Design and calculation method of main parameters of helical gear flowmeter

Abstract

The application provides a design and calculation method of main parameters of helical gear flowmeter, and belongs to the technical field of flowmeter. The design and calculation method is obtained by theoretically analyzing the helical gear flowmeter, and the influence of the number of gears, modulus, pressure angle, helix angle, radial clearance of the flowmeter and end face clearance of the flowmeter on the flow pulsation, clearance flow leakage and power loss of the helical gear flowmeter is discussed. In combination with the particle swarm optimization algorithm, two of the three performance indexes, flow pulsation, leakage and power loss, are changed into constraint conditions according to the design requirements, so that the multi-objective problem is changed into a single-objective problem for solving the main parameters of the helical gear flowmeter. Compared with the traditional method of calculating the displacement of the flowmeter through the empirical formula and the empirical coefficient, the application can improve the displacement design precision of the flowmeter, can clearly determine the influence degree of each parameter on the performance of the flowmeter, and can quickly solve the main parameters of the helical gear flowmeter through the optimization algorithm.

Description

Technical Field

[0001] This invention belongs to the technical field of flow meters and relates to a design and calculation method for the main parameters of a helical gear flow meter. Technical Background

[0002] A volumetric flow meter, abbreviated as PDF, is a measuring element that measures flow by dividing a fluid into multiple fluid units of equal volume. Gear flow meters are a type of volumetric flow meter, characterized by high measurement accuracy, a wide flow range, insensitivity to oil, and strong pressure resistance.

[0003] Gear flow meters generally consist of a gear rotor, a housing, and a signal detection unit. A metering cavity is formed between the gear rotor and the housing, and the rotor rotates under hydraulic pressure, dividing the fluid. The signal detection unit measures the flow rate by detecting the rotor's rotational speed. Based on rotor structure, gear flow meters can be further divided into cylindrical gear flow meters and oval gear flow meters. Cylindrical gear flow meters are more suitable for flow detection under high-pressure conditions, while oval gear flow meters offer better performance under low-pressure, high-flow conditions.

[0004] Among gear flow meters, elliptical gear flow meters are the most widely used, but they suffer from excessive flow pulsation, making them unsuitable for hydraulic systems requiring high-precision control. Cylindrical gear flow meters have relatively smaller flow pulsation, but still cannot compare to helical gear flow meters. The meshing process of helical gears is similar to the meshing of multiple pairs of spur gears, resulting in a more stable flow and lower flow pulsation rate.

[0005] Currently, there is relatively little information available on the design of helical gear flow meters. Therefore, we propose a design and calculation method for the main parameters of helical gear flow meters. Summary of the Invention

[0006] To meet the design requirements of helical gear flow meters, this invention provides a method for designing and calculating the main parameters of helical gear flow meters.

[0007] The present invention has the following technical solutions:

[0008] A method for designing and calculating the main parameters of a helical gear flow meter includes the following steps:

[0009] Step 1: Determine the design parameters and design objectives of the helical gear flow meter. Key parameters include maximum design flow rate, maximum design speed, number of helical gear teeth (z), helix angle (β), and normal module (m). n ), normal engagement angle (α) nThe end face clearance (h1) between the helical gear and the housing, and the radial clearance (h2) also need to be determined. Simultaneously, the design objectives of the helical gear flowmeter need to be determined, primarily including the allowable flow pulsation value and the measurement accuracy under maximum flow conditions, which are determined based on specific operating requirements.

[0010] The maximum design speed can be selected between 3000-8000 r / min; the selection range of the number of teeth and helix angle can be referenced with that of helical gear pumps; the normal module is mainly selected based on the maximum design speed and maximum flow rate; the normal meshing angle is generally selected based on the large meshing angle, which can be selected as a reference angle of 25-27°, or it can be varied according to the actual situation; the size of the end face clearance between the helical gear and the housing can be selected between 0.01-0.06 mm; the size of the radial clearance can be selected between 0.01-0.06 mm.

[0011] Step 2: Solve the parameters of the helical gear using the angle displacement rule. The normal displacement coefficient, end face addendum variation coefficient, addendum circle radius, and dedendum circle radius of the helical gear are solved using the number of teeth (z), helix angle (β), normal module (mn), and normal meshing angle (αn) selected in Step 1.

[0012] Step 3: Solving for the gear tooth volume area and return flow area. Based on all the helical gear parameters obtained in Step 2, the gear tooth profile curve formula can be derived. Integrating the gear tooth profile allows us to calculate the gear tooth volume S1 and the return flow area S2. Since the maximum flow rate and maximum speed of the gear were selected in Step 1, the flow meter's displacement per revolution can be calculated. Combining the flow meter's displacement with the tooth volume area and return flow area, the gear tooth width can be calculated. This completes the solution for all parameters of the helical gear.

[0013] Step 4: Verification of helical gear derived parameters. Based on the helical gear parameters obtained in Steps 1, 2, and 3, calculate the tooth thickness at the addendum circle, longitudinal contact ratio, end face contact ratio, critical helix angle, and critical tooth width of the helical gear, and perform numerical judgment to ensure that the main derived parameters meet the constraint requirements.

[0014] Step 5: Calculate flow meter gap leakage, flow pulsation, power loss, and determine the number of helical gear teeth (z), helix angle (β), and normal module (m). n ), normal engagement angle (α) nThe influence of the end face clearance (h1) and radial clearance (h2) between the helical gear and the housing on them. After the parameters of the helical gear pass the test in step 4, the end face leakage, radial clearance leakage, flow pulsation coefficient, and power loss of the helical gear flowmeter can be calculated. The clearance leakage and power loss of the helical gear flowmeter can be calculated with reference to the clearance leakage method of the cylindrical gear flowmeter. The flow pulsation of the helical gear flowmeter can be calculated with reference to the calculation method of the flow pulsation of the helical gear pump. The number of teeth (z), helix angle (β), and normal module (m) of the helical gear. n ), normal engagement angle (α) n The impact of the helical gear's end face clearance (h1) and radial clearance (h2) on the effect can be calculated using Isight software.

[0015] Step 6: Optimization Calculation. Through the first five steps, z, β, and m are already clear. n α n The relationships between h1, h2 and other derived parameters, and the impact of each parameter on flowmeter gap leakage, flow pulsation calculation, and power loss, are investigated. Therefore, an optimization algorithm can be used to iteratively solve for the five parameters, with power loss as the optimization objective. The leakage and flow pulsation calculations are transformed into constraints, allowing for the determination of the helical gear flowmeter's helical gear tooth number (z), helix angle (β), and normal module (m) that satisfy the constraints. n ), normal engagement angle (α) n ), the end face clearance (h1) between the helical gear and the housing, and the radial clearance (h2).

[0016] The beneficial effects of this invention are as follows:

[0017] (1) This invention provides a design calculation method for the main parameters of a helical gear flow meter. The precise gear tooth groove volume is obtained by integrating the helical gear tooth profile curve, and the main parameters of the helical gear are obtained by calculating the flow meter's return flow rate, thus ensuring the accuracy of the flow meter's discharge capacity. Compared to the traditional method of calculating flow meter discharge capacity using empirical formulas and coefficients, this method improves the design accuracy of the flow meter's discharge capacity.

[0018] (2) Under the premise of clearly defining the design objectives of the helical gear flow meter, such as maximum metering flow rate, maximum metering speed, metering accuracy, and flow pulsation rate, the influence of each parameter on the flow meter's clearance leakage, theoretical flow pulsation rate, and power loss is determined by theoretical calculation and control of the main parameters such as the number of teeth, normal module, helix angle, and radial clearance. The degree of influence of each parameter on the flow meter performance is clarified, and the applicable main parameters of the helical gear flow meter are quickly solved through optimization algorithms. Attached Figure Description

[0019] Figure 1The gear tooth profile shown in the specific example of the present invention mainly includes the tooth tip circle segment, the involute segment, the tooth root transition circle segment, and the tooth root circle segment.

[0020] Figure 2 This is the gear tooth groove area that needs to be solved in a specific embodiment of the present invention.

[0021] Figure 3 This is the flow meter backflow area that needs to be solved in a specific example of the present invention.

[0022] Figure 4 This is the three-dimensional model of the helical gear corresponding to the preliminary calculated parameters in a specific example of the present invention.

[0023] Figure 5 This refers to the degree of influence of each main parameter on flow pulsation analyzed in the specific examples of this invention.

[0024] Figure 6 This refers to the degree of influence of each main parameter on power loss as analyzed in the specific examples of this invention.

[0025] Figure 7 This refers to the degree of influence of each main parameter on the gap leakage rate analyzed in the specific examples of this invention.

[0026] Figure 8 This is a partial calculation process of the particle swarm algorithm used in a specific embodiment of the present invention.

[0027] Figure 9 This is a three-dimensional model of a helical gear drawn based on the final calculated main parameters in a specific embodiment of the present invention. Detailed Implementation

[0028] The following implementation example will further illustrate the design calculation method involved in this invention.

[0029] Compared to traditional cylindrical gear flow meters and elliptical gear flow meters, helical gear flow meters exhibit lower flow pulsation and are better suited for measuring flow signals in high-precision electro-hydraulic servo systems. This invention discloses a design and calculation method for the main parameters of a helical gear flow meter. Through theoretical analysis of the helical gear flow meter, the influence of the number of teeth, module, pressure angle, helix angle, radial clearance, and end face clearance on the flow pulsation, clearance leakage, and power loss of the helical gear flow meter is explored. Furthermore, by combining a particle swarm optimization algorithm, two of the three performance indicators—flow pulsation, leakage, and power loss—are transformed into constraints according to design requirements, thus transforming the multi-objective problem into a single-objective problem for solving the main parameters of the helical gear flow meter. The specific steps are as follows:

[0030] The first step is to determine the design parameters and design objectives of the helical gear flow meter. In this example, the helical gear flow meter has a maximum design flow rate of 21 L / min, a design speed of 3000 r / min, a clearance leakage rate of no more than 0.5% at maximum speed, a flow pulsation rate of no more than 4%, a gear inner diameter of 14 mm, and uses No. 32 hydraulic oil. The initial selections for the original gear are 14 teeth, a module of 3, a normal pressure angle of 26°, a helix angle of 14°, and a flow meter end face clearance and radial clearance of 0.035 mm. The design objectives are determined based on specific operating conditions; the design parameters are selected by referring to and improving upon the design method for spur gear flow meters [Wang Wei. Research on Dynamic Flow Measurement of Gear Flow Meters [D]. Anhui University of Science and Technology, 2015.].

[0031] The second step involves solving for the helical gear parameters using the angular displacement rules. The calculated parameters are: normal displacement coefficient 0.32, end face addendum variation coefficient 0.058, addendum circle radius 25.35 mm, and dedendum circle radius 18.85 mm. In this embodiment, the normal displacement coefficient, end face addendum variation coefficient, addendum circle radius, and dedendum circle radius can be derived from the parameters in step 1.

[0032] The third step is to solve for the gear tooth volume area and the return flow area. Based on all the helical gear parameters obtained in step 2, the gear tooth profile curve formula can be obtained. The gear tooth volume S1 can be obtained by integrating the gear tooth profile. The return flow area S2 can be obtained by referring to the following references: [Hao X, Zhou X, Liu X, et al. Flow characteristics of external gear pumps considering trapped volume[J]. Advances in Mechanical Engineering, 2016, 8(10): 1687814016674100.][Huang KJ, Chang WR, Lian W C. An Optimization approach to the displacement volumes for external spur gear pumps[C] / / Materials ScienceForum. Trans Tech Publications Ltd, 2008, 594: 57-71.]. Based on the maximum flow rate and maximum speed of the gear selected in step 1, the flow meter displacement per revolution can be obtained. Combining the flow meter displacement with the tooth volume area and the return flow area, the gear tooth width can be obtained. Thus, all parameters of the helical gear have been solved. In this embodiment, the tooth groove area S1 and the return area S2 are obtained by integrating the gear tooth profile, and finally the gear tooth width is calculated to be 8.48 mm. A three-dimensional model of the gear is then established as follows. Figure 4 As shown.

[0033] The fourth step is to verify the derived parameters of the helical gear. Combining the helical gear parameters obtained in steps 1, 2, and 3, and referring to the reference [Chen Chen. Research on Measurement Accuracy and Flow Measurement Method of Helical Gear Flowmeter [D]. Lanzhou University of Technology, 2019], the tooth tip circle thickness, longitudinal overlap, end face overlap, critical helix angle, and critical tooth width of the helical gear are calculated and numerically judged to ensure that the main derived parameters meet the constraint requirements. In this embodiment, the calculated tooth tip circle thickness is 1.95 mm, the critical tooth width is 26.2 mm, and the critical helix angle is 38°.

[0034] The fifth step involves calculating the flow meter's gap leakage, flow pulsation, and power loss, and determining the impact of the helical gear's number of teeth (z), helix angle (β), normal module (mn), normal meshing angle (αn), end face clearance between the helical gear and the housing (h1), and radial clearance (h2). The calculations show that under these conditions, the gap leakage accounts for 1.04%, the flow pulsation coefficient is 3.92%, and the power loss is 86.6 W. The analysis of the influence of each parameter is as follows: Figure 5 , 6As shown in Figures 7 and 8.

[0035] Step 6: Optimization calculation. Through the first 5 steps, z, β, and m are already clear. n α n The relationships between h1, h2 and other derived parameters, and the impact of each parameter on flowmeter gap leakage, flow pulsation calculation, and power loss, are investigated. Therefore, an optimization algorithm can be used to iteratively solve for the five parameters, with power loss as the optimization objective. Leakage (in this invention, leakage is considered a constraint, equivalent to the flowmeter's metering accuracy being a constraint. Leakage is generally considered in most literature to be approximately equal to gap leakage, or 1.05 times the gap leakage) and flow pulsation calculation are transformed into constraints. The number of helical gear teeth (z), helix angle (β), and normal module (m) of the helical gear flowmeter that satisfy these constraints are then determined. n ), normal engagement angle (α) n The helical gear and the housing end face clearance (h1) and radial clearance (h2) are considered. This embodiment utilizes a particle swarm optimization algorithm based on natural selection for iterative optimization, such as... Figure 8 As shown. After solving and rounding the parameters, the main parameters of the helical gear flow meter are: normal module of 2.5mm, normal meshing angle of 24.7°, helix angle of 8°, number of teeth of 13, end face clearance of 0.0284mm, radial clearance of 0.0161mm, flow pulsation rate of 4%, clearance leakage rate of 0.5%, and power loss of 62W.

[0036] 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. A method for designing and calculating the main parameters of a helical gear flow meter, characterized in that, It includes the following steps: Step 1: Determine the design parameters and design objectives of the helical gear flow meter; the design parameters include maximum design flow rate, maximum design speed, number of helical gear teeth z, helix angle β, and normal module m. n Normal meshing angle α n The end face clearance h1 between the helical gear and the housing, and the radial clearance h2; the design objectives include the allowable value of flow pulsation and the measurement accuracy under the maximum flow state, which are determined according to the specific working conditions. Step 2: Solve the parameters of the helical gear using the angle displacement rule; use the number of teeth z, helix angle β, normal module mn, and normal meshing angle αn selected in Step 1 to solve for the normal displacement coefficient, end face tooth height variation coefficient, tooth tip circle radius, and tooth root circle radius of the helical gear. Step 3: Solving for the gear tooth volume area and return flow area; Based on all the helical gear parameters obtained in Step 2, solve for the gear tooth profile curve formula, and solve for the gear tooth volume S1 by integrating the gear tooth profile; solve for the return flow area S2; Based on the maximum flow rate and maximum speed of the gear selected in Step 1, calculate the flow meter's displacement per revolution; Combining the flow meter's displacement, tooth volume area, and return flow area, solve for the gear tooth width; At this point, all parameters of the helical gear have been solved. Step 4: Verification of helical gear derived parameters; Based on the helical gear parameters obtained in Steps 1, 2, and 3, calculate the tooth thickness at the addendum circle, longitudinal overlap, end face overlap, critical helix angle, and critical tooth width of the helical gear, and perform numerical judgment to ensure that the main derived parameters meet the constraint requirements. Step 5: Calculate flow meter gap leakage, flow pulsation, power loss, and determine the number of helical gear teeth z, helix angle β, and normal module m. n Normal meshing angle α n The influence of the end face clearance h1 and radial clearance h2 between the helical gear and the housing; after the parameters of the helical gear pass the inspection in step 4, the end face leakage, radial clearance leakage, flow pulsation coefficient, and power loss of the helical gear flowmeter are calculated; the clearance leakage and power loss of the helical gear flowmeter are calculated with reference to the clearance leakage method of the cylindrical gear flowmeter; the flow pulsation of the helical gear flowmeter is calculated with reference to the calculation method of the flow pulsation of the helical gear pump; the number of helical gear teeth z, helix angle β, and normal module m n Normal meshing angle α n The impact of the helical gear's end face clearance h1 and radial clearance h2 on the effect was determined using Isight. Step 6: Optimization calculation; Through the first 5 steps, z, β, and m have been clearly defined. n α n The relationships between h1, h2 and other derived parameters, and the impact of each parameter on flowmeter gap leakage, flow pulsation calculation, and power loss; therefore, the five parameters are iteratively solved using an optimization algorithm, with power loss as the optimization objective. The leakage and flow pulsation calculations are transformed into constraints, and the helical gear number z, helix angle β, and normal module m of the helical gear flowmeter that satisfy the constraints are solved. n Normal meshing angle α n The end face clearance h1 between the helical gear and the housing, and the radial clearance h2.

2. The design and calculation method for the main parameters of a helical gear flow meter according to claim 1, characterized in that, In step 1, the maximum design speed is selected between 3000-8000 r / min; the selection range of the number of helical gear teeth and the helix angle is selected with reference to the helical gear pump. The normal module is selected based on the maximum design speed and maximum flow rate; the normal meshing angle is selected as a reference angle based on the largest meshing angle, or it can be varied within a range according to the actual situation; the size of the clearance between the helical gear and the housing end face can be selected in the range of 0.01-0.06mm; the size of the radial clearance can be selected in the range of 0.01-0.06mm.

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