Oil pump rotor assembly profile design method

Abstract

This invention discloses a method for designing the combined profile of an oil pump rotor. The combined profile includes an inner rotor profile and an outer rotor profile. All teeth in the inner rotor profile have identical profiles, and the profiles of each tooth are symmetrically arranged. Similarly, all teeth in the outer rotor profile have identical profiles, and the profiles of each tooth are symmetrically arranged. There is a tooth gap between the inner and outer rotor teeth. The method further includes the following steps: S1: Designing a half-tooth profile of the inner rotor; S2: Obtaining the complete inner rotor tooth profile; S3: Obtaining the outer rotor profile that satisfies the basic laws of meshing and guarantees a constant transmission ratio; S4: Obtaining an equidistant curve, which is the desired outer rotor profile. Both the inner and outer rotor profiles are obtained through calculation, resulting in high precision for the entire profile. The design method of this application enables the design of arbitrary parameters, providing technical support for new product development.

Description

Technical Field

[0001] This invention belongs to the technical field of oil pumps for automobile engines and transmissions, as well as oil supply devices for machine tools, and specifically relates to a method for designing the combined profile of an oil pump rotor. Background Technology

[0002] Rotary oil pumps are characterized by their small size, simple structure, low noise, smooth operation, and high volumetric efficiency. With the development of the automotive industry, the demand is increasing. However, to date, a large number of these products still need to be imported from abroad. The core components of a rotary oil pump are the inner rotor and the outer rotor, and the meshing between the inner and outer rotors is as follows: Figure 1 As shown, in Figure 1 In this design, O1 is the rotation center of the inner rotor, and O2 is the rotation center of the outer rotor. The distance between O1 and O2 is called the eccentricity e. The angular velocity of the inner rotor is ω1. Driven by the inner rotor, the outer rotor rotates in the same direction with an angular velocity of ω2, achieving the functions of volume change and medium compression. When the profile of the inner rotor changes, the pattern of its volume change affects the overall performance of the oil pump.

[0003] Domestic oil pump manufacturers typically obtain data by testing the profiles of the inner and outer rotors of similar products. Due to the high precision requirements of the profiles, this often involves multiple tests, data modifications, and trials, resulting in a long product development cycle. When different specifications of oil pumps are required, development cannot be completed without existing product references.

[0004] In the prior art, there are cycloidal rotor pumps for individual applications, which have the following disadvantages: (1) The teeth of each gear are in contact at the same time, which makes the teeth wear easily when they are in contact at a relatively large sliding speed; (2) Due to the constraints of design parameters, when the design parameters make the theoretical profile of the profile curve radius small, the actual profile will be distorted, resulting in the design not being completed; (3) Since the teeth of each gear are in contact at the same time, high machining accuracy is required, otherwise the tooth jamming phenomenon will occur when the assembly is in operation, resulting in increased noise. Summary of the Invention

[0005] This invention aims to provide a method for designing the combined profile of an oil pump rotor, which can design an inner rotor and an outer rotor with circular arc tooth profiles.

[0006] Therefore, the technical solution adopted by the present invention is: a method for designing the combined profile of an oil pump rotor, wherein the combined profile includes an inner rotor profile and an outer rotor profile, wherein the profiles of all teeth in the inner rotor profile are the same and the profiles of each tooth are symmetrically arranged, the profiles of all teeth in the outer rotor profile are the same and the profiles of each tooth are symmetrically arranged, and there is a tooth gap between the teeth of the inner rotor and the outer rotor.

[0007] It also includes the following steps:

[0008] S1: Design the semi-tooth profile of the inner rotor. The semi-tooth profile of the inner rotor consists of a first cycloid segment, an involute segment, a circular arc segment, and a second cycloid segment. The first cycloid segment and the second cycloid segment are the same cycloid.

[0009] S2: Symmetricalizing the semi-tooth profile of the inner rotor designed in S1 can yield the single tooth profile of the inner rotor. Then, rotating the single tooth profile of the inner rotor forms the complete tooth profile of the inner rotor.

[0010] S3: Based on the fundamental law of tooth profile meshing, the profile of the outer rotor that satisfies the fundamental law of meshing and guarantees a constant transmission ratio is obtained from the profile of the inner rotor obtained in S2.

[0011] S4: Obtain the equidistant curve from the outer rotor profile obtained in S3. The equidistant curve is the required outer rotor profile.

[0012] As a preferred embodiment of the above scheme, the semi-tooth profile of the inner rotor in S1 is composed of four segments: a first cycloid segment, an involute segment, a circular arc segment, and a second cycloid segment. The involute segment is tangent to the first cycloid segment, and the circular arc segment is tangent to both the involute segment and the second cycloid segment. In S1, the semi-tooth is designed to be located in the third quadrant of the coordinate system, close to the Y-axis. Therefore, the theoretical and actual profile equations of the first and second cycloid segments are:

[0013]

[0014]

[0015]

[0016] in The angle of the rolling circles on the outer rotor. Z1 is the rolling angle of the rollers on the inner rotor, Z2 is the number of teeth on the inner rotor, L is the radius of the forming circle, and e is the eccentricity. ξ=L / (e×Z2), when At time t is the starting point of the cycloid, and the starting point is on the positive half-axis of the X-axis. Since the highest point of the theoretical profile is on the positive half-axis of the Y-axis, the theoretical profile equation needs to be rotated counterclockwise by an angle ψ. Then, by the coordinate rotation formula, the theoretical profile is obtained as follows:

[0017] x L =x mL ×cosψ-y mL ×sinψ

[0018] y L =x mL ×sinψ+y mL ×cosψ

[0019] Where ψ = 0.5π - 0.5λ, λ is the angle of each tooth of the inner rotor, then λ = 2π / Z1.

[0020] Similarly, the actual profile shape is obtained by rotating the actual profile equation counterclockwise by an angle ψ. Then, according to the coordinate rotation formula, the actual profile shape is:

[0021] x S =x mS ×cosψ-y mS ×sinψ

[0022] y S =x mS ×sinψ+y mS ×cosψ

[0023] Independent variable on the first cycloid segment The line connecting a point on the same theoretical profile line and a point on the actual profile line is the normal at the starting point of the involute. A perpendicular line drawn from the center of the inner rotor to the normal intersects it at a single point. The distance from the center of the inner rotor to the normal is the base circle radius *r* of the involute segment. b The line segment between the point on the actual profile line and the intersection of the normal and the perpendicular is the generating line of the involute segment at the starting point. The equation of the generating line is:

[0024] y = y L +K LS ×xK LS ×x L

[0025] Meanwhile, the equation of the straight line connecting the center of the inner rotor with the intersection of the normal and the perpendicular is:

[0026] y = -xK LS

[0027] Where K LS K is the slope of the normal. LS =(y BL -y B ) / (x BL -x B Then the coordinates of the intersection point can be obtained as follows:

[0028] x NB =K LS (x BL -y BL ) / (K LS 2 +1)

[0029] y NB =-(x BL -y BL ) / (KLS 2 +1)

[0030] Then the radius r of the base circle b for:

[0031]

[0032] Then the length of the generating line of the involute segment at the starting point is obtained as:

[0033]

[0034] From the equation of the involute, we can obtain the pressure angle α of the involute segment at the starting point. B Angle of expansion θ B The angle between the starting point and the X-axis is:

[0035] α B =arctan(L B / r b )

[0036] θ B =tanα B -α B

[0037] β B =arctan(y B / x b )

[0038] The initial angle η = β of the involute segment at its starting point on the base circle can be determined. B -θ B Assume the pressure angle at any point on the involute segment is α. K , and α K >α B By the involute equation, the polar radius ρ at that point is... K =r b / cosα K , spread angle θ K =tanα K -α K , with α K If is the independent variable, then:

[0039] x K =ρ K ×cos(η+θ K )

[0040] y K =ρ K ×sin(η+θ K )

[0041] Given the pressure angles at various points on the involute segment and the pressure angle α at the endpoint.C When the coordinates of the entire involute segment are obtained, the arc segment is the smooth transition segment between the involute segment and the second cycloid segment. The arc segment can be directly and uniquely determined by giving the radius of the arc.

[0042] Further optimization involves calculating the outer rotor profile in S3 as follows: Given that the pitch circle radius of the inner rotor is r1 = Z1e and the pitch circle radius of the outer rotor is r2 = Z2e, assuming P1 is a point on the inner rotor profile, the intersection of the normal at point P1 and the pitch circle of the inner rotor is q, and the coordinates of q satisfy x 2 +y 2 =r1 2 The equation of the normal at point P1 satisfies From this, we can obtain the coordinates x of point q. q y q Therefore, the angle between the intersection point, the center of the inscribed circle, and the node can be obtained as follows: Rotate the inner rotor profile by φ1 around a circle until point q coincides with the node. Then point P1 rotates to point P1′. Using the coordinate rotation formula, the coordinates of point P1′ are:

[0043]

[0044]

[0045] Assuming that point P2' is on the outer rotor profile that meshes with the inner rotor profile at point P1', then we have

[0046]

[0047] Assume point P2 is the outer rotor profile before it rotates around the inner rotor pitch circle. At the point of time, it is possible to reverse the rotation of point P2′ around the center of the outer rotor pitch circle. Point P2 can be obtained at that time, where i 12 =Z2 / Z1, and using the coordinate rotation formula, the coordinates of point P2 are:

[0048]

[0049]

[0050] By continuously repeating the above steps for each point on the inner rotor profile, the outer rotor profile that satisfies the basic law of meshing and guarantees a constant transmission ratio can be obtained.

[0051] Further optimization is achieved by calculating the equidistant curve in S4 as follows: Given that the tooth clearance is δ, and point i is a point on the previously calculated outer rotor profile, the slope k of the normal line at point i can be obtained. i The angle between the normal at point i and the X-axis is α.i =arctank i Assume point j is a point on the equidistant curve to be obtained, and the coordinates of point j are:

[0052] x i =x j +δcosα i

[0053] y i =y j +δsinα i

[0054] This yields an equidistant curve, which is the final outer rotor profile.

[0055] The beneficial effects of this invention are as follows: It can design an inner rotor profile and an outer rotor profile with a corrected cycloid. The contact and transmission of the inner and outer rotor teeth are at a position with low relative sliding speed, which reduces wear. Since not all teeth are in contact at the same time, the machining accuracy is reduced while facilitating assembly. Furthermore, the tooth profile satisfies the basic law of tooth profile meshing, resulting in smooth transmission. Both the inner and outer rotors are obtained through calculation, resulting in high precision of the entire profile. Unlike the cycloid, the profile designed in this application has an involute segment in the middle of the cycloid segment for distortion replacement, thus enabling the design of arbitrary parameters and providing technical support for new product development. Attached Figure Description

[0056] Figure 1 This is a schematic diagram of the meshing of the inner and outer rotors in the prior art.

[0057] Figure 2 The profile of a single tooth of the inner rotor in this invention. Figure 1 .

[0058] Figure 3 This is a schematic diagram of the theoretical profile of the cycloid segment on the inner rotor in this invention. Figure 1 .

[0059] Figure 4 This is a schematic diagram of the actual profile of the cycloid segment on the inner rotor in this invention.

[0060] Figure 5 This is a schematic diagram of the theoretical profile of the cycloid segment on the inner rotor in this invention. Figure 2 .

[0061] Figure 6 This is a schematic diagram of the first cycloidal segment and the involute segment on the inner rotor in this invention.

[0062] Figure 7 This is a schematic diagram of the starting line of the involute segment on the inner rotor in this invention.

[0063] Figure 8 This is a schematic diagram of the line generation at any point on the involute segment of the inner rotor in this invention.

[0064] Figure 9 The profile of a single tooth of the inner rotor in this invention. Figure 2 .

[0065] Figure 10 This is a schematic diagram of the meshing of the inner rotor profile and the outer rotor profile in this invention.

[0066] Figure 11 This is a schematic diagram of the intersection point between the normal line of point P1 on the inner rotor profile and the pitch circle in this invention.

[0067] Figure 12 In this invention, point P1 on the inner rotor profile rotates around the center of the pitch circle. The diagram below.

[0068] Figure 13 In this invention, point P2′ on the outer rotor rotates around the center of the outer rotor pitch circle. A schematic diagram of P2 can be obtained at that time.

[0069] Figure 14 This is a meshing diagram of the inner and outer rotors designed in this embodiment of the present invention. Detailed Implementation

[0070] The present invention will be further described below with reference to the embodiments and accompanying drawings:

[0071] like Figures 1-14 As shown, a method for designing the combined profile of an oil pump rotor is provided. The combined profile includes an inner rotor profile and an outer rotor profile. In the inner rotor profile, all the teeth have the same profile, and the profile of each tooth is symmetrically arranged. In the outer rotor profile, all the teeth have the same profile, and the profile of each tooth is symmetrically arranged. There is a tooth gap between the teeth of the inner rotor and the outer rotor.

[0072] The specific design method includes the following steps:

[0073] Step 1: Design the semi-tooth profile of the inner rotor, from... Figure 2 As shown by the profile characteristics of the inner rotor, it can be seen that as long as the profile of the half tooth of the inner rotor is designed, and then symmetrical and rotated, the profile of the entire inner rotor can be obtained. The half tooth profile of the inner rotor is composed of the first cycloid segment, the involute segment, the circular arc segment, and the second cycloid segment, and the first cycloid segment and the second cycloid segment are the same cycloid.

[0074] Specifically, the inner rotor's semi-tooth profile consists of four segments: the first cycloidal segment AB, the involute segment BC, the circular arc segment CD, and the second cycloidal segment DE. The involute segment BC is tangent to the first cycloidal segment AB, and the circular arc segment is tangent to both the involute segment BC and the second cycloidal segment DE. In this embodiment, the semi-tooth is designed to be located in the third quadrant of the coordinate system, close to the Y-axis. Therefore, the theoretical and actual profile equations for the first cycloidal segment AB and the second cycloidal segment DE are as follows: Figure 3 and Figure 4 As shown:

[0075]

[0076]

[0077]

[0078] in The angle of the rolling circles on the outer rotor. Z1 is the rolling angle of the rollers on the inner rotor, Z2 is the number of teeth on the inner rotor, L is the radius of the forming circle, and e is the eccentricity. ξ=L / (e×Z2), when At time t is the starting point of the cycloid, and the starting point is on the positive half-axis of the X-axis. Since the highest point of the theoretical profile is on the positive half-axis of the Y-axis, the theoretical profile equation needs to be rotated counterclockwise by an angle ψ. Then, by the coordinate rotation formula, the theoretical profile is obtained as follows:

[0079] x L =x mL ×cosψ-y mL ×sinψ

[0080] y L =x mL ×sinψ+y mL ×cosψ

[0081] like Figure 5 As shown, where ψ = 0.5π - 0.5λ, λ is the angle of each tooth of the inner rotor, then λ = 2π / Z1.

[0082] Similarly, the actual profile shape is obtained by rotating the actual profile equation counterclockwise by an angle ψ. Then, according to the coordinate rotation formula, the actual profile shape is:

[0083] x S =x mS ×cosψ-y mS ×sinψ

[0084] y S =x mS ×sinψ+ymS ×cosψ

[0085] Since the first cycloid segment is tangent to the involute segment, the independent variable on the first cycloid segment... B on the same theoretical profile line L The line connecting point B to the actual profile line is the normal line at point B, the starting point of the involute. Figure 6 As shown. When the perpendicular line to the normal line drawn through the center O of the inner rotor intersects at a point N. B When the distance from the center of the inner rotor to the normal is ON, B Let r be the base circle radius of the involute segment. b The intersection point N of point B on the actual profile line with the normal and the perpendicular line. B The line segment between them is the generating line BN of the involute segment at the starting point. B Then the line BN occurs. B The equation of the straight line is:

[0086] y = y L +K LS ×xK LS ×x L

[0087] At the same time, the point N passing through the center O of the inner rotor and the intersection of the normal and the perpendicular line. B ON connection between B The equation of the straight line is:

[0088] y = -xK LS

[0089] Where K LS K is the slope of the normal. LS =(y BL -y B ) / (x BL -x B If we solve the system of equations, we can obtain the intersection point N. B The coordinates are:

[0090] x NB =K LS (x BL -y BL ) / (K LS 2 +1)

[0091] y NB =-(x BL -y BL ) / (K LS 2 +1)

[0092] Then the radius r of the base circle b for:

[0093]

[0094] Then the length of the generating line of the involute segment at the starting point is obtained as:

[0095]

[0096] like Figure 7 As shown, the pressure angle α of the involute segment at the starting point B can be obtained from the involute equation. B Angle of expansion θ B The angle between point B and the X-axis is:

[0097] α B =arctan(L B / r b )

[0098] θ B =tanα B -α B

[0099] β B =arctan(y B / x b )

[0100] The initial angle η = β of the involute segment at its starting point on the base circle can be determined. B -θ B .

[0101] like Figure 8 As shown, assume the pressure angle at any point K on the involute segment is α. K , and α K >α B By the involute equation, the polar radius ρ at that point is... K =r b / cosα K , spread angle θ K =tanα K -α K , with α K If is the independent variable, then:

[0102] x K =ρ K ×cos(η+θ K )

[0103] y K =ρ K ×sin(η+θ K )

[0104] Since the involute segment intersects the second cycloidal segment at a corner point, but the entire gear teeth of the inner rotor have a smooth transition, by selecting an appropriate radius to create a segment tangent to both the involute and second cycloidal segments, a circular arc segment can be obtained, such as... Figure 9 As shown in b.

[0105] Step 2: Symmetrically process the semi-tooth profile of the inner rotor designed in Step 1, using the Y-axis as the axis of symmetry, to obtain the single-tooth profile of the inner rotor, such as... Figure 9 As shown in Figure a. Then, using the coordinate rotation formula, the single tooth profile data is rotated sequentially by angles λ1, 2, and 3 to Z1, thus forming a complete inner rotor tooth profile.

[0106] Step 3: Based on the fundamental law of tooth profile meshing, obtain the outer rotor profile that satisfies the fundamental law of meshing and guarantees a constant transmission ratio using the profile of the inner rotor obtained in Step 2. The fundamental law of tooth profile meshing states that a common normal line drawn through the tooth contact point and meshing point should intersect the line connecting centers O1 and O2 at a fixed point C. Point C is called the node. Figure 10 As shown, the pitch circle radius of the inner rotor r1 = Z1e and the pitch circle radius of the outer rotor r2 = Z2e can be obtained.

[0107] The specific calculations are as follows: Figure 11 As shown in Figure a, P1 is a point on the inner rotor profile η1, then nn is the normal at point P1, and ∠P1O1C = α1, as... Figure 11 As shown in Figure b, the intersection point of line nn and the inner rotor pitch circle is q, and the coordinates of q satisfy x 2 +y 2 =r1 2 The equation of the normal at point P1 satisfies From this, we can obtain the coordinates x of point q. q y q At the same time, the angle between the intersection point, the center of the inscribed circle, and the node can also be obtained.

[0108] Rotate the inner rotor profile η1 around a circle If point q coincides with node P1, then point P1 will move to point P1', as shown below. Figure 12 As shown in Figure a. Using the coordinate rotation formula, the coordinates of point P1′ are obtained as follows:

[0109]

[0110]

[0111] Assume that point P2' is on the outer rotor profile that meshes with the inner rotor profile at point P1'. Figure 12 As shown in b, then we have

[0112]

[0113] Assume point P2 is the outer rotor profile before it rotates around the inner rotor pitch circle. At the point of time, it is possible to reverse the rotation of point P2′ around the center of the outer rotor pitch circle. Point P2 can be obtained at that time, where i 12 =Z2 / Z1, and using the coordinate rotation formula, the coordinates of point P2 are obtained as follows: Figure 13 As shown:

[0114]

[0115]

[0116] The circular arc segment is a smooth transition segment between the involute segment and the second cycloid segment. It is necessary to give the radius of the circular arc to directly and uniquely determine the circular arc segment. It can be obtained directly from the radius in the software, so no calculation is required.

[0117] By continuously repeating the above steps for each point on the inner rotor profile, the outer rotor profile that satisfies the basic law of meshing and guarantees a constant transmission ratio can be obtained.

[0118] Step 4: Obtain the equidistant curve from the outer rotor profile obtained in Step 3. The equidistant curve is the required outer rotor profile.

[0119] The calculation method for the equidistant curve is as follows: Given that the tooth clearance is δ, and point i is a point on the obtained outer rotor profile, the slope k of the normal line at point i can be obtained. i The angle between the normal at point i and the X-axis is α. i =arctank i Assume point j is a point on the equidistant curve to be obtained, and the coordinates of point j are:

[0120] x i =x j +δcosα i

[0121] y i =y j +δsinα i

[0122] This yields equidistant curves, which form the final outer rotor profile. Since all the teeth in the outer rotor profile have the same profile, and the profiles of each tooth are symmetrically arranged, the complete outer rotor profile can be obtained by symmetrically rotating the half-tooth profiles of the outer rotor profile.

[0123] To facilitate design in practical applications, the entire design process will be incorporated into the software, and the following parameters will be used for design:

[0124] Z1 = 9, Z2 = 10, e = 3.4 mm

[0125] The cycloidal segment roller radius R and the generating circle radius L are respectively:

[0126] R = 7 mm, L = 38.1 mm

[0127] The tooth tip circle diameter d of the inner and outer rotors can be obtained through calculation. a and the root circle diameter d f They are respectively:

[0128] d a1 =69mm,d f1 =55.4mm

[0129] d a2 =62.2mm, d f2 =75.8mm

[0130] The pressure angle α at the starting point B on the involute segment B Angle of expansion θ B and base circle radius r b They are respectively:

[0131] α B =22.924°, θ B =1.307°, r b =28.99mm

[0132] Finally, the inner rotor profile and outer rotor profile designed in the software are as follows: Figure 14 As shown in Table 1, the specific coordinates of the points on the inner rotor profile are shown in Table 2.

[0133] Table 1 Internal Rotor Profile Coordinates

[0134]

[0135]

[0136] Table 2 Internal Rotor Profile Coordinates

[0137]

[0138]

Claims

1. A method for designing the combined profile of an oil pump rotor, characterized in that: The combined profile includes an inner rotor profile and an outer rotor profile. In the inner rotor profile, all the teeth have the same profile and the profile of each tooth is symmetrically arranged. In the outer rotor profile, all the teeth have the same profile and the profile of each tooth is symmetrically arranged. There is a tooth gap between the teeth of the inner rotor and the outer rotor. It also includes the following steps: S1: Design the semi-tooth profile of the inner rotor. The semi-tooth profile of the inner rotor consists of a first cycloid segment, an involute segment, a circular arc segment, and a second cycloid segment. The first cycloid segment and the second cycloid segment are the same cycloid. S2: Symmetricalizing the semi-tooth profile of the inner rotor designed in S1 can yield the single tooth profile of the inner rotor. Then, rotating the single tooth profile of the inner rotor forms the complete tooth profile of the inner rotor. S3: Based on the fundamental law of tooth profile meshing, the profile of the outer rotor that satisfies the fundamental law of meshing and guarantees a constant transmission ratio is obtained from the profile of the inner rotor obtained in S2. S4: Obtain the equidistant curve from the outer rotor profile obtained in S3. The equidistant curve is the required outer rotor profile. The outer rotor profile in S3 is calculated as follows: Given that the pitch circle radius of the inner rotor is r1 = Z1e, and the pitch circle radius of the outer rotor is r2 = Z2e, where Z1 is the number of teeth on the inner rotor, Z2 is the number of teeth on the outer rotor, and e is the eccentricity. Assuming P1 is a point on the inner rotor profile, the intersection of the normal at point P1 and the pitch circle of the inner rotor is q, and the coordinates of q satisfy x... 2 +y 2 =r1 2 The equation of the normal at point P1 satisfies From this, we can obtain the coordinates x of point q. q y q Therefore, the angle between the intersection point, the center of the inscribed circle, and the node can be obtained as follows: Rotate the inner rotor profile by Φ1 around a circle until point q coincides with the node. Then point P1 rotates to point P1′. Using the coordinate rotation formula, the coordinates of point P1′ are: Assuming that point P2' is on the outer rotor profile that meshes with the inner rotor profile at point P1', then we have Assuming point P2 is the point where the outer rotor profile has not rotated through Φ1 around the inner rotor pitch circle, then point P2 can be obtained by reversing point P2′ around the center of the outer rotor pitch circle by Φ2, where Φ2=-Φ1 / i 12 i 12 =Z2 / Z1, and using the coordinate rotation formula, the coordinates of point P2 are: By continuously repeating the above steps for each point on the inner rotor profile, the outer rotor profile that satisfies the basic law of meshing and guarantees a constant transmission ratio can be obtained. The calculation method for the equidistant curve in S4 is as follows: Given that the tooth clearance is δ, and point i is a point on the already calculated outer rotor profile, the slope k of the normal line at point i can be obtained. i The angle between the normal at point i and the X-axis is α. i =arctank i Assume point j is a point on the equidistant curve to be obtained, and the coordinates of point j are: x i =x j +δcosα i y i =y j +δsinα i This yields an equidistant curve, which is the final outer rotor profile.

2. The oil pump rotor assembly profile design method according to claim 1, characterized in that: The semi-tooth profile of the inner rotor in S1 consists of four segments: a first cycloid segment, an involute segment, a circular arc segment, and a second cycloid segment. The involute segment is tangent to the first cycloid segment, and the circular arc segment is tangent to both the involute and second cycloid segments. The semi-tooth in S1 is designed to be located in the third quadrant of the coordinate system, close to the Y-axis. Therefore, the theoretical and actual profile equations of the first and second cycloid segments are: in The angle of the rolling circles on the outer rotor. Z1 is the rolling angle of the rollers on the inner rotor, Z2 is the number of teeth on the inner rotor, L is the radius of the forming circle, and e is the eccentricity. ξ=L / (e×Z2), when At time t is the starting point of the cycloid, and the starting point is on the positive half-axis of the X-axis. Since the highest point of the theoretical profile is on the positive half-axis of the Y-axis, the theoretical profile equation needs to be rotated counterclockwise by an angle ψ. Then, by the coordinate rotation formula, the theoretical profile is obtained as follows: x L =x mL ×cosψ-y mL ×sinψ and L =x mL ×sinψ+y mL ×cosψ Where ψ = 0.5π - 0.5λ, λ is the angle of each tooth of the inner rotor, then λ = 2π / Z1; Similarly, the actual profile shape is obtained by rotating the actual profile equation counterclockwise by an angle ψ. Then, according to the coordinate rotation formula, the actual profile shape is: x S =x mS ×cosψ-y mS ×sinψ and S =x mS ×sinψ+y mS ×cosψ The angle of rolling of the rollers on the inner rotor of the first cycloidal segment. The line connecting a point on the same theoretical profile line and a point on the actual profile line is the normal at the starting point of the involute. A perpendicular line drawn from the center of the inner rotor to the normal intersects it at a single point. The distance from the center of the inner rotor to the normal is the base circle radius *r* of the involute segment. b The line segment between the point on the actual profile line and the intersection of the normal and the perpendicular is the generating line of the involute segment at the starting point. The equation of the generating line is: y=y L +K LS ×xK LS ×x L Meanwhile, the equation of the straight line connecting the center of the inner rotor with the intersection of the normal and the perpendicular is: y=-xK LS Where K LS K is the slope of the normal. LS =(y BL -y B ) / (x BL -x B Then the coordinates of the intersection point can be obtained as follows: x NB =K LS (x BL -y BL ) / (K LS 2 +1) and NB =-(x BL -and BL ) / (K LS 2 +1) Then the radius r of the base circle b for: Then the length of the generating line of the involute segment at the starting point is obtained as: From the equation of the involute, we can obtain the pressure angle α of the involute segment at the starting point. B Angle of expansion θ B The angle between the starting point and the X-axis is: α B =arctan(L B / r b ) i B =tanā B -a B β B =arctan(y B / x B ) The initial angle η = β of the involute segment at its starting point on the base circle can be determined. B -θ B Assume the pressure angle at any point on the involute segment is α. K , and α K >α B By the involute equation, the polar radius ρ at that point is... K =r b / cosα K , spread angle θ K =tanα K -α K , with α K If is the independent variable, then: x K =ρ K ×cos(η+θ K ) y K =ρ K ×sin(η+θ K ) Given the pressure angles at various points on the involute segment and the pressure angle α at the endpoint. C When the coordinates of the entire involute segment are obtained, the arc segment is the smooth transition segment between the involute segment and the second cycloid segment. The arc segment can be directly and uniquely determined by giving the radius of the arc.

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