A comparative study of the Reynolds equation solution for slider and journal bearings with stochastic roughness on the stator and the rotor

Skaltsas, Dimitrios; Rossopoulos, Georgios N.; Papadopoulos, Christos I.

doi:10.1016/j.triboint.2021.107410

Cited by 16 publications

(3 citation statements)

References 20 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The formulas of extended Stein's lemma, stated in Theorems 1, 2, are useful in engineering applications where averages E g(X)X n arise, see e.g. the recent work [11] in tribology. Note that the respective extensions of Stein's lemma for multivariate Gaussian variables are also feasible and is the topic of a forthcoming work.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

See 1 more Smart Citation

Extension of Stein's lemma derived by using an integration by differentiation technique

Mamis

2022

Preprint

View full text Add to dashboard Cite

We extend Stein's lemma for averages that explicitly contain the Gaussian random variable at a power. We present two proofs for this extension of Stein's lemma, with the first being a rigorous proof by mathematical induction. The alternative, second proof is a constructive formal derivation in which we express the average not as an integral, but as the action of a pseudodifferential operator which is defined via the Gaussian moment-generating function. In extended Stein's lemma, the absolute values of the coefficients of the probabilist's Hermite polynomials appear, revealing yet another link between Hermite polynomials and normal distribution.

show abstract

Section: Introduction and Main Resultsmentioning

confidence: 99%

“…However, the advantage of closed-form formulas (2), ( 5) over a recursive one is manifested for increasing n, see e.g. [11,Sec. 2.3], where keeping track of the repetitive applications of Eq.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Extension of Stein's lemma derived by using an integration by differentiation technique

Mamis

2022

Preprint

View full text Add to dashboard Cite

show abstract

“…Under appropriate boundary conditions and constraints, these numerical methods can solve the Reynolds equation and provide the steady-state pressure distribution characteristics in the gas film. Obviously, the simplified Reynolds equation cannot describe transient unsteady flows or turbulence phenomena inside the gas film, hindering the study of micro-vibrations in fluid lubricated bearings [255].…”

Section: Characterization Of the Microscopic Flow Fieldmentioning

confidence: 99%

Design and optimization of fluid lubricated bearings operated with extreme working performances—a comprehensive review

Zhang,

Huang,

Chen

et al. 2024

Int. J. Extrem. Manuf.

View full text Add to dashboard Cite

Fluid lubricated bearings have been widely adopted for supporting components of high-end equipments in the field of metrology, semi-conductor, aviation, strategic defense, ultra-precision manufacturing, medical treatment and power generations. These fields all involve extreme working conditions such as ultra-high moving precision, ultra-high rotation speed, ultra-heavy bearing load, ultra-high environmental temperature, high radiation and high vacuum, which present challenges for the design and optimization of reliable fluid lubricated bearings. Breakthrough of any related bottlenecks will promote the development course of high-end equipments. To further promote the advancement of high-end equipments, this paper reviews the design and optimization of fluid lubricated bearings operated with typical extreme working performances. Targeting on the realization of extreme working perfor mances, the current challenges, the current solutions, the underlying deficiencies and the promising developing directions regarding to the design and optimization of fluid lubricat ed bearings are systematically pointed out. This paper can provide guidance for choosing suitable fluid lubricated bearings and optimizing their structures based on required extremeworking performances.

show abstract

Steady-state and dynamic performances of journal bearing based on rough surface reconstruction technology

Yang

Zhu

Lee

2022

J Braz. Soc. Mech. Sci. Eng.

View full text Add to dashboard Cite

A comparative study of the Reynolds equation solution for slider and journal bearings with stochastic roughness on the stator and the rotor

Cited by 16 publications

References 20 publications

Extension of Stein's lemma derived by using an integration by differentiation technique

Extension of Stein's lemma derived by using an integration by differentiation technique

Design and optimization of fluid lubricated bearings operated with extreme working performances—a comprehensive review

Steady-state and dynamic performances of journal bearing based on rough surface reconstruction technology

Contact Info

Product

Resources

About