Discriminative Features of Abnormities in a Spiral Groove Gas Face Seal Based on Dynamic Model Considering Contact

It is a difficult task to root the cause of the failure of a gas face seal because different causes may result in similar observations. In the work being presented, the discrimination of multiple types of abnormities in a spiral groove gas face seal is studied. A dynamic model is employed to analyze groups of cases in order to uncover the dynamic behaviors when the face contact is induced by different mixtures of abnormities, whose discriminative features when motion and contact are monitored are studied and uncovered. A circumferential-pattern-related oscillation phenomenon is discovered, which is extracted from contact information and implies the relative magnitude of the moment on stator and the rotor tilt. The experimental observation shows consistent results. It means that the grooves (or other circumferential patterns) generate useful informative features for monitoring. These results provide guidance for designing a monitored gas face seal system.


Introduction
As a kind of non-contacting mechanical face seal, gas face seals run with their relatively rotating faces separated by micro-scale gas films when working properly, and are thus expected a long service life [1]. However, errors from manufacturing, assembling, and servicing, along with perturbations of operating conditions, may result in a seal failure [1][2][3][4]. In most cases, the failure is led by the damage of the end faces when a severe friction beyond the designed level occurs [2].
In order to obtain detailed real-time information, efforts have been made to implant sensors or special measurable structures inside the mechanical face seals (including gas face seals). Researchers have realized seal ring temperature monitoring [5][6][7][8], motion or face separation monitoring [9][10][11][12][13], film pressure field monitoring [8,14], acoustic emission monitoring [15][16][17][18][19][20][21][22], etc.. However, it is still a challenging task to root the cause of the phenomena observed through the sensor(s). For example, one can find abnormal friction through an increased temperature or acoustic emission power [6,15], but must do more to further tell the cause of the abnormal friction. Because implanting sensors involves revising the seal structure and weakening the seal performance, the type of sensors should be carefully decided.
Studies have been working on finding out the seal behavior dependence on the potential abnormities in the seal system through numerical simulation. Miller et al. [23] established a method coupling the lubrication and kinetic equations and analyzed the tracking of a flexibly mounted stator to a 20 μrad rotor tilt. Green et al. [24] studied the coned gas seal responses to initial stator displacements. Lee et al. [25] studied the seal behavior when a 20 μrad tilt was applied to both rings and found that tilting both rings led to slight periodic axial fluctuation, whereas tilting a single ring does not. Hu et al. [26] conducted a parametric study of the  35:22 secondary seal. Chen et al. [27] discussed the impact of gas film thickness disturbance of a gas face seal. Varney et al. [28] took eccentricity, rotordynamics, face contact and inertial maneuver loads into consideration, and described the calculation method for various faults including angular misalignment, eccentric rotating imbalance, and axial offset of the rotating seal element center of mass. Luo et al. [29] studied the dynamic characteristics of an upstream pumping mechanical seal under different extrusion fault degrees. He et al. [30,31] analyzed the seal lubrication and wear under vibration loading. Jia et al. [32] analyzed the impact of the groove manufacturing error in high-speed mechanical face seal. Jin et al. [33] found that specific sealed fluid temperature may cause the two-phase mechanical seal to be unstable. The majority of existing studies mainly focused on the respective impact of single type of abnormity, at least not providing how the combination of different types of abnormities affects the sensor observation. However, the coexistence of multiple faults is the usual trouble in practice, which should be studied for finding out the approaches to diagnose them with specified sensor(s). Besides, the circumferential nonuniformity may also appear in the signals to imply certain modes, and will be paid attention to in the presented study.
Taking the spiral groove gas face seal as an example, the dynamic behaviors when the face contact is induced by different mixtures of common abnormities are simulated. Considering motion monitoring and acoustic emission monitoring, which are recently regarded as of great advantage in terms of the information carried, the features for discriminating the abnormities are analyzed in terms of how the different types of abnormities and the seal geometrics interact.

Dynamic Model of Spiral Groove Gas Face Seals
The structure of the spiral groove gas face seal studied is shown in Figure 1. A stator with a planar face is flexibly mounted on a fixed seat, and a rotor with spiral grooves on the face (as shown in Figure 2) is fixed to the rotating shaft. The faces of two rings form a tribo-pair, which is full-film lubricated during normal operations.
Three degrees of freedom (DOFs) of the flexibly mounted stator are considered in such a model (see Figure 3): axial displacement z s (which increases with separation), and tilt angles γ xs and γ ys around axes X and Y , respectively. The rotor face is usually not perfectly perpendicular to the shaft axis, and the tilt angle is denoted as γ r . The motion of rotor, similarly represented by z r , γ xr and γ yr , are regarded as given.
Generalized displacements are defined below:  The relative generalized displacement, U Rel , determines the clearance distribution as: Eq. (4) is defined on an annulus area, A = x, y |r i ≤ x 2 + y 2 ≤ r o , which is also the domain where gas pressure and contact pressure are defined. h spr is the groove depth. δ is equal to 1 in grooves, and is equal to 0 elsewhere. h coning is the tap height of coning (counting the faces of both rings).
Considering the gas as ideal and inertialess with constant temperature and viscosity, and the flow as laminar flow with non-slip boundary, the absolute gas pressure in the film, p, is governed by the average flow Reynolds equation [34]: where t is the time, r and θ are the radius and angle in polar coordinates, respectively, and µ is the gas dynamic viscosity. ϕ is the flow factor calculated as Eq. (7) [ [34]].
The transient leakage can be calculated as where Ŵ i is the circle of the inner radius. In practice, only the average leakage makes sense.
The contact is simulated with a Chang-Etsion-Bogy (CEB) contact model. The contact is represented with a pressure, p c , depending on local clearance, h , as Eqs. (9) and (10) [35].
where, the mated faces are treated as an ideal rigid smooth surface and an equivalent rough surface with the parameters below: E is Young's modulus, η s is the asperity density, R s is the average radius of asperity tips, σ s is the standard deviation of asperity height, w s is the mean of asperity height beyond the nominal plane, ω c is the critical interference at which the plastic deformation initiates, and p m is the maximum contact pressure. φ(·) represents the probability density function of the standard normal distribution.
The support through the springs and secondary seal is modeled as providing linear stiffness and damping [ [23], 35,36]. Therefore, the stator movement is governed by: where, M = diag(m, J , J ) , C s = diag c zs , c γ s , c γ s , and K s = diag k zs , k γ s , k γ s . The generalized force, Q, includes the force from the tribo-pair (gas film and contact) and a counterbalance which makes Q = 0 when U = 0 . P is composed with the factors concerned which act as force or moment. The system with lubrication, contact, and kinetics coupled was solved by calculating Eqs. (1) to (13) using finite element method. The geometry was meshed into 1344 quadrilateral elements with quadratic Lagrange shape function. A stationary solve of p is first obtained at U Rel = 0 . Then, a transient calculation is conducted, with the abovementioned stationary solve as the initial value of p and a perfect tracing status as the initial value of kinetic variants. The parameters are listed in Table 1.

The Moment on Stator and the Rotor Tilt with Different Relative Magnitudes
Rotor tilt, represented by γ r , exists widely in seals and was studied here. In normal cases, this affects the seal little thanks to the well-designed tracing mechanism, while a usual situation is that the flexible support performs worse than expected, represented as a factor Q s scaling the support stiffness and damping. Another common problem is the circumferential asymmetry of the stator and its supports [ [10]], modelled with a moment around axis X , M x , exerted on the stator.
With the support parameters scaled to Q s = 10 times, a 7.2 N·m moment on the stator and a 4 mrad tilt on the rotor were mixed with varying weights (see Table 2), and the dynamic responses to the mixtures were calculated. Axial force F z and tap height h coning are not considered. These cases will be referred to as Group 1.
The results of Group 1 are listed in the last two columns of Table 2 and illustrated in Figure 4. The figure includes the three dimensions of the generalized stator displacement and the contact force, along with frequency spectrums obtained by Fourier transform exhibiting their oscillation components. Three aspects of phenomena are uncovered from the results: 1) Strong tracing. The motion of the stator is very close to that of the rotor (as long as the latter exists). 2) Fluctuations on shaft revolution period. The amplitudes of two angular stator DOFs increased with rotor tilt due to tracing. As for axial displacement and contact forces, neither isolated M x nor γ r led to fluctuation on the period of shaft revolution, but their combination did. Besides, the coexistence of M x and γ r leads to smaller leakage.

Parameters Values
Outer radius r o (mm) 61.6 Inner radius r i (mm) 51.6 Spiral groove inner radius r spr (mm) 55.5 Gas dynamic viscosity µ(Pa · s) 1.8 × 10 −5 Gas density under 0.1MPaAρ kg/m 3 1.2 Absolute gas pressure at inner radius p i (MPa) 0.1 Absolute gas pressure at outer radius p o (MPa) 0.5 Land clearance at zero displacement h 0 (µm) 1.93 Rotation speed n ω (r/min) 1200 3) Circumferential-pattern-related oscillation. In Case 1-1, M x induced a 12th harmonic in motion and contact (particularly distinct in contact), which corresponded to the 12 spiral grooves on the rotor face. This was not observed in Case 1-7 where only γ r affected the seal. Similar oscillations existed in other cases but were dispersed into multiple harmonics and could be intuitively described as shifting left with increasing rotor tilt weight. Such harmonics will be referred to as "circumferential-pattern-related oscillation" for brevity in this work. Though similar appearance of harmonics has been adopted as significant informative features in the field of bearings [37,38], the phenomenon of dispersing and shifting found here has not been noticed in the existing research of mechanical seals, and will be focused later.

Scaled Support Stiffness and Damping
The stator is flexibly supported by the springs and secondary seal, which inevitably suppresses the tracing behavior [23,26]. This magnifies the impact of rotor tilt because it actually takes effect upon the seal system through tracing errors. The unexpected performance of the supports, especially the secondary seal, has been considered a significant cause of failure [1,2,39]. See Table 3, the scaling factor Q s of supporting stiffness and damping were changed, forming Groups 2a (with the rotor tilt changing reciprocally) and 2b (with the rotor tilt unchanged). The results are listed in Table 3 and illustrated in Figure 5.
Although the motion of the stator is always close to that of the rotor, a greater Q s leads to a weakening of the tracing ability, and thus magnifies the impact of rotor tilt. The abovementioned shifting of circumferential-patternrelated oscillations also show up in the results, and their ineffective in discriminating the influence of γ r and Q s can be uncovered by Group 2a, where a measurement for the motion of the stator is necessary.

Scaled Moment on Stator and the Rotor Tilt
In Section 3.1, cases were formed by mixing the moment on stator and the rotor tilt by weights whose sums are fixed to 1. As another dimension, Group 3 (shown in Table 4) was generated by scaling the magnitudes of M x and γ r based on Case 1-2. The results are listed in Table 4 and illustrated in Figure 6, showing that: (1) When the magnitudes scaled up, the fluctuation of generalized displacement and contact force increased. Moreover, the scaling up increased the duration of contact in each shaft revolution, and eventually led to a continuous contact instead of an intermittent one. (2) However, the frequency band in which the circumferential-pattern-related oscillations distribute does not shift.

The Varying Axial Force
The axial compactness change, which may be induced by an axial size error, is modelled by a force exerted on the stator. Group 4, shown in Table 5, was generated based on Case 1-2 by adding varying axial forces F z on the stator. The results are listed in Table 5 and illustrated in Figure 7. Besides the direct impact on leakage, the results show: The mean of F c changed with axial force monotonically, reaching a minimum at −50 N. This was caused by two opposing mechanisms: ① A force pushing the stator towards the rotor compresses them to induce contact, as a straightforward result. ② A force pulling the stator away from the rotor magnifies the effect of existing rotor tilt and/or moment on stator, thus aggravating contact.
This means that separating the stator with an axial force may not always alleviate or eliminate contact.
As the axial force pushed the stator towards the rotor, the amplitude of circumferential-pattern-related oscillation decreased and eventually became indiscernible. Until getting indiscernible, the circumferential-patternrelated oscillations did not shift, which demonstrated an independence from axial forces.

The Varying Coning Tap Height
Coning is a common type of deformation in gas face seal, and directly affects the hydrostatic effect of the seal. Group 5 was generated based on Case 1-2 by adding varying coning tap height h coning , as shown in Table 6. The results are listed in Table 6 and illustrated in Figure 8, showing that a divergent coning aggravates contact, and a convergent coning prevents contact. The coning tap height has little influence on the periodic fluctuation and harmonics.

Time-frequency Domain Analysis
The results have shown that if the moment on the stator has comparative impact (compared to the tracing error for rotor tilt) and there is not a strong pushing axial force, the high-order harmonics resulted from the spiral grooves would take place. One of their important characteristic is that with the relative impact of the rotor tilt increases, their corresponding components on the frequency spectrum disperse and shift left, and is eventually submerged in the low-order components. Such oscillations only take up an extremely small share in the motions; however, it may be distinct enough in the fluctuation of contact force when contact takes place. We introduced the empirical mode decomposition (EMD) and Hilbert-Huang transform (HHT) to perform a time-frequency inspection on the circumferentialpattern-related oscillations. The EMD was first applied     to the contact forces to expose the high-order harmonics in the 1st-order intrinsic mode function (IMF), whose instant frequency were then estimated with HHT [40]. The instant frequency obtained by HHT was smoothed with a Gaussian function with a kernel of π/6ω. Figure 9 shows the results for Group 1 (only the first three cases) and Group 3. The abovementioned "dispersing" is actually a time-varying instant frequency, which is lower than 12th when the contact reaches maximum, and is higher than 12th in the opposite phase (as long as they are discernible). However, the oscillations are obviously weaker (Case 3-3) or even indiscernible (Cases 1-2, 1-3, 3-1 and 3-2) where they show or should have shown the higher instant frequency. These are the reasons why the frequency distribution showed a left-shifting (compared with Case 1-1) in Figures 4 and 6, and will be referred to as a "masking" effect.
Then, the "unmasked" or intrinsic characteristic is that the instant frequency goes lower when the contact reaches maximum and goes higher in the opposite phase. As the relative impact of the rotor tilt increases, the amplitude of such fluctuation of the instant frequency goes greater.
This means that one can use such feature as an evidence in inferring the seal status: if the oscillations concentrate near the 12th harmonic, then the moment on the stator should be the main cause; otherwise the main cause should be the rotor tilt or the stator support, but they cannot be further discriminated. The feature has enough amplitude for being recognized only in the contact force, but the contact force cannot be directly measured, so the related measurable objects such as torque and acoustic emissions should be considered, and enough frequency-domain resolution should be ensured.

Generalization for More Face Designs
Although the simulations were performed with a spiral groove face seal with 12 grooves, the mechanisms of the phenomenon and regulations found do not rely on the specific groove count or type. Here, the analysis of two cases with different face designs as illustrated in Figure 10 are presented, one with 15 grooves instead of 12 and one using T-shape grooves.
The results are shown in Figure 11. In Case 6-1, where the groove count is 15, the abnormity parameter of Case 1-2 is used. The contact is intermittent, and the circumferential-pattern-related oscillation still exists near 13th harmonic, which can be explained by the abovementioned dispersing (around 15th harmonic) and masking (higher harmonics masked due to intermittent contact) effects.
In Case 6-2, the 12 grooves are substituted with T-shape grooves (9 μm depth in the center region and 6 μm depth in the wings). Because their hydrodynamic effect is weaker than that of the spiral grooves, M x and γ r are halved to M x = 6.3 N · m × 0.5 = 3.15 N · m and γ r = 0.5 mrad × 0.5 = 0.25 mrad . The harmonics are similar with those in Case 3-3 where contact is continuous.
Therefore, it is demonstrated that the phenomenon and regulations found is general for multiple face designs.

Experimental Observations
Experiments were conducted to study the seal behaviors in abnormal conditions [ [15]]. The test rig is of a doubleface structure, where the rotor is matched with two stators with its two working faces. Only the outer tribol-pair was controlled and monitored.
In order to induce face contact against the resistance of gas film stiffness, a load mechanism was appended to the stator, as shown in Figure 12, which exerted a combination of F z and M x when weights were loaded, as listed in  Table 7. With rotation speed and pressure fixed at 1200 r/ min and 3 atmG, respectively, the mass of weights loaded varied from 1 kg to 4 kg. The face contact was monitored by acoustic emission (AE) sensors; the signals from the one which was directly mounted to the stator were used. The short-time rootmean-square (RMS) of the high-pass filtered AE signals was calculated to represent the instant contact strength, and then processed with Fourier transform to extract the oscillation components, similar to what was performed with the simulated results in Section 3.
The results are shown in Figure 13. With the increase of loads, the spectrum tends to shift and concentrate on  the 12th oscillation. This is because that there was an increasing M x , while the rotor tilt γ r brought by uncontrolled manufacturing and assembling errors remained fixed. Therefore, the regulations found by simulation are consistent with experimental observation.

Conclusions
The discrimination of common abnormities in a spiral groove gas face seal is studied through numerical simulation. A dynamic model for spiral groove gas face seal with contact considered is employed to simulate groups of cases in order to uncover the discriminative features of types of abnormities, including the rotor tilt, the moment and force on the stator, the scaling of flexible support stiffness/damping, and the coning tap height. Conclusions are drawn as below: 1) The relative motion between the stator and the rotor takes only a small share compared to their absolute magnitude and is thus submerged when the latter is monitored. More information can be afforded by contact, which is necessary for discriminating the cases where the rotor tilt is at the same value but the state of the stator flexible support differs. 2) A phenomenon of circumferential-pattern-related oscillation is newly found, and is demonstrated by experimental observation. Only in the dynamic contact information may it be discernible. It exhibits fluctuating instant frequency, which intrinsically goes lower when the contact force reaches maximum and Table 7 The force and moment exerted by the load mechanism Mass of the weights loaded (kg) goes higher in the opposite phase, the latter of which may be "masked" by the contact intermittence. This means that the grooves (or other circumferential patterns) can be helpful in monitoring or even intentionally designed for it.