Oil-free twin-screw compressor rotor profile

Abstract

The application discloses an oil-free double-screw compressor rotor profile and relates to the technical field of compressors. The oil-free double-screw compressor rotor profile comprises a male rotor profile and a female rotor profile which are mutually engaged, and the tooth shapes of the two are entirely composed of a double-side asymmetric tooth shape formed by a circular arc and a circular arc envelope line. The tooth profile of the female rotor profile comprises a second large convex circular arc located at a tooth root part, the radius R(BC) of the circular arc is (0.30-0.60)A, wherein A is the center distance of the female and male rotors, the deformation resistance and the structural rigidity of the female rotor are improved by greatly increasing the tooth thickness of the female rotor. The male and female rotor profiles are each composed of six smooth tangent quadratic curve units, and the area of a high-pressure side leakage triangle is effectively controlled, the sealing performance and the volumetric efficiency are improved by the synergistic effect of the optimization of the parameters of the fourth circular arc of the female rotor and the protection angle design of the second circular arc of the male rotor. The profile has the advantages of full smoothness, easy processing, a large area utilization coefficient, stable transmission and the like.

Description

Technical Field

[0001] This invention relates to the field of compressor technology, and specifically to a rotor profile of an oil-free twin-screw compressor. Background Technology

[0002] The rotor of a twin-screw compressor is the core component of the screw compressor, and its profile fundamentally determines the overall performance of the screw compressor. The male and female rotor profiles are composed of several different first- or second-order mathematical curves, such as circular arcs and their envelopes, point (straight line) cycloids, ellipses and their envelopes, parabolas and their envelopes, etc. Each corresponding curve between the male and female rotors is derived analytically based on the meshing envelope principle, and the different curves are tangentially connected with a smooth transition.

[0003] A high-performance rotor profile typically needs to meet several design requirements: (1) Good manufacturability: The tooth profile should be composed of smooth mathematical curves to facilitate high-precision grinding and ensure consistency and economy in mass production; (2) Superior sealing performance: The spatial contact line formed by the meshing of male and female rotors should be continuous and as short as possible to effectively isolate the high-pressure chamber and the low-pressure chamber; at the same time, the area of ​​the "leakage triangle" formed by the contact line, rotor tooth tip and inner wall of the casing should be as small as possible to reduce internal leakage of the working fluid, thereby improving the volumetric efficiency and thermal efficiency of the compressor; (3) Reasonable mechanical and dynamic characteristics: The rotor tooth profile should have sufficient structural strength and rigidity to withstand the gas load and thermal stress during operation; the profile design should help to form hydrodynamic lubrication or achieve smooth transmission to reduce wear, vibration and noise; (4) High area utilization coefficient: Under a given rotor outer diameter, the profile should be able to provide a larger inter-tooth volume, thereby increasing the single-stage compression ratio or gas delivery.

[0004] Chinese patent document CN114876796B discloses a typical modern profile in which the male and female rotor teeth are entirely composed of circular arcs and their envelopes. Through optimized design, it achieves the goals of continuous contact lines and a small leakage triangle. However, this profile design is not specifically optimized for the "oil-free" operating condition.

[0005] Oil-free twin-screw compressors require that the male and female rotors not directly contact each other during operation, typically relying on synchronous gears for non-contact synchronous drive. This feature eliminates the dependence on oil film lubrication, but it also places unique demands on the rotor profile: First, due to the lack of oil film support and cooling between the rotors, the female rotor is more prone to thermoelastic deformation under high pressure and high temperature gas, thus requiring its tooth profile to have higher bending stiffness; second, non-contact operation allows designers to focus more on optimizing the rotor's aerodynamic shape to reduce aerodynamic losses (i.e., "wind resistance") during high-speed rotation, which is crucial for improving the main unit efficiency of high-speed oil-free compressors. Many existing rotor profiles, including the scheme disclosed in CN114876796B, often focus on optimizing contact and sealing performance, lacking in-depth consideration of how to specifically enhance the stiffness of the female rotor and optimize its aerodynamic shape under oil-free conditions. Summary of the Invention

[0006] To address the shortcomings of existing technologies, this invention provides a rotor profile for an oil-free twin-screw compressor that overcomes the deficiencies of existing technologies. By optimizing the parameters of the fourth arc of the female rotor and the protective angle design of the second arc of the male rotor, the area of ​​the high-pressure side leakage triangle is effectively controlled, thereby improving sealing performance and volumetric efficiency.

[0007] To achieve the above objectives, the present invention provides the following technical solution:

[0008] An oil-free twin-screw compressor rotor profile includes a male rotor profile and a female rotor profile that mesh with each other, wherein both the male rotor profile and the female rotor profile are composed of a double-sided asymmetrical tooth shape formed by circular arcs and circular arc envelopes;

[0009] The tooth profile of the female rotor includes a second large convex arc BC located on the belly of its tooth. The radius R(BC) of the second large convex arc BC satisfies: R(BC) = (0.30~0.6)A, where A is the center distance between the male rotor and the female rotor.

[0010] Preferably, the female rotor profile is composed of six sequentially smooth and tangent quadratic curves on the end face, which are in the following order according to the tooth profile direction: female rotor first convex arc AB, female rotor second large convex arc BC, female rotor third concave arc CD, female rotor first arc envelope DE, female rotor fourth arc EF and female rotor tooth tip arc FG.

[0011] The male rotor profile is composed of six sequentially smooth and tangent quadratic curves on the end face, which are in the following order according to the tooth profile direction: the first circular arc envelope line HI of the male rotor, the second circular arc envelope line IJ of the male rotor, the first circular arc line JK of the male rotor, the second circular arc line KL of the male rotor, the third circular arc envelope line LM of the male rotor, and the tooth root circular arc MN of the male rotor.

[0012] Preferably, the first circular arc envelope HI of the male rotor is the conjugate curve of the first convex circular arc AB of the female rotor, and the second circular arc envelope IJ of the male rotor is the conjugate curve of the second large convex circular arc BC of the female rotor; the first circular arc JK of the male rotor is the conjugate curve of the third concave circular arc CD of the female rotor, the second circular arc KL of the male rotor is the conjugate curve of the first circular arc envelope DE of the female rotor, the third circular arc envelope LM of the male rotor is the conjugate curve of the fourth circular arc EF of the female rotor, and the tooth root circular arc MN of the male rotor and the tooth tip circular arc FG of the female rotor are conjugate curves of each other.

[0013] Preferably, with O1 as the center of the male rotor and O2 as the center of the female rotor, R1d, R1t, and R1g are respectively the tip circle radius, pitch circle radius, and root circle radius of the male rotor, respectively, and R2d, R2t, and R2g are respectively the tip circle radius, pitch circle radius, and root circle radius of the female rotor, respectively.

[0014] The center of the second circular arc KL of the male rotor is located on a straight line PD that passes through the center of the third concave circular arc CD of the female rotor. The straight line PD and the line O1O2 connecting the centers of the two rotors form a protection angle θ. The protection angle θ is configured such that the highest point of the tooth profile of the second circular arc KL of the male rotor is lower than the radius R1d of the tip circle of the male rotor, and the radius R(KL) of the second circular arc KL of the male rotor is (0.01~0.09)A.

[0015] Preferably, the center of the fourth arc EF of the female rotor is on the straight line O2F, and the center of the fourth arc EF of the female rotor is located inside the pitch circle of the female rotor. The radius of the fourth arc EF of the female rotor is R(EF) = (0.020~0.038)A, and satisfies the relationship: R2d=R(EF)+R2t-λ.

[0016] Wherein, λ is the distance from the center of the fourth arc EF of the female rotor to the pitch circle of the female rotor, and λ is a positive value.

[0017] Preferably, R1d = (0.65~0.71)A, R1g = (0.39~0.5)A, R2g = A-R1d; R1g = A-R2d.

[0018] Preferably, ∠O2O1H is the wrap angle of the long side of the male rotor, that is, the angle between the straight line O1H and the straight line O1O2;

[0019] ∠NO1O2 is the short side wrap angle of the male rotor, that is, the angle between the straight line O1N and the straight line O1O2;

[0020] ∠AO2O1 is the long side wrap angle of the male rotor, that is, the angle between the straight line O2A and the straight line O1O2;

[0021] ∠GO2O1 is the short side wrap angle of the male rotor, that is, the angle between the straight line O2G and the straight line O1O2;

[0022] Z1 is the number of teeth on the male rotor, and Z2 is the number of teeth on the female rotor. Therefore:

[0023] ∠O2O1H+∠NO1O2= 360° / Z1,

[0024] ∠AO₂O₁ + ∠GO₂O₁ = 360° / Z²

[0025] ∠AO₂O₁:∠O₂O₁H=Z₂:Z₁,

[0026] ∠GO2O1:∠NO1O2 =Z2:Z1

[0027] R1t=A×Z1 / (Z1+Z2),

[0028] R2t=A×Z2 / (Z1+Z2).

[0029] Preferably, the tooth ratio Z1:Z2 between the male rotor and the female rotor is 4-6:5-8.

[0030] Preferably, the radius R(AB) of the first convex arc AB of the female rotor is (0.06~0.102)A, and its center is located on the extension line of the long side wrap angle ∠AO2O1 of the female rotor with the center O2 of the female rotor as the origin and the line connecting O1O2; the first convex arc AB of the female rotor is tangent to the tip circle R2d of the female rotor at point A.

[0031] Preferably, the center of the third concave arc CD of the female rotor is located on the line O1O2 connecting the centers of the two rotors and is on the pitch circle of the female rotor, and its radius R(CD) = (0.2~0.245)A.

[0032] This invention provides a rotor profile for an oil-free twin-screw compressor. It offers the following advantages: By setting a large convex arc of a specific radius on the belly of the female rotor teeth, the material thickness and section modulus of the female rotor tooth root region are significantly increased, resulting in a substantial improvement in mechanical strength. Under the typical high-temperature operating environment of oil-free compressors, the female rotor's ability to resist bending and thermoelastic deformation caused by gas loads is significantly enhanced, thus ensuring the stability of rotor clearance during long-term operation, extending the life of the compressor, and avoiding efficiency reduction or cylinder rubbing risks due to deformation. Furthermore, this large convex arc of the female rotor constitutes the main part of the female rotor tooth profile. Its smooth, streamlined convex profile, similar to an airfoil design, can guide gas flow more smoothly, significantly reducing the gas dynamic losses generated by the female rotor and the surrounding working fluid during high-speed rotation. This directly translates into a reduction in compressor shaft power, improving the operating efficiency of the compressor in the high-speed range.

[0033] Furthermore, by limiting the radius range of the fourth arc of the female rotor and taking a reasonably small positive value for the distance from its center to the pitch circle, the position of the highest point of the meshing line was precisely controlled, bringing it closer to the intersection line of the male and female rotor cavities. By setting a protection angle and controlling the radius of the second arc of the male rotor within (0.01~0.09)A, this section of the tooth profile was protected while further optimizing the contact line morphology. This effectively minimized the leakage triangle area, significantly reducing internal leakage from the high-pressure chamber to the low-pressure chamber, and directly improving the compressor's volumetric efficiency and energy efficiency. Attached Figure Description

[0034] To more clearly illustrate the technical solutions in this invention or the prior art, the accompanying drawings used in the description of the prior art will be briefly introduced below.

[0035] Figure 1 This is a schematic diagram of the meshing state structure of the rotor profile of the oil-free twin-screw compressor of the present invention at its end cross section;

[0036] Figure 2 This is a diagram of the meshing line formed during a complete meshing cycle according to the present invention;

[0037] Figure 3 This is a schematic diagram of a high-voltage side leakage triangle.

[0038] Figure 4 A three-dimensional isometric view of the male and female rotor pairs for applying the profile of this invention. Detailed Implementation

[0039] To make the objectives, technical solutions, and advantages of the present invention clearer, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings.

[0040] Examples, such as Figures 1 to 4 As shown, the present invention provides an oil-free twin-screw compressor rotor profile, including a male rotor profile 1 and a female rotor profile 2 that mesh with each other. Both the male rotor profile 1 and the female rotor profile 2 are composed of a double-sided asymmetrical tooth profile formed by circular arcs and circular arc envelopes. They are installed in the compressor housing (not shown in the figure) and are driven by synchronous gears to achieve non-contact synchronous reverse rotation.

[0041] First, determine the core geometric parameters of a pair of rotors. Let the center of the male rotor be O1 and the center of the female rotor be O2. The distance between the two centers is defined as the center distance A between the male and female rotors, which is a fundamental parameter that determines the overall size of the rotor.

[0042] The number of teeth on the male and female rotors are defined as Z1 and Z2, respectively. For oil-free twin-screw compressors, in order to obtain good dynamic balance and flow characteristics, this invention recommends a tooth ratio Z1:Z2 of (4-6):(5-8). The specific ratio can be selected according to different exhaust pressure conditions; for example, 4:5 or 5:6 can be used for low-pressure conditions, and 5:7 or 6:8 can be used for medium- and high-pressure conditions.

[0043] Based on the center distance A and the number of teeth Z1 and Z2, it can be determined that:

[0044] The pitch circle radius of the male rotor is R1t = A × Z1 / (Z1 + Z2);

[0045] The pitch circle radius of the female rotor is R2t = A × Z2 / (Z1 + Z2);

[0046] The radius of the male rotor tooth tip circle R1d = (0.65~0.71)A;

[0047] The root radius of the male rotor teeth, R1g, is (0.39~0.50)A.

[0048] The radius of the root circle of the female rotor tooth is R2g = A - R1d (based on the geometric complementary relationship).

[0049] The radius of the tip circle of the female rotor tooth, R2d, is defined by a specific curve and its value satisfies R2d=A-R1g.

[0050] refer to Figure 1 Define four key wrap angles to allocate tooth profile space:

[0051] ∠O2O1H is the wrap angle of the long side of the male rotor, that is, the angle between the straight line O1H and the straight line O1O2;

[0052] ∠NO1O2 is the short side wrap angle of the male rotor, that is, the angle between the straight line O1N and the straight line O1O2;

[0053] ∠AO2O1 is the long side wrap angle of the male rotor, that is, the angle between the straight line O2A and the straight line O1O2;

[0054] ∠GO2O1 is the short side wrap angle of the male rotor, that is, the angle between the straight line O2G and the straight line O1O2;

[0055] The above wrap angle satisfies the following meshing motion relationship to ensure correct rotor meshing and uniform tooth splitting:

[0056] ∠O2O1H+∠NO1O2= 360° / Z1,

[0057] ∠AO₂O₁ + ∠GO₂O₁ = 360° / Z²

[0058] ∠AO₂O₁:∠O₂O₁H=Z₂:Z₁,

[0059] ∠GO2O1:∠NO1O2 =Z2:Z1

[0060] R1t=A×Z1 / (Z1+Z2),

[0061] R2t=A×Z2 / (Z1+Z2).

[0062] The female rotor profile 2 consists of six sequentially smooth, tangent (i.e., first-order continuous) quadratic curves on the end face, arranged in the following order according to the tooth profile direction: the first convex arc AB of the female rotor, the second large convex arc BC of the female rotor, the third concave arc CD of the female rotor, the envelope line of the first arc of the female rotor DE, the fourth arc EF of the female rotor, and the tooth tip arc FG of the female rotor; wherein:

[0063] The first convex arc AB of the female rotor is a convex arc, and its center lies on the extension of the line O1O2, which forms the long side enclosing angle ∠AO2O1 of the female rotor, with the center O2 as the origin. The radius of the first convex arc AB of the female rotor is R(AB) = (0.06~0.102)A. This arc is smoothly tangent to the tip circle of the female rotor tooth (radius R2d) at point A, and tangent to the subsequent second large convex arc BC at point B.

[0064] The second largest convex arc BC of the female rotor is one of the core features of this invention. This segment is a large-radius convex arc with a radius R(BC) = (0.30~0.6)A. This design allows for ample material in the web of the female rotor teeth, significantly enhancing the bending stiffness of the female rotor to cope with high-temperature gas loads under oil-free conditions; simultaneously, its gentle convex profile forms an excellent streamline, effectively reducing aerodynamic drag during high-speed rotation of the female rotor. This arc is tangent to the first convex arc AB at point B and to the subsequent third concave arc CD at point C.

[0065] The third concave arc CD of the female rotor is a concave arc, and its center P is located on the line O1O2 connecting the centers of the two rotors, and exactly on the pitch circle of the female rotor. Its radius R(CD) = (0.20~0.245)A.

[0066] The first circular arc envelope DE of the female rotor is not a simple circular arc, but a conjugate curve generated by the motion envelope of the second circular arc KL of the male rotor, defined on the male rotor, according to the meshing principle. The first circular arc envelope DE of the female rotor is tangent to the third concave circular arc CD at point D, and tangent to the subsequent fourth circular arc EF at point E.

[0067] The fourth arc EF of the female rotor is a small-radius convex arc, with its center located on the straight line O2F (point F is the point of tangency between this arc and the tip circle of the female rotor teeth), and its center lies within the pitch circle of the female rotor. Its radius R(EF) = (0.020~0.038)A. The distance from the center of this arc to the pitch circle of the female rotor is defined as λ (λ is a positive value). The radius R2d of the tip circle of the female rotor teeth is determined by the geometric position of this arc, satisfying the following relationship:

[0068] R2d = R(EF) + R2t - λ;

[0069] This formula can be understood geometrically as follows: the distance from the center O2 of the male rotor to the center of the arc EF is (R2t-λ), and adding the radius R(EF) gives the tooth tip circle radius R2d.

[0070] The tip circle FG of the female rotor is a circle with the center O2 of the female rotor as its center, which is a part of the tip circle.

[0071] The male rotor profile 1 is generated conjugately with the female rotor profile 2. On its end face, it also consists of six sequentially smooth, tangent quadratic curves, arranged in the following order according to the tooth profile: the first circular arc envelope HI of the male rotor, the second circular arc envelope IJ of the male rotor, the first circular arc JK of the male rotor, the second circular arc KL of the male rotor, the third circular arc envelope LM of the male rotor, and the root circular arc MN of the male rotor. Each curve segment has a definite conjugate relationship with the female rotor curve, namely:

[0072] The envelope HI of the first circular arc of the male rotor is the conjugate curve of the first convex circular arc AB of the female rotor.

[0073] The envelope of the second circular arc of the male rotor, IJ, is the conjugate curve of the second largest convex circular arc BC of the female rotor.

[0074] The first circular arc JK of the male rotor is the conjugate curve of the third concave circular arc CD of the female rotor.

[0075] The second arc KL of the male rotor is the conjugate curve of the envelope line DE of the first arc of the female rotor. This segment is crucial for optimizing sealing performance. The center of the second arc KL of the male rotor is not on the line connecting O1 and O2, but lies on a straight line PD that passes through the center point P of the third concave arc CD of the female rotor. A protective angle θ is formed between the straight line PD and the line connecting the centers of the two rotors, O1 and O2. This angle design ensures that the highest point of the tooth profile of the second arc KL of the male rotor is controlled within the radius R1d of the tip circle of the male rotor tooth. This "protective angle" design has a dual benefit: firstly, it protects this critical curve from damage during machining and operation; secondly, it works synergistically with the parameters of the fourth arc EF of the female rotor to optimize the leakage triangle. The radius of the second arc KL of the male rotor is R(KL) = (0.01~0.09)A.

[0076] The envelope LM of the third circular arc of the male rotor is the conjugate curve of the fourth circular arc EF of the female rotor.

[0077] The root arc MN of the male rotor is an arc centered at the center O1 of the male rotor, and the tip arc FG of the female rotor is a conjugate curve.

[0078] like Figure 2 As shown, the profile of this invention can form a continuous, closed meshing line, which is the basis for ensuring a good seal. For example... Figure 3 As shown, the key indicator for measuring the degree of internal leakage is the "leakage triangle," which is a small, curved triangular region located near the boundary between the high-pressure and low-pressure chambers. Its three vertices are:

[0079] Point 1: The projection point of the line of intersection between the tip of the female rotor tooth and the inner wall of the compressor housing (i.e., the "rotor cavity") on this end face.

[0080] Point 2: The projection point of the intersection line between the male rotor tooth tip and the inner wall of the compressor casing on this end face. The line connecting point 1 and point 2 constitutes the theoretical dividing line between the male and female rotor cavities (intersection line 12 of male and female rotor cavities).

[0081] Point 3: The highest point of the male and female rotor meshing contact line on the end face (i.e., the end point closest to the exhaust side).

[0082] During rotor rotation, gas in the high-pressure chamber leaks into the low-pressure chamber through the "leakage triangle" formed by points 1, 2, and 3. The area of ​​the leakage triangle directly determines the amount of internal leakage and is one of the most critical factors affecting the compressor's volumetric efficiency and energy efficiency. Therefore, one of the core objectives of optimizing the profile is to minimize the area of ​​the leakage triangle while ensuring other performance characteristics (such as area utilization coefficient).

[0083] This invention effectively controls the area of ​​the leakage triangle by synergistically optimizing the following two key parameters, while ensuring that the area utilization coefficient is not reduced:

[0084] Firstly, there is a parameterized optimization mechanism for the fourth arc EF of the female rotor. Although the fourth arc EF of the female rotor is a small arc, its geometric definition is the primary key to controlling the leakage triangle. This invention limits the radius of the fourth arc EF of the female rotor to a small range of (0.020~0.038)A. A smaller R(EF) helps to make the tooth profile of this segment tighter, thereby directly affecting the shape of its conjugate curve: the envelope line LM of the third arc of the male rotor, ultimately causing the position of the highest point of the meshing line (point 3) to move towards the line connecting the centers of the two rotors, O1O2.

[0085] Furthermore, λ is defined as the distance from the center of the arc EF to the pitch circle of the female rotor. The formula R2d=R(EF)+R2t-λ shows that the value of λ directly determines the "reduction" of the female rotor's tip circle radius R2d based on the pitch circle. Under the premise of ensuring the normal generation of the conjugate curve, selecting a reasonable small positive value of λ can make the tip circle more "inward". This geometric change will cause a slight adjustment to the position of the intersection point (point 1) between the female rotor tip and the machine cavity. More importantly, it will also push the highest point (point 3) of the meshing line formed by the EF segment to move closer to the intersection line of the male and female rotor cavities formed by points 1 and 2.

[0086] By controlling R(EF) to a smaller value and optimizing λ, the highest point of the meshing line (point 3) can be effectively pulled closer to the intersection line 12 of the male and female rotor cavities. Geometrically, this directly reduces the vertical distance from point 3 to the intersection line 12 of the male and female rotor cavities, that is, it significantly compresses the height of the leakage triangle perpendicular to the leakage direction, thereby greatly reducing its area.

[0087] Secondly, the design involves matching the radius R(KL) of the second arc KL of the male rotor with the protection angle θ. The center of this arc is set on a straight line PD that passes through point P (the center of the third concave arc CD of the female rotor) and forms an angle θ with the line connecting O1O2. The core function of the protection angle θ is to actively control the highest point of the arc KL within the radius R1d of the tip circle of the male rotor teeth. This not only has practical value in protecting the tooth profile and avoiding interference between machining and operation, but also has profound significance in optimizing the seal. By adjusting the angle θ, the inclination angle and convexity of the tooth profile of the KL segment can be finely controlled, thereby changing its meshing state with the conjugate curve (the envelope line DE of the first arc of the female rotor), and further fine-tuning the final spatial position of the highest point 3 of the meshing line. The radius R(KL) of the second arc KL of the male rotor is limited to (0.01~0.09)A to ensure that the curve has an appropriate curvature and can work in conjunction with the protection angle θ to form a transitional tooth profile that does not affect the tooth root strength and can form an ideal sealing interface with the DE section of the female rotor.

[0088] The parameters (R(EF), λ) of the fourth arc segment EF of the female rotor primarily "push" the position of the highest point (point 3) of the meshing line from the female rotor side; while the parameters (θ, R(KL)) of the second arc segment KL of the male rotor guide and lock the final shape of this point from the male rotor side. The two act like a precisely matched adjusting mechanism, jointly ensuring that point 3 is accurately positioned at the optimal location closest to the leakage channel (intersection line 12 of the male and female rotor cavities).

[0089] like Figure 3As shown, through the synergistic optimization of this invention, the area of ​​the leakage triangle (△123) is ultimately controlled within a very small range. Point 3 is almost adjacent to the intersection line 12 of the male and female rotor cavities, making the flow channel of high-pressure gas through this triangular region both narrow and long, and the flow resistance increases sharply, thereby greatly suppressing the intensity of internal leakage.

[0090] It is important to emphasize that this synergistic optimization was achieved while ensuring that the strength and aerodynamic advantages brought by the large convex arc BC of the female rotor, as well as the overall advantages such as smooth profile and large area utilization coefficient, are not compromised. This demonstrates the systematic and balanced nature of this invention in addressing the multi-objective, cross-disciplinary (structural mechanics, fluid mechanics, geometry) design challenges of oil-free screw compressors.

[0091] This invention addresses two key characteristics of oil-free compressors: "non-contact operation of the male and female rotors" and "susceptibility of the female rotor to high-temperature gas influences." By incorporating a large convex arc BC of a specific radius (0.30–0.6 Å) on the belly of the female rotor teeth, it significantly increases the material thickness and section modulus at the root region of the female rotor teeth, fundamentally enhancing its mechanical strength. Under the typical high-temperature operating environment of oil-free compressors, the female rotor's ability to resist bending and thermoelastic deformation caused by gas loads is significantly enhanced, ensuring the stability of rotor clearance during long-term operation, extending the lifespan of the main unit, and avoiding efficiency reduction or cylinder rubbing risks due to deformation. This large convex arc BC forms the main part of the female rotor tooth profile. Its smooth, streamlined convex profile, similar to an airfoil design, guides gas flow more smoothly, significantly reducing the gas dynamic losses (i.e., "wind resistance") generated by the female rotor and surrounding working fluid during high-speed rotation. This directly translates into a reduction in compressor shaft power, improving the operating efficiency of the main unit in the high-speed range.

[0092] Furthermore, this invention precisely controls the position of the highest point of the meshing line by limiting the radius range of the fourth arc EF of the female rotor and taking a reasonably small positive value for the distance from its center to the pitch circle, making it closer to the intersection line of the male and female rotor cavities. By setting a protection angle θ and controlling the radius R(KL) of the second arc KL of the male rotor within (0.01~0.09)A, the tooth profile of this segment is protected while further optimizing the contact line morphology. The above synergistic effect effectively minimizes the area of ​​the leakage triangle formed by the points (intersection of the female rotor and the cavity), the point (intersection of the male rotor and the cavity), and the point (highest point of the meshing line), thereby significantly reducing internal leakage from the high-pressure cavity to the low-pressure cavity and directly improving the volumetric efficiency and energy efficiency of the compressor.

[0093] Furthermore, the profile of this invention is entirely composed of circular arcs and conjugate envelopes, with all connection points being tangential, ensuring the smoothness of the tooth profile and the continuity of the contact line during meshing. This eliminates discontinuities on the sealing line, fundamentally reducing leakage paths of the high-pressure working fluid. The smooth, continuous curves also prevent stress concentration and chipping that may occur during machining, contributing to excellent surface quality and ensuring the consistency of the rotor profile in mass production. This is crucial for guaranteeing compressor performance and noise levels.

[0094] Under a given center distance A and addendum circle diameter, the tooth profile design of this invention fully utilizes the inter-tooth volume (i.e., rotor end face area), which is beneficial for increasing single-rotor displacement or compression ratio and making the machine structure more compact. The conjugate tooth profile generated by the meshing principle, combined with a reasonable wrap angle distribution (∠AO2O1:∠O2O1H = Z2:Z1, etc.), ensures the coordinated motion of the male and female rotors driven by synchronous gears, helping to reduce vibration and noise. Through the adjustable range of parameters such as the tooth ratio (4~6:5~8), the radius range of each arc segment, and the protection angle θ, this profile can be flexibly optimized and serialized for different exhaust pressure, displacement, and speed conditions, exhibiting good engineering adaptability and promotional value.

[0095] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A rotor profile for an oil-free twin-screw compressor, comprising a male rotor profile (1) and a female rotor profile (2) meshing with each other, characterized in that: Both the male rotor profile (1) and the female rotor profile (2) are composed of a double-sided asymmetrical tooth shape formed by a circular arc and a circular arc envelope. The tooth profile of the female rotor profile (2) includes a second large convex arc (BC) located on the belly of its tooth. The radius R(BC) of the second large convex arc (BC) satisfies: R(BC) = (0.30~0.6)A, where A is the center distance between the male rotor and the female rotor. The female rotor profile (2) is composed of six sequentially smooth and tangent quadratic curves on the end face, which are arranged in the following order according to the tooth profile direction: the first convex arc (AB) of the female rotor, the second large convex arc (BC) of the female rotor, the third concave arc (CD) of the female rotor, the envelope of the first arc of the female rotor (DE), the fourth arc of the female rotor (EF) and the tooth tip arc of the female rotor (FG). The male rotor profile (1) is composed of six sequentially smooth and tangent quadratic curves on the end face, which are arranged in the following order according to the tooth profile direction: the first circular arc envelope of the male rotor (HI), the second circular arc envelope of the male rotor (IJ), the first circular arc of the male rotor (JK), the second circular arc of the male rotor (KL), the third circular arc envelope of the male rotor (LM), and the tooth root circular arc of the male rotor (MN). With O1 as the center of the male rotor and O2 as the center of the female rotor, R1d, R1t, and R1g are respectively the tip circle radius, pitch circle radius, and root circle radius of the male rotor, respectively; and R2d, R2t, and R2g are respectively the tip circle radius, pitch circle radius, and root circle radius of the female rotor, respectively. The center of the second circular arc (KL) of the male rotor is located on a straight line PD that passes through the center of the third concave circular arc (CD) of the female rotor. The straight line PD and the line O1O2 connecting the centers of the two rotors form a protective angle θ. The protective angle θ is configured such that the highest point of the tooth profile of the second circular arc (KL) of the male rotor is lower than the radius R1d of the tip circle of the male rotor tooth, and the radius R(KL) of the second circular arc (KL) of the male rotor is (0.01~0.09)A. The radius R(AB) of the first convex arc (AB) of the female rotor is (0.06~0.102)A, and its center is located on the extension line of the long side enclosing angle ∠AO2O1 of the female rotor with the center O2 of the female rotor as the origin and the line connecting O1O2; the first convex arc (AB) of the female rotor is tangent to the tip circle R2d of the female rotor tooth at point A; The center of the third concave arc (CD) of the female rotor is located on the line O1O2 connecting the centers of the two rotors and on the pitch circle of the female rotor, and its radius R(CD) = (0.2~0.245)A; the second large convex arc (BC) of the female rotor is tangent to the first convex arc (AB) of the female rotor at point B, and is tangent to the third concave arc (CD) of the female rotor at point C.

2. The rotor profile of the oil-free twin-screw compressor according to claim 1, characterized in that: The first circular arc envelope (HI) of the male rotor is the conjugate curve of the first convex circular arc (AB) of the female rotor; the second circular arc envelope (IJ) of the male rotor is the conjugate curve of the second large convex circular arc (BC) of the female rotor; the first circular arc (JK) of the male rotor is the conjugate curve of the third concave circular arc (CD) of the female rotor; the second circular arc (KL) of the male rotor is the conjugate curve of the first circular arc envelope (DE) of the female rotor; the third circular arc envelope (LM) of the male rotor is the conjugate curve of the fourth circular arc (EF) of the female rotor; and the tooth root circular arc (MN) of the male rotor and the tooth tip circular arc (FG) of the female rotor are conjugate curves of each other.

3. The rotor profile of the oil-free twin-screw compressor according to claim 1, characterized in that: The center of the fourth arc (EF) of the female rotor is on the straight line O2F, and the center of the fourth arc (EF) of the female rotor is located inside the pitch circle of the female rotor. The radius of the fourth arc (EF) of the female rotor is R(EF) = (0.020~0.038)A, and satisfies the relationship: R2d=R(EF)+R2t-λ. Wherein, λ is the distance from the center of the fourth arc (EF) of the female rotor to the pitch circle of the female rotor, and λ is a positive value.

4. The rotor profile of the oil-free twin-screw compressor according to claim 1, characterized in that: R1d=(0.65~0.71)A, R1g=(0.39~0.5)A, R2g=A-R1d; R1g=A-R2d.

5. The rotor profile of the oil-free twin-screw compressor according to claim 1, characterized in that: ∠O2O1H is the wrap angle of the long side of the male rotor, that is, the angle between the straight line O1H and the straight line O1O2; ∠NO1O2 is the short side wrap angle of the male rotor, that is, the angle between the straight line O1N and the straight line O1O2; ∠AO2O1 is the long side wrap angle of the male rotor, that is, the angle between the straight line O2A and the straight line O1O2; ∠GO2O1 is the short side wrap angle of the male rotor, that is, the angle between the straight line O2G and the straight line O1O2; Z1 is the number of teeth on the male rotor, and Z2 is the number of teeth on the female rotor. Therefore: ∠O2O1H+∠NO1O2= 360° / Z1, ∠AO₂O₁ + ∠GO₂O₁ = 360° / Z² ∠AO₂O₁:∠O₂O₁H=Z₂:Z₁, ∠GO2O1:∠NO1O2 =Z2:Z1 R1t=A×Z1 / (Z1+Z2), R2t=A×Z2 / (Z1+Z2).

6. The rotor profile of the oil-free twin-screw compressor according to claim 1, characterized in that: The tooth ratio Z1:Z2 between the male rotor and the female rotor is 4-6:5-8.

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