drop). Making the simplifyingassumptions that Rin Rout D=2 in Eq. (29) and Ain Aout inEq. (30) yields

x / crQ2in

D

1

Ain

� �/

crQin

ffiffiffiffiffiffiffiffiffiffiPopen

pD

(43)

Equation (43) shows that x can be increased at the cost of throt-tling by increasing Popen, at the cost of leakage by increasing cr,or by reducing the spool’s diameter D which reduces surface areaand friction moment arm. Equations (42) and (43) suggest that theself-spinning velocity can be increased without a penalty in transi-tion loss by increasing the spool length L in Eq. (42) to compen-sate for a decrease in diameter. An additional motive fordecreasing D at high speeds, which was not derived explicitly inSec. 4.2, is that the volume of the inlet pressure rail (shown inFig. 3) scales with D, which accounts for a majority of the com-pressible inlet volume. Therefore, a smaller diameter spool hasthe additional benefit of decreasing compressibility losses, whichare important at high PWM frequencies and load pressures.

Table 1 contains the geometric parameters describing the proto-type valve and designs optimized for 15 Hz and 75 Hz PWM fre-quency at Pload¼ 6.9 MPa and Qin¼ 40 lpm using the designequations derived in Secs. 4.1–4.4 (see Ref. [26] for details on theoptimization method). Note that the total compressible volume,Vin, is the volume in the sleeve, Vsleeve, plus one half of the pumpdisplacement. As expected, the optimization algorithm drivesj ! 1 and Ls, the total spool length, to its upper bound whiledecreasing D as the desired PWM frequency is increased from 15to 75 Hz.

Table 2 contains a breakdown of the various forms of loss cal-culated using the design equations for the prototype and optimizedvalves. In both cases, the transition loss is the dominant form ofloss, accounting for as much as 77% of the total losses for therelief circuit and about 67% of the losses for the check circuit.Using the parameters from the optimization for 15 Hz reduces all

Fig. 12 Power required to overcome viscous friction

Table 1 Rotary valve parameters

Prototype Opt. 15 Hz Opt. 75 Hz

D (mm) 25.4 31 17.8Ls (mm) 98.0 127a 127a

Rw (mm) 3.7 8.1 4.7Rh (mm) 6.5 13.3a 13.3a

L1 (mm) 3.2 2 1.6NAin (mm2) 36.5 161.6 93.8NAout (mm2) 140.5 120.0 93.6Popen (MPa) 0.41 0.021 0.062Pspool (MPa) 0.205 0.081 0.318cr (mm) 0.025 0.020 0.023j 0.56 1.0a 1.0a

Vsleeve (cc) 61 9.2 7.9Vin (cc) 72.4 20.5 19.3

aThe parameter is at the bound specified in the optimization.

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of the losses. Fully open losses no longer exist in the optimizedcase when j¼ 1 because the spool is always in transition.

5 Dynamic System Simulations

A dynamic model of a self-spinning rotary valve based VVDP,including the effects of the compressible inlet volume, accumulator,and transition/full open throttling, is developed in this section. Sev-eral approximations are used to simplify the model: the accumulatorgas is assumed to behave adiabatically, line losses are neglected, andthe relief or check valve in the circuit opens instantaneously. Thepressure drop across the spool, Pspool, is also assumed constant.

The VVDP is modeled with two states. The states include theinlet volume pressure Pin, governed by compressible oil dynamics,and the load pressure Pload, governed by accumulator gas dynam-ics. Using the definition of bulk modulus, the dynamics of the oilvolume can be derived as

_Pin ¼bðPinÞ

Vin

Qvol (44)

Vin is the inlet volume and Qvol (defined in Fig. 2) is the net flowinto the inlet volume found by summing all of the input and outputflows to the volume. b(Pin) is the pressure dependent bulk modu-lus described in Sec. 4.2.

The dynamics of the accumulator gas are derived from the idealgas adiabatic compression equation

_Pload ¼ cPð1þ1=cÞload

P1=c0 V0

Qacc (45)

P0 is the gas precharge pressure, V0 is the initial gas volume, Qacc

is the net flow of oil into the accumulator (Fig. 2), and c¼ 1.4 (theratio of specific heats for air and nitrogen). Equations (44) and(45) are simulated using the MATLAB/SIMULINK software package.

6 Experimental Hardware

The prototype rotary valve components (pump housing, valvesleeve, and spools) are shown in Fig. 13. The VVDP test standconsists of a 5.6 kW ac motor driving a 22.8 cc fixed-displacement vane pump modified for use with the rotary valve.The ac motor is controlled with a variable-frequency drive fortesting at different flow rates. Pressure sensors and a cartridgerelief or check valve are mounted on the sleeve. The sleeve con-tains two output ports. One port returns to tank. The other portconnects to a 16 l diaphragm accumulator precharged to 2.1 MPa,a flow meter, an oil filter, and a needle valve load. During self-spinning operation, a small gerotor pump is used to control thespool’s axial position. A special spool with shaft extension (seeFig. 13) is used to control the spool speed externally. This spool isused to characterize the valve at different PWM frequencies for afixed flow rate. Mobile DTE 25 hydraulic oil is used in the teststand with q¼ 876 kg/m3 and l¼ 0.0387 Pa s at 40 C. Duringoperation, both the amplitude and characteristic of the sound pro-duced by the VVDP resemble that of a motorcycle or lawnmower, depending on the PWM frequency.

7 Simulation and Experimental Results

Experimental data were acquired while operating the rotaryvalve between 15 and 75 Hz PWM frequency for a fixed axialposition, load pressure, and input flow rate (Qin¼ 40 lpm).Prelief¼ 8.3 MPa and Pcheck¼ 1.4 MPa.2 Tests were run at a nomi-nal oil temperature of 30 C with data sampled at 2 kHz.

7.1 Pressure Profiles. Simulated and experimental pressureprofiles are presented in Figs. 14–16. The simulated pressure pro-files are matched to experimental data by tuning r, the fraction ofentrained air. r¼ 0.10, or 10% air entrainment, was found to pro-vide a reasonable match at 15 Hz PWM frequency. While thislevel of air entrainment is higher than the typical 2–7% seen inthe literature [27] and via word of mouth in industry, it appearspossible due to the test stand’s unintentional poor reservoirdesign.3

Figure 14 shows good correlation between the simulation andexperimental data at 15 Hz PWM frequency for various load pres-sures at 50% travel. Spool underlap was included in the simulationafter the discovery of an unintentional 26% underlap in the

Table 2 Breakdown of VVDP losses using the parametersPload 5 6.9 MPa, Qin 5 40 lpm, r 5 0.10. Total output power is 4.6kW.

Prototype 15 Hz Opt. 15 Hz

Ptrans,relief (W) 1222 567Ptrans,check (W) 725 368Popen (W) 179 —Pcomp (W) 69 20PleakþPleak,L1 (W) 113 55

Fig. 13 Prototype rotary valve hardware

Fig. 14 15 Hz pressure profiles: 50% travel

2Prelief and Pcheck are sized such that Prelief¼PloadþPcheck at the maximum loadpressure tested (6.9 MPa). Pcheck>PopenþPspool.

3The test stand reservoir is unsealed, contains no baffling, and the return lines arenot submerged and are located near the pump inlet. As a result, splashing occurs inthe oil at the PWM frequency due to the tank line.

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prototype. The underlap decreases the magnitude of the transitionpeak from load to tank providing a better overall match with theexperimental data. The square-wave characteristic of Pin is clearlyvisible at 15 Hz indicating that the rotary valve is pulsing theflow. Figure 14 also shows that the full open pressure drop acrossthe valve spool and sleeve is 0.62 MPa at 15 Hz and Qin¼ 40 lpm(with Popen¼ 0.42 MPa and Pspool¼ 0.2 MPa). This is consistentwith the prediction of 0.61 MPa from simulation and CFD. Thevariation of pulse width with axial position is shown in Fig. 15,thereby validating the helical land duty ratio concept.

At 75 Hz PWM frequency (Fig. 16), more deviation arisesbetween the simulation and the experiment although a reasonablematch is still achieved. More ripples are evident on the experi-mental inlet pressure when the on/off valve is connected to theload branch. This may be due to fluid inertia or water hammereffects, which are not modeled. The simulation is able to capturethe increasing sluggishness of Pin due to compressibility at higherswitching frequencies caused by the large inlet volume of the unop-timized prototype and the higher than usual air entrainment. Thisemphasizes the need for Vin to be small and the importance ofproper reservoir design for efficient operation at high frequencies.

7.2 Self-Spinning Validation. The self-spinning concept isvalidated by controlling the spool’s axial position hydrostatically.Using this method, the spool is completely isolated from the

sleeve and spun solely with fluid forces. Two spool designs, onewith outlet turbines (labeled T in Fig. 13 corresponding to Eq.(29)) and one without (NT, corresponding to Eq. (31)), weretested along with several clearances. Figure 17 confirms that x isproportional to Q2

in and compares the frequencies achieved experi-mentally with the prediction from the angular momentum analy-sis. Aeff (see Eq. (33)) was calculated with ain and aout based on aspool frequency of 25 Hz using a correction factor of k¼ 2 onthese nonbearing surface area shear ratios. Friction due to fluidrecirculation in the bladeless outlet section of the NT spool wasfound to be significant as including aout produced a better matchwith the experiment (NTCALC in Fig. 17).

Figure 17 reveals that the inlet turbine contributes a majority ofthe torque used to spin the spool. The NT spool spins on average23% slower than a T spool of similar clearance. Decreasing clearancehas a similar effect. Between the loose clearance (cr¼ 0.020 mm)and tight clearance (cr¼ 0.013 mm) T spools, the tight clearancespool spins on average 15% slower. Additional experimental datashow that the PWM frequency is independent of axial position, withless than 15% variation in PWM frequency between the normalizedoutput flows of 0.4–0.7.

7.3 Flow Modulation. Figure 18 compares the predicted,simulated, and experimental axial position/output flow relationshipfor both the relief (top) and check (bottom) circuits. In the relief

Fig. 15 15 Hz pressure profiles: Pload 5 2.8 MPa

Fig. 16 75 Hz pressure profiles: 50% travel

Fig. 18 Output flow versus axial position (15 Hz)

Fig. 17 PWM frequency versus Qin (loglog)

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circuit, increasing Pload decreases Qout for a given axial position.Both the analysis and simulation show that as Pload approaches Prelief,the relief valve is open for a greater part of each cycle since Pin

reaches Prelief earlier in the transition. At Pload¼ 2.8 MPa, the simula-tion predicts that the relief valve is open for roughly 1.5 ms, whilethis time increases to 9 ms when Pload¼ 6.9 MPa.

In the check circuit, the duty ratio is greater than the corre-sponding normalized axial position z (i.e., Qout¼ sQin> zQin) aspredicted in Sec. 4.5, although only at low load pressure. Theinconsistency at high load pressure is likely due to compressibilityand valve underlap. Compressibility during the tank transitionscauses the check valve to open later in the transition, thus leadingto less flow bypassed to load. Valve underlap also decreases theflow to load by introducing a leakage path between load and tank.

7.4 Hydraulic Efficiency. The hydraulic efficiency of the ro-tary valve is calculated by comparing the input hydraulic power tothe valve to the output hydraulic power of the system4

g ¼

Xn

i¼1

PloadðiÞQoutðiÞDt

!=Tavg

Xn

i¼1

PinðiÞQinDt

!=Tavg

(46)

n¼ Tavg/Dt is the number of time steps over which the summationis performed. Experimental data are averaged over 10 s with

Dt¼ 0.5 ms, while simulation data are averaged over 1 s withDt¼ 0.01 ms. Since leakage is present in the measured flow, it isincluded in the simulation results. Pump efficiency, however, isnot included.

Figures 19 and 20 compare the experimental and simulatedVVDP efficiencies at 15 Hz PWM frequency with the characteris-tic efficiency of an equivalent bleed off system (Fig. 1). A goodmatch is observed between the experiment and the dynamic mod-els (refer to Sec. 5). In contrast, the efficiency predicted by the an-alytical design equations in Sec. 4 is noticeably lower for therelief circuit (Fig. 19). This is likely due to the dynamic couplingbetween compressibility and throttling that is not captured by thedesign equations, where the two are considered separately. In theactual system (and dynamic model), compressibility slows downthe pressure dynamics, i.e., increases the rise and fall time of theinlet pressure during valve transition. Because incompressibility isassumed in the orifice equation used in the transition loss analysis(Sec. 4.1.2), the analysis predicts that the relief and check valvesopen sooner in the transition than they do when compressibility isincluded. Therefore, transition losses are overpredicted in therelief circuit since the maximum throttling occurs at the reliefpressure. In the check circuit, however, the throttling losses acrossthe check valve are small so there is less impact on efficiency. At15 Hz, the relief circuit exhibits up to 25% efficiency improve-ment over the bleed off system for high load pressures and dis-placements less than 70% (Fig. 19). At high displacements, therotary valve is less efficient due to Popen and Pspool (see Sec.4.1.1), which must be reduced to achieve high efficiency at highdisplacement. Full displacement efficiency can be furtherimproved by eliminating the transition losses at full displacementin the prototype valve. This can be done by increasing the lengthof the center section of the valve (Lin in Fig. 5) without modifyingthe helical lands.

By switching to the check valve configuration shown in Fig.2(b), the efficiency can be further improved up to 5% across a fullrange of displacements and load pressures (Fig. 20). This increase inefficiency is accomplished by limiting transition throttling toPcheckþPload and also by porting the pressurized bypass flow to loadrather than tank. This configuration demonstrates higher efficiencythan the proportional valve system for displacements under 75%.

The optimized curve in Fig. 20 projects the potential efficiencyof the check circuit using the optimized geometry in Table 1.Other improvements include reducing the check valve crackingpressure and eliminating spool underlap. Using these enhance-ments, the simulation predicts up to 22% efficiency improvementincluding 84% efficiency at 50% displacement. Another 5–10%improvement in efficiency can potentially be achieved with “soft-switching” (see Refs. [18,19]) which reduces transition losses byproviding an alternate flow path.

Upon increasing fPWM from 15 to 75 Hz (Fig. 21), there is moreinconsistency between the experiment and the simulation. This isdue to model mismatch which is observed in the pressure profilesshown in Fig. 16. At 75 Hz, the VVDP is only marginally more ef-ficient than the bleed off circuit at higher load pressures and lowdisplacements due to fluid compressibility in the unoptimized pro-totype. Compressibility increases throttling as mentioned beforeby slowing the dynamic response of Pin such that it no longer tran-sitions as sharply between load and tank pressure. The effect iseven greater at high load pressure. If Pload is too high, Pin may betoo sluggish to reach the intended low pressure fully off state.However, upon decreasing Vin from 72.4 to 19.3 cc using CFDand applying the check circuit (with appropriately sized crackingpressure) and optimized geometry, the efficiency of the VVDPcan be improved by up to 27% across a full range of displace-ments at 75 Hz. The optimized simulation predicts an efficiencyof 77% at 50% displacement.

7.5 Volumetric Efficiency. The volumetric efficiencydefined in this section is based on the leakage across the helical

Fig. 19 Efficiency at 15 Hz: relief

Fig. 20 Efficiency at 15 Hz: check

4Efficiency is given on an absolute scale (0–1) rather than percentages.

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land of the rotary valve separating load pressure from tank (Sec.4.3). Leakage across the end land (L1) was not measured becauseit varies significantly depending on the axial positioning methodused. Leakage across the helical land was measured experimen-tally by holding the spool position fixed with the inlet orificesfully open to load such that DP across the land was Pload�Ptank.Each test consisted of measuring the leakage for Pload between 1.4and 6.9 MPa. Figure 22 provides a comparison between the meas-ured leakage and the prediction from Eq. (21). The temperaturescited represent the average temperature over a single test. Leakagewas measured to be within a factor of 3 of the prediction for oiltemperatures up to 35 C and the results indicate a strong depend-ence on oil temperature. For a system flow rate of Qin¼ 40 lpm,Qleak was roughly 0.5% for the tight clearance spool and less than1.5% for the loose clearance. At Pload¼ 6.9 MPa, this correspondsto a volumetric efficiency greater than 98.5%.

8 Conclusions

A novel three-way self-spinning rotary on/off valve designedfor pulse-width-modulation of hydraulic flow has been presented.A prototype valve based on the proposed design has simultane-ously achieved high flow (40 lpm), low full open pressure drop(0.62 MPa), high speed (100 Hz self-spinning PWM frequencywith 2.8 ms transition time), and low actuation power (30 W).

With self-spinning, the entire actuation power is scavenged fromfluid forces and no external power source is required.

A basic model of the valve suitable for design purposes andoptimization has been developed. A two-state dynamic model hasalso been developed and simulated. Both models have been vali-dated by collecting experimental data from a prototype valve uti-lized in a virtually variable displacement pump. The designequations and dynamic model show good agreement with experi-mental data at 15 Hz PWM frequency. However, as the frequencyis raised to 75 Hz, the model shows less consistency with experi-mental data.

The mean output flow of the VVDP has been verified to exhibita linear relationship with the rotary valve’s axial position, therebyvalidating the helical land concept utilized in the spool. In addi-tion, the self-spinning PWM frequency, predicted to be propor-tional to Q2

in, has been confirmed by experiment. A correctionfactor of 2 on the nonbearing surface area (predicted simplisti-cally) is needed to achieve a good match between the model andthe experimental results.

The prototype VVDP has demonstrated efficiency improve-ments in comparison to an equivalent bleed off system over alarge range of displacements at 15 Hz PWM frequency. At 75 Hz,compressibility negates any efficiency improvement due to thelarge 72.4 cc inlet volume of the prototype valve. A CFD analysisof the valve has shown that the inlet volume can be realisticallyreduced to 19.3 cc without a significant increase in throttling.Combining the reduced inlet volume with parameter optimization,the validated model predicts that an optimized VVDP at 50% dis-placement is able to achieve 84% efficiency at 15 Hz and 77% ef-ficiency at 75 Hz. Proper reservoir design can realisticallydecrease the entrained air to more common values (2–7%) whichwould further improve efficiency.

Future work will focus on validating the optimization, demon-strating the VVDP with realistic loads, extending the rotary valveto the control of motors, and exploring the noise and vibrationattributes of the valve.

Acknowledgment

This material is based upon the work supported by the NationalScience Foundation under Grant Nos. EEC-0540834 and ENG/CMS-0409832.

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Fig. 21 Efficiency at 75 Hz: relief

Fig. 22 Leakage across helical land

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