A sinusoidal surface stator and blade forming method for an axial quantitative vane pump

Abstract

The application discloses a kind of axial quantitative vane pump sinusoidal surface stator and vane forming method, including selecting elliptical vane and sinusoidal curve stator;Ellipse curve surface equation in elliptical vane is deduced;Elliptical vane is constructed in three-dimensional modeling software;The ellipse surface of vane is contacted with the sinusoidal surface of stator respectively, and according to the angle of vane rotation, sinusoidal curve equation of stator is deduced;Based on sinusoidal curve equation and ellipse curve surface equation, the coordinates of the tangent point between vane and stator are obtained;Based on the tangent point coordinates, obtain the stator surface equation;Stator surface equation is compiled in Python compiling software Function, run to generate txt data point file, save data point file;The txt data point file is imported into three-dimensional modeling software, and the stator surface is constructed.The vane surface and the stator surface of the application closely fit, the contact line of vane and stator surface is always changing in the rotation process, which can effectively reduce vane wear and reduce leakage.

Description

Technical Field

[0001] This invention relates to the field of curved surface forming technology, and in particular to a sinusoidal curved surface stator and blade forming method for an axial metering vane pump. Background Technology

[0002] Hydraulic transmission technology, with its advantages of fast response, high power ratio, frequent reversing, and stepless speed regulation, has been widely used in various industrial fields such as aerospace, agricultural machinery, construction machinery, and road machinery. As the core of hydraulic transmission technology, the performance of the hydraulic pump directly affects the overall performance of the hydraulic system. Hydraulic pumps mainly include piston pumps, vane pumps, gear pumps, and screw pumps. Vane pumps, widely used in machine tools and metallurgy, have advantages such as small size, compact structure, smooth rotation, and low pulsation. However, in recent years, vane pumps have encountered many problems when developing towards high speed and high pressure, including limitations imposed by their inherent structure and theoretical performance limits, which are difficult to completely eliminate. For example, in vane pumps, as the load pressure increases, the pressure and pulsation peak value of the vane bottom chamber increase, and radial vibration intensifies, leading to increased friction between the vane and the stator inner wall, and increased leakage. The inherent structure of vane pumps causes serious internal leakage problems when developing towards high pressure, reducing working performance and service life. Vane pumps also face a series of problems when developing towards high speed. Increasing the rotational speed will increase the percentage of gas in the internal cavity of the vane pump, leading to cavitation and backflow phenomena.

[0003] To overcome these problems with vane pumps, an axially fixed displacement vane pump is proposed. This pump completely eliminates the distribution structure, sealing zone, and vane root chamber, thus eliminating hydraulic shock and cavitation during the distribution and sealing transition processes of radial vane pumps. It also solves the problem of pressure and flow pulsation caused by changes in the volume of the vane root chamber. In axial vane pumps, the performance of the vane and stator profiles determines the kinematics, dynamics, and output characteristics of the vane, and significantly impacts the pump's noise and lifespan. When selecting vane and stator profiles, it is essential to consider two aspects: firstly, the vane must not detach from the stator, ensuring close contact with the stator surface at both low and high speeds; secondly, the vane must be free of impact vibration and generate low noise, while the stator profile should possess smooth and continuous velocity and acceleration characteristic curves, free from both hard and soft impacts. Summary of the Invention

[0004] To address the shortcomings mentioned above, this invention provides a sinusoidal curved surface stator for an axially displaced vane pump and a method for forming vanes, comprising:

[0005] Select the blade type and stator curve type. The blade type is elliptical blade, and the stator curve type is sinusoidal stator.

[0006] The equation of the elliptical surface in the elliptical blade is derived using the standard formula for an ellipse.

[0007] Based on the equation of the elliptical surface, the elliptical blade is constructed in a 3D modeling software;

[0008] The elliptical surfaces of the blades are in contact with the sinusoidal surfaces of the stator, and the sinusoidal curve equation of the stator is derived based on the rotation angle of the blades.

[0009] Based on the sine curve equation and the elliptic surface equation, the coordinates of the tangent point between the blade and the stator are obtained;

[0010] Based on the coordinates of the tangent point, the equation of the stator surface is obtained;

[0011] The stator surface equations are compiled into a function using Python compiler software, and the resulting txt data point file is saved.

[0012] Import the txt data point file into the 3D modeling software to construct the stator surface.

[0013] Preferably, deriving the equation of the elliptical surface in the elliptical blade using the standard elliptical formula includes:

[0014] Establish a polar coordinate system, with the r-axis on the central axis of the blade, and the blade is symmetrical about the r-axis in all directions.

[0015] The blade unfolds on the cross section r = r2, forming two semi-ellipses, with the major and minor axes of the semi-ellipses being 2a and 2b respectively, and the blade height being H.

[0016] The blade, viewed from the positive z-axis, is a sector shape. The inner radius of the sector is r1, the outer radius is r2, and the angle it occupies is [missing information].

[0017] The standard formula for an ellipse in a rectangular coordinate system is:

[0018]

[0019] Placing the ellipse on the plane r = C in polar coordinates, the formula is:

[0020]

[0021] C is a constant, and the height z of the elliptical surface of the blade is equal at the same angle θ. Then the formulas for the upper and lower elliptical surfaces of the blade are respectively:

[0022]

[0023]

[0024] Preferably, constructing the elliptical blade in 3D modeling software based on the elliptical surface equation includes:

[0025] Take two cross-sections of the blade and calculate the size of each cross-section;

[0026] In the 3D modeling software, a sketch of the cross section is drawn, and two cross sections are connected using a loft operation to generate a solid.

[0027] Draw the inner and outer circular surfaces of the blade in the sketch interface of the entity, and obtain the blade using the extrude cut operation.

[0028] Preferably, the elliptical surface of the blade contacts the sinusoidal surface of the stator, and the sinusoidal curve equation of the stator is derived based on the rotation angle of the blade, including:

[0029] The stator surface includes a lower sector surface, a left-hand helical surface, an upper sector surface, and a right-hand helical surface, wherein the angles of the lower sector surface and the upper sector surface are both... The inner circle has a radius of r1, and the outer circle has a radius of r2.

[0030] A rectangular coordinate system is established on the stator, with the lower sector surface on the z=0 plane and the upper sector surface on the z=T plane. The origin O of the coordinate system is on the central axis of the stator, and the angle between the symmetry plane of the blade and the XOZ plane is α.

[0031] At the blade angle At that time, the height of the sine curve of the stator is z = H / 2; at the blade angle At that time, the height of the stator's sine curve is z = H / 2 + T; therefore, the equation of the stator's sine curve is:

[0032]

[0033] In the formula: l / r2=α, l is the arc length of the blade moving on the outer circular surface.

[0034] Preferably, obtaining the coordinates of the tangent point between the blade and the stator based on the sine curve equation and the elliptic surface equation includes:

[0035] The sine curve of the stator is shifted H / 2 in the negative z-axis direction, which is the path traversed by the vertex of the lower elliptical surface of the blade.

[0036] By translating each point of the sinusoidal curve of the translated stator to the tangent point A(x0,y0) between the blade and the lower stator curve, the equation of the lower stator curve can be obtained as follows:

[0037]

[0038] The lower ellipse of the blade is tangent to the lower stator curve, therefore their slopes k are equal. The formulas for the slopes of the lower ellipse and the lower stator curve are as follows:

[0039]

[0040]

[0041] The tangent point A(x0,y0) is obtained based on this slope formula.

[0042] Preferably, obtaining the stator surface equation based on the tangent point coordinates includes:

[0043] Substituting the coordinates of the tangent point into the sine curve equation of the stator, the formula for the lower stator curve is obtained as follows:

[0044]

[0045] The height z of the blade rotation angle α is equal, so the height z of the lower stator curve at the same angle α can be replaced by the height of the lower stator curve on the outer circular surface. Substituting l / r2=α into the formula for the lower stator curve, we get:

[0046]

[0047] Rewriting the above formula in Cartesian coordinates yields the equation for the stator surface:

[0048]

[0049] Preferably, the equations for the lower sector, the right-hand helical surface, the upper sector, and the left-hand helical surface are as follows:

[0050]

[0051]

[0052]

[0053]

[0054] Preferably, the slope of the sine curve of the stator is:

[0055]

[0056] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0057] In this invention, the blade surface and the stator surface are closely fitted. During the rotation of the blade, the contact line between the blade and the stator surface is constantly changing, which can effectively reduce blade wear and leakage. Moreover, the stator surface is smooth and without abrupt changes, so there are no sudden speed changes during the blade movement, the acceleration changes are gradual, the blade will not come off the ground, and the radial and axial vibration of the blade is eliminated, reducing the noise of the axial vane pump. In addition, the stator surface can accept a larger lead while ensuring the uniformity of flow and the smoothness of blade movement, so as to obtain a higher axial vane pump displacement under the conditions of long service life and low flow pulsation. Attached Figure Description

[0058] Figure 1 This is a flowchart of the method of the present invention.

[0059] Figure 2 This is a diagram illustrating the polar coordinate system and variables of the blades in this invention.

[0060] Figure 3 This is a schematic diagram of the stator coordinate system and stator surface of the present invention.

[0061] Figure 4 This is a schematic diagram of the stator curve and key stator parameters of the present invention.

[0062] Figure 5 This is an illustration of the stator lower helix curve of the present invention. Detailed Implementation

[0063] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0064] The following is in conjunction with the appendix Figure 1-5 The present invention will be described in further detail as follows:

[0065] Reference Figure 1 This invention provides a sinusoidal curved surface stator and blade forming method for an axially metering vane pump, comprising:

[0066] Select the blade type and stator curve type. The blade type is elliptical blade, and the stator curve type is sinusoidal stator.

[0067] Specifically, blade types include elliptical blades, chamfered blades, stepped blades, and double blades. Stator curves include sine curves, constant acceleration-constant deceleration curves, quintic curves, and octet curves. Chamfered and stepped blades have sharp corners and are prone to wear. Quintic and octet curves have good performance, with no sudden changes in velocity or acceleration, but they require high precision, are difficult to fit with mathematical software, and have high requirements for manufacturing, which is not conducive to production. Therefore, after comprehensive consideration, elliptical blades and sine stator curves are selected in this application.

[0068] Derive the equation of the elliptical surface in an elliptical blade using the standard formula for an ellipse;

[0069] Reference Figure 2 Establish a polar coordinate system for the blade, with the r-axis on the central axis of the blade, and the blade is symmetrical about the r-axis in all directions.

[0070] The blade unfolds on the cross section r = r2, forming two semi-ellipses, with the major and minor axes of the semi-ellipses being 2a and 2b respectively, and the blade height being H.

[0071] The blade, viewed from the positive z-axis, is a sector shape with an inner radius of r1 and an outer radius of r2, occupying an angle of...

[0072] The standard formula for an ellipse in a rectangular coordinate system is:

[0073]

[0074] Placing the ellipse on the plane r = C in polar coordinates, the formula is:

[0075]

[0076] If C is a constant, and the height z of the elliptical surface of the blade is equal at the same angle θ, then the formulas for the upper elliptical surface ABCD and the lower elliptical surface EFGH of the blade in polar coordinates are as follows:

[0077]

[0078]

[0079] Other curved surfaces of the blade can be seen intuitively and do not require formulas.

[0080] Based on the equation of elliptical surface, an elliptical blade is constructed in a 3D modeling software;

[0081] Specifically, take two cross-sections of the blade and calculate the size of each cross-section;

[0082] Draw a sketch of the cross-section in a 3D modeling software, and use the loft operation to connect the two cross-sections to generate a solid.

[0083] Draw the inner and outer circular surfaces of the blade in the solid sketch interface, and use the extrude cut operation to obtain the blade shape.

[0084] The elliptical surfaces of the blades contact the sinusoidal surfaces of the stator, and the equation of the sinusoidal curve of the stator is derived based on the rotation angle of the blades.

[0085] Reference Figure 3 The stator surface is divided into four parts: the lower sector (MQTP), the left-hand helical surface (MNRQ), the upper sector (RNOS), and the right-hand helical surface (SOPT). The angles of the two sectors are both... The inner circle has a radius of r1, and the outer circle has a radius of r2. A rectangular coordinate system is established on the stator. The lower sector surface MQTP lies on the z=0 plane, and the upper sector surface lies on the z=T plane. The origin O of the coordinate system is on the central axis of the stator. The angle between the blade's plane of symmetry and the XOZ plane is α, representing the angle the blade rotates through in the stator, and also indicating the blade's position. The contact curve between the stator and the blade is unfolded along the outer circle surface. The stator sine curve (MN) is the trajectory of the blade's center point in the axial hydraulic pump. When the blade is positioned within the stator's sector curve region, the vertices of the upper and lower elliptical surfaces of the blade are in contact with the upper and lower stator curves. When the blade is on the right-hand helical surface ABFE, let A be the point of tangency between the blade and the lower stator surface. A two-dimensional rectangular coordinate system is established on the blade, with the origin O at the center of the lower semi-ellipse. The length of the major semi-axis of the ellipse is a, and the length of the minor semi-axis is b. In a rectangular coordinate system, the coordinates of the tangent point A can be represented as (x0, y0), where x0 ≥ 0 and y0 ≤ 0 during the blade's ascent. The axis l represents the arc length traversed by the blade on the outer circular surface r = r2.

[0086] Reference Figure 4 At the blade angle At that time, the height of the stator sine curve (KW) is z = H / 2. At the blade angle... At that time, the height of the stator sine curve (KW) is z = H / 2 + T. Therefore, the final equation of the sine curve can be expressed as:

[0087]

[0088] In the formula: l / r2=α, l is the arc length of the blade moving on the outer circular surface.

[0089] Based on the equations of sine curves and elliptic surfaces, the coordinates of the tangent point between the blade and the stator are obtained.

[0090] Reference Figure 5Observing the relationship between the sine curve and the lower stator curve, shifting the sine curve in the negative z-axis direction by H / 2 represents the path traversed by the vertex of the lower elliptical surface of the blade. By shifting each point of the translated curve to the point of tangency A between the blade and the lower stator curve, the equation of the lower stator curve can be derived:

[0091]

[0092] Therefore, to derive the expression for the lower stator curve, we must first find the coordinates of A(x0,y0), x0≥0, y0≤0. The lower ellipse of the blade is tangent to the lower stator curve, so their slopes k are equal. This relationship can be used to derive an equation, which can then be solved to find x0.

[0093] By transforming the equation of the ellipse, we can obtain

[0094]

[0095] Take the lower half

[0096]

[0097] Differentiation yields

[0098] Differentiating the equation of the sine curve yields

[0099] We can obtain the following from the two formulas:

[0100]

[0101] In the formula, all values ​​except l and x are fixed. Therefore, for each fixed value of l, x can be solved. Substituting x into the equation of the ellipse, the value of y can be obtained, thus yielding the coordinates of point A (x0, y0).

[0102] Based on the coordinates of the tangent point, the equation of the stator surface is obtained;

[0103] Specifically, substituting the coordinates of the tangent point into the sine curve equation of the stator, we obtain the formula for the lower stator curve as follows:

[0104]

[0105] The equations for the upper and lower stator curves are expanded along the outer circular surface of the stator. Since the height z of the same blade at the same rotation angle α is equal on the stator helical surface, the height z of the lower stator curve at the same angle α can be replaced by the height of the lower stator curve on the outer circular surface. Substituting l / r² = α into the formula for the lower stator curve, we get:

[0106]

[0107] Rewriting the above formula in rectangular coordinates yields the equation for the stator surface:

[0108]

[0109] Furthermore, the equation for the lower sector AEHD is:

[0110]

[0111] The equation for the right-hand helical surface ABFE is:

[0112]

[0113] The equation for the upper sector FBCG is:

[0114]

[0115] When the blade is on the left-hand helical surface, the tangency point A(x0,y0) between the blade and the lower stator curve is x0≤0, y0≤0. Therefore, each point on the OP curve is obtained by shifting each point on the KW curve by x0 in the positive direction of the l-axis and by H / 2-b-y0 in the negative direction of the z-axis, consistent with the derivation above. Thus, by slightly modifying the equation of the right-hand helical surface, the CDHG equation of the left-hand helical surface can be obtained as follows:

[0116]

[0117] It should be noted that the slope of the sine curve MN at this point is:

[0118]

[0119] The stator surface equations are compiled into a function using Python compiler software, and the resulting txt data point file is saved.

[0120] Import the txt data point file into the 3D modeling software to construct the stator surface.

[0121] Taking SolidWorks, the 3D drawing software used in this invention, as an example, to complete the modeling of the stator surface, firstly, the saved point set file is imported into SolidWorks to generate sketch curves, which serve as the reference curves for subsequent sweep and sweep cut. Based on the selected radii r1 and r2 of the inner and outer surfaces of the stator, a sketch is drawn, and an extrusion operation is performed to generate a 3D cylinder. Finally, based on the cylinder and using the imported sketch curves as the reference curves, a sweep cut operation with a specified direction vector is performed, thus completing the shaping of the stator surface.

[0122] Example

[0123] The key parameters of the axial vane pump are shown in Table 1.

[0124] Table 1

[0125]

[0126] Using the parameters in Table 1, the formula for the upper elliptical surface ABCD can be obtained as follows:

[0127]

[0128] The formula for the lower elliptical surface EFGH is:

[0129]

[0130] Take two blade cross-sections, calculate their sizes, and draw sketches in 3D modeling software. Use the loft operation to connect the two cross-sections and generate a solid. Finally, draw the inner and outer circular surfaces of the blade, and use the extrude cut operation to cut out the inner and outer circular surfaces of the blade. This completes the surface shaping of the blade.

[0131] When the blade angle α = 7°, the height z of the stator sine curve (KW) is 15 mm. When the blade angle α = 173°, the height z of the stator sine curve (KW) is 24 mm. The final sine curve equation can be expressed as:

[0132]

[0133] In the formula, l / 25 = α, where l is the arc length of the blade moving on the outer circular surface;

[0134] The slope of the sine curve KW is:

[0135]

[0136] The slope of the blade curve is:

[0137]

[0138] Solving both methods yields the following results:

[0139]

[0140]

[0141] Therefore, the coordinates of point A are obtained as (x0, y0).

[0142] With the coordinates of point A, the lower stator curve can be derived. At this point, the equations of the upper and lower stator curves are expanded along the outer surface of the stator. Since the height z of the same blade at the same rotation angle α is equal on the stator helical surface, the height z of the lower stator curve at the same angle α can be replaced by the height of the lower stator curve on the outer surface. And since l / 25 = α, therefore:

[0143]

[0144] Rewriting it as an equation in a rectangular coordinate system yields the equations for the four parts of the stator surface.

[0145] The equation for the lower sector AEHD is:

[0146]

[0147] For the right-hand helical surface ABFE, taking the result of (x0≥0, y0≤0), the equation is:

[0148]

[0149] The equation for the upper sector FBCG is:

[0150]

[0151] For the left-hand helical surface CDHG, taking the result of (x0≤0, y0≤0), the equation is:

[0152]

[0153] It should be noted that the slope of the sine curve KW when deriving the left-hand spiral CDHG is:

[0154] z' MN (l)2=-0.19518×cos[1.08434×(α-270°)]=k;

[0155] Taking Python as an example, to convert the derived stator surface formula into code, the NumPy, SymPy, and Matplotlib libraries are needed. Using functions like Symbol in SymPy, variables can be defined to generate a formula calculation plot. With the calculation plot, simply substituting the specific values ​​of the defined variables into the plot yields the height of the stator curve at any blade angle α. To import the formula-generated curve into 3D plotting software, the curve needs to be divided into several points, the spatial coordinates of each point recorded, and finally saved as a txt file. The Python code for generating stator curve data points is as follows:

[0156]

[0157]

[0158]

[0159] The above steps have generated the coordinate points required for the sine curve and stator curve. The point set is then exported and saved as a txt file. The code is as follows:

[0160] coordinate11 = np.array([y11,z11,x11]).T

[0161] coordinate11 = np.delete(coordinate11,-1,0)

[0162] coordinate12 = np.array([y2,z12,x2]).T

[0163] coordinate12 = np.delete(coordinate12,-1,0)

[0164] coordinate13 = np.array([y13,z13,x13]).T

[0165] coordinate13 = np.delete(coordinate13,-1,0)

[0166] coordinate14 = np.array([y4,z14,x4]).T

[0167] coordinate11 = np.append(coordinate11,coordinate12,0)

[0168] coordinate11 = np.append(coordinate11,coordinate13,0)

[0169] coordinate11 = np.append(coordinate11,coordinate14,0)

[0170] np.savetxt(r"D:\curve\sine_curve.txt",coordinate11)

[0171] coordinate31 = np.array([y31,z31,x31]).T

[0172] coordinate31 = np.delete(coordinate31,-1,0)

[0173] coordinate32 = np.array([y2,z32,x2]).T

[0174] coordinate32 = np.delete(coordinate32,-1,0)

[0175] coordinate33=np.array([y33,z33,x33]).T

[0176] coordinate33=np.delete(coordinate33,-1,0)

[0177] coordinate34=np.array([y4,z34,x4]).T

[0178] coordinate31=np.append(coordinate31,coordinate32,0)

[0179] coordinate31=np.append(coordinate31,coordinate33,0)

[0180] coordinate31=np.append(coordinate31,coordinate34,0)

[0181] np.savetxt(r"D:\Curve\Lower Stator Curve.txt",coordinate31)

[0182] This generates a txt point set file that can be imported into SolidWorks to generate curves.

[0183] Taking SolidWorks, the 3D drawing software used in this invention, as an example, to complete the modeling of the stator surface, firstly, the saved point set file is imported into SolidWorks to generate sketch curves, which serve as the reference curves for subsequent sweep and sweep cut. Based on the selected radii r1 and r2 of the inner and outer surfaces of the stator, a sketch is drawn, and an extrusion operation is performed to generate a 3D cylinder. Finally, based on the cylinder and using the imported sketch curves as the reference curves, a sweep cut operation with a specified direction vector is performed, thus completing the shaping of the stator surface.

[0184] The above are merely preferred embodiments of the present invention and are not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for forming a sinusoidal curved surface stator and blades for an axially displaced vane pump, characterized in that, include: Select the blade type and stator curve type. The blade type is elliptical blade, and the stator curve type is sinusoidal stator. The equation of the elliptical surface in the elliptical blade is derived using the standard formula for an ellipse. Specifically, it includes: The derivation of the equation of the elliptic surface in the elliptic blade using the standard formula for ellipses includes: Establish a polar coordinate system, and The shaft is on the central axis of the blade, and the blade is about the axis of the blade. The axis is symmetrical in all directions. The blades are When unfolded on this cross section, it forms two semi-ellipses, with the major and minor axes of the semi-ellipses having lengths of 2 and 1, respectively. a and 2 b The blade height is H ; The blade from z The top view along the positive axis is a sector, and the radius of the inner circle of the sector is... The outer radius is The angle occupied is ; The standard formula for an ellipse in a rectangular coordinate system is: ； Place the ellipse on a plane in polar coordinates The formula above is: ； C The constant is the elliptical surface of the blade at the same angle. Height If they are equal, then the formulas for the upper and lower elliptical surfaces of the blade are respectively: ； ； Based on the equation of the elliptical surface, the elliptical blade is constructed in a 3D modeling software; The elliptical surfaces of the blades are in contact with the sinusoidal surfaces of the stator, and the sinusoidal curve equation of the stator is derived based on the rotation angle of the blades. Based on the sine curve equation and the elliptic surface equation, the coordinates of the tangent point between the blade and the stator are obtained; Based on the coordinates of the tangent point, the equation of the stator surface is obtained; The stator surface equations are compiled into a function using Python compiler software, and the resulting txt data point file is saved. Import the txt data point file into the 3D modeling software to construct the stator surface.

2. The method for forming the sinusoidal curved surface stator and blades of the axially displaced vane pump as described in claim 1, characterized in that, Based on the equation of the elliptical surface, constructing the elliptical blade in 3D modeling software includes: Take two cross-sections of the blade and calculate the size of each cross-section; In the 3D modeling software, a sketch of the cross section is drawn, and two cross sections are connected using a loft operation to generate a solid. Draw the inner and outer circular surfaces of the blade in the sketch interface of the entity, and obtain the blade using the extrude cut operation.

3. The method for forming the sinusoidal surface stator and blades of the axially displaced vane pump as described in claim 1, characterized in that, The elliptical surface of the blade contacts the sinusoidal surface of the stator, and based on the rotation angle of the blade, the equation of the sinusoidal curve of the stator is derived as follows: The stator surface includes a lower sector surface, a left-hand helical surface, an upper sector surface, and a right-hand helical surface, wherein the angles of the lower sector surface and the upper sector surface are both... The inner circle has a radius of r1, and the outer circle has a radius of r2. Establish a rectangular coordinate system on the stator, with the lower sector surface on the z=0 plane and the upper sector surface on... z = T On the surface, the origin of the coordinate system On the stator's central axis, the blade's plane of symmetry is parallel to... The angle between the faces is ; At the blade angle At that time, the height of the sine curve of the stator ; at the blade angle At that time, the height of the sine curve of the stator Therefore, the equation of the sine curve of the stator is: ； In the formula: , Let be the arc length of the blade as it moves on the outer circular surface.

4. The method for forming the sinusoidal surface stator and blades of the axially displaced vane pump as described in claim 3, characterized in that, Based on the sine curve equation and the elliptic surface equation, obtaining the coordinates of the tangent point between the blade and the stator includes: The sine curve of the stator is shifted in the negative z-axis direction. That is, the path traversed by the vertex of the lower elliptical surface of the blade; Each point of the translated stator's sine curve is shifted to the point of tangency between the blade and the lower stator curve. By determining the position, the equation of the lower stator curve can be derived as follows: ； The lower ellipse of the blade is tangent to the lower stator curve, therefore the slopes of both are... Equally, the formulas for the slope of the lower ellipse of the blade and the slope of the lower stator curve are respectively: ； ； The tangent point is obtained based on this slope formula. .

5. The method for forming the sinusoidal surface stator and blades of the axially displaced vane pump as described in claim 4, characterized in that, Based on the coordinates of the tangent point, the equation of the stator surface is obtained as follows: Substituting the coordinates of the tangent point into the sine curve equation of the stator, the formula for the lower stator curve is obtained as follows: ； The blade angle height Since they are equal, the height of the lower stator curve on the outer circular surface can be used to represent the same angle. The height of the lower stator curve ,Will Substituting into the formula for the lower stator curve, we get: ； Rewriting the above formula in Cartesian coordinates yields the equation for the stator surface: 。 6. The method for forming the sinusoidal curved surface stator and blades of the axially displaced vane pump as described in claim 5, characterized in that, The equations for the lower sector, the right-hand helical surface, the upper sector, and the left-hand helical surface are as follows: ； ； ； 。 7. The method for forming the sinusoidal curved surface stator and blades of the axially displaced vane pump as described in claim 6, characterized in that, The slope of the sine curve of the stator is: 。

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