The contact pressure on the contact surface between the rubber ring and the cover and the Mises stress inside the rubber ring are essential indicators of the fretting characteristics of the rubber ring. Hydrogen leakage will occur in the combined seal structure when the peak contact pressure is less than the
Ph [
10]. Besides, the possibility of crack or elasticity loss in the rubber ring increases with Mises stress [
26]. Therefore, a focus on the contact pressure and Mises stress will be conducted to analyze the fretting characteristics of the X-ring in this work.
4.1. Stress Distribution of Fretting Seal
The X-ring’s stress distribution and variation rule can be directly reflected by the contact pressure corresponding to the continuous node elements of the contact surface between the X-ring and cover and the Mises stress distribution diagram of the X-ring. The distribution of contact pressure and Mises stress of the X-ring during the first two fretting periods (0–2 T) will be investigated in this section. The Af is 1.2 mm, the Cf is 0.05, the Ph is 35 MPa, and the Rp is 10%.
Figure 3 and
Figure 4 show contact pressure distribution corresponding to the continuous node elements on the contact surface between the X-ring and the cover during 0–1 T and the second fretting period (1–2 T), respectively. At any location during 0–2 T, there are two continuous segments of node elements with contact pressure higher than
Ph (35 MPa), signifying that the X-ring can function as a seal in the fretting seal structure. It is worth mentioning that the peak contact pressures for 0.25 T, 1 T, 1.25 T, and 2 T are almost identical, and for 0.5 T, 0.75 T, 1.5 T, and 1.75 T, as will be elaborated below.
Figure 5 displays the Mises stress distribution of the X-ring during 0–2 T. At 0 T, the Mises stress is symmetrically distributed. There are grain-shaped stress concentration zones in the X-ring’s lower left and right corners. The peak Mises stress is located in the lower right corner of the X-ring, and the height of the upper left and right sealing lip (
h0 and
h1) of the X-ring is the same. Starting at 0.25 T, the Mises stress of the X-ring is no longer symmetrically distributed. During 0–0.25 T, the cover moves along −
y, generating −
y friction on the X-ring. Depending on the friction, the cover drags the X-ring to move together along −
y. Due to the dragging effect of the cover, the upper right sealing lip of the X-ring moves down slightly, and the angle between the stress concentration zone in the lower right corner of the X-ring and the upper surface of the wedge-ring (
θ2) decreases slightly. As the wedge-ring firmly blocks the X-ring, the −
y displacement of the area in the lower right corner of the X-ring is 0. Since the rubber material is approximately incompressible, the area in the lower right corner of the X-ring is squeezed by the upper area, resulting in a significant increase in the Mises stress values of the stress concentration zone in the lower right corner.
Mises stress distribution at 0.75 T is consistent with that at 0.5 T, meaning that the fretting of the X-ring is in the gross slip region during 0.5–0.75 T. In this process, the cover moves along +y, the X-ring stops motionless, and the relative slip is generated in X-ring and cover. Accordingly, it is speculated that the X-ring fretting starts to run in the gross slip region at a specific location of 0.25–0.5 T. The following section will discuss the critical fretting displacement into the gross slip region. It can be preliminarily determined that the critical fretting displacement into the gross slip region is less than or equal to 1.2 mm. Consequently, the height reduction of the upper right sealing lip (h1−h2) and the angle reduction of the lower right stress concentration zone with the upper surface of the wedge-ring (θ1−θ2) during 0–0.25 T, and the height increment of the upper right sealing lip (h3−h2) and the angle increment of the lower right stress concentration zone with the upper surface of the wedge-ring (θ3−θ2) during 0.25–0.5 T, have reached the limit value during the corresponding fretting stage. The influence of the wedge-ring’ blocking effect on the X-ring’s fretting characteristics is further verified.
In 0.75–1 T, the cover moves along −
y, produces a −
y friction on the X-ring, and drags the X-ring to move together along −
y. At 1 T, the fretting is already in the gross slip region. Consequently, the height of the upper right sealing lip (
h4) and the Mises stress value in the lower right corner of the X-ring at 1 T are similar to those at 0.25 T. During 1–1.25 T, the Mises stress distribution of 1.25 T is consistent with that of 1 T because the fretting is still in the gross slip region. During 1.25–1.5 T, the Mises stress distribution of 1.5 T is consistent with that of 0.5 T, as both 0.25 T and 1.25 T are the limit locations of the inward stroke. It can be inferred that the Mises stress distribution of 1.75 T is consistent with that of 0.75 T and 1.5 T. The Mises stress distribution of 2 T is uniform with that of 1 T. These inferences can be verified by the Mises stress patterns in
Figure 5 and the contact pressure distribution in
Figure 3 and
Figure 4.
In summary, the X-ring can play a sealing role in the fretting seal structure. The Mises stress is asymmetrically distributed during fretting. The peak Mises stress is consistently located in the stress concentration zone in the lower right corner of the X-ring. The variation tendency of the angle between the stress concentration zone in the lower right corner of the X-ring and the upper surface of the wedge-ring and the height of the upper right sealing lip of the X-ring are directly affected by the drag direction of the cover. The variation quantity of this angle and height are directly affected by the blocking effect of the wedge-ring. When the fretting displacement is large enough (such as ≥1.2 mm), the fretting of the X-ring runs in the gross slip region, and the fretting cycle starts at 0.5 T with a period of 1 T.
4.2. Effect of Fretting Amplitude
Af directly affects the fretting region of the rubber ring. With the increase of
Af, the fretting of rubber O-ring runs in the sticking region, the mixed slip region, and the gross slip region successively [
18]. This section will further verify whether this rule also applies to X-ring. In addition, as described in the previous section, when the
Af is 1.2 mm, the fretting cycle starts from 0.5 T. Whether there is a similar rule when the
Af is more minor will be discussed in this section. The influence of
Af on the fretting characteristics of X-ring will be explored in this section. The
Cf is 0.05, the
Ph is 35 MPa, and the
Rp is 10%.
Figure 6 manifests the relationship between the peak Mises stress of the X-ring and
Af during 1–2 T. The peak Mises stress of 1 T and 2 T is always equal, verifying the reciprocating periodicity of the X-ring fretting seal with a period of 1 T. Furthermore, when the
Af increases from 0.1 mm to 0.4 mm, the peak Mises stress of 1 T, 1.25 T, and 2 T increases sharply, and the peak Mises stress of 1.5 T and 1.75 T increases slightly, representing that the fretting runs in the sticking region. When the
Af increases from 0.4 mm to 1.2 mm, the peak Mises stress at all locations increases slowly, denoting that the fretting runs in the mixed slip region. When the
Af increases from 1.2 mm to 2 mm, the peak Mises stress at all locations does not change, indicating that fretting runs in the gross slip region. It can be concluded that the critical fretting displacement of the X-ring running into the mixed slip region is 0.4 mm, and that of the X-ring running into the gross slip region is 1.2 mm. Moreover, the peak Mises stress of the X-ring running in the gross slip region is equal at 1 T, 1.25 T, and 2 T, and at 1.5 T and 1.75 T. This rule is in complete agreement with the peak Mises stress variation rule in
Section 4.1.
When the fretting displacement is less than 0.4 mm, the fretting runs in the sticking region. To further clarify the influence of
Af on the fretting characteristics of the X-ring, it is urgent to compare the fretting periodicity of the X-ring running in the sticking and gross slip regions. The X-ring’s change of the peak contact pressure and the peak Mises stress (collectively referred to as “peak stress”) during 0–3 T are investigated when
Af is 0.2 mm, as shown in
Figure 7. At 0.75 T, the peak stress of the X-ring begins to change periodically with a period of 1 T. During each fretting period, taking 0.75–1.75 T as an example, the peak stress values of adjacent locations are different, which further verifies that the X-ring runs in the sticking region when the
Af is 0.2 mm.
Additionally,
Figure 8 reflects the change in the peak stress of the X-ring during 0–3 T when
Af is 1.2 mm. At 0.5 T, the peak stress of the X-ring begins to change periodically with a period of 1 T. During each fretting period, taking 0.5–1.5 T as an example, the peak stress of 0.5 T is equal to 0.75 T. During 0.75–1 T, the peak stress increases significantly. The peak stress of 1.25 T equals that of 1 T. During 1.25–1.5 T, the peak stress decreases substantially. Eventually, the peak stress of 1.5 T equals the peak stress of 0.5 T. These rules are entirely consistent with the peak Mises stress variation rule in
Section 4.1.
In conclusion, when the Af increases from 0 mm to 2 mm, the fretting of the X-ring runs in the sticking region, the mixed slip region, and the gross slip region successively. The critical fretting displacements into the mixed slip region and the gross slip region for the inward and outward strokes are all the same, 0.4 mm and 1.2 mm, respectively. The larger the Af is within a specific range, the earlier the X-ring enters the fretting cycle. The fretting period of the X-ring is not affected by the Af and always remains 1 T.
4.3. Effect of Friction Coefficient
The Cf directly affects the contact surface friction between the X-ring and cover. As the Cf increases, so does the friction, which in turn aggravates the surface damage of the X-ring, thus worsening the fretting performance of the X-ring and reducing the service life of the combined seal structure. The influence of Cf on the fretting characteristics of X-ring will be investigated in this section. The Af is 1.2 mm, the Ph is 35 MPa, and the Rp is 10%.
Figure 9 demonstrates the relationship between the peak contact pressure of the X-ring and
Cf during 1–2 T. When the
Cf increases from 0.03 to 0.07, the peak contact pressure of 1 T, 1.25 T, and 2 T increases significantly. In comparison, the peak contact pressure of 1.5 T and 1.75 T decreases substantially. The main reason is that during 1–1.25 T and 1.75–2 T, the friction of the cover on the X-ring is along −
y. Furthermore, the
Ph is always along −
y, and its value remains constant. As the
Cf increases, friction increases, increasing the net force exerted on the X-ring along −
y. Consequently, the squeezing effect along −
y on the X-ring is enhanced, so the peak contact pressure of 1 T, 1.25 T, and 2 T increases. During 1.25–1.75 T, the friction of the cover on the X-ring is along +
y. When the
Cf increases, the friction increases, decreasing the net force exerted on the X-ring along −
y. Consequently, the squeezing effect along −
y on the X-ring is weakened, so the peak contact pressure of 1.5 T and 1.75 T decreases. Besides, when the
Cf is 0.06, the peak contact pressure of 1.25 T is slightly greater than 1 T, and that of 1.75 T is slightly less than 1.5 T. When the
Cf is 0.07, the peak contact pressure of 1.25 T is significantly greater than 1 T, and that of 1.75 T is substantially less than 1.5 T. This result implies that changes in the
Cf may alter the fretting running region of the X-ring. Specifically, the critical fretting displacement of the X-ring running into the gross slip region increases with the increase of
Cf.
Figure 10 reflects the relationship between the peak Mises stress of X-ring and
Cf during 1–2 T. When the
Cf increases from 0.03 to 0.07, the peak Mises stress increases at most locations. Therefore, the peak Mises stress of the X-ring could be reduced by decreasing the
Cf appropriately, thus reducing the possibility of failure due to crack or elasticity loss.
As the O-ring also has a reciprocating periodicity of fretting [
18], the minimum (Min) peak contact pressure, as well as the maximum (Max) peak Mises stress of the X-ring and O-ring during 1–2 T, can be used as the primary basis for determining the similarities and differences in the fretting characteristics of these two types of rubber rings.
Figure 11 shows the Min peak contact pressure and Max peak Mises stress of X-ring and O-ring at various
Cf during 1–2 T. When the
Cf increases from 0.03 to 0.06, the decreasing trend in the Min peak contact pressure of the X-ring is more significant than that of the O-ring. The Min peak contact pressure of the X-ring is always higher than that of the O-ring. These imply that the fretting sealing characteristics of the X-ring are more excellent than those of the O-ring. When the
Cf is 0.07, the Min peak contact pressure of the X-ring is slightly lower than that of the O-ring, which can be inferred that the O-ring may have better fretting sealing characteristics in a higher
Cf. In addition, the increasing trend of the Max peak Mises stress of the X-ring is weaker than that of the O-ring. The Max peak Mises stress of the X-ring is always lower than that of the O-ring. These signify that crack or elasticity loss inside the X-ring is less likely to occur.
To sum up, during 1–2 T, when the Cf increases from 0.03 to 0.07, the peak contact pressure at 1.25 T increases substantially and is always the Max. In comparison, that at 1.75 T decreases significantly and is always the Min, which means that the hydrogen leak is more likely to occur at the limit location of the outward stroke. Moreover, the peak Mises stress increases at most locations. Thus, the Cf should be controlled at a smaller value. Additionally, the fretting characteristics of the X-ring are generally better than those of the O-ring when Cf is in the range of 0.03–0.07.
4.4. Effect of Hydrogen Pressure
In practical applications, the rubber X-ring directly interacts with high-pressure hydrogen gas. With the increase of Ph, the effect of hydrogen swelling on rubber X-ring becomes more significant, thus affecting the fretting characteristics of the X-ring. Therefore, the fretting characteristics of the X-ring are closely related to Ph. The effect of Ph on the fretting characteristics of the X-ring will be explored in this section. The Af is 1.2 mm, the Cf is 0.05, and the Rp is 10%.
Figure 12 displays the relationship between the peak contact pressure of the X-ring and
Ph during 1–2 T. When the
Ph increases from 25 MPa to 45 MPa, the peak contact pressure increases at all locations. Specifically speaking, the five curves are almost parallel to each other with equal spacing, indicating that the X-ring’s peak contact pressure increases linearly with increasing
Ph, and the direct proportionality coefficient is approximately equal to 1. It signifies that the difference between the peak contact pressure and
Ph does not vary with
Ph. For example, when
Ph is 30 MPa, the difference between the two pressure is 4.0544 MPa at 1.5 T. When
Ph is 35 MPa, the difference between the two pressure is 3.9161 MPa at 1.25 T. These two numbers are very close. As a consequence, if the fretting sealing performance of the X-ring is evaluated only from the difference between the peak contact pressure and
Ph, it can be considered that the fretting sealing performance of these five groups of X-rings is similar under 25–45 MPa. In addition, the peak contact pressure at 1.75 T is always minimal, representing that hydrogen leakage is most likely to occur at the limit location of the outward stroke.
Figure 13 exhibits the relationship between the peak Mises stress of X-ring and
Ph during 1–2 T. When the
Ph increases from 25 MPa to 45 MPa, the peak Mises stress increases at most locations. It suggests that high-pressure hydrogen intensifies the possibility of crack or elasticity loss in the X-ring. In particular, the peak Mises stress at 1.5 T and 1.75 T of the X-ring is close to coincidence when
Ph is 25 MPa and 30 MPa, respectively. Because at lower
Ph values, the degree of swelling due to dissolved hydrogen of the X-ring is diminished, thus weakening the effect of hydrogen pressure on the Mises stress of the X-ring.
Figure 14 manifests the Min peak contact pressure and Max peak Mises stress of X-ring and O-ring at various
Ph during 1–2 T. When the
Ph increases from 15 MPa to 35 MPa, the linear increase in the Min peak contact pressure of the X-ring is similar to that of the O-ring. When the
Ph is 25 MPa, the Min peak contact pressure of the X-ring and O-ring is equal. These results mean that the fretting sealing characteristics of the X-ring and O-ring are similar under 15–35 MPa. Additionally, at lower pressures (such as 15 MPa), the Max peak Mises stress of the X-ring is similar to that of the O-ring. In comparison, at higher pressures (such as 35 MPa), the Max peak Mises stress of the O-ring is much greater than that of the X-ring. It implies that the failure behavior of forming cracks or elasticity loss inside the O-ring is more likely to occur under high-pressure conditions.
On balance, during 1–2 T, when Ph is in the range of 25–45 MPa, the peak contact pressure of the X-ring increases linearly with the rise in Ph, and the direct proportionality coefficient is approximately equal to 1. The X-ring is more susceptible to crack or elasticity loss under a higher Ph, such as 45 MPa. The effect of Ph on the peak Mises stress decreases when Ph is lower, such as 25 MPa. Furthermore, when the Ph is in the range of 15–35 MPa, the fretting characteristics of the X-ring are slightly superior to those of the O-ring.
4.5. Effect of Pre-Compression Ratio
Pre-compression is necessary to ensure the sealing function of the combined seal structure. Choosing an appropriate Rp can effectively improve the fretting characteristics of the rubber ring. Generally speaking, the Rp of the rubber ring in the static seal is between 10% and 20%, and the Rp allowed in the fretting seal is slightly lower than that in the static seal. Rp’s influence on the X-ring’s fretting characteristics will be investigated in this section. The Af is 1.2 mm, the Cf is 0.05, and the Ph is 35 MPa.
Figure 15 shows the relationship between the peak contact pressure of the X-ring and
Rp during 1–2 T. As the
Rp increases from 10% to 14%, the peak contact pressure increases at all locations. The peak contact pressure at 1 T, 1.25 T, and 2 T increases substantially, while at 1.5 T and 1.75 T increases slightly. This indicates that increasing the
Rp can effectively improve the fretting sealing performance of the X-ring, especially during the inward stroke. Additionally, the peak contact pressure at 1.75 T is always minimal, denoting that hydrogen leakage is most likely to occur at the limit location of the outward stroke.
Rp and
Ph’s effect on the X-ring’s fretting sealing characteristics is similar.
Figure 16 demonstrates the relationship between the peak Mises stress of the X-ring and
Rp during 1–2 T. The peak Mises stress of 1 T, 1.25 T, and 2 T decrease slightly, while the peak Mises stress of 1.5 T and 1.75 T increases significantly when the
Rp increases from 10% to 14%. It implies that decreasing
Rp can effectively reduce the possibility of crack or elasticity loss in the X-ring at the limit location of the outward stroke.
Figure 17 displays the Min peak contact pressure and Max peak Mises stress for X-ring and O-ring at various
Rp during 1–2 T. When the
Rp increases from 10% to 14%, the increasing trend of the Min peak contact pressure of the X-ring is similar to that of the O-ring. The Min peak contact pressure of the X-ring is always higher than that of the O-ring, signifying that the fretting sealing characteristics of the X-ring are superior to those of the O-ring. In addition, the decreasing trend of Max peak Mises stress of the X-ring is similar to that of the O-ring. The Max peak Mises stress of the X-ring is always lower than that of the O-ring, indicating that crack or elasticity loss inside the X-ring is less likely to occur.
To summarize, during 1–2 T, when the Rp is in the range of 10–14%, the peak contact pressure of the X-ring increases with the Rp, thus improving the fretting sealing characteristics. Furthermore, the X-ring’s peak Mises stress at the outward stroke’s limit location increases with Rp, aggravating the degree of crack or elasticity loss. Besides, with Rp in 10–14%, the X-ring has better fretting characteristics than the O-ring.