• <tr id="yyy80"></tr>
  • <sup id="yyy80"></sup>
  • <tfoot id="yyy80"><noscript id="yyy80"></noscript></tfoot>
  • 99热精品在线国产_美女午夜性视频免费_国产精品国产高清国产av_av欧美777_自拍偷自拍亚洲精品老妇_亚洲熟女精品中文字幕_www日本黄色视频网_国产精品野战在线观看 ?

    Effects of splined shaft bending rigidity on cylinder tilt behaviour for high-speed electrohydrostatic actuator pumps

    2019-02-27 09:00:12JunhuiZHANGYunCHENBingXUMinPANQunCHAO
    CHINESE JOURNAL OF AERONAUTICS 2019年2期

    Junhui ZHANG,Yun CHEN,Bing XU,Min PAN,Qun CHAO

    aThe State Key Laboratory of Fluid Power and Mechatronic Systems,Zhejiang University,Hangzhou 310027,China

    bDepartment of Mechanical Engineering,University of Bath,Bath BA2 7AY,United Kingdom

    Abstract High-speed axial piston pumps are hydraulic power supplies for electro-hydrostatic actuators(EHAs).The efficiency of a pump directly affects the operating performance of an EHA,and an understanding of the physical phenomena occurring in the cylinder/valve plate interface is essential to investigate energy dissipation.The effects of the splined shaft bending rigidity on the cylinder tilt behaviour in an EHA pump need to be considered,because the deflection and radial expansion of a steel shaft rotating at a high speed cannot be ignored.This paper proposes a new mathematical model to predict the cylinder tilt behaviour by establishing a quantitative relationship between the splined shaft deflection,the cylinder tilt angle,and the tilt azimuth angle.The moments exerted by the splined shaft are included in the equilibrium equation of the cylinder.The effects of solid and hollow splined shafts equipped in an EHA pump prototype are compared at variable speeds of 5000-10,000 r/min.With a weight saving of 29.7%,the hollow shaft is experimentally found to have almost no influence on the volumetric efficiency,but to reduce the mechanical efficiency by 0.6-2.4%.The results agree with the trivial differences of the simulated central gap heights of the interface between the two shafts and the enlargement of the simulated tilt angles by the hollow shaft.The findings could guide designs of the cylinder/valve plate interface and the splined shaft to improve both the efficiency and power density of an EHA pump.

    KEYWORDS Electro-hydrostatic actuator pump;Mathematical models;Rigidity;Splined shaft deflection;Tilt behaviour prediction

    1.Introduction

    High-speed axial piston pumps are commonly applied in aircraft and carrier rockets due to their high power density as well as weight and space savings.Lightweight and compact pumps in small packages with stable operation and high power efficiency over the full operating range are consistently pursued.1,2This challenge requires employing low-density materials and downsizing pump components without compromising their strengths.Replacing the solid shaft with a hollow one is among the methods,since the strength-to-weight ratio of a hollow shaft could be 36%greater than that of a solid shaft with the same outer radius.3However,the shaft bending rigidity is reduced by removing the core of the shaft.According to the structure of a typical axial piston pump used in an electro-hydrostatic actuator(EHA)for aerospace applications,a splined shaft drives and supports the cylinder.The cylinder tilt behaviour will be influenced if the curvature of the splined shaft is large enough.Previous studies have shown that the deflection and radial expansion of a steel shaft due to the bending load and the temperature rise caused by a high operating speed cannot be ignored.4,5Since the cylinder/valve plate interface represents one of the main sources of energy dissipation,6the excessive bending of the splined shaft would reduce the pump efficiency by raising the contact friction and leakage flow.

    The lubrication characteristics of the cylinder/valve plate interface need to be investigated in order to understand the relationship between the splined shaft bending rigidity and the cylinder tilt behaviour.Although some practical and convenient design methods based on the assumption of a constant gap height between the cylinder and the valve plate are popular in the industry,7,8the dynamic characteristics of a cylinder rotating at a high speed are complicated due to various forces acting on it,including the inertia forces of the piston-slipper assemblies.9The micro motion such as the tilt behaviour directly affects the lubricating film geometry and even causes severe wear,which will contribute to a sharp decrease of the pump efficiency or damage the rotating kit.

    Different mathematical models considering the cylinder tilt behaviour were proposed to reveal the characteristics of the oil film in order to estimate the energy losses of the friction pair.Bergada et al.10developed a detailed set of explicit equations to determine pressure distribution,leakage,forces,and moments for the cylinder.Their calculation was based on the assumption that the thickest oil film was on the highpressure side.Zecchi and Ivantysynova11developed a fluid structure thermal interaction model accounting for nonisothermal flow in the gap between the cylinder and the valve plate,as well as pressure and thermal elastic deformations in the solid bodies.Wegner et al.12implemented a simulation model and a solid friction model for the cylinder/valve plate interface to compare different design geometries at various operating points.In these models,the reaction moments of the splined shaft were not considered or assumed to be zero.Yamaguchi13theoretically analysed the motion of the cylinder considering the influence of the elastic splined shaft and predicted the fluid film shape for different load conditions.However,the inertia forces of the piston-slipper assemblies,especially the relation between the splined shaft deflection and the cylinder tilt behaviour,were not taken into account.

    Experimental studies were also undertaken to investigate the influences of operating conditions and relevant dimensions of pumps on the cylinder tilt behaviour.Bergada et al.14measured the clearance between the cylinder and the valve plate.They found that the maximum film thickness position moved to a new location at a low temperature,a small swash plate angle,and a low outlet pressure.Deeken15measured the gap height of the cylinder/valve plate pair on a special test rig.His measured and simulated results showed a good corresponding tendency that the cylinder tilt angle decreased as the outlet pressure increased.It was also found that the variation of the rotational speed gave rise to a change in the tilt azimuth.Kim et al.16measured the fluid film thickness with different structures of the valve plate sliding surfaces.They found that the outlet pressure and the structures significantly affected the thickness and location of the minimum fluid film.The above experiments were conducted at a low speed of less than 2000 r/min,and the effects of the splined shaft bending rigidity were not studied.It can be concluded that the previous findings did not provide enough information for guiding the design of high-speed EHA pumps.

    Splined shafts are commonly used in pumps to transfer rotary motion and torsion to cylinders.The cylinder tilt behaviour can lead to an angular misalignment between the cylinder and the splined shaft which has been recognized as a harmful behaviour to splines because it accelerates fretting and abrasive wear.17Hong et al.18studied the load distributions on the spline at different misalignment angles of 0.04°,0.08°,and 0.12°,demonstrating that a significant load concentration was generated at the edge of the spline and thus resulted in an unnegligible tilt moment which could even deflect the splined shaft.Therefore,the moment equilibrium equation of the cylinder needs to include the tilt moment caused by the splined shaft.

    This paper aims to study the effects caused by the splined shaft bending rigidity on the micro motion of the cylinder and EHA pump performances.A predicting model considering the splined shaft deflection is established to achieve the cylinder tilt angle,tilt azimuth angle,and the central gap height during an entire shaft revolution under various operating conditions.Performance tests of an EHA pump prototype are carried out on a high-speed test rig to verify the predicting model.The effects of solid and hollow splined shafts are compared to guide the design of high-speed EHA pumps.

    2.Mathematical model

    A double-direction EHA pump,which integrates a nine-piston rotating group and can operate at a high speed of up to 10,000 r/min,is used for investigation.The hydraulic circuit of its regulator system and the ideal pressure-displacement characteristic curve are presented in Fig.1.The maximum displacement is 7.25 mL/r.When the pressure at the outlet exceeds the value of the turning point determined by the precompressed length of the spring pressing the swash plate,the displacement decreases linearly as the pressure increases.

    The main inner parts of the EHA pump are shown in Fig.2.In Fig.2(a),a cross-sectional view of the EHA pump with external forces and coordinate systems is depicted.The valve plate is fixed on the shell of the pump with two pins,and a compression spring generating a spring force,Fsp,pushes the cylinder towards it.The cylinder is driven via the splined shaft which is supported by a sleeve bearing and a deep groove ball bearing.The piston-slipper assemblies revolve with the cylinder,and a centrifugal force,Fci,acts at each assembly's centre of mass.Meanwhile,each piston moves back and forth inside the cylinder chamber,periodically suctioning and discharging oil through the valve plate ports.The pressurized fluid inside each cylinder chamber exerts the primary force,Fpi,in theZaxis.The swash plate creates a side force,Fsi,acting on the centre of each piston-slipper ball joint due to its inclination.The friction force produced between the piston and the cylinder bore is not considered.TheZaxis is coincident with the centreline of the splined shaft.The origin of the coordinate systemO-XYis at the supporting point of the deep groove ball bearing.The coordinate systemO1-X1Y1is assigned to the cylinder/valve plate interface.The coordinate systemO2-X2Y2is attached to the intersection point of theZaxis and the plane containing the centre points of each piston-slipper ball joint,which is also in the centre of the spline length.

    The cylinder with sector pads uniformly distributed in a circle outside the external sealing land is illustrated in Fig.2(b).Sealing land and sector pad dimensions as well as the rotation angle θ1are presented,too.The valve plate with main kidney port and timing groove dimensions can be found in Fig.2(c).Because the research object is a double-direction pump,the grooves connecting the ports are axis-symmetrically distributed.Therefore,the sealing lands as well as the main kidney ports and the timing grooves are divided into 18 subregions to evaluate the pressure distribution,respectively,which are numbered from 1 to 18.When the cylinder rotates clockwise as shown in Fig.2(b),the high-and low-pressure ports are distributed as shown in Fig.2(c).

    2.1.Effect of the deflected splined shaft

    Fig.1 Hydraulic circuit of the EHA pump's regulator system(left)and ideal pressure-displacement characteristic curve(right).

    Fig.2 Main inner parts of the EHA pump.

    Fig.3 Fillet,tip clearance,and backlash of the spline pair.

    The fillet,tip clearance,and backlash of the spline pair shown in Fig.3 allow the cylinder to slightly tilt in absence of constraints before interfering with the splined shaft.However,the flash temperature of the spline tooth surfaces can reach about 180°C even at a rotational velocity of 2090 r/min,19which means that the thermal expansion would diminish the clearance between spline teeth.Additionally,when the pump operates,almost all the teeth of the external spline are in contact with the internal spline,and significant load concentrations are caused at the ends of the spline in theZaxis.18Therefore,to derive equations considering the influence of the deflected splined shaft,the following simplifications and assumptions are made in this study:

    I.When the compact EHA pump operates at a high ambient temperature caused by the high operating speed,the clearance between spline teeth is assumed to be diminished so that no matter how small the cylinder tilt angle is,the splined shaft will be deflected at the same angle.

    II.The load concentrations on the cylinder spline are simplified as two concentrated forces,and their acting points are assumed to locate at either edge of the spline as depicted in Fig.4,where the cylinder tilt angle and the splined shaft deflection are exaggerated.

    III.The splined shaft is assumed to be a simply supported beam,aiming to establish practical equations of the relation between the parameters determining the cylinder tilt behaviour and the splined shaft deflection.

    The maximum cylinder tilt angle α and the clearance heighthhave the following relation in a full fluid film lubrication regime10:

    As shown in Fig.5,the maximum tilt angle α occurs at the tilt azimuth angle θαwhere the oil film is thickest.At the same location,the local azimuth angle θ is 0°.h0is the central gap height.

    According to Assumptions I-III,the cylinder is subjected to tilt moments about theX2andY2axes,Mx_shaftandMy_shaft,and the splined shaft bends in the same azimuth as the cylinder tilt,as illustrated in Fig.4.Thus,the directions of the moments acting on the splined shaft are opposite toMx_shaftand

    My_shaft.The angle between the tangent to the deflected shaft at pointO2and theZaxis would be equal to the cylinder tilt angle.The aforementioned relations between the parameters determining the cylinder tilt behaviour and the splined shaft deflections are defined as follows:

    Fig.4 Tilt moments caused by two concentrated forces on the cylinder spline.

    where con1and con2are the balance parameters with the unit of radian;αshaftis the angle between the tangent to the deflected shaft at pointO2(z=l-l2)and theZaxis;θshaftis the angle between the bending direction of the splined shaft and theY1axis at pointz=l-l2+1;wX2andwY2are the deflections of the splined shaft along theX2andY2axes,respectively,which are derived by integrating the differential equation of the deflection curve for a simply supported beam.3Because the values ofwX2andwY2at pointO2are zero,θshaftis calculated at the point which is 1 mm away from pointO2,that is,z=l-l2+1.

    Fig.6 Simplified pressure profile for the first cylinder chamber where θr= π/2- θj- θc- γ.

    2.2.Forces and moments on cylinder

    The pressure distribution for the first cylinder chamber in Fig.2(b)is shown in Fig.6,neglecting the trapping phenomenon and the influence of back flow.From the moment that the cylinder port starts to connect the high-pressure port of the valve plate(θ1= θr)to the moment that it starts to connect the low-pressure port(θ1= π + θr),the cylinder chamber pressure,pc,is equal to the outlet pressureps;otherwise,pcis equal to the inlet pressurep0.Thus,Fpiis described as in Eq.(7).Due to the nonuniform pressure distribution for the cylinder chambers,Fpialso creates moments about theX2andY2axes,Mx_pandMy_p,as in Eqs.(8)and(9).Every 2π/9 rad of rotation,the pressure distribution for the cylinder chambers varies with the rotation angle θ1as

    whereypiandxpiare the moment arms to theX2andY2axes,respectively.

    FciandFsiare shown in Eqs.(10)and(11).They create two moments about theX2axis as in Eqs.(12)and(13).

    Fig.7 Schematic of piston motion on swash plate.

    wherezciandzsiare the moment arms to theX2axis,which are calculated according to the piston motion on the swash plate shown in Fig.7.

    FciandFsiare transferred to the cylinder through the piston/-cylinder lubricating gap.All the forces and moments mentioned above are balanced by the fluid film in the cylinder/valve plate interface.The hydrostatic and hydrodynamic effects play a dominant role in determining the pressure distribution for the sealing lands.For the sector pads outside the external sealing land,the hydrostatic pressure approaches the tank pressure.However,the shear velocity of the sector pads is high enough to generate extra pressure caused by the thermal wedge effect which is much higher than the tank pressure.As a result,the force,Fseal,and moments,Mx_sealandMy_seal,due to the pressure distribution for the sealing lands as well as the main kidney ports and the timing grooves,and the force,Ft,and moments,Mx_tandMy_t,due to the pressure distribution for the sector pads compose the forces and moments generated by the fluid film in the cylinder/valve plate interface.

    The cylinder is balanced when the resultant external force in theZaxis,Fz,and moments about theX2andY2axes,MxandMy,are equal to zero,as written in the following equations:

    2.2.1.Effects of main kidney ports and the timing grooves

    piseal(r,θ)is the pressure distribution for the sealing lands as well as the main kidney ports and the timing grooves,and the subscript denotes an identifier of the sub-regions as shown in Fig.2(c),that is,p1represents the pressure distribution for the internal sealing land along the main kidney port on the high-pressure side.Supposing that the gap flow between the cylinder and the valve plate is laminar and incompressible and moves only in the radial direction,the Reynolds equation in the polar coordinate is

    where iseal=1,2,...,11,12.When iseal=13,15,17,piseal=ps;when iseal=14,16,18,piseal=p0.

    After the first integration,Eq.(17)turns into Eq.(18),and after the second integration,Eq.(19)is obtained.The constantsC1andC2are related to the boundary conditions along the main kidney ports and the timing grooves in Eq.(20).

    The pressure distributionpiseal(iseal=1,2,...,11,12)is given in Eq.(21),and the values of the constantsrn,re,rm,andpxare given in Table 1 for different values of iseal.

    Because the tilt cylinder generates a converging oil film region and a diverging oil film region at the same time,large negative pressures would appear in the diverging region if the Sommerfeld boundary condition is used.20Therefore,the half-Sommerfeld boundary condition is employed,and the negative pressure values ofpiseal(r,θ)are set to bepiseal(r,0).21

    The forces and moments due to the pressure distributionpisealare expressed as in Eqs.(22)-(24).The effect of the tilt azimuth angle θαis considered,while the influence caused by the cylinder rotation angle θ1is ignored.Fiseal,Mx_iseal,andMy_isealrepresent the force and moments created by the corresponding pressure distributionpiseal.The values of the constants θd,θs,rd,andrsare listed in Table 2 for different subregions.

    Thus,the force,Fseal,and moments,Mx_sealandMy_seal,due to the pressure distribution for the sealing lands as well as the main kidney ports and the timing grooves are obtained as follows:

    Table 1 Values of the constants rn,re,rm,and pxfor different values of iseal.

    2.2.2.Thermal wedge effect of sector pads

    The average gap height of every sector pad in a full fluid film lubrication regime is described as follows:

    whereit=1,2,...,Zt,in whichZtis the number of sector pads;rmt=(r6+r5)/2.

    The starting and end azimuth angles of every sector pad can be obtained by

    where θx∈ [0,θtt].

    The heat generated by the Couette flow is assumed to be devoted to the temperature rise of the gap flow.22Using the average shear velocity in Eq.(30)and the energy conservation theory,the relationship between the thermal wedge bearing pressure and the fluid density variation caused by the temperature rise is established in Eq.(31).

    whereKt(it)is a constant for a given sector pad.Then,by integrating Eq.(31),ptis derived as The force and moments due to the pressure distribution for the sector pads are expressed as in Eqs.(33)-(35).They are influenced by both the tilt azimuth angle θαand the cylinder rotation angle θ1.Because Eqs.(34)and(35)couldn't obtain explicit integral formulas,the double integrals are numerically evaluated.

    2.3.Gap flow between cylinder and valve plate

    According to Poiseulle's law,the velocity distribution is as follows:

    Substituting Eq.(18)and the boundary conditions into Eq.(36),the velocity distribution along the average radius is obtained in Eq.(37).The values ofrn,re,rm,andpxare given in Table 1 for different sub-regions.

    Table 2 Values of constants θd,θs,rd,and rsfor different values of iseal.

    For the external sealing lands,the pressure decreases as the radius increases,which leads to the gap flow travelling outward.Therefore,the velocity for the internal sealing lands has an opposite sign compared to that for the external sealing lands.The leakage across each sub-region is shown in Eq.(38).The values of θdand θsare given in Table 2 for different subregions.

    The total leakage for the valve plate is the addition of the leakage across each sub-region of the sealing lands where iseal=1,2,...,11,12 as shown below:

    2.4.Iteration method

    The equations described above compose a simulation model which predicts the cylinder tilt behaviour during an entire shaft revolution under different operating conditions.A schematic of the solving procedure is illustrated in Fig.8.The parameters determining the cylinder tilt behaviour are unknown in advance,so the model starts with the initial values ofh0,α,and θα,and then generates a sequence of iterates converging to a solution by using the SQP(sequential quadratic programming)method.23Since the cylinder/valve plate friction pair is assumed to operate under full fluid film lubrication conditions,the values ofh0and α are checked to avoid solid contact at each iteration step before being substituted into the nonlinear constraint functions.There are two situations for the constraint functions:(1)α=0,and(2)α>0.In the first situation,the cylinder is parallel to the valve plate,so the splined shaft provides a supporting force in theY2axis rather than moments,that is,the constraints ofMx_shaft=0 andMy_shaft=0 need to be satisfied.In the second situation,the cylinder tilts,so the balance parameters,con1andcon2,determining whether the cylinder is moment-balanced are evaluated.The net moments,MxandMy,or the balance parameters,con1andcon2,as well as the net force,Fz,are updated until a solution satisfying the constraints is found.SinceMx,My,con1,con2,andFzcannot reach the ideal value of zero due to computational errors,the simulation eventually terminates when the required accuracies shown in Fig.8 are achieved.The final values of the forces and moments described in Section 2.2 are those calculated at the last iteration step,and the gap flow of the cylinder/valve plate interface can be obtained with the solution ofh0,α,and θα.

    3.Experimental procedure

    Experiments of an EHA pump prototype shown in Fig.9 are conducted to validate the mathematical model.The micro motion of the cylinder and the gap flow of the cylinder/valve plate interface in a high-speed and compact pump are hard to be measured directly.Previous works proved that the cylinder tilt behaviour significantly influences the power losses of a pump.6,24Therefore,the total leakage,the input torque,and the efficiencies of the prototype are measured to investigate the effects of the splined shaft bending rigidity on the cylinder tilt behaviour.

    Photographs of the high-speed test rig for measuring the pump's performance parameters are shown in Fig.9.The prototype is driven by a servo motor which can be continuously adjusted from 0 r/min to 16000 r/min.A speed torque sensor is connected to the output shaft of the servo motor.Pressure and temperature sensors are mounted on a manifold which is connected to the outlet,inlet,and case drain ports of the prototype.The total leakage of the prototype is measured by a flowmeter.The working fluid is pumped to the prototype inlet by a charge pump.Two proportional relief valves are located on the delivery lines of the charge pump and the prototype,respectively.A heat exchanger is utilized to maintain the oil temperature of the tank.Table 3 gives detailed descriptions of the main sensors used in the experiments,and signals obtained from the sensors are collected using NI DAQ modules.

    The solid and hollow splined shafts assembled in the EHA pump prototype are shown in Fig.10,and the inner and outer diameters noted are used to calculate their shaft bending rigidities.On the premise that both the solid and hollow splined shafts satisfy the strength requirement,a weight loss of 0.035 kg is achieved.Compared with the weight of the solid shaft(0.118 kg),about 29.7%weight is reduced for the hollow one.The dimensions of the sealing lands and sector pads are reported in Table 4.The contacting surfaces of the cylinder and the valve plate in the tests were manufactured with a grinding process which gave a surface roughness of 0.2 μm and a flatness of 2 μm,while the mathematical model only considers an ideally smooth surface in full film lubrication.

    Both the solid and hollow splined shafts are studied with a broad range of tests,performed starting from 5000 r/min and increasing in steps of 1000 r/min up to the highest speed of 10000 r/min,at an outlet pressure of 7 MPa.The outlet pressure and the speed are kept constant in each test.The value of the turning point as shown in Fig.1 is adjusted to 7 MPa in order to keep the displacement at the maximum value during the experiments.The pump operates at 1000 r/min,2 MPa for 30 min before data acquisition.

    4.Results and discussion

    4.1.Simulated moments on balanced cylinder

    The simulated moments acting on the balanced cylinder as a function of the speed at the cylinder rotation angle θ1=0°are given in Figs.11 and 12.The magnitudes and directions of the moments are affected by the operating conditions and have a strong relationship with the cylinder tilt behaviour as analysed below.

    (1)Mx_sealandMy_seal:Because the structure of the valve plate is symmetric about theX1axis,the magnitude ofMx_sealwill be zero if the cylinder is parallel to the valve plate.Accordingly,the nonzero values ofMx_sealresult from the nonuniform distribution of the oil film thickness,which leads to a hydrodynamic effect in the converging oil film region and a pressure drop in the diverging oil film region.Consequently,the moment direction ofMx_sealindicates whether the cylinder tilts towards the positive or negativeX2axis,and it can be judged that the location of the minimum gap height lies on the positiveX2axis at all the tested speeds from 5000 to 10000 r/min.The magnitude ofMy_sealgradually declines as the speed rises,stemming from a decreased tilt angle or an increased central gap height while the cylinder tilts towards the negativeY2axis,or from the reason that the location of the minimum gap height moves towards the positiveY2axis.

    Fig.8 Simulation scheme.

    Fig.9 EHA pump prototype and the high-speed test rig.

    Table 3 Detailed descriptions of main sensors used in the experiments.

    Fig.10 Dimensions of splined shafts.

    Table 4 Dimensions of sealing lands and sector pads.

    (2)Mx_tandMy_t:Because of the centrosymmetric distribution of the sector pads,the moments ofMx_tandMy_tare always in the direction opposite to the tilting to prevent a further enlargement of the tilt angle.The simulated pressure and gap distributions at the cylinder rotation angle θ1=0°in Fig.13 also indicate that the location of the peak pressure caused by the thermal wedge effect corresponds to that of the minimum gap height where a green arrow points to.Therefore,the moment direction ofMy_tis opposite to that ofMx_sealat any time.From the moment direction variation ofMx_t,it can be deduced that the changed tilt direction is the main cause of the descent ofMy_seal.

    (3)Mx_shaftandMy_shaft:Due to the assumptions in this paper,the moment directions ofMx_shaftandMy_shaftare opposite to the cylinder tilt direction.At the cylinder rotation angle θ1=0°,Mx_pandMx_sare in the negative direction whileMx_cis positive.As the speed rises,the increasingMx_cgradually counterbalancesMx_pandMx_s,and then exceeds the summation of them.That is why the magnitude ofMx_shaftdecreases at first and then rises in the direction opposite to that ofMx_c,which indicates that the moment created by the centrifugal force exerts a dominant influence on the cylinder tilt behaviour at a high speed.As the magnitude ofMy_sealdecreases with the speed in the preceding analysis,My_shaftincreases to counterbalanceMy_p.Besides the tilt direction,the tilt angle is estimated to reach the lowest value at a speed of 9000 r/min where both the values ofMx_shaftandMy_shaftare close to zero.

    As for the impacts of the splined shaft bending rigidity,theMx_tandMy_tmagnitudes of the solid shaft are lower than those of the hollow shaft,representing that the tilt angles of the hollow shaft are larger than those of the solid shaft.Nevertheless,theMy_shaftmagnitude of the solid shaft is higher,which implies that the solid shaft is able to bear a higher load and generate a smaller deflection.

    4.2.Simulated cylinder tilt behaviour

    The simulated central gap height,tilt angle,and azimuth of the minimum gap height as a function of the speed at the cylinder rotation angle θ1=0°are plotted in Fig.14.A phase difference of 180°exists between the azimuth angle of the thinnest oil film and the tilt azimuth angle θα.It is clearly seen that the central gap height increases almost linearly with the speed because the improved hydrodynamic and thermal wedge effects push the cylinder away from the valve plate.Then,it is important to notice that the trends of the tilt angles and minimum gap height locations are consistent with the variations of the moments acting on the cylinder.The curves of the tilt angles have negative slopes until reaching the same operating points where the magnitudes of bothMx_shaftandMy_shaftare close to zero.The curves of the minimum gap height locations also show transitions when the speed reaches 9000 r/min.At the transition point,the cylinder is almost parallel to the valve plate,and the thinnest oil film is predicted to be at the azimuth angle of about 68°on the high-pressure side.For a speed ranging from 5000 r/min to 8000 r/min,the cylinder is predicted to tilt towards the high-pressure side and be close to the inner dead point;at a speed of 10,000 r/min,it is prone to tilt towards the outer dead point.The simulated results indicate that the operating conditions for a given cylinder to rotate steadily are limited in a range.

    The comparison between the solid and hollow shafts denotes that the splined shaft bending rigidity has little influence on the height values and tilt azimuth angles,but affects the tilt angles slightly.The tilt angles are within a range of 0.0001°-0.0035°,and their maximum disparity between the solid and hollow shafts is less than 0.0005°,which is in agreement with the trivial differences ofMx_shaftandMy_shaftbetween the two shafts.

    Fig.11 Simulated moments about the X2axis on balanced cylinder at outlet pressure ps=7 MPa.

    Fig.12 Simulated moments about the Y2axis on balanced cylinder at outlet pressure ps=7 MPa.

    Fig.13 Simulated pressure and gap height distributions for cylinder/valve plate interface.

    4.3.Comparison between simulated and experimental results

    The simulated azimuths of minimum gap heights as a function of the cylinder rotation angle at 10000 r/min,7 MPa with the hollow shaft are shown in Fig.15.A sudden change of the azimuth at θ1=25°results from a decrease in the number of cylinder chambers connected with the outlet.The EHA pump prototype was dismantled to detect the valve plate surface after running for 30 min at the same operating condition.As shown in Fig.15,a very light scratch was found close to the outer dead point on the high-pressure side.The results show that the simulated azimuth angles roughly correspond to the actual wear location on the valve plate.

    Fig.14 Simulated results of cylinder tilt behaviour for different speeds at outlet pressure ps=7 MPa.

    The simulated gap flow between the cylinder and the valve plate and the measured case drain flow are drawn in Fig.16.It is obvious that both the simulated gap flows and the measured leakages increase almost linearly as a function of the speed,even though the simulated cylinder tilt angles vary in a nonlinear way.Due to the inconspicuous disparity of the simulated tilt angles between the solid and hollow shafts,the gap flow curve of the solid shaft almost coincides with that of the hollow shaft.Meanwhile,the variation of the measured case drain flow between the solid and hollow shafts is less than 0.1 L/min,resulting in a tiny difference of the volumetric efficiencies between them,as found in Fig.17(a).The measured results agree with the simulated ones,and a conclusion that lowering the splined shaft bending rigidity can slightly raise the cylinder tilt angle without affecting the volumetric efficiency can be obtained.

    It is also important to point out that the mechanical ef ficiencies of the hollow shaft are found experimentally to be 0.6-2.4%lower than those of the solid shaft,and an increment of the measured input torques is the direct cause,as shown in Fig.17(b).In addition,the reduced amount of the mechanical efficiency reaches the peak at 5000 r/min,where the increment of the simulated tilt angle between the solid and hollow shafts is the highest,while the simulated central gap height is the lowest.This is because the slightly enlarged tilt angles caused by a lower splined shaft bending rigidity increase the frictional losses of the cylinder/valve plate friction pair dramatically.Ultimately,the overall efficiencies of the solid shaft in the experiments are 0.7-2.1%higher than those of the hollow shaft.Hence,to achieve a weight loss without reducing the mechanical efficiency,the dimensions of the cylinder/valve plate interface need to be redesigned by using a method in which the effects of the splined shaft bending rigidity are taken into account.

    Fig.16 Simulated gap flow between cylinder and valve plate and measured case drain flow of tested prototype at outlet pressure ps=7 MPa.

    Fig.15 Simulated cylinder tilt azimuths at outlet pressure ps=7 MPa and shaft speed ns=10000 r/min(left)and worn valve plate of tested prototype(right).

    Fig.17 Efficiencies and input torques of tested prototype at outlet pressure ps=7 MPa.

    5.Conclusions

    A cylinder tilt behaviour-predicting model considering the splined shaft deflection is established.The moments exerted by the splined shaft are included in the model by establishing a quantitative relationship between the magnitude and direction of the splined shaft deflection,the cylinder tilt angle,and the tilt azimuth angle.A flow rate equation in combination with the cylinder tilt behaviour is built to calculate the gap flow of the cylinder/valve plate friction pair.Numerical and experimental investigations based on an EHA pump prototype are performed with a broad range of operating points,and the following conclusions are drawn:

    (1)Employing a hollow shaft instead of a solid one achieves a weight saving of 29.7%and almost has no influence on the volumetric efficiency of the tested prototype,but reduces the mechanical efficiency of the prototype by 0.6-2.4%.The experimental phenomena can be explained by the trivial differences of the simulated central gap heights between the two shafts and the enlargement of the simulated tilt angles by the hollow shaft.

    (2)Both the simulated gap flows of the cylinder/valve plate interface and the measured case drain flows of the prototype increase almost linearly as a function of the speed,even though the simulated cylinder tilt angles vary in a nonlinear way.

    (3)The actual wear location on the valve plate of the prototype running for 30 min at 10000 r/min,7 MPa with the hollow shaft was close to the outer dead point on the high-pressure side,which roughly corresponds to the simulated azimuths of minimum gap heights.

    (4)In the future,a more specific relationship between the cylinder tilt behaviour and the splined shaft deflection needs to be established,and the micro motion of the cylinder in the EHA pump needs to be measured to provide a direct evidence for conclusions.

    Acknowledgements

    The authors would like to appreciate the financial supports received from the National Basic Research Program of China(973 Program)(No.2014CB046403)and the National Natural Science Foundation of China(Nos.U1509204 and 51605425).

    亚洲男人天堂网一区| 午夜福利在线观看吧| cao死你这个sao货| 在线亚洲精品国产二区图片欧美| 丝袜喷水一区| 久久人妻福利社区极品人妻图片| 精品一区二区三区四区五区乱码| 亚洲中文日韩欧美视频| 亚洲精品国产av成人精品| 啦啦啦中文免费视频观看日本| 91精品伊人久久大香线蕉| 精品一区二区三区av网在线观看 | 捣出白浆h1v1| 欧美激情极品国产一区二区三区| 国产精品.久久久| 免费高清在线观看日韩| 免费观看av网站的网址| 香蕉丝袜av| 久久天躁狠狠躁夜夜2o2o| 香蕉国产在线看| 最新在线观看一区二区三区| 黄色怎么调成土黄色| 久久人人爽人人片av| av欧美777| 男女之事视频高清在线观看| 777米奇影视久久| 人妻人人澡人人爽人人| 国产高清视频在线播放一区 | 人人澡人人妻人| 亚洲专区国产一区二区| 国产免费av片在线观看野外av| 亚洲精品中文字幕一二三四区 | 久久精品国产综合久久久| 在线亚洲精品国产二区图片欧美| 日韩熟女老妇一区二区性免费视频| 亚洲美女黄色视频免费看| 黑人猛操日本美女一级片| 色老头精品视频在线观看| 无遮挡黄片免费观看| 精品久久久久久久毛片微露脸 | 亚洲熟女毛片儿| 午夜福利一区二区在线看| 国内毛片毛片毛片毛片毛片| 操美女的视频在线观看| 美国免费a级毛片| av线在线观看网站| 亚洲性夜色夜夜综合| 三级毛片av免费| 啦啦啦视频在线资源免费观看| 在线观看www视频免费| 国产欧美日韩一区二区三 | 日韩免费高清中文字幕av| www.自偷自拍.com| 久热这里只有精品99| videosex国产| 免费看十八禁软件| 最新在线观看一区二区三区| 欧美精品啪啪一区二区三区 | 99久久国产精品久久久| 黄色怎么调成土黄色| 亚洲自偷自拍图片 自拍| 天天躁日日躁夜夜躁夜夜| 91精品伊人久久大香线蕉| 91九色精品人成在线观看| 欧美日韩av久久| 一区二区三区激情视频| 亚洲国产欧美日韩在线播放| 一个人免费看片子| 巨乳人妻的诱惑在线观看| 午夜福利乱码中文字幕| 99re6热这里在线精品视频| 最近中文字幕2019免费版| 中国美女看黄片| 天堂中文最新版在线下载| 天天操日日干夜夜撸| 久9热在线精品视频| 桃花免费在线播放| 国产高清videossex| 窝窝影院91人妻| 欧美 亚洲 国产 日韩一| 国产精品一二三区在线看| 少妇精品久久久久久久| 热99久久久久精品小说推荐| 亚洲中文av在线| 大型av网站在线播放| 香蕉国产在线看| 91麻豆av在线| 日日夜夜操网爽| 亚洲国产精品成人久久小说| 婷婷成人精品国产| 亚洲欧美色中文字幕在线| 人妻一区二区av| 狠狠婷婷综合久久久久久88av| 最新的欧美精品一区二区| 日本wwww免费看| 免费av中文字幕在线| 国产av国产精品国产| 亚洲一区中文字幕在线| 欧美日韩黄片免| 欧美精品高潮呻吟av久久| 人妻一区二区av| 亚洲黑人精品在线| 午夜精品久久久久久毛片777| 婷婷丁香在线五月| 久久 成人 亚洲| 99久久综合免费| 五月天丁香电影| 欧美+亚洲+日韩+国产| 亚洲成人国产一区在线观看| 中文字幕人妻丝袜制服| 香蕉国产在线看| 国产亚洲欧美精品永久| 日日爽夜夜爽网站| 老司机在亚洲福利影院| 18禁观看日本| 中国美女看黄片| 一级片免费观看大全| 午夜老司机福利片| 青春草亚洲视频在线观看| 天天躁日日躁夜夜躁夜夜| 啦啦啦啦在线视频资源| 亚洲第一av免费看| 亚洲精品美女久久av网站| 欧美在线一区亚洲| 国产国语露脸激情在线看| www.熟女人妻精品国产| 在线观看舔阴道视频| 久久久久久免费高清国产稀缺| 极品少妇高潮喷水抽搐| 免费在线观看完整版高清| 亚洲一码二码三码区别大吗| av福利片在线| 精品一区在线观看国产| 欧美乱码精品一区二区三区| 久久久久久免费高清国产稀缺| 人妻 亚洲 视频| 黑丝袜美女国产一区| 欧美成狂野欧美在线观看| 亚洲欧洲日产国产| 咕卡用的链子| 久久久久久人人人人人| 国产又色又爽无遮挡免| 成在线人永久免费视频| 如日韩欧美国产精品一区二区三区| 一级片'在线观看视频| 亚洲欧美一区二区三区久久| 999精品在线视频| 久久久精品免费免费高清| 国产亚洲精品久久久久5区| 国产成人一区二区三区免费视频网站| 成人影院久久| 免费日韩欧美在线观看| 好男人电影高清在线观看| 国产91精品成人一区二区三区 | av超薄肉色丝袜交足视频| 日本撒尿小便嘘嘘汇集6| 久久久久精品国产欧美久久久 | 18禁观看日本| 人妻 亚洲 视频| 国产欧美日韩精品亚洲av| 久久天躁狠狠躁夜夜2o2o| 亚洲第一欧美日韩一区二区三区 | 国产男女内射视频| 日韩免费高清中文字幕av| 亚洲专区中文字幕在线| 99re6热这里在线精品视频| 午夜福利在线观看吧| 中文精品一卡2卡3卡4更新| 黄色怎么调成土黄色| 国产精品免费视频内射| 在线观看一区二区三区激情| 欧美日韩中文字幕国产精品一区二区三区 | 亚洲成av片中文字幕在线观看| 老鸭窝网址在线观看| 亚洲综合色网址| 天天躁日日躁夜夜躁夜夜| 久热这里只有精品99| 美女主播在线视频| 欧美激情久久久久久爽电影 | 久久精品成人免费网站| 亚洲欧美一区二区三区久久| 高清视频免费观看一区二区| 爱豆传媒免费全集在线观看| 久久人人爽人人片av| 久久精品人人爽人人爽视色| 久久久国产一区二区| 动漫黄色视频在线观看| 国产成人精品无人区| 欧美久久黑人一区二区| 欧美97在线视频| a级毛片在线看网站| 老司机午夜福利在线观看视频 | 国产成人啪精品午夜网站| 女性被躁到高潮视频| 国产精品久久久人人做人人爽| 最新的欧美精品一区二区| 人人妻人人澡人人看| 亚洲第一青青草原| 国产欧美亚洲国产| 后天国语完整版免费观看| 正在播放国产对白刺激| a 毛片基地| 精品一区二区三卡| videosex国产| 一区在线观看完整版| 久久久久精品国产欧美久久久 | 12—13女人毛片做爰片一| 久久精品熟女亚洲av麻豆精品| 叶爱在线成人免费视频播放| 国产熟女午夜一区二区三区| 欧美大码av| 欧美性长视频在线观看| 国产亚洲av片在线观看秒播厂| 五月开心婷婷网| 日韩欧美免费精品| 日本wwww免费看| 免费在线观看日本一区| 欧美成人午夜精品| av视频免费观看在线观看| 男女下面插进去视频免费观看| 亚洲成国产人片在线观看| 亚洲av片天天在线观看| 乱人伦中国视频| 国产亚洲欧美在线一区二区| 久久天躁狠狠躁夜夜2o2o| 十分钟在线观看高清视频www| 亚洲欧美日韩高清在线视频 | 精品一区二区三区av网在线观看 | 无限看片的www在线观看| 免费黄频网站在线观看国产| 国产精品一区二区在线观看99| 操出白浆在线播放| 一级毛片女人18水好多| 美女视频免费永久观看网站| 国产av一区二区精品久久| 麻豆av在线久日| 国产亚洲午夜精品一区二区久久| 久久精品亚洲熟妇少妇任你| 国产在线观看jvid| 国产伦人伦偷精品视频| 可以免费在线观看a视频的电影网站| 亚洲自偷自拍图片 自拍| 青春草视频在线免费观看| 久久人妻熟女aⅴ| 亚洲综合色网址| 欧美日韩av久久| 在线永久观看黄色视频| 欧美日韩成人在线一区二区| 黄色a级毛片大全视频| 国产高清视频在线播放一区 | 精品高清国产在线一区| 人人妻,人人澡人人爽秒播| 午夜福利在线免费观看网站| 国产精品秋霞免费鲁丝片| 亚洲欧美一区二区三区久久| 亚洲成人免费av在线播放| 欧美激情高清一区二区三区| 亚洲成国产人片在线观看| 午夜激情av网站| 国产91精品成人一区二区三区 | 色婷婷av一区二区三区视频| 国产在视频线精品| 国产真人三级小视频在线观看| 在线看a的网站| 亚洲国产中文字幕在线视频| 国产精品1区2区在线观看. | 熟女少妇亚洲综合色aaa.| 在线 av 中文字幕| h视频一区二区三区| 麻豆av在线久日| 黑人欧美特级aaaaaa片| 999精品在线视频| 午夜福利免费观看在线| 两人在一起打扑克的视频| 亚洲国产精品成人久久小说| 人人妻人人爽人人添夜夜欢视频| 美女主播在线视频| 青春草亚洲视频在线观看| 欧美+亚洲+日韩+国产| 亚洲欧美精品自产自拍| av又黄又爽大尺度在线免费看| 欧美激情久久久久久爽电影 | 亚洲少妇的诱惑av| 18在线观看网站| 国产成人av激情在线播放| 99国产极品粉嫩在线观看| 男女免费视频国产| 黄色a级毛片大全视频| av线在线观看网站| 亚洲七黄色美女视频| 国产精品免费大片| 亚洲欧美日韩另类电影网站| 99re6热这里在线精品视频| 亚洲国产精品一区二区三区在线| 色综合欧美亚洲国产小说| 精品福利观看| 久久毛片免费看一区二区三区| 一区二区三区精品91| 脱女人内裤的视频| 新久久久久国产一级毛片| 日本a在线网址| 国产亚洲欧美精品永久| 侵犯人妻中文字幕一二三四区| 美女高潮喷水抽搐中文字幕| 黄色片一级片一级黄色片| 中文字幕精品免费在线观看视频| 国产男女内射视频| 我要看黄色一级片免费的| 国产精品久久久人人做人人爽| 国产av又大| 91精品国产国语对白视频| 日本91视频免费播放| 国产精品久久久久久人妻精品电影 | av网站免费在线观看视频| 久久久久精品国产欧美久久久 | 人人妻人人澡人人爽人人夜夜| 色综合欧美亚洲国产小说| 激情视频va一区二区三区| 日韩熟女老妇一区二区性免费视频| 成年女人毛片免费观看观看9 | 亚洲av欧美aⅴ国产| 黄片播放在线免费| 国产高清视频在线播放一区 | 国产日韩一区二区三区精品不卡| 自拍欧美九色日韩亚洲蝌蚪91| 丰满饥渴人妻一区二区三| 精品国产一区二区三区四区第35| 国产免费视频播放在线视频| 精品国产超薄肉色丝袜足j| 美女中出高潮动态图| 亚洲一码二码三码区别大吗| 国产一区二区 视频在线| 人人妻,人人澡人人爽秒播| 美女大奶头黄色视频| 2018国产大陆天天弄谢| 麻豆乱淫一区二区| 人妻一区二区av| 国产欧美日韩综合在线一区二区| 亚洲欧美一区二区三区久久| 久热这里只有精品99| 一级,二级,三级黄色视频| 欧美精品人与动牲交sv欧美| 丁香六月欧美| 午夜免费观看性视频| 久久香蕉激情| 亚洲自偷自拍图片 自拍| 国产精品久久久人人做人人爽| 日韩一卡2卡3卡4卡2021年| 欧美性长视频在线观看| 国产在线视频一区二区| 人妻久久中文字幕网| 亚洲精品国产av蜜桃| 一个人免费在线观看的高清视频 | 免费在线观看日本一区| 丁香六月天网| 精品免费久久久久久久清纯 | 免费女性裸体啪啪无遮挡网站| 青春草亚洲视频在线观看| 十八禁高潮呻吟视频| 99国产精品一区二区蜜桃av | 成人免费观看视频高清| av网站在线播放免费| 蜜桃国产av成人99| 91av网站免费观看| 亚洲欧美日韩高清在线视频 | 大陆偷拍与自拍| 亚洲色图综合在线观看| videosex国产| 一本综合久久免费| 免费观看av网站的网址| 亚洲国产精品成人久久小说| 午夜福利在线观看吧| 97精品久久久久久久久久精品| 1024视频免费在线观看| 一二三四在线观看免费中文在| av超薄肉色丝袜交足视频| 九色亚洲精品在线播放| 黄片大片在线免费观看| 成人av一区二区三区在线看 | 免费黄频网站在线观看国产| 一级片'在线观看视频| 精品国产一区二区三区四区第35| svipshipincom国产片| 一区福利在线观看| 男女国产视频网站| 宅男免费午夜| 一级毛片女人18水好多| 成人亚洲精品一区在线观看| 99九九在线精品视频| 久久中文字幕一级| 免费日韩欧美在线观看| 色精品久久人妻99蜜桃| 亚洲熟女毛片儿| 成年人黄色毛片网站| 黄色 视频免费看| 成人黄色视频免费在线看| 12—13女人毛片做爰片一| 美女主播在线视频| av天堂在线播放| 性少妇av在线| 国产精品久久久av美女十八| svipshipincom国产片| 91麻豆精品激情在线观看国产 | 色94色欧美一区二区| 亚洲欧美一区二区三区久久| 国产成人精品无人区| 日韩 亚洲 欧美在线| 亚洲av国产av综合av卡| 水蜜桃什么品种好| 成在线人永久免费视频| 亚洲精品久久午夜乱码| 久久天堂一区二区三区四区| 精品久久蜜臀av无| 精品少妇一区二区三区视频日本电影| 亚洲人成77777在线视频| 欧美大码av| 午夜影院在线不卡| 国产熟女午夜一区二区三区| 丝袜脚勾引网站| 大陆偷拍与自拍| 国产成+人综合+亚洲专区| 久久精品国产亚洲av高清一级| 久久久久网色| 欧美日韩成人在线一区二区| 亚洲精品国产av蜜桃| 少妇人妻久久综合中文| 天天影视国产精品| 国产高清videossex| 日本精品一区二区三区蜜桃| 日日摸夜夜添夜夜添小说| 久久久国产精品麻豆| 日韩免费高清中文字幕av| 大型av网站在线播放| 又紧又爽又黄一区二区| 国产av又大| 日韩制服丝袜自拍偷拍| 18禁裸乳无遮挡动漫免费视频| 美女中出高潮动态图| 伦理电影免费视频| 亚洲精品国产精品久久久不卡| 热re99久久国产66热| 免费观看av网站的网址| 亚洲欧美日韩另类电影网站| 国产免费av片在线观看野外av| 久久ye,这里只有精品| 亚洲精品美女久久久久99蜜臀| 国产成人a∨麻豆精品| 欧美激情高清一区二区三区| 欧美精品亚洲一区二区| 波多野结衣一区麻豆| 日韩欧美国产一区二区入口| 国产成人欧美在线观看 | 亚洲精品国产av蜜桃| 亚洲免费av在线视频| avwww免费| 久久人人爽av亚洲精品天堂| 久久久国产精品麻豆| 欧美 亚洲 国产 日韩一| 亚洲精华国产精华精| 欧美日韩黄片免| 精品久久久久久电影网| 男人舔女人的私密视频| 亚洲色图 男人天堂 中文字幕| 天堂俺去俺来也www色官网| 天天操日日干夜夜撸| 在线 av 中文字幕| 精品免费久久久久久久清纯 | 超色免费av| 不卡av一区二区三区| 国产av精品麻豆| 一级毛片精品| 精品少妇黑人巨大在线播放| 男女国产视频网站| 午夜福利一区二区在线看| 黄色a级毛片大全视频| 亚洲人成77777在线视频| 久久久久网色| 久久精品成人免费网站| 一级黄色大片毛片| 久久久精品区二区三区| 国产精品久久久久久精品古装| 91成年电影在线观看| 啦啦啦中文免费视频观看日本| 亚洲精品美女久久久久99蜜臀| 男女国产视频网站| 久久99热这里只频精品6学生| 男人舔女人的私密视频| 在线观看免费日韩欧美大片| 免费日韩欧美在线观看| 国产一区二区三区在线臀色熟女 | 超色免费av| 两性午夜刺激爽爽歪歪视频在线观看 | 国产黄频视频在线观看| netflix在线观看网站| 午夜福利,免费看| 午夜成年电影在线免费观看| 国产亚洲精品第一综合不卡| 亚洲国产av新网站| 国产欧美日韩一区二区三区在线| 麻豆国产av国片精品| 蜜桃国产av成人99| 日本av免费视频播放| 久久久精品区二区三区| 成人手机av| 久久久久国产精品人妻一区二区| 国产av又大| 久久久国产欧美日韩av| 亚洲av电影在线观看一区二区三区| 国产成人精品在线电影| 久热爱精品视频在线9| 亚洲一卡2卡3卡4卡5卡精品中文| 在线观看一区二区三区激情| 青青草视频在线视频观看| 俄罗斯特黄特色一大片| 久久久久国产精品人妻一区二区| 国产成人一区二区三区免费视频网站| 久久亚洲精品不卡| av国产精品久久久久影院| 亚洲欧美一区二区三区黑人| 亚洲精品国产区一区二| 亚洲成国产人片在线观看| 精品乱码久久久久久99久播| 咕卡用的链子| 免费人妻精品一区二区三区视频| 国产在线一区二区三区精| 丰满人妻熟妇乱又伦精品不卡| 久久久水蜜桃国产精品网| 热99国产精品久久久久久7| 欧美亚洲 丝袜 人妻 在线| 午夜免费成人在线视频| 搡老乐熟女国产| 成人亚洲精品一区在线观看| 97精品久久久久久久久久精品| 国产成人一区二区三区免费视频网站| 80岁老熟妇乱子伦牲交| 亚洲国产欧美网| 电影成人av| 日韩制服丝袜自拍偷拍| 伦理电影免费视频| 精品国产一区二区三区久久久樱花| 亚洲精品成人av观看孕妇| 老司机午夜十八禁免费视频| 国产一卡二卡三卡精品| 亚洲国产欧美网| 久久久久国内视频| videos熟女内射| 欧美精品av麻豆av| 丝袜美腿诱惑在线| 国产无遮挡羞羞视频在线观看| 国产区一区二久久| 99精品欧美一区二区三区四区| 欧美人与性动交α欧美软件| 国产精品成人在线| 丝袜喷水一区| 看免费av毛片| 啪啪无遮挡十八禁网站| 午夜精品国产一区二区电影| 国产精品免费大片| 亚洲av电影在线进入| av免费在线观看网站| 日韩制服骚丝袜av| 国产精品久久久人人做人人爽| 99久久99久久久精品蜜桃| 亚洲人成电影观看| 男女午夜视频在线观看| 国产日韩一区二区三区精品不卡| 中文字幕人妻丝袜制服| 每晚都被弄得嗷嗷叫到高潮| 大片电影免费在线观看免费| 岛国毛片在线播放| 亚洲专区国产一区二区| 国产成人免费观看mmmm| 国产精品二区激情视频| 不卡av一区二区三区| 精品熟女少妇八av免费久了| 国产av一区二区精品久久| 丰满少妇做爰视频| 如日韩欧美国产精品一区二区三区| 美女午夜性视频免费| 久久青草综合色| 国产精品 国内视频| 日本五十路高清| 青青草视频在线视频观看| 亚洲一码二码三码区别大吗| 自线自在国产av| 伦理电影免费视频| 国产亚洲精品久久久久5区| 12—13女人毛片做爰片一| 国产精品欧美亚洲77777| 国产成人精品在线电影| 在线观看www视频免费| 午夜激情久久久久久久| 五月开心婷婷网| 日韩一区二区三区影片| 国产成人免费观看mmmm| 国产欧美日韩精品亚洲av| 黄色视频在线播放观看不卡| 操美女的视频在线观看| 91精品三级在线观看| 黄色视频在线播放观看不卡| e午夜精品久久久久久久| 人妻一区二区av| 曰老女人黄片| 色婷婷av一区二区三区视频| 亚洲精品美女久久久久99蜜臀| 欧美精品亚洲一区二区| 最新在线观看一区二区三区| 国产欧美亚洲国产| 黑人巨大精品欧美一区二区mp4| 狂野欧美激情性xxxx| 女人久久www免费人成看片| 侵犯人妻中文字幕一二三四区| 久久久久视频综合| 亚洲av日韩精品久久久久久密| 国产精品一二三区在线看|