An investigation on the lubrication mechanisms of the mechanical radial face seals – II: hydraulic balance of the ring Erdem Koc¸ and Emel E mel Ceyhun Sabir Textile Engineering Department, Faculty of Engineering and Architecture, C¸ukurova University, Adana, Turkey Textile Turkey Abstract Purpose – The main purpose of the research work carried out is to investigate the hydraulic balance conditions of the sealing ring of a mechanical radial face seal in terms of the residual load acting on the ring by employing the theoretical model developed mentioned in the first part of the investigation. Design/methodology/approach – The end load balance conditions for the movable seal ring have been examined by considering the residual load acting on the ring under all running conditions. The main lubrication and sealing mechanism is assumed to be due to the existence of the relative tilt between the mating surfaces, which is formed by the bearing misalignment. The aim of the theoretical model developed is to predict the necessary minimum film thickness between the relatively moving surfaces by considering the non-dimensional running (operating) conditions and the geometrical parameters defined. The theoretical model is based on the main differential equation (Reynolds’ equation) which is achieved by adopting the standard finite difference form. Findings – Under the combination of the hydrostatic clamping forces and hydrodynamic restoring forces, an equilibrium position is reached with the seal ring displaced from its central position. At a particular non-dimensional pressure, the seal ring comes into contact with the stationary plate and this limits the upper value of pressure that can be resisted by the mechanical seal type examined without metal-metal contact. With the theoretical model developed, it was found that the minimum film thickness between the realtively moving surfaces could be predicted. Originality/value – This paper provides a considerable scientific contribution to the field of lubrication and sealing aspect of the mechanical radial face seals. The results presented in the first part of the investigation and the remarks outlined in this paper would be considered as a design tool for the seal designers with special reference to ring behaviour under hydrodynamic and hydrostatic conditions. Keywords Mechanics, Sealing processes, Hydrodynamics, Theoretical physics Paper type Research paper
Nomenclature d h ho hd he h h e hmin hmax k r r i r o r r t Ap A
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diameter of compression spring wire clearance cleara nce (film thickn thickness) ess) central clearance between the sealing rings desig des ign n cl clear earan ance ce be betw twee een n th the e rin rings gs wi with th the movable ring central in its end float ring (plate) misalignment h/ho, non-dimensional film thickness he/hd, non-di non-dimensi mensional onal ring misal misalignmen ignmentt minimum minim um film thickn thickness ess maximum maxim um film thickne thickness ss spring rate (stiffness) radius inner radius of the sealing ring outer radius of the sealing ring r /r o, non-dimensional radius (ho 2 hmin)/ho, non-dimensional ring tilt W /P d, pressure area Ap/r 20, non-dimensional pressure area
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Industrial Lubrication and Tribology 59/4 (2007) (2007) 166–171 q Emerald Group Publishing Limited [ISSN 0036-8792] [DOI 10.1108/003 10.1108/00368790710753 68790710753554] 554]
D G F s F s P P d P d W W W r W r W st st W st
b d d u u max max h v
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mean coil diameter for the spring shear modulus spring load F s/(Gdh0), non-dimensional spring load pressure delivery pressure Ph 2d =ðhv r r 20 Þ, non-di non-dimensio mensional nal deliv delivery ery pressur pressure e axial load acting on the sealing ring W h20 =ðhv r r 40 Þ, non-dimensional hydrodynamic load residual load non-dimensio mensional nal residu residual al load acting W r =ðP d r 20 Þ, non-di on ring hydrostatic load acting at the rear of the ring W st =ðP d r 20 Þ, non-d non-dimen imensiona sionall hydr hydrostat ostatic ic load (pressure area) angular misalignment of the ring shaft bearings displacement of ring from the central position d /hd, non-di non-dimensio mensional nal ring displac displacement ement angle ang le aro around und ring, mea measure sured d in the direction direction of rotation from the line x of the ring centre angle of maximum clearance dynamic viscosity of the fluid angular velocity
The preceding part of this paper (“An inve investiga stigation tion on the lubrication lubrication mechanisms mecha nisms of the mecha mechanical nical radial radial face seals – 1. General theory”) Industrial strial Lubrica Lubrication tion and Tribology, Volume 59 No 2, was published in Indu pp. 85-91.
Investigation on lubrication mechanisms of mechanical radial face seals
Industrial Lubrication and Tribology
Erdem Koc¸ and Emel Ceyhun Sabir
Volume 59 · Number 4 · 2007 · 166– 171
Introduction In general, a mechanical radial face seal consists of two surfaces which in operation slide over each other and support the forces that tend to bring the surfaces into contact. Figure 1 shows a general view of a mechanical seal schematically as a model for the theoretical approach. In this type of seal the ring hydraulic balance is achieved by feeding high pressure to the back of the rotating seal ring. The designing procedure here is to load the seal ring lightly from the rear towards the stationary seal face under all running conditions. The major problem in this type of seal is that of maintaining an adequate film tihckness under all running conditions and of ensuring that the seal ring balance is not upset, resulting in an unstable operation, i.e tilting, lifting off or seizure. Therefore, the hydrostatic and hydrodynamic load and moment balance should be achieved. The main mechanisms put forward to explain the generation of pressure between the paralel surfaces have been reviewed in the first part of this study and they are not rep eated here (Sabir and Koc¸ 2007; Dowson and Hudson, 1963; Etsion, 1979; Ludwing, 1976; Nau, 1964; Etsion et al., 1991; Koc¸ 1989, 1994). The th eoretical model to be used in estimating the seal ring performance with special reference to hydrodynamic and hydrostatic load carrying capacity of the seal ring and hydraulic moment acting on the ring as well as the pressure centre positioned has also been outlined in the first part of the investigation. In the theoretical model it is assumed that two adjacent surfaces are seperated by a lubricating film and the relative movement of the surfaces generate a hydrodynamic pressure which maintains the seperation or sealing function. The main lubrication mechanism is the converging – diverging wedge which is formed by the relative tilt of two sealing surfaces. Figure 1 again shows, schematically, the stationary and moving plate/or ring of a typical mechanical radial face seal as well as the two sides denoted as ends 1 and 2. The misalignment or the tilt of the surface is expressed as he at the tip of the ring. This misalignment would be produced by any hydrostatic moment imbalance between the front and rear surfaces of moving element or by any bearing misalignment that existed in the system. As the sealing ring has two surfaces on which the hydrostatic andhydrodynamic pressure generation takes place,it adoptsthe
Figure 1 A theoretical model for a mechanical face seal
position in which the axial net end load will be zero. Hence, the actual position can be determined by the force equilibrium in the axial direction. The net axial load (force) is expressed as residual load (W r). This residual load is calculated by substracting the sum of the hydrostatic load acting at the rear of the ring and the spring compression load from the end load acting at the front of the ring (between the stationary and moving surfaces), since at the front surface of the ring only the hydrodynamic and hydrostatic pressure are effective whereas, at the rear, the combination of the hydrostatic clamping load and mechanical spring load is to be considered. In this theoretical analysis, end 1 corresponds to stationary ring side whereas, end 2 corresponds to the spring side of the moveable ring. By repeating the calculations for the whole range of different combinations of physical misalignment, position of misalignment (u max) and non-dimensional delivery pressure, the effect of these parameters on the ring behaviour may be investigated. Thegeneral theory developed has been outlined in the first part of the study and here, in this part of the investigation, the end load balance conditions for the movable seal ring have been examined by considering the residual load acting on the ring under all running conditions. The minimum filmthickness that could be necessary for the full hydrodynamic lubrication and sealing between the two relatively moving surfaces of a mechanical face seal has also been predicted by applying the model developed.
Theoretical results and discussion End load balance of the sealing ring The residual load is a primarily important parameter on the hydrodynamic and hydrostatic lubrication and sealing machanism of the mechanical radial face seals. Once a seal ring position is known, it is then possible to determine the running clearance for any balancing end load or residual load. The variation of end load (residual load) with seal ring movement in both directions is given in Figure 2 under delivery pressure of 0.5 for a range of misalignment. In the central position (d ¼ 0) there is a net load acting on the ring so as to tend to move the ring towards end 1 for the misalignments up to 0.7. The hydrodynamic load generated on the sealing face with relatively low values of bearing misalignment is lower than hydrostatic load acting at the rear
Investigation on lubrication mechanisms of mechanical radial face seals
Industrial Lubrication and Tribology
Erdem Koc¸ and Emel Ceyhun Sabir
Volume 59 · Number 4 · 2007 · 166– 171
Figure 2 Variation of residual load (end load) with ring movement (tilt effect)
the effect of hydrostatic pressure and spring load are dominant on the residual load acting on the ring. When the sealing elements are subjected to a high delivery pressure, the central position of the ring in its clearance will diappear. Figure 3 shows the relationship between the residual load and ring movement for a range of misalignment at a normalized pressure of unity. In the central position, there is a net loadacting onthe ring clamping the ring towards end 1. The ring runsunbalanced in its clearance. As thering moves towards end 1, the restoring force occurs and at a certain movement the balance is achieved. Further movement in the same direction creates a separating load for all values of bearing misalignment. The effect of delivery pressure on the sealing behaviour can be seen from Figure 4. In the figure, each curve corresponds to a single value of non-dimensional delivery pressure P d and shows the variation of end load with ring movement. Because of the value of non-dimensional misalignement chosen, h e ¼ 0:8, the non-dimensional displacement d is limited to a maximum of 0.2 in each direction. These curves all display the same hydrostatic unbalance shown earlier. For the delivery pressure of 0.3 and down there
side of the ring combined with spring loads. The resultant hydrostatic axial end load tends to act towards end 1 and the sealing ring runs unbalanced at its clearance. As the ring moves towards end 1 (a positive ring movement), hydrodynamically generated forces will come into action which tends to restore the balance. It may be seen that for low values of misalignment the load generation is very small until the ring moves a long distance. For higher values of misalignment substantial loads are generated for small movements of the ring. The hydrodynamically generated pressures exceed the magnitude of hydrostatic pressures and as a result a positive net separating lift is produced. It may be seen that when h e is 0.9, in the central position (d ¼ 0), the load on the ring tends to act towards end 2. The residual load is always positive and as a result the load acting on the ring tends to separate the relative surfaces. The ring runs unbalanced in its clearance. As the ring moves towards end 2 the restoring force occurs and at a certain movement (in this case very small d ) the balance is achieved. Further, movement in the same direction creates a clamping load for all values of bearing misalignment. Another word, for negative movement (towards end 2) increasing ring movement (over 0.1) always increases the hydrostatic clamping load (negative residual load). When there is a tilt of h e ¼ 0:9 on the movable ring face relative to the stationary one, in the central position (d ¼ 0), the ring has a positive residual load of W r ¼ 0:07 which corresponds to 1,148.4 N separating load, whereas with the non-dimensional tilt of 0.7 and 0.5 creates the negative residual loads clamping the ring towards end 1 taking the values of 2 1804.7 and 2 1968.8 N, respectively. In calculating these loads the geometrical and operational parameters were taken as r 0 5cm, h0 20 mm, n 1,000 rpm and h 0.02Pa s. Decreasing the central clearance down to 10 mm increases load up to 4,593.8 N for the relative tilt of the mating surfaces of 0.9 whereas, it takes the value of 7,875 N for h e 0.5. When the ring movement is 0.2 and over there is always clamping load (negative residual load) acting on the ring irrespective of the non-dimensional ring misalignment. Another word increasing the ring movement in negative direction ð2d Þ from 2 0.2 and over the curves corresponding to all h e values become a single line. This means that after the ring movement of 2 0.2 and over, ¼
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Figure 3 Variation of residual load (end load) with ring movement (tilt effect)
Figure 4 Variation of residual load (end load) with ring movement (pressure effect)
Investigation on lubrication mechanisms of mechanical radial face seals
Industrial Lubrication and Tribology
Erdem Koc¸ and Emel Ceyhun Sabir
Volume 59 · Number 4 · 2007 · 166– 171
are positive residual loads acting on the ring separating the surfaces. With the pressure 0.4 and over, at the central position there is clamping load. As the ring moves towards end 1, the hydrostatic end load decreases and a point is reached at which hydrodynamically generated loads balance the hydrostatic forces. The amount of movement neeeded to produce this balance increases as the delivery pressure is increased. The pressure effect can more clearly be detected in examining the dimensional residual load variation with ring movement. When the seal is subjected to approximately 20bar ðP d ¼ 0:15Þ delivery pressure, in the central position, the ring will carry a positive residual load of 2,461 N r ¼ 0:5Þ. When the delivery pressure is increased to 0.6 ðW (78.75bar) the ring will be subjected to 2 2,165.6N (W r ¼ 20:11) residual load clamping the ring under the same geometrical and running conditions mentioned above. The seal ring behaviour under delivery pressure may more clearly be seen from the Figure 5 for the non-dimensional ring misalignment of h e 0.3. In this case for all pressures at the central position (d ¼ 0:0) there are negative residual loads clamping the ring towards the stationary counterpart. This unbalanced condition is deteriorated with the negative ring movement. The movement in the positive direction reduces the residual load reaching zero at different d values depending on the different delivery pressures. For P d ¼ 1, the ring movement of approximately 0.4 towards end 1 produces a zero residual load, which means that the ring load balance is achieved at this point. Since, the misalignment on the relative surfaces is very small (h e ¼ 0:3Þ, the seal ring movement towards end 1 ðþd Þ up to approximately 0.15 demonstrates the same linear variation on the clamping load for all pressure curves meaning that at these running conditions the hydrostatic pressure (at the rear of the ring) is still more effective than the hydrodynamic pressure (on the front surface of the ring). After this point, depending on the nondimensional pressure, increasing ring movement towards end 1 increases the hydrodynamic seperating load, which in turn decreases the residual load giving positive residual loads after certain ring movement. i.e for P d ¼ 0:05, the ring movement of approximately 0.2 balances the ring, whereas for P d ¼ 0:2, the ring movement of 0.35 creates a ring balance after which the positive residual load occurs on the system.
Zero residual load results The previous section gave the variation of net residual load (end load) acting on the seal ring with misalignment and delivery pressure. However, under most running conditions the net end load acting on the ring is small, depending on the spring stiffness of course, and the minumum film thickness under these conditions is of a particular importance. Under all conditions the seal ring was running with no external load supplied. It is relevant, therefore, to extrapolate the curves given corresponding the behaviour of the ring for the position where the net end load is zero. On doing so, it is possible to determine the minimum film thickness between the two relatively moving surfaces. Once this is established, the effect of pressure, u max and tilt on the minimum film thickness can be assessed. Figure 6 shows the minimum film thickness (hmin/hd) variation with non-dimensional delivery pressure P d for different non-dimensional misalignment h e . Generally increasing misalignment decreases the minimum film thickness. It may be noted that for the misalignment of 0.6 and above, there is a maximum delivery pressure for which the seal ring will run without metal to metal contact. This pressure is 8 for a non-dimensional misalignment of 0.6 and 1.85 for a non-dimensional misalignment of 0.9. For low values of P d the minimum film thickness firstly increases with increasing pressure. The reason for this appears to be that a very small amount of pressure produces a small end load which in turn requires a large movement of the ring to generate a corresponding force to balance it. As P d is increased slightly (in all curves) the minimum clearance increases reaching a maximum for P d between 0.1 and 0.5. Thereafter, further increase in pressure reduces the clearance. The combination of spring load and hydrostatic clamping load tends to be higher than the hydrodynamically generated load on the front surface of the seal ring. The limiting vaue of P d for which the ring will run without metal to metal contact is reduced as misalignment is increased. Examining the 0.7 curve, it can be seen that the minimum film thickness is zero when the non-dimensional pressure is around 4.3 (P d 564.4 bar) and beyond that metal to metal contact will occur. For the misalignment of 0.9 metal to metal contact will occur for all values of pressures larger than 1.85 corresponding to 242.8 bar whereas, for
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Figure 5 Variation of residual load (end load) with ring movement (pressure effect)
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Figure 6 Variation of Minimum film thickness with delivery pressure
Investigation on lubrication mechanisms of mechanical radial face seals
Industrial Lubrication and Tribology
Erdem Koc¸ and Emel Ceyhun Sabir
Volume 59 · Number 4 · 2007 · 166– 171
the misalignment of 0.6 metal to metal contact will be inevitable under the non-dimensional pressure of P d 8 (P d 1,050 bar). For all calculations the geometrical and running parameters have been taken as r 0 5 cm, h0 20 mm, h 0.02Pas and n 1,000 rpm. When the central clearance is decreased to 10 mm, the non-dimensional pressure value of 1.85 corresponding to 971.2 bar for h e 0.9 and the non-dimensional pressure value of 8 corresponding to 4,200 bar for h e 0.6. Figure 7 shows the variation of film thickness hmin/hd with the misalignment, h e , for different non-dimensional pressure P d ranging from 0 to 10 at the value of u max of zero. The complex shape of the curves is due to the interaction of the hydrodynamically and hydrostatically generated pressures via cavitation in the oil film. It may be seen that increasing the misalignment or the pressure reduces the clearance. For the pressures of 1 and above, there is a maximum misalignment for which the seal ring will run without metal to metal contact. This misalignment is 0.98 for non-dimensional delivery pressure of 1 and is 0.57 for non-dimensional delivery pressure of 10. It may be seen that with no delivery pressure the variation in clearances is linear varying from 1 at 0 t o 0 a t h e 1. At zero values of misalignment the h e clearance is indeterminate and the values shown here are limiting values for infinitesmally small values of h e . However, very small chamfer machined on the outer edge of the ring would produce a value of hmin/hd 1 at zero misalignment and in practice, at low he values, the curves will diverge from those shown here and tend towards unity, as shown schematically for the 0.1 case by the broken line. It may be seen that for considerably low values of he (very close to zero) the value of hmin/hd does not approach 1 as might be expected. It would appear that for very low values of tilt at the delivery pressures of 0.5 and over, the curves approach point of approximately 0.58. The reason for this appears to be that a very small amount of tilt produces a small end load and so hydrodynamically generated pressures, which in turn require a large movement of the ring to generate a corresponding force to balance the hydrostatic load acting at the back and the spring opening load. The critical value of minimum film thickness depends on the preload on the springs used and the geometrical parameters of the ring. The spring rate (stiffness), mean coil diameter, shear modules of ¼
the spring materials and the diameter of wire are all effective on the clamping load acting at the rear of the seal ring.
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Figure 7 Variation of minimum film thickness with misalignment
Conclusions With the theoretical study carried out for investigating the performance of mechanical radial face seals, the conclusions drawn are outlined below. The load balance of the ring examined is found to be of a primary importance. Most seal rings can float axially in the total end clearance but are minimally prevented from tilting in anydirection. The position of maximum clearance (u max) seemed to be effective on the seal ring lubrication and load balance, particulary with the cavitated region. The seal ring does not run at the centre of clearance; because of the misalignment, it runs to one side. The actual movement varies with delivery pressure P d and the ratio he/hd (tilt). The hydrostatic pressure area at the rear of the ring and the compression spring characteristics are all effective on the ring balance. As a result of the relative tilt between the stationary and movable seal ring faces, the seal ring is subjected to a net hydrostatic endload (combined with spring clamping load), which tends to displace it. This displacement (clamping) generates a hydrodynamic restoring force. Under the combination of the hydrostatic clamping (displacement) forces and hydrodynamic restoring forces an equilibrium position is reached with the seal ring displaced from its central position. As the delivery pressure is increased, the displacemet also increases and at a particular value of the non-dimensional pressure, the seal ring comes into contact with the stationary plate. This limits the upper value of pressure that can be resisted or overcome by this type of mechanical seal without boundary lubrication. With the theoretical model developed, it was found that the minimum film thickness between the relatively moving surfaces could be predicted depending on the relative tilt occuring between two mating surfaces. It has been shown that for a certain bearing misalignment or ring tilt there is a maximum delivery pressure for which the seal ring will run without metal to metal contact. For the non-dimensional pressure of 1 and above, there is a maximum misalignment for which the metal to metal contact occurs. This misalignment is 0.98 for non-dimensional pressure of 1 and 0.57 or non-dimensional delivery pressure of 10. It has been noted that for the misalignment of 0.6 and above, there is an maximum delivery pressure with which the seal ring will run without metal-metal contact. The limiting value P d for which the ring will run without metal-metal contact is reduced as misalignment is increased. For misalignment of 0.9 metal to metal contact will occur for all values of pressures larger than 1.85 corresponding to 242.8 bar whereas, for the misalignment of 0.6 metal to metal contact will be inevitable under the non-dimensional pressure of P d 8 (P d 1,050 bar). So, the theory developed predicts that there will be an upper limit to the delivery pressure for which succesfull operation can be guaranteed. The remarks outlined in this paper and the results presented in the first part of the investigation would be considered as a design tool for the seal designers with special reference to ring behaviour under hydrodynamic and hydrostatic conditions. .
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Investigation on lubrication mechanisms of mechanical radial face seals
Industrial Lubrication and Tribology
Erdem Koc¸ and Emel Ceyhun Sabir
Volume 59 · Number 4 · 2007 · 166– 171
References Dowson, D. and Hudson, J.D. (1963), “Thermohydrodynamic analysis of the infinite slider bearing: Part II, the parallel-surface bearing”, Inst. of Mech. Engrs, Lubrication and Wear Convension, paper 5, pp. 45-51. Etsion, I. (1979), “Hydrodynamic effect in a misaligned radial face seal”, Trans. of ASME, J. of Lubication Tech. , Vol. 101, pp. 283-92. Etsion, I., Palmor, Z.J. and Harari, N. (1991), “Feasibility study of a controlled mechanical seal”, STLE Lubrication Engineering , Vol. 47 No. 8, pp. 621-5. Koc¸, E. (1989), “Analytical and exprimental investigation into the sealing and lubrication mechanisms of the gear ends in pumps”, Wear , Vol. 135, pp. 79-94. Koc ¸ , E. (1994), “Bearing misalignment effects on the hydrostatic and hydrodynamic behaviour of gears in fixed clearance end plates”, Wear , Vol. 173, pp. 199-206.
Ludwing, L.P. (1976), “Face-seal lubrication I. Proposed and published models”, NASA TND-8101, pp. 1-36. Nau, B.S. (1964), “Hydrodynamics of face seal films”, paper presented at Second International Conference on Fluid Sealing, Cranfield, p. F5. Sabir, E.C. and Koc¸, E. (2007), “An investigation on the lubrication mechanisms of the mechanical radial face sealsI: general theory”, Industrial Lubrication and Tribology, Vol. 59 No. 2, pp. 85-91.
Further reading Pape, J.G. (1968), “Fundamental research on a radial face seal”, ASLE Transactions, Vol. 11, pp. 302-9.
Corresponding author Erdem Koc¸ can be contacted at:
[email protected]
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