Study of frictional wear properties of materials for mechanical seals

Wear of seal materials is a widespread problem in the aerospace, petrochemical, and electric power fields, leading not only to low efficiency of mechanical equipment, but also to increased energy consumption and reduced safety performance. Therefore, this paper establishes the SCA-wear model based on the tensile constraint algorithm to calculate and analyze the friction and wear performance of mechanical seal materials. The friction coefficients of different loads at 200°C and 10 min after the test time stabilize, and fluctuate in the range of 0.35 at 30N, 0.26 at 70N, and 0.48 at 90N. The frictional wear of the C/C composite mechanical seal material is at least 15.6%. The reason is that it is composed entirely of carbon. It has many advantages of carbon and graphite materials. Therefore, the frictional wear of the C/C composite seal material is low.


Introduction
Mechanical seals, i.e., face seals, are widely used in various fields because of their good sealing performance, reliable operation and low power consumption.However, the problem of seal material wear often causes serious safety problems [1][2].In recent years, the percentage of industrial accidents caused by the wear of sealing materials is shown in Table 1.The analysis shows that about 42% of the nearly 1200 accidents in 2021 were caused by seal material wear, resulting in unpredictable economic losses and environmental pollution [3][4].Therefore, how to suppress the wear of materials for seals and ensure production safety is an urgent problem in the machinery industry.Mechanical seal as a major boon to the rotary shaft sealing technology in manufacturing industry.Its emergence has solved the prevalent leakage problem in mechanical equipment [5][6].With its design-inspired superiority, mechanical seals have been widely used in many mechanical equipment such as liquids and gases [7][8].Mechanical seals enhance the safety of manufacturing, improve the efficiency of mechanical equipment, and play an irreplaceable role in industrial manufacturing.The role of mechanical seals is to prevent or reduce fluid leakage and to achieve end face sealing by applying pressure to the end face of the sealing material under the combined effect of the preload of the sealing material and the pressure of the medium [9][10].According to reliable data, roughly 75% of leaks in mechanical equipment are caused by frictional wear of sealing materials.This indicates that the frictional wear of seal materials is very critical in mechanical equipment [11][12].Therefore, it is necessary to choose the right material pair for the seal, paying attention to the wear resistance, lubricity and corrosion resistance.There are also specific requirements for the geometric parameters of the seal material such as area to width ratio, and other performance parameters such as spring load and pressure need to be carefully considered [13][14].In practice, mechanical seal rings are often used to prevent leakage of the seal media [15][16].According to Hamilton [17], the coefficient of friction is the primary basis for the selection of evaluation parameters for mechanical seal criteria.Key parameters such as reliability, life time, and safety are governed by it.In his study, Kim [18] pointed out that boundary friction, mixed friction, and fluid friction are the three frictional states that exist on the end faces of all paired pairs.He [19] showed through numerous studies that leakage determines the seal material life and is the most critical parameter.In industrial equipment, end seal leakage accounts for 80% to 90% of the total quantity [20].Han [21] states that frictional wear is one of the most important factors for seal life.Friction and wear are often present on the dynamic and static ring faces in a mixed friction condition.In the application of clear water media, the end face wear rate should be controlled below 0.2 μm/h to meet the standard.Zhang [22] pointed out in his article that the evaluation parameters for measuring the mechanical seal standard include several parts: leakage, PV value, frictional heat, wear, etc.These parameters are the key factors to ensure the reliability, life, and cost effectiveness of mechanical equipment, and are also the reference basis for practical use that needs to be given attention.Dynamic and static ring materials are the core of ensuring effective sealing [23][24].At the same time, it also greatly affects the service life of mechanical seals.With the rapid development of the industry, gradually appeared such as high-speed, high pressure, high temperature, low temperature, corrosive, flammable, explosive, solid particles and other demanding conditions, more demanding conditions to mechanical seal technology requires a higher standard [25][26].
Mechanical seal materials are selected with reference to several factors such as operating temperature, pressure, and media.Materials for mechanical seals require a combination of mechanical, frictional, and chemical properties to be considered and measured.Materials for mechanical seals should have characteristics such as wear resistance, self-lubrication, corrosion resistance, high strength, good thermal conductivity, low coefficient of friction, compatible friction subsets, and easy processing [27][28].Cemented carbide is the most widely used in mechanical seals because of its high hardness, high temperature resistance, wear resistance, low coefficient of friction, and easy pairing.Among them, cobalt-based, nickel-based, and RC carbide are the most widely used materials for mechanical seals.
Engineering ceramics are becoming one of the ideal materials for mechanical seals because of their high hardness, chemical stability, and wear resistance [29][30].Engineering ceramics usually include chromium corundum, which is resistant to drastic temperature changes, alumina, which has strong mechanical properties, silicon nitride, which is suitable for corrosive environments, boron carbide, which can adapt to severe wear conditions, and silicon carbide, which has a new generation of high specific strength, self-lubricating, and good group pair performance with good overall performance [31][32].Carbon graphite is one of the most widely used sealing materials in traditional dynamic and static rings.Corrosion resistance, good thermal conductivity, good self-lubrication, and high cost performance make it occupy most of the market.The carbon graphite used in mechanical seals is impregnated to improve strength and reduce leakage [33][34].The impregnation can be metal, inorganic, or organic resin, which are the three most traditional and commonly used additive materials.
There are also resin hot-pressed graphite as well as pyrolytic graphite.Carbon steel, high-silicon cast iron, chromium steel, and bronze sealing substrates are also frequently used in mechanical seals.Depending on the difference in performance of different materials, they are applied in different use environments to bring out their material performance characteristics [35].
With the increasing standard of mechanical seal requirements, the previous mechanical seal cannot cope with special working conditions mechanical seal such as high speed, high temperature, variable working conditions, corrosive media, solid particles and other media conditions.These conditions not only require more stringent material performance, but also raise the standard of tribological performance of the materials used for mechanical seals.Therefore, this paper establishes the SCAwear model based on the tensile constraint algorithm, and conducts an in-depth study on the tribological performance of mechanical seal materials.The main research contents include: the study of high temperature friction and wear performance of seal materials and the study of friction and wear performance of different types of mechanical seal materials.

Study of wear model based on tensile constraint algorithm
Since the degree of frictional wear of a material is closely related to the mechanical sealing method, different mechanical sealing methods correspond to different feature extraction paths.In order to construct a frictional wear model of the material, the dynamics of the mesh is decomposed.The vertices and connections in the material mesh are abstracted as a set of mass points and constraints, each mass has a mass , position and velocity .Then, each constraint equation is solved by several iterations to correct and update the position information of each mass, and finally, the combined forces on the material are used to calculate the frictional wear of the masses using the SCA-wear model.

Study of tensile constraint algorithm
First of all, we need to solve how to assign various properties to the material to simulate the morphological changes during the real motion.In the position dynamics, these properties need to establish various constraints to complete the projection of various constraints to limit the position information of the mass point, and in the process of multiple iterations to continuously correct the position information of each mass point, so that they meet the constraints.In this process, the linear momentum and angular momentum conservation laws are always satisfied.The stretch constraint algorithm (SCA) is shown in equation ( 1) and ( 2). (1) Where is the mass of the mass, is the change of position of the mass point in the constraint, and is the radius distance of the mass as it rotates.After the position is given, that is necessary to find satisfies the equation ( 3). ( The equation is expanded using Taylor's formula to obtain the approximate equation ( 4).(4) In order to satisfy the momentum conservation, it is necessary to restrict the position vector to the direction of this constraint gradient , so the scalar coefficient , satisfying equation ( 5) is introduced. ( Substitute equation ( 5) into equation ( 4) to solve for and then substitute into equation ( 5) to solve for the displacement vector as equation ( 6). ( From equation ( 6), the change of displacement of an independent mass point can be defined as equation (7).(7) Where the scale factor is defined as equation (8).
If the masses of the masses appear to be independent and different, then needs to be corrected based on the inverse of the masses, then equation ( 5) is replaced by equation ( 9). ( The resulting scale factor is updated to equation ( 10). ( The final mass position correction is shown in equation ( 11). ( There are various sealing materials made of different materials, and these materials have different degrees of tensile resistance.For example, there are sealing materials that stretch more easily, as well as sealing materials with higher tensile strength.To reflect the structural properties of materials that resist stretching, tensile constraints are defined in the position-based dynamics approach, which is a constraint model used to limit the distance between two mass points. The equation of the tensile constraint is defined as equation ( 12). ( is the initial length of each edge, the gradient of this constraint equation at the two masses is equation (13) and equation (14), respectively.
(13) (14) Where , so the scale factor , and finally the position corrections of the two masses can be obtained as equation (15) and equation ( 16), respectively. ( , , In the model calculation, the material has a rich bending fold form when it moves or interacts with the material.In this way, the bending effect of the material is simulated in different states, which is faster and more stable and controllable. The equation of the dihedral bending constraint is shown in equation ( 17). ( Where and are the unit normal vectors of the two triangular surfaces, and is the initial values of the angle between the two triangular surfaces.Since the bending constraint is only angle-dependent and independent of the edge length, the stretching constraint and the bending constraint are independent of each other.When solving for the displacement correction, the constraint is simplified to: (18) Where , and set , and thus obtaining the normal vectors n1 and n2. ( The gradient components of the constraint equation at each point are obtained from . ( Using the formula for the gradient of the normal vector at a point first requires calculating: ( ) ) ( ) = --q q q q Then the final position correction is equation ( 25). ( Analyzing the solution process, it is found that this bending constraint defined by the dihedral angle has two main problems: first, in the bending constraint of the dihedral angle can only apply bending constraints to the triangular surface with common edges, and it is difficult to apply constraints to each material mass, which has certain application limitations; second, the solution process of this bending constraint using the angle requires multiple derivations of the normal vector and the calculation of the inverse trigonometric function, which is far more complicated than the solution of the constraint based on the distance, and the high computational cost will certainly reduce the efficiency of the simulation.

SCA-wear model study
An optimized distance-based virtual triangle bending SCA-wear model study is proposed to address the problems of dihedral angle bending constraints in the material model, to eliminate the limitation that bending constraints can only be applied between adjacent triangular surfaces, and to reduce the computational complexity and effectively increase the solution speed while ensuring the material bending effect.
In the SCA-wear model study, virtual triangles need to be created based on the mesh topology of the material.Firstly, we select arbitrary mass point in the material mesh and put the mass point directly adjacent to each other into the set of adjacent masses, and then randomly select a mass point in the set as a vertex of the virtual triangle, and then find another mass point from the set of masses as another vertex of the virtual triangle, thus forming a virtual triangle.And make sure that the three points are in a straight line as much as possible, so that the angle they form is the maximum.Then, the bending limit is imposed by controlling the distance from the vertex to the center of gravity of the triangle to avoid the calculation of the inverse trigonometric function in the dihedral bending constraint.
To obtain the coordinates of the center of gravity of the triangle, the equation defining the bending constraint of the triangle is shown in the following equation ( 26). ( Where is the original distance from the mass p to the center of gravity c and is the bending coefficient.The bending coefficient determines the softness of the material, and the material properties are controlled by changing the parameter .However, for multiple iteration cycles of the solver, the effect of is nonlinear.After solver iterations, the residual error of a single bending constraint is , and in order to obtain a linear relationship, instead of directly using this parameter in the constraint projection correction, this paper redefines the bending constraint coefficient as in equation ( 27).Ðp pp p c ( ) Where is the number of iterations.Define , then the generalized inverse mass of this virtual triangle is as in equation ( 28).(28) From this, the position correction values of the three masses are obtained as equation ( 29), equation (30).( 29) (30) The optimized triangular bending constraint avoids the complex derivation of normal vectors and calculation of inverse trigonometric functions, and only a simple distance calculation is required, thus speeding up the solution of the bending constraint and simplifying the SCA-wear model study.

Research on high temperature friction and wear performance of seal materials
For mechanical seals, in general, the end face friction pairing form is often used in the combination of soft and hard, the purpose is to rely on the soft material's own easy to wear characteristics and selflubricating properties, to reduce friction and wear to improve the mechanical seal end face pairing material anti-wear wear characteristics.The commonly used soft material is impregnated reinforced graphite material, and the hard material is high strength carbide.At present, the research on the friction and wear performance of mechanical seal is mainly focused on the dynamic ring and static ring friction pair, and wear occurs not only in soft materials, but also in hard materials.The wear of hard materials mainly manifests itself in the form of surface pitting, cracks and scratches, etc.The wear of hard materials causes metal abrasives to enter the friction subsystem and embed in the surface of soft materials, which will accelerate the wear of the friction subsystem during the operation of the mechanical seal.Usually mechanical seal in the process of work, due to the existence of friction heat end temperature is relatively high, the choice of carbide as a dynamic ring material, due to the high hardness of the material, the use of room temperature is generally able to meet the requirements of use.But high temperature is different from room temperature, in order to explore the frictional wear performance of the seal material in the high temperature state, the use of high-strength stainless steel mechanical seal material, the temperature parameter is 200 ℃.And the relevant material parameters are substituted into dd model for calculation and analysis.The calculation results are shown in Figure 1.The results show that the friction coefficient of the material is higher at 200°C and within 3 min of the test time.30 N load, the friction coefficient of the material is up to 0.87.70 N load, the friction coefficient of the material is up to 0.76.90 N load, the friction coefficient of the material is up to 0.95.This means that the friction wear of the material is high.The coefficient of friction for the different loads stabilized after the test time reached 10 min.at 30 N the coefficient of friction fluctuated up and down in the range of 0.35, at 70 N the coefficient of friction fluctuated up and down in the range of 0.26, and at 90 N the coefficient of friction fluctuated up and down in the range of 0.48.The main reason is that, at the beginning of the break-in phase, the original roughness on the surface of the high-strength stainless steel mechanical seal material gradually decreases after break-in and becomes the surface roughness for normal use.The surface becomes flatter and smoother.As the test progresses, the real contact area on the surface of the material for high-strength stainless steel mechanical seal gradually increases.The wear rate slows down and gradually transitions to a normal and stable wear stage.The friction coefficient gradually tends to balance.The longitudinal comparison shows that the average friction coefficient increases more under 30N load, and the fluctuation range is from 0.50 to 0.60.Under 90N and 70N load, the average friction coefficient changes less, and the fluctuation range is from 0.3 to 0.40.

Study of frictional wear performance of different types of materials for mechanical seals
With the development of modern industry, mechanical operating conditions are becoming increasingly harsh, mechanical seals are widely used in petroleum, chemical and machinery manufacturing because of their reliable work, small leakage, long service life, low power consumption and other characteristics.Due to the increasing working medium of machine pumps and harsh working conditions, the performance of sealing materials becomes the primary factor in determining the reliability of seals.Therefore, in this section, three different materials for mechanical seals are selected to study their frictional wear performance.The temperature parameters are set to room temperature state, and the Cu/carbon graphite mechanical seal material parameters, C/C composite mechanical seal material parameters, and PTFE composite mechanical seal material parameters are substituted into dd model for calculation and analysis.The calculation results are shown in Figure 2. From Figure 2, it can be seen that the friction coefficient of the material is larger within the test time of 3 min.the friction wear degree of Cu/C carbon graphite mechanical seal material is 63%.The friction wear degree of C/C composite mechanical seal material is 41%.The frictional wear degree of PTFE composite mechanical seal material is 77%.The main reason is that, at the beginning of the break-in stage, the original roughness on the surface of the high-strength stainless steel mechanical seal material gradually decreases after the break-in and becomes the normal use of surface roughness.After the test time reaches 10min, the frictional wear degree of different materials basically tends to stabilize, and the frictional wear degree of C/C composite mechanical seal material is the smallest at 15.6%.The reason is that the C/C composite material is composed entirely of carbon.It has many advantages of carbon and graphite materials: low specific gravity, the density of actual material used is about 1.75 g/cm3, excellent mechanical and physical properties, such as high specific strength and high specific mode at high temperature, low coefficient of thermal expansion and ablation rate.It has high thermal conductivity, good fracture toughness, corrosion resistance, high temperature thermal stability, thermal shock resistance and fatigue resistance.Excellent frictional wear properties and biocompatibility, insensitivity to cosmic radiation, increased strength under nuclear radiation, etc.Therefore, C/C composites have a low degree of frictional wear when used as mechanical seal materials.The degree of frictional wear of Cu/carbon graphite mechanical seal material is the second highest at 25.6%.This is due to the fact that Cu/carbon graphite material has excellent self-lubrication, thermal conductivity, corrosion resistance, thermal shock resistance and low coefficient of friction.However, Cu/carbon-graphite materials are brittle materials with low tensile strength, shear strength, and poor impact resistance, and have defects such as poor gas tightness and high wear rate.And for industrial production, Cu/graphite composites prepared by powder metallurgy method, hot molding, high-temperature sintering, multiple impregnation and other processes have the disadvantages of complex process, long production cycle and high cost.The maximum degree of frictional wear of PTFE composite mechanical seal material is 43.6%.Although, PTFE composite material has good toughness and high strength, its microfiber strength is much higher than the general non-ferrous metal strength, has a very high wear-resistant grain wear characteristics, good low temperature impact resistance, self-lubricating, water resistant chemical corrosion resistance, non-toxic.However, the material has low heat deformation temperature, poor processing and forming, and low wear resistance variability.And it has some inherent defects, especially the cooling and processing performance is poor.Therefore, PTFE composite mechanical seal material has the greatest degree of frictional wear.

Conclusion
The diversification of industrial production needs, such as high-speed, high temperature, variable working conditions, corrosive media, solid particles and other media conditions under special working conditions mechanical seals.These conditions require more stringent material performance, and also raise the standard of comprehensive performance of mechanical seals.Therefore, this paper

Figure 1 .
Figure 1.Analysis of high-temperature friction and wear performance of seal materials

Figure 2 .
Figure 2. Analysis of friction and wear performance of different types of materials for mechanical seals

Table 1 .
Percentage of industrial accidents caused by wear of materials for seals, 2018-2021