STUDY ON OIL FILM CHARACTERISTICS OF SLIPPER WITHIN AXIAL PISTON PUMP UNDER DIFFERENT WORKING CONDITION

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1 STUDY ON OIL FILM CHAACTEISTICS OF SLIPPE WITHIN AXIAL PISTON PUMP UNDE DIFFEENT WOKING CONDITION Yi Sun, Jihai-Jiang. Harbin Institute o Technology, School o Mechtrionics Engineering, China ABSTACT In order to accurate master lubrication condition between slier and swash-late under ractical oeration condition, ressure ield and oil ilm characteristics o slier were studied. By analysis motion and orce o slier, establishing mechanics model o it, and simulated in Matlab sotware, variation laws o the ilm thickness with rotation angle, angle o swash late, rotational seed and ressing orce in dierent osition were obtained, The simulation results show that in the range o general working conditions, rotational seed and swashlate angle o iston um will not exceed bearing caacity o oil ilm, but it will have inluence on hydrostatic bearing o slier i exceed certain range, esecially raid change o inertia orce because o increasing rotate seed. KEY WODS Slier, Mathematical model, Oil ilm NOMENCLATUE : Vertical comonent orce o high-ressure oil rom iston that act on the slier d : Diameter o the iston : Discharge oil ressure. t : Horizontal orce rom the sring a : Precomression orce rom center-sring Z : Number o the istons in the um g : Horizontal inertia orce rom single air o the slier and the iston m : Weight o the single iston air φ : Angle rotating instantaneous. : The total ressing orce : Inner radius o slier s sealing region : Outer radius o slier s sealing region s : Pressure o oil groove under the slier. Q : Leakage rom sealing region under the slier Q : The oil lowing into the slier through daming oriice rom iston h : Oil ilm thickness μ : Oil viscosity. d : Diameter o daming oriice l : Length o daming oriice. INTODUCTION The axial iston um is widely used in hydraulic systems to rovide ressure and low or various machines in industry, but there are some several challenging issues associated with it, such as conlicts between lubrication and wear. The slier ad and swashlate orm a key riction air in the axial iston um, excessive wear between them may signiicant inluences the erormance

2 o the um. Hydrostatic slier bearing is an eective way to maintain a luid ilm between slier ad and swash late that slide against each other, and to thereby mitigate direct surace-to-surace contact. There have been many ublications in hydrostatic slier bearing over the ast 0 years, many concerned with imroving the slier erormance o the iston ums. Most o the work has ocused on analyzing the ormation mechanism o hydrostatic bearing over the slier [-]. The eects o slier sin, tangential velocity, tilt, slier non-latness, inlet oriice, and conditions or metal to metal contact, were investigated in [5-9]. The luid-ilm thickness between the thrust bearing and the running surace were also measured within an actual alication, this work was conducted under high seed conditions and showed that a slightly convex bearing design was required or successul oeration[0]. A good analytical understanding o slier behaviour in iston ums is crucial to good design, and a large amount o work has been done in this area [-]. Here we develoed a mathematical model that relected the lubrication condition between slier and swash-late, and the erormance o the hydrostatic slier bearing was analyzed through system simulation. STUCTUE AND WOKING PINCIPLE OF HYDOSTATIC BEAING The rincile o the hydrostatic slier bearing is shown in ig. High-ressure oil rom iston ass through daming oriice and then low into the slier groove, thus generate the bearing orce. The bearing orce can balance the ressing orce which act on the slier i design reasonable, and thus orm a certain thickness oil ilm. The ressing orce is always changing during the um oeration, but because o daming eect, that is daming rom throttle oriice and daming rom ga between the slier and the swashlate which created by the oil ilm, it ensure the oil ilm will maintain stable with load variation. Consequently, reliable luid lubrication is assured and wearing between the slier and the swashlate can be reduced. MOVEMENT AND FOCE OF THE SLIPPE Because the slier bears the high-ressure oil and great ressing orce in the oil discharge ort, and severe wear o the slier mainly occurred in this region too, so this aer mainly study the state o movement and orce o the slier when it in the oil discharge ort. The motion trajectory o the slier is shown in ig. Suose the swashlate angle is γ, the radius o distribution circle in the cylinder is, i regards oxyz as coordinate system, then we can see the trajectory o the slier erendicular to the direction o axis is a circle, while the trajectory in the o' y' z ' lane is a ellise. I the iston rotary as angular velocity ω, and takes to dead center as initial osition, then the um will absorb oil in interval o 0 ~80, and discharge oil in interval o 80 ~60. Fig. Motion trajectory o the slier The orce received by the slier can be seen in ig, the slier mainly bears comonent orce rom iston, sring orce, inertia orce o the iston and hydraulic suorting orce rom oil ilm. Fig. Bearing orce condition o the slier Vertical comonent orce o high-ressure oil rom iston that act on the slier can be exressed as ormula () Fig. Structure roile o hydrostatic slier bearing π d cosγ = ()

3 Horizontal orce rom the sring can be written as equation (). Z a t = () Horizontal inertia orce rom single air o the slier and the iston can be exressed as ormula () m ω tan( γ ) cos( ϕ) g = () Then the total ressing orce can be written as equation (). = t g + cosγ + cosγ () From equation () can be seen that the total ressing orce is constantly changing with rotation angle o the slier, so ressure o oil groove under the slier is also changing constantly, and inally aect the oil ilm thickness under the sier. MATHEMATICAL MODEL OF SLIPPE IN THE OIL DISCHAGE POT The hydraulic suorting orce o hydrostatic slier bearing is shown in ig. π ( ) = s (5) According to the hydrostatic bearing theory, suorting orce should equal to the total ressing orce, so ressure o oil groove under the slier can be exressed as ormula (6) s = π ( ) According to hydrodynamic theory, leakage rom sealing region under the slier can be exressed as ormula (7) Q π h s 6μ (6) = (7) The oil lowing into the slier through daming oriice rom iston can be denoted as ormula (8) π d Q = ( s ) (8) 8μl On the basis o low rate continuation equation, Q is equal to Q, and then it can be exressed as ormula (9) Fig. Hydraulic suorting orce under the slier According to the literature [], the suorting orce can be written as equation (5) F = π s r + π r sdr π d π h s ( s ) = (9) 8μl 6μ From ormula (9) we can obtain relationshi between and s, it can be written as ormula (0) s = + 6 l / d h (0) Then uts the ormula (0) into ormula (6), and then obtains a new ormula ().

4 π ( ) = + 6 l / d h () Outer radius o. sealing region mm Length o oriice. mm Diameter o oriice 0.8 mm We can see rom ormula (), that once the strcture o um is ixed, several arameters can be determined. I suose 6 / k d =, l = k π ( ) then we can abtained the ormulat as ollws h k k = () From ormula () we can see, i the strcture o um is determined, the oil ilm thickness o slier can be exressed as the unction o and, that is to say the oil ilm thickness will be inluenced by outside actor in oerating, such as the load, the inclination angle o the swashlate or the rotation seed. ANALYSIS ON CHAACTEISTICS OF OIL FILM UNDE DIFFEENT WOKING CONDITIONS From above analysis we can see, hydrostatic bearing is an eective way to solve severe wear, while by analysis o oil ilm thickness we can estimate whether or not the hydrostatic bearing can be ormed. Fig 5 shown the oil ilm thickness o the slier ollow with rotation angle, it is obtained based on ormula(). The arameter o simulation is shown in table, load and revolution seed is MPa and 500r/m resectively, and inclination angle is. Table Main arameters o the slier air Parameters Nominal value Dimension Oil viscosity 0.07 Pa s Weight o the single 85 iston air g adius o iston 8.5 mm Density o oil 870 kg/ m Inner radius o. sealing region mm Fig.5 Variaton o oil ilm thickness ollow with rotation angle Because the axial iston um structure is comact and low state under comlex, it is diicult to installation measurement device inside the um, esecially to the high-seed slier, it almost imossible to measure low arameters which is continuous variation. Due to the limitation o exeriment condition, we use exerimental data in reerences [0] roved the accuracy o our simulation, the reerences [0] measuring oil ilm thickness o the slier when the ressure is Ma and rotate seed is 500 rm, and indicated that the average thickness o the oil ilm when the slier in the oil discharge ort is about 5um, this conclusion is conormity with our simulation results, it has ully roven the slier s mechanical model in the oil discharge ort this aer rovides is correct. The inluence o inclination angle From ormula() we can see that the ressing orce act on the slier could be aected by rotation seed o the um, the swashlate angle and the system load, and eventually inluence the oil ilm thickness, so it is necessary to analyse the oil ilm o the hydrostatic slier bearing under dierent conditions. Fig 6 shows variation o the ressing orce with rotation angle in the oil discharge ort under dierent inclination angle. Fig 7 shows variation o the oil ilm thickness with rotation angle corresonding to the ressing orce in ig 6.

5 Fig.6 Variaton o ressing orce ollow with rotation angle under dierent inclination angle when the ratio<, the theory value o oil ilm thickness will less than zero. Surely the oil ilm thickness can not reach negative in ractice, the simulation results only illustrate the ressing orce have already overtaken the ultimate load that the oil ilm can endure at the moment, that is to say the hydrostatic bearing is diicult to orm, and the slier can only oerate in redundant ressing orce condition this time. The inluence o rotation seed From equation () can be seen that the rotation seed also have an eect on the ressing orce and oil ilm thickness. When the inclination angle and the system load remain unchanged, variation o the ressing orce with rotation angle is shown in ig 8. Fig 9 shows variation o the oil ilm thickness with rotation angle corresonding to the ressing orce in ig 8. Fig.7 Variaton o oil ilm thickness ollow with rotation angle under dierent inclination angle From ig 6 we can see, the generally trend o the ressing orce increase gradually with rotation angle in the oil discharge ort, because according to ormula (), the inertia orce o the slier and iston is directly roortional to square o the rotation seed, and varies with the rotation angle, esecially in the case o high rotation seed, the inertia orce increased gradualy in the oil discharge ort. When the rotation seed and the system load kee invariant, the ressing orce increases with increasing inclination angle, this is consists with ormula(), ormula () and ormula (), in that both the ressing orce and the inertia orce increase with the increasing inclination angle. From ig 7 we can see, the oil ilm thickness decrease gradually as the ressing orce increased, and even reached negative when the inclination angle is 7. The answer is: based on the ormula (), the ressing orce is denominator, while numerator remains unchanged, this time their ratio will reduction with increased ressing orce, Fig.8 Variaton o ressing orce ollow with rotation angle under dierent rotation seed Fig.9 Variaton o oil ilm thickness ollow with rotation angle under dierent rotation seed We could see rom ig 8, though the generally trend o the ressing orce increase gradually, it decrease with increasing rotation seed beore the slier reached 70

6 when the inclination angle and the system load remain unchanged, only ater rotating 70, the ressing orce rose sharly with rotation angle. Because according to ormula (), the inertia orce not only roortional to square o the rotation seed, but also directly as cosine o rotation angle, in interval o 80~70 cosine o rotation angle is negative, while it is ositive in interval o 70~60. So when the slier just rotated in the oil discharge ort, the inertia orce decrease as the rotation angle increase, until the slier rotated to 70, the inertia orce increase with the rotation angle. Fig 9 also shows the oil ilm thickness decrease as the ressing orce increase, while it aearance negative when the rotation seed reached 000rm. This situation is similar to the receding, when the ressing orce is more than a certain extent, the oil ilm can not suort the ressing orce, this shows that the oil ilm can not orm this time. From above analysis we can see, the inertia orce o the slier and iston has a great inluence on the oil ilm, esecially at high rotation seed. CONCLUSION In this research, the mathematical model that relected the lubrication condition o the hydrostatic slier bearing is resented, through analyzing the characteristics o the oil ilm under dierent working conditions, some conclusions are obtained as ollows:. Though bearing caacity o the oil ilm o the hydrostatic slier can alies to a wide range o working condition, it is not ininite, once exceed the extreme, it will aec the ormation o the oil ilm, and hydrostatic bearing status o the slier will be destroyed at this time.. When the working conditon remains unchanged, inertial orce o the slier and iston is the key actor aecting the thickness o the bearing o the oil ilm, esecially in the high rotaton seed condtion, the oil ilm will be greatly changed by the inertial orce. Oriice Size Oset and Overclam atio on the Lubrication o Slier Bearing.Tribology International, 996, (9), Koc E, Hooke CJ, Li KY. Slier Balance in Axial Piston Pums and Motors. ASME J Tribol 99, (), Hooke CJ. The Lubrication o Sliers in Axial Piston Pums and Motors-the Eect o Tilting Coules[J]. Proc Inst Mech Eng Part C:J Mech Eng Sci 989, 0(C), Li KY, Hooke CJ. Note on the Lubrication o Comosite Sliers in Water-Based Axial Piston Pums and Motors. Wear 99, 7(), Tanaka, Nakahara. Motion Characteristics o Slier Bearing in Swash late Tye Piston Pum and Motor. Transactions o the Jaan Society o Mechanical Engineers Par.007,. 6-. Yulin Li. Hydraulic Comonents and Systems Design.Beijing:989,.-59. Bihai He, JianguoSun. Calculation and Analysis on Film Thickness o the Sliers Based on Hydrostatic Bearing in the Aeronautical Fuel Piston Pum. Journal o aerosace ower. 009,(),.8~87. Yongge Pan, Decai Han, Tienong Zhou. Exerimental Study on Dynamical Characteristics o Sliers in Axial Piston Pum. Journal o Yanshan University, 990, 6(),.9- EFEENCES. Shengwu XU. Hydraulic Pum o Piston Tye. Beijing, 985, Desheng Wen. Oen-Circuit Axial Piston Pums o Swashlate. Beijing, Desheng Wen. Innovation and Develoment o Hydraulic Comonents. Beijing, Peixiang Qu. Design Method o Axial Piston Pums. Beijing, E. Koc, C. J. Hooke. Considerations in the Design o Partially Hydrostatic Slier Bearings. Tribology International, 998, (0), E. Koc, C. J. Hooke. Investigation into the Eects o