Calculation of the characteristics of seals with floating rings

Floating rings are widely used in the sealing assemblies of the shafts of pumps and turbine pump units. However, information about the use and design of floating rings is not widely available in the literature and does not satisfy the practical interest in their use. The article touches on questions related to the operating mechanism of seal assemblies with floating rings and the structural realization of these assemblies, and considers questions related to their design. The potential of the computational method in the use of the traditional approach to the calculation of the flow through a seal and the input losses in a groove channel is analyzed and a technique of improving the computational method is proposed.

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In the radial groove seals of a shaft with fixed position of the parts of the stator and rotor groups, the gap in this channel must exceed the misalignment of the rotor relative to the axis of the recess in the housing of the stator in order to prevent contacts between the surfaces of the parts forming the radial groove channel.

From existing standards (for example, [1]), the vibration rate v on the housings of the bearings of pumps with high rotational speed must not exceed 3 mm/sec. For the harmonic vibrations of the rotor, the amplitude of the vibration displacements u = v/[omega]. At a rotational speed [omega] = 600 1/sec, the amplitude of the vibration displacements that is acceptable in the region of the housings of the bearings u = 5 [micro]m. The vibrations of the shaft in the region where the seals are located may be 10 times greater than on the bearings [2]. On the basis of operating experience, the gaps in groove seals are usually set in the range 0.2-0.5 mm (depending on the dimensions of the machine).

With smaller gaps in the seals (so as to reduce leakages), constructions with radially moveable floating rings are used. These support the minimal eccentricity relative to the axis of the rotor and the operation of the seal without any contact with the shaft in the case of radial gaps of 0.1-0.2 mm [2].

The friction surfaces of the front joint of the rings are most often kept in fixed position to prevent relative displacements in the circumferential direction (only one slides against the other in the radial direction with insignificant heat release in the front joint).

The selection of the radial working gaps in seals with floating rings is made depending on the construction of the assembly, the rotational speed of the shaft, the weight of the floating rings, and the material of the parts forming a seal couple.

A seal assembly with floating ring is a device containing a separate sleeve-type annular part with small radial gaps in the channel through which the medium flows and is situated in the cavity of the pocket between the rotor and stator; it is supported by a bearing end face on a body or rotor part and possesses some free play in the diametral plane.

Two basic designs of seal assemblies with floating rings are distinguished.

1. The basic channel through which the medium flows between the sealed part and the floating ring is found lateral to the inner diameter of the floating ring, while the floating ring itself is found in a pocket situated in the stator. Floating rings used in such an operational design may be referred to as stator floating rings.

2. The basic channel through which medium flows between the sealed part and the floating ring is found lateral to the outer diameter of the floating ring, while the floating ring itself is found in a pocket situated in the rotor. Floating rings used in such an operational design may be referred to as rotor floating rings.

Figure 1 a, presents a seal with stator floating ring for protecting the oil trap of the rotor of an airplane gas turbine engine. The working conditions are as follows: sliding velocity 150 m/sec; air temperature 920 K; and pressure differential 1 MPa. Leakage through such a seal is one-seventh that through previously used crested groove seals [3].

Figure 1 b, presents the structural configuration of the seal assembly of the rotor of a gas-turbine engine with rotor floating ring. In this seal, the basic leakage channel is found along the outer diameter of the ring.

Such seal assemblies have constraints which, in terms of sliding velocity and pressure differential, are greater than those of seal assemblies that contain floating rings with basic flow channel of the medium along the inner diameter. These have become widespread due to structural simplicity and low overall dimensions [3].

Advantages of seals with floating rings as compared to groove seals: smaller gaps and, consequently, lesser leakage; tracking of small radial and angular displacements of the shaft by the ring; possibility of effective use of short seal assemblies; reduction of radial forces in the bearings of the rotor.

Disadvantages of seals with floating rings: structural and technological complexity; high cost of assemblies; the presence of an additional seepage channel in the auxiliary front joint of the seal.

Floating rings are widely used in the seal assemblies of the shafts of rotor engines (for example, in pump units) that function with high pressure differentials (up to 40 MPa) and high sliding velocities (up to 250 m/sec), at low and high temperatures (from 20 to 650 K), and in corrosive, explosive, radioactive, low-boiling, cryogenic, and other media [4].

Seals with floating rings are principally used in the assemblies of inter-step and auxiliary seals and sometimes as end seals. An analysis of the costs (including repair costs) over the life cycle of a pump used in an atomic power plant showed that it is best to use face seals as end seal assemblies in the case of circumferential rotational velocities of the shaft up to 50 m/sec, while at velocities greater than 50 m/sec, seals with floating rings should be used [5].

A centrifugal force appears in the case of eccentric displacement of the shaft in the recess of the body of a floating ring with one end tightened to the reciprocal part of the stator (rotor) in the narrowed part of the radial channel between the floating ring and the rotor; the force arises due to the increase in the pressure differential in this part of the channel [2]. Under the effect of hydrodynamic forces and the inertia of the weight of the body and the medium, the ring shifts in the radial direction (without loss of contact in the front junction) until equilibrium of the equivalent radial forces (created by the pressure in the channel and the opposing friction force in the front junction) is attained. The radial hydrodynamic force F, which is proportional to the eccentricity of the axis of the ring relative to the axis of the shaft, supports self-centering of the ring if it exceeds (in terms of magnitude) the friction force R = fF in the front contact (f is the friction force in the front pair).

The friction and inertial forces are usually low by comparison with the hydrodynamic forces. The processes that occur in the groove channels of floating rings (particularly in the case of a viscous liquid) are analogous to the processes in gaps of mildly loaded radial plain bearings.

The advantages of seals with floating rings are realized when the following two conditions are satisfied: first, the centrifugal force in the groove channel caused by hydrodynamic effects exceeds the friction force on the contact end face; second, the magnitude of the precession of the shaft is contained in the difference between the diameter of the recess of the ring and the diameter of the shaft (including the influence of the nutation angle of the shaft at the site where the seal is situated). If these conditions are not satisfied (especially the second condition), contact wearing away of the cylindrical surface occurs in the longitudinal groove channel and the mated surfaces in the front pair.

The operating characteristics of a floating ring depend on the form and dimensions of the groove channel (in the circumferential and axial directions), which are influenced by the current eccentricity and nonparallelness of the axes of the ring and rotor and the deformation of the body of the floating ring under the effect of the load pressure with respect to the outer and inner diameters. For most floating rings, heat release in the front joint does not affect the shape of the sealing groove channel (one exception are seal assemblies of short service life with floating rings without clamping to prevent circumferential displacement used, for example, in the turbine-pump units of single-use rocket engines). A calculation of the thermal deformations of such rings may be performed using the technique of [6].

Let us consider the design of floating rings using as an example stator floating rings, which are the type most often used in practical applications. In the calculation, we will use the load factor K of the floating ring, which is equal to the ratio of the contact pressure q in the front pair to the sealed pressure differential [DELTA]p, i.e., K = q/[DELTA]p.

With respect to axial compression, floating rings, like face seals, are distinguished in terms of loaded and unloaded. In the case of a standard load in the design regime, the following working schemes are possible: with contact between the surfaces in the front coupling (as in the case of ordinary face seals with K [greater than or equal to] 1); without contact between the surfaces in the front coupling (as in contact-free face seals with K < 1). Stator unitized floating rings are used both with clamping systems to prevent circumferential shift and tightening spring-actuated systems as well as without such systems (Fig. 2).

Dependences based on the Amantons-Coulomb law are used to describe the friction processes between the faces of seals functioning according to the K [greater than or equal to] 1 design.

Thus, friction coefficients are used in calculating the forces and power costs in a front sealing junction, where the use of these coefficients involves a recognition of the existence of a solid contact in the junction of a pair relative to the displaced sealing surfaces of the ring. Dependences based on Darcy's law for the flow of liquids and gases in a porous medium are used to calculate the leakages through a front sealing joint. In calculating the specific pressure in a front coupling, it is necessary to know the form of the coupling between the surfaces of the contact joint.

Deformable U-shaped floating rings are of significant interest [2,7-9]. Seal assemblies with such rings (Fig. 3) are effective when used in corrosive, explosive, radioactive, low-boiling, cryogenic, and other media that do not contain abrasive particles.

The body of a floating ring becomes deformed (buckles) with maximal sagging near the flange from the side of the low-pressure cavity (cf. Fig. 3) when a uniformly distributed pressure acts on the outer surface of the ring and a pressure that is variable along its length acts on the inner surface. The flow section of the groove channel then decreases and leakage of media is reduced. The form of the flow channel becomes convergent, and the load-carrying force in the channel grows with radial shifting of the ring. Moreover, the front coupling of the ring with the body part also becomes convergent and is realized along a narrow collar on the inner diameter of the plane contact surface. The specific load in the front coupling does not exceed the pressure of the sealed medium, as a result of which the radial mobility of the floating ring grows.

With this effect of the pressures on a thick-walled ring (cf. Fig. 2b), the effect produced by deformation of the ring will be caused by the action of the moment [M.sub.ben], the forces [Q.sub.1] and [Q.sub.2], and the rotation of the ring relative to the center of gravity. In this case, the dimension of the flow section of the groove channel remains nearly invariant, though the form of the flow channel becomes convergent and the load-carrying force in the channel and leakage of medium both increase. The front coupling of the ring with the body part is divergent and is realized along a narrow collar on the outer diameter of the plane contact surface. The specific load and friction force in the coupling increase and the radial mobility of the floating ring drops.

In most cases, the flow of medium in a radial groove channel is turbulent and the empirical relationships that are employed in the design of groove channels are used to describe the losses of pressure in the channel and the flow rates of medium through the channel. The processes in the front joint of the surfaces of the ring with the reciprocal parts are similar to processes in face seals at low (or zero) rotational speeds of the shaft; these processes are unimportant when a seal assembly functions with a floating ring.

It is not possible to determine the dimensions and form of a radial groove channel in a seal with U-shaped floating ring by means of approximate methods on the basis of the theory of elasticity. To solve this problem, it is necessary to employ a joint solution of the elasticity and hydromechanics equations with the use of the method of finite elements, for which a computational program has been developed [8].

The calculation consists in determining the hydrodynamic characteristics of the flow of a medium, including the pressure diagrams in the radial groove channel, taking into account the influence of variations in the pressure diagram on the geometry of the ring corresponding to some (new) equilibrium state. Thus, a realization of the solution is performed by the method of successive approximations.

In the initial computational scheme, a load acting on the inner cylindrical surface of the ring corresponds to a distribution of the pressure in the concentric undeformed groove channel. Following a calculation of the deformations of the ring, the pressure distribution in the deformed groove channel is determined, the load is redetetermined, and the calculation of the deformations is repeated. The number of iterations in the computational cycle is governed by the specified precision.

The flow regime of liquid in a constricting groove channel is self-similar turbulent.

The distribution of pressure in a constricting groove channel is determined by a solution of the equations of turbulent isothermal flow of an incompressible viscous liquid in a short concentric annulus with fixed walls. The influence of the rotation of the shaft on the flow rate and distribution of pressure at the inlet to the groove channel and along its length is taken into account by a correction to the friction coefficient of the liquid for an averaged gap in the channel [10, 11].

The body of a floating ring is an axisymmetric body of revolution made of an isotropic material.

The floating ring is kept fixed to prevent displacements in the axial direction by attaching one or more nodes of a finite-element grid.

A mathematical model for the solution of the problem is described in [8]. The calculation is performed until a specified condition of precision of the calculation is satisfied, with respect to the radial gap and with respect to a given difference in the values of the pressure [DELTA]p in the constructed annular elements of the space of the groove channel.

The computational method is based on the dependence [DELTA]p = [DELTA][p.sub.in] + [DELTA][p.sub.fr] + [DELTA][p.sub.out], which may be represented in the form

[DELTA]p = 0.5[rho][w.sup.2.sub.in][[zeta].sub.in] + 0.5[rho][w.sup.2.sub.x][C.sub.fr] + 0.5[rho][w.sup.2.sub.x][C.sub.out],

or, with certain simplifying assumptions,

[DELTA]p = 0,5[rho][w.sup.2.sub.x]([[zeta].sub.in] + [[zeta].sub.fr] + [[zeta].sub.out]),

where [DELTA][p.sub.in], [DELTA][p.sub.fr], and [DELTA][p.sub.out] are the pressure drop in the inlet and outlet segments and along the transport length of the groove channel; [w.sub.x], axial flow rate of medium in the channel; and win, flow rate at inlet to channel (the flow rate [w.sub.x] with the magnitude of the swirling of the flow at the inlet to the groove channel superimposed on its value [10]). The values of the loss coefficients at the inlet, outlet, and along the transport length of the groove channel [C.sub.in] = 1.5, [C.sub.out] = 0.3, and [C.sub.fr] = [lambda]/2h are used according to the traditional techniques [2, 4, 10]; the initial value of the friction coefficient of the channel [lambda] = 0.04 is selected as for a self-similar turbulent longitudinal flow of medium. The Yamada equation [11] is used to calculate the reduced velocity of spiral flow of medium in the channel and to take into account the influence of the rotation of the shaft on the value of [lambda].

The program enables us to calculate the pressure diagrams and flow rates in channels of "unit width" and thus obtain a picture of the flow of medium in an eccentric channel.

The results of calculations of a seal assembly with floating ring (Fig. 4) with different thicknesses [delta] of the wall were compared to the data of experimental studies (Fig. 5). The tests were performed in water with a pump plant functioning at rotational speeds of the shaft up to 20000 rpm.

There is only a slight difference in the nature of the computed relationships (forms of groove channel and forms of pressure diagram) for different thicknesses 8 of the walls of the rings (Fig. 6). This is also confirmed by the small difference in the nature of the obtained computed curves of the flow through a seal for different thicknesses of the walls of the floating ring between the flanges (cf. Fig. 5). The shortcomings of the traditional method of calculation of the characteristics of the flow of medium in a groove channel with which such results are associated are demonstrated in [12].

The advantages of the software product that has been described are that a representation of the nature of the form and dimensions of a deformed groove channel as well as a representation of the nature of the pressure diagram in such a channel and a representation of the trends in their variation are obtained for the first time by a computational approach. To perform a more exact computation, the method of flow constants [13] must be used to describe the losses along the length of the groove channel, while the losses of pressure at the inlet to the groove channel are determined by means of the techniques of [14,15].

Thus, a calculation performed by the method of flow constants for a ring with thickness of the wall 8 = 7.0 mm with loading pressure differential [DELTA]p = 5 MPa has shown that with a computed leakage of medium (cf. Fig. 5), the magnitude of the gap in the groove channel must be [h.sub.0] = 0.056 mm. Using the traditional method of calculation for this case, a gap [h.sub.0] = 0.053 mm is obtained. The differences in the results may be significantly greater in a calculation of rings with greater deformations in their bodies.

However, it is difficult to implement a method of calculation based on flow constants due to the insufficient volume of available data for obtaining the loss coefficients of the potential flow rate of medium in channels of different lengths with gaps from 0.02 to 0.1 mm.

Conclusions

1. The use of the nature of deformations to the body of a floating ring caused by the pressure differential affecting a seal assembly is one of the promising directions for optimization of the functional qualities of seal assemblies with floating rings.

2. The solution of the problem of designing deformable floating rings can be achieved only with the joint solution of a problem of elasticity and hydromechanics by means of the method of finite elements.

3. Calculations of the flow rate through a seal assembly with floating rings according to the traditional method yield results that significantly differ from those obtained in experiments.

4. A more precise solution of the problem of designing floating rings may be obtained if the method of flow constants [13] is used in the description of the losses along the length of the groove channel, and if losses at the inlet to the annulus are determined by the techniques of [14, 15].

5. To achieve a more precise calculation of deformable floating rings, studies must be performed to determine the coefficients of losses of the potential flow rates of medium in channels of different lengths with gaps from 0.02 to 0.1 mm.

REFERENCES

[1.] ANSI/API Standard 610, Centrifugal Pumps for Petroleum, Petrochemical, and Natural Gas Industries, 10th ed., Oct., 2004.

[2.] V. A. Martsinkovskii, Groove Seals. Theory and Applications [in Russian], Izd. Sumsk. Univ., Sumy (2005).

[3.] S. V. Falaleev and D. E. Chegodaev, Contact-Free Face Seals for Aircraft Engines [in Russian], MAI, Moscow (1998).

[4.] A. I. Golubev and L. I. Kondakov (eds.), Seals and Seal Technology: Handbook [in Russian], Mashinostroenie, Moscow (1994).

[5.] B. Brekht, U. Brunks, V. Kokhanovskii, et al., "Analysis of costs over the life cycle of a high-capacity atomic power plant pump," Vestn. Yuzh.-Ural. Gos. Univ., No. 1, 126-135 (2005).

[6.] V. A. Mel'nik, Face Seals of Shafts [in Russian], Mashinostroenie, Moscow (2008).

[7.] USSR Inventor's Certificate 1451385A1, "Shaft seal," F16J 15/44 (1987).

[8.] V. A. Khvorost, S. V. Pryadko, V. A. Mel'nik, et al., "Method of calculating floating seals," Vestn. Mashinostr., No. 6, 23-25 (1987).

[9.] V. A. Mel'nik, "Contact-free groove seals of a rotor with controlled form of convergent groove," Khim. Neftegaz. Mashinostr., No. 5, 28-31 (2003).

[10.] V. A. Martsinkovskii, Contact-Free Seals of Rotary Engines [in Russian], Mashinostroenie, Moscow (1980).

[11.] Y. Yamada, "Resistance of a flow through an annulus with an inner rotating cylinder," Bull. JSME, 5, No. 18, 302-310 (1962).

[12.] V. A. Mel'nik, "Calculations of leakages in radial groove seals of rotary machines. Part 1. Method based on calculated and empirical coefficients of local pressure losses," Khim. Neftegaz. Mashinostr., No. 9, 35-39 (2009).

[13.] V. A. Mel'nik, "Calculations of leakages in radial groove seals of rotary machines. Part 2. Method of flow constants of grooves," Khim. Neftegaz. Mashinostr., No. 11, 20-22 (2009).

[14.] A. A. Lomakin, "Calculation of critical number of revolutions of rotor and conditions to assure dynamic stability of the rotors of high-pressure hydraulic machines, taking into account the forces arising in the seals," Energomashinostr., No. 4, 1-5 (1958).

[15.] V. A. Mel'nik, "Calculation of radial forces in smooth groove seals of a shaft," Khim. Neftegaz. Mashinostr., No. 9, 19-22 (2011).

V. A. Mel'nik

VIGO SMIT Company, Moscow, Russia; e-mail: vam37@list.ru. Translated from Khimicheskoe i Neftegazovoe Mashinostroenie, No. 8, pp. 33-37, August, 2013.