Arc envelope rotor tooth profile structure, design method and positive displacement flowmeter

Abstract

The present application relates to the technical field of fluid measurement, and provides a circular arc envelope rotor tooth profile structure, a design method and a positive displacement flowmeter. The tooth profile structure comprises a first rotor and a second rotor arranged in pairs. The tooth profiles of the first rotor and the second rotor each comprise a circular arc envelope segment and a circular arc segment. The circular arc envelope segment of the first rotor and the circular arc segment of the second rotor are conjugate trajectories of each other, and the circular arc segment of the first rotor and the circular arc envelope segment of the second rotor are conjugate trajectories of each other. The circular arc segment is arranged at the joint position of the tooth profile and the reference base circle or the outer circle reference surface. The radius of the circular arc segment is u, and the circular arc envelope segment is derived according to the circular arc segment through a conjugate motion relationship. The present application replaces the traditional acute angle sharp corner with a parameterized transition circular arc, thereby solving the stress concentration problem at the joint of the rotor tooth profile from the structure, avoiding fatigue cracks, corner collapse and fracture problems during the operation of the rotor, and greatly improving the structural strength and service life of the rotor.

Description

Technical Field

[0001] This invention relates to the field of fluid measurement technology, and in particular to a circular arc envelope rotor tooth profile structure, design method, and volumetric flow meter. Background Technology

[0002] Cycloidal tooth profiles, as classic conjugate meshing tooth profiles, are widely used in the instrumentation industry. Their formation principle is based on the trajectory of a point fixed on a circle as it rolls purely on one circle. Existing cycloidal rotor structures all follow the traditional cycloidal formation theory in their design. In practical engineering applications, the intersection of the cycloid with the outer circular reference plane and the mating rolling circle will form a geometrically acute angle.

[0003] To ensure motion accuracy and thus instrument precision, the instrumentation industry generally accepts this structural defect. Currently, it cannot be eliminated through simple subsequent machining, because such machining would increase the movement clearance by the same amount as the chamfer, thus failing to meet design requirements. Retaining this defect will cause a series of technical problems during rotor operation: Firstly, there is a significant stress concentration effect at sharp corners. Even if the rotor is operating independently at low speed, without load, and without contact, the centrifugal force and alternating stress generated by long-term rotation will still form fatigue microcracks at the sharp corners. As the operating time increases, the cracks gradually expand, eventually leading to rotor corner breakage and fracture, which greatly reduces the reliability and service life of the rotor structure.

[0004] Secondly, sharp angles and corners are prone to cracking, chipping, and dimensional deviations during the machining and heat treatment processes of parts due to uneven local heat dissipation rates and concentrated stress. This increases the scrap rate of parts and raises production costs.

[0005] Thirdly, sharp angles can easily cause injury during the production, storage, transportation, assembly, and maintenance of parts.

[0006] To address the shortcomings of existing technologies, the industry currently lacks a method that allows for flexible adjustment of transition fillet parameters and the derivation of its conjugate curve based on the fillet. Therefore, a method and structure capable of solving these problems is urgently needed. Summary of the Invention

[0007] The purpose of this invention is to solve a series of mechanical problems caused by the forced retention of sharp angles in the tooth profile of traditional cycloidal rotors to ensure motion accuracy. This invention provides a circular arc envelope rotor tooth profile structure, design method, and volumetric flow meter. By replacing traditional geometric sharp angles with parametric circular arcs, and deriving the circular arc envelope from the arcs, mechanical defects are eliminated while ensuring overall machine accuracy, improving rotor structural strength and service life, and adapting to flexible design requirements under different operating conditions. Details are as follows: This invention provides a circular arc envelope rotor tooth profile structure, including a first rotor and a second rotor arranged in pairs. Both the first rotor and the second rotor are provided with teeth, and the teeth of the first rotor and the second rotor are arranged in the same way. The tooth profile of the first rotor includes a circular arc envelope segment and a circular arc segment, and the tooth profile of the second rotor also includes a circular arc envelope segment and a circular arc segment. The circular arc envelope segment of the first rotor and the circular arc segment of the second rotor are conjugate trajectories, and the circular arc segment of the first rotor and the circular arc envelope segment of the second rotor are conjugate trajectories. The circular arc segment is located at the intersection of the tooth profile and the reference pitch circle or the outer circular reference surface. The radius of the circular arc segment is u, and the circular arc envelope segment is derived from the circular arc segment through the conjugate motion relationship.

[0008] According to the circular arc envelope rotor tooth profile structure provided by the present invention, the coordinate derivation equation of the circular arc envelope segment is as follows: ; ; ; Where r and r1 are the rolling circle radii of the first rotor and the second rotor, respectively, a is the distance from the center of the arc segment to the center of the rotor in which it is located, u is the radius of the arc segment, φ is the angle of rotation of the second rotor around the first rotor, and β is the angle between the line connecting the tangent point and the center of the arc with radius u, and the line connecting the centers of the two rotors.

[0009] According to the circular arc envelope rotor tooth profile structure provided by the present invention, the circular arc segment is connected to the circular arc envelope segment and the reference pitch circle by a tangential connection.

[0010] According to the circular arc envelope rotor tooth profile structure provided by the present invention, both the first rotor and the second rotor include a first circular arc envelope, a second circular arc envelope, and a third circular arc envelope, and both the first rotor and the second rotor include a first circular arc segment, a second circular arc segment, and a third circular arc segment; wherein, the first circular arc envelope of the first rotor is the conjugate trajectory of the first circular arc segment of the second rotor; the second circular arc envelope of the first rotor is the conjugate trajectory of the second circular arc segment of the second rotor; the third circular arc envelope of the first rotor is the conjugate trajectory of the third circular arc segment of the second rotor; the first circular arc envelope of the second rotor is the conjugate trajectory of the first circular arc segment of the first rotor; the second circular arc envelope of the second rotor is the conjugate trajectory of the second circular arc segment of the first rotor; and the third circular arc envelope of the second rotor is the conjugate trajectory of the third circular arc segment of the first rotor.

[0011] According to the circular arc envelope rotor tooth profile structure provided by the present invention, the inner edge profile of the tooth portion includes a first circular arc envelope and a second circular arc envelope, the outer edge profile of the tooth portion includes a third circular arc envelope, the root profile of the tooth portion is a root circular arc, and the tip profile of the tooth portion is a tip circular arc; wherein, the termination point of the first circular arc envelope is connected to the first endpoint of the tip circular arc by a first circular arc segment; the termination point of the third circular arc envelope is connected to the second endpoint of the tip circular arc by a third circular arc segment, and the termination point of the second circular arc envelope is connected to the rotor base by a second circular arc segment.

[0012] According to the circular arc envelope rotor tooth profile structure provided by the present invention, the tooth profiles of the teeth are tangentially connected at the junction position by a transition circular arc.

[0013] According to the circular arc envelope rotor tooth profile structure provided by the present invention, the axes of the first rotor and the second rotor are arranged horizontally.

[0014] The present invention also provides a design method for generating the above-mentioned circular arc envelope rotor tooth profile structure, comprising the following steps: Step S1: Determine the basic parameters of the rotor tooth profile and identify the geometric sharp angle at the intersection of the tooth profile and the reference pitch circle or outer circle reference surface; Step S2: Based on the expected operating conditions of the rotor, pre-select the radius u of the arc segment so that the arc segment replaces the geometric sharp angle identified in step S1; Step S3: Using the arc segment selected in step S2 as the component curve of the tooth profile, derive the arc envelope segment of the arc segment on the conjugate rotor according to the derivation equation of conjugate kinematics. Step S4: The arc segment and the arc envelope segment are respectively set on the first rotor and the second rotor in such a way that they are connected tangentially at the tangent point to form a complete conjugate tooth profile pair; In step S2, the radius u selected is used as a design variable and substituted into the derived equation in step S3 for solution, so that the arc segment and the arc envelope segment are set as conjugates, and the meshing clearance between them is the same as the theoretical meshing clearance of the tooth profile.

[0015] The present invention also provides a volumetric flow meter, comprising: case; The first rotor and the second rotor are disposed within the housing, and the first rotor and the second rotor have the circular arc envelope rotor tooth profile structure provided above.

[0016] This invention provides a circular arc envelope rotor tooth profile structure, design method, and volumetric flow meter. By replacing the traditional sharp angles with parameterized transition arcs, it structurally solves the stress concentration problem at the junction of rotor tooth profiles, avoids fatigue cracks, chipping, and fracture during rotor operation, and significantly improves the structural strength and service life of the rotor. Attached Figure Description

[0017] To more clearly illustrate the technical solutions in this invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0018] Figure 1 This is one of the schematic diagrams of the circular arc envelope rotor tooth profile structure provided by the present invention.

[0019] Figure 2 This is the second schematic diagram of the circular arc envelope rotor tooth profile structure provided by the present invention.

[0020] Figure 3 This is a flowchart illustrating the design method of the circular arc envelope rotor tooth profile structure provided by the present invention.

[0021] Figure label: 10. First rotor; 11. First circular arc envelope; 111. First circular arc segment; 12. Second circular arc envelope; 121. Second circular arc segment; 13. Third circular arc envelope; 131. Third circular arc segment; 14. Tooth tip circular arc; 20. Second rotor. Detailed Implementation

[0022] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0023] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains; the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the application; the terms “comprising” and “having”, and any variations thereof, in the specification, claims, and foregoing description of the drawings are intended to cover non-exclusive inclusion.

[0024] In the description of the embodiments of this application, technical terms such as "first" and "second" are used only to distinguish different objects and should not be construed as indicating or implying relative importance or implicitly specifying the number, specific order, or primary and secondary relationship of the indicated technical features. In the description of the embodiments of this application, "multiple" means two or more, unless otherwise explicitly defined.

[0025] In this document, the term "embodiment" means that a particular feature, structure, or characteristic described in connection with an embodiment may be included in at least one embodiment of this application. The appearance of this phrase in various places throughout the specification does not necessarily refer to the same embodiment, nor is it a separate or alternative embodiment mutually exclusive with other embodiments. It will be explicitly and implicitly understood by those skilled in the art that the embodiments described herein can be combined with other embodiments.

[0026] In the description of the embodiments of this application, the technical terms "center," "longitudinal," "lateral," "length," "width," "thickness," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," "outer," "clockwise," "counterclockwise," "axial," "radial," and "circumferential" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are only for the convenience of describing the embodiments of this application and simplifying the description, and are not intended to indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on the embodiments of this application.

[0027] In the description of the embodiments of this application, unless otherwise expressly specified and limited, technical terms such as "installation," "connection," "joining," "fixing," and "corresponding" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral part; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; they can refer to the internal communication of two components or the interaction between two components. Those skilled in the art can understand the specific meaning of the above terms in the embodiments of this application according to the specific circumstances.

[0028] In related technologies, the tooth profile of the cycloidal rotor structure (i.e., the tooth profile of the cycloidal tooth) and the intersection of the outer circular reference surface and the mating rolling circle form geometrically acute angles. The structure of the acute angles leads to a significant stress concentration effect, which in turn causes a series of mechanical problems.

[0029] Regarding the problems in related technologies, such as Figures 1 to 2As shown, the present invention provides a circular arc envelope rotor tooth profile structure, including a first rotor 10 and a second rotor 20 arranged in pairs. Both the first rotor 10 and the second rotor 20 are provided with teeth, and the teeth of the first rotor 10 and the teeth of the second rotor 20 are arranged in the same way. The tooth profile of the first rotor 10 includes a circular arc envelope segment and a circular arc segment, and the tooth profile of the second rotor 20 includes a circular arc envelope segment and a circular arc segment. The circular arc envelope segment of the first rotor 10 and the circular arc segment of the second rotor 20 are conjugate trajectories, and the circular arc segment of the first rotor 10 and the circular arc envelope segment of the second rotor 20 are conjugate trajectories. The circular arc segment is located at the intersection of the tooth profile of the tooth and the reference pitch circle or the outer circle reference surface. The radius of the circular arc segment is u, and the circular arc envelope segment is derived from the circular arc segment through the conjugate motion relationship.

[0030] Traditional cycloidal rotors exhibit sharp, geometrically acute angles at their intersections with the reference pitch circle and outer datum surface. These angles create significant stress concentration effects. Even under low-speed, unloaded, and contactless independent operation, the centrifugal force and alternating stress generated by long-term rotation can still lead to fatigue microcracks at these angles. As operating time increases, these cracks gradually propagate, eventually causing the rotor to chip and break. Furthermore, these sharp angles are highly susceptible to cracking, edge chipping, and dimensional deviations during machining and heat treatment due to uneven local heat dissipation and stress concentration. While eliminating these sharp angles through chamfering or rounding later can reduce the flow meter's measurement accuracy by increasing the meshing clearance, this can also lead to a decrease in accuracy.

[0031] In this embodiment, an arc segment with radius u is set at the intersection of the tooth profile and the reference pitch circle or outer circular reference surface. This arc segment is used as a pre-design unit, and the arc envelope segment is derived through conjugate motion relationships, so that the arc segment and the arc envelope segment form a complete conjugate meshing pair. This arc segment participates in the conjugate meshing calculation as a component of the tooth profile during the parametric design stage of the rotor tooth profile, rather than requiring post-processing modification of the already formed tooth profile. This structurally avoids the mechanical problems caused by sharp angles.

[0032] Specifically, both the first rotor 10 and the second rotor 20 are screw rotors with their axes parallel to each other. A preset center distance (r + r1, where r is the radius of the first rotor 10 and r1 is the radius of the second rotor 20) is maintained between the first rotor 10 and the second rotor 20. The tooth profiles of the first rotor 10 and the second rotor 20 extend helically along the rotor axis to form complete teeth. In specific embodiments, r and r1 can be set to be equal or unequal, and the specific values ​​are selected as needed.

[0033] The first rotor 10 and the second rotor 20 each have one tooth, which is formed by a spiral. The arc segment of the tooth is located at the intersection of the tooth profile and the reference pitch circle or outer circumference surface. One end of the arc segment is tangentially connected to the tooth profile, and the other end is tangentially connected to the reference pitch circle or outer circumference surface, forming a smooth transition continuous curved surface.

[0034] The circular arc envelope segment is the trajectory of the circular arc segment on the conjugate rotor, and its shape is determined by the radius u of the circular arc segment and the conjugate motion parameters of the rotor. In this embodiment, both the circular arc segment and the circular arc envelope segment are component curve segments that constitute the tooth profile, and together they replace the geometric sharp corner structures that originally existed in the traditional tooth profile.

[0035] Understandably, by placing the arc segment at the intersection of the tooth profile and the reference pitch circle or outer circular reference surface, the original sharp-angled geometric structure is replaced by the arc segment, thus eliminating the geometric conditions for stress concentration. Simultaneously, since the arc envelope segment is derived from the arc segment through conjugate motion relations, and the two are strictly conjugate, the meshing clearance between the arc segment and the arc envelope segment remains consistent with the theoretical meshing clearance of the original tooth profile. This prevents an additional increase in meshing clearance due to the elimination of sharp corners, thereby ensuring that the flowmeter's measurement accuracy is not affected.

[0036] Specifically, the coordinate derivation equation of the circular arc envelope segment is as follows: ; ; ; Where r and r1 are the rolling circle radii of the first rotor 10 and the second rotor 20, respectively, a is the distance from the center of the arc segment to the center of the rotor circle, u is the radius of the arc segment, φ is the rolling angle, and β is the angle between the line connecting the tangent point and the center of the arc with radius u, and the line connecting the centers of the two rotors.

[0037] Where φ is the independent variable (its change reflects the relative rolling of the two circles), a, r, r1, and u are user-defined parameters determined before design. β is an introduced variable, which is determined by the above formula.

[0038] In this embodiment, the derivation of the circular arc envelope segment is based on the principle of conjugate kinematics. Taking the first rotor 10 as a reference (stationary), the motion trajectory of the second rotor 20 and the circular arc segment on it is studied.

[0039] At this point, the motion becomes the second rotor 20 rolling around the first rotor 10. The motion can be decomposed into: the second rotor 20 rotating around the center O of the first rotor 10 (rotation speed w), and the second rotor 20 rotating around its own center O1 (rotation speed w1). The motion relationship satisfies w·r=w1·r1.

[0040] During the rolling process, the rolling circles of the two rotors are tangent to each other at point P.

[0041] Connect point P to the center O2 of the arc segment, and extend the line to intersect the arc at point P1. The trajectory of point P1 is the envelope segment of the arc.

[0042] The variables are defined as follows: φ is the angle of rotation of the second rotor 20 around the center of the first rotor 10; φ1 is the rotation angle of the second rotor 20, which can be obtained from the kinematic relationship as φ1=φ·r / r1; L is the length from the rolling circle tangent point P of the two rotors to the center O2 of the arc segment on the second rotor 4; β is the angle of ∠O1PO2.

[0043] Based on geometric relationships, we have: L = ; After simplification, we get: cos(β) = (r1 - a·cos(φ1)) / L. From this, we derive the expressions for the X and Y coordinates of the circular envelope segment mentioned above. Specifically, the steps are as follows: Step 1: Determine the design parameters, such as the radii r and r1 of the two rolling circles, the center distance r + r1; the distance a and radius u of the arc on the moving circle from the center, the radius a + u of the moving circle's addendum circle, and the radius r + r1 - (a + u) of the fixed circle's root circle. Step 2: According to the formula, calculate the circular envelope on the fixed circle and extract the required portion. Step 3: Exchange the settings of the fixed circle (e.g., the first rotor 10) and the moving circle (e.g., the second rotor 20), and repeat the above steps to complete the tooth profiles of the first and second rotors. When r = r1, the remaining parameters are consistent, the two rotors are symmetrical, and only one formula is needed to generate the circular envelope; the rest can be obtained through translation, rotation, or mirroring.

[0044] It is understandable that, through the coordinate derivation equations described above, the shape of the circular envelope segment is jointly determined by the radius u of the circular arc segment and the conjugate motion parameters (r, r1, a, φ) of the rotor. Among these, u, as an independent variable, directly determines the specific shape and position of the generated circular envelope segment. When the value of u changes, the curvature and position of the circular envelope segment change accordingly, but its conjugate relationship with the circular arc segment remains unchanged, thus ensuring that the meshing clearance is the theoretical clearance under different u values.

[0045] Specifically, the arc segment, the arc envelope segment, and the reference pitch circle are connected by a tangent point. A tangent point connection means that the arc segment and the arc envelope segment have a common tangent direction at the connection point, achieving a first-order smooth connection.

[0046] Similarly, the arc segment and the reference pitch circle share the same tangent direction at the connection point. Specifically, the first end of the arc segment is tangentially connected to the root of the tooth profile, the second end of the arc segment is tangentially connected to the reference pitch circle, one end of the arc envelope segment is tangentially connected to the arc segment, and the other end of the arc envelope segment is tangentially connected to other tooth profile curve segments (such as the tooth root arc).

[0047] Understandably, by connecting the tangential points, the entire tooth profile forms a smooth and continuous curved surface, without any sharp points or non-smooth connection points. This not only improves the stress distribution of the tooth profile and avoids stress concentration at sharp points, but also reduces the flow resistance of gas or liquid on the tooth profile surface, thus improving the metering stability of the flow meter. At the same time, the tangential connection ensures a continuous transition between each curve segment, avoiding additional meshing clearance caused by non-smooth connection points.

[0048] Specifically, theoretically, the radius u of the circular arc segment only needs to be greater than 0. When u = 0, the curve degenerates into a cycloid state, forming an acute angle. When u is between 0 and 0.5, the stress-relieving effect is relatively insignificant. The remaining values ​​depend on the actual usage.

[0049] Finite element simulations have verified that geometrically sharp-cornered structures exhibit a "stress singularity" phenomenon in theoretical mechanics and finite element simulations—when the radius of curvature approaches zero, the theoretical stress tends to be infinitely large, and the finer the mesh, the greater the calculated stress value and the non-convergence. Although real materials do not withstand infinitely large stresses, extreme stress concentration points will form at this structure, where the force converges and is amplified by tens of times.

[0050] Specifically, when u=0.5, the stress at the arc segment is amplified by a factor of 2 compared to the geometrically sharp corner structure; when u=1, the stress at the arc segment is not amplified compared to the geometrically sharp corner structure; when u=2, the stress at the arc segment is reduced by 30% compared to the geometrically sharp corner structure; and when u=4, the stress at the arc segment is reduced by 50% compared to the geometrically sharp corner structure. That is, within the u value range of 0.5mm to 4mm, the stress concentration factor at the arc segment is at least not amplified compared to the geometrically sharp corner structure, and the stress gradually decreases as the u value increases.

[0051] It should be understood that the values ​​of u in the above examples are merely illustrative and not a limitation on the value of u. The meshing clearance between the arc segment and the arc envelope segment always remains at the theoretical meshing clearance and does not change with the value of u.

[0052] Understandably, by setting the radius u of the arc segment within the range of 0.5mm to 4mm, the stress concentration problem caused by the geometric sharp corners can be effectively eliminated while maintaining the meshing clearance, thus achieving the technical effect of both stress elimination and accuracy maintenance.

[0053] Designers can flexibly select the u-value within this range according to specific operating conditions. For example, for low-speed, no-load, and non-contact operating conditions, a smaller value (such as 0.5mm to 1.5mm) can be selected to minimize the impact on the tooth profile shape while ensuring the elimination of sharp corners; for high-speed or loaded operating conditions, a larger value (such as 2mm to 4mm) can be selected to prioritize structural strength. In practical applications, the smaller the u-value, the closer the arc envelope is to the theoretical conjugate trajectory of the original tooth profile, and the better the design accuracy retention of the flow meter; the larger the u-value, the smoother the arc transition, the more significant the stress relief effect, and the higher the structural strength of the rotor.

[0054] In specific settings, such as Figure 1 As shown, both the first rotor 10 and the second rotor 20 include a first circular arc envelope 11, a second circular arc envelope 12, and a third circular arc envelope 13. Both the first rotor 10 and the second rotor 20 also include a first circular arc segment 111, a second circular arc segment 121, and a third circular arc segment 131. The first circular arc envelope 11 of the first rotor 10 is the conjugate trajectory of the first circular arc segment 111 of the second rotor 20; the second circular arc envelope 12 of the first rotor 10 is the second circular arc segment 131 of the second rotor 20. The conjugate trajectory of arc segment 121; the third circular arc envelope 13 of the first rotor 10 is the conjugate trajectory of the third circular arc segment 131 of the second rotor 20; the first circular arc envelope 11 of the second rotor 20 is the conjugate trajectory of the first circular arc segment 111 of the first rotor 10; the second circular arc envelope 12 of the second rotor 20 is the conjugate trajectory of the second circular arc segment 121 of the first rotor 10; the third circular arc envelope 13 of the second rotor 20 is the conjugate trajectory of the third circular arc segment 131 of the first rotor 10.

[0055] In this embodiment, each tooth of the first rotor 10 and the second rotor 20 is provided with three arc segments and three corresponding arc envelope segments. The first arc segment 111, the second arc segment 121, and the third arc segment 131 are respectively located at different positions on the tooth: the first arc segment 111 is located at the junction of the inner side of the tooth profile and the tooth tip, the second arc segment 121 is located at the junction of the inner side of the tooth profile and the tooth root, and the third arc segment 131 is located at the junction of the outer side of the tooth profile and the tooth tip. Correspondingly, the first arc envelope 11 is the motion trajectory of the first arc segment 111 on the conjugate rotor, the second arc envelope 12 is the motion trajectory of the second arc segment 121 on the conjugate rotor, and the third arc envelope 13 is the motion trajectory of the third arc segment 131 on the conjugate rotor.

[0056] Understandably, by setting arc segments at multiple junctions in the teeth, all junctions that might otherwise have sharp geometric angles are replaced by arc segments, effectively eliminating the risk of stress concentration. Simultaneously, each arc segment has its corresponding arc envelope derived through conjugate motion relationships, ensuring that each meshing pair maintains the theoretical meshing clearance, thus maintaining consistent accuracy throughout the entire meshing cycle.

[0057] Specifically, such as Figure 1 As shown, the inner profile of the tooth portion includes a first circular arc envelope 11 and a second circular arc envelope 12, the outer profile of the tooth portion includes a third circular arc envelope 13, the root profile of the tooth portion is a root arc, and the tip profile of the tooth portion is a tip arc 14. The termination point of the first circular arc envelope 11 is connected to the first endpoint of the tip arc 14 via a first circular arc segment 111; the termination point of the third circular arc envelope 13 is connected to the second endpoint of the tip arc 14 via a third circular arc segment 131; and the termination point of the second circular arc envelope 12 is connected to the rotor base via a second circular arc segment 121.

[0058] In this embodiment, the complete tooth profile is formed by the following line segments connected end to end in sequence. Taking the first rotor 10 as an example, as follows... Figure 1 As shown, Figure 1 Points P1 to P9 are the connection points of each curve segment, arranged in a clockwise direction as follows: The starting point P1 of the third circular envelope 13 is connected to the outer circular reference surface of the rotor (this is a non-circular transition connection, that is, the starting end of the third circular envelope 13 directly starts from the outer circular reference surface of the rotor); the ending point P2 of the third circular envelope 13 is connected to the starting point P2 of the third circular segment 131 (the two are tangentially connected); the ending point P3 of the third circular segment 131 is connected to the starting point P3 of the tooth tip circular arc 14 (the two are tangentially connected); the ending point P4 of the tooth tip circular arc 14 is connected to the starting point P4 of the first circular segment 111 (the two are tangentially connected); the first circular... The termination point P5 of arc segment 111 is connected to the starting point P5 of the first circular arc envelope 11 (the two are tangentially connected); the termination point P6 of the first circular arc envelope 11 coincides with the starting point P7 of the second circular arc envelope 12, and the two are tangentially connected to the inner circumferential surface of the rotor at this coincidence point; the termination point P8 of the second circular arc envelope 12 is connected to the starting point P8 of the second circular arc segment 121 (the two are tangentially connected); the termination point P9 of the second circular arc segment 121 is connected to the outer circular reference surface of the rotor (the two are tangentially connected), thus completing the tooth profile closure of a complete tooth.

[0059] In other words, starting from the starting point P1 of the third circular envelope 13 (starting from the outer circular reference plane), the tooth passes through the following in a clockwise direction: the third circular envelope 13, the third circular segment 131, the tooth tip circular arc 14, the first circular segment 111, the first circular envelope 11, the second circular envelope 12 (where the end point of the first circular envelope 11 and the starting point of the second circular envelope 12 coincide and are tangent on the inner circumference of the rotor), and the second circular segment 121, finally returning to the outer circular reference plane to form a complete closed tooth profile.

[0060] The first circular arc envelope 11 and the second circular arc envelope 12 are located on the inner side of the tooth (i.e., the side of the tooth profile facing radially inward), and their connection point is tangent to the inner circumferential surface of the rotor. The third circular arc envelope 13 is located on the outer side of the tooth (i.e., the side of the tooth profile facing radially outward), and it originates from the outer circular reference surface. The third circular arc segment 131 is disposed between the third circular arc envelope 13 and the tooth tip circular arc 14, serving as a smooth transition connection. The first circular arc segment 111 is disposed between the tooth tip circular arc 14 and the first circular arc envelope 11, serving as a smooth transition connection. The second circular arc segment 121 is disposed between the second circular arc envelope 12 and the outer circular reference surface, serving as a smooth transition connection.

[0061] Understandably, through the combination of the aforementioned tooth profile segments, the entire tooth profile is composed of continuous circular arc segments and circular arc envelope segments. Except for the starting end of the third circular arc envelope 13, which intersects and connects with the outer circular reference plane, all other segments are connected tangently at their points of contact, forming a complete and smooth continuous curved surface. This tooth profile structure has no geometrical sharp corners or rough connection points, fundamentally eliminating the risk of stress concentration and machining cracking.

[0062] Specifically, the tooth profiles of the tooth are tangentially connected at the junction by transition arcs. In this application, "junction" refers to the boundary between different curve segments in the tooth profile, including but not limited to: the junction between the tooth profile and the reference pitch circle, the junction between the tooth profile and the outer circular reference surface, the junction between the inner side of the tooth profile and the tooth tip, the junction between the inner side of the tooth profile and the tooth root, and the junction between the outer side of the tooth profile and the tooth tip.

[0063] The transition arc, also known as the aforementioned arc segment, has a radius of u and is positioned at each of the above-mentioned intersection points, replacing the original geometric sharp angle structure. The two ends of the transition arc are tangent to the adjacent curve segments at their respective points, ensuring the smooth continuity of the entire tooth profile.

[0064] Understandably, by setting transition arcs at all intersections of the tooth profile, the entire tooth profile is free of stress concentration points, thereby significantly improving the rotor's structural strength and service life. Furthermore, the radius u of all transition arcs can be flexibly selected according to operating conditions, forming a universal design method.

[0065] Specifically, the axes of the first rotor 10 and the second rotor 20 are horizontally aligned. The axes of the first rotor 10 and the second rotor 20 are parallel to each other and both extend horizontally. Both the first rotor 10 and the second rotor 20 are rotatably supported within the flowmeter housing by bearings (preferably deep groove ball bearings). Synchronizing gears (preferably helical gears) are respectively provided at the ends of the first rotor 10 and the second rotor 20. The two synchronizing gears mesh with each other to ensure that the first rotor 10 and the second rotor 20 remain synchronized and do not contact each other during rotation. A sealed cavity is formed between the first rotor 10 and the second rotor 20 and the inner wall of the housing. The sealed cavity has a fixed volume, and the measured medium enters the flowmeter and drives the rotor to rotate.

[0066] Understandably, by setting the axes of the first rotor 10 and the second rotor 20 horizontally, the axial dimension of the flow meter can be effectively reduced, making the structure more compact. At the same time, a horizontally set axis facilitates smooth flow of the measured medium, reduces flow resistance, and improves measurement accuracy.

[0067] Regarding the problems in related technologies, such as Figure 3 As shown, the present invention provides a design method for a rotor tooth profile structure with an arc envelope, comprising the following steps: Step S1: Determine the basic parameters of the rotor tooth profile and identify the geometric sharp angles at the intersection of the tooth profile and the reference pitch circle or outer circle reference surface.

[0068] In this step, the basic parameters of the rotor tooth profile are first determined based on the design displacement and accuracy requirements of the flow meter. These parameters include, but are not limited to: rolling circle radii r and r1, center distance d = r + r1, and the distance a from the center of the arc of radius u to the center of the rotor. The addendum circle radius of the tooth containing u is a + u, and the root circle radius of the other tooth is d - (a + u). Another pair of parameters is determined by another pair of conjugate curves and arcs. The circle containing the arc determines the addendum circle radius. The circle containing the conjugate curve determines the root circle radius. In practical applications, the first rotor 10 and the second rotor 20 are the same size and symmetrically arranged, so they can be determined in one step. Then, the theoretical curve of the tooth profile is generated based on the above basic parameters, and the intersection position of the tooth profile with the reference pitch circle or outer circle reference surface is identified. At these intersection positions, since the tooth profile intersects or is tangential to the pitch circle or outer circle, geometric sharp angles with curvature radii approaching zero will be formed. The specific positions and dimensions of these geometric sharp angles are determined through geometric analysis or computer-aided design software.

[0069] Step S2: Based on the expected operating conditions of the rotor, pre-select the radius u of the arc segment so that the arc segment replaces the geometric sharp corner identified in step S1.

[0070] In this step, the radius u of the arc segment is pre-selected based on the rotor's expected operating conditions (including speed, load state, contact type, etc.). Specifically, for low-speed, no-load, and no-contact operating conditions, the value of u is preferably 0.5mm to 1.5mm (e.g., u=0.5 or u=1.0), minimizing the impact on the tooth profile shape while ensuring the elimination of sharp corners; for high-speed or loaded operating conditions, the value of u is preferably 2mm to 4mm (e.g., u=2 or u=4), prioritizing structural strength. The selected u value serves as a design variable and will directly participate in the derivation and calculation of the arc envelope segment in step S3. Unlike later shaping, the u value in this step is predetermined during the tooth profile parametric design stage, rather than being used to chamfer or round the sharp corners after the rotor is machined.

[0071] Step S3: Using the circular arc segment selected in step S2 as the component curve of the tooth profile, derive the circular arc envelope segment on the conjugate rotor based on the derivation equation of conjugate kinematics.

[0072] In this step, the arc segment selected in step S2 is used as the constituent curve of the tooth profile, and it is set at the geometric apex position identified in step S1, replacing the original apex structure. Then, using this arc segment as the parent curve, based on the principle of conjugate kinematics (i.e., when two rotors are performing pure rolling motion, the trajectory of the curve on one rotor on the other rotor is the conjugate curve), the arc envelope segment on the conjugate rotor is derived. The specific derivation process is as described above, using coordinate derivation equations, where u is substituted into the equation as the radius value selected in step S2, directly determining the shape and position of the generated arc envelope segment.

[0073] Step S4: The arc segment and the arc envelope segment are respectively set on the first rotor 10 and the second rotor 20 in such a way that they are connected tangently at the tangent point to form a complete conjugate tooth profile pair.

[0074] In step S2, the radius u selected is used as a design variable and substituted into the derived equation in step S3 for solution, so that the arc segment and the arc envelope segment are set as conjugates, and the meshing clearance between them is the same as the theoretical meshing clearance of the tooth profile.

[0075] In this step, the arc segment selected in step S2 is placed at the sharp corner of the tooth profile of the first rotor 10, and the arc envelope segment derived in step S3 is placed at the corresponding position of the second rotor 20, with the arc segment and the arc envelope segment connected tangently at the connection point. This process is repeated, replacing all sharp corner positions of the first rotor 10 and the second rotor 20 with arc segments and their corresponding arc envelope segments, forming a complete conjugate tooth profile pair. In the resulting tooth profile, the meshing clearance between the arc segment and the arc envelope segment is the same as the theoretical meshing clearance of the original tooth profile.

[0076] Understandably, through the above design method, the u-value is selected during the parametric design stage of the tooth profile and participates in the derivation and calculation of the circular envelope segment, ensuring that the circular arc segment and the circular envelope segment are strictly conjugate mathematically. Therefore, changes in the u-value will not alter the meshing clearance between the circular arc segment and the circular envelope segment; this meshing clearance always remains at the theoretical meshing clearance. This overcomes the technical contradiction that subsequent profile modification inevitably results in a loss of accuracy. Furthermore, designers can flexibly select the u-value according to different working conditions, giving this design method good versatility and adaptability to various working conditions.

[0077] To address the problems in related technologies, the present invention provides a volumetric flow meter, including a housing and a first rotor 10 and a second rotor 20 disposed within the housing. The first rotor 10 and the second rotor 20 have the circular arc envelope rotor tooth profile structure as described above.

[0078] Understandably, since the first rotor 10 and the second rotor 20 adopt the circular arc envelope rotor tooth profile structure as described above, there are no geometric sharp corners on their tooth profiles. Therefore, problems such as fatigue cracks, chipping, and fracture caused by stress concentration at sharp corners will not occur, significantly improving the service life and reliability of the rotors. At the same time, since the theoretical meshing clearance is always maintained between the circular arc segment and the circular arc envelope segment, the metering accuracy of the flowmeter will not decrease due to the elimination of sharp corners, thus achieving both high reliability and high accuracy. Through the above description of the embodiments, those skilled in the art can clearly understand that each embodiment has the following beneficial effects: First, it completely eliminates the hidden danger of stress concentration: by replacing the traditional sharp corners with parametric transition arcs, it solves the problem of stress concentration at the junction of rotor tooth profiles from the structural root, avoids fatigue cracks, chipping, and fracture during rotor operation, and greatly improves the structural strength and service life of the rotor under low-speed non-contact conditions.

[0079] Second, ensure the overall design accuracy: the transition arc and the arc envelope rotor tooth profile and the reference circle are connected by tangent points, and the resulting arc-like envelope composite tooth profile completely obtains the real motion trajectory without adding extra meshing clearance or trajectory deviation. Compared with the traditional fixed fillets and process chamfers, it completely solves the technical contradiction of shape modification affecting accuracy.

[0080] Third, the design is flexible and versatile: the transition arc radius is defined by a variable parameter (u), which eliminates the limitation of fixed size. Designers can independently select the value of (u) according to different rotor sizes and operating conditions to form a set of universal rotor tooth profile optimization design schemes that can adapt to the application needs of multiple scenarios.

[0081] Fourth, optimized machining process: The smooth, rounded transition structure avoids sharp corner chipping and quenching cracking during machining and heat treatment, reducing the scrap rate of parts, simplifying the production process, and improving product qualification rate and production efficiency. Specifically, in actual comparative tests, the first-pass yield rate (the rate of products that achieve design accuracy on the first inspection) for products retaining the geometric sharp corner structure is approximately 81%. Products using the technical solution of this application have a first-pass yield rate of 95%, and the causes of corresponding non-conforming products were investigated, with most being due to abnormalities in other parts. Therefore, the first-pass yield rate of parts machining is significantly improved.

[0082] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; 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; and these 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 circular arc envelope rotor tooth profile structure, comprising a first rotor and a second rotor arranged in pairs, wherein both the first rotor and the second rotor are provided with teeth, and the teeth of the first rotor and the teeth of the second rotor are arranged in the same manner, characterized in that, The tooth profile of the first rotor includes a circular arc envelope segment and a circular arc segment, and the tooth profile of the second rotor includes a circular arc envelope segment and a circular arc segment; The circular arc envelope segment of the first rotor and the circular arc segment of the second rotor are conjugate trajectories. The arc segment is located at the intersection of the tooth profile and the reference pitch circle or outer circle reference surface of the tooth. The radius of the arc segment is u, and the arc envelope segment is derived from the arc segment through the conjugate motion relationship.

2. The circular arc envelope rotor tooth profile structure according to claim 1, characterized in that, The coordinate derivation equation of the circular arc envelope segment is as follows: ； ； ； Where r and r1 are the rolling circle radii of the first rotor and the second rotor, respectively, a is the distance from the center of the arc segment to the center of the rotor in which it is located, u is the radius of the arc segment, φ is the angle of rotation of the second rotor around the first rotor, and β is the angle between the line connecting the tangent point and the center of the arc with radius u, and the line connecting the centers of the two rotors.

3. The circular arc envelope rotor tooth profile structure according to claim 1 or 2, characterized in that, The arc segment is tangent to the arc envelope segment and the reference pitch circle by means of a tangent point connection.

4. The circular arc envelope rotor tooth profile structure according to claim 1, characterized in that, Both the first rotor and the second rotor include a first circular arc envelope, a second circular arc envelope, and a third circular arc envelope, and both the first rotor and the second rotor include a first circular arc segment, a second circular arc segment, and a third circular arc segment; Wherein, the first circular arc envelope of the first rotor is the conjugate trajectory of the first circular arc segment of the second rotor; the second circular arc envelope of the first rotor is the conjugate trajectory of the second circular arc segment of the second rotor; and the third circular arc envelope of the first rotor is the conjugate trajectory of the third circular arc segment of the second rotor. The first circular arc envelope of the second rotor is the conjugate trajectory of the first circular arc segment of the first rotor; the second circular arc envelope of the second rotor is the conjugate trajectory of the second circular arc segment of the first rotor; and the third circular arc envelope of the second rotor is the conjugate trajectory of the third circular arc segment of the first rotor.

5. The circular arc envelope rotor tooth profile structure according to claim 4, characterized in that, The inner edge profile of the tooth portion includes a first circular arc envelope and a second circular arc envelope; the outer edge profile of the tooth portion includes a third circular arc envelope; the root profile of the tooth portion is a root circular arc; and the tip profile of the tooth portion is a tip circular arc. The termination point of the first arc envelope is connected to the first endpoint of the tooth tip arc by a first arc segment; the termination point of the third arc envelope is connected to the second endpoint of the tooth tip arc by a third arc segment; and the termination point of the second arc envelope is connected to the rotor base by a second arc segment.

6. The circular arc envelope rotor tooth profile structure according to claim 4, characterized in that, The tooth profiles of the teeth are tangentially connected at the junction by a transition arc.

7. The circular arc envelope rotor tooth profile structure according to claim 1, characterized in that, The axes of the first rotor and the second rotor are set horizontally.

8. A design method for generating the circular arc envelope rotor tooth profile structure according to any one of claims 1-7, characterized in that, Includes the following steps: Step S1: Determine the basic parameters of the rotor tooth profile and identify the geometric sharp angle at the intersection of the tooth profile and the reference pitch circle or outer circle reference surface; Step S2: Based on the expected operating conditions of the rotor, pre-select the radius u of the arc segment so that the arc segment replaces the geometric sharp angle identified in step S1; Step S3: Using the arc segment selected in step S2 as the component curve of the tooth profile, derive the arc envelope segment of the arc segment on the conjugate rotor according to the derivation equation of conjugate kinematics. Step S4: The arc segment and the arc envelope segment are respectively set on the first rotor and the second rotor in such a way that they are connected tangentially at the tangent point to form a complete conjugate tooth profile pair; In step S2, the radius u selected is used as a design variable and substituted into the derived equation in step S3 for solution, so that the arc segment and the arc envelope segment are set as conjugates, and the meshing clearance between them is the same as the theoretical meshing clearance of the tooth profile.

9. A volumetric flow meter, characterized in that, include: case; A first rotor and a second rotor are disposed within the housing, the first rotor and the second rotor having a circular arc envelope rotor tooth profile structure as described in any one of claims 1 to 7.

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