Method and Product for Generating Diaphragm Compressor Chamber Profile Based on Brachistochrone Line

Abstract

A method and product for generating the membrane cavity profile of a diaphragm compressor based on the brachistochrone curve are disclosed. The method includes establishing an XOY coordinate system; defining a first rolling circle S1 and a second rolling circle S2, centered above and below the X-axis and tangent to it; the two rolling circles moving along the X-axis with angular velocity ω while remaining tangent to the X-axis and moving in opposite directions; the trajectory ONQ of a feature point initially located at the origin O on each rolling circle, traversed by the first rolling circle S1, serves as the membrane cavity generation line, forming a cycloid OMK with the movement of the second rolling circle S2; defining the membrane cavity radius, membrane cavity deflection, and the ratio of the radii of the two generated rolling circles, establishing a series of membrane cavity profiles; and selecting the optimal profile from these profiles based on specific conditions to obtain a membrane cavity profile that meets the requirements. The membrane cavity profile generation method proposed in this invention is a multi-parameter profile control method with adjustable characteristic tilt angles and the ratio of the radii of the two generated rolling circles, offering greater design flexibility.

Description

Technical Field

[0001] This invention relates to the field of diaphragm compressor technology, and specifically to a method and product for generating the membrane cavity profile of a diaphragm compressor based on the steepest descent line. Background Technology

[0002] A diaphragm compressor is a positive displacement compressor that separates the oil and gas sides using a diaphragm. Its working principle is as follows: a motor drives a crankshaft connecting rod, which in turn drives a piston in reciprocating motion, pressurizing and depressurizing the high-pressure oil. This high-pressure oil then pushes the diaphragm to compress and discharge the gas. Due to its excellent sealing and high pressure ratio, diaphragm compressors are widely used in the hydrogen energy industry, with hydrogen refueling stations being a particularly important application scenario. However, diaphragm lifespan, volumetric efficiency, and diaphragm head strength are critical and challenging issues in the development of diaphragm compressors.

[0003] The diaphragm is a key component for the stable operation of a diaphragm compressor, and its performance directly affects the reliability of the compressor. During diaphragm failure, the main forms of damage are collapse, torsional deformation, wear cracks, and mechanical fatigue. Damage to the diaphragm will lead to the destruction of its mechanical properties, and in severe cases, can even result in significant economic losses.

[0004] Currently, the membrane cavity profiles of diaphragm compressors widely used in China adopt a single-index, small-deflection profile, which has proven to have good reliability and a solid practical foundation through long-term practice and verification. However, in the development and design of new diaphragm compressor models, the traditional single-index membrane cavity profile, which is adjusted by controllable parameters such as the membrane cavity index, has a limited optimization range and cannot meet the urgent market demands for technological advancements in diaphragm compressors and the development of new high-pressure, high-speed models. Multi-parameter membrane cavity profile optimization design is an effective way to improve the reliability and reduce the cost of diaphragm compressors. Summary of the Invention

[0005] The purpose of this invention is to address the problems in the prior art by providing a method and product for generating the membrane cavity profile of a diaphragm compressor based on the steepest descent line, thereby meeting the needs of multi-parameter membrane cavity profile optimization design and improving design flexibility.

[0006] To achieve the above objectives, the present invention provides the following technical solution:

[0007] Firstly, a method for generating the membrane cavity profile of a diaphragm compressor based on the steepest descent line is provided, comprising:

[0008] Establish an XOY coordinate system. Define a first rolling circle S1 and a second rolling circle S2, with their centers located above and below the X-axis and tangent to the X-axis, respectively. The two rolling circles move along the X-axis with angular velocities ω, maintaining tangency to the X-axis and moving in opposite directions. The trajectory ONQ of a feature point initially located at the origin O on the rolling circle as it moves with the first rolling circle S1 is used as the membrane cavity generation line. Define the point of tangency between the rolling circle and the X-axis when the feature point is located at N as P. N The angle of rotation of the rounding is When the feature point is located at Q, the point of tangency between the rounded circle and the X-axis is P. Q The angle of rotation of the rounding is As the second rolling circle S2 moves, a cycloid OMK is formed;

[0009] Define the characteristic tilt angle Δθ of the membrane cavity profile, and solve for the trajectory ONQ in the XOY coordinate system to determine A=(x A ,y A The angle of inclination of the tangent from point O to point B changes by Δθ. B = (x - 0) is determined using the cycloid OMK. B ,y B The change in tangent angle from point O to point O is Δθ. The rolling angular velocities of the first rolling circle S1 and the second rolling circle S2 are defined to be the same, and their motion times are also the same. Based on this, the specific membrane cavity profile can be calculated. The cavity profile L is composed of two cycloids AO and BO, which have the properties of the brachistochrone. A new coordinate system X'O'Y' is established with the tangent of the cavity profile L at point A as the horizontal axis O'X' and the normal of the cavity profile L at point B as the vertical axis O'Y'. The coordinate profile equation of the cavity profile L in the X'O'Y' coordinate system is then established.

[0010] Define the membrane cavity radius R max =|x' A -x' B | Membrane cavity deflection H max =|y' A -y' B |, the ratio of the two generated rounding radii A series of membrane cavity profiles are established, and the best one is selected from the series of membrane cavity profiles according to the conditions to obtain a membrane cavity profile that meets the requirements.

[0011] As a preferred option, based on the required membrane cavity profile, the diaphragm compressor has an air inlet at the inflection point O and an exhaust port at the point of maximum deflection B.

[0012] As a preferred embodiment, the trajectory ONQ traversed by the feature point initially located at the origin O on the rolling circle as the first rolling circle S1 moves satisfies the following equation:

[0013]

[0014] In the formula, x PNx PQ Let x and y be the x-coordinates of points PN and PQ in the XOY coordinate system, respectively. At the initial moment, the x-coordinates of the centers of the first rolling circle S1 and the second rolling circle S2 coincide with the origin O. After one revolution, the first rolling circle S1 is tangent to the X-axis at point PN. After two revolutions, the first rolling circle S1 is tangent to the X-axis at point PQ. S1 y S1 These are the x and y coordinates of trajectory ONQ in the XOY coordinate system, respectively; R S1 S is the first rounding radius; Δt Let S1 be the distance traveled by the first rolling circle S1 within time Δt; Let Δt be the angle of rotation of the first rolling circle within Δt; Δt is the rolling circle's motion time.

[0015] As a preferred embodiment, the cycloid OMK formed by the movement of the second rolling circle S2 satisfies the following equation:

[0016]

[0017] As a preferred embodiment, the motion of the first rolling circle S1 and the second rolling circle S2 is specifically described by the following expression:

[0018]

[0019] In the formula, To find the derivative operator, These are the angles of rotation of the first rolling circle S1 and the second rolling circle S2, respectively.

[0020] As a preferred embodiment, the coordinate profile equation of the membrane cavity profile L in the X'O'Y' coordinate system is expressed as follows:

[0021]

[0022] In the formula, (x',y') are the coordinates of a point on the membrane cavity profile L in the X'O'Y' coordinate system.

[0023] As a preferred embodiment, when selecting the series of membrane cavity profiles based on certain conditions, the selection conditions include the membrane cavity volume V. L,Set The maximum stress δmax on the diaphragm surface of the membrane with the aforementioned cavity profile L is less than the allowable stress [σ] of its material, specifically described by the following expression:

[0024]

[0025] As a preferred embodiment, the diaphragm surface stress of the membrane cavity profile L is calculated according to the following formula:

[0026]

[0027] δ min =min{δ Pr ±δ Mr ,δ Pt ±δ Mt}

[0028] δ max =max{δ Pr ±δ Mr ,δ Pt ±δ Mt}

[0029] In the formula, H is the equation of the membrane cavity profile with respect to radius r; E is the Young's modulus of the membrane material; μ is the Poisson's ratio of the membrane material; t is the membrane thickness; ∫ is the mathematical integral operator; d is the mathematical differential operator; δ Pr The radial normal stress of the diaphragm; δ Pt The circumferential normal stress of the diaphragm; δ Mr For the radial shear stress of the diaphragm; δ Mr For the circumferential shear stress of the diaphragm; δ min The minimum stress on the diaphragm surface; δ max This represents the maximum stress on the diaphragm surface.

[0030] Secondly, a diaphragm compressor cavity profile generation system based on the steepest descent line is provided, comprising:

[0031] The circular motion trajectory definition module is used to establish an XOY coordinate system. It defines a first circular circle S1 and a second circular circle S2, with their centers located above and below the X-axis and tangent to it. The two circular circles move along the X-axis with angular velocities ω, maintaining tangency and moving in opposite directions. The trajectory ONQ of a feature point initially located at the origin O on each circular circle, traversed by the first circular circle S1, is used as the membrane cavity generation line. The point of tangency between the circular circle and the X-axis when the feature point is located at N is defined as P. N The angle of rotation of the rounding is When the feature point is located at Q, the point of tangency between the rounded circle and the X-axis is P. Q The angle of rotation of the rounding is As the second rolling circle S2 moves, a cycloid OMK is formed;

[0032] The membrane cavity profile coordinate transformation module is used to define the characteristic tilt angle Δθ of the membrane cavity profile and solve for the trajectory ONQ in the XOY coordinate system to determine A=(x A ,y A The angle of inclination of the tangent from point O to point B changes by Δθ. B = (x - 0) is determined using the cycloid OMK. B ,y B The change in tangent angle from point O to point O is Δθ. The rolling angular velocities of the first rolling circle S1 and the second rolling circle S2 are defined to be the same, and their motion times are also the same. Based on this, the specific membrane cavity profile can be calculated. The cavity profile L is composed of two cycloids AO and BO, which have the properties of the brachistochrone. A new coordinate system X'O'Y' is established with the tangent of the cavity profile L at point A as the horizontal axis O'X' and the normal of the cavity profile L at point B as the vertical axis O'Y'. The coordinate profile equation of the cavity profile L in the X'O'Y' coordinate system is then established.

[0033] The membrane cavity profile selection module is used to define the membrane cavity radius R. max =|x' A -x' B | Membrane cavity deflection H max =|y' A -y' B |, the ratio of the two generated rounding radii A series of membrane cavity profiles are established, and the best one is selected from the series of membrane cavity profiles according to the conditions to obtain a membrane cavity profile that meets the requirements.

[0034] Thirdly, a diaphragm compressor is provided, having a membrane cavity generated by the diaphragm compressor cavity profile generation method based on the steepest descent line as described above.

[0035] Compared with the prior art, the present invention has at least the following beneficial effects:

[0036] The diaphragm compressor's cavity profile is composed of two cycloids, AO and BO, each exhibiting the characteristics of a brachistochrone (maximum descent) curve. The inclination angle Δθ of the cavity profile can be flexibly adjusted to regulate the stress distribution when the diaphragm is close to the cavity surface, thus improving diaphragm lifespan. Adjusting the ratio χ of the two generated rounding radii allows for adjustment of the position of the cavity profile's inflection point and the diaphragm stress distribution near that point, facilitating flexible placement of the diaphragm compressor's suction port. By fixing the ratio χ of the two generated rounding radii and the characteristic inclination angle Δθ of the cavity profile, adjusting the generated rounding radius can generate diaphragms with the same slope change trend and a cavity radius R. max and membrane cavity deflection H max Proportional change, membrane cavity volume V L A series of similar membrane cavity profiles with positive correlation changes are beneficial for the serialized design of membrane cavity surfaces and simplify the design of membrane cavity profiles. Compared with the single-exponential membrane cavity profile, which is the profile adjustment method that adjusts the single membrane cavity index Z, the membrane cavity profile generation method of the diaphragm compressor proposed in this invention is a multi-parameter profile control method with adjustable membrane cavity profile characteristic inclination angle Δθ and two ratios of the generated rounding radii χ. It has higher design flexibility and can solve the problems of insufficient optimization parameters, limited optimization range, and difficulty in adjusting the inflection point slope in traditional single-exponential profile design. Products manufactured based on this method can adapt to diverse market demands, optimize the reliability of diaphragm compressors, and increase diaphragm life.

[0037] Furthermore, the present invention optimizes the gas flow during the membrane cavity intake and exhaust process by setting an air inlet at the inflection point O of the membrane cavity profile based on the steepest descent line and an exhaust outlet at the point of maximum deflection B. Attached Figure Description

[0038] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the specific embodiments or the prior art are briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0039] Figure 1 This is a schematic diagram illustrating the principle of the membrane cavity profile generation method for a diaphragm compressor based on the steepest descent line according to an embodiment of the present invention.

[0040] Figure 2 This invention provides a method for fixing two ratios of the generated rounding radii χ = 1 and a characteristic tilt angle, as provided in Embodiment 1 of the present invention. Design of membrane cavity profile line clusters ∑L Case1 ;

[0041] Figure 3 The profile cluster ∑L provided in Embodiment 1 of the present invention Case1 A curve showing the slope variation along the radial direction;

[0042] Figure 4 The profile cluster ∑L provided in Embodiment 1 of the present invention Case1 Radial equivalent stress Change curve graph;

[0043] Figure 5 The profile cluster ∑L provided in Embodiment 1 of the present invention Case1 Maximum radial stress δ on the diaphragm surface max and the minimum stress δ on the diaphragm surface min Change curve graph;

[0044] Figure 6 The design membrane cavity volume V provided in Embodiment 1 of the present invention L,Set =1200000mm 3 1. Fix the ratio of the two generated rounding radii χ = 1 and the characteristic tilt angle. L-shaped membrane cavity based on the steepest descent line Case1 ;

[0045] Figure 7 The membrane cavity profile L based on the steepest descent line provided in Embodiment 1 of the present invention Case1 Maximum radial stress δ on the diaphragm surface max and the minimum stress δ on the diaphragm surface min Change curve graph.

[0046] In the attached diagram: the ω-shaped line generates the rolling angular velocity of the circle; - The angle through which the profile is formed and rounded over time Δt; S Δt - The distance the profile rolls over time Δt; ρ - Defines the equivalent radius of the membrane cavity; k L - The slope of the membrane cavity profile in the X'O'Y' coordinate system; - Equivalent stress when the diaphragm of a diaphragm compressor is close to the membrane cavity profile; R S1 - Radius of the first rounded circle S1; (x L y L - Design the coordinates of any point on the membrane cavity profile L. Detailed Implementation

[0047] The technical solution of the present invention will be clearly and completely described below with reference to the embodiments. 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.

[0048] Please see Figure 1 The present invention provides a method for generating the membrane cavity profile of a diaphragm compressor based on the steepest descent line, comprising:

[0049] Step 1: Establish an XOY coordinate system. Define a first rolling circle S1 and a second rolling circle S2, with their centers located above and below the X-axis and tangent to the X-axis, respectively. The two rolling circles move along the X-axis with angular velocity ω, maintaining tangency to the X-axis and moving in opposite directions. The trajectory ONQ of the feature point initially located at the origin O on the rolling circle as it moves with the first rolling circle S1 is used as the membrane cavity generation line. Define the point of tangency between the rolling circle and the X-axis when the feature point is located at N as P. N The angle of rotation of the rounding is When the feature point is located at Q, the point of tangency between the rounded circle and the X-axis is P. Q The angle of rotation of the rounding is As the second rolling circle S2 moves, a cycloid OMK is formed;

[0050] Step 2: Define the characteristic tilt angle Δθ of the membrane cavity profile, solve for the trajectory ONQ in the XOY coordinate system, and determine A = (x A ,y A The angle of inclination of the tangent from point O to point B changes by Δθ. B = (x - 0) is determined using the cycloid OMK. B ,y B The change in tangent angle from point O to point O is Δθ. The rolling angular velocities of the first rolling circle S1 and the second rolling circle S2 are defined to be the same, and their motion times are also the same. Based on this, the specific membrane cavity profile can be calculated. The cavity profile L is composed of two cycloids AO and BO, which have the properties of the brachistochrone. A new coordinate system X'O'Y' is established with the tangent of the cavity profile L at point A as the horizontal axis O'X' and the normal of the cavity profile L at point B as the vertical axis O'Y'. The coordinate profile equation of the cavity profile L in the X'O'Y' coordinate system is then established.

[0051] Step 3: Define the cavity radius R max =|x' A -x' B | Membrane cavity deflection H max =|y' A -y' B |, the ratio of the two generated rounding radii Based on the above method, a complete profile of the central sectional surface of the diaphragm compressor membrane cavity is established, which has a first rounding radius R. S1 Second rolling radius R S2 The design parameters of the membrane cavity profile, such as the characteristic inclination angle Δθ, can be used to establish a series of membrane cavity profiles. By selecting the optimal membrane cavity profiles according to the conditions, the diaphragm stress is reduced and the radius of the membrane cavity profile is smaller, so as to improve the diaphragm life of the diaphragm compressor and reduce the cost, thus obtaining a membrane cavity profile that meets the requirements.

[0052] Furthermore, in this embodiment of the invention, based on the required membrane cavity profile, the diaphragm compressor has an air inlet at the inflection point O and an exhaust port at the point of maximum deflection B, which is beneficial for optimizing the gas flow during the membrane cavity intake and exhaust process.

[0053] In one possible implementation, the trajectory ONQ traversed by the feature point initially located at the origin O on the rolling circle in step Step 1 as the first rolling circle S1 moves satisfies the following equation:

[0054]

[0055] In the formula, x PN x PQ Let x and y be the x-coordinates of points PN and PQ in the XOY coordinate system, respectively. At the initial moment, the x-coordinates of the centers of the first rolling circle S1 and the second rolling circle S2 coincide with the origin O. After one revolution, the first rolling circle S1 is tangent to the X-axis at point PN. After two revolutions, the first rolling circle S1 is tangent to the X-axis at point PQ. S1 y S1 These are the x and y coordinates of trajectory ONQ in the XOY coordinate system, respectively; R S1 S is the first rounding radius; Δt Let S1 be the distance traveled by the first rolling circle S1 within time Δt; Let Δt be the angle of rotation of the first rolling circle within Δt; Δt is the rolling circle's motion time.

[0056] Similarly, the cycloid OMK formed with the movement of the second rolling circle S2 satisfies the following equation:

[0057]

[0058] In one possible implementation, the motion of the first rolling circle S1 and the second rolling circle S2 in step Step 2 is specifically described by the following expression:

[0059]

[0060] In the formula, To find the derivative operator, These are the angles of rotation of the first rolling circle S1 and the second rolling circle S2, respectively.

[0061] The coordinate profile equation of the membrane cavity profile L in the X'O'Y' coordinate system is as follows:

[0062]

[0063] In the formula, (x',y') are the coordinates of a point on the membrane cavity profile L in the X'O'Y' coordinate system.

[0064] In one possible implementation, when Step 3 describes the optimal selection of a series of membrane cavity profiles based on certain conditions, the optimal selection conditions include the membrane cavity volume V. L,Set The maximum stress δmax on the diaphragm surface of the membrane with the aforementioned cavity profile L is less than the allowable stress [σ] of its material, specifically described by the following expression:

[0065]

[0066] Furthermore, the surface stress of the diaphragm using the aforementioned diaphragm cavity profile L is calculated according to the following formula:

[0067]

[0068]

[0069] δ min =min{δ Pr ±δ Mr ,δ Pt ±δ Mt}

[0070] δ max =max{δ Pr ±δ Mr ,δ Pt ±δ Mt}

[0071] In the formula, H is the equation of the membrane cavity profile with respect to radius r; E is the Young's modulus of the membrane material; μ is the Poisson's ratio of the membrane material; t is the membrane thickness; ∫ is the mathematical integral operator; d is the mathematical differential operator; δ Pr The radial normal stress of the diaphragm; δ Pt The circumferential normal stress of the diaphragm; δ Mr For the radial shear stress of the diaphragm; δ Mr For the circumferential shear stress of the diaphragm; δ min The minimum stress on the diaphragm surface; δ max This represents the maximum stress on the diaphragm surface.

[0072] The above steps generate a diaphragm compressor cavity profile based on the steepest descent line. This profile allows for flexible adjustment of the cavity profile inclination angle Δθ to regulate stress distribution when the diaphragm is close to the cavity surface, thus improving diaphragm lifespan. Adjusting the ratio of the two generated rounding radii χ allows for adjustment of the position of the cavity profile inflection point and the diaphragm stress distribution near the inflection point, facilitating flexible setting of the diaphragm compressor cavity intake position. By fixing the ratio of the two generated rounding radii χ and the characteristic inclination angle Δθ of the cavity profile, adjusting the generated rounding radius can generate profiles with the same slope change trend and a cavity radius R. max and membrane cavity deflection H max Proportional change, membrane cavity volume V L A series of similar membrane cavity profiles with positive correlation changes are beneficial for the serialized design of membrane cavity surfaces and simplify the design of membrane cavity profiles. By setting the air inlet at the inflection point O of the membrane cavity profile based on the steepest descent line and the exhaust port at the maximum deflection B, it is beneficial to optimize the gas flow during the membrane cavity intake and exhaust process. Compared with the profile adjustment method of adjusting the single membrane cavity index Z by adjusting the single index membrane cavity profile, the membrane cavity profile generation method of the diaphragm compressor proposed in this invention is a multi-parameter profile control method with adjustable membrane cavity profile characteristic inclination angle Δθ and two generation rounding radius ratios χ, which has higher design flexibility.

[0073] Another embodiment of the present invention verifies the proposed method for generating the membrane cavity profile of a diaphragm compressor based on the steepest descent line, wherein the design requires a membrane cavity profile volume V. L,Set =1200000mm 3 Fix the ratio of the two generated rounding radii and characteristic dip angle Adjust the radius R of the first rolling circle S1 S1 This allows the generation of a series of line clusters ∑L Case1 like Figure 2 As shown.

[0074] Furthermore, the equivalent radius of the membrane cavity is defined. The slope of the membrane cavity profile L Therefore, the generated line cluster ∑L is obtained by solving this problem. Case1 All L-shaped linesCase1 They have the same profile slope characteristics, specifically as follows: Figure 3 As shown.

[0075] Furthermore, based on the fourth strength theory, the equivalent stress on the diaphragm surface of the diaphragm compressor with the above-mentioned membrane cavity profile is applied. It can be described by the following formula:

[0076]

[0077] In the formula: - Equivalent stress on the diaphragm surface; δ Pr -Radial stress of the diaphragm; δ Mr - Circumferential stress of the diaphragm; Q - Shear stress of the diaphragm; [σ] - Allowable stress of the diaphragm material.

[0078] Furthermore, the generated line cluster ∑L is calculated. Case1 All L-shaped lines Case1 They have nearly similar equivalent forces Features, specifically as follows Figure 4 As shown.

[0079] Furthermore, the tangentially generated line cluster ∑L was calculated. Case1 Small diameter R in max L-shaped lines Case1 The maximum surface stress δ of a 0.5 mm thick diaphragm max and minimum value δ min Distribution as Figure 5 As shown, with the first profile radius R of the membrane cavity S1 With the increase of , the maximum surface stress δ max Gradually decrease, when the radius R of the first type of line S1 When the diameter is 15m, the maximum surface stress of the diaphragm is less than the allowable stress of the material, which is 210MPa. Therefore, under the fixed design parameters of this embodiment, the first profile radius R of the diaphragm cavity is... S1 It should be greater than 15m.

[0080] Furthermore, the set membrane cavity volume V is obtained by solving. L,Set The first design line radius R S1 =25.325m, the designed membrane cavity profile L Case1 like Figure 6 As shown, the maximum radius R of the membrane cavity profile design max =400mm, design maximum deflection H max

[0081] =8.3mm.

[0082] Furthermore, the maximum surface stress δ of the diaphragm that closely matches the aforementioned designed membrane cavity profile is obtained by solving the problem. maxand minimum stress δ min The distribution along the radial equivalent radius ρ is as follows Figure 7 As shown, the maximum surface stress is 154 MPa.

[0083] Furthermore, the air inlet of the diaphragm compressor is located at the membrane cavity profile ρ=0.5, and the exhaust port is located at the membrane cavity profile ρ=1.

[0084] Thus, the designed membrane cavity volume V is satisfied. L,Set A membrane cavity profile design based on the steepest descent line, which meets the allowable stress [σ] requirement of the diaphragm.

[0085] Another embodiment of the present invention also proposes a diaphragm compressor cavity profile generation system based on the steepest descent line, comprising:

[0086] The circular motion trajectory definition module is used to establish an XOY coordinate system. It defines a first circular circle S1 and a second circular circle S2, with their centers located above and below the X-axis and tangent to it. The two circular circles move along the X-axis with angular velocities ω, maintaining tangency and moving in opposite directions. The trajectory ONQ of a feature point initially located at the origin O on each circular circle, traversed by the first circular circle S1, is used as the membrane cavity generation line. The point of tangency between the circular circle and the X-axis when the feature point is located at N is defined as P. N The angle of rotation of the rounding is When the feature point is located at Q, the point of tangency between the rounded circle and the X-axis is P. Q The angle of rotation of the rounding is As the second rolling circle S2 moves, a cycloid OMK is formed;

[0087] The membrane cavity profile coordinate transformation module is used to define the characteristic tilt angle Δθ of the membrane cavity profile and solve for the trajectory ONQ in the XOY coordinate system to determine A=(x A ,y A The angle of inclination of the tangent from point O to point B changes by Δθ. B = (x - 0) is determined using the cycloid OMK. B ,y B The change in tangent angle from point O to point O is Δθ. The rolling angular velocities of the first rolling circle S1 and the second rolling circle S2 are defined to be the same, and their motion times are also the same. Based on this, the specific membrane cavity profile can be calculated. The cavity profile L is composed of two cycloids AO and BO, which have the properties of the brachistochrone. A new coordinate system X'O'Y' is established with the tangent of the cavity profile L at point A as the horizontal axis O'X' and the normal of the cavity profile L at point B as the vertical axis O'Y'. The coordinate profile equation of the cavity profile L in the X'O'Y' coordinate system is then established.

[0088] The membrane cavity profile selection module is used to define the membrane cavity radius R. max =|x' A -x' B | Membrane cavity deflection Hmax =|y' A -y' B |, the ratio of the two generated rounding radii A series of membrane cavity profiles are established, and the best one is selected from the series of membrane cavity profiles according to the conditions to obtain a membrane cavity profile that meets the requirements.

[0089] Another embodiment of the present invention also proposes a diaphragm compressor having a diaphragm cavity generated by the diaphragm compressor cavity profile generation method based on the steepest descent line.

[0090] The above-described embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application, and should all be included within the protection scope of this application.

Claims

1. A method for generating the membrane cavity profile of a diaphragm compressor based on the steepest descent line, characterized in that, include: Establish an XOY coordinate system, and define a first rolling circle S1 and a second rolling circle S2, whose centers are located above and below the X-axis and are tangent to the X-axis, respectively. The two rolling circles have angular velocities of... Moving along the X-axis while maintaining tangency to it and moving away from it; the trajectory ONQ of the feature point initially located at the origin O on the rolling circle as the first rolling circle S1 moves is used as the membrane cavity generation line. The point of tangency between the first rolling circle S1 and the X-axis when the feature point is located at N is defined as... The first rolling circle S1 rotates at an angle of . When the feature point is located at Q, the point of tangency between the first rolling circle S1 and the X-axis is... The first rolling circle S1 rotates at an angle of . As the second rolling circle S2 moves, a cycloid OMK is formed; Define the characteristic tilt angle of the membrane cavity profile. Solve the trajectory ONQ in the XOY coordinate system to determine The change in the tangent angle from point O to point O is as follows: Determined by cycloidal OMK The change in the tangent angle from point O to point O is as follows: The first rolling circle S1 and the second rolling circle S2 are defined to have the same rolling angular velocity and the same motion time; the specific membrane cavity profile is calculated accordingly. membrane cavity profile L It consists of two cycloids, AO and BO, each with the properties of the brachistochrone; each with a membrane cavity shape. L The tangent at point A is the horizontal axis O'X' and the membrane cavity profile. L Establish a new coordinate system X'O'Y' with the normal at point B as the vertical axis O'Y', and thereby establish the membrane cavity profile. L The coordinate profile equation in the X'O'Y' coordinate system; Define the membrane cavity radius membrane cavity deflection The ratio of the two generated round radii , Let S1 be the radius of the first rolling circle; establish a series of membrane cavity profiles, and select the optimal membrane cavity profile according to the conditions to obtain the membrane cavity profile that meets the requirements.

2. The method for generating the membrane cavity profile of a diaphragm compressor based on the steepest descent line according to claim 1, characterized in that, Based on the required membrane cavity profile, the diaphragm compressor has an air inlet at the inflection point O and an exhaust port at the point of maximum deflection B.

3. The method for generating the membrane cavity profile of a diaphragm compressor based on the steepest descent line according to claim 1, characterized in that, The trajectory ONQ traversed by the feature point initially located at the origin O on the rolling circle as the first rolling circle S1 moves satisfies the following equation: In the formula, , Points P N and points P Q In the XOY coordinate system, the x-coordinate of the initial center of the first rolling circle S1 and the second rolling circle S2 coincides with the origin O. After the first rolling circle S1 completes one revolution, it is tangent to the X-axis at point O. P N After the first rolling circle S1 rotates twice, it becomes tangent to the X-axis at point [missing information]. P Q ; , These are the x-coordinate and y-coordinate of trajectory ONQ in the XOY coordinate system, respectively; For the first rolling circle S1 in time The distance traveled inward; For the first round in The angle of internal rotation; The time for the rolling motion.

4. The method for generating the membrane cavity profile of a diaphragm compressor based on the steepest descent line according to claim 3, characterized in that, The cycloid OMK formed by the movement of the second rolling circle S2 satisfies the following equation: 。 5. The method for generating the membrane cavity profile of a diaphragm compressor based on the steepest descent line according to claim 4, characterized in that, The motion of the first rolling circle S1 and the second rolling circle S2 is specifically described by the following expression: In the formula, To find the derivative operator, , These are the angles of rotation of the first rolling circle S1 and the second rolling circle S2, respectively.

6. The method for generating the membrane cavity profile of a diaphragm compressor based on the steepest descent line according to claim 5, characterized in that, The membrane cavity profile L The equation of the coordinate profile in the X'O'Y' coordinate system is expressed as follows: In the formula, ( , ) is the membrane cavity profile L The coordinates of the point on the X'O'Y' coordinate system.

7. The method for generating the membrane cavity profile of a diaphragm compressor based on the steepest descent line according to claim 6, characterized in that, When selecting the optimal membrane cavity profile based on certain conditions, the selection criteria include membrane cavity volume. and the maximum stress on the diaphragm surface using the aforementioned diaphragm cavity profile L. Less than the allowable stress of its material Specifically, it is described as the following expression: 。 8. The method for generating the membrane cavity profile of a diaphragm compressor based on the steepest descent line according to claim 7, characterized in that, Application of the membrane cavity profile L The surface stress of the diaphragm is calculated according to the following formula: In the formula, For about radius r The equation for the membrane cavity profile; Young's modulus of the diaphragm material; Poisson's ratio of the diaphragm material; For diaphragm thickness; It is a mathematical integral operator; It is a mathematical differential operator; This refers to the radial normal stress of the diaphragm. The circumferential normal stress of the diaphragm; This refers to the radial shear stress of the diaphragm. This refers to the circumferential shear stress of the diaphragm. This represents the minimum stress on the diaphragm surface. This represents the maximum stress on the diaphragm surface.

9. A diaphragm compressor cavity profile generation system based on the brachistochrone line, characterized in that, include: The circular motion trajectory definition module is used to establish an XOY coordinate system, defining a first circular circle S1 and a second circular circle S2 with their centers located above and below the X-axis and tangent to the X-axis, respectively. The two circular circles move at angular velocities... Moving along the X-axis while maintaining tangency to it and moving away from it; the trajectory ONQ of the feature point initially located at the origin O on the rolling circle as the first rolling circle S1 moves is used as the membrane cavity generation line. The point of tangency between the first rolling circle S1 and the X-axis when the feature point is located at N is defined as... The first rolling circle S1 rotates at an angle of . When the feature point is located at Q, the point of tangency between the first rolling circle S1 and the X-axis is... The first rolling circle S1 rotates at an angle of . As the second rolling circle S2 moves, a cycloid OMK is formed; The membrane cavity profile coordinate transformation module is used to define the characteristic tilt angle of the membrane cavity profile. Solve the trajectory ONQ in the XOY coordinate system to determine The change in the tangent angle from point O to point O is as follows: Determined by cycloidal OMK The change in the tangent angle from point O to point O is as follows: The first rolling circle S1 and the second rolling circle S2 are defined to have the same rolling angular velocity and the same motion time; the specific membrane cavity profile is calculated accordingly. membrane cavity profile L It consists of two cycloids, AO and BO, each with the properties of the brachistochrone; each with a membrane cavity shape. L The tangent at point A is the horizontal axis O'X' and the membrane cavity profile. L Establish a new coordinate system X'O'Y' with the normal at point B as the vertical axis O'Y', and thereby establish the membrane cavity profile. L The coordinate profile equation in the X'O'Y' coordinate system; The membrane cavity profile selection module is used to define the membrane cavity radius. membrane cavity deflection The ratio of the two generated round radii , Let S1 be the radius of the first rolling circle; establish a series of membrane cavity profiles, and select the optimal membrane cavity profile according to the conditions to obtain the membrane cavity profile that meets the requirements.

10. A diaphragm compressor, characterized in that, The membrane cavity is generated by the membrane cavity profile generation method of the diaphragm compressor based on the steepest descent line as described in any one of claims 1 to 8.

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