Smooth multi-point meshing type roots pump rotor and design method thereof

Abstract

The invention discloses a smooth multi-point meshing type roots pump rotor and a design method thereof. A roots pump is composed of a left multi-point meshing type rotor, a right multi-point meshing type rotor and a pump cavity. The left multi-point meshing type rotor and the right multi-point meshing type rotor have the same end face molded line, and each blade of the end face molded line of the left multi-point meshing type rotor and the end face molded line of the right multi-point meshing type rotor is composed of 23 sections of smooth curves. In the working process, the left multi-point meshing type rotor and the right multi-point meshing type rotor can be correctly meshed, and it is ensured that the rotors on the two sides achieve multi-position synchronous meshing; the rotor end face molded line flow channel structure of the roots pump is in a multi-section turning form and has good tortuosity and side face meshing performance; the novel multi-point meshing design has high sealing performance, the leakage flux of a meshing gap of a traditional structure is reduced, the design scheme can be expanded and applied to rotor configurations with different blade numbers, and standardized manufacturing of a product pedigree can be achieved easily.

Description

Technical Field

[0001] This invention belongs to the field of fluid machinery engineering technology, and specifically relates to a smooth multi-point meshing Roots pump rotor and its design method. Background Technology

[0002] In the field of hydrogen energy equipment, hydrogen circulation pumps are primarily responsible for the transportation and circulation of high-purity hydrogen. Their working medium often contains trace amounts of water vapor and metal particles, requiring efficient gas transfer and pressure stability within the hydrogen fuel cell system. Roots pumps, as a type of volumetric fluid device without internal compression, have gained widespread application in hydrogen-powered vehicles and chemical hydrogen production due to their structural reliability. This device utilizes a pair of conjugate meshing rotors rotating synchronously in opposite directions, employing a periodically changing sealed chamber to achieve gas intake, isochoric transport, and discharge.

[0003] The rotor profile of a Roots pump directly affects its volumetric efficiency and clearance sealing characteristics. The area utilization coefficient determines the flow output capacity per unit volume, while the uniformity of the meshing clearance relates to the level of internal leakage control for small-particle media such as hydrogen molecules. Currently, the mainstream rotor profiles include three technical routes: circular arc, involute, and cycloidal. Patent CN107725364A discloses a multi-lobe Roots pump rotor profile, providing the parametric equations for the multi-lobe Roots pump profile, resulting in a high rotor area utilization coefficient and increased air volume and pumping speed. Patent CN118273948A proposes a Roots rotor profile design method. The proposed Roots rotor profile has good self-meshing properties, reducing flow and pressure pulsations generated by the two rotors during operation, and reducing circulating working fluid leakage. Currently, the Roots rotor profile has the following problems: ① Due to poor sealing performance at the meshing points, leakage occurs, resulting in low volumetric efficiency. ② Commonly used rotor profiles are mostly two-lobe or three-lobe rotor profiles, while multi-lobe rotor profiles are less common. Summary of the Invention

[0004] To address the problem of low volumetric efficiency caused by media leakage at the meshing point of arc-involute rotors, this invention proposes a smooth multi-point meshing Roots pump rotor and its design method. The Roots pump consists of a left multi-point meshing rotor, a right multi-point meshing rotor, and a pump chamber. The disclosed left and right multi-point meshing rotors have the same end face profile. Each blade of the end face profile of the left and right multi-point meshing rotors is composed of 23 smooth curve segments. During operation, the left and right multi-point meshing rotors can form a precise conjugate motion relationship, ensuring... The double-sided rotor achieves multi-position synchronous meshing; the rotor end face profile flow channel structure of the disclosed Roots pump presents a multi-segment folding shape, which significantly enhances the spatial compositeness of the sealing interface while maintaining non-interference meshing, and has good tortuosity and lateral meshing performance; the smooth connection between the arc and the involute improves the pressure pulsation at the outlet of the Roots pump. At the same time, the new multi-point meshing design has high sealing performance and reduces the leakage flux of the meshing gap in the traditional structure. This design can be extended to rotor configurations with different numbers of blades, which is conducive to the standardized manufacturing of the product series. Its modular characteristics are particularly suitable for batch processing scenarios.

[0005] The technical solution adopted by this invention to solve its technical problem is:

[0006] A smooth, multi-point meshing Roots pump rotor includes a left multi-point meshing rotor and a right multi-point meshing rotor. The left multi-point meshing rotor has n blades on its end face profile, and the right multi-point meshing rotor also has n blades on its end face profile, where n = 2, 3, or 4. Each blade of the rotor refers to an independent curve unit in the actual profile of the cam, and its shape determines the motion trajectory of the follower. The three profile segments of the three-lobe cam are geometrically centrally symmetrical, with each segment corresponding to one "blade."

[0007] The end face profile of the left multi-point meshing rotor consists of 23 curve segments per blade, arranged clockwise as follows: left first involute OP, left first arc PQ, left second arc QR, left third arc RS, left second involute ST, left fourth arc TU, left fifth arc UV, left sixth arc VW, left third involute WX, left seventh arc XA, left first tooth tip arc AB, left eighth arc BC, left fourth involute CD, left ninth arc DE, left tenth arc EF, left eleventh arc FG, left fifth involute GH, left twelfth arc HI, left thirteenth arc IJ, left fourteenth arc JK, left sixth involute KL, and left first tooth root arc LM.

[0008] The end face profile of the left multi-point meshing rotor has n axes of symmetry.

[0009] The end face profile of the left multi-point meshing rotor is rotationally symmetrical about its rotation center O1. Rotating the end face profile of the left multi-point meshing rotor counterclockwise around the rotation center O1... Then, it overlaps with itself;

[0010] The end face profile of the right multi-point meshing rotor is exactly the same as that of the left multi-point meshing rotor.

[0011] The end face profile of the right multi-point meshing rotor consists of 23 curve segments per blade, arranged counterclockwise as follows: right first involute op, right first arc pq, right second arc qr, right third arc rs, right second involute st, right fourth arc tu, right fifth arc uv, right sixth arc vw, right third involute wx, right seventh arc xa, right first tooth tip arc ab, right eighth arc bc, right fourth involute cd, right ninth arc de, right tenth arc ef, right eleventh arc fg, right fifth involute gh, right twelfth arc hi, right thirteenth arc ij, right fourteenth arc jk, right sixth involute kl, and right first tooth root arc lm.

[0012] A smooth multi-point meshing Roots pump rotor as described in claim 1, characterized in that: during the synchronous and opposite-directional double-rotation motion of the left and right multi-point meshing rotors, the end face profiles of the left and right multi-point meshing rotors can achieve correct meshing, and the meshing relationship is as follows: the left seventh arc XA and left eighth arc BC in the end face profile of the left multi-point meshing rotor mesh with the right first tooth root arc lm in the end face profile of the right multi-point meshing rotor; the left fourth involute CD, left ninth arc DE, left tenth arc EF, and left... The eleventh arc FG, the fifth involute on the left GH, the twelfth arc on the left HI, the thirteenth arc on the left IJ, the fourteenth arc on the left JK, and the sixth involute on the left KL mesh with the fourth involute on the right cd, the ninth arc on the right de, the tenth arc on the right ef, the eleventh arc on the right fg, the fifth involute on the right gh, the twelfth arc on the right hi, the thirteenth arc on the right ij, the fourteenth arc on the right jk, and the sixth involute on the right kl in the end face profile of the right multi-point meshing rotor. The first tooth root arc LM in the end face profile of the left multi-point meshing rotor meshes with the eighth arc on the right bc and the seventh arc on the right xa in the end face profile of the right multi-point meshing rotor.

[0013] 2. The design method of a smooth multi-point meshing Roots pump rotor as described in claim 1, characterized by comprising the following steps:

[0014] 1) Given the number of leaves n; given the addendum circle radius R1; given the pitch circle radius R2; find the radius R3 of the arc, R3 = (R1 - R2)·C, where C is a constant;

[0015] Establish a coordinate system O1xy with the rotation center O1 of the left multi-point meshing rotor as the origin, and draw the tooth tip circle with the rotation center O1 and radius R1, the pitch circle with the rotation center O1 and radius R2, the arc with the center U and radius R3, and the tooth root circle with the center T and radius R3 respectively.

[0016] 2) Determine the equations of various component curves of the end face profile of the left multi-point meshing rotor:

[0017] ①The equation of the left first tooth tip arc AB is:

[0018]

[0019] Where: R1—radius of the tooth tip arc, mm; t—angular variable, rad; β—central angle of the left first tooth tip arc AB, rad; β=0.0698rad;

[0020] ② Determine the central angle θ of the arc as:

[0021]

[0022] Where: R2—radius of the pitch circle, mm; R3—radius of the arc, mm; θ—central angle of the arc, rad;

[0023] ③The equation of the eighth left arc BC is:

[0024]

[0025] In the formula: γ—the angle between the normal of the eighth left circular arc BC at point B and the x-axis, in rad;

[0026] ④ Determine the fourth involute CD, the fifth involute GH, and the sixth involute KL from the left using the following steps:

[0027] Determine the angle between the normal to the involute at point C and the x-axis.

[0028] Determine the angle between the normal to the involute at point B and the x-axis: θ2 = θ;

[0029] Obtain the base circle radius R of the involute b for:

[0030] R b =R2sin(θ);

[0031] The involute generation angle α is obtained as follows:

[0032]

[0033] The equation of the sixth involute from the left, KL, is:

[0034]

[0035] In the formula: R b — Radius of the base circle of the involute, mm; α — Angle of origin of the involute, rad;

[0036] After cutting off the sixth involute KL from the left and rotating it counterclockwise by an angle δ, we obtain the fifth involute GH from the left. After cutting off the sixth involute KL from the left and rotating it counterclockwise by an angle 2×δ, we obtain the fourth involute CD from the left.

[0037] ⑤ The left tenth circular arc EF and the left thirteenth circular arc IJ are formed by cutting circular arcs with radius R4 and R5, with the rotation center O1 of the left multi-point meshing rotor as the origin.

[0038] In the formula: R4, R5—radii of the arc;

[0039] ⑥ The ninth arc DE on the left is an arc with a radius of R6 that is tangent to the fourth involute CD on the left and the tenth arc EF on the left. The eleventh arc FG on the left is an arc with a radius of R6 that is tangent to the fifth involute GH on the left and the tenth arc EF on the left. The twelfth arc DE on the left is an arc with a radius of R6 that is tangent to the fifth involute GH on the left and the thirteenth arc IJ on the left. The fourteenth arc JK on the left is an arc with a radius of R6 that is tangent to the sixth involute KL on the left and the thirteenth arc IJ on the left.

[0040] ⑦ The equation for the left first tooth root arc LM is:

[0041]

[0042] 3) Move the eighth left arc BC, the fourth left involute CD, the ninth left arc DE, the tenth left arc EF, the eleventh left arc FG, the fifth left involute GH, the twelfth left arc HI, the thirteenth left arc IJ, the fourteenth left arc JK, and the sixth left involute KL along the axis Mirror symmetry yields the seventh left arc XA, the first involute OP, the first left arc PQ, the second left arc QR, the third left arc RS, the second left involute ST, the fourth left arc TU, and the fifth left arc.

[0043] UV, sixth arc from the left VW, third involute from the left WX;

[0044] The first involute from the left (OP), the first arc from the left (PQ), the second arc from the left (QR), the third arc from the left (RS), the second involute from the left (ST), the fourth arc from the left (TU), the fifth arc from the left (UV), the sixth arc from the left (VW), the third involute from the left (WX), and the seventh arc from the left...

[0045] XA, left first tooth tip arc AB, left eighth arc BC, left fourth involute CD, left ninth arc DE, left tenth arc EF, left eleventh arc FG, left fifth involute GH, left twelfth arc HI, left thirteenth arc IJ, left fourteenth arc JK, left sixth involute KL, left first tooth root arc LM are arranged in three ring arrays with the rotation center O1 of the left multi-point meshing rotor as the center, to obtain the end face profile of the left multi-point meshing rotor;

[0046] 4) The end face profile of the left multi-point meshing rotor is mirror-symmetric along the y-axis to obtain the end face profile of the right multi-point meshing rotor.

[0047] 3. A Roots pump, characterized in that it uses a left multi-point meshing rotor and a right multi-point meshing rotor as described in claim 1.

[0048] The beneficial effects of this invention are as follows:

[0049] ① The proposed smooth multi-point meshing Roots pump rotor achieves multi-position synchronous meshing of the double-sided rotor, enhances the spatial compositeness of the sealing interface, reduces the leakage of the circulating working fluid, and has high sealing performance.

[0050] ②The proposed smooth multi-point meshing Roots pump rotor has an equation applicable to the design of multi-lobe rotors, which facilitates the serial production of rotors;

[0051] ③ The proposed smooth multi-point meshing Roots pump rotor, with its smooth connection between the arc and the involute, improves the pressure pulsation at the Roots pump outlet. Attached Figure Description

[0052] Figure 1 This is a schematic diagram of the rotor end face profile of a two-lobe, smooth, multi-point meshing Roots pump.

[0053] Figure 2 This is a schematic diagram of the rotor end face profile of a three-lobe smooth multi-point meshing Roots pump.

[0054] Figure 3 This is a schematic diagram of the rotor end face profile of a four-lobe smooth multi-point meshing Roots pump.

[0055] Figure 4 This is a diagram showing the end face profile design method for a three-bladed, left-smooth, multi-point meshing rotor (1).

[0056] Figure 5 This is a schematic diagram showing the meshing relationship between the end face profile (101) of a three-lobe left multi-point meshing rotor (1) and the end face profile (201) of a right multi-point meshing rotor (2). It is also a schematic diagram of the structure of a Roots pump rotor with a pump chamber.

[0057] Figure 6This is a schematic diagram of the rotor of a Roots pump with a pump chamber.

[0058] In the figure: 1—Left multi-point meshing rotor (1); 2—Right multi-point meshing rotor (2); 3—Pump chamber (3); R1—Tooth tip radius, mm; R2—Pitch circle radius, mm; R3—Radius of the arc, mm; θ—Central angle of the arc, rad; R b —Radius of the base circle of the involute, mm; α—Angle of origin of the involute, rad; β—Central angle of the left first tooth tip arc AB, rad; γ—Angle between the normal to the left second arc BC at point B and the x-axis, rad. Detailed Implementation

[0059] The invention will now be further described with reference to the accompanying drawings.

[0060] like Figure 1 The figure shows a schematic diagram of the rotor end face profile of a two-lobe smooth multi-point meshing Roots pump, with the rotation centers O1 and O2 being the centers of the two rotors, respectively.

[0061] like Figure 2 The figure shows a schematic diagram of the rotor end face profile of a three-lobe smooth multi-point meshing Roots pump, with the rotation centers O1 and O2 being the centers of the two rotors, respectively.

[0062] like Figure 3 The figure shows a schematic diagram of the rotor end face profile of a four-lobe smooth multi-point meshing Roots pump, with the rotation centers O1 and O2 being the centers of the two rotors, respectively.

[0063] like Figure 4 The diagram shows a design method for the end face profile of a three-bladed left multi-point meshing rotor 1. Each blade of the end face profile consists of 23 curve segments, arranged clockwise as follows: left first involute OP, left first arc PQ, left second arc QR, left third arc RS, left second involute ST, left fourth arc TU, left fifth arc UV, left sixth arc VW, left third involute WX, left seventh arc XA, left first tooth tip arc AB, left eighth arc BC, left fourth involute CD, left ninth arc DE, left tenth arc EF, left eleventh arc FG, left fifth involute GH, left twelfth arc HI, left thirteenth arc IJ, left fourteenth arc JK, left sixth involute KL, and left first tooth root arc LM.

[0064] The design methodology includes the following steps:

[0065] 1) Given the number of leaves n = 3; given the addendum circle radius R1; given the pitch circle radius R2; find the radius R3 of the arc, R3 = (R1 - R2)·C, where C is a constant;

[0066] Establish a coordinate system O1xy with the rotation center O1 of the left multi-point meshing rotor (1) as the origin, and draw the tooth tip circle with the rotation center O1 and radius R1, the pitch circle with the rotation center O1 and radius R2, the arc with the center U and radius R3, and the tooth root circle with the center T and radius R3 respectively.

[0067] 2) Determine the equations of various component curves of the end face profile (101) of the left multi-point meshing rotor (1):

[0068] ①The equation of the left first tooth tip arc AB is:

[0069]

[0070] Where: R1—radius of the tooth tip arc, mm; t—angular variable, rad; β—central angle of the left first tooth tip arc AB, rad; β=0.0698rad;

[0071] ② Determine the central angle θ of the arc as:

[0072]

[0073] Where: R2—radius of the pitch circle, mm; R3—radius of the arc, mm; θ—central angle of the arc, rad;

[0074] ③The equation of the eighth left arc BC is:

[0075]

[0076] In the formula: γ—the angle between the normal of the eighth left circular arc BC at point B and the x-axis, in rad;

[0077] ④ Determine the fourth involute CD, the fifth involute GH, and the sixth involute KL from the left using the following steps:

[0078] Determine the angle between the normal to the involute at point C and the x-axis.

[0079] Determine the angle between the normal to the involute at point B and the x-axis: θ2 = θ;

[0080] Obtain the base circle radius R of the involute b for:

[0081] R b =R2sin(θ);

[0082] The involute generation angle α is obtained as follows:

[0083]

[0084] The equation of the sixth involute from the left, KL, is:

[0085]

[0086] In the formula: R b — Radius of the base circle of the involute, mm; α — Angle of origin of the involute, rad;

[0087] After cutting off the sixth involute KL from the left and rotating it counterclockwise by an angle δ, we obtain the fifth involute GH from the left. After cutting off the sixth involute KL from the left and rotating it counterclockwise by an angle 2×δ, we obtain the fourth involute CD from the left.

[0088] ⑤ The left tenth arc EF and the left thirteenth arc IJ are cut from the arcs with the rotation center O1 of the left multi-point meshing rotor (1) as the origin and the radius R4 and R5.

[0089] In the formula: R4, R5—radii of the arc;

[0090] ⑥ The ninth arc DE on the left is an arc with a radius of R6 that is tangent to the fourth involute CD on the left and the tenth arc EF on the left. The eleventh arc FG on the left is an arc with a radius of R6 that is tangent to the fifth involute GH on the left and the tenth arc EF on the left. The twelfth arc DE on the left is an arc with a radius of R6 that is tangent to the fifth involute GH on the left and the thirteenth arc IJ on the left. The fourteenth arc JK on the left is an arc with a radius of R6 that is tangent to the sixth involute KL on the left and the thirteenth arc IJ on the left.

[0091] ⑦ The equation for the left first tooth root arc LM is:

[0092]

[0093] 3) Move the eighth left arc BC, the fourth left involute CD, the ninth left arc DE, the tenth left arc EF, the eleventh left arc FG, the fifth left involute GH, the twelfth left arc HI, the thirteenth left arc IJ, the fourteenth left arc JK, and the sixth left involute KL along the axis Mirror symmetry yields the seventh left arc XA, the first involute OP, the first left arc PQ, the second left arc QR, the third left arc RS, the second left involute ST, the fourth left arc TU, and the fifth left arc.

[0094] UV, sixth arc from the left VW, third involute from the left WX;

[0095] The first involute from the left (OP), the first arc from the left (PQ), the second arc from the left (QR), the third arc from the left (RS), the second involute from the left (ST), the fourth arc from the left (TU), the fifth arc from the left (UV), the sixth arc from the left (VW), the third involute from the left (WX), and the seventh arc from the left...

[0096] XA, left first tooth tip arc AB, left eighth arc BC, left fourth involute CD, left ninth arc DE, left tenth arc EF, left eleventh arc FG, left fifth involute GH, left twelfth arc HI, left thirteenth arc IJ, left fourteenth arc JK, left sixth involute KL, left first tooth root arc LM are arranged in three ring arrays with the rotation center O1 of the left multi-point meshing rotor (1) as the center, to obtain the end face profile (101) of the left multi-point meshing rotor (1);

[0097] 4) The end face profile 101 of the left multi-point meshing rotor 1 is mirror-symmetric along the y-axis to obtain the end face profile 201 of the right multi-point meshing rotor 2.

[0098] Above: t—angle independent variable, rad; n—number of blades; R1—tooth tip radius, mm; R2—pitch circle radius, mm; R3—radius of the arc, mm; R b —Radius of the base circle of the involute, mm; β—Central angle of the left first tooth tip arc AB, rad; α—Involute generating angle, rad; θ—Central angle of the arc, rad; γ—Angle between the normal to the left second arc BC at point B and the x-axis, rad.

[0099] like Figure 5 The diagram shows the meshing relationship between the end face profile 101 of a three-lobe left multi-point meshing rotor 1 and the end face profile 201 of a right multi-point meshing rotor 2. During synchronous, opposite-direction double-rotation operation, the left multi-point meshing rotor 1 and the right multi-point meshing rotor 2 can achieve correct meshing. The meshing relationship is as follows: the left seventh arc XA and left eighth arc BC in the end face profile (101) of the left multi-point meshing rotor (1) mesh with the right first tooth root arc lm in the end face profile (201) of the right multi-point meshing rotor (2). The left fourth involute CD, left ninth arc DE, left tenth arc EF, left eleventh arc FG, left fifth involute GH, left twelfth arc HI, and left thirteenth arc in the end face profile (101) of the left multi-point meshing rotor (1) are also meshed. The arc IJ, the fourteenth left arc JK, the sixth left involute KL and the fourth right involute cd, the ninth right arc de, the tenth right arc ef, the eleventh right arc fg, the fifth right involute gh, the twelfth right arc hi, the thirteenth right arc ij, the fourteenth right arc jk, and the sixth right involute kl in the end face profile (201) of the right multi-point meshing rotor (2) mesh with each other. The first left tooth root arc LM in the end face profile (101) of the left multi-point meshing rotor (1) meshes with the eighth right arc bc and the seventh right arc xa in the end face profile (201) of the right multi-point meshing rotor (2).

[0100] like Figure 6The diagram shows a schematic of the rotor structure of a Roots pump with a pump chamber, including: a left multi-point meshing rotor 1, a right multi-point meshing rotor 2, and a pump chamber 3. During the operation of the Roots pump, the left multi-point meshing rotor 1 and the right multi-point meshing rotor 2 perform synchronous and opposite double-rotation motions within the pump chamber 3. The two rotors and the pump chamber 3 form a periodically changing working chamber, and the working chamber is periodically connected to the suction and exhaust ports, thereby completing the liquid suction, isochoric transport, and discharge processes of the Roots pump.

[0101] While the specific embodiments of the present invention have been described above in conjunction with the accompanying drawings, this is not intended to limit the scope of protection of the present invention. Those skilled in the art should understand that various modifications or variations that can be made by those skilled in the art without creative effort based on the technical solutions of the present invention are still within the scope of protection of the present invention.

Claims

1. A smooth, multi-point meshing Roots pump rotor, comprising: The left multi-point meshing rotor (1) and the right multi-point meshing rotor (2) are characterized in that: the number of blades on the end face profile of the left multi-point meshing rotor is n, and the number of blades on the end face profile of the right multi-point meshing rotor is n, where n = 2, 3 or 4; The multi-point meshing of the left multi-point meshing rotor (1) and the right multi-point meshing rotor (2) is formed by involute and circular arc to form a segmented meshing structure; The end face profile (101) of the left multi-point meshing rotor (1) consists of 23 curve segments per blade, arranged in clockwise order as follows: left first involute OP, left first arc PQ, left second arc QR, left third arc RS, left second involute ST, left fourth arc TU, left fifth arc UV, left sixth arc VW, left third involute WX, left seventh arc XA, left first tooth tip arc AB, left eighth arc BC, left fourth involute CD, left ninth arc DE, left tenth arc EF, left eleventh arc FG, left fifth involute GH, left twelfth arc HI, left thirteenth arc IJ, left fourteenth arc JK, left sixth involute KL, and left first tooth root arc LM. The end face profile (101) of the left multi-point meshing rotor (1) has n axes of symmetry; The end face profile (101) of the left multi-point meshing rotor (1) is rotationally symmetrical about its rotation center O1. The end face profile (101) of the left multi-point meshing rotor (1) is rotated counterclockwise around the rotation center O1. Then, it overlaps with itself; The end face profile (201) of the right multi-point meshing rotor (2) is exactly the same as the end face profile (101) of the left multi-point meshing rotor (1); The end face profile (201) of the right multi-point meshing rotor (2) consists of 23 curve segments per blade, which are arranged in counterclockwise order as follows: right first involute op, right first arc pq, right second arc qr, right third arc rs, right second involute st, right fourth arc tu, right fifth arc uv, right sixth arc vw, right third involute wx, right seventh arc xa, right first tooth tip arc ab, right eighth arc bc, right fourth involute cd, right ninth arc de, right tenth arc ef, right eleventh arc fg, right fifth involute gh, right twelfth arc hi, right thirteenth arc ij, right fourteenth arc jk, right sixth involute kl, and right first tooth root arc lm.

2. The smooth multi-point meshing Roots pump rotor as described in claim 1, characterized in that: During the synchronous and opposite double-rotation motion of the left multi-point meshing rotor (1) and the right multi-point meshing rotor (2), the end face profile (101) of the left multi-point meshing rotor (1) and the end face profile (201) of the right multi-point meshing rotor (2) can achieve correct meshing. The meshing relationship is as follows: the left seventh arc XA and the left eighth arc BC in the end face profile (101) of the left multi-point meshing rotor (1) mesh with the right first tooth root arc lm in the end face profile (201) of the right multi-point meshing rotor (2). The left fourth involute CD, the left ninth arc DE, the left tenth arc EF, and the left eleventh arc in the end face profile (101) of the left multi-point meshing rotor (1) are also meshed. FG, the fifth involute on the left GH, the twelfth arc on the left HI, the thirteenth arc on the left IJ, the fourteenth arc on the left JK, the sixth involute on the left KL and the fourth involute on the right cd, the ninth arc on the right de, the tenth arc on the right ef, the eleventh arc on the right fg, the fifth involute on the right gh, the twelfth arc on the right hi, the thirteenth arc on the right ij, the fourteenth arc on the right jk, and the sixth involute on the right kl in the end face profile (201) of the right multi-point meshing rotor (2) mesh with each other. The first tooth root arc LM in the end face profile (101) of the left multi-point meshing rotor (1) meshes with the eighth arc bc and the seventh arc xa in the end face profile (201) of the right multi-point meshing rotor (2).

3. A design method for a smooth multi-point meshing Roots pump rotor as described in claim 1, characterized in that: Includes the following steps: 1) Given the number of leaves n; given the addendum circle radius R1; given the pitch circle radius R2; find the radius R3 of the arc, R3 = (R1 - R2)·C, where C is a constant; Establish a coordinate system O1xy with the rotation center O1 of the left multi-point meshing rotor (1) as the origin, and draw the tooth tip circle with the rotation center O1 and radius R1, the pitch circle with the rotation center O1 and radius R2, the arc with the center U and radius R3, and the tooth root circle with the center T and radius R3 respectively. 2) Determine the equations of various component curves of the end face profile (101) of the left multi-point meshing rotor (1): ①The equation of the left first tooth tip arc AB is: Where: R1—radius of the tooth tip arc, mm; t—angular variable, rad; β—central angle of the left first tooth tip arc AB, rad; ② Determine the central angle θ of the arc as: Where: R2—radius of the pitch circle, mm; R3—radius of the arc, mm; θ—central angle of the arc, rad; ③The equation of the eighth left arc BC is: In the formula: γ—the angle between the normal of the eighth left circular arc BC at point B and the x-axis, in rad; ④ Determine the fourth involute CD, the fifth involute GH, and the sixth involute KL from the left using the following steps: Determine the angle between the normal to the involute at point C and the x-axis. Determine the angle between the normal to the involute at point B and the x-axis: θ2 = θ; Obtain the base circle radius R of the involute b for: R b =R2sin(θ); The involute generation angle α is obtained as follows: The equation of the sixth involute from the left, KL, is: In the formula: R b — Radius of the base circle of the involute, mm; α — Angle of origin of the involute, rad; After cutting off the sixth involute KL from the left and rotating it counterclockwise by an angle δ, we obtain the fifth involute GH from the left. After cutting off the sixth involute KL from the left and rotating it counterclockwise by an angle 2×δ, we obtain the fourth involute CD from the left. ⑤ The left tenth arc EF and the left thirteenth arc IJ are cut from the arcs with the rotation center O1 of the left multi-point meshing rotor (1) as the origin and the radius R4 and R5. In the formula: R4, R5—radii of the arc; ⑥ The ninth arc DE on the left is an arc with a radius of R6 that is tangent to the fourth involute CD on the left and the tenth arc EF on the left. The eleventh arc FG on the left is an arc with a radius of R6 that is tangent to the fifth involute GH on the left and the tenth arc EF on the left. The twelfth arc DE on the left is an arc with a radius of R6 that is tangent to the fifth involute GH on the left and the thirteenth arc IJ on the left. The fourteenth arc JK on the left is an arc with a radius of R6 that is tangent to the sixth involute KL on the left and the thirteenth arc IJ on the left. ⑦ The equation for the left first tooth root arc LM is: 3) Move the eighth left arc BC, the fourth left involute CD, the ninth left arc DE, the tenth left arc EF, the eleventh left arc FG, the fifth left involute GH, the twelfth left arc HI, the thirteenth left arc IJ, the fourteenth left arc JK, and the sixth left involute KL along the axis By mirror symmetry, we obtain the seventh left arc XA, the first involute OP, the first left arc PQ, the second left arc QR, the third left arc RS, the second left involute ST, the fourth left arc TU, the fifth left arc UV, the sixth left arc VW, and the third left involute WX. The left first involute OP, left first arc PQ, left second arc QR, left third arc RS, left second involute ST, left fourth arc TU, left fifth arc UV, left sixth arc VW, left third involute WX, left seventh arc XA, left first tooth tip arc AB, left eighth arc BC, left fourth involute CD, left ninth arc DE, left tenth arc EF, left eleventh arc FG, left fifth involute GH, left twelfth arc HI, left thirteenth arc IJ, left fourteenth arc JK, left sixth involute KL, and left first tooth root arc LM are arranged in three annular arrays with the rotation center O1 of the left multi-point meshing rotor (1) as the center, to obtain the end face profile (101) of the left multi-point meshing rotor (1). 4) The end face profile (101) of the left multi-point meshing rotor (1) is mirror-symmetric along the y-axis to obtain the end face profile (201) of the right multi-point meshing rotor (2).

4. A Roots pump, characterized in that: The left multi-point meshing rotor (1) and the right multi-point meshing rotor (2) as described in claim 1 are used.

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