Macroscopic features

5.3.2.1 Waviness amplitude, A, variations

The effect of the waviness on the Stribeck curve was measured for 5 different seal combinations. Both seals were made of self-sintered silicon carbide, the

104 5. Verification of model with experimental results

rotating seal face flat to within 0.1µm, the stationary seal face with 2 waves and no coning. In Table 5.2 the operational conditions are given for the 5 com-binations, where “s” is the stationary seal face, “r” the rotating seal face and σ_ini and σ_after the standard deviation of the surface height distribution before and after the experiment, respectively. In Table 5.1 the material properties of the seal faces are given. The standard deviation of the summits, σ_s, and the radius of the summits, β, are the combined values of both faces after an experiment. They are defined as:

σ_s =p

σ_s1²+ σ_s2², (5.1)

1 β = 1

β₁ + 1

β₂. (5.2)

We were concerned only with hydrodynamic effects, and therefore the mea-surements were performed without sealed fluid pressure, i.e. P_f = 0. In

Table 5.2: Seal face properties of seals with varying waviness and no coning.

Experimental

conditions 1 2 3 4 5

rotating/stationary r s r s r s r s r s

A [µm] 0 1.1 0 1.7 0 2.9 0 3.8 0 5.0

σ_ini [nm] 17 287 11 400 33 467 7 457 4 454

σ_after [nm] 29 140 12 112 32 115 6 110 10 57

η_s (×10⁹) [m⁻²] 14.5 12.3 11 10.7 6.4

β [µm] 55.9 70.0 105 97.4 174.4

σ_s [nm] 62 58 43 48 45.0

F_N [N] 240 240 240 240 240

v_texp [m/s] 0.15 0.12 0.10 0.11 0.11

Fig. 5.7 the measured Stribeck curves of experimental condition 1 (Table 5.2) are presented, together with the predicted Stribeck curve (dashed line), which was calculated on the basis of the model presented in Chapter 3 and the pa-rameters of Table 5.2. It can be seen that the measured curves are predicted quite accurately by the calculated Stribeck curve. Unfortunately, the speed

5.3 Theoretical vs. experimental results 105

of the motor could not lowered any further, so the transition from mixed to boundary lubrication was not measured. In the model, the value of the friction coefficient for the boundary lubrication regime, f_c, was taken to be 0.25, which is a practical value for silicon carbide/silicon carbide contacts under boundary lubricated conditions, see e.g. Summers-Smith (1988). Another comparison of an experimental Stribeck curve with a predicted curve is shown in Fig. 5.8.

Experimental condition 5 in Table 5.2 was taken, and also here the measured Stribeck curves were very well predicted by the theoretical Stribeck curve.

As shown in Table 5.2, the roughness of the stationary seal face decreased strongly during the test. The roughness was measured at the top of the waves, where the contact of the faces occurs. No roughness change was observed in the valleys of the seal faces with waviness.

5.3.2.2 Radial coning angle, a

As mentioned in Section 5.2.2, it was not possible to obtain seals with different coning angles. The experiments all showed the same frictional behaviour.

Table 5.3: Seal face properties of experiments with constant coning.

rotating/stationary r s

Coning a (×10⁻⁴) [rad] 0 2.3

A [µm] 0 0.9

σ_ini [nm] 26.4 232

σ_after [nm] 18.6 23.9

η_s (×10⁹) [m⁻²] 7.9

β [µm] 338

σ_s [nm] 16

F_N [N] 240

v_texp [m/s] 0.1

In Figure 5.10, 4 measured Stribeck curves are shown, with operational condi-tions as given in Table 5.3. The material properties are presented in Table 5.1.

From the theoretical results it was expected that, as a result of coning, the transition from hydrodynamic lubrication to mixed lubrication would shift to the right, see Fig. 3.26. However, the transition HL–ML occurred at a lower velocity than that observed without coning; see Fig. 5.7.

106 5. Verification of model with experimental results

The dashed Stribeck curve in Fig. 5.10 was calculated on the basis of the data of Table 5.3. It can be seen that the measured Stribeck curves are not well predicted by the calculated Stribeck curve. In fact, the measured curves are located more than one order of magnitude in velocity to the left of the calculated curve. After the experiment, 3D interference scans of the complete surface were made. The scans revealed that on the outside contact diameter of the wavy face with coning, the face was locally worn flat in the radial direction, with a width of about 2.4 mm, as indicated in Fig. 5.9.

Thus, another Stribeck curve was calculated, this time according to the situ-ation shown in Fig. 5.9. The seal width was taken as 2.4 mm, and the coning angle was set to a = 0 rad. This new situation is described by the dash-dotted curve and it can be seen that this curve predicts the measured transition from hydrodynamic to mixed lubrication rather well. Measurements with lower ve-locities could not be performed, due to the operational limitations of the test rig and because the frictional behaviour was unstable.

Hence, it can be concluded that the measured Stribeck curves were very well predicted by the calculated Stribeck curves. It appeared that friction mea-surements with coning, as described by the model, could not be performed, as the coning wears partly away in a very short time and a radially flat-to-flat contact between the faces remains.

In the next section the transition from hydrodynamic to mixed lubrication will be analyzed.

5.3.2.3 Influence of macroscopic features on the transition from full film to mixed lubrication

As mentioned in Section 1.2, the transition from hydrodynamic to mixed lubri-cation would be the ideal operational regime for mechanical face seals. Here, a low coefficient of friction is associated with a relatively low leakage and low wear. Therefore, it is fortunate that this regime can now be determined as a function of the present operational conditions.

The transitions from full film lubrication to mixed lubrication, which are de-termined from the Stribeck curve according to the method described in Sec-tion 1.2, can be reflected in a so-called transiSec-tion diagram. In Fig. 5.11, ˜v_t, defined as the experimentally determined transition, v_texp, divided by the cal-culated transition, v_tcal, is plotted as a function of the waviness amplitude. It is shown that the experimentally determined values of v_t (v_texp) are in good agreement with the calculated values (v_tcal). In fact, the maximum difference between v_texp and v_tcal amounts to not more than 10%.

According to Fig. 3.25, v_t should be nearly independent of amplitude, A, for the amplitude range given in Table 5.2. The differences between different v_texp

5.3 Theoretical vs. experimental results 107

values are nearly entirely due to differences in some of the other parameters, notably σ_s.