Paper: Fast performance-analysis of rectangular-rounded hydraulic reciprocating seals: mathematical model and experimental validation at temperatures between 54 and +135 °C.

Author: George K. Nikas

Published in: Tribology International, 2018, 128, 34-51

Errata: In Table 2 of the published paper, the unit for seal dimensions bx, by and bz should be "mm", not microns as misprinted in the paper. Also, Eq. (42) should be corrected as follows:

Corrected Eq. (42)

The correct Eq. (42) is expected to give much lower temperature rise at –54 ºC and better agreement with the experimental results at said temperature used for validating purposes in the paper. The differences at the other two temperatures, namely, at +23 and +135 ºC by this correction are either small or negligible.


Solid mechanics and rough thermoelastohydrodynamics of hydraulic, rectangular-rounded, reciprocating seals with hydrodynamic, asperity, deformation and van-der-Waals stresses are analytically formulated. Seal swelling or shrinkage by fluid exchange and fluid contact starvation are easily set. Computations require less than 0.05 s of a personal computer’s time, allowing for extremely fast parametric studies. Experimental validation follows at –54, +23 and +135 ºC, far exceeding other studies at both ends of the scale. Theoretical and experimental results are compared after 1000 stroking cycles. This has not been attempted to this extent before but is important to judge a model’s applicability post running-in and in effect of seal abrasive wear, and not just for the first few stroking cycles with a brand new seal.


Hydraulic, reciprocating, polymeric seals are met in many engineering applications and are critical components in machine reliability. This article presents an analytical, mathematical model with (almost entirely) exact algebraic equations for the performance evaluation of rectangular-rounded seals involving solid mechanics, contact mechanics of rough surfaces and thermoelastohydrodynamics. Four components of friction are included, namely hydrodynamic (viscous), asperity (adhesive), deformation (ploughing) and van-der-Waals interaction. Additionally, fluid starvation, seal swelling by fluid uptake and shrinkage by plasticizer depletion during operation are easily treated in the model. Computational analysis takes less than 0.05 s of the CPU time of a personal computer, allowing for parametric studies with hundreds of test cases to be completed in a matter of seconds. Experimental validation on both friction force and leakage results is for the first time presented not only at room temperature but at extreme temperatures of –54 and +135 °C (temperatures relevant in aerospace applications) with the current state-of-the-art in experimental testing. Crucially, the tests include proper running-in of the seals and seal abrasive wear after 1000 stroking cycles, that is, they deal with conditions that reflect normal engineering applications and not some “sanitised” experiments with brand new seals for the first few stroking cycles in the service life of the seals.

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