Method for generating molded line of diaphragm cavity of diaphragm compressor based on brachistochrone and product

Abstract

The invention discloses a diaphragm compressor diaphragm cavity molded line generation method based on a brachistochrone and a product. The diaphragm cavity molded line generation method comprises the steps that an XOY coordinate system is established, the circle centers of the first rolling circle S1 and the second rolling circle S2 are located above and below the X axis respectively, the first rolling circle S1 and the second rolling circle S2 are tangent to the X axis, and the two rolling circles run along the X axis at the angular speed omega and keep tangent to the X axis oppositely; a track ONQ of a feature point located at the original point O at the initial moment on the rolling circle along with the movement of the first rolling circle S1 is used as a film cavity generation line, and a cycloid OMK is formed along with the movement of the second rolling circle S2; and the mold cavity radius, the mold cavity deflection and the ratio of the two generated rolling radiuses are defined, a series of mold cavity molded lines are established, the series of mold cavity molded lines are preferentially selected according to conditions, and the mold cavity molded lines meeting the requirements are obtained. The diaphragm compressor diaphragm cavity molded line generation method provided by the invention is a multi-parameter molded line control method with an adjustable diaphragm cavity molded line characteristic inclination angle and an adjustable ratio of two generated rolling radiuses, and has higher design flexibility.

Description

Technical Field

[0001] The invention relates to the technical field of diaphragm compressors, and in particular to a method and product for generating a diaphragm compressor diaphragm cavity profile based on a brachistocentric drop line. Background Art

[0002] A diaphragm compressor is a positive displacement compressor that uses a diaphragm to separate the oil side and the gas side. Its working principle is: the motor drives the crankshaft connecting rod to drive the piston to reciprocate, thereby increasing and releasing the pressure of the high-pressure oil, and then the high-pressure oil pushes the diaphragm to compress and discharge the gas. Diaphragm compressors are widely used in the hydrogen energy industry due to their good sealing and high pressure ratio. In particular, hydrogen refueling stations are one of their important usage scenarios. The diaphragm life, volumetric efficiency and diaphragm head strength are very critical and difficult issues in the development of diaphragm compressors.

[0003] The diaphragm is a key component in the stable operation of the diaphragm compressor, and its working performance can directly affect the reliability of the compressor operation. In the process of diaphragm damage, the damage forms are mainly collapse, distortion, wear and tear, and mechanical fatigue. The damage of the diaphragm will lead to the destruction of its mechanical properties, and even cause great economic losses in severe cases.

[0004] At present, the diaphragm compressor diaphragm cavity profile widely used in China adopts the single-exponent small deflection diaphragm cavity profile. After long-term practice and verification, it has good reliability and practical basis. However, in the process of developing and designing new diaphragm compressor models, the traditional single-exponent diaphragm cavity profile is adjusted by controllable parameters such as the diaphragm cavity index, and the profile optimization range is limited. It cannot adapt to the urgent needs of the market demand for the technical development of diaphragm compressors and the development of new high-pressure and high-speed models. The multi-parameter diaphragm cavity profile optimization design is an effective way to improve the reliability of diaphragm compressors and reduce costs. Summary of the invention

[0005] The purpose of the present invention is to address the problems in the above-mentioned prior art and provide a method and product for generating the diaphragm cavity profile of a diaphragm compressor based on the brachistoline, so as to meet the needs of multi-parameter diaphragm cavity profile optimization design and enhance design flexibility.

[0006] In order to achieve the above object, the present invention has the following technical solutions:

[0007] In a first aspect, a method for generating a diaphragm compressor cavity profile based on a brachistodes curve is provided, comprising:

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

[0009] Define the characteristic inclination angle Δθ of the membrane cavity profile, solve the trajectory ONQ in the XOY coordinate system to determine A=(x A ,y A The inclination angle of the tangent from point ) to point O changes to Δθ, and B is determined by the cycloid OMK to be (x B ,y B The tangent angle from point ) to point O changes to Δθ, and the rolling angular velocity of the first rolling circle S1 and the second rolling circle S2 are defined to be the same, and the movement time is also the same; thus, the specific membrane cavity profile is calculated The membrane cavity line L is composed of two cycloids AO and BO with the property of the brachistodes; a new coordinate system X'O'Y' is established with the tangent of the membrane cavity line L at point A as the horizontal axis O'X' and the normal of the membrane cavity line L at point B as the vertical axis O'Y', thereby establishing the coordinate line equation of the membrane cavity line L in the X'O'Y' coordinates;

[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 rolling circle radii A series of membrane cavity profiles are established, and the best membrane cavity profiles are selected according to conditions to obtain membrane cavity profiles that meet the requirements.

[0011] As a preferred solution, according to the membrane cavity profile that meets the requirements, the diaphragm compressor is provided with an air inlet at the inflection point O and an exhaust port at the maximum deflection point B.

[0012] As a preferred solution, the trajectory ONQ of the feature point initially located at the origin O on the rolling circle along with the movement of the first rolling circle S1 satisfies the following formula:

[0013]

[0014] In the formula, x PN、x PQ are the abscissas of point PN and point PQ in the XOY coordinate system respectively. The abscissas of the centers of the first rolling circle S1 and the second rolling circle S2 coincide with the origin O at the initial moment. After the first rolling circle S1 rotates one circle, it is tangent to the X-axis at point PN. After the first rolling circle S1 rotates two circles, it is tangent to the X-axis at point PQ. S1 ,y S1 are the horizontal and vertical coordinates of the trajectory ONQ in the XOY coordinate system; R S1 is the first rolling radius; S Δt is the distance that the first rolling circle S1 advances within the time Δt; is the rotation angle of the first rolling circle within Δt; Δt is the rolling circle movement time.

[0015] As a preferred solution, the cycloid OMK formed with the movement of the second rolling circle S2 satisfies the following formula:

[0016]

[0017] As a preferred solution, the movement of the first rolling circle S1 and the second rolling circle S2 is specifically described as follows:

[0018]

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

[0020] As a preferred solution, the coordinate line equation of the membrane cavity line L in the X'O'Y' coordinates is as follows:

[0021]

[0022] Wherein, (x', y') is the coordinate of the point on the membrane cavity line L in the X'O'Y' coordinate system.

[0023] As a preferred solution, when the series of membrane cavity profiles are selected according to conditions, the conditions for the selection include the membrane cavity volume V L,Set The maximum stress δmax of the diaphragm surface to which the diaphragm cavity profile L is applied is less than the allowable stress [σ] of its material, which is specifically described by the following expression:

[0024]

[0025] As a preferred solution, the surface stress of the diaphragm using the diaphragm cavity line 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] Where H is the equation of the membrane cavity line 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 is the radial normal stress of the diaphragm; δ Pt is the circumferential normal stress of the diaphragm; Mr is the radial shear stress of the diaphragm; δ Mr is the circumferential shear stress of the diaphragm; min is the minimum stress on the diaphragm surface; δ max is the maximum stress on the diaphragm surface.

[0030] In a second aspect, a system for generating a diaphragm compressor cavity profile based on a brachistodes curve is provided, comprising:

[0031] The rolling circle motion trajectory definition module is used to establish an XOY coordinate system, define the first rolling circle S1 and the second rolling circle S2 whose centers are located above and below the X-axis respectively and are tangent to the X-axis. The two rolling circles move along the X-axis at an angular velocity ω and keep tangent to the X-axis in opposite directions; the trajectory ONQ of the feature point on the rolling circle located at the origin O at the initial moment along with the movement of the first rolling circle S1 is used as the membrane cavity generation line, and the tangent point of the rolling circle and the X-axis when the feature point is located at N is defined as P N The angle of the rolling circle is When the feature point is located at Q, the tangent point between the rolling circle and the X axis is P Q The angle of the rolling circle is As the second rolling circle S2 moves, a cycloid OMK is formed;

[0032] The membrane cavity line coordinate conversion module is used to define the characteristic inclination angle Δθ of the membrane cavity line, solve the trajectory ONQ in the XOY coordinate system to determine A=(x A ,y A The inclination angle of the tangent from point ) to point O changes to Δθ, and B is determined by the cycloid OMK to be (x B ,y B The tangent angle from point ) to point O changes to Δθ, and the rolling angular velocity of the first rolling circle S1 and the second rolling circle S2 are defined to be the same, and the movement time is also the same; thus, the specific membrane cavity profile is calculated The membrane cavity line L is composed of two cycloids AO and BO with the property of the brachistodes; a new coordinate system X'O'Y' is established with the tangent of the membrane cavity line L at point A as the horizontal axis O'X' and the normal of the membrane cavity line L at point B as the vertical axis O'Y', thereby establishing the coordinate line equation of the membrane cavity line L in the X'O'Y' coordinates;

[0033] Membrane cavity profile selection module, 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 rolling circle radii A series of membrane cavity profiles are established, and the best membrane cavity profiles are selected according to conditions to obtain membrane cavity profiles that meet the requirements.

[0034] According to a third aspect, a diaphragm compressor is provided, comprising a diaphragm cavity generated by the method for generating a diaphragm compressor diaphragm cavity profile based on the brachistocentric curve.

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

[0036] The diaphragm compressor diaphragm cavity profile is composed of two cycloids AO and BO with the property of the fastest descending line. The inclination angle change Δθ of the diaphragm cavity profile can be flexibly adjusted to adjust the stress distribution when the diaphragm is close to the diaphragm cavity profile, which is beneficial to improving the life of the diaphragm. By adjusting the ratio of two generated rolling circle radii χ, the position of the inflection point of the diaphragm cavity profile and the diaphragm stress distribution near the inflection point can be adjusted, which is beneficial to the flexible setting of the position of the diaphragm cavity suction port of the diaphragm compressor. By fixing the ratio of two generated rolling circle radii χ and the characteristic inclination angle Δθ of the diaphragm cavity profile, the generated rolling circle radius can be adjusted to generate a diaphragm cavity radius R with the same slope change trend. max and membrane cavity deflection H max Proportional change, membrane cavity volume V L A series of similar membrane cavity profile clusters with positively correlated changes are beneficial to the serialized design of membrane cavity profiles and simplify the design of membrane cavity profiles. Compared with the single-exponential membrane cavity profile, that is, the profile adjustment method of adjusting the single membrane cavity index Z, the diaphragm compressor membrane cavity profile generation method proposed in the present invention is a multi-parameter profile control method with adjustable membrane cavity profile characteristic inclination angle Δθ and two generated rolling circle radii ratio χ, which has higher design flexibility and can solve the problems of insufficient optimization parameters, limited optimization range and difficult to adjust inflection point slope in traditional single-exponential profile design. Products manufactured based on this method can adapt to diversified market demands, optimize the reliability of diaphragm compressors and increase the life of diaphragms.

[0037] Furthermore, the present invention is conducive to optimizing the gas flow during the membrane cavity suction and exhaust process by arranging an air inlet at the inflection point O of the membrane cavity profile based on the brachistodes line and arranging an exhaust port at the maximum deflection point B. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] In order to more clearly illustrate the specific implementation methods of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the specific implementation methods or the description of the prior art. Obviously, the drawings described below are some implementation methods of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0039] Figure 1 It is a schematic diagram of the principle of a method for generating a diaphragm compressor cavity profile based on the brachistocentric curve according to an embodiment of the present invention;

[0040] Figure 2 A method for fixing the ratio of two generated rolling circle radii χ=1 and the characteristic inclination angle provided in Example 1 of the present invention Design of membrane cavity type line cluster ∑L Case1 ;

[0041] Figure 3 The profile cluster ΣL provided in Example 1 of the present invention Case1 Slope variation curve along radial direction;

[0042] Figure 4 The profile cluster ΣL provided in Example 1 of the present invention Case1 Equivalent stress in radial direction Change curve chart;

[0043] Figure 5 The profile cluster ΣL provided in Example 1 of the present invention Case1 The maximum stress on the diaphragm surface along the radial direction is max and the minimum stress δ on the diaphragm surface min Change curve chart;

[0044] Figure 6 The designed membrane cavity volume V provided in Example 1 of the present invention is L,Set =1200000mm 3 , fix the ratio of the two generated rolling circle radii χ = 1 and the characteristic inclination angle The membrane cavity profile L based on the brachistocentre curve Case1 ;

[0045] Figure 7 The membrane cavity profile L based on the brachistodes curve provided in Example 1 of the present invention Case1 The maximum stress on the diaphragm surface along the radial direction is max and the minimum stress on the diaphragm surface δ min Change curve graph.

[0046] In the attached figure: ω-shaped line generates rolling angular velocity of rolling circle; -The angle of the rolling circle generated by the profile after Δt time; S Δt -The distance that the rolling circle generated by the profile rolls after Δt time; ρ-Defines the equivalent radius of the membrane cavity; k L -The slope of the membrane cavity line in the X'O'Y' coordinate system; -Equivalent stress when the diaphragm of the diaphragm compressor is close to the diaphragm cavity profile; R S1 - radius of the first rolling circle S1; (x L ,y L )-Design the coordinates of any point on the membrane cavity line L. DETAILED DESCRIPTION

[0047] The technical solution of the present invention will be clearly and completely described below in conjunction with the embodiments. Obviously, the described embodiments are part of the embodiments of the present invention, rather than all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0048] See also Figure 1 The method for generating the diaphragm compressor cavity profile based on the brachistodes curve in an embodiment of the present invention comprises:

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

[0050] Step 2: Define the characteristic inclination angle Δθ of the membrane cavity profile, and solve the trajectory ONQ in the XOY coordinate system to determine A=(x A ,y A The inclination angle of the tangent from point ) to point O changes to Δθ, and B is determined by the cycloid OMK to be (x B ,y B The tangent angle from point ) to point O changes to Δθ, and the rolling angular velocity of the first rolling circle S1 and the second rolling circle S2 are defined to be the same, and the movement time is also the same; thus, the specific membrane cavity profile is calculated The membrane cavity line L is composed of two cycloids AO and BO with the property of the brachistodes; a new coordinate system X'O'Y' is established with the tangent of the membrane cavity line L at point A as the horizontal axis O'X' and the normal of the membrane cavity line L at point B as the vertical axis O'Y', thereby establishing the coordinate line equation of the membrane cavity line L in the X'O'Y' coordinates;

[0051] Step 3: 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 rolling circle radii According to the above method, a complete profile of the central section of the diaphragm compressor cavity is established, which has a first rolling radius R S1 , the second rolling radius R S2 , the characteristic inclination angle Δθ of the diaphragm cavity profile and other profile design parameters, thereby a series of diaphragm cavity profiles can be established. By selecting the series of diaphragm cavity profiles according to the conditions, the diaphragm stress is smaller and the radius of the diaphragm cavity profile is smaller to increase the diaphragm life of the diaphragm compressor and reduce the cost, and a diaphragm cavity profile that meets the requirements is obtained.

[0052] Furthermore, according to the membrane cavity profile that meets the requirements, the diaphragm compressor in the embodiment of the present invention is provided with an air inlet at the inflection point O and an exhaust port at the maximum deflection point B, which is beneficial to optimizing the gas flow during the membrane cavity suction and exhaust process.

[0053] In a possible implementation manner, in step Step1, the trajectory ONQ of the feature point initially located at the origin O on the rolling circle as the first rolling circle S1 moves satisfies the following formula:

[0054]

[0055] In the formula, x PN 、x PQ are the abscissas of point PN and point PQ in the XOY coordinate system respectively. The abscissas of the centers of the first rolling circle S1 and the second rolling circle S2 coincide with the origin O at the initial moment. After the first rolling circle S1 rotates one circle, it is tangent to the X-axis at point PN. After the first rolling circle S1 rotates two circles, it is tangent to the X-axis at point PQ. S1 ,y S1 are the horizontal and vertical coordinates of the trajectory ONQ in the XOY coordinate system; R S1 is the first rolling radius; S Δt is the distance that the first rolling circle S1 advances within the time Δt; is the rotation angle of the first rolling circle within Δt; Δt is the rolling circle movement time.

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

[0057]

[0058] In a possible implementation manner, the movements of the first rolling circle S1 and the second rolling circle S2 in step Step2 are specifically described as follows:

[0059]

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

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

[0062]

[0063] Wherein, (x', y') is the coordinate of the point on the membrane cavity line L in the X'O'Y' coordinate system.

[0064] In a possible implementation manner, when the series of membrane cavity profiles are selected according to conditions in step 3, the conditions for the selection include the membrane cavity volume V L,Set The maximum stress δmax of the diaphragm surface to which the diaphragm cavity profile L is applied is less than the allowable stress [σ] of its material, which is specifically described by the following expression:

[0065]

[0066] Furthermore, the surface stress of the diaphragm using the diaphragm cavity line 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] Where H is the equation of the membrane cavity line 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 is the radial normal stress of the diaphragm; δ Pt is the circumferential normal stress of the diaphragm; Mr is the radial shear stress of the diaphragm; δ Mr is the circumferential shear stress of the diaphragm; min is the minimum stress on the diaphragm surface; δ max is the maximum stress on the diaphragm surface.

[0072] Through the above steps, a diaphragm compressor diaphragm cavity profile based on the brachistocentric curve is generated, which can flexibly adjust the inclination angle change Δθ of the diaphragm cavity profile to adjust the stress distribution when the diaphragm is close to the diaphragm cavity profile surface, which is beneficial to improving the life of the diaphragm; by adjusting the ratio of two generated rolling circle radii χ, the position of the inflection point of the diaphragm cavity profile and the diaphragm stress distribution near the inflection point can be adjusted, which is beneficial to the flexible setting of the position of the diaphragm cavity suction port of the diaphragm compressor; by fixing the ratio of two generated rolling circle radii χ and the characteristic inclination angle Δθ of the diaphragm cavity profile, adjusting the generated rolling circle radius can generate a diaphragm cavity radius R with the same slope change trend. max and membrane cavity deflection H max Proportional change, membrane cavity volume V L A series of similar membrane cavity profile clusters with positively correlated changes are beneficial to the serialized design of membrane cavity profiles and simplify the design of membrane cavity profiles; by setting an air inlet at the inflection point O of the membrane cavity profile based on the brachistoline and an exhaust port at the maximum deflection B, it is beneficial to optimize the gas flow during the membrane cavity suction and exhaust processes; compared with the profile adjustment method of adjusting the single membrane cavity index Z by using a single-exponential membrane cavity profile, the diaphragm compressor membrane cavity profile generation method proposed in the present invention is a multi-parameter profile control method with adjustable characteristic inclination angle Δθ of the membrane cavity profile and ratio χ of two generated rolling circle radii, which has higher design flexibility.

[0073] Another embodiment of the present invention verifies the proposed method for generating the diaphragm compressor cavity profile based on the brachistodes curve. The design requires the volume V of the diaphragm cavity profile to be L,Set =1200000mm 3 , fix the ratio of the two generated rolling circle radii and characteristic inclination Adjust the radius R of the first rolling circle S1 S1 , from which a series of line clusters ∑L can be generated Case1 like Figure 2 shown.

[0074] Furthermore, the equivalent radius of the membrane cavity is defined as The slope of the membrane cavity line L The generated line cluster ∑L is obtained from this solution. Case1 All the lines LCase1 Have the same profile slope characteristics, such as Figure 3 shown.

[0075] Furthermore, according to the fourth strength theory, the equivalent stress on the diaphragm surface of the diaphragm compressor using the above-mentioned diaphragm cavity profile is It can be described by the following formula:

[0076]

[0077] Where: -Equivalent stress on the diaphragm surface; δ Pr -Diaphragm radial stress; δ Mr - circumferential stress of the diaphragm; Q- diaphragm shear stress; [σ]- allowable stress of the diaphragm material.

[0078] Furthermore, the generated line cluster ∑L is calculated Case1 All the lines L Case1 With nearly similar equivalent stress Features, such as Figure 4 shown.

[0079] Furthermore, the calculation obtains the close generation line cluster ∑L Case1 Small diameter R max Type Line L Case1 The maximum surface stress of the 0.5 mm thick diaphragm is max and the minimum value δ min Distribution Figure 5 As shown, with the radius R of the first profile of the membrane cavity S1 The increase of the maximum surface stress δ max Gradually decreases, when the first profile radius R S1 =15m, the maximum stress on the diaphragm surface is less than the allowable stress of its material 210MPa. Therefore, under the fixed design parameter conditions of this embodiment, the radius of the first mold line of the membrane cavity R S1 Should be greater than 15m.

[0080] Furthermore, the set membrane cavity volume V is obtained by solving L,Set The design first profile radius R S1 =25.325m, the designed membrane cavity line 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 close to the aforementioned design diaphragm cavity profile is obtained. maxand the minimum stress δ min The distribution of the radial equivalent radius ρ is as follows: Figure 7 As shown, the maximum surface stress is 154MPa.

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

[0084] Thus, the designed membrane cavity volume V is achieved. L,Set A diaphragm cavity profile design based on the brachistocentric curve and the diaphragm allowable stress [σ] requirements.

[0085] Another embodiment of the present invention further provides a diaphragm compressor diaphragm cavity profile generation system based on the brachistodes curve, comprising:

[0086] The rolling circle motion trajectory definition module is used to establish an XOY coordinate system, define the first rolling circle S1 and the second rolling circle S2 whose centers are located above and below the X-axis respectively and are tangent to the X-axis. The two rolling circles move along the X-axis at an angular velocity ω and keep tangent to the X-axis in opposite directions; the trajectory ONQ of the feature point on the rolling circle located at the origin O at the initial moment along with the movement of the first rolling circle S1 is used as the membrane cavity generation line, and the tangent point of the rolling circle and the X-axis when the feature point is located at N is defined as P N The angle of the rolling circle is When the feature point is located at Q, the tangent point between the rolling circle and the X axis is P Q The angle of the rolling circle is As the second rolling circle S2 moves, a cycloid OMK is formed;

[0087] The membrane cavity line coordinate conversion module is used to define the characteristic inclination angle Δθ of the membrane cavity line, solve the trajectory ONQ in the XOY coordinate system to determine A=(x A ,y A The inclination angle of the tangent from point ) to point O changes to Δθ, and B is determined by the cycloid OMK to be (x B ,y B The tangent angle from point ) to point O changes to Δθ, and the rolling angular velocity of the first rolling circle S1 and the second rolling circle S2 are defined to be the same, and the movement time is also the same; thus, the specific membrane cavity profile is calculated The membrane cavity line L is composed of two cycloids AO and BO with the property of the brachistodes; a new coordinate system X'O'Y' is established with the tangent of the membrane cavity line L at point A as the horizontal axis O'X' and the normal of the membrane cavity line L at point B as the vertical axis O'Y', thereby establishing the coordinate line equation of the membrane cavity line L in the X'O'Y' coordinates;

[0088] Membrane cavity profile selection module, 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 rolling circle radii A series of membrane cavity profiles are established, and the best membrane cavity profiles are selected according to conditions to obtain membrane cavity profiles that meet the requirements.

[0089] Another embodiment of the present invention further provides a diaphragm compressor having a diaphragm cavity generated by the method for generating a diaphragm compressor diaphragm cavity profile based on the brachistocentric curve.

[0090] The embodiments described above are only used to illustrate the technical solutions of the present application, rather than to limit them. Although the present application has been described in detail with reference to the aforementioned embodiments, a person skilled in the art should understand that the technical solutions described in the aforementioned embodiments may still be modified, or some of the technical features may be replaced by equivalents. Such modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present application, and should all be included in the protection scope of the present application.

Claims

1. A method for generating a diaphragm compressor cavity profile based on the brachistocentre curve, characterized in that: include: Establish an XOY coordinate system, define the first rolling circle S1 and the second rolling circle S2 whose centers are respectively above and below the X-axis and tangent to the X-axis, and the two rolling circles move along the X-axis at an angular velocity ω and keep tangent to the X-axis in opposite directions; the trajectory ONQ of the feature point on the rolling circle initially located at the origin O along with the movement of the first rolling circle S1 is used as the membrane cavity generation line, and define the tangent point of the rolling circle and the X-axis when the feature point is located at N as P N The angle of the rolling circle is When the feature point is located at Q, the tangent point between the rolling circle and the X axis is P Q The angle of the rolling circle is As the second rolling circle S2 moves, a cycloid OMK is formed; Define the characteristic inclination angle Δθ of the membrane cavity profile, solve the trajectory ONQ in the XOY coordinate system to determine A=(x A ,y A The inclination angle of the tangent from point ) to point O changes to Δθ, and B is determined by the cycloid OMK to be (x B ,y B The tangent angle from point ) to point O changes to Δθ, and the rolling angular velocity of the first rolling circle S1 and the second rolling circle S2 are defined to be the same, and the movement time is also the same; thus, the specific membrane cavity profile is calculated The membrane cavity line L is composed of two cycloids AO and BO with the property of the brachistodes; a new coordinate system X'O'Y' is established with the tangent of the membrane cavity line L at point A as the horizontal axis O'X' and the normal of the membrane cavity line L at point B as the vertical axis O'Y', thereby establishing the coordinate line equation of the membrane cavity line L in the X'O'Y' coordinates; 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 rolling circle radii A series of membrane cavity profiles are established, and the best membrane cavity profiles are selected according to conditions to obtain membrane cavity profiles that meet the requirements.

2. The method for generating the diaphragm compressor cavity profile based on the brachistodes curve according to claim 1, characterized in that: According to the membrane cavity profile that meets the requirements, the diaphragm compressor is provided with an air inlet at the inflection point O and an exhaust port at the maximum deflection point B.

3. The method for generating the diaphragm compressor cavity profile based on the brachistocentric curve according to claim 1, characterized in that: The trajectory ONQ of the feature point initially located at the origin O on the rolling circle along with the movement of the first rolling circle S1 satisfies the following formula: In the formula, x PN 、x PQ are the abscissas of point PN and point PQ in the XOY coordinate system respectively. The abscissas of the centers of the first rolling circle S1 and the second rolling circle S2 coincide with the origin O at the initial moment. After the first rolling circle S1 rotates one circle, it is tangent to the X-axis at point PN. After the first rolling circle S1 rotates two circles, it is tangent to the X-axis at point PQ. S1 ,y S1 are the horizontal and vertical coordinates of the trajectory ONQ in the XOY coordinate system; R S1 is the first rolling radius; S Δt is the distance that the first rolling circle S1 advances within the time Δt; is the rotation angle of the first rolling circle within Δt; Δt is the rolling circle movement time.

4. The method for generating the diaphragm compressor cavity profile based on the brachistodes curve according to claim 3, characterized in that: The cycloid OMK formed with the movement of the second rolling circle S2 satisfies the following formula:

5. The method for generating the diaphragm compressor cavity profile based on the brachistodes curve according to claim 4, characterized in that: The motions of the first rolling circle S1 and the second rolling circle S2 are specifically described as follows: In the formula, To find the derivative operator, are the rotation angles of the first rolling circle S1 and the second rolling circle S2 respectively.

6. The method for generating the diaphragm compressor cavity profile based on the brachistocentric curve according to claim 5, characterized in that: The coordinate line equation of the membrane cavity line L in the X'O'Y' coordinate is as follows: Wherein, (x', y') is the coordinate of the point on the membrane cavity line L in the X'O'Y' coordinate system.

7. The method for generating the diaphragm compressor cavity profile based on the brachistocentric curve according to claim 6, characterized in that: When the series of membrane cavity profiles are selected according to conditions, the conditions for the selection include the membrane cavity volume V L,Set The maximum stress δmax of the diaphragm surface to which the diaphragm cavity profile L is applied is less than the allowable stress [σ] of its material, which is specifically described by the following expression:

8. The method for generating the diaphragm compressor cavity profile based on the brachistocentric curve according to claim 7, characterized in that: The surface stress of the diaphragm using the diaphragm cavity line L is calculated according to the following formula: d min =min{δ Pr ±δ Mr ,d Pt ±δ Mt } d max =max{δ Pr ±δ Mr ,d Pt ±δ Mt } Where H is the equation of the membrane cavity line 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 is the radial normal stress of the diaphragm; δ Pt is the circumferential normal stress of the diaphragm; δ Mr is the radial shear stress of the diaphragm; δ Mr is the circumferential shear stress of the diaphragm; min is the minimum stress on the diaphragm surface; δ max is the maximum stress on the diaphragm surface.

9. A diaphragm compressor cavity profile generation system based on the brachistocentre curve, characterized in that: include: The rolling circle motion trajectory definition module is used to establish an XOY coordinate system, define the first rolling circle S1 and the second rolling circle S2 whose centers are located above and below the X-axis respectively and are tangent to the X-axis. The two rolling circles move along the X-axis at an angular velocity ω and keep tangent to the X-axis in opposite directions; the trajectory ONQ of the feature point on the rolling circle located at the origin O at the initial moment along with the movement of the first rolling circle S1 is used as the membrane cavity generation line, and the tangent point of the rolling circle and the X-axis when the feature point is located at N is defined as P N The angle of the rolling circle is When the feature point is located at Q, the tangent point between the rolling circle and the X axis is P Q The angle of the rolling circle is As the second rolling circle S2 moves, a cycloid OMK is formed; The membrane cavity line coordinate conversion module is used to define the characteristic inclination angle Δθ of the membrane cavity line, solve the trajectory ONQ in the XOY coordinate system to determine A=(x A ,y A The inclination angle of the tangent from point ) to point O changes to Δθ, and B is determined by the cycloid OMK to be (x B ,y B The tangent angle from point ) to point O changes to Δθ, and the rolling angular velocity of the first rolling circle S1 and the second rolling circle S2 are defined to be the same, and the movement time is also the same; thus, the specific membrane cavity profile is calculated The membrane cavity line L is composed of two cycloids AO and BO with the property of the brachistodes; a new coordinate system X'O'Y' is established with the tangent of the membrane cavity line L at point A as the horizontal axis O'X' and the normal of the membrane cavity line L at point B as the vertical axis O'Y', thereby establishing the coordinate line equation of the membrane cavity line L in the X'O'Y' coordinates; Membrane cavity profile selection module, 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 rolling circle radii A series of membrane cavity profiles are established, and the best membrane cavity profiles are selected according to conditions to obtain membrane cavity profiles that meet the requirements.

10. A diaphragm compressor, characterized in that: A diaphragm cavity generated by the method for generating a diaphragm compressor diaphragm cavity profile based on the steepest descent line as claimed in any one of claims 1 to 8.

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