Paper: Study of leakage and friction of flexible seals for steady motion via a numerical approximation method.
Authors: Nikas, G. K., and Sayles, R. S.
Where: Tribology International (Elsevier), 2006, 39(9), 921-936. Available from the publisher.
A numerical model has been developed to solve the steady-state, smooth-surface elastohydrodynamic problem of flexible (polymeric or elastomeric) seals of nominally rectangular or toroidal shape, most commonly found in linear and rotary hydraulic actuators for reciprocating motion. The seals can be fluid-pressurized or even act as wipers. The model offers the advantage of stable and very fast, approximate numerical solution of the EHL sealing problem, which has not been given much attention in the literature in the last 40 years. This model by-passes common obstacles in elastohydrodynamics of soft contacts. It uses an approach similar to that at the beginning of the Inverse Hydrodynamic theory but then deviates from it, avoiding the tricky part of solving a cubic equation. It is relatively easy to program and requires no more than a few hundredths of a second of processing time of a modern personal computer for a complete solution and performance analysis, which is a leap forward compared with previous studies in the literature that required hundreds of iterations and Finite Element Analysis to achieve similar results. In this study and for demonstration purposes, it is applied for a wide range of operating conditions, namely operating temperature between –54 and +99 °C, average contact pressure between 5 and 180 MPa and sliding speed between 0.6 and 38 mm/s (although these limits can safely be exceeded with the model). Results are presented for the contact pressure and film thickness distribution, seal leakage and hydrodynamic friction force. A study on the effects of the seal initial interference, sliding speed, seal geometry, and fluid starvation on lubrication and sealing performance have been derived for the previously mentioned range of operating conditions and for initially conformal and non-conformal sealing contacts, with the seals both stationary and non-stationary. The results are in agreement with those of several well-known theoretical and experimental studies in this field. The present study is for steady-state conditions and will be extended to a transient elastohydrodynamic analysis in another study.
Some figures from this work
The development of the model is based on the geometry and seal seal assemblies shown in Fig. 1. A flexible seal of nominally rectangular geometry with generally rounded corners is installed in a rigid housing and restricted in the three principal directions.
Fig. 1. Stator and rotor seals (“non-conformal” and “conformal” contact; exaggerated view).
As can be seen in Fig. 1, both cases of conformal and non-conformal contact have been modelled. A "stator seal" is fixed in space (on a stator) and seals a reciprocating rotor as on the left picture in Fig. 1, whereas a "rotor seal" is assembled on a reciprocating rotor and seals the surface of a space-fixed stator as on the right picture in Fig. 1. All dimensions, material properties, speed and operating temperature are variables. Sealing is achieved by the initial interference of the seals on their counterfaces. Variable sealed pressure may be exerted on the left or the right side of a seal, although such pressure is kept very low in the paper and the seals merely act as wipers.
There are 18 figures and diagrams in the article, demonstrating various performance variables of the problem for both types of sealing contact, covering a broad spectrum of temperature and contact pressure. For example, Fig. 2 shows the computed contact pressure and fluid film thickness for the rotor seal at room temperature.
Fig. 2. Example of film thickness and contact pressure for the rotor seal at 22 °C.
One can see the variation of pressure and film thickness in the sealing contact from the inlet to the outlet. Notice the very thin film (average thickness of about 25.8 nanometres; note: the contact is assumed perfectly smooth, that is, surface roughness effects have not been included). As for another example, Fig. 3 shows the hydrodynamic friction force for both types of sealing contact and how this is affected by the normal (z) interference of the seals at various temperatures.
Fig. 3. Effect of the seal z-interference.
Results are presented in the paper for the contact pressure and film thickness distribution, seal leakage and hydrodynamic friction force. A detailed study is presented on the effects of the seal initial interference, sliding speed, seal geometry, and fluid starvation on lubrication for temperatures between –54 and +99 °C, average contact pressure between 5 and 180 MPa and sliding speed between 0.6 and 38 mm/s, which cover the majority of seal applications.
For more information in this research area, please see the author's related sealing project.
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