A Numerical Analysis Method of Hydraulic Seals for Downhole Equipments

Abstract

The aim of this paper is to present a numerical method to predict the work performance of hydraulic seals used in downhole equipments. The impact of key factors, namely, compression rate and the number of seals, on the wearing behavior of seal components is studied. To simulate the wear process of sealing contact surface, a methodology is built with the iterative wear prediction procedure in which the geometry of the contact interfaceprogressively changes according to the wear model. In this method, the structural and the thermal coupled mechanism is investigated and the performance of seal structure containing different number of seals is discussed. By taking a gear pump used in the downhole robots as a case study, both numerical analysis with proposed method and practical experiment are presented. The simulation results of the worn volume of the seals are consistent with the experiment data. This work provides an effective computerized approach to aid seal components design and manufacturing for downhole equipments.

1. Introduction

Nowadays more and more people care about the exploitation of the natural resources, such as oil [1]. With the fast increase of population and the appearance of more factories, oil is getting less and less year after year. Deep well exploitation has been a concern in the oil industry. For example, in China, 70 percent of oil resources are distributed in the belts which are five kilometers under the ground. The downhole equipments will encounter harsh work conditions in such an environment, such as high pressure (with an extent of 70∼80 MPa) and high temperature (always above 100°C). Therefore, a more rigorous requirement is proposed for the steady working of the downhole equipments.

The seal components may have a rather profound effect on the downhole equipments [2, 3]. It helps to prevent surrounding drilling fluid (often called the “mud”) from flowing into the inner structure of equipments. This high temperature, high pressure, and abrasive liquid will lead to eventual seal degradation. So it is important to predict the service life of a seal to replace a new one in time. The method adopted previously is through experience which is used to determine when the seals are not able to meet the engineering requirements. The common method is to set up a test rig which is able to provide the test running conditions. The working process of the seal is simulated and the related environment parameters, such as temperature and pressure, can be monitored during the test. However, as the environment underground is extremely harsh, it is a time and money consuming project to set up a test rig which is able to simulate the downhole environment.

Other than the experiential ways to predict the life of seal components, the numerical prediction method is also available. As the computer technology develops, to predict the service life of seal components through a numerical way is possible. Kim et al. [4] analyzed the sealing performances of O-ring through Finite Element (FE) method and the influence of friction coefficient for the deformation of O-ring was also considered. Lin et al. [5] analyzed the sealing structure of the reactor pressure vessel through FE method. The thermal effect and the plastic deformation were included. However, this investigation focused on the static sealing. Lingerkar and Khonsari [6] obtained the laws on how the sliding speed and the pressure affect the sealing performances through analyzing the flow field in the gap between O-ring and rod with FE method. Azhikannickal and Wild [7] analyzed the stress distribution of elastomeric foam seal through FE method and modified the structure of the area with stress concentration. Ötingün et al. [8] also utilized the FE method to analyze the sealing performances of O-ring under mixed lubricated conditions.

FE method was applied in the researches mentioned above. Many other studies adopted numerical methods. Yuan et al. [9] set up the flow model of the spiral groove face seals with the Reynolds equation. Besides, the thermal effect was also analyzed. Zhou et al. [10] proposed an elastohydrodynamic model to describe the sealing performances of lip seal. Full film lubrication was assumed during the analysis. The Reynolds equation and the deformation equation of the seal were concurrently solved. The laws of relevant parameters such as the pressure distribution in the film and the thickness of the film are obtained. Thomas et al. [11] presented a thermoelastohydrodynamic model to analyze the sealing performances of rotating seals. Nikas [12] described the extrusion behavior of rectangle-section seal numerically. He also analyzed the sealing behaviors of rectangle-section seal with elastohydrodynamic model [13].

The wear behaviors of the seals are not considered in the researches mentioned above. Even though some researches involve the mixed lubrication, they are based on the assumption of low friction coefficient. The seals used in the downhole equipments do not accord with this assumption. High pressure and high temperature make the seals contact tightly with the executive components. So the wear effect of the executive components for the seals cannot be neglected. However, there are few studies concerning the wear of seals through simulation ways. Hambli et al. [14] proposed an FE method to predict the lifetime of the blanking tool considering the wear effect. The similar work was also fulfilled by Hambli et al. [15]. It is easy to realize this simulation method for the “hard” material because the influence of the wear on the change of the mechanical behaviors is apparent but does not work for the “soft” material such as rubber. Bagci and Ozcelik [16] also studied the influence of the wear on the twist drill through FE method. The thermal effect was considered. Mamalis et al. [17] studied the process of material removal during grinding with the FE method in which the thermal factor was included.

Few studies have been presented on the wear simulation of the seals. Nandor et al. [18, 19] proposed an FE method for wear simulation of reciprocating seal. Archard's wear model was included to model the variation of the seal's profile and subsequently the mesh reconstruction technology was applied on the modified field of the seal. The next simulation cycle began. But sharp corners may emerge on the worn profile of the seal and this will bring some troubles for remeshing operation with FE method. So a new FE method for wear simulation of the seals is presented in this paper which is able to overcome this disadvantage.

When designing the sealing components of the downhole equipments, two ways are often adopted to enhance the reliability of seal system, which is increasing the compression rate of the seals and adopting multiple seals. The authors take the rotating sealing system in the downhole equipments as an example in this paper in order to investigate how the compression rate and the seal number affect the wear behavior of O-ring.

In order to model the wear process of the seal, an FE method for wear simulation of the seal component is presented in this paper. This method overcomes the problem of sharp corners on the profile. Besides, due to the fact that the shaft rotates with a high speed, the effect of friction heat is considered during the wear simulation. A thermal-structural coupled algorithm is presented for the simulation process. The worn volumes of O-rings under different compression rates and with different number of seals are given through both numerical analysis and experiment. The comparisons imply that the results from both methods coincide well. The simulation method presented in this paper can be used to predict the life of O-ring in the downhole equipments.

2. Description of Seal Problem

In the downhole equipments, the specified motions for drilling or measurement are accomplished by the executive components and these components are controlled by the hydraulic systems in the equipment. The function of the seals is to prevent the flow of fluid on both sides in order to make sure that there are enough pressure differences to make the executive components run accurately. Once the leakage is extensive, the executive components will not reach their positions correctly. Even worse, some protruding components may not be able to return to their original positions which will lead to the scrap of the well. This brings a huge economic loss.

A typical rotating sealing system is displayed in Figure 1(a). The system is composed of the shaft, the chamber, and the O-ring. The slot holding the O-ring is machined in the chamber in this paper. So the O-ring is installed in the slot and keeps still with the chamber while the shaft rotates with a high speed. The compression rate Δ is decided by the height of the slot h and the initial sectional diameter of O-ring d. Thus, the compression rate of O-ring can be given as Δ = (d – h)/d × 100%. In order to increase the sealing pressure, one way is to increases the compression rate and another is to increase the number of O-rings. Generally, the depth of the oil well is less than 10 kilometers and three O-rings in one slot are enough to accomplish the sealing mission. Therefore, the upper limit of the number of O-rings is defined as three. The sealing systems with two and three O-rings in one slot are shown in Figures 1(b) and 1(c).

Figure 1:

Typical rotating sealing systems. (a) Sealing system with a single O-ring in a slot. (b) Sealing system with a couple of O-rings in a slot. (c) Sealing system with three O-rings in a slot.

3. Wear Simulation with FE Method

3.1. Sliding Wear

Many factors decide the wear behaviors of mechanical components, for example, the geometry of the contact surfaces, normal loads, relative sliding speeds, hardness of the contact materials, and the friction characteristics. The wear process can be seen as a function of these factors as given in

W = f (geometry, normal load, sliding speed, \dots),

(1)

where W is the worn volume.

The most widely used wear model is the linear wear model which was proposed by Rabinowicz et al. in the 1900s [20, 21]. This model was based on the experimental data and the results demonstrated that the worn volume is proportional to the normal load and sliding distance while inversely proportional to hardness of the softer material. The linear wear model is given in the following:

W = K \frac{F}{H} L,

(2)

where K is the dimensionless wear coefficient, H is the hardness of the softer material, F represents the normal load, and L is the sliding distance.

In order to apply the wear model into the simulation, both sides of (2) are divided by the time increment dt and the equation can be modified as

\frac{d W}{d t} = k_{H} F v,

(3)

where dW/dt is the volume worn rate, $k_{H} = K / H$ is the wear coefficient, and v is the sliding speed.

If both sides of (3) are divided by the contact area A, a new form will be given as

d h = k_{H} P v \cdot d t,

(4)

where dh is worn height increment and P is the normal contact pressure.

In order to model the wear of nodes in FE simulation, the discrete form of (4) is applied:

d h_{i} = k_{H} P_{i} v \cdot d t,

(5)

where dh_i is the nodal worn height increment and P_i is the nodal normal pressure.

3.2. Structural FE Model

According to the geometric model of the sealing system shown in Figure 1, structural 2D finite element models are built as displayed in Figure 2. The relationship between the compression rate of O-ring and sealing pressure, as well as the relationship between the number of O-rings and the sealing pressure, can be analyzed through these models. Figure 2(a) represents that only one single O-ring is installed in the sealing seat. The sealing systems with two and three O-rings in the sealing seats are shown in Figures 2(b) and 2(c), respectively.

Figure 2:

FE models of sealing system. (a) Sealing system with a single O-ring in a slot. (b) Sealing system with a couple of O-rings in a slot. (c) Sealing system with three O-rings in a slot.

According to the symmetrical characteristic, half of the geometrical model is built in the FE model for saving the computing time. Since rubber is a kind of hyperelastic material, a hyperelastic element is adopted when building the finite element models of O-ring.

In reality, deformation always occurs when the seal is installed in the slot. But the deformation cannot be precalculated in FE model. So O-ring is modeled as an uncompressed state at the beginning of the simulation. The pre-compression effect can be simulated through setting contact pairs between the shaft and O-ring. The influence from the fluid is also considered. The fluid pressure is set as one of the boundary conditions. Left side of O-ring is assumed to undertake the fluid pressure. As the right side of O-ring will be compressed on the surface of the chamber, the fluid pressure is ignored on the right side.

Therefore, two steps are operated to model the deformation of O-ring. The first is to compress the seal along the radial direction to model the precompression when installed (① in Figure 2(a)) and the second is to compress the seal along the axial direction to model the compression effect caused by the fluid (② in Figure 2(b)). Besides, the fluid temperature is set as the initial condition. Before the simulation starts, the temperature distribution in O-ring is assumed to be steady. So the whole domain of O-ring is set with the fluid temperature.

Asymmetrical meshing strategy is adopted when meshing the domain of O-ring. As mentioned above, there is relative motion between the O-ring and the shaft. So the wear of O-ring mainly occurs on the area where O-ring contacts with the shaft. In order to simulate the wear behavior of the seal precisely and reduce the computing time, the area where the seal contacts with the shaft is densely meshed and the other area of the seal is sparsely meshed.

3.3. Transient Thermal Analysis

The influence of friction heat on the wear of the seal cannot be neglected when the shafts rotate with a high speed. The circumferential shear stress at node i on the seal's surface can be given as

τ_{i} = f p_{i},

(6)

where f is the friction coefficient and p_i is the normal nodal pressure.

In high speed rotating sealing system, the friction heat will affect the wear behavior of the seal and the loss of the material will affect the distribution of the contact pressure. The friction heat will be influenced in return. Coupled effect of the thermal and structural stress is required to analyze the wear behavior of the seal. It is a complicated coupled problem. Recently, some researchers have adopted the method that the thermal effect and structural effect are independently analyzed for this subject [22 –24]. The heat flux density at node i on the surface of the seal can be expressed as

q_{i} = ψ τ_{i} v = ψ f p_{i} v,

(7)

where ψ is the percentage of transition from mechanical work to friction heat and v is the relative circumferential speed. According to [25], the friction heat can be thought to be completely transformed, it means ψ = 1.0.

Since the nodal temperature in the seal dynamically changes with time, it belongs to transient analysis problem. The nodal temperature can be solved by the following equation:

[C] [\dot{T}] + [K] [T] = [P],

(8)

where [C] is the specific heat matrix, [K] is thermal conduction coefficient matrix, [P] is the thermal load matrix, [T] is the nodal temperature matrix, and $[\dot{T}]$ is the derivative of [T]. The elements in these matrices can be expressed by the following equations:

\begin{matrix} K_{i j} = \sum K_{i j}^{e} + \sum H_{i j}^{e}, \\ C_{i j} = \sum C_{i j}^{e}, \\ P_{i} = \sum P_{q_{i}}^{e} + \sum P_{H_{i}}^{e}, \end{matrix}

(9)

where K_ij^e represents the contribution to the thermal conduction matrix from elements, H_ij^e represents the contribution to the thermal conduction matrix from boundary conditions, C_ij^e represents the contribution to the specific heat matrix from elements, and P_{q
_i}^e and P_{H
_i}^e are the thermal loads from elements.

Figure 3 shows the thermal analysis model of O-ring with finite element method. A single O-ring is analyzed in Figure 3(a). Firstly, deformation of O-ring is obtained from the results of the structural analysis. It is more close to reality to set thermal boundary conditions on the deformed finite element model. It is assumed that the seal has reached a thermal equilibrium state before simulation and the fluid temperature T_fluid is set as the initial condition of the nodes. The value of T_fluid keeps independent of time. The heat flux density of the friction heat in the sealing area varies with time. The heat flux density at each node on the contact area can be written as follows:

q (u_{contact}, t) = f p (u_{contact}, t) v,

(10)

where u_contact is the coordinate vector of the nodes contacting with the shaft.

Figure 3:

Thermal finite element model of the sealing system. (a) Thermal FE model of the system with a single seal. (b) Thermal FE model of the system with two seals. (c) Thermal FE model of the system with three seals.

The thermal FE models with two and three O-rings are, respectively, displayed in Figures 3(b) and 3(c). The difference between the FE model with two or three seals and the FE model with a single seal is that the boundary of the seal, except the area where the seal contacts with the shaft, is set with the boundary condition of the fluid temperature in the single seal model. However, since the temperature of the seal varies with time in this study, the contact boundary where the adjacent seals contact with each other is set with the temperature of the opposite seal in the two or three seals model which is marked with a red ellipse in Figures 3(b) and 3(c).

Though the thermal conduction coefficient of the steel is several orders of magnitude bigger than that of the rubber, the thermal expansion coefficient of the rubber is several orders of magnitude greater than that of the steel. Thus, the effect of thermal deformation of the seal cannot be ignored. It should be noted that though the thermal conduction coefficient and thermal expansion coefficient of both materials vary with the temperature, the variation stays in a small extent because the friction heat is not enough to change the environmental temperature greatly. Thus, both of the two parameters are thought to be independent of the temperature. Since most parts of the friction heat dissipate through the shaft for its high thermal conduction coefficient, only a little is absorbed by the seal. The heat flux density accepted by the seal in the sealing area is approximately k_rubber/k_steel times the total value. So the boundary condition in the sealing region q_seal can be calculated as

q_{seal} (u_{contact}, t) \approx \frac{k_{rubber}}{k_{steel}} q (u_{contact}, t) .

(11)

In addition, the initial condition is given as

T (u, t = 0) = T_{fluid} .

(12)

The change of temperature will lead to linear expansion of the seal. The shear strain on the contact area can be ignored. The strain caused by thermal deformation can be taken as initial strain set on the finite element model. For 2D model the initial strain can be given as

∊_{0} = α (T - T_{0}) {[\begin{bmatrix} 1 & 1 & 0 \end{bmatrix}]}^{'},

(13)

where α is the thermal expansion coefficient, T₀ is the initial temperature, and T is the transient temperature. The equation which is used to solve the coupled stress is given as

[K^{e}] [q^{e}] = [F^{e}] + [F_{0}^{e}] .

(14)

In (14), [K^e] is the elemental stiffness matrix, [q^e] is the nodal displacement matrix, and [F^e] and [F₀^e] are structural stress matrix and equivalent structural stress matrix.

The stress distribution in the seals caused by thermal effect is shown in Figure 4 when the simulation process has been operated for one minute.

Figure 4:

Stress distribution caused by thermal effect. (a) Stress distribution in a single seal. (b) Stress distribution in a couple of seals. (c) Stress distribution in three seals.

3.4. Remeshing Strategy

Mesh reconstruction is a key technique to realize wear process simulation with finite element method. Though global remeshing strategy proposed by Nandor et al. [18] can be used to simulate the wear process of the seal, the whole domain needs to be remeshed. Once the worn profile owns some sharp corners which are generated due to the movement of the profile points, the remeshing work will be more complicated. Killing elements strategy is more suitable for finite element analysis software. If the contact pressures in the elements exceed the predefined threshold, these elements will be “killed.” However, the wear depth is limited by the size of the contact elements. Only the wear process whose wear depth is larger than the size of the contact elements can be simulated. To overcome this restriction, in the current work, not only the contact elements are remeshed but also the elements adjacent to them can be remeshed by the wear processor, if required.

Mesh distribution of O-ring after being compressed is shown in Figure 5. The elements near the sealing area are quadrangles. Since the wear only occurs in the elements near the sealing area, the proposed remeshing method is applied to the elements in this region.

Figure 5:

Mesh distribution of O-ring.

The presented remeshing strategy is demonstrated in Figure 6. One of the contact elements and its neighboring elements are chosen as an example. Node N1 is moved based on the wear increment in (5). The wear depth of N1 is equal to h₁. H_1–2 is defined as initial vertical distance between N1 and N2. The current vertical distance H_1–2^c becomes

H_{1 - 2}^{c} = H_{1 - 2} - d h_{1},

(15)

where H_1–2^pre is defined as the critical vertical distance between N1 and N2. Once H_1–2^c is no more than H_1–2^pre, the relative position of N1 and N2 is fixed with the vertical distance H_1–2^pre and the wear processor moves node N2 to N3. By moving N2, the current vertical distance of N2 and N3 H_2–3^c becomes

H_{2 - 3}^{c} = H_{2 - 3} - d h_{2} .

(16)

Figure 6:

Illustration of the remeshing strategy.

In this equation, H_2–3 is the initial vertical distance between N2 and N3. dh₂ is the vertical displacement of N2. Similar to node N1, H_2–3^pre is defined as the critical vertical distance between N2 and N3. Once H_2–3^c is no more than H_2–3^pre, the relative position of N2 and N3 is fixed with the vertical distance H_2–3^pre and the wear processor moves node N3 to N4. Here, dh₂ is the difference of dh₁ and H_1–2^pre that can be given as dh₂ = dh₁ – H_1–2^pre. So the current vertical distance H_2–3^c can be expressed as

H_{2 - 3}^{c} = H_{1 - 2}^{pre} + H_{2 - 3} - d h_{1} .

(17)

Repeat this process and the wear depth can be expanded to any number of layers of elements in the proximity of the contact region. More generally, the vertical distance between node Ni and Ni + 1 can be written with a similar way:

H_{i - (i + 1)}^{c} = {\begin{cases} H_{i - (i + 1)}, & d h_{1} \leq \sum_{n = 1}^{i - 1} H_{n - (n + 1)}^{pre} \\ H_{i - (i + 1)}^{pre}, & d h_{1} \geq \sum_{n = 1}^{i} H_{n - (n + 1)}^{pre} \\ \sum_{n = 1}^{i - 1} H_{n - (n + 1)}^{pre} + H_{i - (i + 1)} - d h_{1}, & \sum_{n = 1}^{i - 1} H_{n - (n + 1)}^{pre} < d h_{1} < \sum_{n = 1}^{i} H_{n - (n + 1)}^{pre} . \end{cases}

(18)

With this method, the wear depth of the simulation process is no longer limited by the size of the contact elements. Besides, a safe aspect ratio can be ensured for these contact elements through this way. The value of total wear depth can be bigger than the size of the contact elements. The effect of wear simulation of the seal is shown in Figure 7.

Figure 7:

Wear effect of the seal with mesh reconstruction.

3.5. Thermal-Structure Coupled Simulation Algorithm

In general, wear phenomenon is a continuous process. However, in order to simulate the process with an FE method, the continuous material removal in time needs to be approximated at a discrete set of time. Iterative mechanism is widely used in the subject of wear analysis and simulation. In our approach, the geometry of O-ring is updated in the end of each cycle to reflect the evolution of wear behaviors. Entirely coupled thermal-structure simulation analysis is operated in every cycle. The flowchart of the simulation process is shown in Figure 8. One cycle of the simulation contains four main modules, namely, initial contact analysis, thermal analysis, comprehensive contact analysis, and wear simulation.

Figure 8:

Flowchart for the wear simulation of thermal-structure coupled analysis.

A precompressed FE model is built in the first module. O-ring is compressed on the surface of the shaft in the first step to simulate the radial compression. The axial load is set on the left surface of O-ring in the second step to model the pressure distribution of the fluid.

According to the contact pressure distribution determined in the first module, a transient thermal FE analysis is run in the second module. The flux density of friction heat at each contact node is calculated as one of the boundary conditions of the FE model. The temperature of the fluid is assumed as the initial condition. The initial temperature distribution in the following cycles can be obtained from the result of the previous thermal simulation.

In the third module, another FE contact model which takes into account the effect of thermal expansion is operated. The nodal wear depths can be calculated in the last module of the cycle. Once the wear depth at each node is known, the worn profile of the seal can be reconstructed. The modified geometry model will be the input of the next simulation cycle.

3.6. Determination of Cycle Time

The selection of suitable time for simulation cycle is a key problem in iterative simulation analysis of wear. As the sealing system with a single seal is the fundamental element of the system with two or three seals, the determination of the cycle time is operated in the sealing system with a single seal.

The cycle of the simulation process presented above is solved for different time increments. The nodal pressure distribution for five stochastically selected contact nodes (namely from node-1 to node-5) is plotted for different time increments in Figure 9. In order to save the computing cost, the process of selecting suitable cycle time is accomplished in the first 30 s. It can be seen that as the cycle time is increased the pressure distribution starts varying considerably. This behavior of FE model affects the overall solution. Though a model solved with a smaller cycle time gives more accurate results, it comes at the expense of computational time. Therefore, the cycle time is to be selected accordingly. In this case, the cycle time 6 s was used.

Figure 9:

Distribution of the nodal contact pressure with different cycle time. (a) Cycle time = 2 s. (b) Cycle time = 6 s. (c) Cycle time = 10 s.

4. Case Study

4.1. Introduction of the Gear Pump

In order to verify the numerical analysis method presented in this paper, a gear pump in the downhole robots is chosen as the experimental subject. The structure of the gear pump is shown in Figure 10. The power for motions of the robots is supplied by the power source assembly which is composed of oil block, hydraulic valves and the gear pump, as shown in Figure 10(a). Dynamo (which is not displayed in the figure) rotates the driving gear shaft in the gear pump and then the driven gear shaft is also rotated. The space between the two gears is divided into sucking space and compressing space. The two spaces are, respectively, connected with the oil way outside the pump to construct a complete loop which supplies power for the executive components.

Figure 10:

Structure of the gear pump. (a) The gear pump in the power source assembly of downhole robots. (b) Sectional drawing of the gear pump. (1) Top end cap-1; (2) bolt; (3) top end cap-2; (4) seal seat; (5) driven gear shaft; (6) driving gear shaft; (7) static O-ring; (8) dowel pin; (9) static O-ring; (10) pump body; (11) bottom end cap-1; (12) bottom end cap-2; (13) dynamic O-ring.

Sectional drawing of the pump is shown in Figure 10(b). To make sure that there is enough pressure to drive the executive components to their right positions, it is necessary to prevent the fluid in the pump from leaking. The O-rings marked with blueness are used as static seals. They still keep corresponding to the pump body and there is no relative motion in the sealing area. The O-rings marked with redness are used as dynamic seals. They are installed in the seat and their inner sides contact with the rotating shafts. Once the shafts rotate, there are relative motions where the seals contact with the shafts. The wear of the seals mainly happens in these areas. Because this paper concerns the wear simulation of the seals in the downhole equipments, the static seals are not considered in the following content.

4.2. Worn Volume of the Seal

The wear volume can be calculated through the following way. For the seal which is assembled without eccentricity, the wear on each section is absolutely the same if the influence of gravity is neglected. We can suppose that if O-ring is cut off along the section, the shape of the worn volume can be seen as a column. So the worn volume can be calculated through the volume of column.

The geometry model for the calculation of the worn volume is illustrated in Figure 11, where r is the inner radius of O-ring. The height of the column can be approximately replaced by the circumference of the inner circle. Since the worn section is irregular, an approach based on the FE nodes is proposed to calculate the area of the worn region approximately. Only the change of the positions of the contacting nodes, which are distributed on the profile of the seal in the sealing region, is considered during the calculation. If the worn height of node i is marked as dh_i, make a rectangle with the length of dh_i and the width of L_i, and the value of L_i can be obtained through its neighboring nodes i – 1 and i + 1. L_i can be given as follows:

L_{i} = \frac{1}{2} (h_{(i - 1) - i} + h_{i - (i + 1)}),

(19)

where h_{(i – 1) – 1} and h_{i – (i + 1)} represent the horizontal distances between node i – 1 and i and between node i and i + 1, respectively.

Figure 11:

Geometry model for worn volume.

So the worn volume of O-ring can be expressed as

V = 2 π r \sum_{i = 1}^{n} L_{i} \cdot d h_{i},

(20)

where n represents the number of the contacting nodes on the profile of O-ring.

4.3. Numerical Results

The material and geometry parameters which will be used in the simulation process are given in Table 1. The materials of the shaft and the chamber are defined as steel, while the material of O-ring is defined as fluororubber. The angular speed of the shaft is set to be 3000 r/min.

Table 1:

Material and geometry parameters.

Parameters	Value

Elastic modulus of fluororubber	7.84 MPa
Poisson's ratio of fluororubber	0.49
Elastic modulus of steel	201 GPa
Poisson's ratio of steel	0.3
Density of fluororubber	1400 kg/m³
Density of steel	7850 kg/m³
Thermal conduction coefficient of rubber	0.16 W/mK
Thermal conduction coefficient of steel	44 W/mK
Thermal expansion coefficient of rubber	6.9 × 10⁻⁴/°C
Specific heat of rubber	1700 J/kgK
Temperature of fluid	80°C
Pressure of fluid	1 MPa
Diameter of the shaft	30 mm
Sectional radius of O-ring	20 mm
Friction coefficient between the steel and the fluororubber	0.3

In order to study the influence of the compression rate on the wear behavior of the seal, three compression rates are selected in this work: 20%, 25%, and 30%. Under each compression rate, the sealing systems with a single seal, a couple of seals, and three seals are, respectively simulated and tested to obtain the worn volume of the seals. The variations of the compression rate and the number of the seals are fulfilled through changing different sizes of sealing seats. The results are displayed in Figure 12.

Figure 12:

Worn volume of O-ring through simulation way. (a) Sealing system with a single seal. (b) Sealing system with a couple of seals. (c) Sealing system with three seals.

The worn volume of the seal in the sealing system with a single seal is shown in Figure 12(a). It implies that the wearing speed in the initial period is fast. In about two hours, the tendency of the worn volume varies linearly. According to the wearing law, we can affirm that the seal has entered the running-in period. What is more, as the compression rate is increased, the worn extent of the seal is also increased. And the worn speed in the running-in period is faster.

The result of the worn volume in the sealing system with a couple of seals is displayed in Figure 12(b). In order to obtain the wearing behavior of each seal, the result of each seal is given individually. For convenience, the left seal in Figure 2(b) is simply marked as “Left” while the other one is simply marked as “Right”. The tendency of the worn volume of each seal is similar as the result shown in Figure 12(a). Beyond that, we can find that the worn extent of the right-hand seal is bigger.

The result of the worn volume in the sealing system with three seals is displayed in Figure 12(c). The seals in Figure 2(c) are simply marked as “left,” “middle,” and “right” from the left side to the right side. It can be seen from the result that the worn extent of the “right” seal is the biggest when the three seals are installed in series, while the worn extent of the “middle” seal is the smallest.

4.4. Experiment Results

The test rig is shown in Figure 13. The rig is composed of four modules.

Heating module: this part is in charge of heating the oil which will be infused into the testing module. The oil is heated to the required temperature in the heating container by four heaters. Then, the heated oil is transferred to the pressure module.

Pressure module: the oil enters into the pressure container and is pressured by the pressure cylinder laid beside the pressure container. The oil is pressured linearly to the value which the test requires.

Test module: the downhole robot is mounted in a cylinder where the heated and pressured oil representing the harsh environment is also accommodated. The robot accomplishes the specified orders sent by the control module, including the continuous working of the gear pump.

Control module: this module is comprised of electric closet and control cabinet. Its function is to send orders to the robot and other modules to fulfill specified mission. In the meantime, it accepts the signals sent by the sensors to monitor the variation of the parameters. However, the concern of this paper is on the worn of O-rings. This can be finished through weighing the seals before and after the test. So this module is not in charge of recording the parameters in this paper.

Figure 13:

Test rig for downhole equipment development. (a) Structure of the test rig. (b) Tested robot.

The experimental results are shown in Figure 14. The variation of the worn volume of a single seal is displayed in Figure 14(a). The worn volume of the seal under bigger compression rate is also bigger. And the wear speed is faster. These are quite consistent with the simulation results. However, we can note that the experimental data is a little smaller than the simulation data. This can be explained that in reality there is a thin film in the gap between the seal and the shaft. So the wear effect will be weakened due to this film. Thus, the experimental results are smaller than the simulation results.

Figure 14:

Worn volume of O-ring through simulation way. (a) Sealing system with a single seal. (b) Sealing system with a couple of seals. (c) Sealing system with three seals.

The variation of the worn volume of the two-seal system is shown in Figure 14(b). The law of the compression rate affecting the worn volume is similar to that in Figure 14(a). In addition, the experimental data prove that the worn extent of the “right” seal is bigger. This agrees with the simulation results.

Figure 14(c) displays the worn volume of the sealing system with three seals in a slot. Similar to the simulation result, the “right” seal is worn most and the “middle” seal is worn least. It implies that the simulation method is able to model the true wear effect of the seals underground.

4.5. Discussion

The results from both simulation and experiment are almost coincident. The worn volume for a single seal displays a tendency that the initial speed of worn volume is faster. This can be explained that the initial contact pressure between the seal and the shaft is larger and the effect of the friction heat is apparent. This leads to an even larger contact pressure. So the wear speed is faster according to Archard's model. With the removal of the seal material, the contact pressure between the seal and the shaft as well as the effect of the friction heat decreased. Consequently, the wear speed of the seal is reduced. A high compression rate increases the contact pressure. So the fact that higher compression rate speeds up the worn behavior can be easily explained.

In the two-seal sealing system, the worn extent of the “right” seal is a little bigger than the “left” one. The explanation of this result is that the deformation of the chamber is much smaller than the seals and the “right” seal is constrained by the chamber on the right surface. So the deformation of the “right” seal is larger than the “left” one which leads to the contact pressure of the “right” seal being bigger than the “Left” one. The subsequent explanation is the same as introduced in last section.

This explanation is also suitable for the three-seal sealing system. The “right” seal is constrained by the chamber. So its deformation as well as the contact pressure is the largest. That is why the “right” seal is worn most. Oppositely, as the “middle” seal is constrained by two seals on both sides, its deformation will be slightly released. Thus, the extent of the “middle” seal's worn is the smallest.

5. Conclusions

The wear phenomenon of seal component in downhole equipments is investigated with a numerical method in this paper. The effect of initial compression rate and the number of seals on the wearing behavior of O-rings is discussed. A structural and thermal coupled FE approach is presented to simulate the wear process of seal component under high temperature and high pressure condition. A remeshing strategy is proposed to simulate the behavior of the material removal of the seal. A rotating hydraulic seal component in the self-developed downhole robot is taken as in experimental subject. Both numerical analysis and practical experiment are conducted. The results of the numerical analysis method are consistent with the experiment data. This work can be used to predict the life of O-ring indirectly through predicting worn volume of the seal.

Since the downhole environment is quite complicated, a further study on the influence of other factors on the wear of the seal is needed. One factor is that sometimes the seal will be working with contamination particles. So the wear type is abrasive wear instead of adhesion wear. How to simulate the wear process of the seal with an abrasive wear is the next aim of the authors.

Footnotes

Acknowledgments

This research was supported by the National Natural Science Foundation of China (no. 51275119, no. 50905047) and Self-Planned Task of State Key Laboratory of Robotics and System (HIT) (no. SKLRS201203C). Their support is gratefully acknowledged.

References

Tang

Zhou

Y. K.

Zhu

, and Yang

H. F.

, “The effect of surface texturing on reducing the friction and wear of steel under lubricated sliding contact,” Applied Surface Science, vol. 273, pp. 199–204, 2013.

Kurokouchi

Okabe

, and Morita

, “Taper-seal type metal sealing system and available applications,” Applied Surface Science, vol. 169–170, pp. 799–802, 2001.

Smith

G. C.

Park

Titchener

K. J.

Davies

R. E.

, and West

R. H.

, “Surface studies of oil-seal degradation,” Applied Surface Science, vol. 90, no. 3, pp. 357–371, 1995.

Kim

H. K.

Park

S. H.

Lee

H. G.

Kim

D. R.

, and Lee

Y. H.

, “Approximation of contact stress for a compressed and laterally one side restrained O-ring,” Engineering Failure Analysis, vol. 14, no. 8, pp. 1680–1692, 2007.

Lin

Long

, and Ou

, “Three-dimensional transient sealing analysis of the bolted flange connections of reactor pressure vessel,” Nuclear Engineering and Design, vol. 236, no. 24, pp. 2599–2607, 2006.

Lingerkar

and Khonsari

M. M.

, “On the effects of sliding velocity and operating pressure differential in rotary O-ring seals,” Journal of Engineering Tribology, vol. 224, no. 7, pp. 649–657, 2010.

Azhikannickal

and Wild

P. M.

, “Finite element analysis of the design of an elastomeric foam seal for an automotive air filter,” Journal of Materials: Design and Applications, vol. 218, no. 1, pp. 37–46, 2004.

Ötingün

André

Bartel

, and Deters

, “An axisymmetric hydrodynamic interface element for finite-element computations of mixed lubrication in rubber seals,” Journal of Engineering Tribology, vol. 222, no. 3, pp. 471–481, 2008.

Yuan

Zhang

Zhao

, and Yang

, “Theoretical and experimental approach for the characteristics of water-lubricated, high-speed double spiral-groove face seals,” in Proceedings of the STLE/ASME International Joint Tribology Conference (IJTC '06), San Antonio, Tex, USA, October 2006.

10.

Zhou

Z. M.

Sang

S. J.

Tang

J. P.

, and An

, “A numerical simulation method for hydrodynamic lubrication of lip seal,” Journal of Engineering Tribology, vol. 226, no. 2, pp. 99–110, 2012.

11.

Thomas

Brunetière

, and Tournerie

, “Thermoelastohydrodynamic behavior of mechanical gas face seals operating at high pressure,” Journal of Tribology, vol. 129, no. 4, pp. 841–850, 2007.

12.

Nikas

G. K.

, “Analytical study of the extrusion of rectangular elastomeric seals for linear hydraulic actuators,” Journal of Engineering Tribology, vol. 217, no. 5, pp. 365–374, 2003.

13.

Nikas

G. K.

, “Elastohydrodynamics and mechanics of rectangular elastomeric seals for reciprocating piston rods,” Journal of Tribology, vol. 125, no. 1, pp. 60–69, 2003.

14.

Hambli

Soulat

, and Chamekh

, “Finite element prediction of blanking tool cost caused by wear,” International Journal of Advanced Manufacturing Technology, vol. 44, no. 7–8, pp. 648–656, 2009.

15.

Hambli

Guerin

, and Dumon

, “Numerical evaluation of the tool wear influence on metal-punching processes,” International Journal of Advanced Manufacturing Technology, vol. 21, no. 7, pp. 483–493, 2003.

16.

Bagci

and Ozcelik

, “Finite element and experimental investigation of temperature changes on a twist drill in sequential dry drilling,” International Journal of Advanced Manufacturing Technology, vol. 28, no. 7–8, pp. 680–687, 2006.

17.

Mamalis

A. G.

Kundrák

Manolakos

D. E.

Gyáni

, and Markopoulos

, “Thermal modelling of surface grinding using implicit finite element techniques,” International Journal of Advanced Manufacturing Technology, vol. 21, no. 12, pp. 929–934, 2003.

18.

Nandor

Karoly

, and David

, “Wear simulation of a reciprocating seal,” Journal of Tribology, vol. 133, no. 3, Article ID 031601, 6 pages, 2011.

19.

Békési

and Váradi

, “Wear simulation of a reciprocating seal by global remeshing,” Periodica Polytechnica, Mechanical Engineering, vol. 54, no. 2, pp. 71–75, 2010.

20.

Põdra

and Andersson

, “Simulating sliding wear with finite element method,” Tribology International, vol. 32, no. 2, pp. 71–81, 1999.

21.

Rabinowicz

, Friction and Wear of Materials, Wiley, New York, NY, USA, 1995.

22.

Gong

Z. Q.

and Komvopoulos

, “Thermomechanical analysis of semi-infinite solid in sliding contact with a fractal surface,” Journal of Tribology, vol. 127, no. 2, pp. 331–342, 2005.

23.

and Komvopoulos

, “Three-dimensional finite element analysis of elastic-plastic layered media under thermomechanical surface loading,” Journal of Tribology, vol. 125, no. 1, pp. 52–59, 2003.

24.

Gong

Z. Q.

and Komvopoulos

, “Mechanical and thermomechanical elastic-plastic contact analysis of layered media with patterned surfaces,” Journal of Tribology, vol. 126, no. 1, pp. 9–17, 2004.

25.

Uetz

and Föhl

, “Wear as an energy transformation process,” Wear, vol. 49, no. 2, pp. 253–264, 1978.