Dimension reduction method for complex profile curve of unloading groove of aviation fuel gear pump

Abstract

The invention discloses a dimension reduction method for a complex profile curve of an unloading groove of an aviation fuel gear pump. Step 1; a Douglas-Peucker algorithm is adopted to intelligently screen contour point clouds, a curve of a complex part is separated independently, the curve of the part is separated from the whole, 100 points are extracted from the separated complex curve to serve as target points, and the coordinates of the target points are stored as a. Txt file; 2, selecting four points to describe a complex curve; and step 3, using a genetic algorithm to compare one hundred points generated by using the Bezier curve in each group with the original points extracted from the complex curve, performing iteration, and finally obtaining two most coincident points. And 4, connecting the complex curve part obtained by using the Bezier curve and the genetic algorithm with the simple curve of the profile of the unloading groove of the aviation fuel gear pump, comparing with the original curve, and verifying the curvature continuity. The method has the characteristics of few variables, easiness in control and convenience in subsequent optimization.

Description

Technical Field

[0001] This invention relates to the field of aviation fuel gear pump technology, and in particular to a method for reducing the dimension of complex contour curves of unloading grooves in aviation fuel gear pumps. Background Technology

[0002] The profile curve of the unloading groove of the aviation fuel gear pump is complex and cannot usually be described by a simple equation, making it difficult to establish a surrogate model for parameterization in optimization.

[0003] Regarding the profile shape of the unloading groove in gear pumps, Qi Guoning's 2024 article, "Comparative Analysis of Typical Unloading Grooves in High-Speed ​​High-Pressure Fuel Gear Pumps," compared and analyzed many typical unloading grooves in high-speed high-pressure fuel gear pumps. The profile curve of the new unloading groove was complex, and the study only examined its cavitation characteristics against other unloading groove shapes, without optimizing the profile of the new unloading groove based on these characteristics. Du Haoqiang's 2024 article, "Experimental Study on Leakage Calculation, Unloading Groove Optimization, and Performance Testing of Gear Pumps," proposed an improved unloading groove, but did not describe its profile curve in detail. It also mentioned that no relevant literature has provided a theoretically optimal solution for the unloading groove shape, making further improvement impossible. However, the Bézier curve method allows for further optimization by adjusting control points to modify the unloading groove shape.

[0004] In his 2024 paper, "A Review of Key Technologies for Long-Life, High-Reliability Fuel Gear Pumps for Aero-engines," Fu Jiangfeng mentioned that the design of unloading grooves requires an iterative optimization process. The problems include the complexity of the design process necessitating iterative optimization, the limited ability of existing traditional structures to alleviate trapped fuel, and the complex contours of the new designs bringing about issues related to machining, wear, and unloading capacity. Furthermore, the original curve requires altering too many points, and further optimization necessitates reducing control variables.

[0005] In summary, the shortcomings of existing technologies are that the optimization design of the unloading groove of aviation fuel gear pump is complex, the unloading groove shapes proposed by various domestic scholars are complex and not easy to optimize, and there is no method to reduce the dimensionality of the curve and use fewer control variables to optimize the design. Summary of the Invention

[0006] To overcome the above technical problems, the present invention aims to provide a dimensionality reduction method for the complex contour curve of the unloading groove of an aviation fuel gear pump, which has the characteristics of being able to simply describe the complex contour of the unloading groove, being easy to control the shape of the gear pump unloading groove, and facilitating subsequent simulation and optimization research of the gear pump.

[0007] The technical solution adopted in this invention is: A method for reducing the dimension of a complex profile curve of an unloading groove in an aviation fuel gear pump includes the following steps; Step 1: The Douglas-Puk algorithm is used to intelligently filter the complex contour point cloud of the aviation fuel gear pump unloading groove, separate the complex part of the curve, isolate the part of the curve from the whole, extract 100 points from the separated complex curve as target points, save their coordinates as a .txt file, and use them as target points for the genetic algorithm later.

[0008] Step 2: Set the upper and lower bounds of the control points and the parameters required for the genetic algorithm, including population size, number of iterations, mutation rate, crossover scheme, and fitness function. Define the Bézier curve. This paper uses a fourth-order Bézier curve. If there are more complex curves, fifth-order or sixth-order Bézier curves can be used to provide a foundation for the operation of the genetic algorithm in Step 3.

[0009] Step 3: Use a genetic algorithm to screen and iteratively optimize the population from Step 2, generating 100 populations. Each population contains 50 sets of points. Each set is fitted with a cubic Bézier curve. When the maximum number of iterations is reached or the set fitness value is reached (i.e., the sum of the distances between the fitted curve and the points in the coordinates.txt file separated in Step 1 is less than the set value), the point obtained at this time is the final control point.

[0010] Step 4: Use the two points obtained in Step 3 to perform Bézier curve fitting. Connect the complex curve obtained by using Bézier curve and genetic algorithm with the simple curve of the unloading groove profile of aviation fuel gear pump. Compare with the original curve to verify the curvature continuity. The complex part of the curve of aviation fuel gear pump unloading groove profile can be controlled by the two points obtained in Step 3, thus achieving dimensionality reduction.

[0011] The detailed steps of step one are as follows: 11) The Douglas-Pock algorithm is applied with an initial tolerance of ε = 0.2 mm, and a recursive segmentation algorithm is executed: ① Connect the first and last points of the line to form a baseline straight line; ② Calculate the perpendicular distance from all intermediate points to the line; ③ Record the maximum deviation value d_max and its corresponding point P_max; ④ If d_max > ε, then divide the curve at P_max and recursively process each sub-segment. ⑤ Repeat the iteration until all sub-segments meet the tolerance requirements. 12) Target point sampling and data storage: ① Store both ends of the complex curves selected by the Douglas-Puk algorithm in a matrix; ② Use the stored points as the start and end points of the Bézier curve in the next step.

[0012] The second step is specifically as follows: 21) Setting Genetic Algorithm Parameters Set the range of control points. The lower bound of the range of control points is set to the minimum value of all target point coordinates minus one, and the upper bound is the maximum value of all target point coordinates plus one. At the same time, ensure that the curvature of the start and end points of the Bézier curve meets the engineering feasibility. This will ensure that the Bézier curves fitted by the generated control points are mostly meaningful and will not differ too much from the original unloading trough complex curve. Set appropriate population size, iteration number, mutation rate, crossover scheme and fitness function. 22) Fitting curves using Bézier curves Define the formula for Bézier curves: For each set of control points Use the Bézier curve formula to generate points on the curve, and set the parameters... t Take 100 values ​​at equal intervals from 0 to 1, and calculate each... t The corresponding coordinates of the curve points are used to store the 100 generated curve points into a matrix.

[0013] Step three specifically involves: 31) Initialize the population: Generate multiple sets of control points (based on population size), with each set generated randomly. P 1 、P 2 Two control points, each group of which uses a Bézier curve to generate 100 points.

[0014] 32) Assess fitness: In Bézier curve optimization, the fitness value represents the fitting error between the curve and the target point; a higher fitness value indicates a better individual curve. Simultaneously, it's crucial to ensure the generated curve is applicable and enables the gear pump to operate normally (without causing oil leaks, abnormal gear cavity pressure, etc.). The fitness value can be lowered to prevent issues with abnormal flow rates and gear cavity pressures during simulation, thus preventing iterations to the next generation.

[0015] 33) Cross: New individuals are generated through crossover operations, and the control points of the complex profile curves of different individuals are exchanged (the AB individual and the CD individual are exchanged to produce AD ​​and BC). This allows the new individuals to have control points that are more in line with the requirements of the parent generation, i.e., more in line with the complex profile curve of the original gear pump. The characteristics of the two populations with low fitness values ​​are preserved. 34) Mutation: Random perturbation is applied to individuals in the population to increase its diversity and provide more control points. This prevents the generation of control points from failing to produce control points that conform to the complex unloading groove curve. Furthermore, if the population with the highest fitness value also fails to conform to the unloading groove curve, the desired result will not be achieved in continuous iteration. Therefore, the mutation operation range is controlled by mutating the control points that control the complex contour curve of the gear pump unloading groove within a 0.5mm range of their coordinates. By using mutation operations to partially change the control points during iteration, more suitable control points can be obtained. 35) Update the population: A new individual with a better fitness and more in line with the original unloading trough curve is selected. The newly generated individual is combined with the parent individual to form the next generation population. At this time, control points that meet the requirements are selected. 36) Iteration: Repeat the above steps until the maximum number of iterations or the fitness value converges, and obtain the final optimal control point.

[0016] The detailed steps of step four are as follows: 41) Connect the simple curve and the complex curve of the unloading groove of the aviation fuel gear pump and store them in a matrix, and calculate the curvature of the transition between the simple curve and the complex curve.

[0017] 42) Compare the calculated curvature with the curvature of the original curve to ensure that the difference in curvature is less than 5%, and at the same time ensure that the simple curve is tangent to the tooth tip circle.

[0018] The beneficial effects of this invention are: This invention addresses the complexity of unloading groove contour design in aviation fuel gear pumps by proposing a dimensionality reduction modeling method based on Bézier curves. Traditional unloading groove contours often employ composite curves composed of multiple circular arcs, involutes, and straight lines. Establishing a parametric model frequently requires numerous geometric parameters, leading to high computational dimensionality and low iteration efficiency in subsequent fluid dynamics simulations and performance optimization. The innovation of this invention lies in reconstructing the complex contour using cubic Bézier curves. Through mathematical modeling, the curve, which originally required multiple parameters, is reduced to a precise representation using only two control point coordinates (corresponding to four independent variables). This method leverages the second-order continuity of Bézier curves, reducing the unloading groove contour parameter dimension from 70 dimensions to 10 dimensions—an 85% reduction in variables—while ensuring normal flow rate and gear cavity pressure. Attached Figure Description

[0019] Figure 1 A schematic diagram of the complex contour curve of the unloading groove of an aviation fuel gear pump.

[0020] Figure 2A schematic diagram of the complex contour curve of the unloading groove of an aviation fuel gear pump.

[0021] Figure 3 A schematic diagram illustrating the Douglas-Puk algorithm for separating complex curves.

[0022] Figure 4 This is a schematic diagram of fitting the first complex curve using a genetic algorithm.

[0023] Figure 5 A schematic diagram of fitting the complex curve in the second part using a genetic algorithm.

[0024] Figure 6 This is a schematic diagram of the unloading groove curve formed by reconnecting the fitted parts.

[0025] Figure 7 This is a schematic diagram showing the simulation comparison of tooth cavity pressure before and after using the fitted contour curve. Detailed Implementation

[0026] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0027] A method for reducing the dimension of a complex profile curve of an unloading groove in an aviation fuel gear pump includes the following steps; Step 1; Currently, the profile curve of the unloading groove of aviation fuel gear pump has significant non-uniform curvature characteristics, such as... Figure 2 The profile curve of the unloading groove of the aviation fuel gear pump shown has two parts with large curvature, and the points describing the curve are very dense. Using the Douglas-Peucker algorithm for intelligent filtering of the profile point cloud, the parts with excessive curvature, i.e., those that deviate too far from the curve, can be filtered out, separating the complex parts of the curve separately, such as... Figure 3 As shown, the curve fitted by the Douglas-Puk algorithm is far from the points on the original curve. Therefore, this part of the curve is separated from the whole, and 100 points are extracted from the separated complex curve as target points, and their coordinates are saved as a .txt file. Figure 1 The straight line and the contour curve of the Douglas-Puk fitting shown in this part are too far apart; The detailed steps of step one are as follows: 11) The Douglas-Pock algorithm is applied with an initial tolerance of ε = 0.05 mm, and a recursive segmentation algorithm is executed: ① Connect the first and last points of the point column to form a reference straight line. ② Calculate the perpendicular distance from all intermediate points to the straight line. ③ Record the maximum deviation value d_max and its corresponding point P_max. ④ If d_max > ε, then segment the curve at P_max and recursively process each segment. ⑤ Repeat the iteration until all segments meet the tolerance requirements. 12) Target point sampling and data storage Data normalization processing: Establish a local coordinate system (with the origin set on the gear pump axis). Unify the units Store point data on the separation curve Step 2: Generate two random points within the range of the starting and ending points. Ensure the generated curves have certain curvature constraints, such as tangency to the addendum circle, to guarantee the feasibility of the gear pump project. Generate 100 populations, each with 50 sets of points. Each set is fitted using a cubic Bézier curve. When the maximum number of iterations is reached, or the set fitness value is achieved (i.e., the sum of the distances between the fitted curve and all points in the complex curve of the original aviation fuel gear pump unloading groove is less than the set value), the resulting point is the final control point.

[0028] A complex curve can be described by selecting only four points. When describing a curve, the starting and ending points are mostly determined, that is... and Since it is known, we only need to find the matching ones. and The genetic algorithm ultimately yields two points, with their x and y coordinates as variables. This transforms a complex curve that requires a large number of points into a curve that only needs four variables, achieving dimensionality reduction. This facilitates the control of complex curves such as the unloading groove of an aviation fuel gear pump and is of great significance for subsequent applications such as establishing surrogate models.

[0029] like Figure 1 This is the outline curve of the unloading groove at the inlet of the aviation fuel gear pump; the complex curved portion is enclosed by an ellipse. Figure 2 This is a scatter plot of the profile curve of the unloading groove at the inlet of an aviation fuel gear pump. Complex sections of the curve require at least 20 points to fit a smooth curve. To more clearly and conveniently identify points with excessive curvature, the Douglas-Peucker algorithm is used for filtering. The line fitted by the Douglas-Peucker algorithm is compared with the original profile curve; the parts with the largest differences are the complex curve sections, which are then fitted using Bézier curves. Figure 3 The image shown is a complex curve section where the Douglas-Puk algorithm and the original image are compared.

[0030] Using MATLAB, two random points are generated within the range of the start and end points, resulting in 100 populations. Each population contains 50 sets of points, and each set is fitted with a cubic Bézier curve.

[0031] A curve can be described using only four points, and the starting and ending points are mostly fixed when describing a curve. and Since it is known, we only need to find the matching ones. and The x-coordinate and y-coordinate of two points are used as variables, transforming a complex curve that requires a large number of points into a curve that can be described by only four variables. This dimensionality reduction is significant for subsequent applications such as building surrogate models. 100 points are generated by taking 100 equally spaced values ​​of Bézier curve t from 0 to 1 to describe the curve.

[0032] The second step is specifically as follows: 21) Generate a population of random control points The control point range is defined by setting the lower bound to the minimum coordinate of all target points minus one, and the upper bound to the maximum coordinate of all target points plus one. For each population, 50 sets of random control points are generated. Each control point set contains 4 variables, which are generated using a random number generation function within the defined range.

[0033] 22) Fitting curves using Bézier curves Define the formula for Bézier curves: For each set of control points Use the Bézier curve formula to generate points on the curve, and set the parameters... t Take 100 values ​​at equal intervals from 0 to 1, and calculate each... t The corresponding curve point coordinates are used to store the 100 generated curve points into a cell array.

[0034] Step 3: Use a genetic algorithm to screen and iteratively optimize the population from Step 2, generating 100 populations. Each population contains 50 sets of points. Each set is fitted with a cubic Bézier curve. When the maximum number of iterations is reached or the set fitness value is reached (i.e., the sum of the distances between the fitted curve and the points in the coordinates.txt file separated in Step 1 is less than the set value), the point obtained at this time is the final control point.

[0035] Step three specifically involves: 31) Initialize the population: Generate multiple sets of control points (based on population size), with each set generated randomly. P 1 、P 2Two control points are used to generate the Bézier curves. Each set of control points represents a complex contour curve of the unloading groove of the aviation fuel gear pump. 32) Assess fitness: In Bézier curve optimization, the fitness value is the peak and minimum values ​​of the gear pump tooth cavity pressure obtained from simulation. The higher the fitness value, the better the individual. At the same time, it is necessary to ensure that the generated curve is applicable and can enable the gear pump to work normally. The fitness value is lowered for abnormal simulated flow and tooth cavity pressure to prevent iteration to the next generation. 33) Cross: New individuals are generated through crossover operations, and the control points of the complex profile curves of different individuals are exchanged (the AB individual and the CD individual are exchanged to produce AD ​​and BC). This allows the new individuals to have control points that are more in line with the requirements of the parent generation, i.e., more in line with the complex profile curve of the original gear pump. The characteristics of the two populations with low fitness values ​​are preserved. 34) Mutation: Random perturbation is applied to individuals in the population to increase its diversity and provide more control points. This prevents the generation of control points from failing to produce control points that conform to the complex unloading groove curve. Furthermore, if the population with the highest fitness value also fails to conform to the unloading groove curve, the desired result will not be achieved in continuous iteration. Therefore, the mutation operation range is controlled by mutating the control points that control the complex contour curve of the gear pump unloading groove within a 0.5mm range of their coordinates. By using mutation operations to partially change the control points during iteration, more suitable control points can be obtained. 35) Update the population: A new individual with a better fitness and more in line with the original unloading trough curve is selected. The newly generated individual is combined with the parent individual to form the next generation population. At this time, control points that meet the requirements are selected. 36) Iteration: Repeat the above steps until the maximum number of iterations or the fitness value converges, and obtain the final optimal control point.

[0036] like Figure 4 , 5 As shown In the figure, the red dots are the target points extracted from the complex curve, the green dots are the optimal control points in the Bézier curve finally obtained using the genetic algorithm, and the blue curve is the optimal Bézier curve finally obtained using the genetic algorithm. It can be seen that the drawn Bézier curve is very similar to the original complex curve and the transition is smoother.

[0037] Step 4: Use the two points obtained in Step 3 to perform Bézier curve fitting. Connect the complex curve obtained using the Bézier curve and genetic algorithm with the simple curve of the aviation fuel gear pump unloading groove profile, and compare it with the original curve to verify the curvature continuity. For example... Figure 6 As shown, this is a graph where the curves generated by Bézier curves are connected to form a single curve representing the profile of the unloading groove of an aviation fuel gear pump. This curve is then imported into simulation software for simulation, and the final gear cavity pressure curve is shown below. Figure 7 As shown.

[0038] Step four specifically involves: 41) Connect the simple curve and the complex curve of the unloading groove of the aviation fuel gear pump and store them in a matrix, and calculate the curvature of the transition between the simple curve and the complex curve.

[0039] 42) Compare the calculated curvature with the curvature of the original curve to ensure that the difference in curvature is less than 5%, and at the same time ensure that the simple curve is tangent to the tooth tip circle.

Claims

1. A method for dimensionality reduction of the complex contour curve of the unloading groove of an aviation fuel gear pump, characterized in that, Includes the following steps; Step 1: The Douglas-Puk algorithm is used to intelligently filter the complex contour point cloud of the aviation fuel gear pump unloading groove, separate the complex part curves, isolate the part curves from the whole, extract the target points from the separated complex curves, and save their coordinates as a .txt file, which will be used as the target points for the genetic algorithm later. Step 2: Set the upper and lower bounds of the control points and the parameters required for the genetic algorithm, such as population size, number of iterations, mutation rate, crossover scheme, and fitness function. Define the Bézier curve to provide a foundation for the operation of the genetic algorithm in Step 3. Step 3: Use a genetic algorithm to screen and iteratively optimize the population from Step 2 to generate population groups. Each group is fitted with a cubic Bézier curve. When the maximum number of iterations is reached or the set fitness value is reached (i.e., the sum of the distances between the fitted curve and the points in the coordinates.txt file separated in Step 1 is less than the set value), the point obtained at this time is the final control point. Step 4: Use the two points obtained in Step 3 to perform Bézier curve fitting. Connect the complex curve obtained by using Bézier curve and genetic algorithm with the simple curve of the unloading groove profile of aviation fuel gear pump. Compare with the original curve to verify the curvature continuity. The complex part of the curve of aviation fuel gear pump unloading groove profile can be controlled by the two points obtained in Step 3, thus achieving dimensionality reduction.

2. The method for dimensionality reduction of the complex contour curve of the unloading groove of an aviation fuel gear pump according to claim 1, characterized in that, Step one specifically includes: 11) The Douglas-Pock algorithm is applied with an initial tolerance of ε = 0.2 mm, and a recursive segmentation algorithm is executed: ① Connect the first and last points of the line to form a baseline straight line; ② Calculate the perpendicular distance from all intermediate points to the line; ③ Record the maximum deviation value d_max and its corresponding point P_max; ④ If d_max > ε, then divide the curve at P_max and recursively process each sub-segment. ⑤ Repeat the iteration until all sub-segments meet the tolerance requirements. 12) Target point sampling and data storage: ① Store both ends of the complex curves selected by the Douglas-Puk algorithm in a matrix; ② Use the stored points as the start and end points of the Bézier curve in the next step.

3. The method for dimensionality reduction of the complex contour curve of the unloading groove of an aviation fuel gear pump according to claim 1, characterized in that, The second step is specifically as follows: 21) Setting Genetic Algorithm Parameters Set the range of control points. The lower bound of the range of control points is set to the minimum value of all target point coordinates minus one, and the upper bound is the maximum value of all target point coordinates plus one. At the same time, ensure that the curvature of the start and end points of the Bézier curve meets the engineering feasibility. This will ensure that the Bézier curves fitted by the generated control points are mostly meaningful and will not differ too much from the original unloading trough complex curve. Set appropriate population size, iteration number, mutation rate, crossover scheme and fitness function. 22) Fitting curves using Bézier curves Define the formula for Bézier curves: For each set of control points Use the Bézier curve formula to generate points on the curve, and set the parameters... t Values ​​are taken at equal intervals from 0 to 1, and each is calculated. t The corresponding curve point coordinates are stored in a matrix. The more values ​​t have, the smoother the generated curve and the better it fits the complex contour curve of the original aviation fuel gear pump unloading groove.

4. The method for dimensionality reduction of the complex contour curve of the unloading groove of an aviation fuel gear pump according to claim 1, characterized in that, Step three specifically involves: 31) Initialize the population: Generate multiple sets of control points (based on population size), with each set generated randomly. P 1 、P 2 Two control points are used to generate the Bézier curves. Each set of control points represents a complex contour curve of the unloading groove of the aviation fuel gear pump. 32) Assess fitness: In Bézier curve optimization, the fitness value is the peak and minimum values ​​of the gear pump tooth cavity pressure obtained from simulation. The higher the fitness value, the better the individual. At the same time, it is necessary to ensure that the generated curve is applicable and can enable the gear pump to work normally. The fitness value is lowered for abnormal simulated flow and tooth cavity pressure to prevent iteration to the next generation. 33) Cross: New individuals are generated through crossover operations, and the control points of the complex profile curves of different individuals are exchanged (the AB individual and the CD individual are exchanged to produce AD ​​and BC). This allows the new individuals to have control points that are more in line with the requirements of the parent generation, i.e., more in line with the complex profile curve of the original gear pump. The characteristics of the two populations with low fitness values ​​are preserved. 34) Mutation: Random perturbation is applied to individuals in the population to increase its diversity and provide more control points. This prevents the generation of control points from failing to produce control points that conform to the complex unloading groove curve. Furthermore, if the population with the highest fitness value also fails to conform to the unloading groove curve, the desired result will not be achieved in continuous iteration. Therefore, the mutation operation range is controlled by mutating the control points that control the complex contour curve of the gear pump unloading groove within a 0.5mm range of their coordinates. By using mutation operations to partially change the control points during iteration, more suitable control points can be obtained. 35) Update the population: A new individual with a better fitness and more in line with the original unloading trough curve is selected. The newly generated individual is combined with the parent individual to form the next generation population. At this time, control points that meet the requirements are selected. 36) Iteration: Repeat the above steps until the maximum number of iterations or the fitness value converges, and obtain the final optimal control point.

5. The method for dimensionality reduction of the complex contour curve of the unloading groove of an aviation fuel gear pump according to claim 1, characterized in that, The detailed steps of step four are as follows: 41) Connect the simple curve and the complex curve of the unloading groove of the aviation fuel gear pump and store them in a matrix, and calculate the curvature of the transition between the simple curve and the complex curve. 42) Compare the calculated curvature with the curvature of the original curve to ensure that the difference in curvature is less than 5%, and at the same time ensure that the simple curve is tangent to the tooth tip circle.

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