Rotary oil pump arc tooth profile design method

Abstract

This invention discloses a method for designing the arc tooth profile of a rotary oil pump. The arc tooth profile includes the arc tooth profile of an inner rotor and the arc tooth profile of an outer rotor. In the inner rotor's arc tooth profile, all teeth have the same profile, and the profiles of each tooth are symmetrically arranged. Similarly, in the outer rotor's arc tooth profile, all teeth have the same profile, 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 rotors are obtained through calculation, resulting in high precision of 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 design method for the circular arc tooth profile of a rotor oil pump. 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 existing technology, there is a design theory for cycloidal rotor pumps, but it has the following disadvantages: (1) all gear teeth are in contact at the same time, which makes the gear 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 curvature radius of the theoretical profile of the profile small, the actual profile formed will be distorted, resulting in the design not being completed. Summary of the Invention

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

[0006] Therefore, the technical solution adopted by the present invention is as follows: a design method for the circular arc tooth profile of a rotor oil pump, wherein the circular arc tooth profile of the rotor oil pump includes the circular arc tooth profile of the inner rotor and the circular arc tooth profile of the outer rotor, wherein the profile of all teeth in the circular arc tooth profile of the inner rotor is the same, and the profile of each tooth is symmetrically arranged, and the profile of all teeth in the circular arc tooth profile of the outer rotor is the same, and the profile of each tooth is 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, which consists of several smooth circular arc curves and a transition curve.

[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 six circular arc curves (1′-2′, 2′-3′, 3′-4′, 4′-5′, 5′-6′, 6′-7′) and a quadratic equation transition curve (0′-1′). In S1, the semi-tooth is designed to be located in the third quadrant of the coordinate system, close to the Y-axis. Point 7′ is the intersection of the inner rotor's tooth tip and the Y-axis, and point 0′ is a point on the inner rotor's tooth root circle. The angle between the tangent at point 0′ and the horizontal line is β. Therefore, the coordinates of points 0′ and 7′ are:

[0013] x 0′ =-r f1 sinβ, y 0′ =r f1 cosβ, x 7′ =0, y 7′ =r a1

[0014] Where β is the half-angle of the inner rotor tooth, derived from the formula Calculations show that Z1 is the number of teeth on the inner rotor, and r... f1 Let r be the radius of the tooth root circle of the inner rotor. a1 Let r be the radius of the tooth tip circle of the inner rotor, and r a1 =r f1 +2e, where e is the eccentricity between the inner and outer rotors;

[0015] From the general form of the quadratic equation y = ax 2 Differentiating +bx+c, we can obtain the equation of the tangent line as follows: Substitute the coordinates of points 0′ and 1′, where the coordinates of point 1′ are set values, into the quadratic equation. Simultaneously, from the tangent line at point 0′, we can obtain:

[0016]

[0017] Solving the system of equations simultaneously yields the coefficients a, b, and c of the quadratic equation, which in turn gives the transition curve from 0′ to 1′. Then, the coordinates x of the center of curvature at point 1′ are obtained. q1 y q1 The value is:

[0018] x q1 =x 1′ -(b+2ax 1′ (1+(b+2ax)) 1′ ) 2 ) / 2a

[0019] y q1 =y 1′ +(1+(b+2ax 1′ ) 2 ) / 2a

[0020] Then the radius of curvature ρ at point 1′ is:

[0021]

[0022] Since the 0′-1′ segment and the 1′-2′ segment are smoothly connected, the arc center 1 of the 1′-2′ segment lies on the line connecting the center of curvature at point 1′ and point 1′. Therefore, the angle α0 between the centers of curvature at points 0′ and 1′ is:

[0023]

[0024] After specifying the radius R1 of the arc segment 1′-2′, the coordinates of the center point 1 of the arc segment 1′-2′ are:

[0025] x1=x q1 +(ρ-R1)sin(β+α0)

[0026] y1=y q1 +(ρ-R1)cos(β+α0)

[0027] After specifying the central angle α1 of the segment 1′-2′, the coordinates of 2′ are:

[0028] x 2′ = x1 + R1sin(β + α0 + α1)

[0029] y 2′ = y1 + R1cos(β + α0 + α1)

[0030] Since segments 1′-2′ and 2′-3′ are smoothly connected, the center point 2 of the arc in segment 2′-3′ lies on the line connecting point 2′ and point 1. After specifying the central angle α2 of segment 2′-3′ and the radius R2 of segment 2′-3′, the coordinates of the center point 2 and the coordinates of point 3′ of the arc in segment 2′-3′ are:

[0031] x2=x1+(R1-R2)sin(β+α0+α1)

[0032] y2=y1+(R1-R2)cos(β+α0+α1)

[0033] x 3′ = x² + R²sin(β + α₀ + α₁ + α₂)

[0034] y 3′ = y² + R²cos(β + α₀ + α₁ + α₂)

[0035] Since segments 2′-3′ and 3′-4′ are smoothly connected, the center point 3 of the arc in segment 3′-4′ lies on the line connecting point 3′ and point 2. After specifying the central angle α3 of segment 3′-4′ and the radius R3 of segment 3′-4′, the coordinates of the center point 3 and the coordinates of point 4′ of the arc in segment 3′-4′ are:

[0036] x3=x2+(R2-R3)sin(β+α0+α1+α2)

[0037] y3=y2+(R2-R3)cos(β+α0+α1+α2)

[0038] x 4′ =x3+R3sin(β+α0+α1+α2+α3)

[0039] y 4′ =y3+R3cos(β+α0+α1+α2+α3)

[0040] Since point 7′ in segment 6′-7′ lies on the Y-axis, and the right half of the tooth on the Y-axis is symmetrical to the left half and smoothly connected, the arc center 6 of segment 6′-7′ lies on the Y-axis. After specifying the arc radius R6 and central angle of segment 6′-7′, the coordinates of the arc centers 6 and 6′ of segment 6′-7′ are:

[0041] x6 = 0

[0042] y6=r a1 -R6

[0043] x 6′ =x6-R6sinα6

[0044] y 6′ =y6+R6cosα6

[0045] Since segments 5′-6′ and 6′-7′ are smoothly connected, the center point 5 of the arc in segment 5′-6′ lies on the line connecting points 6′ and 6′. After specifying the central angle α5 of segment 5′-6′ and the radius R5 of segment 5′-6′, the coordinates of the center point 5 of the arc in segment 5′-6′ and the coordinates of point 5′ are:

[0046] x5=-(R6-R5)sinα6

[0047] y5=y6+(R6-R5)cosα6

[0048] x 5′ = x5 - R5sin(α5 + α6)

[0049] y 5′ = y5 - R5cos(α5 + α6)

[0050] The slope K of the line connecting points 3 and 4′ 34′ The slope K of the line connecting point 5 and point 5′ 55′ for:

[0051]

[0052]

[0053] Since 3′-4′, 4′-5′, and 5′-6′ are all smoothly connected, the center 4 of the arc in segment 4′-5′ lies at the intersection of the line connecting points 3 and 4′ and the line connecting points 5 and 5′. Therefore, the coordinates of the center 4 of the arc in segment 4′-5′ are:

[0054] x4=(y3-K 34′ x3)-(y5-K 55′ x5) / (K 55′ -K 34′ )

[0055] y4=K 34′ x4+(y3-K 34′ x3)

[0056] The distance L from point 3 to point 4 34 for:

[0057]

[0058] Then the radius R4 of the arc segment 4′-5′ and the central angle α4 of the arc segment 4′-5′ are:

[0059] R4 = L 34 -R3

[0060]

[0061] This allows us to obtain the coordinates of the center of each arc segment, the starting angle and the ending angle, and the coordinates of each intersection point, thus completing the design of the semi-tooth profile of the inner rotor.

[0062] 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, where Z1 is the number of teeth on the inner rotor, and the pitch circle radius of the outer rotor is r2 = Z2e, where Z2 is the number of teeth on the outer rotor, 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 around a circle If point q coincides with node P1, then point P1 will rotate to point P1′. Using the coordinate rotation formula, the coordinates of point P1′ are:

[0063]

[0064]

[0065] Assuming that point P2' is on the outer rotor profile that meshes with the inner rotor profile at point P1', then we have

[0066]

[0067] 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 Using the coordinate rotation formula, the coordinates of point P2 are obtained as follows:

[0068]

[0069]

[0070] 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.

[0071] 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 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:

[0072] xi =x j +δcosα i

[0073] y i =y j +δsinα i

[0074] This yields an equidistant curve, which is the final outer rotor profile.

[0075] The beneficial effects of this invention are as follows: It enables the design of an inner and outer rotor with circular arc teeth. The contact and transmission of the teeth of the inner and outer rotors are located at positions with relatively low sliding speeds, making them less prone to wear. Since not all teeth are in contact simultaneously, the machining accuracy is reduced while facilitating assembly. Furthermore, the tooth profile satisfies the basic law of tooth profile meshing, resulting in smooth transmission. Due to the circular arc teeth, the teeth make surface contact under the action of the oil film, resulting in low pressure, low contact stress, and long service life. The inner and outer rotors are designed using calculated data, resulting in high precision of the overall profile. Unlike cycloids, the design method of this application can achieve the design of arbitrary parameters, providing technical support for new product development. Attached Figure Description

[0076] Figure 1 This is a schematic diagram of the meshing of the inner and outer rotors in the prior art.

[0077] Figure 2 This is a profile diagram of the inner rotor in this invention.

[0078] Figure 3 This is a schematic diagram of the semi-tooth profile of the inner rotor in this invention.

[0079] Figure 4 This is a schematic diagram of the meshing of the inner rotor profile and the outer rotor profile in this invention.

[0080] Figure 5 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.

[0081] Figure 6 In this invention, point P1 on the inner rotor profile rotates around the center of the pitch circle. The diagram below.

[0082] Figure 7 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.

[0083] Figure 8 This is a schematic diagram of the inner rotor half-tooth profile obtained after inputting parameters in the software in this invention.

[0084] Figure 9 This is a schematic diagram of the single tooth profile of the inner rotor obtained in the software in this invention.

[0085] Figure 10 This is a schematic diagram of the complete inner rotor profile obtained in the software in this invention.

[0086] Figure 11 This is a schematic diagram of the single tooth profile of the external rotor obtained in the software in this invention.

[0087] Figure 12 This is a schematic diagram of the complete external rotor profile obtained in the software in this invention.

[0088] Figure 13 This is a meshing diagram of the inner and outer rotors designed in this embodiment of the present invention. Detailed Implementation

[0089] The present invention will be further described below with reference to the embodiments and accompanying drawings:

[0090] like Figures 1-7 As shown, a method for designing the arc tooth profile of a rotary oil pump is disclosed. The arc tooth profile of the rotary oil pump includes the arc tooth profile of the inner rotor and the arc tooth profile of the outer rotor. In the arc tooth profile of the inner rotor, all the tooth profiles are the same and the profiles of each tooth are symmetrically arranged. In the arc tooth profile of the outer rotor, all the tooth profiles are the same and the profiles of each tooth are symmetrically arranged. There is a tooth gap between the teeth of the inner rotor and the outer rotor.

[0091] The specific design method includes the following steps:

[0092] Step 1: Design the semi-tooth profile of the inner rotor, from... Figure 2 As shown in the profile characteristics of the inner rotor, it can be seen that by designing the profile of one half-tooth of the inner rotor, and then performing symmetry and rotation, the profile of the entire inner rotor can be obtained. The profile of one half-tooth of the inner rotor consists of several smooth circular arc curves and a transition curve. For ease of calculation, in this calculation, the profile of one half-tooth of the inner rotor consists of six smooth circular arc curves and a transition curve, as shown in the figure. Figure 3 As shown.

[0093] Specifically, the semi-tooth profile of the inner rotor consists of six circular arc curves (1′-2′, 2′-3′, 3′-4′, 4′-5′, 5′-6′, 6′-7′) and a quadratic equation transition curve (0′-1′). It is designed to be a semi-tooth located in the third quadrant of the coordinate system, close to the Y-axis. Point 7′ is the intersection of the inner rotor's tooth tip and the Y-axis, and point 0′ is a point on the inner rotor's tooth root circle. The angle between the tangent at point 0′ and the horizontal line is β. Therefore, the coordinates of points 0′ and 7′ are:

[0094] x 0′ =-rf1 sinβ, y 0′ =r f1 cosβ, x 7′ =0, y 7′ =r a1

[0095] Where β is the half-angle of the inner rotor tooth, derived from the formula Calculations show that Z1 is the number of teeth on the inner rotor, and r... f1 Let r be the radius of the tooth root circle of the inner rotor. a1 Let r be the radius of the tooth tip circle of the inner rotor, and r a1 =r f1 +2e, where e is the eccentricity between the inner and outer rotors;

[0096] From the general form of the quadratic equation y = ax 2 Differentiating +bx+c, we can obtain the equation of the tangent line as follows: Substitute the coordinates of points 0′ and 1′, where the coordinates of point 1′ are set values, into the quadratic equation. Simultaneously, from the tangent line at point 0′, we can obtain:

[0097]

[0098] Solving the system of equations simultaneously yields the coefficients a, b, and c of the quadratic equation, which in turn gives the transition curve from 0′ to 1′. Then, the coordinates x of the center of curvature at point 1′ are obtained. q1 y q1 The value is:

[0099] x q1 =x 1′ -(b+2ax 1′ (1+(b+2ax)) 1′ ) 2 ) / 2a

[0100] y q1 =y 1′ +(1+(b+2ax 1′ ) 2 ) / 2a

[0101] Then the radius of curvature ρ at point 1′ is:

[0102]

[0103] Since the 0′-1′ segment and the 1′-2′ segment are smoothly connected, the angle α0 between the curvature centers of points 0′ and 1′ can be obtained on the line connecting the arc center 1 of the 1′-2′ segment and the center of curvature at point 1′.

[0104]

[0105] After specifying the radius R1 of the arc segment 1′-2′, the coordinates of the center point 1 of the arc segment 1′-2′ are:

[0106] x1=x q1 +(ρ-R1)sin(β+α0)

[0107] y1=y q1 +(ρ-R1)cos(β+α0)

[0108] After specifying the central angle α1 of the segment 1′-2′, the coordinates of 2′ are:

[0109] x 2′ = x1 + R1sin(β + α0 + α1)

[0110] y 2′ = y1 + R1cos(β + α0 + α1)

[0111] Since segments 1′-2′ and 2′-3′ are smoothly connected, the center point 2 of the arc in segment 2′-3′ lies on the line connecting point 2′ and point 1. After specifying the central angle α2 of segment 2′-3′ and the radius R2 of segment 2′-3′, the coordinates of the center point 2 and the coordinates of point 3′ of the arc in segment 2′-3′ are:

[0112] x2=x1+(R1-R2)sin(β+α0+α1)

[0113] y2=y1+(R1-R2)cos(β+α0+α1)

[0114] x 3′ = x² + R²sin(β + α₀ + α₁ + α₂)

[0115] y 3′ = y² + R²cos(β + α₀ + α₁ + α₂)

[0116] Since segments 2′-3′ and 3′-4′ are smoothly connected, the center point 3 of the arc in segment 3′-4′ lies on the line connecting point 3′ and point 2. After specifying the central angle α3 of segment 3′-4′ and the radius R3 of segment 3′-4′, the coordinates of the center point 3 and the coordinates of point 4′ of the arc in segment 3′-4′ are:

[0117] x3=x2+(R2-R3)sin(β+α0+α1+α2)

[0118] y3=y2+(R2-R3)cos(β+α0+α1+α2)

[0119] x 4′ =x3+R3sin(β+α0+α1+α2+α3)

[0120] y 4′ =y3+R3cos(β+α0+α1+α2+α3)

[0121] Since point 7′ in segment 6′-7′ lies on the Y-axis, and the right half of the tooth on the Y-axis is symmetrical to the left half and smoothly connected, the arc center 6 of segment 6′-7′ lies on the Y-axis. After specifying the arc radius R6 and central angle of segment 6′-7′, the coordinates of the arc centers 6 and 6′ of segment 6′-7′ are:

[0122] x6 = 0

[0123] y6=r a1 -R6

[0124] x 6′ =x6-R6sinα6

[0125] y 6′ =y6+R6cosα6

[0126] Since segments 5′-6′ and 6′-7′ are smoothly connected, the center point 5 of the arc in segment 5′-6′ lies on the line connecting points 6′ and 6′. After specifying the central angle α5 of segment 5′-6′ and the radius R5 of segment 5′-6′, the coordinates of the center point 5 of the arc in segment 5′-6′ and the coordinates of point 5′ are:

[0127] x5=-(R6-R5)sinα6

[0128] y5=y6+(R6-R5)cosα6

[0129] x 5′ = x5 - R5sin(α5 + α6)

[0130] y 5′ = y5 - R5cos(α5 + α6)

[0131] The slope K of the line connecting points 3 and 4′ 34′ The slope K of the line connecting point 5 and point 5′ 55′ for:

[0132]

[0133]

[0134] Since 3′-4′, 4′-5′, and 5′-6′ are all smoothly connected, the center 4 of the arc in segment 4′-5′ lies at the intersection of the line connecting points 3 and 4′ and the line connecting points 5 and 5′. Therefore, the coordinates of the center 4 of the arc in segment 4′-5′ are:

[0135] x4=(y3-K 34′ x3)-(y5-K 55′x5) / (K 55′ -K 34′ )

[0136] y4=K 34′ x4+(y3-K 34′ x3)

[0137] The distance L from point 3 to point 4 34 for:

[0138]

[0139] Then the radius R4 of the arc segment 4′-5′ and the central angle α4 of the arc segment 4′-5′ are:

[0140] R4 = L 34 -R3

[0141]

[0142] This allows us to obtain the coordinates of the center of each arc segment, the starting angle and the ending angle, and the coordinates of each intersection point, thus completing the design of the semi-tooth profile of the inner rotor.

[0143] Step 2: Symmetrically process the semi-tooth profile of the inner rotor designed in Step 1 with the Y-axis as the axis of symmetry to obtain the single tooth profile of the inner rotor. Then, using the coordinate rotation formula, rotate the single tooth profile data sequentially by angles β2, 4, 6 to 2Z1 to form the complete tooth profile of the inner rotor.

[0144] 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 the common normal line drawn through the tooth contact point (meshing point) should intersect the line connecting centers O1O2 at a fixed point C. Point C is called the node. Figure 4 As shown, the pitch circle radius of the inner rotor can be obtained as r1 = Z1e, where Z1 is the number of teeth of the inner rotor, and the pitch circle radius of the outer rotor is obtained as r2 = Z2e, where Z2 is the number of teeth of the outer rotor.

[0145] The specific calculations are as follows: Figure 5 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 5 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 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 η1 around a circle If point q coincides with node P1, then point P1 will move to point P1', as shown below. Figure 6 As shown in Figure a. Using the coordinate rotation formula, the coordinates of point P1′ are obtained as follows:

[0146]

[0147]

[0148] Assume that point P2' is on the outer rotor profile that meshes with the inner rotor profile at point P1'. Figure 6 As shown in b, then we have

[0149]

[0150] 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 Using the coordinate rotation formula, the coordinates of point P2 are obtained as follows: Figure 7 As shown:

[0151]

[0152]

[0153] 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.

[0154] Step 4: Obtain the equidistant curve from the outer rotor profile obtained in Step 3. The equidistant curve is the required outer rotor profile.

[0155] 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:

[0156] x i =x j +δcosα i

[0157] y i =y j +δsinα i

[0158] This yields equidistant curves, which form the final outer rotor profile. Since all teeth in the outer rotor's circular arc tooth profile have the same profile, and each tooth's profile is symmetrically arranged, the complete outer rotor profile can be obtained by symmetrically rotating the half-tooth profile of the outer rotor after obtaining it.

[0159] To facilitate design in practical applications, the entire design process is incorporated into the software. Taking a rotor pump with Z1=9 and Z2=10 teeth as an example.

[0160] The specific parameters of the design are as follows: r f1 =24.95mm, e=3.2mm, then the inner rotor half-tooth design is as follows Figure 8 As shown, it is then symmetrical about the Y-axis to generate single-tooth data as follows. Figure 9 As shown, the inner rotor profile is then generated by rotation, as follows: Figure 10 As shown in Table 1, the specific coordinates of the points on the designed inner rotor profile are as follows.

[0161] Table 1 Internal Rotor Profile Coordinates

[0162]

[0163]

[0164] Based on the inner rotor profile, the single tooth profile of the outer rotor is obtained by determining the tooth gap, as shown below. Figure 11 As shown, then rotate to generate the complete outer rotor profile, as... Figure 12 As shown in Table 2, the specific coordinates of the points on the designed outer rotor profile are shown in Table 2.

[0165] Table 2 Internal Rotor Profile Coordinates

[0166]

[0167]

Claims

1. A method for designing the arc tooth profile of a rotor oil pump, characterized in that: The circular arc tooth profile of the rotor oil pump includes the circular arc tooth profile of the inner rotor and the circular arc tooth profile of the outer rotor. In the circular arc tooth profile of the inner rotor, all the tooth profiles are the same and the profiles of each tooth are symmetrically arranged. In the circular arc tooth profile of the outer rotor, all the tooth profiles are the same and the profiles of each tooth are 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 is formed by... Six-segment circular curve and It consists of a transition curve of a quadratic equation; 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. S1 is designed to be located in the third quadrant of the coordinate system, close to Half a tooth of the shaft, and The point is located at the tooth tip of the inner rotor and... The intersection of the axes, The point is located on the root circle of the inner rotor teeth. The angle between the tangent at point and the horizontal line is ,but Point and The coordinates of the point are: ， in The half-angle of the inner rotor tooth is given by the formula. Calculations show that, where This represents the number of teeth on the inner rotor. Let be the radius of the tooth root circle of the inner rotor. Let be the radius of the tooth tip circle of the inner rotor, and ,in This is the eccentricity between the inner and outer rotors; From the general form of the quadratic equation Differentiating, we can obtain the equation of the tangent line as follows: ,Will Point and The coordinates of the point, where The coordinates of the point are set values, substituted into the quadratic equation, and simultaneously... The tangent at a point can be obtained as: ， Solving the system of equations simultaneously yields the coefficients of the quadratic equation. Then we get The transition curve is then obtained in the segment. Coordinates of the center of curvature at point The value is: ， but radius of curvature at point for: ， because Duan Yu If the segments are smoothly connected, then The center point of the arc of the segment is at point 1. The center of curvature at point and On the line connecting the points, we get Point and Angle between the centers of curvature for: ， In the specified The radius of the arc of the segment back, The coordinates of point 1, the center of the arc of segment 1, are: ， In the specified Central angle of the segment After that, The coordinates are: ， because Duan Yu If the segments are smoothly connected, then The center of the arc of the segment is at point 2. On the line connecting point 1 and point 2, at the specified... Segmental central angle and radius of segment back, The coordinates of the two points at the center of the arc segment and The coordinates are: ， because Duan Yu If the segments are smoothly connected, then The center of the arc of the segment is at 3 points On the line connecting point 1 and point 2, at the specified Segmental central angle and radius of segment back, The coordinates of the three points at the center of the arc segment and The coordinates are: ， because Duan Zhong Dot at On the axis, and satisfying the condition that it is located on the axis If the right half of the tooth on the shaft is symmetrical to the left half and smoothly connected, then... The center of the arc of the segment is 6. On the axis, specify The radius of the arc of the segment and central angle back, The center of the arc of the segment 6 and The coordinates are: ， because Duan Yu If the segments are smoothly connected, then The center of the arc of the segment is at 5 points. On the line connecting point 6 and point 7, in the designated... Central angle of the segment and radius of segment back, The coordinates of the 5 points at the center of the arc segment and The coordinates are: ， 3 points and slope of the line connecting the points and 5 points and slope of the line connecting the points for: ， ， because , and If all connections are smooth, then The center of the arc of the segment is at point 3 and Connecting the dots and the sum of the five dots At the intersection of the lines connecting the points, we can obtain... The coordinates of the center 4 of the arc of segment 4 are: ， The distance from point 3 to point 4 for: ， but The radius of the arc of the segment and Central angle of the segment for: ， ， This allows us to obtain the coordinates of the center of each arc segment, the starting angle and the ending angle, and the coordinates of each intersection point, thus completing the design of the semi-tooth profile of the inner rotor.

2. The method for designing the circular arc tooth profile of a rotor oil pump according to claim 1, characterized in that: The outer rotor profile in S3 is calculated as follows: Given the pitch circle radius of the inner rotor... ,in The number of teeth on the inner rotor and the pitch circle radius on the outer rotor are given. in Let the number of teeth on the outer rotor be denoted as . If it is a point on the inner rotor profile, then The intersection of the normal at point A and the pitch circle of the inner rotor is... ,and The coordinates satisfy Among them The equation of the normal at point satisfies From this, we can obtain coordinates of the point 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 around a circle ,make If a point coincides with a node, then The click has been completed. The point is obtained using the coordinate rotation formula. The coordinates of the point are: ， ， Assuming in The point on the outer rotor profile that meshes with the inner rotor profile is... Then there is ， Assumption point The outer rotor profile does not rotate around the inner rotor segment circle. At the point of time, one can obtain the... Rotation of the outer rotor pitch circle center When can be obtained Points, among which , The result can be obtained from the coordinate rotation formula. The coordinates of the point 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.

3. The method for designing the arc tooth profile of a rotor oil pump according to claim 2, characterized in that: The calculation method for the equidistant curve in S4 is as follows: Given that the tooth gap is... , If the point is a point on the already determined outer rotor profile, then we can obtain... slope of the normal line at a point , The normal of the point and The included angle of the axis is Assuming The point is a point on the equidistant curve to be obtained. The coordinates of the point are: ， ， This yields an equidistant curve, which is the final outer rotor profile.

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