An optimization method for gear flowmeter considering various performance indexes

Abstract

This invention relates to an optimization method that comprehensively considers various performance indicators of gear flow meters, belonging to the field of flow meter optimization design. It analyzes the influence of gear structural parameters on the gear flow meter based on the calculation formulas for various performance indicators. Combining the gear structural parameters, it analyzes the mutual influence trends among various performance indicators. Then, based on the actual operating conditions, it selects the indicator with the highest requirement as the objective, uses the other two indicators as constraint functions, and determines the design variables to establish an optimization model. Finally, it selects a suitable optimization algorithm to solve the optimization equations, obtaining the optimal structural parameters of the gear flow meter under actual operating conditions. Compared with existing single-objective optimization methods for gear flow meters, this invention can fully consider multiple performance indicators affecting the gear flow meter, ensuring that multiple indicators of the gear flow meter are taken into account and eliminating the problem that multi-objective optimization cannot obtain a definite optimal solution.

Description

Technical Field

[0001] This invention relates to the field of flow meter optimization design, and specifically to an optimization method for improving the overall performance of a gear flow meter by considering various performance indicators. Background Technology

[0002] Gear flow meters are a type of positive displacement flow meter. They are widely used in applications requiring high-precision flow signal measurement, such as aircraft control and machine tool precision control, due to their advantages including high measurement accuracy, wide flow range, insensitivity to oil, and strong pressure resistance. Typically, cylindrical gear flow meters can achieve a measurement accuracy of ±0.5% and an operating pressure exceeding 40 MPa, making them suitable for accurate measurement of fluids such as hydraulic oil, silicone resin, and diesel fuel. However, some foreign brands of flow meters can achieve a measurement accuracy of ±0.1% and a maximum operating pressure as high as 63 MPa. Against the backdrop of domestic manufacturing upgrading and the rapid development of high-precision manufacturing, cylindrical gear flow meters will play an even greater role in application value. At the same time, this also presents greater challenges to the structural design and manufacturing of flow meters.

[0003] Flow pulsation coefficient, internal leakage, and total power loss are three crucial performance indicators of gear flow meters, and also important optimization metrics in their design. Excessive flow pulsation leads to significant pressure pulsation, affecting system stability; therefore, flow pulsation should be minimized in high-precision electro-hydraulic servo systems. Excessive internal leakage severely impacts the accuracy of gear flow meters, and the presence of gaps also results in leakage power loss and viscous friction loss. Total power loss is also a critical indicator; higher viscous friction resistance leads to excessive total power loss, negatively affecting the dynamic response characteristics and measurement accuracy of the gear flow meter.

[0004] Numerous factors influence the performance of gear flow meters. Gear structural parameters (number of teeth, module, and pressure angle), clearance heights (radial and axial clearances), the viscosity of the oil medium, and external environmental factors such as temperature and pressure all have a certain impact. Therefore, these factors should be comprehensively considered during the design and optimization of gear flow meters. However, currently, the selection of structural parameters in gear flow meter design mainly relies on experience, and the impact of these factors on gear flow meter performance is insufficiently considered. Therefore, this paper develops a gear flow meter optimization design method that comprehensively considers various factors and performance indicators. Summary of the Invention

[0005] To address the shortcomings of existing optimization designs, the present invention aims to provide an optimization method that reduces the total power loss of the gear flow meter while ensuring low flow pulsation and low leakage, thereby solving the problem of not being able to simultaneously achieve the desired performance indicators.

[0006] To address the existing problems in gear flow meter design, the technical solution adopted in this invention is as follows:

[0007] An optimization method that comprehensively considers various performance indicators of a gear flow meter mainly includes the following steps:

[0008] Step 1: Based on the calculation formulas for the flow pulsation coefficient, internal leakage, and total power loss of the gear flow meter, analyze the influence of the main structural parameters of the gear flow meter on the above three performance indicators. The main structural parameters include gear structure parameters and the size of radial clearance and axial clearance. The three performance indicators include the flow pulsation coefficient, the internal leakage calculation formula, and the total power loss.

[0009] In step 1, the analysis of the structural parameters of the gear flowmeter and its three performance indicators reveals that lower oil viscosity results in less viscous internal friction of the gears, leading to greater internal leakage. Therefore, when designing the flowmeter, it is advisable to select hydraulic oil with the lowest possible viscosity for optimization. The external temperature is selected as T = 40℃, and the design is performed under rated speed conditions. Specifically, the following steps are included:

[0010] Step 1.1: Based on the flow pulsation calculation formula, select the number of gear teeth z and the meshing angle α that affect the flow pulsation coefficient of the gear flow meter. t As design variables, since the gear values ​​of a gear flowmeter are generally in the range of z = [10, 20], and the meshing angle values ​​are in the range of α... t =[20°,30°], using the controlled variable method for analysis, the influence trend of structural parameters on flow pulsation is analyzed.

[0011] Step 1.2: The internal leakage of the gear flowmeter mainly consists of radial clearance leakage and axial clearance leakage. Based on the internal leakage calculation formula, the influence trends of gear module m, number of teeth z, meshing angle α, radial clearance h1, and axial clearance h2 on radial and axial clearance leakage are selected using data analysis software. The range of gear module in the gear flowmeter is m = [2,4], z = [10,20], and the range of meshing angle α is... t = [20°, 30°], the axial and radial clearance values ​​are h1 = [0.01, 0.1], h2 = [0.01, 0.1], both in mm. Analysis using the controlled variable method yields the conclusion regarding the influence trend of the gear flowmeter's structural parameters on internal leakage loss.

[0012] Step 1.3: Based on the total power loss calculation formula, select gear structural parameters including gear module m, number of teeth z, meshing angle α, radial clearance h1, and axial clearance h2 as design variables using data analysis software. The value range of the above variables is shown in Step 1.2. Use the controlled variable method to analyze and obtain the influence trend of gear flow meter structural parameters on total power loss.

[0013] Step 2: Based on Step 1, select the highest performance index as the target index under different working conditions, and use the Design of Experiments (DOE) method to analyze the changing trends of the other two indexes during the improvement of the target index, so as to draw conclusions about the influence trends among the three performance indexes under this working condition.

[0014] Step 3: Based on the analysis of this operating condition in Step 2, select the main indicators as the objective function according to the operating conditions, and convert the other two indicators into constraint functions. Select the design structural parameters of the gear flowmeter as design variables, namely gear module m, number of teeth z, and meshing angle α. t Including radial clearance h1 and axial clearance h2, an optimized design model for the flow meter is constructed. Details are as follows:

[0015] Step 3.1: Based on the analysis in Step 2, select the main indicators as the objective function of the optimization model;

[0016] Step 3.2: After determining the objective function, determine the allowable values ​​of the other two indicators based on the operating conditions to construct the performance indicator constraint equations;

[0017] Step 3.3: Since the number of teeth of the gear in the design of the gear flow meter is generally in the range of 10-20, there are cases where the number of teeth is less than 17. Therefore, it is necessary to perform gear displacement and tooth profile correction. The displacement conditions that need to be followed during the gear displacement process, such as no undercut, no tip cut, overlap constraint, and no tooth tip thinning, are transformed into constraint conditions and added to the optimization equation, thereby constructing a complete constraint condition equation.

[0018] Step 3.4: Based on the above steps, construct a complete optimization model.

[0019] Step 4: Select a suitable optimization algorithm to solve the optimization model, obtaining the optimal solution of the objective function under the optimization model in Step 3 and the corresponding structural parameters of the gear flow meter. Specifically:

[0020] Step 4.1: Implement the optimization model constructed above in the software, and use the algorithm toolbox to solve it to obtain the optimal values ​​of the structural parameters of the gear flow meter.

[0021] Furthermore, in step 2, based on the factors influencing a single performance indicator in step 1, the influence relationships between multiple performance indicators are analyzed, specifically including the following steps:

[0022] Step 2.1: Select the operating condition. Gear flow meters mainly correspond to the following three operating conditions:

[0023] (1) For applications with high requirements for flow pulsation, flow pulsation is the main indicator, while internal leakage and power loss are secondary indicators for analysis.

[0024] (2) For applications where high accuracy of gear flow meters is required, internal leakage is used as the main indicator, while flow pulsation and power loss are used as secondary indicators for analysis.

[0025] (3) For applications requiring high heat generation indicators, total power loss is used as the primary indicator, while flow pulsation and internal leakage are used as secondary indicators for analysis.

[0026] Step 2.2: Based on the selected operating conditions, analyze the changing trend of secondary indicators as the main indicators increase.

[0027] The beneficial effects of this invention are:

[0028] (1) This invention provides an optimization design method for improving the overall performance of a gear flow meter by considering various performance indicators. This ensures that, while meeting other performance requirements, the optimized structural parameters of the gear flow meter can meet the optimal performance required under specific operating conditions. Compared with traditional gear flow meter optimization design methods, this method takes into account various performance indicators of the gear flow meter. While ensuring the required performance indicators, other performance indicators are also well considered and guaranteed. This allows the designed gear flow meter to fully guarantee stability and reduce heat loss while ensuring high accuracy. Therefore, this invention can more fully consider various performance indicators in the optimization design process of gear flow meters.

[0029] (2) The gear flow meter optimization design method provided by this invention can optimize the design for various operating conditions. By determining the operating conditions, the performance index with the highest requirements under these conditions can be selected, and the other two performance indexes can be restricted, thereby obtaining the optimal solution for the operating conditions. Different operating conditions correspond to different optimization models, proving that the proposed optimization method has a wide range of applicability. Attached Figure Description

[0030] Figure 1 This refers to different gear tooth numbers z and meshing angle α involved in a specific embodiment of the present invention. t A schematic diagram illustrating the trend of the influence of the flow pulsation coefficient;

[0031] Figures 2a-2b These are schematic diagrams illustrating the influence trends of different radial and axial clearances on radial and axial leakage, respectively, according to a specific embodiment of the present invention.

[0032] Figure 3a ~3c represent the parameters related to the number of teeth z, module m, and meshing angle α in a specific embodiment of the present invention. t A schematic diagram illustrating the trend of total power loss during the change process;

[0033] Figure 4 This is a schematic diagram illustrating the evolutionary principle of a multi-population genetic algorithm (MPGA) according to a specific embodiment of the present invention;

[0034] Figure 5 This is a schematic diagram illustrating the iterative process to the optimal solution of a multi-population genetic algorithm (MPGA) according to a specific embodiment of the present invention. Detailed Implementation

[0035] The following embodiments further illustrate an optimization method for improving the overall performance of a gear flow meter by considering various performance indicators.

[0036] In this embodiment, the number of teeth z ranges from 10 to 20, the module m ranges from 2 to 4 mm, and the meshing angle α... t The values ​​range from 22° to 27°, the radial clearance h1 ranges from 0.01 to 0.1 mm, the axial clearance h2 ranges from 0.01 to 0.1 mm, and the flow rate ranges from 0.15 to 15 L / min. The specific process of the optimization method will be explained in detail below, and the steps are as follows:

[0037] Step 1: Based on the calculation formulas for the flow pulsation coefficient, internal leakage, and total power loss of the gear flow meter, analyze the impact of the main structural parameters of the gear flow meter on the above three performance indicators. This includes the following steps:

[0038] Step 1.1: As Figure 1 As shown, based on the factors affecting the flow pulsation coefficient being the number of gear teeth z and the meshing angle α, data analysis using MATLAB software reveals that, under the premise of the same number of teeth, the flow pulsation coefficient first decreases and then increases as the meshing angle α increases; and under the same meshing angle, the flow pulsation coefficient continuously decreases as the number of teeth increases.

[0039] Step 1.2: As shown in Figures 2(a)-(b), it can be seen from the radial clearance leakage formula that, given a fixed gear parameter, increasing the radial clearance will increase the radial clearance leakage; similarly, increasing the axial clearance will increase the axial clearance leakage.

[0040] Step 1.3: The total power loss consists of leakage power loss, radial friction power loss, and axial friction power loss. As shown in Figures 3(a)-(c), the effect of clearance on total power loss is exactly the opposite of its effect on internal leakage. Excessive clearance leads to excessive leakage, but it also reduces viscous frictional resistance, thus reducing the total power loss. Conversely, insufficient clearance has the opposite effect. Among the gear structure parameters, the total power loss decreases as the number of teeth z, module m, and meshing angle α decrease, with module m and number of teeth z having the most significant impact, while the meshing angle α has a very small impact on the total power loss.

[0041] Step 2: Select the optimal operating condition for the gear flow meter as an application requiring high dynamic response characteristics and total power loss, and analyze the influence relationship between the corresponding performance indicators under this operating condition. This includes the following steps:

[0042] Step 2.1: For applications where total power loss is a critical factor, the analysis focuses on total power loss as the primary objective, with flow pulsation and internal leakage as secondary indicators.

[0043] Step 2.2: Based on the selected operating conditions, the total power loss is selected as the main target, and data analysis is performed using software such as MATLAB. As shown in Figures 3(a)-(c), it is concluded that the internal leakage and flow pulsation coefficient show an increasing trend during the process of reducing the total power loss. This indicates that the improvement of one performance index comes at the cost of sacrificing other performance indexes. Therefore, the optimal optimization index should be selected according to the specific operating conditions.

[0044] Step 3: Based on the influence trend analysis between the primary and secondary objectives under specific working conditions in Step 2, construct an optimization model for this working condition, which includes the following steps:

[0045] Step 3.1: Select the total power loss as the objective function under this optimization model;

[0046] Step 3.2: In cases where flow pulsation requirements are high, the allowable value for the flow pulsation coefficient constraint is selected as 5%, and the allowable value for the internal leakage constraint is 1% of the total flow, i.e., the allowable value for the internal leakage constraint is 0.15L / min. The total power loss under the condition of 15L / min is then optimized.

[0047] Step 3.3: Since the number of teeth z ranges from 10 to 20, displacement needs to be considered in the gear design process. Therefore, the conditions that should be followed during the displacement process, such as no undercutting, no overcutting, and no interference of transition curves, are transformed into constraints and added to the constraint conditions to construct a complete constraint condition equation.

[0048] Step 3.4: Optimize design variables x = [m, z, α] t [h1, h2], the range of values ​​for the design variables is as described above. Combine the objective function and constraints constructed in steps 3.1-3.3 to construct a complete optimization model.

[0049] Step 4: The constructed optimization model is optimized using a multi-population genetic algorithm (MPGA), which includes the following steps:

[0050] Step 4.1: As Figure 4 As shown, the optimization process of the multi-population genetic algorithm adds a migration operator and an elite population to the traditional genetic algorithm (GA) based on inheritance, mutation, and crossover. The diversity of the population is increased through migration between populations. The program segment of the multi-population genetic algorithm (MPGA) is written using functions from the genetic algorithm toolbox of the University of Sheffield, and real-valued encoding is used for the optimization design variables.

[0051] Step 4.2: Optimal values ​​are obtained by implementing this in MATLAB.

[0052] Step 4.4: As Figure 5 As shown, after satisfying the iteration termination condition, the optimal value and the corresponding optimal solution x=[m,z,α,h1,h2]=[2,12,25.5°,0.026,0.028] are obtained under this working condition, and the optimal value of total power loss is 18.02w.

[0053] The above-described embodiments are merely illustrative of the implementation methods of the present invention, but should not be construed as limiting the scope of the present invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these modifications and improvements all fall within the protection scope of the present invention.

Claims

1. An optimization method that comprehensively considers various performance indicators of a gear flow meter, characterized in that, Includes the following steps: Step 1: Based on the calculation formulas for the flow pulsation coefficient, internal leakage, and total power loss of the gear flow meter, analyze the influence of the main structural parameters of the gear flow meter on the above three performance indicators. The main structural parameters include gear structural parameters and the size of radial clearance and axial clearance. Step 2: Based on Step 1, select the performance index with the highest requirements as the target index under different working conditions, and use the Design of Experiments (DOE) method to analyze the changing trends of the other two indexes as the target index is improved, so as to draw conclusions about the influence trends among the three performance indexes under this working condition. Step 3: Based on the analysis of this operating condition in Step 2, select the main indicators as the objective function according to the operating conditions, and convert the other two indicators into constraint functions. Select the design structural parameters of the gear flowmeter as design variables, namely gear module m, number of teeth z, and meshing angle α. t Including radial clearance h1 and axial clearance h2, an optimized design model for the flow meter is constructed; the details are as follows: Step 3.1: Based on the analysis in Step 2, select the main indicators as the objective function of the optimization model; Step 3.2: After determining the objective function, determine the allowable values ​​of the other two indicators based on the operating conditions to construct the performance indicator constraint equations; Step 3.3: Since the number of teeth of the gear in the design process of the gear flow meter is in the range of 10-20, that is, there are cases where the number of teeth is less than 17. Therefore, it is necessary to perform gear displacement and tooth profile correction. The constraints of no undercut, no tip cut, overlap, tooth tip not being too thin or other displacement conditions to be followed during the gear displacement process are transformed into constraints and added to the optimization equation, thereby constructing a complete constraint condition equation. Step 3.4: Based on the above steps, construct a complete optimization model; Step 4: Solve the optimization model to obtain the optimal solution of the objective function under the optimization model in Step 3 and the optimal values ​​of the corresponding gear flow meter structural parameters.

2. The optimization method for a gear flow meter that comprehensively considers various performance indicators according to claim 1, characterized in that, The analysis of the structural parameters of the gear flow meter in step 1 regarding its impact on the three performance indicators suggests that a lower viscosity hydraulic oil should be selected for optimized design, with an external temperature of T = 40℃, and the design should be carried out under rated speed conditions. This includes the following steps: Step 1.1: Based on the flow pulsation calculation formula, select the number of gear teeth z and the meshing angle α that affect the flow pulsation coefficient of the gear flow meter. t As design variables, since the gear values ​​of the gear flowmeter range from z = [10, 20], and the meshing angle ranges from α... t =[20°,30°], using the controlled variable method for analysis, the influence trend of structural parameters on flow fluctuation is analyzed; Step 1.2: The internal leakage of the gear flowmeter mainly consists of radial clearance leakage and axial clearance leakage. Based on the internal leakage calculation formula, the influence trends of gear module m, number of teeth z, meshing angle α, radial clearance h1, and axial clearance h2 on radial and axial clearance leakage are selected using data analysis software. The range of gear module in the gear flowmeter is m = [2,4], z = [10,20], and the range of meshing angle α is... t = [20°, 30°], the range of axial and radial clearance is h1 = [0.01, 0.1], h2 = [0.01, 0.1], the unit is mm; Analysis using the controlled variable method yielded the conclusion that the structural parameters of the gear flow meter influence the internal leakage loss trend. Step 1.3: Based on the total power loss calculation formula, select gear structural parameters including gear module m, number of teeth z, meshing angle α, radial clearance h1, and axial clearance h2 as design variables using data analysis software. The value range of the above variables is shown in Step 1.

2. Use the controlled variable method to analyze and obtain the influence trend of gear flow meter structural parameters on total power loss.

3. The optimization method for a gear flow meter that comprehensively considers various performance indicators according to claim 1, characterized in that, Step 2, based on the influencing factors of a single performance index in Step 1, analyzes the influence relationships between multiple performance indicators, specifically including the following steps: Step 2.1: Select the operating condition. Gear flow meters mainly correspond to the following three operating conditions: (1) For applications with high requirements for flow pulsation, flow pulsation is used as the main indicator, while internal leakage and power loss are used as secondary indicators for analysis. (2) For applications where high accuracy of gear flow meters is required, internal leakage is used as the main indicator, while flow pulsation and power loss are used as secondary indicators for analysis. (3) For applications requiring high heat generation indicators, total power loss is used as the primary indicator, while flow pulsation and internal leakage are used as secondary indicators for analysis. Step 2.2: Based on the selected operating conditions, analyze the changing trend of secondary indicators as the main indicators increase.

Images