Design and calculation method for spring specific pressure of corrugated pipe type diffusion type self-pumping dynamic pressure mechanical seal zero leakage

Abstract

The invention discloses a method for designing and calculating the specific pressure of a corrugated pipe type diffusion type self-pumping dynamic pressure mechanical seal zero-leakage spring, and the method comprises the steps: determining a balance relation between a closing force and an opening force according to a dynamic pressure mechanical seal stable operation principle; the closing force is used as a function changing along with the specific pressure of the spring; a dynamic pressure mechanical seal is opened to a stable operation state, and opening force calculation is divided into two stages, namely a contact stage and a non-contact stage; the opening force in the contact stage is composed of the liquid film bearing force and the micro-convex body contact force; the non-contact stage is formed by liquid film dynamic pressure between the sealing rings; calculating to obtain the maximum and minimum value of the opening force when the dynamic pressure mechanical seal runs in the full cycle; and the optimal spring specific pressure can be inversely solved by using the axial force balance condition met by the whole process operation. According to the method, the specific pressure of the dynamic pressure mechanical seal spring can be designed efficiently and accurately, and the problem that the specific pressure design of the mechanical seal spring depends on artificial experience at present is solved.

Description

Technical Field

[0001] The present invention belongs to the technical field of dynamic pressure mechanical seals, and relates to a design and calculation method for the sealing spring specific pressure of a bellows-type diffuser self-pumping dynamic pressure mechanical seal with zero leakage that integrates percolation theory and computational fluid dynamics, and more specifically to a design and calculation method for the spring specific pressure of a bellows-type diffuser self-pumping dynamic pressure mechanical seal when zero leakage is achieved. Background Art

[0002] The pressure-expanding self-pumping mechanical seal is an axial end face sealing device that relies on the elastic element to pre-tighten the static and dynamic ring end face sealing pair and relies on the formation of a dynamic pressure fluid film between the end faces to block the leakage channel to achieve sealing. It is mainly composed of a dynamic ring with a spiral groove, a static ring with a drainage hole, 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 groove on the end face of the dynamic ring to form a dynamic pressure fluid film with the static ring installed on the end cover, achieving long-term operation and "zero leakage". Mechanical seals are widely used in industries such as petrochemicals, oceans, shipbuilding, and aerospace industries to prevent leakage of fluid media in the sealing cavity.

[0003] At present, the selection of spring pressure ratio of non-contact mechanical seal elastic elements is mainly based on the experience of technicians. Although it is a fast and effective method in many cases, it cannot take into account all working conditions and cannot achieve the optimal performance of the system, which may cause seal 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 diffusion pressure self-pumping dynamic pressure mechanical seal with zero leakage is needed, which can be applied in the design of non-contact mechanical seals to make the sealing device more stable and reliable during operation. Summary of the invention

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

[0006] S1. Obtaining the structural parameters and operating parameters of the bellows-type expansion pressure self-pumping fluid mechanical seal;

[0007] S2. Determine the closing force according to the structural parameters and the working condition parameters, and take the closing force as a function of the spring specific pressure;

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

[0009] S4, the process of DSPHMS from static to running to rated working speed is divided into two stages; when 0≤n <n c When n is , the micro-convex body of the sealing end face is in contact, and the opening force is composed of the liquid film bearing force and the micro-convex body contact force; when n is c ≤n≤n w At this stage, the microconvex body of the sealing end face separates, and the opening force of the sealing end face is borne by the sealing medium; where n c To disengage the speed, when n = n c When n, the microconvex body of the sealing end face is at the critical point of contact and separation; w is the rated operating speed;

[0010] The stable operation of DSPHMS requires that the dynamic pressure mechanical seal can achieve stable sealing without leakage when it is stationary, and can achieve the separation and sealing of the sealing end face when the equipment reaches the rated speed; the axial force balance condition is met during the operation of DSPHMS, that is, F c ≡F o , by inverse solving F c ≡F o The relationship gives the spring specific pressure.

[0011] Specifically, 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 spiral groove, the root diameter of the spiral groove and the pressure of the sealing medium; the outer diameter of the sealing ring is r o Indicates that the inner diameter of the sealing ring is r i Indicates that the outer diameter of the spiral groove is r k Indicates that the root diameter of the spiral groove is r g Indicates that the sealing medium pressure is p o express

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

[0013]

[0014] where F c-fluid Closing force provided by the sealing medium pressure, F c-bellow The closing force provided by the bellows, re is the equivalent radius of the bellows, p i is the pressure at the inner diameter of the sealing ring, p sp The spring specific pressure provided for the bellows;

[0015] The closing force is a function of the spring pressure ratio, and equation (1) is simplified to: F c =f1(p sp ).

[0016] Specifically, in step S3, when the DSPHMS is started to the rated operating speed, the opening force is a function of the speed and the thickness of the liquid film. sp The value range of F is converted into o In the full cycle operation stage, the maximum value problem is calculated using formula (2) o Maximum and minimum values ​​during the full cycle operation phase:

[0017]

[0018] Among them, F o,min F o The minimum value during the full cycle operation phase, F o,max F o The maximum value during the full cycle operation stage;

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

[0020] In the stable operation stage of the whole cycle, p sp,min For p sp The minimum value of p sp,max For p sp The maximum value of .

[0021] Specifically, in step S4:

[0022] In the contact stage, the opening force of the sealing end face is determined by the liquid film bearing force F o-fluid and the asperity contact force F o-contact In the non-contact stage, the opening force of the sealing end face is composed of the liquid film bearing force F o-fluid At this time, the contact force F o-contact =0N; During the operation of DSPHMS, the specific calculation of the opening force is shown in formula (3):

[0023]

[0024] Among them, p c is the contact pressure of the micro-convex body between the sealing end faces, p f is the liquid film pressure between the sealing end faces, r is the polar diameter, and θ is the polar angle;

[0025] The contact stage refers to the stage when the micro-convexities on the sealing end faces are in contact, and the non-contact stage refers to the stage when the micro-convexities on the sealing end faces are not in contact with each other;

[0026] (1) When 0≤n <n c hour:

[0027] At this time, the microconvex body of the sealing end face is in contact, and the opening force at this stage is determined by the liquid film bearing force F o-fluid and the asperity contact force F o-contact Together, it is specifically calculated by formula (3). As the speed increases, the micro-convex bodies that contact each other between the sealing end faces gradually separate. In this process, F o-contact Gradually decrease to 0;

[0028] When n = 0, in order to ensure that DSPHMS achieves effective sealing, the contact pressure p of the micro-convex body between the sealing end faces is calculated according to the critical percolation threshold. c , then find F o-contact The liquid film pressure p between the sealing end faces is obtained by using the steady-state performance analytical method of spiral groove mechanical seals f According to formula (3), the liquid film bearing capacity F is obtained o-fluid , at this time F o-contact With F o-fluid The sum of the two is the opening force in the contact stage. At the same time, F c-o,min and F c-o,max Determined by formula (4) and formula (5) respectively:

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

[0030] where F c-o,min is the minimum opening force during the contact phase.

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

[0032] where F c-o,max is the maximum opening force in the contact phase, n c is the disengagement speed, h c To release the film thickness;

[0033] At the same time, it can be determined that when n = 0 and the closing force F c Greater than the minimum opening force F in the contact phase c-o,min When , its minimum porosity is less than the critical percolation threshold, that is, the sealed contact interface does not percolate under static conditions;

[0034] (2) When n c ≤n≤nw hour:

[0035] In this stage, there is no contact between the micro-convex body of the sealing end face, and the opening force is completely borne by the sealing medium; when the speed changes from the disengagement speed n c Accelerate to rated operating speed n w During the process, the thickness of the liquid film increases, the opening force decreases and always remains equal to the closing force; when the speed n=n c When h=h c , and h can be obtained by equation (6) c ; When the speed reaches the rated working speed n w When h=h w , use the leakage rate to determine h w size;

[0036]

[0037] where h c The speed is the disengagement speed n c The thickness of the liquid film at this time is referred to as the detachment thickness, h w is the thickness of the liquid film at rated speed, Ra d With Ra j are the surface roughness of the sealing end faces of the dynamic ring and the static ring respectively; the liquid film thickness h at the rated speed is obtained by using formula (7) w , the leakage rate is Q i express:

[0038]

[0039] Among them, 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 dynamic ring and the static ring, r is the polar diameter; θ is the polar angle; the leakage rate is the set value; the leakage rate can be set according to different requirements, or according to the corresponding national standards, industry standards or enterprise standards. When the national standard is adopted, the specific leakage rate can be set according to the provisions on mechanical seal leakage rate in "GB / T33509-2017 General Specification for Mechanical Seals";

[0040] According to equations (8) and (9), the maximum opening force and the minimum opening force after reaching the disengagement speed are calculated:

[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 stage, F w-o,max is the maximum opening force in the non-contact stage;

[0044] By comparing the minimum opening force and maximum opening force in the contact stage and the non-contact stage, as shown in formula (10) (11), the minimum and maximum opening force of 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] Formula (10) determines the minimum opening force to ensure that the sealing device can still ensure sealing at the minimum closing force, while formula (11) sets the maximum opening force to avoid excessive closing force causing the sealing end face to be unable to disengage.

[0048] Specifically, in step S5, the DSPHMS should satisfy the axial force balance condition during the entire operation process, that is, F c ≡F o , according to equation (12) and equation (13), we can solve p sp,min and p sp,max , as follows:

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

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

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

[0052] This application determines the balance relationship between closing force and opening force based on the stable operation principle of dynamic pressure mechanical seal; makes the closing force a function that changes with the spring pressure ratio; uses the dynamic pressure mechanical seal to open to a stable operation state, and divides the opening force calculation into two stages: contact stage and non-contact stage; the opening force in the contact stage is composed of the liquid film bearing capacity and the micro-convex contact force; the non-contact stage is composed of the liquid film dynamic pressure between the sealing rings; calculates and obtains the maximum value of the opening force when the dynamic pressure mechanical seal is running in the full cycle; and uses the axial force balance condition satisfied by the whole process operation to reversely solve the optimal spring pressure ratio. The present invention can efficiently and accurately realize the design of the dynamic pressure mechanical seal spring pressure ratio, and get rid of the problem that the current mechanical seal spring pressure ratio design relies on manual experience. BRIEF DESCRIPTION OF THE DRAWINGS

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

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

[0055] Figure 3 This is the plan structure diagram of the dynamic ring.

[0056] Figure 4 This is a schematic diagram of the structure of the static ring.

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

[0058] Figure 6 The speed is 0 <n<n c When the closing force is 3640N, the opening force changes with the liquid film thickness and rotation speed.

[0059] Figure 7 is the speed n c ≤n≤n w When the closing force is 3640N, the opening force changes with the liquid film thickness and rotation speed. DETAILED DESCRIPTION

[0060] The embodiments of the present invention are described in detail below in conjunction with the accompanying drawings. First, the structure of the bellows-type diffuser self-pumping dynamic pressure mechanical seal targeted by the present application is described below.

[0061] See also Figure 1The bellows-type expansion pressure self-pumping dynamic pressure mechanical seal comprises a main shaft 1 and a sleeve 10 fixedly sleeved on the main shaft, on which 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 sleeved from inside to outside in sequence, wherein a set screw is screwed into a threaded hole 9 of the bellows seat 8 and tightly pressed against the sleeve 10, and the set screw is not shown in the attached drawings. The end cover 2 is sealed against the static ring 4 through the sealing ring 3, and the static ring is pressed under the dynamic ring under the push of the end cover, and a sealing interface is formed between the dynamic ring and the static ring under the push of the bellows.

[0062] See also Figure 2 and Figure 3 The dynamic ring 5 has a first sealing end face 31 facing the stationary ring 4, and the first sealing end face is composed of a sealing dam 32, a spiral groove area 39 and a diffusion ring groove 34 from the inside to the outside in the radial direction. Ten spiral grooves 33 are opened in the spiral groove area 39, and the spiral grooves are backward-bent spiral grooves. The ten spiral grooves 33 are evenly spaced around the central axis 100 of the main shaft, and the area between two adjacent spiral grooves 33 forms a sealing weir 36.

[0063] The pressure-expanding annular groove 34 is formed by an axial depression on the radial outer side of the first sealing end face 31, and the pressure-expanding annular groove 34 penetrates the outer peripheral surface 35 of the dynamic ring outwardly, so that the pressure-expanding annular groove 34 has a circumferential side surface 344 surrounding the rotating shaft and a first annular bottom surface 345 extending in the radial direction. Each spiral groove has a fluid outlet 334 that penetrates the circumferential side surface of the pressure-expanding annular groove, and the direction of the fluid outlet 334 is opposite to the rotation direction of the dynamic ring. Figure 3 The arrow 200 in FIG. 2 indicates the rotation direction of the moving ring.

[0064] See also Figure 4 The stationary ring 4 has a second sealing end face 51 facing the moving ring. A collecting ring groove 52 is provided on the second sealing end face 51 of the stationary ring 4. The collecting ring groove 52 extends around the central axis 100 of the main shaft. A plurality of drainage holes 56 are provided in the ring body of the stationary ring 4. Figure 4 In the figure, a drainage hole 56 is shown as an example. The inlet 54 of each drainage hole 56 is located on the outer peripheral surface 55 of the stationary ring 4, and the outlet 53 of each drainage hole 56 is located in the collecting ring groove 52. The drainage hole 56 connects the sealing cavity with the collecting ring groove 52. Observing along the axial direction of the rotating shaft, the collecting ring groove 52 is partially located in the spiral groove area 39, so that the collecting ring groove 52 is connected to the spiral groove 33. In this embodiment, the collecting ring groove 52 is located at the radial inner side of the spiral groove.

[0065] The gap between the second sealing end surface and the diffuser ring groove forms an annular diffuser cavity with a radial opening.

[0066] Along the axial direction of the main axis, the area of ​​the second sealing end surface 51 facing the diffusion chamber is in a plane perpendicular to the main axis.

[0067] Each spiral groove 33 has two inner side surfaces arranged along the circumferential direction, one of which is an inner convex side surface 332 protruding toward the inside of the spiral groove, and the other inner side surface is an inner concave side surface 331 recessed toward the outside of the spiral groove.

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

[0069] See also Figure 5 The following is an explanation of the design and calculation method for the zero-leakage sealing spring specific pressure of the bellows-type expansion pressure self-pumping dynamic pressure mechanical seal. The design and calculation method specifically includes the following steps:

[0070] S1. Obtain the structural parameters and operating parameters of DSPHMS. The specific structural parameters and operating parameters are shown in Table 1.

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

[0072]

[0073]

[0074] In Table 1, the radial expansion groove length ratio is the ratio of the radial length of the pressure expansion ring groove to the radial length of the spiral groove, wherein the radial length of the pressure expansion ring groove refers to the difference between the inner and outer diameters of the pressure expansion ring groove, and the radial length of the spiral groove refers to the difference between the inner and outer diameters of the spiral groove. The groove platform width ratio is based on the circumference of the circumferential side surface 344 of the pressure expansion ring groove 34, and is the ratio of the sum of the arc lengths of the fluid outlets 334 of all the spiral grooves.

[0075] S2. Use the closing force formula to calculate the parameters of the full process closing force of the expansion pressure self-pumping mechanical seal.

[0076] First, use the following formula to calculate the equivalent radius of the bellows:

[0077]

[0078] Among them, r e is the equivalent radius of the bellows, r bk is the outer diameter of the bellows, r bi is the inner diameter of the bellows. Substitute the relevant data in Table 1 into formula (1).

[0079]

[0080] where F cis the closing force, F c-fluid Closing force provided by the sealing medium pressure, F c-bellow The closing force provided by the bellows, p o is the sealing medium pressure, r o is the outer diameter of the sealing ring, r i is the inner diameter of the sealing ring, p i is the pressure at the inner diameter of the sealing ring, p sp The spring specific pressure provided by the bellows; that is, the closing force F c is the spring specific pressure p provided by the bellows sp Function, Formula 1 is simplified to: F c =f1(p sp ).

[0081] According to formula (1) c =f1(p sp ) to calculate, we get:

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

[0083] S3, DSPHMS starts to rated working speed n w During the process, the force F o is a function of the rotation speed n and the thickness of the liquid film. sp The value range of F is converted into o In the full cycle operation stage, the maximum value problem is calculated using formula (2) o Maximum and minimum values ​​during the full cycle operation phase:

[0084]

[0085] Among them, p sp,min For p sp The minimum value during the full cycle operation phase, p sp,max For p sp The maximum value during the full cycle operation stage; F o,min F o The minimum value during the full cycle operation phase, F o,max F o The maximum value in the full cycle operation stage, the full cycle operation stage is the process of DSPHMS starting to rated operating speed. The liquid film thickness is represented by h. In this application, the liquid film thickness h refers to the thickness of the sealing medium between the first sealing end face 31 and the second sealing end face 51.

[0086] S4. The process of DSPHMS from static to running to rated working speed is divided into two stages. When 0≤n <nc At this time, the micro-convex bodies on the sealing end faces of the dynamic ring and the static ring are in contact with each other, that is, the micro-convex bodies on the sealing end faces are in contact. The opening force at this stage is determined by the liquid film bearing force F o-fluid and the asperity contact force F o-contact Together. When n c ≤n≤n w When the rotating ring and the stationary ring are rotated, the micro-convex bodies on the sealing ends of the moving ring and the stationary ring are separated from each other, that is, the micro-convex bodies on the sealing end faces are separated, and the opening force of the sealing end faces is borne by the sealing medium. c To disengage the speed, when n = n c When n, the microconvex body of the sealing end face is at the critical point of contact and separation; w is the rated operating speed.

[0087] The specific instructions are as follows:

[0088] (1) When 0≤n <n c hour:

[0089] At this stage, when the specific pressure of the sealing end faces of the dynamic ring and the static ring increases, causing the porosity of the sealing end face to drop below 0.312, the channel that penetrates the sealing end face disappears, so there is no longer a channel that may cause fluid leakage. When the speed n = 0, in order to ensure that DSPHMS can achieve effective sealing, a critical percolation threshold φ is introduced, and φ = 0.312. This critical percolation threshold 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 between leakage and no leakage.

[0090] The contact pressure of the sealing micro-convex body is calculated according to the critical percolation threshold, and then the contact force F of the micro-convex body is calculated. o-contact , use formula (3) to calculate the liquid film bearing capacity F o-fluid , F o-contact With F o-fluid The sum of the opening force is F o,min .

[0091]

[0092] Among them, p f is the liquid film pressure between the sealing end faces of the static ring and the dynamic ring, p c is the contact pressure of the micro-convex body between the sealing end faces of the static ring and the dynamic ring, r is the polar diameter, and θ is the polar angle.

[0093] To solve the opening force when the speed n=0, the parameters of the sealing ring surface material are required, such as: 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 scale coefficient of the sealing ring and the fractal dimension of the sealing ring. The specific parameters can be found in Table 2.

[0094] Table 2 Spiral groove mechanical seal end face material parameters

[0095]

[0096] In order to ensure that the sealing medium in the sealing cavity cannot leak through the gap between the moving ring and the static ring when the moving ring does not rotate, the porosity between the moving ring and the static ring needs to be less than or equal to 0.312. The characteristic scale coefficient and elastic modulus of the moving and static rings and the moving ring are compounded using equations (4-1) and (4-2) to obtain the composite characteristic scale coefficient G = 5.802×10 -10 And the elastic modulus after composite is E=92.492GPa.

[0097]

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

[0099]

[0100] In the formula, D represents the fractal dimension, and the fractal dimension D of the static ring is used. j Calculate; a Lm is the bottom area of ​​the largest convex body, i.e. a Lm =πl 2 / 4; l represents the base diameter of the largest micro-convex body, that is

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

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

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

[0104] The actual contact area a after deformation of the dynamic ring and the static ring L , critical elastic deformation contact area a ec, plastic deformation contact area a pc The relationship between the actual contact area of ​​the sealing end face and the total contact load borne by the micro-convex body is discussed from the following three aspects.

[0105] when a L ec When , all contact points on the sealing end face are in an elastic deformation state, and the load they bear is the elastic contact load, which is expressed as follows:

[0106]

[0107]

[0108] Among them, 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-convex body, a is the area.

[0109] when a ec L pc When the elastic deformation and plastic deformation of the micro-convex body coexist, that is, elastic-plastic deformation occurs. At this stage, the relationship between the contact area and contact pressure of the micro-convex body is no longer a single corresponding relationship in the elastic deformation or complete plastic deformation stage. The specific calculation formula is as follows:

[0110]

[0111]

[0112] Among them, e is a natural constant.

[0113] For a L >a pc , the micro-convex body on the contact surface is in the plastic deformation stage, and the contact load F contact It is also equal to the sum of the corresponding elastic load, elastoplastic load and plastic contact load, that is:

[0114]

[0115] Calculate the contact pressure p of the micro-convex body between the sealing end faces when the sealing ring rotates at a speed of n = 0 c It can be calculated using the following formula:

[0116]

[0117] ​​​In the formula, A0 is the sum of the cross-sectional areas of the largest micro-convex body and all other small micro-convex bodies. In order to obtain the magnitude of the contact force of the micro-convex body, the contact pressure p of the micro-convex body can be obtained. c With nominal area A n Get F M-contact =p c ·A n , where F M-contact It is the maximum contact load when the moving ring and the static ring are relatively static, that is, the maximum contact load when the moving ring is static.

[0118] Without considering the complexity of the contact force change of the sealing ring during the opening process, the contact force of the micro-convex body is calculated using the following formula:

[0119] F o-contact =F M-contact -k·h

[0120] Where k is F o-contact As the sealing gap height decreases, h c The speed is the disengagement speed n c The thickness of the liquid film at this time is referred to as the detachment thickness; h represents the liquid film thickness.

[0121] When 0 <n<n c The opening force at this stage is determined by the liquid film bearing capacity F o-fluid and the asperity contact force F o-contact Together they constitute the liquid film bearing capacity F o-fluid It can also be obtained by using the analytical method for steady-state performance of spiral groove mechanical seals in "Analysis of Steady-State Performance of Spiral Groove Mechanical Seals" written by Song Pengyun (first edition in April 2023). The calculation process is as follows:

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

[0123]

[0124] Among them, p1 is the sealing medium pressure in the spiral groove; μ is the dynamic viscosity of the sealing medium; ω is the angular velocity of the moving ring; h is the thickness of the liquid film; m s h is the mass flow rate of the sealing medium pumped out of the diffuser ring groove from the spiral groove area; i is the thickness of the liquid film in the spiral groove area, h i =h+h g ;h gis the spiral groove depth; g1 and g2 are the spiral groove coefficients, γ1 is the platform groove width ratio, and its expression is:

[0125]

[0126]

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

[0128] The relationship between the pressure of the sealing medium in the expansion ring groove and the radius from the outer diameter of the spiral groove to the outer diameter of the sealing ring is:

[0129]

[0130] Wherein, p2 is the sealing medium pressure in the expansion ring groove; h k The depth of the diffuser ring groove.

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

[0132]

[0133] Among them, p3 is the sealing medium pressure in the sealing dam area.

[0134] The pressure in each area between the sealing end faces is known, and the liquid film opening force is calculated according to the calculation formula of the fluid opening force in formula (3).

[0135]

[0136] The liquid film bearing capacity F o-fluid and the asperity contact force F o-contact The opening force formed is combined to draw F c =3640N, the opening force changes with the liquid film thickness and rotation speed as follows Figure 6 shown.

[0137] Depend on Figure 6 It can be seen that the closing force provided by the spring specific pressure provided by the bellows must be greater than the opening force when the speed n = 0, so as to ensure that the sealing device can effectively seal the sealing medium to achieve no leakage at the sealing contact interface in a 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 during the contact phase.

[0140] F c-o,max =f2(n=n c ,h=h c ) (5)

[0141] where F c-o,max is the maximum opening force during the contact phase.

[0142] When the speed n = 0, the minimum opening force F in the contact stage c-o,min =3095.587N, only the closing force F c Greater than the minimum opening force F in the contact phase c-o,min , which can ensure that no percolation occurs at the sealing contact interface in a static state;

[0143] (2) When n c ≤n≤n w hour

[0144] In this stage, the microconvex body of the sealing end face separates, and the opening force of the sealing end face is borne by the sealing medium. c Speed ​​up to n w During the process, the thickness of the liquid film increases, the opening force decreases and always remains equal to the closing force. The surface roughness Ra of the sealing end face of the dynamic ring is known. d =0.06μm, the surface roughness Ra of the sealing end face of the stationary ring j =0.167μm, and through formula (5) we can get h in this example c =6.65×10 -7 m.

[0145]

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

[0147]

[0148] It can be drawn that c ≤n≤n w And the closing force F c =3640N, the opening force is affected by the thickness of the liquid film and the rotation speed as follows Figure 7 shown.

[0149] according to Figure 7 It is possible to analyze the opening force F at this stage o The minimum and maximum values ​​during the full cycle operation phase are used to prove formulas (8) and (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, 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 shown in equations (10) and (11), the maximum and minimum opening force of 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 at the minimum closing force, while formula (11) sets the maximum opening force to avoid excessive closing force causing the sealing end face to be unable to disengage.

[0157] S5. In this example, the DSPHMS should satisfy the axial force balance condition during the entire operation process, that is, the opening force is equal to the closing force, F c ≡F o , solve for p sp,max The appropriate range of 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 this example is 4000r / min, and the range of the closing force is (3638.810~3654.784)N. The spring pressure ratio range can be determined by equations (12) and (13). When the steady working speed is 4000r / min, the spring pressure ratio range is (0.6515~0.6555)MPa. The spring pressure ratio of the bellows within this range can ensure that the sealing contact interface does not percolate in the static state, and can ensure the normal disengagement of the sealing end face, and at the same time can control the leakage rate within the range of (2.0572~5.0)ml / h.

Claims

1. A design and calculation method for the spring specific pressure of a bellows-type expansion pressure self-pumping dynamic pressure mechanical seal with zero leakage, characterized in that: The steps include: S1. Obtaining the structural parameters and operating parameters of the bellows-type expansion pressure self-pumping fluid mechanical seal; S2. Determine the closing force according to the structural parameters and the working condition parameters, and use the closing force as a function of the spring specific pressure; S3. During the process of bellows-type pressure-expanding self-pumping dynamic pressure mechanical seal starting up to the rated working speed, the opening force is taken as a function of the speed and the liquid film thickness, and the closing force is taken as a constant; the speed is represented by n, the liquid film thickness is represented by h, the bellows-type pressure-expanding self-pumping dynamic pressure mechanical seal is represented by DSPHMS, and the opening force is represented by F o The closing force is expressed as F c ; S4, the process of DSPHMS from static to running to rated working speed is divided into two stages; when 0≤n <n c When n is , the micro-convex body of the sealing end face is in contact, and the opening force is composed of the liquid film bearing force and the micro-convex body contact force; when n is c ≤n≤n w At this stage, the microconvex body of the sealing end face separates, and the opening force of the sealing end face is borne by the sealing medium; where n c To disengage the speed, when n = n c When n, the microconvex body of the sealing end face is at the critical point of contact and separation; w is the rated operating speed; S5. The stable operation of DSPHMS requires that the dynamic pressure mechanical seal can achieve stable sealing without leakage when in a stationary state, and can achieve the separation and sealing of the sealing end face when the equipment reaches the rated speed; the DSPHMS operation process meets the axial force balance condition, that is, F c ≡F o , by inversely solving F c ≡F o The relationship gives the spring specific pressure.

2. The design calculation method according to claim 1, characterized in that: In step S1, the structural parameters and working condition parameters of 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 pressure of the sealing medium; the outer diameter of the sealing ring is r o Indicates that the inner diameter of the sealing ring is r i Indicates that the outer diameter of the spiral groove is r k Indicates that the root diameter of the spiral groove is r g Indicates that the sealing medium pressure is p o express.

3. The design calculation method according to claim 2, characterized in that: In step S2, the closing force is determined according to the structural parameters and working condition parameters of DSPHMS. The closing force of the whole process is calculated by formula (1): where F c-fluid Closing force provided by the sealing medium pressure, F c-bellow The closing force provided by the bellows, r e is the equivalent radius of the bellows, p i is the pressure at the inner diameter of the sealing ring, p sp The spring specific pressure provided for the bellows; The closing force is a function of the spring pressure ratio, and equation (1) is simplified to: F c =f1(p sp ).

4. The design calculation method according to claim 3, characterized in that: In step S3, when the DSPHMS is started to the rated operating speed, the opening force is a function of the speed and the thickness of the liquid film. sp The value range of F is converted into o In the full cycle operation stage, the maximum value problem is calculated using formula (2) o Maximum and minimum values ​​during the full cycle operation phase: Among them, F o,min F o The minimum value during the full cycle operation phase, F o,max F o The maximum value during the full cycle operation stage; The full cycle operation stage is the process of DSPHMS starting to the rated operating speed; In the stable operation stage of the whole cycle, p sp,min For p sp The minimum value of p sp,max For p sp The maximum value of .

5. The design calculation method according to claim 4, characterized in that: In step S4: In the contact stage, the opening force of the sealing end face is determined by the liquid film bearing force F o-fluid and the asperity contact force F o-contact In the non-contact stage, the opening force of the sealing end face is composed of the liquid film bearing force F o-fluid At this time, the contact force F o-contact =0N; During the operation of DSPHMS, the specific calculation of the opening force is shown in formula (3): Among them, p c is the contact pressure of the micro-convex body between the sealing end faces, p f is the liquid film pressure between the sealing end faces, r is the polar diameter, and θ is the polar angle; The contact stage refers to the stage when the micro-convexities on the sealing end faces are in contact, and the non-contact stage refers to the stage when the micro-convexities on the sealing end faces are not in contact with each other; (1) When 0≤n <n c hour: At this time, the microconvex body of the sealing end face is in contact, and the opening force at this stage is determined by the liquid film bearing force F o-fluid and the asperity contact force F o-contact Together, it is specifically calculated by formula (3). As the speed increases, the micro-convex bodies that contact each other between the sealing end faces gradually separate. In this process, F o-contact Gradually decrease to 0; When n = 0, in order to ensure that DSPHMS achieves effective sealing, the contact pressure p of the micro-convex body between the sealing end faces is calculated according to the critical percolation threshold. c , then find F o-contact The liquid film pressure p between the sealing end faces is obtained by using the steady-state performance analytical method of spiral groove mechanical seals f According to formula (3), the liquid film bearing capacity F is obtained o-fluid , at this time F o-contact With F o-fluid The sum of the two is the opening force in the contact stage. At the same time, F c-o,min and F c-o,max Determined by formula (4) and formula (5) respectively: F c-o,min =f2(n=0,h=0) (4) where F c-o,min is the minimum opening force in the contact stage; F c-o,max =f2(n=n c ,h=h c ) (5) where F c-o,max is the maximum opening force in the contact phase, n c is the disengagement speed, h c To release the film thickness; At the same time, it can be determined that when n = 0 and F c Greater than F o,min When , its minimum porosity is less than the critical percolation threshold, that is, the sealed contact interface does not percolate under static conditions; (2) When n c ≤n≤n w hour: In this stage, there is no contact between the micro-convex body of the sealing end face, and the opening force is completely borne by the sealing medium; when the speed changes from the disengagement speed n c Accelerate to rated operating speed n w During the process, the thickness of the liquid film increases, the opening force decreases and always remains equal to the closing force; when the speed n=n c When h = h c , h can be obtained by formula (6) c ; When the speed reaches the rated working speed n w When h = h w , use the leakage rate to determine h w size; where h c The speed is the disengagement speed n c The thickness of the liquid film at this time is referred to as the detachment thickness, h w is the thickness of the liquid film at rated speed, Ra d With Ra j are the surface roughness of the sealing end faces of the dynamic ring and the static ring respectively; the liquid film thickness h at the rated speed is obtained by using formula (7) w , the leakage rate is Q i express: Among them, 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 dynamic ring and the static ring, r is the polar diameter; θ is the polar angle; the leakage rate is the set value; According to equations (8) and (9), the maximum opening force and the minimum opening force after reaching the disengagement speed are calculated: F w-o,min =f2(n=n w ,h=h w ) (8) F w-o,max =f2(n=n c ,h=h c ) (9) where F w-o,min is the minimum opening force in the non-contact stage, F w-o,max is the maximum opening force in the non-contact stage; By comparing the minimum opening force and maximum opening force in the contact stage and the non-contact stage, as shown in formula (10) (11), the minimum and maximum opening force of the whole process can be obtained; F o,min =max(F c-o,min ,F w-o,min ) (10) F o,max =min(F c-o,max ,F w-o,max ) (11) Formula (10) determines the minimum opening force to ensure that the sealing device can still ensure sealing at the minimum closing force, while formula (11) sets the maximum opening force to avoid excessive closing force causing the sealing end face to be unable to disengage.

6. The design calculation method according to claim 5, characterized in that: In step S5, the DSPHMS should satisfy the axial force balance condition during the whole operation process, that is, F c ≡F o , according to equation (12) and equation (13), we can solve p sp,min and p sp,max , as follows: f1(p sp,min )=F o,min (12) f1(p sp,max )=F o,max (13) When the steady-state operating speed of the dynamic pressure mechanical seal is known, the design range of the spring specific pressure can be determined using equations (12) and (13).

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