A single screw pump fixed rotor structure parameter optimization design method

Abstract

This invention relates to the field of single-screw pump structural design technology, and discloses an optimized design method for the stator and rotor structural parameters of a single-screw pump. Based on the target theoretical single-rotor displacement, the proportional relationship between the stator and rotor structures, and the accuracy of parameter values, numerical screening is performed on the eccentricity, rotor cross-sectional diameter, and axial pitch to obtain candidate parameter combinations. Fluid simulation is used to compare the outlet volumetric flow rate and rotor fluid pressure load of each candidate combination to determine the optimal stator and rotor structural parameters. Furthermore, local directional compensation is performed on the stator inner surface according to the radial fluid pressure main load direction of the optimal structure, and the compensation effect is evaluated in conjunction with the geometrically effective flow area, stator-rotor geometric clearance, outlet volumetric flow rate, and radial fluid pressure load. This invention can improve the rationality of stator and rotor structural parameter selection under micro-metering and conveying conditions, and improve the radial fluid pressure load state of the rotor.

Description

Technical Field

[0001] This invention relates to the field of single screw pump structural design technology, specifically to a method for optimizing the design of stator and rotor structural parameters of a single screw pump for micro-metering and conveying applications, and a method for local compensation of the stator internal surface based on the rotor radial fluid pressure load on the basis of the optimized stator and rotor structure. Background Technology

[0002] A single screw pump typically consists of a single-headed helical rotor and a mating double-headed helical stator. When the rotor moves eccentrically within the stator, a working volume cavity that moves axially is formed between the rotor and stator, enabling continuous transport of the medium.

[0003] For micro-metering and conveying applications, the theoretical displacement of a single screw pump is determined by structural parameters such as eccentricity, rotor diameter, and screw pitch. Once the target displacement is determined, the combination of structural parameters that can meet the theoretical displacement requirement is usually not unique, and each structural parameter is also limited by the stator-rotor structural ratio and the accuracy of parameter values. Therefore, it is difficult to directly determine suitable stator-rotor structural parameters based solely on the theoretical displacement.

[0004] Meanwhile, under actual operating conditions with stator-rotor clearance and inlet-outlet pressure difference, even if different parameter combinations have the same or similar theoretical displacement, their actual outlet volumetric flow rate and rotor fluid pressure load may still differ. Especially when the outlet volumetric flow rates of different candidate parameter combinations are relatively close, it is difficult to further determine the optimal structure based solely on flow rate indicators.

[0005] In addition, even with the preferred structure, there may still be a situation where radial fluid pressure loads are concentrated in a specific direction during operation. Further local adjustments to the inner surface of the stator are needed to improve the radial stress state of the rotor, while avoiding significant adverse effects on the effective flow area, stator-rotor clearance, and outlet conveying capacity. Summary of the Invention

[0006] This invention aims to solve the problem that there are many combinations of stator and rotor structural parameters under the condition of target micro displacement, and it is difficult to determine the optimal structure based solely on theoretical displacement. By combining theoretical displacement constraints, structural ratio constraints, parameter value accuracy, numerical traversal, outlet volume flow rate and rotor fluid pressure load for staged screening, the stator and rotor structural parameters suitable for the target working condition are determined.

[0007] Furthermore, the present invention also addresses the problem of radial fluid pressure load concentration in the preferred stator and rotor structure. Under the condition of basically maintaining the effective flow area, the minimum geometric gap between the stator and rotor, and the outlet conveying capacity, local directional compensation is implemented on the inner surface of the stator to improve the radial fluid pressure load state of the rotor.

[0008] To solve the above-mentioned technical problems, the present invention provides an optimization design method for the stator and rotor structural parameters of a single screw pump. The single screw pump includes a single-head helical rotor and a double-head helical stator that cooperates with it. The eccentricity e, the rotor cross-sectional circle diameter D, and the axial pitch t of the stator and rotor helical tooth surfaces are used as the stator and rotor structural parameters to be optimized.

[0009] The optimization design method includes:

[0010] Based on the relationship between the target single-rotor theoretical displacement and the theoretical displacement of the single screw pump, the target structural parameter relationship between the eccentricity e, the rotor cross-sectional circle diameter D, and the axial pitch t is determined.

[0011] Based on the stator and rotor structure ratio constraints and parameter value accuracy constraints, the stator and rotor structure parameters are numerically screened to obtain multiple candidate stator and rotor structure parameter combinations.

[0012] Under the same operating conditions, fluid simulation was performed on the candidate stator and rotor structural parameter combinations to obtain the outlet volume flow rate and rotor fluid pressure load corresponding to each candidate stator and rotor structural parameter combination.

[0013] The candidate stator and rotor structural parameter combinations are screened in stages based on the outlet volume flow rate and rotor fluid pressure load. When the outlet volume flow rates corresponding to multiple candidate stator and rotor structural parameter combinations are relatively close, the rotor fluid pressure load is further compared to determine the preferred stator and rotor structural parameter combination under the target operating condition.

[0014] Furthermore, after determining the preferred combination of stator and rotor structural parameters, the direction of the main radial fluid pressure load is determined based on the rotor radial fluid pressure load of the preferred stator and rotor structure during the stable motion cycle. The local compensation position of the stator inner profile is determined based on the direction of the main radial fluid pressure load. The stator inner profile corresponding to the local compensation position is locally geometrically adjusted. The results of the local geometric adjustment are evaluated based on the effective geometric flow area before and after the local geometric adjustment, the rotor-stator geometric clearance, the outlet volume flow rate, and the rotor radial fluid pressure load, so as to obtain the compensated stator inner profile.

[0015] Beneficial technical effects:

[0016] This invention first uses theoretical displacement relationship, structural proportion relationship and parameter value accuracy to numerically screen the stator and rotor structural parameters, which can narrow down the range of candidate parameters that need to be simulated by fluid. Then, the candidate parameters are further compared by outlet volume flow rate and rotor fluid pressure load, so that the selection of structural parameters takes into account both theoretical displacement and actual flow state.

[0017] By comparing different eccentricity ranges step by step, the parameter range can be further narrowed down and the optimal stator and rotor structure parameters under the target micro-transportation conditions can be determined.

[0018] Based on this, local directional compensation is performed on the inner surface of the stator according to the main load direction of the rotor radial fluid pressure load. The radial fluid pressure load state of the rotor can be improved by maintaining the area, minimum geometric clearance, outlet volume flow rate and radial fluid pressure load. Attached Figure Description

[0019] Figure 1 This is a schematic diagram of the overall structure of the micro-screw pump used in this invention;

[0020] Figure 2 This is a schematic diagram illustrating the formation of the rotor of the single screw pump of the present invention;

[0021] Figure 3 This is a three-dimensional structural schematic diagram of the rotor of the single screw pump of the present invention;

[0022] Figure 4 This is a schematic diagram of the formation of the stator of the single screw pump of the present invention;

[0023] Figure 5 This is a cross-sectional schematic diagram of the stator and rotor assembly model of the single screw pump of the present invention;

[0024] Figure 6 The outlet volumetric flow rate curve is shown when the eccentricity e = 0.88 mm and the rotor speed is 60 r / min.

[0025] Figure 7 The outlet volumetric flow rate curve is shown when the eccentricity e = 0.88 mm and the rotor speed is 240 r / min.

[0026] Figure 8 The outlet volumetric flow rate curve is shown when the eccentricity e = 0.88 mm and the rotor speed is 360 r / min.

[0027] Figure 9 The outlet volumetric flow rate curve is shown when the eccentricity e = 1.25 mm and the rotor speed is 60 r / min.

[0028] Figure 10 The outlet volumetric flow rate curve is shown when the eccentricity e = 1.25 mm and the rotor speed is 240 r / min.

[0029] Figure 11 The outlet volumetric flow rate curve is shown when the eccentricity e = 1.25 mm and the rotor speed is 360 r / min.

[0030] Figure 12The outlet volumetric flow rate curve is shown when the eccentricity e = 1.77 mm and the rotor speed is 60 r / min.

[0031] Figure 13 The outlet volumetric flow rate curve is shown when the eccentricity e = 1.77 mm and the rotor speed is 240 r / min.

[0032] Figure 14 The outlet volumetric flow rate curve is shown when the eccentricity e = 1.77 mm and the rotor speed is 360 r / min.

[0033] Figure 15 The graph shows the variation of the resultant pressure in the X direction of the rotor with simulation time under different combinations of candidate parameters when the eccentricity e = 1.77 mm and the rotor speed is 60 r / min.

[0034] Figure 16 The graph shows the variation of the resultant pressure in the Y direction of the rotor with simulation time under different combinations of candidate parameters when the eccentricity e = 1.77 mm and the rotor speed is 60 r / min.

[0035] Figure 17 The graph shows the variation of the resultant pressure in the Z direction of the rotor with simulation time under different combinations of candidate parameters when the eccentricity e = 1.77 mm and the rotor speed is 60 r / min.

[0036] Figure 18 This is a magnified view of the peak region of the rotor X-direction pressure resultant force within a variation cycle under different combinations of candidate parameters when the eccentricity e = 1.77 mm and the rotor speed is 240 r / min.

[0037] Figure 19 This is a magnified view of the peak region of the rotor Y-direction pressure resultant force within a variation cycle under different combinations of candidate parameters when the eccentricity e=1.77mm and the rotor speed is 240r / min.

[0038] Figure 20 The graph shows the variation of the resultant pressure in the Z direction of the rotor with simulation time under different combinations of candidate parameters when the eccentricity e = 1.77 mm and the rotor speed is 240 r / min.

[0039] Figure 21 This is a magnified view of the peak region of the rotor X-direction pressure resultant force within a variation cycle under different combinations of candidate parameters when the eccentricity e=1.77mm and the rotor speed is 360r / min.

[0040] Figure 22 This is a magnified view of the peak region of the rotor Y-direction pressure resultant force within a variation cycle under different combinations of candidate parameters when the eccentricity e=1.77mm and the rotor speed is 360r / min.

[0041] Figure 23 The graph shows the variation of the resultant pressure in the Z direction of the rotor with simulation time under different combinations of candidate parameters when the eccentricity e = 1.77 mm and the rotor speed is 360 r / min.

[0042] Figure 24 The graph shows the comparison of the change in the outlet volumetric flow rate of the screw pump with simulation time under the condition of rotor speed 240 r / min, when the eccentricity e is in the range of 1.71~1.77 mm.

[0043] Figure label:

[0044] 1-Servo motor; 2-Reducer; 3-Direct connection frame; 4-Seal; 5-Drive shaft; 6-Universal joint; 7-Rotor; 8-Stator; 9-Outlet short circuit; 10-Inlet cavity body. Detailed Implementation

[0045] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be noted that the following embodiments are used to illustrate the technical concept and implementation process of the present invention, and are not intended to limit the scope of protection of the present invention.

[0046] This invention provides an optimized design method for the stator and rotor structural parameters of a single screw pump. Targeting micro-metering and conveying applications, the method, based on pre-defined constraints on the stator and rotor structural parameters, combines target displacement constraints and parameter accuracy constraints. The method employs theoretical calculations and MATLAB numerical traversal to perform a first-stage coarse screening of the stator and rotor structural parameters. A second-stage fine screening is then conducted using PumpLinx fluid simulation to evaluate the outlet volumetric flow rate and rotor triaxial forces of candidate parameter combinations. This process gradually narrows down the parameter value range, ultimately determining the optimal stator and rotor structural parameter combination for the target operating condition.

[0047] Furthermore, based on the aforementioned optimized stator and rotor structural parameters, local directional micro-compensation is implemented on the inner surface of the stator according to the main load direction of the rotor radial fluid pressure load during the stable motion cycle. The compensation effect is evaluated by the effective geometric flow area, minimum geometric clearance, average outlet volume flow rate during the stable cycle, and rotor fluid pressure load, thereby obtaining stator and rotor structural parameters and local compensation structure suitable for the target micro-metering and conveying conditions.

[0048] Example 1:

[0049] See Figure 1 The micro-screw pump used in this embodiment includes: a servo motor 1, a reducer 2, a direct connection frame 3, a seal 4, a drive shaft 5, a universal joint 6, a rotor 7, a stator 8, an outlet short connector 9, and an inlet chamber 10.

[0050] Servo motor 1 is used to provide power for the operation of the screw pump. When the rated torque of servo motor 1 is lower than the driving torque required to drive rotor 7, a reducer 2 can be installed to reduce speed and increase torque.

[0051] The seal 4 is located near the drive end to prevent the pumped medium from leaking outward. The seal 4 can be a mechanical seal or a packing seal.

[0052] The drive shaft 5 is used to transmit the power output by the servo motor 1. Since the rotor 7 rotates planetarily around the center of the stator 8 when it is working, the axis of motion of the rotor 7 does not coincide with the axis of the power source. Therefore, a universal joint 6 is set between the drive shaft 5 and the rotor 7 to realize variable angle power transmission, so that the power source can drive the rotor 7 to perform corresponding planetary motion.

[0053] The direct connection frame 3, the outlet short connector 9, and the inlet chamber 10 are used for connection and fastening between related components, wherein the inlet chamber 10 is located on the medium suction side, and the outlet short connector 9 is located on the medium discharge side.

[0054] The rotor 7 and stator 8 are the main working components of the single screw pump. The rotor 7 has a single-start helical structure, and the stator 8 is located outside the rotor 7, with its interior forming a double-start helical cavity that mates with the rotor 7. The stator 8 is usually made of rubber or other wear-resistant materials. After the rotor 7 is assembled inside the stator 8, the outer surface of the rotor 7 mates with the inner helical surface of the stator 8, and a predetermined rotor-stator geometric clearance is set according to actual design requirements, forming a working volume cavity that moves axially between them.

[0055] During operation, the power output from the servo motor 1 is transmitted to the rotor 7 via the reducer 2, drive shaft 5, and universal joint 6, driving the rotor 7 to rotate planetarily around the center of the stator 8. As the rotor 7 moves continuously, the sealed cavities formed between the rotor 7 and the stator 8 maintain a constant volume and move continuously along the axial direction, thereby conveying the medium from the inlet chamber 10 to the outlet short circuit 9. For each revolution of the rotor 7, the conveyed medium advances axially along the sealed cavity by the distance corresponding to one sealed cavity.

[0056] See Figure 2 and Figure 3 The cross-section of rotor 7 is a circle with radius R and diameter D, where D = 2R. Figure 2 In the diagram, O1 is the point corresponding to the helical axis on the rotor cross-section, O2 is the center of the rotor cross-section circle, and the distance between O1 and O2 is the eccentricity e. The rotor 7 is formed by continuously scanning the circular cross-section along a helical trajectory with a pitch of t.

[0057] Where R represents the radius of the rotor cross-section circle, in mm; D represents the diameter of the rotor cross-section circle, in mm; e represents the eccentricity, in mm; and t represents the axial pitch of the stator and rotor helical teeth, in mm.

[0058] See Figure 4 To characterize the fundamental geometric relationship between a single-start helical rotor and a double-start helical stator, the theoretically generated cross section of the stator with zero clearance is first defined. This theoretically generated cross section consists of two semicircular arcs, each with radius R, and two parallel straight line segments connecting the two semicircles. The distance between the centers of the two semicircles is 4e. Therefore, the dimension of the theoretically generated cross section with zero clearance in the minor axis direction is 2R, which is the diameter D of the rotor cross-section circle. The total dimension in the major axis direction is D + 4e.

[0059] The cross-section generated by the zero-gap theory is used to determine the basic structural parameter relationship between the stator and rotor pair, but it does not mean that there is no gap between the outer surface of the rotor and the inner surface of the stator under actual working conditions.

[0060] When an actual single-screw pump is configured with a nominal rotor-stator geometric clearance c0, the theoretically generated cross section with zero clearance is offset at an equal distance c0 in the direction of stator cavity expansion, resulting in a stator reference generated cross section with a predetermined rotor-stator geometric clearance. Thus, the theoretically generated cross section with zero clearance is used for structural parameter design and determination of theoretical geometric relationships, while the offset stator reference generated cross section is used to establish a geometric model and a fluid calculation model considering the actual rotor-stator clearance.

[0061] The stator cross-section extends continuously along the helical direction of stator 8 to form a double-headed helical cavity. Rotor 7 has a single-headed helical structure, and stator 8 has a double-headed helical structure; the axial pitch of the corresponding helical tooth surfaces of both is denoted as t. For a single-headed helical rotor, its lead is equal to the axial pitch t; for a double-headed helical stator, its lead is twice the axial pitch t. The stator lead is denoted as T, i.e., T = 2t.

[0062] See Figure 5 The rotor 7 is assembled in the double-headed helical cavity of the stator 8. The two mesh with each other to form a stator-rotor pair, and form a sealed volume cavity that moves continuously along the axial direction during operation.

[0063] Example 2:

[0064] This embodiment optimizes the stator and rotor structural parameters for a micro-metering delivery condition where the theoretical discharge volume of the screw pump is 0.648 mL per revolution of the rotor. Since 1 mL equals 1000 mm... 3 Therefore, the target theoretical displacement per revolution is 648mm. 3 .

[0065] When the rotor rotates one revolution, based on the geometric relationship of the working volume cavity formed by the single-head rotor and the double-head stator, the theoretical discharge volume of the screw pump per revolution satisfies:

[0066] q=4×e×D×t (1)

[0067] In the formula, q is the theoretical discharge volume of the screw pump when the rotor rotates one revolution, in mm. 3 e represents the eccentricity in mm; D represents the diameter of the rotor cross-section circle in mm; t represents the axial pitch of the stator and rotor helical teeth in mm. For the single-start helical rotor used in this invention, its lead is equal to the axial pitch t; for the double-start helical stator that mates with it, its lead T is twice the axial pitch t, ​​i.e., T = 2t. Unless otherwise specified, t in this document refers to the aforementioned axial pitch.

[0068] When the rotor runs at a speed of n, the theoretical outlet volumetric flow rate of the screw pump is obtained according to equation (1) and after conversion between time and volume units:

[0069] Q=(4×e×D×t×n)÷(60×1000) (2)

[0070] In the formula, Q is the theoretical outlet volumetric flow rate of the screw pump, in mL / s; n is the rotor speed, in r / min; 60 is the conversion factor for minutes to seconds; and 1000 is the conversion factor for mm³ to mL.

[0071] The target single-cycle theoretical displacement is 648mm. 3 Under the condition of 0.648 mL, when the rotor speed n is 60 r / min, 240 r / min and 360 r / min respectively, the theoretical outlet volumetric flow rates calculated according to formula (2) are 0.648 mL / s, 2.592 mL / s and 3.888 mL / s respectively. The theoretical outlet volumetric flow rates are used for comparison of subsequent simulation results.

[0072] Based on the target single-rotor theoretical displacement requirement, the stator and rotor structural parameters should satisfy the following theoretical target relationship:

[0073] 4×e×D×t=648, that is: e×D×t=162 (3)

[0074] In the formula, 162 represents the target theoretical displacement of 648 mm / s per revolution. 3 The target value is the product of the structural parameters obtained by dividing by a coefficient of 4.

[0075] Furthermore, based on the preset proportional relationship between the stator and rotor of the single screw pump, constraints are imposed on the eccentricity e, the rotor cross-sectional circle diameter D, and the axial pitch t:

[0076] 0.1×D≤e≤0.22×D

[0077] 1.4×D≤t≤2.5×D (4)

[0078] In the formula, 0.1 and 0.22 are the lower and upper limits of the proportionality of the eccentricity e relative to the rotor cross-sectional diameter D, respectively; 1.4 and 2.5 are the lower and upper limits of the proportionality of the axial pitch t relative to the rotor cross-sectional diameter D, respectively.

[0079] Considering the accuracy of actual parameter values, the values ​​of eccentricity e and rotor cross-sectional circle diameter D are both retained to 2 decimal places, and the value of axial pitch t is retained to 3 decimal places.

[0080] Using eccentricity e, rotor cross-sectional diameter D, and axial pitch t as design variables, define the design variable vector:

[0081] X = [x1, x2, x3] T ;

[0082] Where x1=e, x2=D, and x3=t.

[0083] Considering the accuracy requirements of the above parameter values, in order to make the obtained parameter combination satisfy the target single-rotation theoretical displacement relationship determined by equation (3) as much as possible, the following objective function is established:

[0084]

[0085] In the formula, f(X) is the objective function, representing the squared error between the product of the current combination of structural parameters and the target structural parameters; the meanings of X, x1, x2, and x3 are the same as before; 162 is the target value of the product of structural parameters determined by formula (3); min indicates that the optimization objective is to minimize the objective function f(X). The smaller f(X) is, the closer the theoretical single-revolution displacement of the corresponding parameter combination is to 0.648 mL.

[0086] Combining the structural proportions shown in equation (4), the range of design variable values, and the accuracy requirements for parameter values, the constraints for parameter selection in the first stage are:

[0087] 0.1×x²≤x₁≤0.2²×x²

[0088] 1.4 × x² ≤ x³ ≤ 2.5 × x²

[0089] 1≤x²≤200

[0090] x1 is rounded to two decimal places.

[0091] x2 is rounded to two decimal places and taken in increments of 0.01 mm.

[0092] x3 is rounded to 3 decimal places (6)

[0093] In the formula, x1, x2 and x3 have the same meaning as before, and the value of x2 ranges from 1 to 200 mm.

[0094] Therefore, the structural parameter target relationship corresponding to the target single-rotor theoretical displacement is determined by equation (3), the basic ratio range between the stator and rotor structural parameters is limited by equation (4), and the objective function shown in equation (5) and the constraint conditions shown in equation (6) are established in combination with the parameter value accuracy, thus forming the first-stage stator and rotor structural parameter screening model for subsequent MATLAB numerical traversal.

[0095] Example 3:

[0096] Based on the target single-rotor theoretical displacement relationship, the stator-rotor structural parameter ratio relationship, and the parameter value accuracy requirements determined in Example 2, MATLAB was used to numerically traverse the eccentricity e, the rotor cross-sectional circle diameter D, and the axial pitch t to obtain candidate parameter combinations that meet the design conditions.

[0097] First, the search range of the rotor cross-sectional circle diameter D is set to 1~200mm, and each D value is iterated in increments of 0.01mm. For each D value, the lower limit and upper limit of the eccentricity e are determined according to the proportional relationship between the eccentricity and the rotor cross-sectional circle diameter shown in equation (4):

[0098] e_min = 0.1 × D;

[0099] e_max=0.22×D.

[0100] In the formula, e_min and e_max represent the lower limit and upper limit of the eccentricity corresponding to the current D value, respectively, and the unit is mm.

[0101] Within the range of e_min to e_max, the eccentricity e is traversed in steps of 0.01mm, and e is retained to 2 decimal places.

[0102] For each pair of e and D, according to the target structure parameter relationship shown in equation (3):

[0103] e×D×t=162;

[0104] Inversely calculate the corresponding theoretical axial pitch:

[0105] t_theory = 162 ÷ (e × D).

[0106] In the formula, t_theory is the theoretical axial pitch corresponding to the current e and D, in mm.

[0107] Further calculate the allowable range of axial pitch corresponding to the current D value according to equation (4):

[0108] t_min = 1.4 × D;

[0109] t_max = 2.5 × D.

[0110] In the formula, t_min and t_max represent the lower limit and upper limit of the axial pitch corresponding to the current D value, respectively, and the unit is mm.

[0111] Determine if t_theory satisfies:

[0112] t_min≤t_theory≤t_max.

[0113] When t_theory is within the above-mentioned allowable range, t_theory is retained to 3 decimal places according to the parameter value precision to obtain the corresponding axial pitch t; when t_theory is not within the above-mentioned allowable range, the current parameter combination is discarded, and the calculation continues for the next set of e and D.

[0114] For parameter combinations that satisfy the above conditions, further calculations are performed:

[0115] P = e × D × t.

[0116] In the formula, P is the product of e, D, and t after parameter value precision processing, and the unit is mm. 3 .

[0117] According to the MATLAB program used in this embodiment, the parameters are discretized to improve their accuracy. The squared error f(X) of the discretized parameter combination relative to the product of the target structural parameters 162 is calculated according to equation (5) to evaluate the degree to which the parameter combination meets the target single-rotor theoretical displacement. At the same time, the discretized e, D and t are re-verified according to the structural ratio relationship shown in equation (4), and the parameter combination that passes the verification is saved as the first-stage candidate parameter combination.

[0118] After completing the traversal of all D and e according to the above steps, the resulting candidate parameter combinations are summarized. First, they are sorted from smallest to largest according to the eccentricity e; for parameter combinations corresponding to the same eccentricity e, they are sorted from largest to smallest according to the axial pitch t, ​​and the sorted e, D, t and their product P are exported to an Excel file for saving, so as to select candidate parameters for subsequent fluid simulation.

[0119] MATLAB numerical traversal results show that, under the above target displacement and structural parameter ratio conditions, the eccentricity e among the obtained candidate parameters gradually increases from 0.87 mm to 1.77 mm, and the corresponding rotor cross-sectional circle diameter D and axial pitch t change with the change of eccentricity e.

[0120] For example, when e=0.87mm, the candidate range of D is approximately 8.64~8.70mm; where, when D=8.64mm, the corresponding t is approximately 21.552mm, and when D=8.70mm, the corresponding t is approximately 21.403mm.

[0121] When e = 0.88 mm, the candidate range of D is approximately 8.59~8.80 mm, corresponding to t of approximately 21.431~20.919 mm; when e = 1.25 mm, the candidate range of D is approximately 7.20~9.62 mm, corresponding to t of approximately 18.000~13.472 mm; when e increases to 1.77 mm, the candidate range of D narrows to approximately 8.05~8.08 mm, corresponding to t of approximately 11.370~11.327 mm.

[0122] The above numerical traversal results constitute the first-stage parameter coarse screening results and serve as the basis for selecting candidate parameters for subsequent PumpLinx fluid simulations.

[0123]

[0124] Example 4:

[0125] The PumpLinx fluid dynamics simulation software was used to simulate the flow field and rotor force on the candidate stator and rotor structural parameter combinations obtained from the first stage of MATLAB screening.

[0126] The pump's inlet and outlet regions utilize a binary tree Cartesian mesh with a mesh size of 0.1 mm. The stator and rotor fluid domains employ an adaptive fluid domain mesh for the rotor region, with a uniform stator-rotor clearance of 0.05 mm. Local mesh refinement is applied to the areas near the stator and rotor. The total number of meshes in the computational model is approximately 850,000, with a mesh quality greater than 0.85. All candidate stator and rotor structural parameter combinations adhere to the same mesh control principles to ensure the comparability of simulation results between different candidate structures.

[0127] The simulation model adopts a three-stage pump structure, with one stator lead corresponding to one stage, forming a total of 6 independent volume chambers. The structure of the simulation model is consistent with that of the physical prototype.

[0128] The transport medium is 25°C clean water, and its dynamic viscosity is set according to the physical properties of clean water at this temperature. The flow model adopts the standard K-ε turbulence model.

[0129] In the boundary conditions, the absolute pressure at the pump inlet is set to one standard atmosphere, i.e., 101325 Pa, and the absolute pressure at the pump outlet is also set to 101325 Pa. This means no additional pressure difference is applied between the pump inlet and outlet, and the inlet-outlet pressure difference Δp = 0 Pa. Under different combinations of candidate stator and rotor structural parameters and different rotor speeds, the inlet pressure, outlet pressure, and other solution conditions remain consistent to ensure the comparability of simulation results between different candidate structures.

[0130] The rotor speeds were set to 60 r / min, 240 r / min, and 360 r / min, respectively. Under each operating condition, the rotor rotated continuously for 3 revolutions, with 30 transient time steps per revolution, resulting in a total of 90 transient time steps for each operating condition. Correspondingly, the total simulation times under the 60 r / min, 240 r / min, and 360 r / min conditions were 3.0 s, 0.75 s, and 0.50 s, respectively. Different candidate stator and rotor structural parameter combinations were used with the same time discretization settings to compare the relative changes in outlet volumetric flow rate and rotor fluid pressure load under unified calculation conditions.

[0131] During the simulation, the volumetric flow rate at the screw pump outlet and the resultant pressure forces acting on the rotor in the X, Y, and Z directions are monitored in real time. Here, Fx represents the resultant pressure force in the X direction of the rotor, in N; Fy represents the resultant pressure force in the Y direction of the rotor, in N; and Fz represents the resultant pressure force in the Z direction of the rotor, in N.

[0132] Fx represents the resultant pressure force in the X direction of the rotor, and Fy represents the resultant pressure force in the Y direction of the rotor. These two forces characterize the radial stress state of the rotor. Since Fx and Fy change periodically with the phase of motion during rotor movement and may change in both positive and negative directions, this embodiment primarily evaluates the radial stress state of the rotor by comparing the absolute peak values ​​and fluctuation amplitudes of Fx and Fy. Under the same conditions, a smaller absolute peak value or fluctuation amplitude of Fx and Fy indicates a relatively smaller radial fluid pressure load on the rotor.

[0133] Fz represents the resultant pressure force in the axial direction of the rotor, generated by the flow of the medium within the volumetric cavity. In the evaluation system of this embodiment, Fz represents the resultant force of fluid pressure acting on the rotor in the axial direction, used to characterize the axial fluid pressure load borne by the rotor. The outlet conveying performance is mainly evaluated through the outlet volumetric flow rate; Fz is not directly used as a criterion for improving conveying performance. Based on the premise that the outlet volumetric flow rate meets the requirements, the peak value, average value, and periodic variation characteristics of Fz are compared to determine whether different structural parameters lead to abnormal axial pressure loads.

[0134] Therefore, based on the premise that the outlet volumetric flow rate meets the target requirements, the peak absolute values ​​and fluctuation amplitudes of Fx and Fy are used as the main evaluation indicators of radial fluid pressure load. Combined with the peak value, average value and periodic variation characteristics of Fz, the rotor stress state of different candidate parameter combinations is further compared.

[0135] Example 5:

[0136] In this embodiment, except that the candidate stator and rotor structural parameters and rotor speed are set according to the comparison requirements below, the conveying medium, inlet pressure, inlet and outlet pressure difference, stator and rotor clearance, grid control principles, and other fluid calculation conditions are consistent with those in Embodiment 4. Based on the candidate parameter set obtained from the first stage of MATLAB screening, e=0.88mm, e=1.25mm, and e=1.77mm were selected as small, medium, and large eccentricities for group simulation.

[0137] When e = 0.88 mm, select the following 8 sets of parameters:

[0138]

[0139] The outlet volumetric flow rate was simulated at three rotational speeds of 60 r / min, 240 r / min, and 360 r / min, and the simulation results are as follows: Figure 6 , Figure 7 and Figure 8 As shown. Among them, Figure 6 , Figure 7 and Figure 8 Curves 1-8 in the table correspond to the stator and rotor structural parameters in groups 1-8 of Table 2, respectively. Figure 6 , Figure 7 and Figure 8 It can be seen that under the three rotational speeds of 60 r / min, 240 r / min, and 360 r / min, the outlet volumetric flow rate of each candidate parameter combination fluctuates periodically with the simulation time, and the overall level of the outlet volumetric flow rate increases with the increase of the rotor speed. Under the same eccentricity and rotational speed, as D increases and t decreases accordingly, the outlet volumetric flow rate corresponding to each candidate parameter combination generally shows an increasing trend.

[0140] When e=1.25mm, select the following 9 sets of parameters:

[0141]

[0142] The outlet volumetric flow rate was simulated at three rotational speeds: 60 r / min, 240 r / min, and 360 r / min. The simulation results are as follows: Figure 9 , Figure 10 and Figure 11 As shown. Among them, Figure 9 , Figure 10and Figure 11 Curves 1-9 in the table correspond to the stator and rotor structural parameters in groups 1-9 of Table 3, respectively. Figure 9 , Figure 10 and Figure 11 It can be seen that under the three rotational speeds of 60 r / min, 240 r / min, and 360 r / min, the outlet volumetric flow rate of each candidate parameter combination exhibits periodic changes, and the overall flow rate level increases with the increase of rotor speed. Within this parameter range, when the eccentricity is kept at 1.25 mm, the outlet volumetric flow rate generally shows an increasing trend as D increases and t decreases accordingly.

[0143] Combining the results from the two sets of e=0.88mm and e=1.25mm, it can be seen that the overall level of the outlet volumetric flow rate increases with the increase of rotor speed; under the two sets of eccentricity conditions compared, the outlet volumetric flow rate of the e=1.25mm group is generally higher than that of the e=0.88mm group; when the eccentricity remains unchanged, within the range of the tested parameters, as D increases and t decreases accordingly, the outlet volumetric flow rate generally shows an increasing trend.

[0144] Further increasing the eccentricity to e=1.77mm, the following 4 sets of candidate parameters were selected:

[0145]

[0146] The outlet volumetric flow rate was simulated under conditions of 60 r / min, 240 r / min, and 360 r / min. The simulation results are as follows: Figure 12 , Figure 13 and Figure 14 As shown. Among them, Figure 12 , Figure 13 and Figure 14 Curves 1-4 in the table correspond to candidate parameters groups 1-4 in Table 4, respectively. Figure 12 , Figure 13 and Figure 14 It can be seen that under the three rotational speeds of 60 r / min, 240 r / min and 360 r / min, the outlet volumetric flow rate of each candidate parameter combination fluctuates periodically, and the overall flow rate level increases with the increase of rotor speed.

[0147] Compared to the conditions of e=0.88mm and e=1.25mm, the outlet volumetric flow rate curves of different candidate combinations of D and t are more similar under the condition of e=1.77mm. It is difficult to further distinguish the comprehensive performance of each candidate parameter combination based solely on the outlet volumetric flow rate. Therefore, a further comparison is made of the rotor pressure results in the X, Y, and Z directions corresponding to the above four sets of parameters.

[0148] Under the condition of a rotor speed of 60 r / min, the resultant pressure forces in the X, Y, and Z directions of the rotor corresponding to the above four sets of candidate parameters were compared, and the results are as follows: Figure 15 , Figure 16 and Figure 17 As shown. Among them, Figure 15 The variation of the resultant pressure force in the rotor's X direction with simulation time is shown. Figure 16 The variation of the resultant pressure force in the rotor's Y direction with simulation time is shown. Figure 17 The variation of the resultant pressure force in the Z direction of the rotor with simulation time is shown.

[0149] Under the condition of rotor speed of 240 r / min, the resultant pressure curves in the X and Y directions are quite similar. To further compare the differences between different candidate parameter combinations, the peak regions within one variation cycle are locally magnified, and the results are as follows. Figure 18 and Figure 19 As shown; the result of the change of the resultant pressure in the Z direction with simulation time is as follows. Figure 20 As shown.

[0150] Under the condition of rotor speed of 360 r / min, the local magnified results of the peak region of the resultant pressure in the X and Y directions within one variation cycle are as follows: Figure 21 and Figure 22 As shown, the resultant pressure in the Z direction changes with simulation time. Figure 23 As shown.

[0151] Depend on Figures 15 to 23 It can be seen that, under the condition of e=1.77mm, the resultant force of the rotor's three-dimensional pressure corresponding to different candidate parameter combinations all exhibits periodic changes with rotor motion. Among these, under the unified time discretization and other calculation conditions used in this embodiment, the resultant force is obtained from... Figure 18 , Figure 19 , Figure 21 and Figure 22 The magnified results show that as D increases and t decreases accordingly, the peaks of the resultant pressure in the X and Y directions generally show a decreasing trend; Figure 17 , Figure 20 and Figure 23 It can be seen that the variation law of the resultant pressure in the Z direction corresponding to each candidate parameter combination is generally similar.

[0152] Combination Figures 12 to 14The outlet volumetric flow rate results show that, under the condition of e=1.77mm, the differences in outlet volumetric flow rates among the candidate parameter combinations are small. Therefore, a comprehensive comparison is further conducted by considering the radial and axial force characteristics of the rotor. Among the four candidate parameter groups corresponding to this eccentricity, the parameter combination of D=8.08mm and t=11.327mm exhibits superior overall performance. Therefore, it is selected as the preferred parameter combination under the condition of e=1.77mm and used for further comparison among preferred parameter combinations with different eccentricities.

[0153] Example 6:

[0154] According to the MATLAB numerical traversal results of Example 3, under the joint constraints of the target structure parameter relationship shown in Equation (3), the stator-rotor structure ratio relationship shown in Equation (4), and the preset parameter value accuracy, when the eccentricity e is discretely selected in a step size of 0.01mm, the maximum discrete value of the eccentricity e in the obtained feasible parameter combination is 1.77mm.

[0155] When e = 1.77 mm, the corresponding feasible rotor cross-sectional circle diameter D narrows to approximately 8.05–8.08 mm, and the axial pitch t is approximately 11.370–11.327 mm. Therefore, under the target single-rotor theoretical displacement, structural proportion constraints, and parameter value accuracy conditions adopted in this embodiment, e = 1.77 mm is taken as the upper limit value for subsequent comparison of large eccentricity candidate parameters.

[0156] According to the relationship e×D×t=162, as the eccentricity e increases, the product of D and t needs to decrease accordingly to meet the target single-rotor theoretical displacement requirement. Simultaneously, constrained by the structural ratio relationships e≤0.22D and 1.4D≤t≤2.5D, when the eccentricity e approaches its feasible upper limit, the feasible range of D values ​​narrows significantly, and the feasible values ​​of t generally change towards smaller values. Under the combined influence of the target single-rotor theoretical displacement, stator-rotor structural ratio constraints, and the accuracy of preset parameter values, when the eccentricity e is discretely selected in 0.01mm increments, its maximum feasible discrete value is 1.77mm. Therefore, in this embodiment, 1.77mm is used as the upper limit for subsequent comparison of large eccentricity candidate parameters.

[0157] In the first stage of MATLAB calculations, the initial search range for D is 1~200mm. First, a feasible parameter set is obtained based on the target single-rotor theoretical displacement relationship, stator and rotor structural proportional constraints, and parameter accuracy requirements. On this basis, the candidate parameter range is gradually narrowed by combining the outlet volumetric flow rate and rotor fluid pressure load results obtained from PumpLinx simulation.

[0158] For the large eccentricity range of e = 1.71~1.77 mm, a representative set of candidate D and t combinations were selected from the feasible parameter set of MATLAB for further comparison, as shown in Table 5:

[0159]

[0160] In this stage, the rotor speed is set to 240 r / min, and the rotor rotates continuously for 3 revolutions, with 30 transient time steps per revolution. The conveying medium is 25°C clean water, and the absolute pressure at both the pump inlet and outlet is set to 101325 Pa, i.e., the pressure difference between the inlet and outlet Δp = 0 Pa. Except for the stator and rotor structural parameters being compared, the fluid medium, boundary conditions, mesh control principles, and solution settings are consistent with Example 4.

[0161] The outlet volumetric flow rate of the above 7 sets of preferred parameter combinations was simulated, and the changes in outlet volumetric flow rate of each parameter combination were compared under the same transient time step setting and other solution conditions. The results are as follows: Figure 24 As shown. Among them, Figure 24 Curves 1 to 7 in the table correspond to the parameter combinations 1 to 7 in Table 5, respectively. Figure 24 The results of outlet volumetric flow rate variation for various parameter combinations within the simulation time range of 0~0.5s are presented. Under the same initial conditions, boundary conditions, and solution settings, the outlet volumetric flow rate of each parameter combination exhibits repetitive periodic fluctuations. Except for the initial flow field establishment stage, the subsequent multiple flow rate fluctuation cycles have similar variation patterns. Therefore, this embodiment uses the overall horizontal and relative variation trends of the curves within this time range to compare different parameter combinations.

[0162] Depend on Figure 24 It can be seen that within the range of e=1.71~1.77mm, as the eccentricity e gradually increases, the outlet volumetric flow rate curve of each eccentricity corresponding to the preferred parameter combination gradually shifts upward. In multiple repeated flow fluctuation cycles, the relative change trends of each parameter combination are basically consistent, and the outlet volumetric flow rate of the parameter combination corresponding to e=1.77mm is generally at a higher level among the compared parameter combinations.

[0163] Based on the above phased screening results, within the range of e = 1.71~1.77 mm, the outlet volumetric flow rate of each eccentricity-corresponding optimal parameter combination was first compared, and it was determined that the parameter combination corresponding to e = 1.77 mm had a higher outlet volumetric flow rate level. For the four candidate parameter groups with relatively close outlet volumetric flow rates under the condition of e = 1.77 mm, the variation characteristics of the radial pressure resultant force in the X and Y directions and the axial pressure resultant force in the Z direction of the rotor were further compared. Therefore, within the screening conditions and the range of candidate parameters compared in this embodiment, the preferred stator and rotor structural parameter combination was determined to be e = 1.77 mm; D = 8.08 mm; t = 11.327 mm.

[0164] Since the stator lead T is twice the axial pitch t, ​​the corresponding stator lead T = 22.654 mm.

[0165] Using the above parameter combinations, at rotor speeds of 60 r / min, 240 r / min, and 360 r / min, the outlet volumetric flow rate obtained from PumpLinx simulations all exhibited periodic fluctuations, with the overall flow rate level increasing accordingly with increasing rotor speed. Figure 12 , Figure 13 and Figure 14 As shown; the theoretical outlet volumetric flow rates calculated according to equation (2) are 0.648 mL / s, 2.592 mL / s and 3.888 mL / s, respectively.

[0166] The results above show that, among the preferred parameter combinations for e=1.71~1.77mm, the parameter combination corresponding to e=1.77mm, D=8.08mm, and t=11.327mm generally exhibits a higher outlet volumetric flow rate. Furthermore, within the candidate parameter group corresponding to e=1.77mm, this parameter combination demonstrates superior overall performance considering the variation characteristics of the resultant pressure in the rotor's X, Y, and Z directions. Therefore, this parameter combination is determined as the preferred stator and rotor structural parameter combination for this target micro-transportation condition.

[0167] Example 7:

[0168] The comparison in this embodiment Figures 6 to 24 The corresponding fluid simulation results were obtained using the operating conditions specified in Examples 4 to 6. For different candidate stator and rotor structural parameter combinations within the same comparison group, the rotor speed, fluid medium, inlet pressure, inlet and outlet pressure difference, and corresponding solution conditions remained consistent, except for the stator and rotor structural parameters. To further illustrate the above parameter selection method and results, a comprehensive comparison of flow simulation results under different eccentricity conditions was conducted.

[0169] Depend on Figures 6 to 14It can be seen that within the parameter range studied in this embodiment, the outlet volumetric flow rate corresponding to each candidate parameter combination changes periodically with the rotor motion, and under the same structural parameter conditions, the overall level of the outlet volumetric flow rate increases with the increase of rotor speed.

[0170] Under the conditions of e=0.88mm and e=1.25mm, when the eccentricity remains constant, the outlet volumetric flow rate generally shows an increasing trend as the rotor cross-sectional diameter D increases and the axial pitch t decreases accordingly. Under the condition of e=1.77mm, the outlet volumetric flow rate curves corresponding to different combinations of candidate parameters D and t are quite similar. It is difficult to further distinguish between the various candidate parameter combinations based solely on the outlet volumetric flow rate. Therefore, the combined pressure forces in the X, Y, and Z directions of the rotor are further introduced for comparison.

[0171] Depend on Figures 15 to 23 It can be seen that the resultant force of the rotor's three-dimensional pressure varies periodically with the rotor motion for different combinations of candidate parameters. Among them, by locally magnifying the peak regions of the resultant force in the X and Y directions, the radial force differences between different combinations of candidate parameters can be further compared; the resultant force in the Z direction, combined with its overall variation law, is used as an evaluation parameter for the rotor's axial force state.

[0172] Furthermore, by Figure 24 It can be seen that within the range of e = 1.71~1.77 mm, as the eccentricity e gradually increases, the outlet volumetric flow rate of each eccentricity-corresponding optimal parameter combination generally shows an increasing trend. In summary, this invention adopts a phased screening method: firstly, the candidate range for different eccentricity parameter groups is gradually narrowed down based on the outlet volumetric flow rate; for candidate parameter combinations with relatively close outlet volumetric flow rates, a further fine comparison is made based on the rotor radial fluid pressure load and the variation characteristics of the axial fluid pressure load. Following the above screening process, within the screening conditions and compared candidate parameter range established in this embodiment, e = 1.77 mm, D = 8.08 mm, and t = 11.327 mm are determined as the optimal stator and rotor structural parameter combination for the target micro-metering and conveying condition.

[0173] Example 8:

[0174] Based on the preferred stator and rotor structural parameters determined in Example 6, this embodiment implements local directional micro-compensation on the inner surface of the stator according to the main direction of the rotor radial fluid pressure load, and evaluates the compensation effect by the effective geometric flow area, minimum geometric clearance, average outlet volume flow rate during stable period, and rotor fluid pressure load.

[0175] The stator and rotor structural parameters determined in Example 6 are as follows: eccentricity e = 1.77 mm, rotor cross-sectional circle diameter D = 8.08 mm, axial pitch t = 11.327 mm, and stator lead T = 22.654 mm.

[0176] A baseline fluid computational model, denoted as the BASE model, is established using the stator and rotor structure without local directional micro-compensation. The radial fluid pressure main load axis is determined by the resultant radial fluid pressure of the rotor during the stable motion cycle of the BASE model, and this main load axis serves as the reference for the stator's local compensation direction. Centrally symmetrical local compensation regions are established in the direction of the main load axis and in the direction perpendicular to it. The stator's internal profile is altered by local normal micro-displacements, and the second compensation amount is determined through geometric area closure. The compensated fluid computational model is denoted as the COMP model. The BASE model and COMP model maintain the same structural parameters, motion relationships, fluid medium, boundary conditions, and solution settings, except for the stator's local internal profile. Compared to Examples 4 to 7, this example employs higher time discretization accuracy and local geometric region mesh resolution for a more detailed comparison of performance changes before and after local directional micro-compensation.

[0177] 1. Determination of geometric parameters of the BASE model

[0178] This embodiment uses a single-headed helical rotor and a double-headed helical stator to form a 1:2 type stator-rotor pair.

[0179] The radius R of the rotor cross-section circle is:

[0180] R = D / 2 (8-1)

[0181] Substituting D=8.08mm, we get: R=4.04mm.

[0182] Rotor 7 has a single-start helical structure, and stator 8 has a double-start helical structure. The axial pitch of the corresponding helical teeth on both is t. For the single-start rotor, its lead is equal to the pitch t; for the double-start stator, its lead T is twice the pitch t, ​​that is:

[0183] T=2t (8-2)

[0184] Therefore: T = 22.654 mm.

[0185] Based on the theoretical displacement relationship described in Example 2, the theoretical single-rotor displacement q corresponding to the preferred combination of stator and rotor structural parameters in this example is determined according to the following formula:

[0186] q=4eDt.

[0187] Substituting e=1.77mm, D=8.08mm, and t=11.327mm, we get: q=647.9769mm 3 That is, q = 0.64798 mL.

[0188] This value is basically consistent with the target theoretical displacement of 0.648 mL per revolution. The slight difference comes from the discretization of the stator and rotor structural parameters according to the preset value accuracy.

[0189] The nominal rotor-stator geometric clearance c0 in the BASE model is taken as: c0 = 0.050 mm.

[0190] The effective spiral working length Ls of the stator and rotor is taken as 3 complete stator leads, that is: Ls=3T=67.962mm.

[0191] First, the zero-gap theoretical cross-section is generated according to the stator cross-section structure described in Example 1. This theoretically generated cross-section consists of two semicircular arcs with radius R and two parallel straight line segments connecting the two semicircular arcs. The distance between the centers of the two semicircular arcs is 4e.

[0192] The cross-section generated by the zero-gap theory is offset by a distance c0 along the cavity expansion direction to obtain the stator reference generated cross-section C0 of the BASE model. After offsetting, the center positions of the arcs at both ends remain unchanged, and the arc radius R0 satisfies:

[0193] R0 = R + c0 (8-3)

[0194] The result is: R0 = 4.09 mm.

[0195] The cavity area A0 enclosed by the stator reference generated cross section C0 is calculated according to the following formula:

[0196] A0=π×R0 2 +8×e×R0 (8-4)

[0197] The calculated value is: A0 = 110.4673 mm 2 .

[0198] The cross-sectional area Ar of the rotor's circular shape is calculated using the following formula:

[0199] Ar=π×R 2 (8-5)

[0200] We obtained: Ar = 51.2758 mm 2 .

[0201] The difference between the stator cavity area and the rotor generated cross-sectional area is used as the benchmark for comparing the geometrically effective flow area of ​​the reference cross-section before and after compensation. The geometrically effective flow area Af,BASE of the reference cross-section in the BASE model is:

[0202] Af,BASE=A0-Ar (8-6)

[0203] We obtained: Af,BASE = 59.1915 mm 2 .

[0204] The Af,BASE is used to compare the change in the geometric area of ​​the reference cross section before and after local compensation, and is not used as the theoretical displacement of a single screw pump per revolution.

[0205] 2. Obtaining Radial Fluid Pressure Load in the BASE Model

[0206] Establish a global rectangular coordinate system O-XYZ fixed to the stator. The origin O is located at the center of the stator reference generated cross section; the X-axis is along the major axis of the uncompensated stator reference generated cross section C0; the Y-axis is located in the same cross section and is perpendicular to the X-axis; the Z-axis coincides with the stator axis, and the direction from the pump inlet to the pump outlet is defined as the positive direction of the Z-axis.

[0207] The coordinate system described above is fixed to the stator and does not rotate or translate with the rotor during transient fluid calculations.

[0208] The BASE model employs a 1:2 type stator-rotor conjugate eccentric motion relationship that matches the aforementioned single-start helical rotor and double-start helical stator. The rotor helical axis maintains an eccentricity e relative to the stator axis and moves continuously according to the established stator-rotor pair's corresponding conjugate eccentric motion relationship.

[0209] The driving phase angle ψ = 0° is defined as the initial rotor position in the BASE model. When the rotor completes a full cycle and returns to a position equivalent to the initial stator and rotor relative geometric state, it is defined as ψ = 360°. Therefore, a full cycle is represented by 0° ≤ ψ < 360°.

[0210] The BASE and COMP models use the same eccentricity, initial phase, direction of motion, and relative motion function between the stator and rotor.

[0211] The fluid pressure load evaluated in this embodiment is the resultant pressure force of the working medium acting on the rotor fluid contact surface, excluding the mechanical contact force between the rotor and the stator.

[0212] The outer working surface of the rotor helix that is in direct contact with the working medium within the effective helical working length Ls is defined as the pressure integral surface Sr. The BASE model and the COMP model use the exact same Sr range.

[0213] When PumpLinx directly outputs the Pressure Force on Sr, the components of the resultant pressure force in the X, Y, and Z directions, Fx, Fy, and Fz, are obtained respectively.

[0214] When using surface discrete elements for calculation, for the i-th surface element on Sr, let its pressure be pi, the reference pressure be pref, and the element area be ΔSi. The components of the unit outward normal vector from the rotor body to the fluid region in the X, Y, and Z directions are nx,i, ny,i, and nz,i, respectively. Then, the components of the resultant pressure force in the three directions are calculated according to the following formulas:

[0215] Fx=-Σ[(pi-pref)×nx,i×ΔSi] (8-7)

[0216] Fy=-Σ[(pi-pref)×ny,i×ΔSi] (8-8)

[0217] Fz=-Σ[(pi-pref)×nz,i×ΔSi] (8-9)

[0218] In the formula, the summation range is all surface discrete elements on Sr; pref adopts the reference pressure consistent with the PumpLinx pressure output diameter, and the BASE model and COMP model adopt the same pressure reference; the negative sign indicates that the pressure direction of the fluid acting on the rotor is opposite to the direction of the rotor's external normal vector.

[0219] 3. Determination of the radial fluid pressure principal load axis

[0220] After the BASE model reaches a periodic steady state, Fx and Fy within the last complete 360° motion cycle are used for radial fluid pressure principal load direction analysis.

[0221] Within a complete stable period, N=120 sampling positions are selected with equal phase, and the driving phase difference between adjacent sampling positions is:

[0222] Δψ = 360° / N = 3° (8-10)

[0223] The driving phase angle ψj corresponding to the j-th sampling position is:

[0224] ψj=(j-1)×Δψ, j=1, 2,...,N (8-11)

[0225] Therefore, the 120 sampling positions correspond to 0°, 3°, 6°, ..., 357° in sequence, and the 360° endpoints equivalent to the 0° position are sampled without repetition.

[0226] When the number of time steps used in the formal transient calculation is greater than 120 steps / revolution, data from 120 sampling positions are extracted from the last stable cycle according to the above driving phase; when the specified sampling phase does not completely coincide with the calculation time step, linear interpolation is performed based on the data from adjacent time steps.

[0227] The resultant fluid pressures in the X and Y directions corresponding to the j-th sampling position are denoted as Fx,j and Fy,j, respectively.

[0228] Calculate the average squared value of the pressure load in the X direction (Mxx), the average squared value of the pressure load in the Y direction (Myy), and the average product of the pressure loads in the X and Y directions (Mxy) over a complete steady-state period:

[0229] Mxx=(1 / N)×Σ(Fx,j) 2 (8-12)

[0230] Myy=(1 / N)×Σ(Fy,j) 2 (8-13)

[0231] Mxy=(1 / N)×Σ(Fx,j×Fy,j) (8-14)

[0232] Define the nonnegativity discriminant dM:

[0233] (dM) 2 =(Mxx-Myy) 2 +4×(Mxy) 2 , and dM≥0 (8-15)

[0234] Therefore, the two eigenvalues ​​λ1 and λ2 corresponding to the second moment of the radial fluid pressure load are determined:

[0235] λ1=(Mxx+Myy+dM) / 2 (8-16)

[0236] λ2=(Mxx+Myy-dM) / 2 (8-17)

[0237] Where: λ1≥λ2.

[0238] Define the radial fluid pressure load directionality coefficient ηM. When Mxx + Myy > 0:

[0239] ηM=(λ1-λ2) / (λ1+λ2) (8-18)

[0240] When Mxx+Myy=0, ηM is defined as 0.

[0241] The value of ηM ranges from 0 to 1. The larger the value of ηM, the more concentrated the radial fluid pressure load is in a specific direction.

[0242] In this embodiment, ηM=0.05 is used as the reference for determining the orientation compensation of a single main load axis. When ηM≥0.05, the angle θp between the radial fluid pressure main load axis and the fixed X-axis is calculated according to the following formula:

[0243] θp=0.5×atan2(2Mxy,Mxx-Myy) (8-19)

[0244] In the formula, atan2 is a bivariate arctangent function that determines the quadrant of the result based on the signs of the two input parameters. The calculation results are uniformly converted to the range of 0°≤θp<180°. Since the subsequent compensation regions are set in pairs about the center O of the cross section, θp and θp+180° represent the same principal load axis.

[0245] The radial fluid pressure principal load axis angle of the BASE model is: θp = 8.0°.

[0246] The radial fluid pressure load directionality coefficient of the BASE model is: ηM,BASE=0.22.

[0247] Since ηM,BASE is greater than 0.05, the radial principal load axis determined by θp is used as the directional reference for the stator local orientation micro-compensation.

[0248] 4. Determination of the local compensation center

[0249] Establish a local compensation coordinate system O-UV with point O as the origin, where the U-axis coincides with the radial fluid pressure main load axis, and the V-axis passes through point O and is perpendicular to the U-axis.

[0250] For any point P on the boundary of the stator reference generated cross section C0, let its coordinates in the fixed XY coordinate system be x and y, then the projected coordinates of point P in the U-axis and V-axis directions are respectively:

[0251] u(P)=x×cosθp+y×sinθp (8-20)

[0252] v(P)=-x×sinθp+y×cosθp (8-21)

[0253] Among all boundary points of C0, the position where u(P) is maximum is determined as the compensation center PU+ in the positive direction of the U-axis, and the position where u(P) is minimum is determined as the compensation center PU- in the negative direction of the U-axis; the position where v(P) is maximum is determined as the compensation center PV+ in the positive direction of the V-axis, and the position where v(P) is minimum is determined as the compensation center PV- in the negative direction of the V-axis.

[0254] When the corresponding extreme value is obtained by a single boundary point, that boundary point is used as the compensation center; when the corresponding extreme value is obtained by a series of continuous boundary segments, the midpoint of the boundary segment with the extreme value along the arc length of C0 is used as the compensation center.

[0255] This yields four local compensation centers, PU+, PU-, PV+, and PV-, which are symmetrical about the center O of the cross section.

[0256] 5. Local Compensation Zones and Smooth Transition

[0257] Local compensation zones are set along the C0 boundary with PU+, PU-, PV+, and PV- as the centers respectively.

[0258] The full compensation half-arc length lU in the U direction is taken as: lU=1.25mm.

[0259] The full compensation half-arc length lV in the V direction is taken as: lV=3.50mm.

[0260] Smooth transition zones with a length of ltr are set at both ends of each full compensation zone: ltr=0.50mm.

[0261] Let s be the shortest arc length distance along the C0 boundary from the corresponding compensation center to the boundary point to be calculated.

[0262] For the U-direction compensation zone, when 0≤s≤lU:

[0263] w(s)=1 (8-22)

[0264] When lU<s≤lU+ltr:

[0265] w(s)=0.5×{1+cos[π×(s-lU) / ltr]} (8-23)

[0266] When s>lU+ltr:

[0267] w(s)=0 (8-24)

[0268] The local compensation weights wU+(P) and wU-(P) are calculated with PU+ and PU- as the centers respectively, and the total U-direction compensation weight is:

[0269] wU(P)=wU+(P)+wU-(P) (8-25)

[0270] The same weight calculation method is adopted for the V direction, lU is replaced with lV, wV+(P) and wV-(P) are calculated respectively, and it is obtained that:

[0271] wV(P)=wV+(P)+wV-(P) (8-26)

[0272] After the compensation zones are determined using lU, lV and ltr described in this embodiment, the four groups of full compensation zones and their smooth transition zones do not overlap with each other.

[0273] 6. Local Normal Micro-Compensation for Stator Reference Generation Cross-Section

[0274] For any point P on the C0 boundary, the unit normal vector pointing from the stator solid to the cavity fluid region is denoted as n(P).

[0275] The displacement of P along the n(P) direction is defined as positive displacement, at which time the stator boundary moves toward the cavity fluid region and the local cavity shrinks; the displacement of P along the opposite direction of n(P) is defined as negative displacement, at which time the local cavity expands.

[0276] The absolute value of the maximum normal compensation in the complete compensation area in the U direction, Δa, is taken as: Δa = 0.020 mm.

[0277] The absolute value of the maximum normal compensation in the complete compensation region in the V direction is denoted as Δb, and is determined by the area closure described later.

[0278] A compensation direction parameter κ is defined to determine the opposite geometric adjustment directions of the two local compensation regions in the U and V directions. κ can be +1 or -1. When κ = -1, the local cavity in the U direction expands, and the local cavity in the V direction shrinks; when κ = +1, the local cavity in the U direction shrinks, and the local cavity in the V direction expands. For different stator and rotor structures and operating conditions, candidate compensation structures corresponding to different κ values ​​can be established, and evaluated according to the compensated geometric effective flow area, the minimum geometric clearance between the rotor and stator, the outlet volumetric flow rate, and the radial fluid pressure load to determine the corresponding compensation direction. In this embodiment, κ = -1 is used, that is, the local cavity in the U direction expands, and the local cavity in the V direction shrinks.

[0279] Therefore, the local cavity expands in the U direction and shrinks in the V direction.

[0280] The normal displacement δ(P) corresponding to any point P on the boundary C0 is:

[0281] δ(P)=κ×Δa×wU(P)-κ×Δb×wV(P) (8-27)

[0282] After compensation, the new boundary point P' corresponding to P is:

[0283] P'=P+δ(P)×n(P) (8-28)

[0284] The trajectory of P' obtained by continuously transforming all points on the C0 boundary according to equation (8-28) is defined as the compensated stator reference generation cross section C1.

[0285] 7. Determination of the area closed loop of the second compensation amount Δb

[0286] To ensure that the effective flow area of ​​the reference cross-section remains essentially unchanged before and after local compensation, the second compensation amount Δb is determined through area closure.

[0287] Based on the weighted integrals of the aforementioned complete compensation region and smooth transition region, the first-order equivalent length LU corresponding to the two centrally symmetric compensation regions in the U direction is:

[0288] LU = 4 × lU + 2 × ltr (8-29)

[0289] Substituting the parameters into this embodiment, we get: LU = 6.00 mm.

[0290] The first-order equivalent length LV corresponding to the two centrally symmetric compensation regions in the V direction is:

[0291] LV = 4 × lV + 2 × ltr (8-30)

[0292] The result is: LV = 15.00 mm.

[0293] Therefore: LU / LV = 0.400.

[0294] Based on the equivalent length relationship, the initial value of the second compensation amount Δb,0 is:

[0295] Δb,0 = Δa × LU / LV (8-31)

[0296] The calculation yields: Δb,0 = 0.0080 mm.

[0297] The compensation cross section C1 is generated according to Δb,0, and the actual cavity area enclosed by C1 is measured by CAD software.

[0298] Let the second compensation amount used in the k-th iteration be Δb,k, and the corresponding compensated cavity area measured by CAD be A1,k, and define the area error Ek:

[0299] Ek=A1,k-A0 (8-32)

[0300] If the area error does not meet the requirements, the second compensation amount in the next iteration will be adjusted according to the following formula:

[0301] Δb,k+1=Δb,k-Ek / (κ×LV) (8-33)

[0302] Each time Δb is adjusted, C1 is regenerated and the actual closed cavity area is measured by CAD software until the area retention requirement is met.

[0303] After area closure, this embodiment determines that Δb = 0.0081 mm.

[0304] At this point, the cavity area of ​​the stator reference cross-section after compensation is: A1 = 110.4685 mm². 2 .

[0305] The compensated reference cross-sectional geometric effective flow area Af,COMP is:

[0306] Af,COMP=A1-Ar (8-34)

[0307] We obtained: Af,COMP = 59.1927 mm 2 .

[0308] The relative change rate εA of the effective flow area of ​​the reference cross-section before and after compensation is:

[0309] εA=|Af,COMP-Af,BASE| / Af,BASE×100% (8-35)

[0310] The calculated value is εA = 0.0021%.

[0311] In this embodiment, εA ≤ 0.10%.

[0312] Therefore, the effective flow area of ​​the reference cross-section geometry before and after compensation meets the area retention requirement.

[0313] 8. Generation and geometric inspection of the internal surface of the three-dimensional stator after compensation.

[0314] The location of the compensated reference cross-section C1 is set as z=0, and the axial distance along the positive Z-axis is denoted as z.

[0315] The rotation angle φ(z) of the stator generated cross section at axial position z relative to the reference generated cross section at z=0 position satisfies:

[0316] φ(z)=σ×360°×z / T (8-36)

[0317] In the formula, σ is the rotation direction parameter that is consistent with the stator helix rotation direction used in Examples 1 to 6. The BASE model and COMP model use the same σ.

[0318] C1 is continuously rotated within the range of 0≤z≤Ls according to equation (8-36) and generated along the Z-axis to obtain the three-dimensional stator inner surface of the COMP model.

[0319] The U and V directions determined by θp are the compensation directions on the reference generated cross section at z=0. As C1 rotates axially according to equation (8-36), the local compensation regions in the U and V directions rotate synchronously with the reference generated cross section, forming a local compensation region that extends continuously along the stator helical direction on the inner surface of the three-dimensional stator.

[0320] After the three-dimensional surface is generated, the continuity of the compensation boundary curve and the three-dimensional surface is checked. It is required that there are no boundary self-intersections, surface self-intersections, unclosable fluid regions, or interference between the stator and rotor entities.

[0321] Further examine the complete effective working length Ls and the minimum rotor-stator geometric clearance within the complete rotor motion cycle.

[0322] The minimum Euclidean distance between the effective spiral working outer surface of the rotor and the inner surface of the stator within the range of 0≤z≤Ls and 0°≤ψ<360° is denoted as cmin.

[0323] In this embodiment, the minimum allowable geometric clearance creq is specified as: creq = 0.020 mm.

[0324] First, a driving phase increment of no more than 1° is used to search for the complete motion cycle. After determining the phase interval where the minimum gap is located, a phase increment of no more than 0.1° is used for local densification. The phase increment is then reduced until the change in cmin after further reducing the phase step size does not exceed 0.001mm.

[0325] Geometric inspection yielded: cmin = 0.0415 mm.

[0326] Since cmin > creq, the COMP model satisfies the minimum geometric gap requirement.

[0327] 9. Fluid computation conditions for the BASE and COMP models

[0328] Establish BASE fluid computation model and COMP fluid computation model respectively.

[0329] The BASE model uses the stator inner surface without local orientation micro-compensation; the COMP model uses the compensated three-dimensional stator inner surface generated according to the aforementioned method.

[0330] Except for the difference in the local internal surface of the stator, the rotor geometry, eccentricity, axial pitch, stator lead, effective working length, initial phase, rotor motion relationship, fluid medium, rotational speed, inlet boundary, outlet boundary, wall boundary, mesh control method, flow model, dynamic mesh processing method and solution settings of the two models are consistent.

[0331] The conveying medium is 25℃ clean water with a density of ρ = 997 kg / m³. 3 .

[0332] The dynamic viscosity is taken as μ = 0.00089 Pa·s.

[0333] The rotor speed is set to n = 240 r / min.

[0334] The absolute pressure at the pump inlet is: pin = 101325 Pa.

[0335] The absolute pressure at the pump outlet is taken as: pout = 301325 Pa.

[0336] Therefore, the pressure difference between the inlet and outlet is: Δp = pout - pin = 200000 Pa, that is: Δp = 0.20 MPa.

[0337] The rotor fluid contact wall is a non-slip wall that moves with the rotor, while the stator inner wall is a fixed non-slip wall. The flow model uses the same standard K-ε turbulence model as in Example 4; the BASE and COMP models use the same wall treatment and dynamic mesh motion implementation methods.

[0338] 10. Grid and Time Step Settings

[0339] The BASE and COMP models adopt the same overall mesh control principle, and perform local mesh refinement in the rotor-stator narrow gap region, the U-direction compensation region, the V-direction compensation region, and the smooth transition region.

[0340] The characteristic mesh size hmin near the minimum gap satisfies:

[0341] hmin≤cmin / 5 (8-37)

[0342] Sensitivity checks are performed by progressively increasing the mesh density before the formal comparison calculation.

[0343] Let Qavg,m be the steady-state periodic average outlet volumetric flow rate obtained from the finer mesh level between two adjacent mesh levels, and Qavg,m-1 be the coarser mesh level. Then the relative difference in flow rate meshes, δQ,mesh, is:

[0344] δQ,mesh=|Qavg,m-Qavg,m-1| / |Qavg,m|×100% (8-38)

[0345] Let the root mean square values ​​of the radial fluid pressure resultant force obtained from two adjacent grid levels be Fr,rms,m and Fr,rms,m-1, respectively. Then the relative difference δF,mesh of the radial pressure load grid is:

[0346] δF,mesh=|Fr,rms,m-Fr,rms,m-1| / Fr,rms,m×100% (8-39)

[0347] When δQ,mesh≤1% and δF,mesh≤2%, a finer first-order mesh is used to compare the formal BASE model and COMP model.

[0348] Under the condition of n=240r / min, the time τrev required for one complete 360° motion cycle is:

[0349] τrev=60 / n=0.25s.

[0350] Initially, each complete motion cycle consists of 120 transient time steps: Nstep = 120.

[0351] The corresponding time step Δt is:

[0352] Δt=τrev / Nstep=0.0020833s (8-40)

[0353] Further time-step sensitivity checks were performed using 240 steps / revolution.

[0354] When the relative difference between the steady-state periodic average outlet volumetric flow rate obtained from 240 steps / revolution and 120 steps / revolution does not exceed 1%, and the relative difference between the root mean square values ​​of the radial fluid pressure resultant force does not exceed 2%, 120 steps / revolution is used for formal comparison; otherwise, 240 steps / revolution is used for formal calculation.

[0355] Each transient time step undergoes internal iteration, and the iteration results of the inlet and outlet mass flow rates within that time step are required to meet the preset convergence criteria; the BASE model and the COMP model use the same internal iteration settings and convergence criteria.

[0356] 11. Determining a Periodic Steady State

[0357] Both the BASE and COMP models calculate at least three complete rotor motion cycles and continue calculating until the average outlet volumetric flow rate and radial fluid pressure load of adjacent complete cycles reach stability.

[0358] Let the average outlet volumetric flow rate of the k-th complete motion cycle be Qavg,k, and the previous complete motion cycle be Qavg,k-1. Then the relative rate of change of the average flow rate between adjacent cycles, δQ,cyc, is:

[0359] δQ,cyc=|Qavg,k-Qavg,k-1| / |Qavg,k|×100% (8-41)

[0360] Let the root mean square value of the radial fluid pressure resultant force in the k-th complete motion cycle be Fr,rms,k, and the value of the previous complete motion cycle be Fr,rms,k-1. Then the relative rate of change of radial load between adjacent cycles, δF,cyc, is:

[0361] δF,cyc=|Fr,rms,k-Fr,rms,k-1| / Fr,rms,k×100% (8-42)

[0362] When adjacent complete motion cycles simultaneously satisfy δQ,cyc≤1% and δF,cyc≤1%, the model is considered to have reached a periodic stable state.

[0363] The last complete 360° motion cycle after reaching a periodic stable state is taken as the formal evaluation cycle.

[0364] 12. Performance comparison between the BASE model and the COMP model

[0365] (1) Steady-state periodic average outlet volumetric flow rate

[0366] Let Qj be the instantaneous outlet volumetric flow rate corresponding to the j-th sampling position within the formal evaluation period, and define the direction of fluid flow from the pump to the outlet boundary as the positive direction; when instantaneous outlet backflow occurs, Qj retains a negative value according to the actual flow direction.

[0367] The steady-state periodic average outlet volumetric flow rate Qavg is:

[0368] Qavg=(1 / N)×ΣQj (8-43)

[0369] The steady-state periodic average outlet volumetric flow rates corresponding to the BASE model and the COMP model are denoted as Qavg,BASE and Qavg,COMP, respectively.

[0370] The steady-state periodic average outlet volumetric flow rate change ηQ of the COMP model relative to the BASE model is:

[0371] ηQ=(Qavg,COMP-Qavg,BASE) / Qavg,BASE×100% (8-44)

[0372] In this embodiment, ηQ≥-1% is defined as the criterion for determining that the outlet conveying capacity is basically maintained after local directional micro-compensation.

[0373] When the rotor speed is 240 r / min, according to the aforementioned optimal combination of stator and rotor structural parameters, the theoretical single-rotor displacement q = 0.64798 mL, and the theoretical outlet volumetric flow rate Qth is:

[0374] Qth = q × n / 60;

[0375] Substituting q=0.64798mL and n=240r / min, we get: Qth=0.64798×240 / 60=2.59192mL / s.

[0376] The volumetric efficiency of the BASE model is: ηv,BASE=90.67%.

[0377] The volumetric efficiency of the COMP model is: ηv,COMP = 90.28%.

[0378] The steady-state periodic average outlet volumetric flow rate of the BASE model is: Qavg,BASE=Qth×ηv,BASE, which gives: Qavg,BASE=2.350mL / s.

[0379] The steady-state periodic average outlet volumetric flow rate of the COMP model is: Qavg,COMP = Qth × ηv,COMP, which gives: Qavg,COMP = 2.340 mL / s. Substituting the above value into equation (8-44), we get: ηQ = -0.43%.

[0380] ηQ is greater than -1%, which satisfies the stable periodic average outlet volume flow rate maintenance condition specified in this embodiment.

[0381] (2) Radial fluid pressure load

[0382] The magnitude of the radial fluid pressure resultant force at the j-th sampling position is denoted as Fr,j, and it is stipulated that Fr,j≥0, and its square satisfies:

[0383] (Fr,j) 2 =(Fx,j) 2 +(Fy,j) 2 (8-45)

[0384] The root mean square value of the radial fluid pressure resultant force over a complete steady-state period is denoted as Fr,rms, and it is stipulated that Fr,rms ≥ 0, and its square satisfies:

[0385] (Fr,rms) 2 =(1 / N)×Σ(Fr,j) 2 (8-46)

[0386] The maximum value of the radial fluid pressure resultant force Fr,max within a complete steady cycle is:

[0387] Fr,max=max{Fr,1,Fr,2,...,Fr,N} (8-47)

[0388] The root mean square values ​​of the radial fluid pressure resultant force in the BASE and COMP models are denoted as Fr,rms,BASE and Fr,rms,COMP, respectively.

[0389] The rate of change of the root mean square value of the radial fluid pressure resultant force ηFr,rms of the COMP model relative to the BASE model is:

[0390] ηFr,rms=(Fr,rms,COMP-Fr,rms,BASE) / Fr,rms,BASE×100% (8-48)

[0391] The maximum values ​​of the radial fluid pressure resultant force in the BASE and COMP models are denoted as Fr,max,BASE and Fr,max,COMP, respectively.

[0392] The rate of change of the maximum radial fluid pressure resultant force ηFr,max of the COMP model relative to the BASE model is:

[0393] ηFr,max=(Fr,max,COMP-Fr,max,BASE) / Fr,max,BASE×100% (8-49)

[0394] The root mean square value of the steady-state periodic radial fluid pressure resultant force of the BASE model is: Fr,rms,BASE=32.0N.

[0395] The root mean square value of the steady-state periodic radial fluid pressure resultant force of the COMP model is: Fr,rms,COMP=29.5N.

[0396] From equation (8-48), we get: ηFr,rms = -7.81%.

[0397] The maximum radial fluid pressure resultant force of the BASE model is: Fr,max,BASE=47.0N.

[0398] The maximum radial fluid pressure resultant force of the COMP model is: Fr,max,COMP=43.5N.

[0399] From equation (8-49), we get: ηFr,max = -7.45%.

[0400] Therefore, after local directional micro-compensation, the root mean square value of the radial fluid pressure resultant force decreased by 7.81%, and the maximum value of the radial fluid pressure resultant force decreased by 7.45%.

[0401] (3) Directionality of radial fluid pressure load

[0402] Using the same data sampling and calculation methods as the BASE model, the radial fluid pressure load directionality coefficient is calculated according to equations (8-12) to (8-18) based on Fx and Fy within the formal evaluation period of the COMP model.

[0403] The directionality coefficient of the BASE model is: ηM,BASE=0.22.

[0404] The directionality coefficient of the COMP model is: ηM,COMP=0.15.

[0405] The COMP model reduces the directionality coefficient by 31.8% compared to the BASE model.

[0406] Therefore, after localized micro-compensation, the concentration of radial fluid pressure load along the original main load axis is reduced, and the distribution of radial pressure load in different directions of the cross section tends to be more balanced.

[0407] (4) Axial fluid pressure load

[0408] The maximum absolute value of the resultant axial fluid pressure within a complete stable cycle is used as an auxiliary evaluation parameter.

[0409] Let Fz,j be the resultant axial fluid pressure at the j-th sampling position, then:

[0410] Fz,max=max{|Fz,1|,|Fz,2|,...,|Fz,N|} (8-50)

[0411] The maximum absolute value of the resultant axial fluid pressure in the BASE model is: Fz,max,BASE=10.8N.

[0412] The maximum absolute value of the resultant axial fluid pressure in the COMP model is: Fz,max,COMP=11.0N.

[0413] The COMP model increases by 1.85% compared to the BASE model.

[0414] Therefore, the force change after local directional micro-compensation in this embodiment is mainly reflected in the reduction of the overall level, peak value and directional concentration of radial fluid pressure load, and is not based on the synchronous reduction of axial fluid pressure load as a criterion.

[0415] 13. Evaluation and Implementation Effect of the COMP Model

[0416] This embodiment evaluates the COMP model at three levels: geometric feasibility, outlet delivery performance, and radial fluid pressure load.

[0417] In terms of geometric feasibility, the relative change rate of the effective flow area of ​​the reference cross section before and after compensation satisfies: εA≤0.10%, the minimum rotor-stator geometric clearance within the complete effective working length and complete motion cycle satisfies: cmin≥0.020mm, and there is no boundary self-intersection, surface self-intersection, or stator-rotor solid interference in the inner surface of the stator after compensation.

[0418] In this embodiment, when κ=-1, Δa=0.020mm, Δb=0.0081mm, lU=1.25mm, lV=3.50mm and ltr=0.50mm, the relative change rate of the effective flow area of ​​the reference cross-section before and after compensation is 0.0021%, and the minimum geometric gap within the complete motion cycle is 0.0415mm, which satisfies the above geometric constraints.

[0419] Regarding the outflow performance, the steady-state periodic average outflow volumetric flow rate of the COMP model, compared to the BASE model, satisfies: ηQ≥-1%.

[0420] Regarding radial fluid pressure loads, Fr,rms is used to evaluate the overall level of radial loads within a complete steady-state period, Fr,max is used to evaluate the peak value of radial loads, and ηM is used to evaluate the directional concentration of radial pressure loads.

[0421] According to the results obtained in Part 12, the COMP model meets the requirement of maintaining the steady periodic average outlet volume flow rate, while the root mean square value of the radial fluid pressure resultant force, the maximum value of the radial fluid pressure resultant force, and the radial fluid pressure load directionality coefficient are all lower than those of the BASE model.

[0422] Therefore, under the conditions of basically maintaining the effective flow area of ​​the reference cross-section geometry, meeting the minimum geometric clearance requirement of the complete motion cycle, and maintaining the outlet conveying capacity, this embodiment implements local directional micro-compensation on the inner surface of the stator according to the radial fluid pressure main load axis, so as to redistribute the rotor radial fluid pressure load, reduce the overall level and peak value of the radial fluid pressure load in the stable period, and weaken the concentration of the radial fluid pressure load along the original main load axis direction.

[0423] In this embodiment, κ, Δa, Δb, lU, lV, and ltr constitute a set of local directional micro-compensation implementation parameters. For different stator and rotor structural dimensions, operating speeds, inlet and outlet pressure differences, and conveying media, the corresponding compensation parameters can be adjusted according to the radial main load direction identification, compensation center determination, local normal compensation, area closed-loop, three-dimensional surface generation, and BASE model and COMP model comparison methods described in this embodiment. The effective flow area of ​​the reference cross-section geometry, the minimum geometric clearance of the complete motion cycle, the average outlet volumetric flow rate of the stable cycle, and the radial fluid pressure load are used as constraints and evaluation indicators.

Claims

1. A method for optimizing the design parameters of the stator and rotor structure of a single screw pump, wherein the single screw pump includes a single-head helical rotor and a double-head helical stator that cooperates with the single-head helical rotor, and the stator and rotor structure parameters include eccentricity e, rotor cross-sectional circle diameter D, and axial pitch t of the helical teeth of the stator and rotor, characterized in that, include: Based on the target single-rotor theoretical displacement and the theoretical displacement relationship q=4×e×D×t, the target structural parameter relationship between eccentricity e, rotor cross-sectional circle diameter D and axial pitch t is determined. Based on the structural ratio constraints of the stator and rotor and the accuracy constraints of parameter values, numerical screening is performed on the eccentricity e, the rotor cross-sectional circle diameter D and the axial pitch t to obtain multiple candidate combinations of stator and rotor structural parameters. Under the same operating conditions, fluid simulation was performed on the candidate stator and rotor structural parameter combinations to obtain the outlet volume flow rate and rotor fluid pressure load corresponding to each candidate stator and rotor structural parameter combination. The candidate stator and rotor structural parameter combinations are screened in stages based on the outlet volumetric flow rate and rotor fluid pressure load to determine the preferred stator and rotor structural parameter combinations under the target operating conditions.

2. The method for optimizing the design parameters of the stator and rotor structure of a single screw pump according to claim 1, characterized in that, When the rotor operates at a speed of n, the theoretical outlet volumetric flow rate Q of the single screw pump is determined according to the following formula: Q=(4×e×D×t×n)÷(60×1000); Where Q is in mL / s, e, D and t are in mm, and n is in r / min.

3. The method for optimizing the design parameters of the stator and rotor structure of a single screw pump according to claim 1, characterized in that, The proportional constraints of the stator and rotor structure include: 0.1×D≤e≤0.22×D; 1.4×D≤t≤2.5×D; The parameter value accuracy constraints include: the eccentricity e and the rotor cross-sectional circle diameter D are retained to 2 decimal places, and the axial pitch t is retained to 3 decimal places.

4. The method for optimizing the design parameters of the stator and rotor structure of a single screw pump according to claim 3, characterized in that, The numerical filtering includes: Select D within the search range of the rotor cross-sectional circle diameter D; The allowable range of eccentricity e corresponding to the current D is determined based on the structural proportional relationship between eccentricity e and rotor cross-sectional circle diameter D, and eccentricity e is selected within the allowable range. For each set of eccentricity e and rotor cross-sectional circle diameter D, the corresponding theoretical axial pitch is determined according to the relationship of the target structural parameters. Determine whether the theoretical axial pitch satisfies the structural ratio constraint between the axial pitch t and the rotor cross-sectional circle diameter D. The parameters that satisfy the structural proportion constraints are discretized according to the preset parameter value precision, and the structural proportion of the discretized stator and rotor structural parameters are re-verified. The parameter combinations that pass the verification are used as candidate stator and rotor structural parameter combinations.

5. The method for optimizing the design parameters of the stator and rotor structure of a single screw pump according to claim 1, characterized in that, During the fluid simulation, different candidate stator and rotor structural parameter combinations use the same fluid medium, inlet pressure, inlet and outlet pressure difference, and corresponding solution conditions, and obtain the outlet volume flow rate and the resultant radial pressure and axial pressure of the fluid pressure acting on the rotor for each candidate stator and rotor structural parameter combination.

6. The method for optimizing the design parameters of the stator and rotor structure of a single screw pump according to claim 5, characterized in that, Based on the outlet volumetric flow rate, candidate parameter combinations with different stator and rotor structural parameters are compared and the range of candidate parameters is gradually narrowed down. When the outlet volume flow rates corresponding to multiple candidate stator and rotor structural parameter combinations are relatively close, the rotor radial fluid pressure loads corresponding to the multiple candidate stator and rotor structural parameter combinations are further compared, and the preferred parameter combination is determined by combining the variation characteristics of the axial fluid pressure load. The rotor radial fluid pressure load is evaluated at least based on the peak value and fluctuation of the radial pressure resultant force.

7. The method for optimizing the design parameters of the stator and rotor structure of a single screw pump according to any one of claims 1-6, characterized in that, The target single-cycle theoretical displacement is 648mm. 3 The determined optimal combination of stator and rotor structural parameters is: eccentricity e = 1.77 mm, rotor cross-sectional circle diameter D = 8.08 mm, axial pitch t = 11.327 mm, corresponding to a lead T = 22.654 mm for the double-headed spiral stator.

8. The method for optimizing the design parameters of the stator and rotor structure of a single screw pump according to claim 1, characterized in that, After determining the preferred combination of stator and rotor structural parameters, the method further includes local orientation compensation of the stator inner surface, wherein the local orientation compensation includes: Establish a reference fluid calculation model for the stator and rotor structure without local directional compensation; The direction of the main radial fluid pressure load is determined based on the rotor radial fluid pressure load during the stable motion cycle of the reference fluid calculation model. The local compensation position of the stator inner surface is determined according to the direction of the radial fluid pressure main load, and the local geometric adjustment is performed on the stator inner surface corresponding to the local compensation position; The results of the local geometric adjustment are evaluated based on the effective flow area, rotor-stator geometric clearance, outlet volumetric flow rate, and rotor radial fluid pressure load before and after the local geometric adjustment, so as to determine the inner surface of the stator after compensation.

9. The method for optimizing the design parameters of the stator and rotor structure of a single screw pump according to claim 8, characterized in that, The main load axis of the radial fluid pressure load is determined based on the resultant force of the fluid pressure in two mutually perpendicular radial directions within a complete stable motion cycle. The main load axis is taken as the first compensation direction, and the direction that passes through the center of the stator reference generated cross section and is perpendicular to the first compensation direction is taken as the second compensation direction. The local compensation position is determined based on the extreme values ​​of the projection of the stator reference generated cross section boundary in the first compensation direction and the second compensation direction, and local compensation regions symmetrical about the center of the stator reference generated cross section are set in the first compensation direction and the second compensation direction, respectively.

10. The method for optimizing the design parameters of the stator and rotor structure of a single screw pump according to claim 9, characterized in that, In the local compensation regions corresponding to the first compensation direction and the second compensation direction, local normal displacements are applied to the stator reference generated cross section boundary, so that the local cavity corresponding to one compensation direction is enlarged and the local cavity corresponding to the other compensation direction is reduced. The compensation amount is determined based on the geometric relationship between the local compensation areas corresponding to the two compensation directions, and at least one of the compensation amounts is adjusted based on the area difference between the stator reference generated cross section after compensation and the stator reference generated cross section before compensation, so that the geometric effective flow area before and after compensation meets the area retention requirement. The compensated stator reference cross section is generated along the stator helical direction to generate the compensated three-dimensional stator inner surface. The rotor-stator geometric clearance is verified on the compensated three-dimensional stator inner surface, and the outlet volume flow rate and rotor radial fluid pressure load before and after local compensation are compared.

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