CN111368486B - Design method for hydrostatic support of spherical pump piston - Google Patents

Design method for hydrostatic support of spherical pump piston Download PDF

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CN111368486B
CN111368486B CN202010185399.0A CN202010185399A CN111368486B CN 111368486 B CN111368486 B CN 111368486B CN 202010185399 A CN202010185399 A CN 202010185399A CN 111368486 B CN111368486 B CN 111368486B
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piston
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CN111368486A (en
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杨楠
李竞
沈辉
龚俊杰
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Yangzhou University
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Abstract

The invention discloses a design method of a spherical pump piston static pressure support, which comprises the following steps of 1, establishing a piston-cylinder static pressure support model: lubricating liquid is sprayed between the surface of the piston and the cylinder body through high pressure to form a lubricating film; 2. deducing the supporting force of the spherical piston and the effective bearing area of the spherical piston according to the static pressure supporting model in the step 1; 3. establishing an equivalent fluid bridge model according to the structural characteristics of the spherical pump and the structure of the hydrostatic pressure channel; 4. and (3) carrying out systematic analysis on the static pressure support of the spherical pump piston to obtain the piston angle theta when the oil film flow speed on the surface of the spherical pump piston is the lowest, so as to ensure the stability of the flow speed of the support oil film. The invention carries out systematic analysis on the hydrostatic support of the spherical pump piston by establishing a model to obtain the piston angle when the oil film flow rate on the surface of the spherical pump piston is the lowest, thereby effectively reducing the friction coefficient between the kinematic pair, improving the support performance, reducing the friction and abrasion of the piston and avoiding the blocking.

Description

Design method for hydrostatic support of spherical pump piston
Technical Field
The invention relates to the technical field of hydrostatic pressure support, in particular to a design method of a hydrostatic pressure support of a spherical pump piston.
Background
The literature "kinetic modeling, analysis and test on a quick technical pump" proposes a spherical pump which is simple and compact in structure and has a working pressure greater than that of a gear pump. However, the spherical pump has a disadvantage that the contact surface between the piston and the cylinder is ball-and-socket contact, which inevitably increases friction force although good sealing effect can be ensured, and especially, the sliding friction is too large to break the supporting oil film during high-speed operation. When the axes of the piston and the turntable coincide, the driving torque of the main shaft is instantaneously reduced to 0; due to the existence of friction force, the phenomenon of blocking between the piston and the cylinder cover is easy to occur; the essence is that the friction force between the piston and the cylinder body is larger than the motion inertia force of the piston. In order to avoid this phenomenon, it is necessary to effectively reduce the friction force between the piston and the cylinder, including two schemes of reducing the contact force and the friction coefficient.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provide a design method for a hydrostatic support of a spherical pump piston, which effectively reduces the friction coefficient between the kinematic pairs, improves the support performance, reduces the friction and wear of the piston and avoids the jamming.
The purpose of the invention is realized as follows: a design method for hydrostatic support of a piston of a spherical pump comprises the following steps:
step 1, establishing a piston-cylinder static pressure support model: lubricating liquid is sprayed between the surface of the piston and the cylinder body through high pressure to form a lubricating film;
step 2, deducing the supporting force of the spherical piston and the effective bearing area of the spherical piston according to the static pressure supporting model in the step 1;
step 3, establishing an equivalent fluid bridge model according to the structural characteristics of the spherical pump and the structure of the hydrostatic pressure channel;
and 4, carrying out systematic analysis on the static pressure support of the spherical pump piston to obtain a piston angle theta when the oil film flow rate on the surface of the spherical pump piston is the lowest, and ensuring the flow rate of the support oil film to be stable.
As a further limitation of the present invention, said step 2 comprises the steps of:
(a) in spherical coordinates, the equation of continuity for incompressible lubricating fluid is:
Figure RE-GDA0002459799300000021
wherein u isr，uθ，
Figure RE-GDA0002459799300000022
Representing a liquid velocity component; because of the fact that
Figure RE-GDA0002459799300000023
ur0, so formula (1) above translates to:
Figure RE-GDA0002459799300000024
(b) assuming that the lubricating fluid is flowing at a constant rate, then
Figure RE-GDA0002459799300000025
Irrespective of inertia of the lubricating fluid
Figure RE-GDA0002459799300000026
Due to the piston along
Figure RE-GDA0002459799300000027
Is symmetrical in direction, so
Figure RE-GDA0002459799300000028
The Navier-Stokes equation for incompressible lubricating fluids with uniform viscosity:
Figure RE-GDA0002459799300000029
can be simplified to the following formula:
Figure RE-GDA0002459799300000031
wherein μ represents a kinetic viscosity coefficient, ρ represents a lubricating fluid density, and p represents a lubricating oil pressure;
(c) substituting the continuity equation into the above equation (4) can obtain
Figure RE-GDA0002459799300000032
Indicating that the lubricating oil pressure p varies only with theta; the pressure distribution of p in the theta direction, which can be obtained from the flow theory between parallel surfaces, is:
Figure RE-GDA0002459799300000033
integrating r gives:
Figure RE-GDA0002459799300000034
wherein a and b are two different integration constants; substituting boundary conditions uθ|r＝R0 and uθ|r＝R+hThe speeds available at different θ are 0:
Figure RE-GDA0002459799300000035
wherein h represents a clearance between the piston surface and the cylinder inner surface;
(d) the flow rate of the lubricating liquid obtained from the above is as follows:
Figure RE-GDA0002459799300000036
substituting h ═ ecos θ into the above equation (6), the integral is calculated using a variable separation method:
Figure RE-GDA0002459799300000037
wherein the eccentricity e represents the distance between the center of the piston and the center of the cylinder; p is a radical ofsRepresenting the inlet pressure of the spherical piston lubricating fluid; theta1Indicating the initial angle of the lubrication film; the pressure profile of the lubricating fluid is therefore expressed as:
Figure RE-GDA0002459799300000038
(e) when theta is equal to theta2When the pressure p of the lubricating fluid is equal to 0, where θ2Is the lubrication film termination angle; by substituting this boundary condition into the above equation (7), the flow rate of the lubricating liquid leaking on the piston surface can be obtained:
Figure RE-GDA0002459799300000041
the lubricating fluid pressure distribution obtained by the above formula (8) is:
Figure RE-GDA0002459799300000042
(f) when d is eliminated2-d1The supporting force of the spherical piston can be obtained at the supporting force in the gap:
Figure RE-GDA0002459799300000043
the above formula (10) can be simplified to F ═ psSeWherein
Figure RE-GDA0002459799300000044
Showing the effective bearing area of the ball piston.
As a further limitation of the present invention, said step 3 comprises the steps of:
equivalent fluid bridge of hydrostatic support system, in which lubricating oil is injected from the gap between piston pin and cylinder head, the fluid resistance of the gap being RcExpressed as a constant; rgShowing hydrostatic bearing adjustable fluid resistance. Based on the continuity theorem, one can obtain:
Figure RE-GDA0002459799300000045
wherein p isc＝pr-psRepresenting the pressure drop, p, at the piston pin-cylinder head gapsIndicating the pressure drop of the lubricating fluid, i.e. the fluid-supporting pressure drop, prThe total pressure drop is expressed, so the pressure drop ratio of the piston to the whole system, i.e. the pressure drop coefficient, is expressed as:
Figure RE-GDA0002459799300000046
obviously, the larger the pressure drop coefficient alpha is, the larger the pressure drop at the position of the supporting oil film is, the higher the oil film supporting efficiency is,
and R iscExpressed as:
Figure RE-GDA0002459799300000051
wherein d is1And d2The diameters of the piston pin and its mating hole, the axial length of the rotary joint is l, and the clearance between the piston pin and the cylinder head mating hole is hc＝(d2-d1) (iii) the fluid resistance between the spherical surface of the piston and the cylinder head is RsExpressed as:
Figure RE-GDA0002459799300000052
thereby to obtain
Figure RE-GDA0002459799300000053
Is provided with
Figure RE-GDA0002459799300000054
Then:
Figure RE-GDA0002459799300000055
KBCand KBSIs a structural parameter, related to its own structural and geometric properties, and the above formula (17) is also called TettAnd (4) a characteristic equation reflecting the supporting performance of the whole static pressure supporting system.
Compared with the prior art, the technical scheme adopted by the invention has the beneficial effects that: the structure and the working principle of the static pressure support used in the spherical pump are different from those of the traditional static pressure support method, the static pressure support of the spherical pump piston is systematically analyzed by establishing a model, the piston angle when the oil film flow rate on the surface of the spherical pump piston is the lowest is obtained, the friction coefficient between the kinematic pairs is effectively reduced, the support performance is improved, the friction and the abrasion of the piston are reduced, and the blocking is avoided.
Drawings
FIG. 1 is a flow chart of the present invention.
Fig. 2 is a piston-cylinder hydrostatic bearing model of the invention.
Figure 3 is a graph of hydrostatic pressure as a function of piston radius.
FIG. 4 is a graph of hydrostatic pressure as a function of piston pin diameter to piston radius ratio.
FIG. 5 is a graph of support force versus lubrication film termination angle θ2The graph is varied.
Fig. 6 is an equivalent fluid bridge of a hydrostatic support system.
FIG. 7 shows the pressure drop coefficient at different hcGraph below as a function of lubricating film thickness.
FIG. 8 is KBSGraph of the effect on the pressure drop coefficient.
FIG. 9 is a graph of dimensionless stiffness coefficients at different hcGraph below as a function of lubricating film thickness.
FIG. 10 is KBSA graph of the effect on dimensionless stiffness coefficients.
FIG. 11 shows leakage at different psThe graph with variation of eccentricity is shown below.
FIG. 12 is a graph of the effect of lubrication pressure on leakage.
FIG. 13 shows leakage at different μ0Lower graph with temperature.
FIG. 14 is a graph of flow rates at different psThe graph of the angle variation is shown below.
Detailed Description
As shown in fig. 1, a design method for a hydrostatic support of a piston of a spherical pump includes the following steps:
step 1, as shown in fig. 2, establishing a piston-cylinder static pressure support model: lubricating liquid is sprayed between the surface of the piston and the cylinder body through high pressure to form a lubricating film;
step 2, deducing the supporting force of the spherical piston and the effective bearing area of the spherical piston according to the static pressure supporting model in the step 1;
step 3, establishing an equivalent fluid bridge model according to the structural characteristics of the spherical pump and the structure of the hydrostatic pressure channel;
and 4, carrying out systematic analysis on the static pressure support of the spherical pump piston to obtain the piston angle when the oil film flow rate on the surface of the spherical pump piston is the lowest, and ensuring the stability of the flow rate of the support oil film.
The step 2 specifically comprises the following steps:
(a) in spherical coordinates, the equation of continuity for incompressible lubricating fluid is:
Figure RE-GDA0002459799300000071
wherein u isr，uθ，
Figure RE-GDA0002459799300000072
Representing a liquid velocity component; because of the fact that
Figure RE-GDA0002459799300000073
ur0, so formula (1) above translates to:
Figure RE-GDA0002459799300000074
(b) assuming that the lubricating fluid is flowing at a constant rate, then
Figure RE-GDA0002459799300000075
Irrespective of inertia of the lubricating fluid
Figure RE-GDA0002459799300000076
Due to the piston along
Figure RE-GDA0002459799300000077
Is symmetrical in direction, so
Figure RE-GDA0002459799300000078
The Navier-Stokes equation for incompressible lubricating fluids with uniform viscosity:
Figure RE-GDA0002459799300000079
can be simplified to the following formula:
Figure RE-GDA0002459799300000081
wherein μ represents a kinetic viscosity coefficient, ρ represents a lubricating fluid density, and p represents a lubricating oil pressure;
(c) substituting the continuity equation into the above equation (4) can obtain
Figure RE-GDA0002459799300000082
Indicating that the lubricating oil pressure p varies only with theta; the pressure distribution of p in the theta direction, which can be obtained from the flow theory between parallel surfaces, is:
Figure RE-GDA0002459799300000083
integrating r gives:
Figure RE-GDA0002459799300000084
wherein a and b are two different integration constants; substituting boundary conditions uθ|r＝R0 and uθ|r＝R+hThe speeds available at different θ are 0:
Figure RE-GDA0002459799300000085
wherein h represents a clearance between the piston surface and the cylinder inner surface;
(d) the flow rate of the lubricating liquid obtained from the above is as follows:
Figure RE-GDA0002459799300000086
substituting h ═ ecos θ into the above equation (6), the integral is calculated using a variable separation method:
Figure RE-GDA0002459799300000087
wherein the eccentricity e represents the distance between the center of the piston and the center of the cylinder; p is a radical ofsRepresenting the inlet pressure of the spherical piston lubricating fluid; theta1Indicating the initial angle of the lubrication film; the pressure profile of the lubricating fluid is therefore expressed as:
Figure RE-GDA0002459799300000088
(e) when theta is equal to theta2When the pressure p of the lubricating fluid is equal to 0, where θ2Is the lubrication film termination angle; by substituting this boundary condition into the above equation (7), the flow rate of the lubricating liquid leaking on the piston surface can be obtained:
Figure RE-GDA0002459799300000091
the lubricating fluid pressure distribution obtained by the above formula (8) is:
Figure RE-GDA0002459799300000092
(f) when d is eliminated2-d1The supporting force of the spherical piston can be obtained at the supporting force in the gap:
Figure RE-GDA0002459799300000093
the above formula (10) can be simplified to F ═ psSeWherein
Figure RE-GDA0002459799300000094
Showing the effective bearing area of the ball piston. Effective bearing area SeLubricated angle θ1And theta2Is dependent on Se. Initial angle theta of lubricating film1By piston pin diameter d1And (6) determining. Thus, d1And theta2May directly affect the hydrostatic support performance. Because the lubricating film thickness h is eco θ and h > 0, θ2Typically less than 90.
As shown in fig. 3, at θ2Hydrostatic pressure curve at 60 ° F5000N, angle θ2And hydrostatic pressure p when the supporting force is constantsDecreases with increasing piston radius because the bearing area increases with increasing piston radius. When the piston pin diameter is half the piston radius, the required lubricating oil film pressure is minimal for a given load capacity and structural parameters.
As shown in fig. 4, at θ 260 DEG, F5000N, hydrostatic pressure is plotted as a function of piston pin diameter to piston radius ratio, theta is generally constant with support force2The larger the required hydrostatic pressure; theta2Different, hydrostatic pressure with d1The change trend of/R is different, d when the lowest hydrostatic pressure occurs1R is different, so for a particular theta2The optimum ratio d corresponding to the lowest hydrostatic pressure can be found by figure 31and/R. I.e. a larger theta for obtaining the same supporting force2The static pressure required is less, i.e. a small working chamber volume requires less static pressure, while a large working chamber (small theta)2) The required static pressure is large
As shown in fig. 5, when R is 20mm, psWhen the pressure is 15MPa, the supporting force follows the end angle theta of the lubricating film2The graph is varied. Supporting force with different growth rate with theta2Is increasedAnd then increases. d1the/R also affects the piston holding force when theta2When changing from 60 to 90, d1The smaller the/R, the larger the amount of increase in the supporting force. That is, when the static pressure and the size of the piston are constant, the supporting force is along with theta2The supporting force of the piston can be increased by increasing, i.e. reducing the volume of the working chamber.
Fig. 6 shows an equivalent fluid bridge of the hydrostatic bearing system, with lubrication oil injected from the clearance between the piston pin and the cylinder head. Fluid resistance R of gapcExpressed as a constant; rgShowing hydrostatic bearing adjustable fluid resistance. Based on the continuity theorem, one can obtain:
Figure RE-GDA0002459799300000101
wherein p isc＝pr-psRepresenting the pressure drop, p, at the piston pin-cylinder head gapsIndicating the pressure drop of the lubricating fluid, i.e. the fluid-supporting pressure drop, prIndicating the total pressure drop. The pressure drop ratio of the piston to the entire system, i.e. the pressure drop coefficient, is expressed as:
Figure RE-GDA0002459799300000102
obviously, the larger the pressure drop coefficient alpha is, the larger the pressure drop at the position of the supporting oil film is, and the higher the oil film supporting efficiency is.
And R iscExpressed as:
Figure RE-GDA0002459799300000103
wherein d is1And d2The diameters of the piston pin and its mating hole, the axial length of the rotary joint is l, and the clearance between the piston pin and the cylinder head mating hole is hc＝(d2-d1)/2. The fluid resistance between the spherical surface of the piston and the cylinder head is RsExpressed as:
Figure RE-GDA0002459799300000111
thereby to obtain
Figure RE-GDA0002459799300000112
Is provided with
Figure RE-GDA0002459799300000113
Then:
Figure RE-GDA0002459799300000114
KBCand KBSIs a structural parameter, relating to the structural and geometric characteristics of itself. The above equation (17), also called a characteristic equation, reflects the support performance of the entire static pressure support system.
KBCAnd KBSThe effect on the support performance is shown in fig. 7 and 8, the piston pin being 5mm in diameter and length. As shown in fig. 7, θ1And theta 215 ° and 75 °, respectively, the pressure drop coefficient decreasing with increasing lubricating film thickness; when h is generatedcThe increase in pressure drop coefficient from 0.02mm to 0.1mm is increasingly less sensitive to lubricant film thickness, indicating that lubricant film stiffness varies with hcIs increased and decreased; is obviously hcThe smaller the size, the higher the support rigidity can be obtained, but the thickness of the lubricating film must be within a suitable range. I.e. the smaller the piston pin clearance, the more sensitive the pressure drop coefficient, and when the clearance size becomes maximum, the pressure drop coefficient changes most gradually, and the pressure drop ratio of the piston bearing surface is also maximum.
FIG. 8(a) shows the angle θ1Influence curve on pressure drop coefficient, theta in the figure2Fixed at 60 DEG constant, theta1Respectively 5 degrees, 15 degrees and 25 degrees, namely the diameters of the piston pin shafts are gradually increased, and the increase theta is known from fig. 8(a)1The stiffness of the lubricating film will become greater, i.e. when θ2Constant, theta1The larger the pressure drop coefficient is, the more sensitive it is; FIG. 8(b) lists the angle θ2To each otherInfluence curve of coefficient of decrease, theta in the figure1Fixed at 10 deg. constant, theta 260 DEG, 70 DEG and 80 DEG, respectively, that is, the volume of the working chamber becomes smaller gradually, and the increase theta is known from FIG. 8(b)2The rigidity of the lubricating film becomes small, and theta2Influence on pressure drop coefficient is larger than theta1I.e. theta2The smaller the pressure drop coefficient the more sensitive. Thus appropriately reducing theta1While increasing theta2The stability of the supporting oil film can be effectively improved.
The lubrication film stiffness is defined as:
Figure RE-GDA0002459799300000121
wherein F represents the supporting force and h represents the lubricating film thickness. Substituting the formula to obtain:
Figure RE-GDA0002459799300000122
from the above equation (19), it can be understood that the lubricating film rigidity is not only influenced by the structural parameter KBCAnd KBSIs also influenced by the hydrostatic pressure prEffective bearing area SeAnd the effect of the lubricating film thickness h. When in use
Figure RE-GDA0002459799300000126
An extreme value of the film thickness can be obtained, and the maximum lubricating film thickness is as follows:
Figure RE-GDA0002459799300000123
the maximum pressure drop coefficient α is thus 2/3 and the maximum support stiffness:
Figure RE-GDA0002459799300000124
the dimensionless stiffness coefficient δ is then:
Figure RE-GDA0002459799300000125
KBCand KBSThe influence on the dimensionless stiffness coefficient of the lubricating film is shown in fig. 9 and 10, and the piston pin is 5mm in both diameter and length. As can be seen from fig. 9 and 10, the dimensionless stiffness coefficient initially increases to the maximum value of 1 with an increase in the lubricating film thickness, and then decreases with an increase in the lubricating film thickness at different rates of change.
As shown in FIG. 9, hcThe smaller, the maximum stiffness occurs when the lubricating film thickness is smaller; namely, the oil film rigidity coefficient is firstly increased and then reduced along with the thickness of the oil film, the smaller the piston pin gap is, the higher the rigidity coefficient reaches the maximum value.
FIG. 10(a) shows the angle θ1Influence curve to oil film rigidity coefficient. In the figure theta2Fixed at 60 DEG constant, theta1Respectively 5 degrees, 15 degrees and 25 degrees, namely the diameters of the piston pin shafts are gradually increased, and the increase theta is known from fig. 10(a)1And when the maximum rigidity of the oil film is smaller than the thickness of the oil film. FIG. 10(b) lists the angle θ2Curve of influence on oil film stiffness coefficient, theta in the figure1Fixed at 10 deg. constant, theta2Respectively 60 degrees, 70 degrees and 80 degrees, namely the volume of the working chamber is gradually reduced. As can be seen from FIG. 10(b), the smaller θ2The maximum oil film stiffness can be achieved when the oil film thickness is small. Thus increasing theta1And decrease theta2The maximum support stiffness can be obtained at the thin oil film thickness. As can be seen from the combination of FIGS. 10(a) and 10(b), θ is increased1Or decrease theta2The maximum stiffness coefficient of the oil film under the thickness of the thin oil film can be obtained, and the maximum stiffness coefficient can be selected according to specific working conditions according to the graph 10 during specific design.
Proper fit clearance should exist between the spherical piston and the cylinder body, so leakage through the clearance cannot be avoided. Leakage and lubrication pressure psEccentricity e3Proportional, inversely proportional to the dynamic viscosity μ, and also to the structural parameter θ1And theta2It is related.
As shown in FIG. 11, the dynamic viscosity was 0.01 pas, θ1And theta2Respectively 15 deg. and 75 deg., and it can be seen from the figure that the leakage amount increases sharply with the increase of the eccentricity, and the larger the lubrication pressure is, the more the leakage is, i.e. the larger the eccentricity of the spherical pump piston is, the larger the leakage amount is.
The angle θ is given as FIG. 12(a)1Curve of influence on leakage Q, theta in the figure2Fixed at 60 DEG constant, theta1Respectively 5 degrees, 15 degrees and 25 degrees, namely the diameters of the piston pin shafts are gradually increased, and the increase theta is known from fig. 12(a)1The amount of leakage will increase linearly with pressure. FIG. 12(b) lists the angle θ2Curve of influence on leakage Q, theta in the figure1Fixed at 15 deg. constant, theta 260 DEG, 70 DEG and 80 DEG, respectively, that is, the volume of the working chamber becomes smaller gradually, and as can be seen from FIG. 12(b), the increase theta2The leakage amount becomes small, and theta2Influence on leakage quantity greater than theta1. As can be seen from the combination of FIGS. 12(a) and 12(b), θ is reduced1Or increase theta2The leakage amount of the oil film can be effectively reduced.
When the spherical pump is operated, the temperature of the lubricating medium inevitably rises, so that the viscosity of the lubricant decreases. The viscosity-temperature equation is:
Figure RE-GDA0002459799300000141
wherein mu0Denotes the initial viscosity, beta denotes the viscosity-temperature coefficient, t0Indicating the initial temperature. The relationship between temperature and leakage was thus obtained:
Figure RE-GDA0002459799300000142
as shown in fig. 13, initial temperature t0The viscosity-temperature coefficient beta of the mixture is 1/20℃ at 20 DEG C-1Lubricating pressure ps15MPa, eccentricity of 0.05mm and structural parameter theta1And theta 215 deg. and 60 deg., respectively. As can be seen, the leakage increases nonlinearly with increasing temperature, and at temperatures below 80 deg.C, the leakage increases nonlinearlyIncreases sharply with increasing temperature. And the greater the initial dynamic viscosity, the more leakage.
The transparent leakage of the support film can be expressed as:
Q＝VfrSfr＝Vfr2πR sinθh (25)
wherein, VfrIndicating the flow velocity of a particular surface perpendicular to the piston axis, which is constituted by the clearance between the piston and the cylinder head. SfrRepresenting the area of the particular surface, is equal to 2 pi Rsin θ h. The surface flow velocities at different angles θ are:
Figure RE-GDA0002459799300000143
as shown in fig. 14, the structural angle θ1And theta2Respectively at 15 degrees and 75 degrees, the piston radius is 20mm, the dynamic viscosity mu is 0.01 Pa.s, and the eccentricity is 0.05 mm. As can be seen, the influence of θ on the flow rate is similar to a quadratic curve, with the flow rate being lowest when θ equals 45 °; when theta is<At 45 deg., the flow rate increases; when the temperature is 45 °<θ<At 75 deg., the flow rate increases. Indicating that the oil film flow velocity at the piston surface is lowest at a piston angle theta of 45 deg.. And when the flow rate is more or less than 45 degrees, the flow rate is increased. Therefore, at the time of design, θ should be reduced appropriately<45 DEG and 45 DEG<θ<And the 75-degree clearance can ensure the stability of the flow velocity of the support oil film.
In conclusion, the invention establishes a spherical pump hydrostatic support theoretical model under a spherical coordinate, reasonably and effectively deduces and simplifies the model, establishes an equivalent fluid bridge model according to the structural characteristics of the spherical pump and the structure of a hydrostatic passage, and systematically analyzes the hydrostatic support of the spherical pump piston to obtain the piston angle theta equal to 45 degrees when the flow rate of an oil film on the surface of the spherical pump piston is the lowest.
The present invention is not limited to the above-mentioned embodiments, and based on the technical solutions disclosed in the present invention, those skilled in the art can make some substitutions and modifications to some technical features without creative efforts according to the disclosed technical contents, and these substitutions and modifications are all within the protection scope of the present invention.

Claims (3)

1. A design method for hydrostatic support of a piston of a spherical pump is characterized by comprising the following steps:
step 1, establishing a piston-cylinder static pressure support model: lubricating liquid is sprayed between the surface of the piston and the cylinder body through high pressure to form a lubricating film;
step 2, deducing the supporting force of the spherical piston and the effective bearing area of the spherical piston according to the static pressure supporting model in the step 1; wherein
Figure FDA0003084441950000011
SeRepresenting the effective bearing area, theta, of the ball piston2To theta1The corresponding cylinder part is the effective bearing area, R is the radius of the spherical piston, d1And d2The diameters of the piston pin and its mating bore, respectively;
step 3, establishing an equivalent fluid bridge model according to the structural characteristics of the spherical pump and the structure of the hydrostatic pressure channel; the equivalent fluid bridge model is the formula:
Figure FDA0003084441950000012
in which lubricating oil is injected from the gap between piston pin and cylinder head, the fluid resistance of the gap being RcExpressed as a constant; rgRepresenting hydrostatic bearing adjustable fluid resistance, pc＝pr-psRepresenting the pressure drop, p, at the piston pin-cylinder head gapsIndicating the pressure drop of the lubricating fluid, i.e. the fluid-supporting pressure drop, prRepresents the total pressure drop;
step 4, carrying out systematic analysis on the spherical pump piston static pressure support to obtain a piston angle theta when the oil film flow rate on the surface of the spherical pump piston is the lowest, and ensuring the flow rate of the support oil film to be stable; ball-shaped activitySupporting force F ═ p of plugsSe，psIndicating the inlet pressure, S, of the lubricating fluid of the ball pistoneThe effective bearing area of the spherical piston is expressed, the supporting force of the spherical piston is directly related to the effective bearing area of the spherical piston, the bearing capacity of the piston depends on the effective bearing area, and the effective bearing area SeLubricated angle θ1And theta2Influence of, initial angle of lubricating film θ1By piston pin diameter d1Determine, therefore, d1And theta2May directly affect hydrostatic support performance; rcAnd d is further reacted with1And d2Are directly related, as
Figure FDA0003084441950000013
Namely RcDetermine theta1And theta2By a different angle of theta1And theta2And analyzing an oil film rigidity coefficient curve to obtain a piston angle when the oil film flow speed on the surface of the spherical pump piston is the lowest, and defining the piston angle at the moment as theta.
2. The design method for hydrostatic support of spherical pump pistons according to claim 1, wherein the step 2 comprises the following steps:
(a) in spherical coordinates, the equation of continuity for incompressible lubricating fluid is:
Figure FDA0003084441950000021
wherein u isr，uθ，
Figure FDA0003084441950000022
Representing a liquid velocity component; because of the fact that
Figure FDA0003084441950000023
urNot equal to 0, so that the above formula (1) is converted into：
Figure FDA0003084441950000024
(b) Assuming that the lubricating fluid is flowing at a constant rate, then
Figure FDA0003084441950000025
Irrespective of inertia of the lubricating fluid
Figure FDA0003084441950000026
Due to the piston along
Figure FDA0003084441950000027
Is symmetrical in direction, so
Figure FDA0003084441950000028
The Navier-Stokes equation for incompressible lubricating fluids with uniform viscosity:
Figure FDA0003084441950000029
can be simplified to the following formula:
Figure FDA0003084441950000031
wherein μ represents a kinetic viscosity coefficient, ρ represents a lubricating fluid density, and p represents a lubricating oil pressure;
(c) substituting the continuity equation into the above equation (4) can obtain
Figure FDA0003084441950000032
Indicating that the lubricating oil pressure p varies only with theta; the pressure distribution of p in the theta direction, which can be obtained from the flow theory between parallel surfaces, is:
Figure FDA0003084441950000033
integrating r gives:
Figure FDA0003084441950000034
wherein a and b are two different integration constants; substituting boundary conditions uθ|r＝R0 and uθ|r＝R+hThe speeds available at different θ are 0:
Figure FDA0003084441950000035
wherein h represents a clearance between the piston surface and the cylinder inner surface;
(d) the flow rate of the lubricating liquid obtained from the above is as follows:
Figure FDA0003084441950000036
substituting h ═ ecos θ into the above equation (6), the integral is calculated using a variable separation method:
Figure FDA0003084441950000037
wherein the eccentricity e represents the distance between the center of the piston and the center of the cylinder; p is a radical ofsRepresenting the inlet pressure of the spherical piston lubricating fluid; theta1Indicating the initial angle of the lubrication film; the pressure profile of the lubricating fluid is therefore expressed as:
Figure FDA0003084441950000038
(e) when theta is equal to theta2When the pressure p of the lubricating fluid is equal to 0, where θ2Is the lubrication film termination angle; by substituting this boundary condition into the above equation (7), the flow rate of the lubricating liquid leaking on the piston surface can be obtained:
Figure FDA0003084441950000041
the lubricating fluid pressure distribution obtained by the above formula (8) is:
Figure FDA0003084441950000042
(f) when d is eliminated2-d1The supporting force of the spherical piston can be obtained at the supporting force in the gap:
Figure FDA0003084441950000043
the above formula (10) can be simplified to F ═ psSeWherein
Figure FDA0003084441950000044
Representing the effective bearing area of the spherical piston, theta is the piston angle, R is the radius of the spherical piston, and d1And d2The diameter of the piston pin and its mating bore, respectively, r is a radius variable,
Figure FDA0003084441950000046
is the z direction in the xyz volume model.
3. The design method for hydrostatic support of spherical pump piston according to claim 1, wherein the step 3 comprises the following steps:
equivalent fluid bridge of hydrostatic support system, in which lubricating oil is injected from the gap between piston pin and cylinder head, the fluid resistance of the gap being RcExpressed as a constant; rgRepresenting the adjustable fluid resistance of the hydrostatic support, based on the continuity theorem, the following can be obtained:
Figure FDA0003084441950000045
wherein p isc＝pr-psRepresenting the pressure drop, p, at the piston pin-cylinder head gapsIndicating the pressure drop of the lubricating fluid, i.e. the fluid-supporting pressure drop, prThe total pressure drop is represented, and the pressure drop ratio of the piston to the whole system, namely the pressure drop coefficient, is represented as:
Figure FDA0003084441950000051
and R iscExpressed as:
Figure FDA0003084441950000052
wherein d is1And d2The diameters of the piston pin and its mating hole, the axial length of the rotary joint is l, and the clearance between the piston pin and the cylinder head mating hole is hc＝(d2-d1) (iii) the fluid resistance between the spherical surface of the piston and the cylinder head is RsExpressed as:
Figure FDA0003084441950000053
thereby to obtain
Figure FDA0003084441950000054
Is provided with
Figure FDA0003084441950000055
Then:
Figure FDA0003084441950000056
KBCand KBSIs a structural parameter, a junction with itselfThe above equation (17), which is also called a characteristic equation, reflects the support performance of the entire static pressure support system.
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