pompa axiala

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doi:10.1016/j.tr

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Tribology International 39 (2006) 1342–1354

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Tribological study on hydrostatic slipper bearing with annular orificedamper for water hydraulic axial piston motor

S.L. Niea,��, G.H. Huangb,�, Y.P. Lib

aSchool of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan, Hubei 430074, ChinabFaculty of Engineering, University of Regina, Regina, Sask., Canada S4S 0A2

Received 29 October 2004; received in revised form 26 July 2005; accepted 21 October 2005

Available online 1 December 2005

Abstract

Hydrostatic slipper bearing is an effective way to maintain a fluid film between slipper pad and swash plate that slide against each

other, and thereby mitigate direct surface-to-surface contact in water hydraulic axial piston motor (WHAPM). The hydrostatic slipper

bearing with an annular orifice damper is proposed, and the reaction force of the bearing in WHAPM is investigated. The effects from

the friction within the cylinder bore, the dynamics of the piston, and the centrifugal force of the piston–slipper assembly are examined.

The characteristic equation of the hydrostatic slipper bearing with an annular orifice damper is formulated, where the effects of various

geometric parameters (e.g. damping length, supporting length, and clearance between the piston and the cylinder bore) are reflected. The

relevant criterion for designing the hydrostatic slipper bearing can then be established. Results of the theoretical analyses indicate that (a)

the friction coefficient, the swash plate angle, and the inertia and centrifugal loads (generated under a high motor rotating speed) would

have significant influences on the reaction force; (b) an appropriate swash plate angle can help eliminate the fluctuation of the reaction

force; (c) the load-carrying capacity of the hydrostatic slipper bearing is more sensitive to the damping length than to the supporting

length of the piston; (d) a short damping length can help enhance the load-carrying capacity; (e) a small clearance between the piston and

the cylinder bore would help improve the adaptive ability to the varying load for the hydrostatic slipper bearing, when clearance between

the slipper pad and the swash plate ranges from 5 to 20 mm. Experimental studies of the slipper pads sliding against the swash plates are

conducted at a custom-manufactured test apparatus, given different material combinations and design methods. The experimental results

indicate that the hydrostatic slipper bearing with an annular orifice damper would decrease the possibility of the severe wear between the

slipper pad and the swash plate in comparison with the hydrostatic clamping ratio bearing in the WHAPM, and the CRA laser cladding

(compared to the ZrO2 �MgO-plasma-sprayed coating and the stainless steel 2Cr13) is a promising candidate as the tribo-material when

sliding against composite materials in water lubrication system. The hydrostatic slipper bearing with an annular orifice damper has been

successfully applied to a WHAPM developed at the Huazhong University Science and Technology. The result demonstrates that the

developed bearing has a satisfactory tribolgical performance, and can be extended to the manufacture of water hydraulic axial piston

pumps.

r 2005 Elsevier Ltd. All rights reserved.

Keywords: Annular orifice damper; Dynamics; Hydrostatic slipper bearing; Piston; Reaction force; Water hydraulic axial piston motor

1. Introduction

Water hydraulic transmission has caught attention as arenascent technique during the past two decades. This isdue to its advantages from both economic and environ-

ee front matter r 2005 Elsevier Ltd. All rights reserved.

iboint.2005.10.007

rrespondence.

ing author. Tel.: +306 585 4095; fax: +306 585 4855.

esses: [email protected] (S.L. Nie),

uregina.ca (G.H. Huang), [email protected] (Y.P. Li).

mental points of view, as characterized by its durability,reliability, safety and cleanness. It has been widely appliedto fields of food processing, papermaking, metalworking,medicine production, atomic power generation, andoceanic development [1,2]. Water hydraulic motor is animportant component in a water hydraulic transmissionsystem. There are several challenging issues associated withthe motor, such as conflicts between lubrication and wear,and between sealing and leakage [1]. Particularly, in awater hydraulic axial piston motor (abbreviated as

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Nomenclature

ps supply pressure (MPa)j angular position (deg)g angle of swash plate (deg)d diameter of piston (mm)R distribution radius of piston (mm)n speed of rotor of motor (r/min)o angular velocity of rotor of motor (rad/s)Fa, Fb acting forces of piston (N)B viscous damping coefficientmp mass of piston–slipper assembly (kg)L theoretical length of piston (mm)L0 piston length remaining in cylinder bore (mm)La, Lb stress distribution lengths of piston (mm)Lc distance from the centroid of piston to spherical

center of piston (mm)f kinetic friction coefficientN reaction force of single slipper (N)Nmax maximum of reaction force (N)Nmin minimum of reaction force (N)Nmean mean of reaction force (N)d fluctuation ratio of reaction force (%)x additive load coefficientx axial position of single piston (m)

u axial velocity of single piston (m/s)a axial acceleration of single piston (m2/s)qv1 flow rate through the clearance between slipper

pad and swash plate (m3/s)qv2 flow rate from the annular orifice to the pocket

(m3/s)pc control pressure inside the pocket (MPa)R1 internal radius of the pocket (mm)R2 external radius of the pocket (mm)h1 lubrication film thickness between slipper pad

and swash plate (mm)Ce1 impact coefficient of laminar entry flow for

slipper padCe2 impact coefficient of laminar entry flow be-

tween piston and cylinder borem dynamic viscosity of fluid(Pa s)l1 damping length of piston (mm)l2 supporting length of piston (mm)h2 clearance between piston and cylinder bore

(mm)a pressure ratio a ¼ pc=ps

W load-carrying capacity of the hydrostatic slip-per bearing (N)

J load stiffness of the hydrostatic slipper bearingJ ¼ @W=@h1

S.L. Nie et al. / Tribology International 39 (2006) 1342–1354 1343

WHAPM), slipper pad and swash plate can form a keyfriction pair, where the above conflicts exist and may resultin significant influences on the motor’s performance.

Hydrostatic slipper bearing is an effective way tomaintain a fluid film between slipper pad and swash platethat slide against each other, and to thereby mitigate directsurface-to-surface contact. Previously, a number of studieson hydrostatic thrust bearing in hydraulic axial pistonequipment were carried out through considering multipleimpact factors such as operating conditions, geometricparameters, and matching materials. Kazama and Yama-guchi [3,4] studied a flat oil-lubricated metallic slipperbearing. Basic equations for the effects from cyclic changesin supply pressure, eccentric loads, fluidic properties andelastic deformation of the parts were derived. Reasonabledesign criteria for optimum sizes of the bearing and the sealparts of the hydraulic equipment were presented under theconditions of concentric loads and steady state. Mixedlubrication characteristics of hydrostatic thrust bearingswere examined experimentally in another research [5]. Theeffects of surface roughness, supply pressure, bearing load,rotation speed, restrictor size, leakage flow rate, and powerlosses were clarified. A significant agreement existedbetween the experimental outputs and the theoreticalresults from a mixed lubrication model. Pang et al. [6]investigated oil film pressure distribution and load char-acteristics through considering (a) the pressure–viscosityeffect of the lubricant, (b) the pressure–elasticity effect ofthe lubricating surface, and (c) the properties of dynamic

stiffness in the oil film. A laser holographic photoelasticexperimental study was conducted for system verification.Thus, an innovative basis in terms of system design andparameter estimation for a high-pressure plunger pumpwould be provided. Koc and Hooke et al. [7,8] studied theeffects of deformation in slipper pad, clamping ratio andorifice size on the load-carrying capacity of hydrostaticthrust bearing under a low-speed condition in axial pistonpumps and motors. They concluded that (a) polishing ofthe running face to a slightly convex form appeared to beessential for successful operation under all conditions; (b)the orifice in under-clamped slippers could increase theclearance and destabilize the slipper, which would result inthe slipper becoming sensitive to the effect of tiltingcouples; (c) the design for over-clamped slippers seemedto depend on the precise value of the clamping ratio andthe width of the slipper land. These theoretical results weresupported by measurements of slipper clearance obtainedfrom an axial piston pump under normal operatingconditions. In another research [9], frictions of water-basedslippers were measured. The results were consistent withthe clearances predicted using the model developed for oil-based slippers. It was reported that a roughness (of theslipper surfaces) of lower than 1 mm would be beneficial forsuccessfully operating the water-based hydraulic system.Manring et al. [10] investigated the effects of pressure-induced deformations on the characteristics of hydrostaticthrust bearing. They developed a mathematical model thatreflected the pressure distribution between the two sliding

ARTICLE IN PRESS

qv

h 2

l2 l1

R1

R2

d

h1

pspc

Swash plate Slipper

Annular orifice fixed damperChangeable damperPocket

Middle chamber

L

Piston Cylinder Screw

Fig. 1. Hydrostatic slipper bearing with an annular orifice damper.

S.L. Nie et al. / Tribology International 39 (2006) 1342–13541344

surfaces, the flow rate from the system supply, and theload-carrying capacity of the bearing. A comparisonanalysis for concave and convex thrust surfaces wasconducted with respect to the magnitude of deformation.The results demonstrated that all deformations wouldincrease the flow rate of the bearing, and that the concavedeformation would increase the load-carrying capacity. Nieet al. [11,12] developed a hydrostatic slipper bearing withan annular orifice damper, which could provide a strongerpower to resist pollution and a higher reliability incomparison with the traditional configuration that wasequipped with a slim-tube damper. The relevant mathe-matical model was established, and the performance of thedeveloped bearing was analyzed through system simula-tion. The results indicated that the load-carrying capacityof the developed hydrostatic slipper bearing was notcorrelated with system pressure, water viscosity, tempera-ture, or rotor speed.

Recently Wang and Yamaguchi [13,14] clarified experi-mentally and theoretically the effects of nozzle andthermoplastic materials on the characteristics of hydro-static bearing/seal parts in water hydraulic axial pumps andmotors. A two-dimensional elastohydrostatic model in-cluding an elastic deformation was developed. The load-carrying capacity, power loss, and load stiffness of thehydrostatic slipper bearing (including effect of elasticdeformation, equivalent Young’s modulus, and eccentricload) were discussed theoretically. It was reported that thebearing made of elastic/rigid materials exhibited largerload-carrying capacity and lower power loss in comparisonwith that composed of materials of the same rigidity.Compared with cases of hydraulic oil, the power loss due toleakage flow in water hydraulic systems was slightly higher,while the loss due to friction torque was much lower.

The tribological properties of different material combi-nations under water lubrication were studied in the pastdecades [15–22]. However, the tribological performance ofmatching materials under low load and low velocity isdifferent from that of hydrostatic slipper bearings in waterhydraulic motors under high load and high sliding velocity.Brookes et al. [23] explored approaches for analysis, designand testing of key friction pairs in seawater hydraulicpump/motor, conducted material screening under thecondition of water lubrication, and investigated the effectof eccentric load on the abrasion of slipper pad and piston.Using pad-on-plate and pin-on-disk tests, a combination ofadvanced engineering ceramics sliding on fiber-reinforcedpolymers in water was evaluated. Terava et al. [24]elaborated a special friction pair testing stand to simulatepiston–cylinder and slipper–swash plate pairs in a waterhydraulic piston pump, and finite element method (FEM)analyses were completed for slipper sliding on a swashplate; it was found that the friction coefficient of stainlesssteel AISI420 against PEEK decreased with increasingsliding velocity under water lubrication. Li et al. [25]explored the wear and lubrication characteristics of Torlonslipper against stainless steel EN431 swash plate in water-

based axial piston pumps and motors, and found that agood friction matching was of benefit in forming ahydrodynamic effect. Yang et al. [26] investigated the wearcharacteristics of matching materials and reported thatengineering ceramics matching with engineering plasticswas preferred for the piston and cylinder of water hydraulicaxial piston equipment.As an extension of literature [12], this research will focus

on the development of a hydrostatic slipper bearing with anannular orifice damper for WHAPM. The objectives aredetailed as follows: (1) reaction force of the slipper pad in aswash-plate-type WHAPM will be investigated, consider-ing the effects of the friction within the cylinder bore, thedynamics of the piston, and the centrifugal force ofthe piston–slipper assembly; (2) characteristic equationof the bearing performance will be developed, such that adesign criterion of the bearing can be established; (3)simulation for the performance of the bearing undervarious geometry and operating conditions will be under-taken; (4) experiments of the slipper pads sliding againstthe swash plates for WHAPM under different materialcombinations and design options will be performedthrough a custom-manufactured testing apparatus, todemonstrate advantages of the developed hydrostaticslipper bearing with an annular orifice damper.

2. Theoretical analyses

2.1. Bearing description

It is crucial to adopt appropriate structures andmatching materials for the slipper and swash-plate pair inWHAPM to mitigate corrosion, wear and leakage. Ahydrostatic slipper bearing with an annular orifice damperis shown in Fig. 1. The hydrostatic slipper bearing consistsof a fixed damper and a changeable damper. The annularorifice typed fixed damper is employed to keep a laminarflow through the clearance between the piston and thecylinder bore. The clearance between the slipper pad andthe swash plate varies with the bearing load. A screw is set

ARTICLE IN PRESS

γ

Z axis

O Y axis

La

Lb

Fb

�d

L

L0Fa

Lc

N sinN

N cos

Fp

o1

X axis

c

Z axis

O

�

f Fb

f Fa

Fig. 2. Forces analyses on a piston.


to form a middle chamber inside the piston, while the fourradial holes on the piston are used to inject fluid into themiddle chamber. A passage at the center of the piston isused to communicate the middle chamber with the pocketwithout any pressure loss. A fluid pressure profile isgenerated between the slipper pad and the swash plate,which acts to support the slipper pad against the swashplate and creates a separating force (W) to balance thebearing load.

2.2. Load characteristics of the piston

2.2.1. Mechanical analysis

To design the hydrostatic slipper bearing properly, it issignificant to simulate the forces that act on the slipper. Asketch of mechanical kinetics analysis for the piston insidethe high-pressure zone is shown in Fig. 2. As the pistonreciprocates within the cylinder bore of WHAPM, it ispushed by the high-pressure fluid against the swash plateby means of the slipper pad. Here the reaction force of theslipper pad is given as N. The supply pressure of the systemis assumed to be constant within the high-pressure zone.Viscous damping and friction coefficient for the reciproca-tion process of the piston are assumed to be identical. Thecentrifugal force of the piston–slipper assembly is lumpedat centroid C. The normal reaction forces of the pistonagainst the cylinder bore are lumped as Fa and Fb, while therelevant friction forces are shown on the contact lineswithin the cylinder bore as fFa and fFb, respectively. Thetotal contacting length between the piston and the cylinderbore is constant during the reciprocation of the pistonowing to the special piston profile. Considering the effect ofthe hydrostatic slipper bearing, the friction force betweenthe slipper pad and the swash plate can be negligible.Actually, for the hydraulic axial piston motor, the springforce for piston return is also negligible [27].

N ¼p=4d2ps �mpRo2 tan g cos jþ fmpRo2 co

cos gþ f sin g

When the piston draw back the cylinder block com-pletely, we have j ¼ 0 and x ¼ 0. For the piston inside thehigh-pressure zone, its position, axial velocity, and axialacceleration can be described as follows:

x ¼ R tan gð1� cos jÞ, (1)

u ¼dx

dt¼ Ro tan g sin j, (2)

a ¼d2x

dt2¼ Ro2 tan g cos j. (3)

The force equilibrium along the X-axis and the momentequilibrium relative to the center of the piston joint can beexpressed as follows:

mpa ¼p4

d2ps �N cos g� f ðF a þ FbÞ � Bu, (4)

Fa � Fb �N sin gþmpRo2 cos j ¼ 0, (5)

Fa L� L0 þLa

3

� �� Fb L�

Lb

3

� �

þmpRo2 cos j� Lc þd

2f ðF a � FbÞ ¼ 0. ð6Þ

Furthermore, the two stress-distributing triangles of thepiston caused by elasticity deformation are similar to eachother [27]. Therefore, we have:

La ¼3L� L0 � L2

0

6L� 3L0, (7a)

Lb ¼3L� L0 � 2L2

0

6L� 3L0. (7b)

By solving Eqs. (1)–(7), the reaction force (N) of theslipper pad can be obtained as follows:

s j½3ðL� LcÞ=L0 þ La=L0 � 2� � BRo tan g sin jð3L=L0 þ La=L0 � 2Þ

. (8)

ARTICLE IN PRESSS.L. Nie et al. / Tribology International 39 (2006) 1342–13541346

2.2.2. Sensitivity analysis

To analyze the sensitivity of the reaction force (N) to thegeometrical and operating conditions, simulation of thereaction force is conducted through the MATLABpackage. The fluctuation of the reaction force within thehigh-pressure zone (j ¼ 021801) is highlighted, while thelow-pressure effect in WHAPM is considered negligible.Parameter d is used to express the fluctuation ratio of thereaction force, which is defined as follows:

d ¼Nmax �Nmin

Nmean� 100%. (9)

Several parameters associated with the mechanicalmodel (8) are obtained from Nie [12], while the othersare estimated based on information from the existingliterature [27,28]. The main parameters used for thesimulation are listed in Table 1.

N ¼p=4 d2ps �mpRo2 tan g cos jþ fmpRo2 cos j½3ðL� LcÞ=L0 þ La=L0 � 2�

cos g. (10)

The effects of the kinetic friction coefficient (f) on thereaction force are illustrated in Fig. 3(a). It is indicated thatthe kinetic friction coefficient has significant effects on thefluctuation ratio of the reaction force within the high-pressure zone (j ¼ 021801). When f is low (e.g. less than0.1), the reaction force would be raised under an increasedj level and, thus, the inertia force would be prominent(instead of the friction force). Conversely, when f is high(e.g. more than 0.2), the friction force would becomeprominent. The reaction force would become nearlyconstant when f is between 0.1 and 0.15; however, anincrease in f level would lead to significant fluctuations inthe reaction force.

Figs. 3(b)–(d) show the effects of supply pressure,rotating speed and swash-plate angle on the reaction force,respectively. It can be seen from Fig. 3(b) that a highsupply pressure would result in a raised reaction force and

Table 1

Main simulation parameters of the hydraulic slipper bearing

Parameter Value Unit Parameter Value Unit

ps 14 MPa n 1500 r/min

g 10 deg m 0.55� 10�3 Pa s

B 0.028 — f 0.05–0.1 —

h1 5–15 mm h2 15–20 mmd 16 mm R 35 mm

R1 8 mm R2 10.25 mm

l1 6 mm l2 28 mm

Ce1 1.3 — Ce2 2 —

L 51.0 mm L0 34 mm

Lc 16 mm mp 0.08 kg

thus alleviate its fluctuation, and the reaction force wouldalso be raised under an increased j level. Fig. 3(c) showsthat a high rotating speed would lead to a significantfluctuation of the reaction force; such a fluctuation wouldbe raised when the j level is increased. Fig. 3(d) presentsthe fluctuation ratios (d) under different swash-plateangles. When the swash-plate angle ranges between 71and 101, the fluctuation of the reaction force becomesinsignificant, where the friction and inertia forces arecounterbalanced to each other. When the swash-plate angleis between 71 and 8.51, the reaction force would be reducedas the j level is raised. When the swash-plate angle isbetween 8.51 and 151, the reaction force becomes increasedas the j level is raised. In addition, it is apparent that theeffects of viscous damping of the piston on the reactionforce are weak and negligible. Therefore Eq. (8) can berewritten as follows:

2.3. Design criterion

þ f sin gð3L=L0 þ La=L0 � 2Þ

2.3.1. Characteristic equation

Assume that the flow between the slipper pad and theswash plate is laminar and its pressure profile is a naturallogarithmic type curve within the range of sealing zone [27].Then the flow rate through the clearance (h1) can be writtenas follows:

qv1 ¼ph3

1pc

6mCe1 ln ðR2=R1Þ. (11)

Because eccentricity of the piston inside the cylinder boreis uncertain, the volumetric flow rate through the annularorifice could be calculated according to the averageeccentricity. Although clearance h2 is very small, thecross-section area of the annular orifice is relatively largein comparison with the slim-tube damper in the hydrostaticslipper bearing under oil lubrication [12]. Based on theconventional equation for a low Reynolds’ number flowassociated with the effect of a laminar inceptive flow, theflow rate from the annular orifice to the pocket can berepresented as follows:

qv2 ¼pd

12ml1Ce2h32ðps � pcÞ � 1:75þ

pd

2h2n

�pd

12ml2Ce2h32pc � 1:75þ

pd

2h2n

� �

¼pd

12mCe2h32

ps � pc

l1�

pc

l2

� �� 1:75. ð12Þ

Define the pressure ratio as a ¼ pc=ps. Based onthe continuity equation of fluid flow, the chara-cteristic equation of the bearing can be derived

ARTICLE IN PRESS

Fig. 3. Effects of different factors on the reaction force.


from Eqs. (11) and (12):

a ¼1

1þ l1=l2 þ ð8l1Ce2=7dh32Ce1 ln ðR2=R1ÞÞh

31

¼1

1þ k1 þ k2h31

, ð13Þ

where k1 ¼ l1=l2 and k2 ¼ 8l1Ce2=½7dh32Ce1 ln ðR2=R1Þ�.

It can also be deduced from Eq. (13) that if h1! 0 thena! 1=ð1þ k1Þ. This means that the pressure ratio (a) ofthe hydrostatic slipper bearing lies between 0 and1=ð1þ k1Þ.

2.3.2. Load-carrying capacity

In the light of the assumptions for Eq. (11), the supportforce (W) generated from the pressure profile of the slipperpad can be expressed as follows:

W ¼p2

R22 � R2

1

ln ðR2=R1Þ

� �pc ¼

p2

R22 � R2

1

ln ðR2=R1Þ

� �psa. (14)

The support force (W), which acts to resist the load ofthe bearing, denotes the load-carrying capacity of thebearing. From Eq. (14), the load-carrying capacity ofthe bearing is proportional to the pressure ratio (a) and the

supply pressure (ps). Substituting Eq. (13) into Eq. (14), wehave

W ¼p2

R22 � R2

1

ln ðR2=R1Þ

� ��

ps

1þ k1 þ k2h31

. (15)

The load stiffness of the hydrostatic slipper bearing canbe denoted as J ¼ @W=@h1. The pressure ratio (a) underthe maximum load stiffness and the correspondinglubrication-film thickness can be derived from the limitingvalue of @J=@h1 ¼ 0:

a Jmaxj ¼2

3ð1þ k1Þ, (16)

h1 Jmaxj ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffi1þ k1

2k2

3

s. (17)

To explore the sensitivity of the load-carrying capacity tothe clearance (h2) and the contacting length between pistonand cylinder bore, relation curves of the pressure ratio (a)and the clearance (h1) under different h2, l1 and l2 levels arepresented in Fig. 4. A steep curve indicates a strongadaptive capability to the variable load, implying that anysmall variation in the clearance (h1) will result in significant


variations in the pressure (pc) inside the pocket as well asthe load-carrying capacity.

Fig. 4(a) shows that the clearance (h2) between the pistonand the cylinder bore has a significant impact on pressureratio (a), where the detailed conditions under differentclearance levels (h2 ¼ 10, 12, 15, 20, 25 and 30 mm) areprovided. A lower clearance (h2) exhibits a strongeradaptive ability to the variations of the load when h1ranges from 5 to 20 mm. For the WHAPM, an over-sizedclearance (h2) between the piston and the cylinder borewould result in a high leakage flow and a low volumetricefficiency due to the low viscosity of water. Conversely, adesire to reach an extremely low clearance (h2) would leadto significantly increased manufacturing cost, although itmay be of benefit to the bearing operation. Therefore, it isappropriate to set h2 ¼ 15225mm for the hydrostaticslipper bearing in the WHAPM. The effect of thesupporting length between the piston and the cylinderbore (l2) on the pressure ratio (a) is illustrated in Fig. 4(b),under l2 ¼ 25, 28, 35, 40 and 45mm. The longer thesupporting length (l2) is, the higher the maximum pressureratio (a) becomes and thus the load-carrying capacity forthe bearing; however, the pressure ratio (a) is insensitive tol2 when h1 is between 5 and 15 mm.

The effects of the damping length (l1) on the pressureratio (a) are illustrated in Fig. 4(c), under l1 ¼ 4, 6, 8 and10mm. A short damping length (l1) could help enhance thepressure inside the pocket (pc) as well as the pressure ratio(a), leading to an increased load-carrying capacity. At thesame time, as shown in Eqs. (12) and (13), a short dampinglength (l1) would also correspond to a short supportinglength (l2), leading to a shortened sealing length betweenthe piston and the cylinder and thus an increased leakageflow; conversely, a long damping length (l1) wouldcorrespond to a long supporting length (l2), resulting indifficulties in configuring the piston. In general, the load-carrying capacity of the bearing is more sensitive to thedamping length (l1) than the supporting length (l2).Therefore, choice of the damping length (l1) should beconsidered eclectically.

Fig. 4. Effects of different factors on the pressure ratio.

2.3.3. Geometrical constraint

In fact, the reaction force (N) of the slipper is the load tothe bearing, which is resisted by the support force (W). Asshown in Fig. 3, the reaction force varies with the angularposition (j) of the slipper. Within the high-pressure zone,its maximum corresponds to a large a and a small h1, whileits minimum corresponds to a small a and a large h1. Tosimplify the design, the mean value of reaction forces canbe assumed to be the loads of the bearing under thedesignated clearance ðh1jJmaxÞ. Therefore, integrating Eqs.(10), (15) and (17), we have

d2

cos gþ f sin gð3L=L0 þ La=L0 � 2Þ¼

R22 � R2

1

ln ðR2=R1Þ

� �4

3ð1þ k1Þ.

(18)

Eq. (18) is thus the design criterion for the hydrostaticslipper bearing in the WHAPM. Obviously, the kineticfriction coefficient between the piston and the cylinder bore

ARTICLE IN PRESS

Piston-slipperassembly

Measuringgraduaten

WaterbasinSwash

plate

Accumulator

Filter

Flowmeter

Throttlevalve

Check valvesblock

Pump

Waterreservoir

Pressuregauge B

Reliefvalve B

Reliefvalve A

Pressuregauge A

Axes

Fig. 5. Sketch of test bench.


has significant effects on the geometry of the bearing.However, this coefficient would vary with differentmaterial combinations and is of uncertain feature duringthe reciprocation process of the piston. Assume that thefriction coefficient between the engineering composites andthe corrosion-resistant metals varied between 0.10 and 0.20[15], Eq. (18) can be rearranged as follows:

d2

cos gx ¼

R22 � R2

1

ln ðR2=R1Þ

� �4

3ð1þ k1Þ, (19)

where the additive load coefficient is defined as x ¼ 1=½1þf tan gð3L=L0 þ La=L0 � 2Þ�. Generally x ¼ 0:9320:96.

3. Experimental research

3.1. Experimental method

3.1.1. Apparatus

The simulation bench (Fig. 5) was built based on aswash-plate-type single piston equipment, which wasemployed to simulate the slipper-pad vs. swash-plateinterface and the piston vs. cylinder bore interface inhigh-pressure water. In this device, the swash plate wasdriven by an electromotor associated with a frequencyinverter (from 0 to 2000 r/min), while the cylinder blockwas set stationary. The angle of the swash plate was 101,and the maximum diameter of the piston was 25mm whileits distribution radius in reference to the rotating axis of theswash plate was 35mm. The medium used in the apparatuswas synthetic seawater, which was produced according tothe ASTM D1142-52 and purified through a 10-mm filter.The pressurized water was supplied by a water hydraulicpower package. The system pressure could be regulatedfrom 6 to 16MPa through a water throttle valve, and theflow rate could be adjusted from 8 to 17L/min by means ofa water hydraulic axial piston pump driven by a frequencyinverter (from 700 to 1500 r/min). Relief valves A and Bacted as a safety support system. The testing temperatureof the fluid medium was controlled within the range of20–30 1C. To examine the wearing status of the testedspecimen, the slipper pad was separated from the slippersuch that the swash plate could be easily disconnected fromthe rotating axis.

3.1.2. Measurement

The wearing rates of the slipper pad and the swash platecould be represented by their thickness differences withinoperation duration. The operating procedures included: (1)four equal markers were marked on the reverse of thetested samples; (2) all engineering plastic specimens wereimmerged in pure water to reach saturation; (3) all sampleswere cleaned with acetone in an ultrasonic bath for 10minbefore the test; (4) the average of the three measured valuesfor each marker was regarded as the measuring result forthe marker, and then the average of the measured valuesfor all markers was noted as the measuring result for the

specimen. The roughnesses of the samples were measuredthrough Hommel Tester T8000. All micrographs of thesamples were taken through Smartscope 250 AutomaticPhotomicrography System. The engineering ceramic sam-ples should undergo carbon sedimentation on its workinginterface electrically prior to the examination on S-570HITACHI EDAX scanning electron microscope (SEM).

3.1.3. Specimen

To investigate the friction and wear of the slipper-padand swash-plate materials, several pairs of piston–slipperassemblies were designed and fabricated based on theabove theoretical analyses. According to the literature onfriction match under water lubrication [15–26], thecharacteristics of the tested samples were listed in Table 2.

3.2. Result analysis

In this research, the supply pressure was 14MPa, therotating speed of the swash plate was 1200 r/min, andthe mean sliding velocity of the slipper pad relative to theswash plate was approximately 4.3m/s. The operatingperiod was 8 h.Fig. 6 shows the wearing depths of the slippers pads

sliding against the swash plates under different materialcombinations within the operating period. The wearingdepths of the slipper pads were sensitive to the materials ofthe swash plates. For a slipper pad made of an identicalmaterial (either PEEK or TX), its wearing depth would be

ARTICLE IN PRESS

Table 2

Specifications of the tested samples

Part Material Average roughness (mm) Hardness

Piston 17-4 PHa Ra 0.80 HRC 42–45

Cylinder sleeve PEEKb Ra 0.45 M102

Slipper Ti6A14V — —

Slipper pad TXc Ra 0.23 M94

PEEK Ra 0.11 M102

Swash plate ZrO2 �MgO plasma sprayed on 1Cr18Ni9Ti Ra 1.08 HRC 56–58

CRAd laser clad on Ti6Al4V Ra 0.07 HRC 53–55

2Cr13 (Hardened) Ra 0.35 HRC 47–53

aThe 17-4 PH is an abbreviation of 0Cr17Ni4Cu4Nb; it is produced through special heat treatment for hardening.bPEEK including carbon fiber reinforced with graphite and PTFE lubricant.cTX is a polyethylene terephthalate compound incorporated with a uniformly dispersed solid lubricant.dCRA is an abbreviation of corrosion-resistant alloy, with its composition being: C ¼ 0.7–0.9%, Co ¼ 12–15%, Cr ¼ 22–24%, W ¼ 4–5%,

Mo ¼ 3.5–4.5%, Feo3%, rare elementso1%, Si+B ¼ 3.5–4.5%, and Ni ¼ others.

2.4

4.4

0.2 0.6 1.2

12.6

0

5

10

15

PEEK / ZrO2 TX / ZrO2 PEEK / CRA TX / CRA PEEK / 2Cr13 TX / 2Cr13

Wea

ring

dep

ths

/ um

Fig. 6. Wear depths of the slipper pads.


the highest when sliding against the ZrO2 �MgO-plasma-sprayed swash plate, the next highest when against the2Cr13 swash plate, and the lowest when against the CRA-laser cladding swash plate.

Fig. 7 shows the SEM images of the ZrO2 �MgO-plasma-sprayed coating on the 1Cr18Ni9Ti swash plate as well asthe CRA-laser cladding on the Ti6Al4V swash plate. Itcould be seen from Figs. 7(a) and (b) that, there wereseveral tiny air holes and impurities at the transition zoneof the plasma sprayed coatings, which were mechanicallycombined with 1Cr18Ni9Ti metallic substrate. Some ofthose holes might communicate to each other and formfluid channels. Consequently, seawater could access themetallic substrate and thus erode the interphase. Theerosion could cripple the combined strength of the coatingand the 1Cr18Ni9Ti metallic substrate, causing debris topeel off and thereby to increase abrasion wear. The CRAlaser cladding was metallurgically bonded with theTi6Al4V metallic substrate. As shown in Figs. 7(c) and(d), minor problems such as air hole and impurity existedin the laser cladding. The phase structure was generallydense and uniform. Therefore, the wearing depth of itscomposite counterpart was lower than that in theZrO2 �MgO-plasma-sprayed coating. For the 2Cr13 swashplate, a thimbleful of metal debris sticking on its compositecounterpart (either PEEK or TX) could be found. This wasattributed to the low hardness of 2Cr13 that might lead to

an adhesion tendency between the composite slipper padand the 2Cr13 swash plate under high load and slidingvelocity. Hence, both composite counterparts of the 2Cr13swash plates exhibited larger wearing depths than that ofthe CRA laser cladding. Thus, the CRA laser cladding wasa promising candidate as the tribo-material when slidingagainst composite materials in water lubrication system.In order to validate the advantages of the bearing

developed through this research, several comparisonexperiments with the bearings designed through thehydrostatic clamping ratio method were performed. Thedesign method for the hydrostatic slipper bearing with anannular orifice damper was denoted as Method A, whilethe design method for the bearing with the hydrostaticclamping ratio is 1.1 (e ¼ 1:1) was denoted as Method B.No auxiliary supporting area would be adopted on thesliding surfaces of the slipper pads in either Method A or B.The experimental conditions were exactly identical exceptthat two different design methods were used.Fig. 8 shows the wearing depths of the TX and PEEK

slipper pads sliding on the CRA-laser-cladding swash platewithin the operating period. It is indicated that the wearingrates of the bearing under such a condition were lower thanthose under a hydrostatic clamping ratio (e) of 1.1; also, thehydrostatic slipper bearing with an annular orifice damperwould have a reduced wearing rate for the slipper pad.Fig. 9 shows the micrographs of the tested slipper pads.

The hydrostatic slipper bearing could provide a lubricationfilm between the friction pair, which would help avoidor alleviate directly rubbing against each other. FromFigs. 9(c) and (d), the composite surface of the slipper pad(either PEEK or TX) would not be scratched severely by itscounterpart swash plate. The TX slipper pad’s higherwearing rate (than the PEEK slipper pad) as well as itsmechanical scuffing was ascribed to the relatively lowhardness of the TX. In addition, a thimbleful of metaldebris sticking on the worn surface of the TX slipper pad,as shown in Fig. 9(d), could be identified. This implied theexistence of an adhesion tendency between the TX slipperpad and the CRA laser cladding under high load and

ARTICLE IN PRESS

Fig. 7. SEM of swash plates.

0.6

3.5

0.2

1.3

0

0.5

1

1.5

2

2.5

3

3.5

4

TX (A) TX (B) PEEK (A) PEEK (B)

Wea

ring

dep

ths

/ um

Fig. 8. Wear depths of different slipper pads sliding on CRA swash plates.


sliding-velocity conditions. Generally, the composite slip-per pad sliding on CRA laser claddings supported by awater lubrication film would result in a satisfactorytribological performance.

For the slipper bearing designed based on Method B, acontinual lubrication film could hardly be formed betweenthe friction pair, due to the existence of a high residualcompacting force. When sliding against the CRA-laser-cladding swash plate as shown in Figs. 9(e) and (f), there

would appear several grooves on both of the PEEK andTX slipper pads because of the mechanical plowing.Especially, there would be adhesion debris flaking offfrom the TX slipper pad. The high contact pressure andadhesion at local contact points could lead to an increasedsurface temperature and thus a ‘‘heat fusion’’. The shearstrength of the contact points would normally be lowerthan that of the CRA laser cladding (850MPa) but higherthan that of the TX (59MPa). Thus, under a high slidingvelocity, the adhesion debris would flake off from the TXsurface and in turn plow on this surface, owing to the lowhardness (M94, ASTM D785) and low tensile strength(72MPa) of the TX. Lack of a continual lubrication filmbetween the friction pair would thus lead to a raisedoperating temperature.With increasing temperature, the adhered debris would

gradually peel off the swash plate due to thermal and stressfatigues, leading to severe multi-body abrasion between theslipper pad and the swash plate. This process wasconsistent with the high wearing depth of the TX slipperpad in comparison with the PEEK slipper pad. For the TXslipper pad, several suspending particles could be foundin the seawater basin. Moreover, the flaked TX debriswas washed away and ground into the mini-holes on the

ARTICLE IN PRESS

Fig. 9. Micrographs of the slipper pads sliding on CRA swash plates.


CRA-laser-cladding surface, which formed discontinuousthin plastic layers. Such a phenomenon was not found inthe PEEK-slipper pad. This was attributed to the relativelyhigh melting temperature and high hardness of PEEK.

4. Discussion

(1)
For the WHAPM, to mitigate fluctuations of the outputtorque, determination for the angle of the swash plateshould be based on (a) geometric parameters of thepiston–slipper assembly, and (b) kinetic friction coeffi-cient between the piston and the cylinder bore. In fact, ifthe swash plate angle is designated as g ¼ tan�1
f ð3ðL� LcÞ=L0 þ La=L0 � 2Þ� �

, the fluctuation of thereaction force could then be eliminated, and thereby thereaction force of the WHAPM would equal the mean ofthe reaction forces; this forms the basis for designing thehydrostatic slipper bearing. The key parts of the custom-manufactured testing apparatus could be designedaccording to the criterion as shown in Eq. (18).

(2)
It is crucial that the hardness of the metallic parts,when sliding against composite counterparts, should belarger than HRC 50. An increased surface hardnesswould be beneficial for improving the wearing perfor-mance of matching material [27]. However, the predic-tion results would not completely agree with the actualwearing rates of the metallic counterparts, as shown inFig. 6. As to the composite parts, the wearing rateswere significantly affected by the roughness of slipperpads as well as the hardness of PEEK (higher than thatof TX). A rougher TX would lead to a higher wearingdepth on the slipper pad and could thus permit moredirect contact than a smoother PEEK [29] (Fig. 8).Therefore, a lower roughness level (for the compositeslipper pad) would help facilitate successful operationsof the water hydraulic system, which is consistent withthe results of Ref. [9].
(3)
The reaction force of the slipper is dependent on thekinetic friction coefficient between the piston and thecylinder bore. From Fig. 3(a), an increased kinetic

ARTICLE IN PRESSS.L. Nie et al. / Tribology International 39 (2006) 1342–1354 1353

friction coefficient (f) would not only boost up thefluctuation ratio of the reaction force within the high-pressure zone, but also lessen the magnitude of thereaction force. When f varies from 0.1 to 0.3, the meanreaction force would decrease from 2730 to 2490N witha decreasing ratio of 8.8%. This implies that the sameshare output-torque loss would occur due to thefrictional loss originated from the interface of thepiston and the cylinder bore. Although a low f levelcorresponds to a high reaction force (and thusincreased contact stress between the slipper pad andthe swash plate), the developed hydrostatic slipperbearing could help effectively reduce the possibility ofdirect rubbing against each other. This result isconsistent with the experimental output as shown inFig. 8.

(4)
The kinetic friction coefficient of Cotton Fiber FilledBakelite (abbreviated as CFFB) sliding against stainlesssteel is 0.01–0.03 as introduced in Ref. [27], while thatof PEEK sliding against stainless steel (such as thehardened 17-4 PH) is 0.19–0.21 [12]. A cylinder sleevemade of CFFB was initially employed to match againstthe hardened 17-4 PH piston, so as to validate theeffects of varied f on the reaction force and wearing rateof the slipper pad. However, the clearance between thehardened 17-4 PH piston and the CFFB cylinder sleevewould become unsteady, due to the unstable linearexpansion coefficient of the CFFB with the increasedoperating temperature as well as immersion saturationwater absorption ratio. In this study, since the pistonwas often enclasped and thus could hardly runsmoothly, the relevant comparison experiments becamehard to be implemented successfully.
(5)
Due to the lack of effective means for measuring thewater-film thickness, it became difficult to quantify (a)the lubrication film between the slipper pad and theswash plate, or (b) the kinetic friction betweenthe piston and cylinder bore. Also, it is desired thatthe correlations between the water film thickness andthe leakage flow and between the friction coefficientand the wearing rates (of the matching materials) beinvestigated. Further research efforts into these areaswould be beneficial for enhancing the bearing’sperformance.
5. Conclusions

(1)
In this research, the hydrostatic slipper bearing with anannular orifice damper has been proposed, and thereaction force of the bearing in a swash-plate axialpiston motor has been investigated. The effects of thefriction within the cylinder bore, the dynamics of thepiston, and the centrifugal force of the piston–slipperassembly, are addressed. The simulation analyses haveindicated that, the friction coefficient, the swash plate
angle, and the inertia and centrifugal loads due to thehigh rotating speed of the motor have significantinfluences on the reaction force; the appropriate swashplate angle can eliminate the fluctuation of the reactionforce.

(2)
The characteristic equation of the hydrostatic slipperbearing with an annular orifice damper has beenestablished including the effects of geometrical para-meters, such as the clearance (h2), the damping length(l1) and the supporting length (l2) between the pistonand cylinder bore. The load stiffness of the hydrostaticslipper bearing has been investigated. And then thedesign criterion of the hydrostatic slipper bearing withan annular orifice damper has been derived.
(3)
The sensitivity analyses of the load-carrying capacity tothe geometry of the hydrostatic slipper bearing with anannular orifice damper have been elaborated. The load-carrying capacity of the hydrostatic slipper bearing ismore sensitive to the damping length (l1) than thesupporting length (l2), and the short damping length (l1)can enhance the load-carrying capacity. The smallclearance (h2) is helpful to improving the adaptiveability to the change of load for the hydrostatic slipperbearing when h1 ranges from 5 to 20 mm.
(4)
The material screening experiments for the slipper padssliding against the swash plates have been conducted ata custom-manufactured testing apparatus. The experi-mental results have indicated that the hydrostaticslipper bearing with an annular orifice damper woulddecrease the possibility of the severe wear between theslipper pad and swash plate in comparison with thehydrostatic-clamping-ratio bearing in the WHAPM,and the CRA laser cladding (compared to theZrO2 �MgO-plasma-sprayed coating and the stainlesssteel 2Cr13) is a promising candidate as the tribo-material when sliding against composite materials inwater lubrication system.
(5)
The developed hydrostatic slipper bearing has beensuccessful applied to WHAPM [12]. The WHAPM canbe driven by seawater or fresh water with its volumetricefficiency reaching approximately 86% under a pres-sure of 10MPa. Since December 2002, the WHAPMhas been equipped to a brush/grinder driven by aseawater hydraulic power system, which has beenoperated by an underwater engineering team. Thosedemonstrate that the developed bearing has a satisfac-tory tribolgical performance.
(6)
Although this hydrostatic slipper bearing has beendeveloped for the WHAPM in this research, the relatedmechanism could be extended to the design andmanufacture of water hydraulic axial piston pumps.
Acknowledgments

The authors would like to thank the anonymousreviewers for their insightful comments and suggestions


that were very helpful for improving the manuscript. Theauthors were also grateful to Dr. Q.G. Tang for histechnical assistance and advice. This research was fundedby the Natural Science Foundation of China (No.50375056).

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pompa axiala

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