Undesired acoustic emissions of mechanical face seals: Model and simulations

Tribology International 71 (2014) 125–131

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Undesired acoustic emissions of mechanical face seals: Model and simulations C. Braccesi, M.C. Valigi n Dipartimento di Ingegneria Industriale, DIN, via G.Duranti, 93-06125 Perugia, Italy

art ic l e i nf o

a b s t r a c t

Article history: Received 31 May 2013 Received in revised form 7 November 2013 Accepted 14 November 2013 Available online 1 December 2013

Mechanical face seals are used with most types of mechanical equipment, thus understanding the behavior of sealing systems is required for improved performance. The present paper investigates a type of seal utilized in automotive cooling water pumps, which, under particular service conditions, generates undesired acoustic emissions and manifests malfunctioning. The problem is examined through a lumped parameter model together with a mixed friction tribological model. Numerical simulations demonstrate that the phenomenon is caused by the insurgence of stick-slip vibrations during shaft deceleration. In addition, the stability threshold is investigated and the influences of some design parameters are evaluated. & 2013 Elsevier Ltd. All rights reserved.

Keywords: Mechanical face seal Ringing phenomenon Stick-slip Lumped parameter model Mixed friction

1. Introduction Mechanical seal is a device that helps join systems or mechanism together preventing leakage, containing pressure, excluding contamination. The applications for industrial products are innumerable such as for pumps, mixers, dryers and other specific equipment (e.g. [1–6]). In this paper an outside pressurized mechanical face seal in silicon carbide (SiC) and carbon with a primary rotating ring and a spring mechanism needed to hold the annular surfaces together, is investigated (shown in Fig. 1). It is used in automotive applications, having water as a cooling liquid. The mechanical face seals are usually composed of two mainly flat rings, in relative motion, separating a pressurized fluid from the atmosphere, with a compression spring and a drive mechanism. Typically, they run in a mixed lubrication region defined by a given value of the duty parameter G [7]. However, if the leakage rate of the seal rises, hydrodynamic lubrication takes a part in the sliding contact. In any case, seals may operate in any of the following three lubrication regimes according to A.O. Lebeck's principles [1]:


Full film lubrication: seals develop a significant film thickness, so that the entire load is supported by fluid pressure. In such

n

Corresponding author. E-mail addresses: [email protected] (C. Braccesi), [email protected] (M.C. Valigi). 0301-679X/$ - see front matter & 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.triboint.2013.11.014







cases, almost no touching occurs, friction is low, and there is very little wear. Mixed lubrication: this is probably the most common operation mode for many seals. Mixed friction is characterized by the fact that a part of the load is carried by actual mechanical contact, even though the majority of the load may be carried by fluid pressure. Boundary lubrication: is characterized by the situation where either the quantity of present lubricant is so small, or speeds are so low that fluid pressure has not developed. Even in this case, some small fraction of the load may be carried by fluid pressure, if more than just a surface layer of lubricant is present. However, the resulting excessive mechanical contact between the two seal faces leads to high frictional heat generation rates, as well as high friction induced stress on the seal faces.

The individuation of some behaviors and the development of models are useful in many cases, during their design, in order to forecast performance. Dayan et al. [8] and Zou et al. [9] simulated the dynamics of mechanical face seals and studied the sensitivity of the relative misalignment to prevent possible contact between surfaces. Brunetiére et al. [10] and Brunetiére and Tournerie [11] have presented numerical analysis of the behavior of a mechanical seal solving the Reynolds equation operating in a mixed lubrication regime. Brunetiére and Apostolescu have proposed a semianalytical analysis of mechanical face seals: the model takes account of thermal effects and face distortions [12]. Several authors have developed numerical-thermo-elasto-hydro-dynamic

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rig, mounting the examined seal, is shown in Fig. 2. Experimental tests have reproduced the phenomenon obtaining some measures. In addition, in Fig. 5 the diagram temperature-shaft speed displays the zone where the studied seal rings. The authors have indicated some points on the main boundary line. Fig. 3 shows the friction torque and Fig. 4 the acoustic emissions during a test at 500 rpm with a fluid temperature of 70 1C. It is possible to see that the maximum peak of frictional torque is 304 Hz, corresponding to the resonance frequency of the seal. A thing to notice is that the association of the torque friction with the corresponding measured acoustic emissions. Thus it can

Fig. 1. Mechanical face seal.

models in non-contacting mechanical face seals [13,14]. Researchers used acoustic emissions in order to detect incipient seal failure [15,16]. Salant [17] has indicated that the use of a train of ultrasonic wave packets provides an effective means of detecting the collapse of the lubricating film between seals. In this paper, the authors analyze the problem of the seal that under particular conditions exhibits unwanted noise (ringing) together with malfunctioning. Experimental results show that the noise is related to friction torque and reveals the poor seal functioning. Ringing phenomena in mechanical face seals are rarely studied because of the difficulty in reproducing these phenomena. Anyway, Nau [18] describing the mechanical seal face materials and discussed the failure modes including the ‘ringing’. Hirabayashi et al. [19] investigated the causes of ‘ringing phenomena’ as a consequence of the blow-off of boiling liquid near the sealing surfaces. Kiryu et al. analyzed experimentally the phenomena in [20–22] where they reached the conclusions that the acoustic emissions (‘ringing’) were generated by ‘stick-slip’ phenomena due to both the lubrication regime of the seal and the dynamic characteristics of the rotating shaft system. Based on A.O. Lebeck's theory [1] and on the results of numerical simulations obtained by a lumped parameter model, the present paper supports the hypothesis that stick-slip phenomenon occurs, according to the conclusions of Kiryu et al. [20–22]. Stick-slip, as explained in detail in several papers [23–28], is a phenomenon, of intermittent movement caused by friction force, depending on speed and on the mechanical properties of the system. Many authors have dealt with the problem in various ways, however, in recent studies, the friction force has been considered as a function of the relative speed between the surfaces in contact. Subsequently, experimental tests and mathematical models have demonstrated that stick-slip is due to deceleration motion [29–31].

Fig. 2. Test rig.

Frequency [Hz] Fig. 3. Spectrum of friction torque.

2. Position of problem and experimental evidence According to technical documents and experimental tests, the analyzed mechanical face seal presents the ringing phenomenon, which is observable when there are shaft deceleration and low running shaft speed. Such a statement is compatible with the stickslip hypothesis: an intermittent movement due to the friction forces function of speed, in combination with the mechanical characteristics of the system (inertia, stiffness and damping) [23–28]. The test

Fig. 4. Spectrum of acoustic emissions.

C. Braccesi, M.C. Valigi / Tribology International 71 (2014) 125–131

full film lubrication is carried out by the following equation: ( !) ( !) 3 1 δ h δp δ rh3 δp r ω δh þ ¼ r δθ 12μδθ δr 12μ δr 2 δθ

Table 1 Properties of the seal. Internal pressure in the seal External pressure in the seal Internal radius of surface contact in the seal

p1 [Pa] p2 [Pa] r1 [m]

105 2n105

External radius of surface contact in the seal

r2 [m]

11:1n10  3

9:3n10  3

ð4Þ

and due to the cylindrical symmetry:

Mating ring mass

mm [kg]

2:4n10

Case mass

mc [kg]

5:7n10  3

δh ¼ 0; δθ

Spring mass

ms [kg]

Initial compression of spring Linearized axial stiffness of spring Linearized torsional stiffness of spring Axial damping Torsional damping

K0 [N] K [N/m] Kt [N m/rad] C [N s/m] Ct [N ms/rad]

1:9n10  3 314 42,142 1.2404 2.0529

Eq. (4) becomes: ( !) δ rh3 δp ¼ 0: δr 12μ δr

Standard deviation of roughness

s[m]

Mating moment of inertia

Jm ½kg m 

2:6n10

Spring moment of inertia Compressive strength Coning angle

Js ½kg m2  Sc [Pa] m [rad]

0:78n10  7 234n106

Viscosity

μ [Pas]

3

6:5n10  5 0:152n10  6

2

127

7

8:33n10  4 700n10  6

be deduced that the noise is a sign of the friction torque fluctuation. The main properties of the studied seal are listed in Table 1.

δp ¼0 δθ

ð5Þ

ð6Þ

By solving Eq. (6) with the boundary conditions, the fluid pressure is obtained: Z r p p1 1 dr þ p1 ð7Þ pðrÞ ¼ 2 3 R r2 1 r 1 rh dr r1 3 rh The pressure evaluated in both lubrication regimes can be added together and considered acceptable for any regime, within negligible errors, because the film pressure is maximum when the contact pressure is minimum and vice versa.

3. Tribological model and actions in the seal The actions in the seal are evaluated by Lebeck's theory [1] taking into consideration the different lubrication regimes: the theory combines the hydrodynamic lubrication model with a sliding contact model in boundary conditions. The seal is annulus shaped and the hypothesis of the simple convergent radial taper volume between rings is assumed, so that an axial-symmetric problem can be solved in order to evaluate the pressure. The geometry of the volume between rings is described by hðrÞ ¼ h1 þ mðr  r 1 Þ

ð1Þ

with r 1 r r r r 2 where the minimum distance between surfaces is h1. 3.1. Contact pressure in boundary lubrication

h

where f(z) is the probability density function of roughness where the standard deviation of roughness is considered to be equal to 0:152n10  6 ½m. The contact pressure pc is evaluated by pc ¼ bm Sc

Fig. 5. Ringing zone (area A) in the diagram temperature-shaft speed.

x 105

h =10-9 1

15

h =4.5x10-9 1

h1=2x10-8 h1=9x10-8

pressure [Pa]

At any area where the two surfaces are overlapped, it is assumed that the normal stress on the asperities equal to the compressive strength of the weaker material Sc, but where no contact occurs the contact pressure is considered to be equal to zero. As well it is assumed that the distribution of the roughness of two surfaces is Gaussian and remains the same even though they may be modified by contact itself. To find the contact pressure it is necessary to find the fraction area bm ¼ bm ðhÞ where the contact occurs that is evaluated as the Normal Cumulative Distribution Function [1]: Z 1 bm ¼ f ðzÞ dz; ð2Þ

h =4x10-7 1

10

h =8.4x10-6 1

h =1.7x10-4 1

h =7.7x10-4 1

5

h [m] 1

ð3Þ

According to the Reynolds theory, for a Newtonian, incompressible and homogenous fluid, the evaluation of lubricant pressure in

r [m] Fig. 6. Pressure for different distance between rings.

0. 01 12

0. 01 1

0. 01 08

0. 01 06

0. 01 04

0. 01 02

0. 01

0. 00 98

0. 00 96

0. 00 94

0. 00 92

0

3.2. Lubricant pressure in full film lubrication

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Considering the differential pressure across the seal ðp2 p1 Þ equal to 105 ½Pa, Fig. 6 shows the pressure versus radius for different values of minimum distance h1 between faces as the sum of (3) and (7). It is possible to see that the pressure contact due to asperities prevails on fluid pressure with decreasing of h1 and vice versa. For this reason the axial force Fðh1 Þ acting on the seal is evaluated by the integration of pressure as the sum of (3) and (7) that is illustrated in Fig. 7 as a function of h1. The moment Mðh1 ; ωÞ is evaluated by summarizing the torque Mb and Ml. The Mb is the moment acting on the seal in the condition of boundary lubrication, where f ðωÞ is the friction coefficient: Z Mb ¼

r2 r1

2π f ðωÞpr 2 dr

100 10

Moment [Nm]

10-2

ð8Þ

Ml ¼

r2

r1

3

r dr 2πμω hðh1 Þ

10-3 10-4 10-5 10-6 10-7 angular speed [rad/sec]

10-8

the Moment of Ml is evaluated in the condition of full film lubrication with the hypothesis of Newtonian fluid: Z

0.66 rad/sec 2 rad/sec 11 rad/sec 18 rad/sec 33 rad/sec 57 rad/sec 100 rad/sec 85 rad/sec 120 rad/sec 140 rad/sec 180 rad/sec

-1

10-9 10-9

10-8

10-7

10-6

10-5

10-4

10-3

h1 [m]

ð9Þ

Fig. 9. Torque acting on the seal versus distance between surfaces.

F(h1) [N]

103

102

101 Fig. 10. Lumped parameter model.

10

-8

10

-7

-6

10

-5

10

-4

10

10

-3

Fig. 8 shows the moment Mðh1 ; ωÞ versus angular speed ω, and for different values of h1. Fig. 9 shows the moment function of h1, as well as for different values of ω.

h1[m] Fig. 7. Axial force acting on the seal.

4. Lumped parameter model A lumped parameter model of the seal is proposed. The volume between the annular surfaces is assumed to be a convergent radial taper with axial-symmetric geometry (1). Fig. 10 shows the model with two degrees of freedom (the translation h1 and the rotation θ between the stator and the support), where the mass m includes the case mass, the mating ring mass and the spring mass; and the inertial moment J includes the inertial moment of the spring. All of this, is connected to the frame by the axial and the torsional stiffness, respectively K and Kt, and by the axial and the torsional damping C and Ct. The primary ring, rotating together with the shaft, slides against the mass and generates the relative rotation and translation between the rings, so that the force Fðh1 Þ and the moment Mðh1 ; ωÞ in the seal are produced. Such actions are evaluated by the previously described tribological model, in order that the dynamic behavior of the seal can be expressed by the following system of equations:

100

Moment [ N m]

10-2

10-4

10-6

10-8

10-10

10-12 10-4

10-3

10-2

10-1

100

101

angular speed [rad/sec] Fig. 8. Torque acting on the seal versus angular speed.

102

(

mh€1 þ C h_1 þKh1 ¼ Fðh1 Þ J θ€ þ C θ_ þ K θ ¼ Mðh ; ωÞ t

t

1

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129

5. Simulations

5.1. Simulation results and stability analysis

The system of equations is solved numerically according to the scheme as shown in Fig. 11. The model has been implemented in Matlab. After the initialization of the mathematical system the cyclic integration of the two differential equations begins as described below. The force and the moment evaluated by initialization are introduced in the system of differential equations, so that the movement between the two faces is instantaneously obtained. The new values of the force and the moment are recalculated and reintroduced in the differential equations.

The seal motion is obtained through the proposed model: specifically, the angular displacement with the rotational speed of the secondary ring. The simulations are performed by decreasing shaft speed ΩðtÞ, which together with the response plot, are shown in Figs. 12 and 13, as well as in Fig. 14. In the example illustrated in Fig. 12, at about 2.18 s of simulation time the instability appears at the critical speed of 82 rad/s. In Fig. 13 the critical speed is 130 rad/s and in Fig. 14 it is 95 rad/s. Results show the seal instability. Stability threshold research is performed by changing the friction law f ðωÞ [32]. The different friction laws used for the simulations are obtained by the normal probability density function as shown here: R1 ω Rf ðzÞ dz f ðωÞ ¼ f d þ ðf s  f d Þ 1 max ω f ðzÞ dz

ð10Þ

with different standard deviation of angular speed of friction coefficient and where fs and fd are the static and dynamic friction coefficient respectively obtained by a manufacturer. Fig. 15 demonstrates the different friction laws with corresponding critical speeds, obtained by simulations (results can be compared with the signed points of Fig. 5).

Fig. 11. Simulation scheme.

120

180 160

100

shaft speed [rad/sec]

shaft speed [rad/sec]

140 80

60

40

120 100 80 60 40

20

20 0

0

1

2

3

4

5

6

0

7

0

1

2

3

time [s]

5

6

7

0.06

0.04 θ

θ

0.04

[rad]

0.03 0.02

[rad]

4

time [s]

0.01 0

0.02

0 -0.02

-0.01 -0.02

-0.04 0

0.5

1

1.5

2

0

2.5

0.5

1

time [s]

20 0 -20 -40

2

100

ω

40

[rad/sec]

[rad/sec]

60

1.5

2.5

time [s] ω

50 0 -50 -100

-60 2.02

2.04

2.06

2.08

2.1

2.12

2.14

time [s] Fig. 12. Simulation results.

2.16

2.18

2.2

1.9

1.95

2

2.05

2.1

time [s] Fig. 13. Simulation results.

2.15

2.2

2.25

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C. Braccesi, M.C. Valigi / Tribology International 71 (2014) 125–131

140

shaft speed [rad/sec]

120

100

80

60

40

20

0

0

1

2

3

4

5

6

7

time [s]

0.04

θ

0.03

[rad]

0.02 0.01 0 -0.01 -0.02

0

0.5

1

1.5

2

2.5

[rad/sec]

time [s]

lubrication to boundary lubrication. In particular the negative slope in friction-velocity curve produces the condition for steady sliding instability. The oscillation is not only influenced by the nature of the surface in contact and the lubrication regime but also by the dynamics of the system. The vibration frequency of oscillation is equal to the torsional natural frequency. Numerical simulations demonstrate that phenomenon is due to the insurgence of stick-slip vibrations during shaft deceleration. These conclusions are the same obtained experimentally by Kiryu. Since temperature influences the phenomenon, a study varying the friction law with temperature is also realized. Taking into account the base case of Fig. 14, an increase in dry friction and a decrease in dynamic friction with temperature are considered. Fig. 16 illustrates the different friction laws with the corresponding critical speeds obtained by simulations. It emerges that the growing temperature increases the critical speed according to the empiric results of Fig. 5. In order to obtain better seal control, another parametric study has been realized by varying the axial and the torsional stiffness. The obtained results are listed in Table 2. In the case of fixed torsional stiffness, results show that the critical speed decreases with axial stiffness (up to 5% for a reduction of the value equal to 30%). Since a reduction in axial stiffness implies a reduction in contact force between rings, a reduction of temperature can also be generated and leakages may occur). In addition, one can observe that a reduction of the contact force causes a decrease in temperature, which, in turn influences the value of critical speed. In summary, the decrease in critical speed is due to the variation of axial stiffness and to the consequent reduction of temperature. However, having an excessive reduction of K may cause seal malfunctioning.

ω

60 40 20 0 -20 -40 -60 -80

0.25 T=65°C

0.2

2.05

2.1

2.15

2.2

critical speed 135 rad/sec 130 rad/sec 95 rad/sec

T=55°C

2.25 0.15

f[w]

time [s] Fig. 14. Simulation results.

T=45°C

0.1 0.1 0.095 0.09 0.085

critical speed

0.05

149 rad/sec 130 rad/sec 118 rad/sec 93 rad/sec 84 rad/sec

0 0

20

40

60

f (w)

0.08

80

100

120

140

160

180

w[rad/sec]

0.075

Fig. 16. Friction coefficient.

0.07 0.065

Table 2 Results.

0.06 0.055 0.05

0

50

100

150

200

250

w [rad/sec] Fig. 15. Friction coefficient.

Instabilities occur due to a change in the lubrication regime. When the relative speed between surfaces decreases stick-slip occurs because there is a passage from the condition of mixed

K (%)

Kt (%)

Critical speed ½rad=s

0 0 þ30 0  30 þ 30 þ 30  30  30

þ0 þ30 0  30 0  30 þ 30 þ 30  30

95 100 91 85 98 97 96 110 87

C. Braccesi, M.C. Valigi / Tribology International 71 (2014) 125–131

6. Conclusions A lumped parameter model of a mechanical face seal combined with a tribological model has been created in order to investigate the reason why friction torque fluctuations, with consequent undesired noise, occur. The results achieved through the simulations, have shown that the noise is a result of stick slip vibrations that are depending on lubricating conditions between sealing surfaces. In addition, a dynamic analysis has been carried out together with a study that varies some significant parameters. The proposed model is a useful instrument for designers whose aim is to identify the conditions in which stick-slip vibration occurs. Acknowledgments The problem studied in this paper has been supported by Meccanotecnica Umbra S.p.A.; with particular thanks, on behalf of the authors, to engineers M. Borasso and L. Renzi. References [1] Lebeck AO. Principles and design of mechanical face seal. New York: Wiley Interscience Publication; 1991. [2] Peng XD, Xie YB, Gu YQ. Evaluation of mechanical face seals operating with hydrocarbon mixtures. Tribol Int 2003;36:199–204. [3] Zhang J, Yuan S, Fu Y, Fang Y. A numerical simulation of 3-d inner flow in upstream pumping mechanical seal. J Hydrodyn 2006;18(Ser B (5)):572–7. [4] Summers-Smith D. Laboratory investigation of the performance of a radial face seal. In: Proceedings of the first international conference on fluid sealing. Cranfield: BHRA, Paper D1; 1961. [5] Di Puccio F, Ciulli E, Squarcini R. Comparison of two sealing coupling geometries from e direct fuel injector. Tribol Int 2006;39(8):781–8. [6] Tournerie B, Frene J. Principal research areas on mechanical face-seals. Tribol Int 1984;17(4):179–84. [7] Qu S, Xia W, Wang Y. Study on lubricating and sealing for engine valve guide bush. Lubr Eng 2004(Part 5):67–70. [8] Dayan J, Zou M, Green I. Sensitivity analysis for the design and operation of non-contacting mechanical face seal. Proc IMechE, Part C 2000;214:1207–18. [9] Zou M, Dayan J, Green I. Dynamic simulation and monitoring of non-contac ting flexibly mounted rotor mechanical face seal. Proc IMechE Part C 2000; 214:1195–1206. [10] Brunetiere N. An analytical approach of the thermoelastohydrodynamic behaviour of mechanical face seals operating in mixed lubrication. Proc IMechE, Part J, J Eng Tribol 2010;224:1221–33.

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