Design calculation method of spring pressure ratio for zero leakage of bellows type expansion self-pumping mechanical seal

Abstract

The application discloses a design and calculation method of spring specific pressure of a bellows type pressure-increasing self-pumping dynamic pressure mechanical seal zero leakage, which comprises the following steps: according to the stable operation principle of the dynamic pressure mechanical seal, the balance relationship between the closing force and the opening force is determined; the closing force is taken as a function of the spring specific pressure; the opening force is calculated in two stages, i.e., a contact stage and a non-contact stage, by using the state of the dynamic pressure mechanical seal opening to stable operation; the opening force in the contact stage is composed of the liquid film bearing force and the micro-convex body contact force; the opening force in the non-contact stage is composed of the liquid film dynamic pressure between the sealing rings; the maximum value of the opening force in the whole cycle operation of the dynamic pressure mechanical seal is obtained; and the best spring specific pressure can be inversely solved by using the axial force balance condition met in the whole process operation. The application can efficiently and accurately realize the design of the spring specific pressure of the dynamic pressure mechanical seal, and get rid of the problem that the design of the spring specific pressure of the mechanical seal currently depends on artificial experience.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of dynamic pressure mechanical seal, and relates to a design and calculation method for the sealing spring specific pressure of a bellows type pressure expansion self-pumping dynamic pressure mechanical seal zero leakage combined with percolation theory and computational fluid dynamics, and more particularly to a design and calculation method for the spring specific pressure of a bellows type pressure expansion self-pumping dynamic pressure mechanical seal when reaching zero leakage. BACKGROUND

[0002] The pressure expansion self-pumping mechanical seal is an axial end face sealing device relying on the pre-tightening of the elastic element to the static and dynamic ring end face sealing pair and relying on the dynamic pressure fluid film formed between the end faces to block the leakage passage to achieve sealing, which is mainly composed of a dynamic ring with spiral grooves, a static ring with flow guide holes, an elastic element (bellows) and an auxiliary seal (O-ring). Among them, the elastic element is installed on the shaft and rotates with the shaft to pre-tighten the static and dynamic ring end face sealing pair. At the same time, the dynamic ring installed on the elastic element relies on the spiral grooves of the dynamic ring end face to form a dynamic pressure fluid film with the static ring installed at the end cover to achieve long-period operation and "zero leakage". The mechanical seal is widely used in petrochemical, marine and shipbuilding industries, aerospace industries and other industries to prevent leakage of fluid medium in the sealing cavity.

[0003] At present, the spring specific pressure selection of the non-contact mechanical seal elastic element is mainly through the experience of technical personnel, which is a quick and effective method in many cases, but it cannot consider all working conditions and cannot achieve the optimal performance of the system, which may lead to sealing failure and reduce the service life of the seal.

[0004] Therefore, in order to overcome these shortcomings, a design and calculation method for the sealing spring specific pressure of a bellows type pressure expansion self-pumping dynamic pressure mechanical seal zero leakage is needed to be applied in the design of non-contact mechanical seal, so that the sealing device is more stable and reliable in the running process. SUMMARY

[0005] In order to solve the above-mentioned deficiencies of the existing non-contact mechanical seal in the spring specific pressure selection method, the present application provides a design and calculation method for the sealing spring specific pressure of a bellows type pressure expansion self-pumping dynamic pressure mechanical seal zero leakage based on axial force balance, which includes the following steps:

[0006] S1, obtaining the structure parameters and working condition parameters of the bellows type pressure expansion self-pumping fluid mechanical seal;

[0007] S2, determining the closing force according to the structure parameters and working condition parameters, and taking the closing force as a function of the spring specific pressure;

[0008] S3, in the process of starting up to rated working speed of the bellows type diffuser self-pumping dynamic pressure mechanical seal, the opening force is a function of the rotating speed and the liquid film thickness, and the closing force is a constant; wherein the rotating speed is represented by n, the liquid film thickness is represented by h, the bellows type diffuser self-pumping dynamic pressure mechanical seal is represented by DSPHMS, the opening force is represented by F o , and the closing force is represented by F c .

[0009] S4, the process of starting up from static state to rated working speed of the DSPHMS is divided into two stages; when 0≤n<n c , the micro-convexes of the sealing end surface are in contact, and the opening force is composed of the liquid film bearing force and the micro-convex contact force; when n c ≤n≤n w , the micro-convexes of the sealing end surface are separated, and the opening force of the sealing end surface is borne by the sealing medium; wherein n c is the separation rotating speed, when n=n c , the micro-convexes of the sealing end surface are at the critical point of contact and separation; n w is the rated working speed.

[0010] The stable running of the whole process of the DSPHMS requires that the dynamic pressure mechanical seal can realize stable sealing without leakage in the static state, and can realize the separation of the sealing end surface and sealing when the equipment reaches the rated rotating speed; the whole process of the running of the DSPHMS satisfies the axial force balance condition, i.e. F c ≡F o , and the spring specific pressure is obtained by inverse solution of the relationship F c ≡F o .

[0011] Specifically, in step S1, the structure parameters and working condition parameters of the DSPHMS include the outer diameter of the sealing ring, the inner diameter of the sealing ring, the outer diameter of the spiral groove, the root diameter of the spiral groove, and the sealing medium pressure; the outer diameter of the sealing ring is represented by r o , the inner diameter of the sealing ring is represented by r i , the outer diameter of the spiral groove is represented by r k , the root diameter of the spiral groove is represented by r g , and the sealing medium pressure is represented by p o .

[0012] Specifically, in step S2, the closing force is determined according to the structure parameters and working condition parameters of the DSPHMS, and the closing force in the whole process is calculated by formula (1):

[0013]

[0014] wherein F c-fluid is the closing force provided by the sealing medium pressure, F c-bellow is the closing force provided by the bellows, and re Equivalent radius of bellows, p i Pressure at inner diameter of seal ring, p sp Spring pressure provided by bellows;

[0015] Closure force is a function of spring pressure, equation (1) is simplified as: F c = f1(p sp ).

[0016] Specifically, in step S3, the process of starting up to rated operating speed, the opening force is a function of speed and liquid film thickness, the value range of p sp is converted to F o The maximum and minimum values in the full cycle operation stage: o The maximum value and the minimum value in the full cycle operation stage:

[0017]

[0018] Where, F o,min is the minimum value of F o in the full cycle operation stage, F o,max is the maximum value of F o in the full cycle operation stage;

[0019] The full cycle operation stage is the process of starting up to rated operating speed of DSPHMS;

[0020] In the full cycle stable operation stage, p sp,min is the minimum value of p sp , p sp,max is the maximum value of p sp .

[0021] Specifically, in step S4:

[0022] In the contact phase, the opening force of the sealing end face is composed of the liquid film bearing force F o-fluid and the micro convex contact force F o-contact ; In the non-contact phase, the opening force of the sealing end face is composed of the liquid film bearing force F o-fluid , at this time, the micro convex contact force F o-contact = 0N; In the running process of DSPHMS, the specific calculation of opening force is shown as equation (3):

[0023]

[0024] Where, p c is the micro convex contact pressure between the sealing end faces, p f is the liquid film pressure between the sealing end faces, r is the polar radius, and θ is the polar angle;

[0025] The contact stage refers to a stage when the micro-convexities of the sealing end surfaces are in contact, and the non-contact stage refers to a stage when the micro-convexities of the sealing end surfaces are not in contact;

[0026] (1) When 0≤n<n c :

[0027] At this time, the micro-convexities of the sealing end surfaces are in contact, and the opening force of this stage is composed of the liquid film bearing force F o-fluid and the micro-convexity contact force F o-contact , which is specifically calculated by formula (3). With the increase of the rotating speed, the micro-convexities in contact between the sealing end surfaces gradually separate, and F o-contact gradually decreases to 0 in this process;

[0028] When n=0, in order to ensure that the DSPHMS realizes effective sealing, the micro-convexity contact pressure p c between the sealing end surfaces is calculated according to the critical percolation threshold, then F o-contact is calculated, the liquid film pressure p f between the sealing end surfaces is calculated by using the analytical method for the steady-state performance of the spiral groove mechanical seal, and the liquid film bearing force F o-fluid is calculated according to formula (3). At this time, the sum of F o-contact and F o-fluid is the opening force in the contact stage, and F c-o,min and F c-o,max are respectively determined by formula (4) and formula (5):

[0029] F c-o,min = f2(n=0, h=0) (4)

[0030] wherein F c-o,min is the minimum opening force in the contact stage.

[0031] F c-o,max = f2(n=n c , h=h c ) (5)

[0032] wherein F c-o,max is the maximum opening force in the contact stage, n c is the breakaway rotating speed, and h c is the breakaway film thickness.

[0033] At the same time, it can be determined that when n=0 and the closing force F c is greater than the minimum opening force F c-o,min in the contact stage, the minimum porosity is less than the critical percolation threshold, that is, the sealing contact interface is not percolated in the static state;

[0034] (2) When n c ≤n≤nw When:

[0035] In this stage, the micro convex of the sealing end face does not contact, and the opening force is completely borne by the sealing medium; when the rotating speed is accelerated from the disengagement rotating speed n c to the rated working rotating speed n w , the liquid film thickness increases, the opening force decreases and is always equal to the closing force; when the rotating speed n = n c , h = h c , h c is calculated by formula (6); when the rotating speed reaches the rated working rotating speed n w , h = h w , the size of h w is determined by the leakage rate;

[0036]

[0037] Where h c is the liquid film thickness when the rotating speed is the disengagement rotating speed n c , simply referred to as the disengagement thickness, h w is the liquid film thickness at the rated rotating speed, Ra d and Ra j are the surface roughnesses of the sealing end faces of the rotating ring and the stationary ring respectively; the liquid film thickness h w at the rated rotating speed is obtained by formula (7), and the leakage rate is represented by Q i :

[0038]

[0039] Where r i is the inner diameter of the sealing ring; μ is the dynamic viscosity of the sealing medium; is the fluid pressure distribution between the sealing end faces of the rotating ring and the stationary ring, r is the polar radius, θ is the polar angle, the leakage rate is a set value, and the leakage rate can be set according to different requirements, or can be set according to the corresponding national standard, industry standard or enterprise standard. When the national standard is adopted, the specific leakage rate can be set according to the provisions of the leakage rate of the mechanical seal in the “GB / T 33509-2017 General Specification for Mechanical Seals”;

[0040] The maximum opening force and the minimum opening force after reaching the disengagement rotating speed are calculated according to formula (8) and formula (9):

[0041] F w-o,min = f2 (n = n w , h = h w ) (8)

[0042] F w-o,max = f2 (n = n c , h = h c) (9)

[0043] where F w-o,min is the minimum opening force in the non-contact phase, F w-o,max is the maximum opening force in the non-contact phase;

[0044] By comparing the minimum opening force and the maximum opening force in the contact phase and the non-contact phase, as shown in equations (10) and (11), the minimum and maximum values of the opening force in the whole process can be obtained;

[0045] F o,min = max(F c-o,min , F w-o,min ) (10)

[0046] F o,max = min(F c-o,max , F w-o,max ) (11)

[0047] Equation (10) determines the minimum opening force to ensure that the sealing device can still guarantee sealing when the minimum closing force is applied, and equation (11) sets the maximum opening force to avoid excessive closing force causing the sealing end face to be unable to separate.

[0048] Specifically, in step S5, the DSPHMS should satisfy the axial force balance condition in the whole process, i.e., F c ≡ F o , and p sp,min and p sp,max are inversely solved according to equations (12) and (13), as follows:

[0049] f1(p sp,min ) = F o,min (12)

[0050] f1(p sp,max ) = F o,max (13)

[0051] In the case where the steady-state running speed of the dynamic pressure mechanical seal is known, the design range of the spring specific pressure can be determined by using equations (12) and (13).

[0052] The application determines the balance relationship of the closing force and the opening force according to the stable operation principle of the dynamic pressure mechanical seal; the closing force is taken as a function of the spring specific pressure; the opening force is calculated in two stages, i.e., the contact stage and the non-contact stage, by using the state of opening to the stable operation of the dynamic pressure mechanical seal; the opening force in the contact stage is composed of the liquid film bearing force and the micro convex body contact force; the opening force in the non-contact stage is composed of the liquid film dynamic pressure between the sealing rings; the maximum value of the opening force in the whole cycle operation of the dynamic pressure mechanical seal is obtained; and the optimal spring specific pressure can be inversely solved by using the axial force balance condition met in the whole process operation. The application can efficiently and accurately realize the design of the spring specific pressure of the dynamic pressure mechanical seal, and get rid of the problem that the design of the spring specific pressure of the mechanical seal currently depends on the artificial experience. BRIEF DESCRIPTION OF DRAWINGS

[0053] Figure 1 It is a structural schematic diagram of the bellows type pressure expanding self-pumping dynamic pressure mechanical seal.

[0054] Figure 2 It is a three-dimensional structural diagram of the dynamic ring.

[0055] Figure 3 It is a planar structural diagram of the dynamic ring.

[0056] Figure 4 It is a structural schematic diagram of the static ring.

[0057] Figure 5 It is a flow chart of the design and calculation method of the spring specific pressure of the bellows type pressure expanding self-pumping dynamic pressure mechanical seal.

[0058] Figure 6 It is a diagram of the opening force with the liquid film thickness and the rotational speed when the rotational speed is 0 c and the closing force is 3640 N.

[0059] Figure 7 It is a diagram of the opening force with the liquid film thickness and the rotational speed when the rotational speed is n c ≤n≤n w and the closing force is 3640 N. DETAILED DESCRIPTION

[0060] The embodiments of the application will be described in detail below with reference to the accompanying drawings. Firstly, the structure of the bellows type pressure expanding self-pumping dynamic pressure mechanical seal to which the application is directed will be described.

[0061] Please refer to Figure 1The bellows type expansion self-pumping dynamic pressure mechanical seal comprises a main shaft 1 and a shaft sleeve 10 fixedly sleeved on the main shaft 1, and a bellows seat 8, a bellows 7, a dynamic ring seat 6, a dynamic ring 5, a static ring 4 and an end cover 2 are sequentially sleeved on the shaft sleeve 10 from inside to outside, wherein a set screw is screwed in a threaded hole 9 of the bellows seat 8 and tightly presses on the shaft sleeve 10, and the set screw is not shown in the drawings. The end cover 2 is tightly pressed on the static ring 4 through a sealing ring 3, and the static ring is pressed on the dynamic ring under the pushing of the end cover, and a sealing interface is formed between the dynamic ring and the static ring under the pushing of the bellows.

[0062] Please refer to Figure 2 and Figure 3 The dynamic ring 5 has a first sealing end face 31 facing the static ring 4, and the first sealing end face sequentially comprises a sealing dam 32, a spiral groove area 39 and an expansion ring groove 34 from inside to outside in the radial direction, ten spiral grooves 33 are formed in the spiral groove area 39, the spiral grooves are backward spiral grooves, and the ten spiral grooves 33 are uniformly and spacedly arranged around the central axis 100 of the main shaft, and a region between adjacent two spiral grooves 33 is formed as a sealing weir 36.

[0063] The expansion ring groove 34 is formed by being recessed in the axial direction from the outside of the radial direction of the first sealing end face 31, and the expansion ring groove 34 penetrates through the outer circumferential surface 35 of the dynamic ring outwardly, so that the expansion ring groove 34 has a circumferential side surface 344 around the rotating shaft and a first bottom surface 345 extending in the radial direction. Each spiral groove has a fluid outlet 334 penetrating through the circumferential side surface of the expansion ring groove outwardly, and the fluid outlet 334 is opposite to the rotating direction of the dynamic ring, Figure 3 The arrow 200 in the figure indicates the rotating direction of the dynamic ring.

[0064] Please refer to Figure 4 The static ring 4 has a second sealing end face 51 facing the dynamic ring, and a flow collecting ring groove 52 is arranged on the second sealing end face 51 of the static ring 4, the flow collecting ring groove 52 extends around the central axis 100 of the main shaft, a plurality of flow guide holes 56 are arranged in the ring body of the static ring 4, and Figure 4 One flow guide hole 56 is exemplarily shown in the figure. The inlet 54 of each flow guide hole 56 is located on the outer circumferential surface 55 of the static ring 4, the outlet 53 of each flow guide hole 56 is located in the flow collecting ring groove 52, and the flow guide hole 56 communicates the sealing cavity with the flow collecting ring groove 52. In the axial direction of the rotating shaft, the flow collecting ring groove 52 is partially located in the spiral groove area 39, so that the flow collecting ring groove 52 communicates the spiral grooves 33. In the embodiment, the flow collecting ring groove 52 is located on the radially inner side of the spiral grooves.

[0065] The gap between the second sealing end face and the expansion ring groove forms an expansion cavity which is annular and has a radial opening.

[0066] In the axial direction of the main shaft, the second sealing end face 51 is perpendicular to the area of the region of the diffuser cavity in a plane perpendicular to the main shaft.

[0067] Each spiral groove 33 has two circumferentially arranged inner sides, one of which is an inner convex side 332 protruding towards the inside of the spiral groove, and the other is an inner concave side 331 recessed towards the outside of the spiral groove.

[0068] In this application, the first sealing end face and the second sealing end face are collectively referred to as the sealing end face; the dynamic ring and the static ring are collectively referred to as the sealing ring, and the inner diameter and the outer diameter of both the dynamic ring and the static ring are the same.

[0069] Please refer to Figure 5 , the following describes the design and calculation method of the specific pressure of the zero-leakage sealing spring of the bellows type diffuser self-pumping dynamic pressure mechanical seal, which specifically includes the following steps:

[0070] S1, obtain the structure parameters and working condition parameters of the DSPHMS, and the specific structure parameters and working condition parameters are shown in Table 1.

[0071] Table 1: Process parameters and operating condition parameters of the spiral groove mechanical seal end face

[0072]

[0073]

[0074] In Table 1, the radial slot length ratio is the ratio of the radial length of the diffuser ring slot to the radial length of the spiral groove, wherein the radial length of the diffuser ring slot refers to the difference between the inner and outer diameters of the diffuser ring slot, and the radial length of the spiral groove refers to the difference between the inner and outer diameters of the spiral groove. The slot width ratio is the ratio of the total arc length of the fluid outlet 334 of all spiral grooves to the circumference of the circumferential side 344 of the diffuser ring slot 34.

[0075] S2, use the closing force formula to calculate the full process closing force parameters of the diffuser self-pumping mechanical seal.

[0076] First, the equivalent radius of the bellows is calculated using the following formula:

[0077]

[0078] Where r e is the equivalent radius of the bellows, r bk is the outer diameter of the bellows, and r bi is the inner diameter of the bellows. The relevant data in Table 1 is brought into formula (1).

[0079]

[0080] Where F cF is the closing force c-fluid F is the closing force provided by the sealing medium pressure c-bellow p is the closing force provided by the bellows o r is the sealing medium pressure o r is the outer diameter of the sealing ring i p is the inner diameter of the sealing ring i p is the pressure at the inner diameter of the sealing ring sp p is the spring pressure provided by the bellows; that is, the closing force F c p is the spring pressure provided by the bellows sp F is simplified as: F c = f1(p sp ).

[0081] According to the calculation of F c = f1(p sp ) according to formula (1), we obtain:

[0082] F c = f1(p sp ) = 1023 + 4.015 x 10 -3 p sp

[0083] S3, during the process of starting the DSPHMS to the rated working speed n w , the opening force F o is a function of the speed n and the liquid film thickness, and the value range of p sp is converted into the maximum and minimum values of F o in the full cycle running stage, and F o in the full cycle running stage is calculated by using formula (2):

[0084]

[0085] wherein p sp,min is the minimum value of p sp in the full cycle running stage, p sp,max is the maximum value of p sp in the full cycle running stage; F o,min is the minimum value of F o in the full cycle running stage, and F o,max is the maximum value of F o in the full cycle running stage, and the full cycle running stage is the process of starting the DSPHMS to the rated working speed. The liquid film thickness is represented by h, and in this application, the liquid film thickness h refers to the thickness of the sealing medium between the first sealing end surface 31 and the second sealing end surface 51.

[0086] S4, the process of starting the DSPHMS from static to running to the rated working speed is divided into two stages, when 0≤nc At this time, the micro asperities on the sealing end faces of both the dynamic ring and the static ring are in contact with each other, i.e., the micro asperities on the sealing end faces are in contact, and the opening force at this stage is borne by the liquid film bearing force F o-fluid and the micro asperity contact force F o-contact together constitute the opening force F c When n w ≤n≤n c , the micro asperities on the sealing ends of both the dynamic ring and the static ring are separated from each other, i.e., the micro asperities on the sealing end faces are separated, and the opening force of the sealing end face is borne by the sealing medium. Wherein, n represents the rotating speed, n c is the disengagement rotating speed, when n=n w , the micro asperities on the sealing end face are at the critical point of contact and separation; n c is the rated working rotating speed.

[0087] The specific description is as follows:

[0088] (1) When 0≤n<n c :

[0089] At this stage, when the specific pressure of the sealing end faces of both the dynamic ring and the static ring increases, the porosity of the sealing end face is reduced to below 0.312, the channels through the sealing end face disappear, and therefore there is no longer a channel that can cause fluid leakage. When the rotating speed n=0, in order to ensure that the DSPHMS can achieve effective sealing, a critical percolation threshold φ is introduced, and φ=0.312, which represents the porosity when the sealing end face achieves effective sealing. When the porosity reaches this critical percolation threshold, the sealing end face is in a critical state of leakage and no leakage.

[0090] According to the critical percolation threshold, the sealing micro asperity contact pressure is obtained, and then the micro asperity contact force F o-contact is obtained, the liquid film bearing force F o-fluid is obtained by using formula (3), and the sum of F o-contact and F o-fluid constitutes the opening force, i.e., F o,min .

[0091]

[0092] Wherein, p f is the liquid film pressure between the sealing end faces of the static ring and the dynamic ring, p c is the micro asperity contact pressure between the sealing end faces of the static ring and the dynamic ring, r is the polar radius, and θ is the polar angle.

[0093] To solve the opening force when the rotating speed n=0, the parameters of the sealing ring surface material are required, such as the Poisson's ratio of the sealing ring, the elastic modulus of the sealing ring, the maximum surface roughness of the sealing end face of the sealing ring, the characteristic dimension coefficient of the sealing ring, and the fractal dimension of the sealing ring. The specific parameters can be referred to Table 2.

[0094] Table 2 Material parameters of spiral groove mechanical seal end face

[0095]

[0096] To achieve that the sealing medium in the sealing cavity cannot leak through the gap between the dynamic ring and the static ring when the dynamic ring does not rotate, the porosity requirement between the dynamic ring and the static ring is required to be less than or equal to 0.312. The characteristic scale coefficient and the elastic modulus of the dynamic ring and the static ring are respectively compounded by using formula (4-1) and formula (4-2), and the compounded characteristic scale coefficient G = 5.802 x 10 -10 and the compounded elastic modulus E = 92.492 GPa.

[0097]

[0098] From the W-M function, the height h M of the maximum micro-convex body on the sealing end face of the dynamic ring and the static ring is h M = 0.746 (Ry d + Ry j ), and the initial porosity φ0 is obtained according to the following formula:

[0099]

[0100] In the formula, D represents the fractal dimension, and the fractal dimension D j of the static ring is calculated; a Lm is the base area of the maximum micro-convex body, that is, a Lm = πl 2 / 4; and l represents the base diameter of the maximum micro-convex body, that is,

[0101] The porosity φ1 of the sealing end face of the dynamic ring and the static ring after deformation is φ1 = (h M φ0- δ) / (h M - δ), in which: φ0 is the initial porosity of the sealing end face; φ1 is the porosity of the sealing end face of the dynamic ring and the static ring after deformation; h M is the height of the maximum micro-convex body; and δ is the compression amount of the sealing end face after being loaded.

[0102] The relationship between the actual contact area a L of the deformed dynamic ring and the static ring and δ is:

[0103] The value of the actual contact area a L after deformation can be solved.

[0104] Based on the actual contact area a L of the deformed dynamic ring and the static ring, the critical elastic deformation contact area a ec, plastic deformation contact area a pc The relationship between the real contact area of the sealing end face and the total contact load borne by the micro asperities is discussed from the following three aspects.

[0105] When a L <a ec , all the contact points on the sealing end face are in the elastic deformation state, and the load borne by them is the elastic contact load, whose formula is as follows:

[0106]

[0107]

[0108] Where F contact is the contact load; D s is the three-dimensional fractal dimension of the static ring end face profile, D s =D j +1; n(a) is the contact area distribution density function of the three-dimensional micro asperities, and a is the area.

[0109] When a ec <a L <a pc , the micro asperities in the elastic deformation and plastic deformation coexist, i.e. the elastic-plastic deformation occurs, and the relationship between the micro asperity contact area and the contact pressure in this stage is no longer the single corresponding relationship of the elastic deformation or complete plastic deformation stage, and the specific calculation formula is as follows:

[0110]

[0111]

[0112] Where e is the natural constant.

[0113] For a L >a pc , the micro asperities on the contact surface are in the plastic deformation stage, and the contact load F contact borne by them is also equal to the sum of the corresponding elastic load, elastic-plastic load and plastic contact load, i.e.

[0114]

[0115] The micro asperity contact pressure p c between the sealing end faces of the sealing ring at the rotating speed n=0 can be calculated by the following formula:

[0116]

[0117] ​where A0 is the sum of the cross-sectional area of the largest asperity and all other small asperities, which is calculated by the formula The force of the asperity contact is obtained by the asperity contact pressure p c and the nominal area A n The force F M-contact is obtained by the formula c = p n · A M-contact , where F o-contact is the maximum contact load of the dynamic ring and the static ring when they are relatively stationary, i.e., the maximum contact load when the dynamic ring is stationary.

[0118] Without considering the complexity of the change of the contact force of the sealing ring during opening, the asperity contact force is calculated by the formula

[0119] F o-contact = F M-contact -k·h

[0120] where k is the rate of decrease of F o-contact with the decrease of the sealing gap height, h c is the liquid film thickness when the rotational speed is the release rotational speed n c , which is referred to as the release thickness; and h represents the liquid film thickness.

[0121] When 0 < n < n c , the opening force at this stage is composed of the liquid film bearing force F o-fluid and the asperity contact force F o-contact . The liquid film bearing force F o-fluid can also be obtained by the analytical method of the steady-state performance of the spiral groove mechanical seal in the book “Analytical Method of Steady-State Performance of Spiral Groove Mechanical Seal” by Song Pengyun (first edition in April 2023), and the calculation process is as follows:

[0122] After the sealing medium of the pressure-increasing self-pumping mechanical seal enters the root of the spiral groove from the drainage hole, it is pumped out into the sealing cavity through the spiral groove and the pressure-increasing ring groove. In this process, the pressure of the sealing medium in the spiral groove changes with the change of the radius from the root radius of the spiral groove to the outer radius of the spiral groove, and the specific relationship is as follows:

[0123]

[0124] where p1 is the pressure of the sealing medium in the spiral groove; μ is the dynamic viscosity of the sealing medium; ω is the angular velocity of the dynamic ring; h is the liquid film thickness; m s is the mass flow rate of the sealing medium pumped out of the spiral groove area to the pressure-increasing ring groove; h i is the liquid film thickness in the spiral groove area, h i = h + h g ; h gγ is the depth of the spiral groove; g1 and g2 are the spiral groove coefficients, and γ1 is the ratio of the groove width to the platform width, expressed as:

[0125]

[0126]

[0127] Among them, H i H is the ratio of the liquid film thickness to the liquid film thickness in the spiral groove region. i =h / (h+h) g ); α is the helix angle of the helical groove.

[0128] The relationship between the pressure of the sealing medium inside the diffuser ring groove and the radius varies from the outer diameter of the spiral groove to the outer diameter of the sealing ring is as follows:

[0129]

[0130] Where p2 is the pressure of the sealing medium inside the diffuser ring groove; h k The depth of the diffuser ring groove.

[0131] The relationship between the sealing medium pressure within the sealed dam area and the radius from the inner diameter of the sealing ring to the root diameter of the spiral groove is as follows:

[0132]

[0133] Where p3 is the pressure of the sealing medium within the sealed dam area.

[0134] Given the pressure in each region between the sealing end faces, the liquid film opening force is calculated according to the fluid opening force calculation formula in formula (3).

[0135]

[0136] The liquid film bearing capacity F o-fluid Contact force F with micro-convexity o-contact The resulting opening force is combined to draw F. c When the opening force is 3640N, the changes in opening force with liquid film thickness and rotational speed are as follows: Figure 6 As shown.

[0137] Depend on Figure 6 It can be seen that the closing force provided by the spring pressure of the bellows must be greater than the opening force when the rotation speed n = 0, so as to ensure that the sealing device can effectively seal the sealing medium to achieve the sealing contact interface without leakage in the static state, that is, to prove formulas (4) and (5):

[0138] F c-o,min =f2(n=0,h=0) (4)

[0139] Where F c-o,minis the minimum opening force in the contact stage.

[0140] F c-o,max is the maximum opening force in the contact stage. c is the minimum opening force in the contact stage. c (5)

[0141] F c-o,max is the maximum opening force in the contact stage.

[0142] When the rotational speed n = 0, the minimum opening force F c-o,min = 3095.587 N in the contact stage, only if the closing force F c is greater than the minimum opening force F c-o,min in the contact stage, it can be ensured that the sealing contact interface does not occur in the percolation in the static state;

[0143] (2) when n c ≤ n ≤ n w

[0144] In this stage, the microconvexes of the sealing end surface are separated, and the opening force of the sealing end surface is borne by the sealing medium. In the process of accelerating the rotational speed from n c to n w , the liquid film thickness increases, and the opening force always remains equal to the closing force. Given that the surface roughness Ra d of the sealing end surface of the rotating ring is 0.06 μm, and the surface roughness Ra j of the sealing end surface of the static ring is 0.167 μm, the h c = 6.65 × 10 -7 m in this example can be obtained by formula (5).

[0145]

[0146] When the rotational speed reaches the steady-state working rotational speed n w , h = h w (the value can be obtained by force balance interpolation), but the size of h w directly affects the leakage rate Q i , and the value of h w needs to be determined by limiting Q i . According to the provisions of the national standard “GB / T 33509-2017 General Specification for Mechanical Seals”, when the sealing fluid is liquid, the sealing working pressure is 0-5 MPa, and the shaft outer diameter is 50-120 mm, the leakage of the seal should be less than 5.0 ml / h, and the h w = 8.94 × 10 -7 m in this example can be obtained by formula (6).

[0147] ​

[0148] The opening force F c ≤n≤n w and the closing force F c =3640N, the opening force with the film thickness and the rotational speed is shown as follows. Figure 7

[0149] According to Figure 7 The minimum and maximum values of the opening force F o in the full cycle running stage can be analyzed, which proves the formula (8) (9).

[0150] F w-o,min =f2(n=n w ,h=h w ) (8)

[0151] F w-o,max =f2(n=n c ,h=h c ) (9)

[0152] Where F w-o,min is the minimum opening force in the non-contact stage, and F w-o,max is the maximum opening force in the non-contact stage.

[0153] By comparing the maximum opening force and the minimum opening force in the contact stage and the non-contact stage, as formula (10) (11), the maximum and minimum values of the opening force in the whole process can be obtained.

[0154] F o,min =max(F c-o,min ,F w-o,min ) (10)

[0155] F o,max =min(F c-o,max ,F w-o,max ) (11)

[0156] Formula (10) determines the minimum opening force to ensure that the sealing device can still ensure sealing when the minimum closing force, and formula (11) sets the maximum opening force to avoid excessive closing force leading to the sealing end face unable to separate.

[0157] S5, in this example, the DSPHMS running the whole process should meet the axial force balance condition, that is, the opening force is equal to the closing force, F c ≡F o , the appropriate range of p sp,max is solved inversely, and the specific formula is shown in formula (8) (9).

[0158] f1(p sp,min )=F o,min (12) ​

[0159] f1(p sp,max )=F o,max (13)

[0160] The steady-state operating speed of the present example is 4000 r / min, and the range of closing force is (3638.810-3654.784) N. Through equations (12) and (13), the spring specific pressure range can be determined. In the case of a stable working speed of 4000 r / min, the range of spring specific pressure is (0.6515-0.6555) MPa. The spring specific pressure of the bellows is within this range, which can ensure that the sealing contact interface does not exceed the percolation in the static state, and can ensure that the sealing end face is normally separated, while the leakage rate can be controlled within the range of (2.0572-5.0) ml / h.

Claims

1. A method for calculating the spring pressure of a zero-leakage bellows-type expansion self-pumping dynamic pressure mechanical seal, characterized in that, Comprising the following steps: S1, obtaining the structure parameters and working condition parameters of the bellows type diffuser self-pumping fluid mechanical seal; S2, determine the closing force according to the structure parameters and working condition parameters, and take the closing force as a function of the spring specific pressure, specifically F c = f1(p sp ), F c is the closing force, p sp is the spring specific pressure provided by the bellows; S3. During the start-up process of the bellows-type diffuser-type self-pumping dynamic pressure mechanical seal to its rated operating speed, the opening force is a function of the rotational speed and the liquid film thickness, while the closing force is treated as a constant. Here, the rotational speed is represented by n, the liquid film thickness by h, the bellows-type diffuser-type self-pumping dynamic pressure mechanical seal by DSPHMS, and the opening force by F. o express; The opening force is a function of the rotational speed and the liquid film thickness, and the value range of p sp is converted to the value range of F o The maximum and minimum values in the full cycle running phase are calculated by using formula (2) o The maximum and minimum values in the full cycle running phase are calculated by using formula (2) （2） where F o,min is F o at the minimum of the full cycle operating phase, F o,max is F o at the maximum of the full cycle operating phase; The full cycle operation stage is the process from the start of the DSPHMS to the rated working speed; During the stable operation phase throughout the entire cycle, p sp,min For p sp The minimum value of p sp,max For p sp The maximum value; S4, the process of starting up the DSPHMS from static to rated working speed is divided into two stages; when 0 ≤ n < n c , the micro asperities of the sealing surface are in contact, the opening force is composed of the liquid film bearing force and the micro asperities contact force; when n c ≤ n ≤ n w , the micro asperities of the sealing surface are separated, the opening force of the sealing surface is borne by the sealing medium; wherein n c is the separation speed, when n = n c , the micro asperities of the sealing surface are at the critical point of contact and separation; n w is the rated working speed; The opening force of the sealing end face is composed of the liquid film bearing force F o-fluid and the micro-convex body contact force F o-contact in the contact phase; in the non-contact phase, the opening force of the sealing end face is composed of the liquid film bearing force F o-fluid , at this time, the micro-convex body contact force F o-contact = 0 N; in the operation process of the DSPHMS, the specific calculation of the opening force is shown in formula (3): （3） where p c is the asperity contact pressure between the sealing faces, p f is the liquid film pressure between the sealing faces, r is the polar radius, and θ is the polar angle. The above contact stage refers to the stage when the micro convex bodies of the sealing end surface are in contact, and the non-contact stage refers to the stage when the micro convex bodies of the sealing end surface are not in contact; (1) when 0 < n < n c max and n < n c max: At this time, the micro asperities of the sealing end face are in contact, and the opening force of this stage is borne by the liquid film force F o-fluid and the micro asperity contact force F o-contact together constitute, and are specifically calculated by formula (3). As the rotating speed increases, the micro asperities in mutual contact between the sealing end faces gradually separate, and during this process, F o-contact gradually decreases to 0. When n = 0, to ensure that the DSPHMS realizes effective sealing, the micro-convex contact pressure p between the sealing end faces is calculated according to the critical percolation threshold c Then F is calculated o-contact The liquid film pressure p between the sealing end faces is calculated by using the analytical method for steady-state performance of the spiral groove mechanical seal f The liquid film bearing force F is calculated according to formula (3) o-fluid At this time, the sum of F o-contact and F o-fluid is the opening force in the contact stage, and F c-o,min and F c-o,max are determined by formula (4) and formula (5) respectively: （4） where F c-o,min is the minimum opening force in the contact phase; （5） where F c-o,max is the maximum opening force in the contact phase, n c is the breakaway rotational speed, h c is the breakaway film thickness; At the same time, it can be determined that when n = 0 and F c is greater than F o,min , the minimum porosity is less than the critical percolation threshold, that is, the sealing contact interface is not percolated in the static state. (2) when n c ≤ n ≤ n w : In this stage, the micro convexes of the sealing end face are not in contact, and the opening force is completely borne by the sealing medium; when the rotating speed is from the disengaging rotating speed n c to the rated working rotating speed n w , the liquid film thickness increases, the opening force decreases and is always equal to the closing force; when the rotating speed n = n c , h = h c , h c is calculated by formula (6); when the rotating speed reaches the rated working rotating speed n w , h = h w , and the size of h w is determined by the leakage rate. （6） where h c is the liquid film thickness at the breakaway speed n c , referred to as the breakaway thickness, h w is the liquid film thickness at the rated speed, Ra d , and Ra j are the surface roughnesses of the sealing end faces of the rotating ring and the stationary ring, respectively; the liquid film thickness h w at the rated speed is obtained using equation (7), and the leakage rate is represented by Q i : （7） where r i is the inner diameter of the seal ring; μ is the dynamic viscosity of the sealing medium; is the fluid pressure distribution between the sealing faces of the dynamic and static rings, r is the polar radius; θ is the polar angle; the leakage rate is a set value; According to formula (8) and formula (9), the maximum opening force and the minimum opening force after reaching the disengagement speed are calculated: （8） （9） Fmin = F0- F0* (1 - e- (t / τ) ) where F0 w-o,min Fmax = F0+ F0* (1 - e- (t / τ) ) is the minimum opening force in the non-contact phase, F w-o,max Fmax = F0+ F0* (1 By comparing the minimum opening force and the maximum opening force of the contact stage and the non-contact stage, as formula (10) (11), the minimum value and the maximum value of the opening force of the whole process can be obtained; （10） （11） Formula (10) determines the minimum opening force to ensure that the sealing device can still ensure sealing at the minimum closing force, and formula (11) sets the maximum opening force to avoid excessive closing force leading to the sealing end surface unable to disengage; S5, the whole process of DSPHMS stable operation requires dynamic pressure mechanical seal in the static state can realize no leakage stable sealing, when the equipment reaches the rated speed, the sealing end face can be separated and sealed; the whole process of DSPHMS operation meets the axial force balance condition, that is, F c ≡ F o , through the inverse solution F c ≡ F o relationship, the spring specific pressure is obtained.

2. The design calculation method of claim 1, wherein, In step S1, the structural parameters and working condition parameters of the DSPHMS include the outer diameter of the sealing ring, the inner diameter of the sealing ring, the outer diameter of the helical groove, the root diameter of the helical groove, and the sealing medium pressure; the outer diameter of the sealing ring is represented by r o , the inner diameter of the sealing ring is represented by r i , the outer diameter of the helical groove is represented by r k , the root diameter of the helical groove is represented by r g , and the sealing medium pressure is represented by p o .

3. The design calculation method of claim 2, wherein, In step S2, the closing force is determined according to the structure parameters and working condition parameters of the DSPHMS, and the closing force of the whole process is calculated by formula (1): （1） where F c-fluid is the closing force provided by the sealing medium pressure, F c-bellow is the closing force provided by the bellows, r e is the equivalent radius of the bellows, p i is the pressure at the sealing ring inner diameter.

4. The design calculation method of claim 1, wherein, In step S5, the DSPHMS running the whole process should satisfy the axial force balance condition, i.e. F c ≡ F o , according to the inverse solution of formula (12) and formula (13), p sp,min and p sp,max are solved, specifically as follows: （12） （13） In the case of knowing the steady-state running speed of the dynamic pressure mechanical seal, the design range of the spring specific pressure can be determined by using formula (12) and formula (13).

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