The Optimum One-Dimensional Hydrodynamic Gas Rayleigh Step Bearing

1970 ◽  
Vol 92 (3) ◽  
pp. 504-508 ◽  
Author(s):  
G. M. Wylie ◽  
C. J. Maday

The optimum Rayleigh gas slider bearing is determined for a range of bearing numbers. Numerical methods are used to calculate step location, step pressure, and load capacity for given values of step height ratio, bearing number, and flow parameter. These methods are used to determine as many data points as desired so that it is possible to obtain the optimum configuration dimensions to a very high degree of accuracy. An inherent feature of this analytical experiment is the acquisition of data pertaining to the near-optimum bearings and such data are presented for bearings with load capacities ranging down to seven-tenths of the load associated with the optimum Rayleigh bearing. At low bearing numbers it is found that the optimum Rayleigh bearing has only slightly lower load-carrying capability than the optimum gas slider bearing. For bearing numbers of 50, 100, and 500 the optimum Rayleigh slider bearings were, respectively, 5.8, 8.3, and 15.3 percent lower in load-carrying capability than the corresponding optimum bearings.

1968 ◽  
Vol 90 (1) ◽  
pp. 281-284 ◽  
Author(s):  
C. J. Maday

Bounded variable methods of the calculus of variations are used to determine the optimum or maximum load capacity hydrodynamic one-dimensional gas slider bearing. A lower bound is placed on the minimum film thickness in order to keep the load finite, and also to satisfy the boundary conditions. Using the Weierstrass-Erdmann corner conditions and the Weierstrass E-function it is found that the optimum gas slider bearing is stepped with a convergent leading section and a uniform thickness trailing section. The step location and the leading section film thickness depend upon the bearing number and compression process considered. It is also shown that the bearing contains one and only one step. The difference in the load capacity and maximum film pressure between the isothermal and adiabatic cases increases with increasing bearing number.


1962 ◽  
Vol 84 (1) ◽  
pp. 197-202 ◽  
Author(s):  
William T. Snyder

An analysis is presented of the slider bearing using an electrically conducting lubricant, such as a liquid metal, in the presence of a magnetic field. The solution permits the calculation of the load-carrying capacity of the bearing. A comparison is made with the classical slider bearing solution. It is shown that the load capacity of the bearing depends on the electromagnetic boundary conditions entering through the conductivity of the bearing surfaces. Numerical data are presented for nonconducting surfaces with the emphasis on a comparison between the classical bearing and the magnetohydrodynamic bearing characteristics. It is shown that a significant increase in load capacity is possible with liquid metal lubricants in the presence of a magnetic field.


1969 ◽  
Vol 91 (1) ◽  
pp. 45-51 ◽  
Author(s):  
R. C. DiPrima

The methods of matched asymptotic expansions are used in a systematic manner to obtain the load-carrying capacity of an infinitely long slider bearing correct through terms 0 (1/Λ) where Λ is the bearing number. The expression for the load is extremely simple. It is shown that the error is 0 (1/Λ2), and the procedure for obtaining higher order terms is discussed. Results are given for the case of a converging film thickness with a parabolic shape and for a partial arc journal bearing.


1978 ◽  
Vol 100 (1) ◽  
pp. 70-73 ◽  
Author(s):  
Aron Sereny ◽  
Vittorio Castelli

The method of matched asymptotic expansion is applied to obtain the pressure distribution and the load carrying capacity for an infinitely long slider bearing, operating under high-speed, low-height, with slip boundary conditions. The pressure distribution is easily applicable as the starting solution for the iterative numerical solution of Reynolds equation. Two examples given show extremely good correlation between this expansion and the numerical solution. It is shown that, for a tapered slider bearing with a bearing number above 100, the reduction in load because of slip is minimal and that, for a parabolic slider, there exists a certain unique bearing number for which the load carrying capacity is independent of the parabolic crown of the slider. It is shown that for a wide slider bearing with large bearing number, the effect of slip is on the order of 1/A.


1978 ◽  
Vol 100 (2) ◽  
pp. 254-260 ◽  
Author(s):  
J. A. Schmitt ◽  
R. C. DiPrima

The method of matched asymptotic expansions is used to develop an asymptotic expression for the load-carrying capacity of a finite width gas slider bearing for large bearing numbers and for film thicknesses varying both in the sliding and transverse directions. The individual terms in the formula for the load are independent of the bearing number and are related to the interior portion, the side edge boundary layers, and the trailing edge boundary layer of the bearing. Only the terms associated with the side leakage phenomena must be computed numerically. Two special cases are discussed: (i) the film thickness varying only in the sliding direction, and (ii) the film thickness having linear or parabolic variation in the sliding direction and parabolic variation in the transverse direction.


2015 ◽  
Vol 813-814 ◽  
pp. 921-937
Author(s):  
P.S. Rao ◽  
Santosh Agarwal

This paper presents the theoretical study and analyzes the comparison of porous structures on the performance of a couple stress fluid based on rough slider bearing. The globular sphere model of Kozeny-Carman and Irmay’s capillary fissures model have been subjected to investigations. A more general form of surface roughness is mathematically modeled by a stochastic random variable with non-zero mean, variance and skewness. The stochastically averaged Reynolds type equation has been solved under suitable boundary conditions to obtain the pressure distribution in turn which gives the expression for the load carrying capacity, frictional force and coefficient of friction. The results are illustrated by graphical representations which show that the introduction of combined porous structure with couple stress fluid results in an enhanced load carrying capacity more in the case of Kozeny-Carman model as compared to Irmay’s model.


2021 ◽  
Vol 28 (1) ◽  
pp. 71-83
Author(s):  
Mazin Abdulrahman ◽  
Shakir Salih ◽  
Rusul Abduljabbar

In this research, an experimental study is conducted to investigate the behavior and strength of high strength reinforced concrete corbels externally bonded with CFRP fabric sheets and Plates with different patterns taking into account the effect of adopted variables in enhancing the ultimate strength; the effect of shear span to effective depth (a/d), configuration, type and amount of bonding. Eleven high strength reinforced corbels were cast and tested under vertical loads. Test results showed there was an improvement in the behavior and load carrying capacity of all strengthened corbels. An increasing in the ultimate strength of strengthened corbel by inclined CFRP strips reached to (92.1%) while the increasing reached to (84.21%) for using one horizontal CFRP Plates compared to un-strengthened reference specimen. Also, it can be conducted that the increase of (a/d) ratio from (0.6 to 0.8) resulted in decreasing by 21.05% in ultimate load capacity of corbels and from (0.4 to 0.6) by 31.25% and 58.69% in cracking and ultimate loads respectively Using CFRP .


2020 ◽  
Vol 44 (3) ◽  
pp. 151-158
Author(s):  
S. Tomilov

Так как в настоящее время в эксплуатации находится достаточно много автодорожных мостов, запроектированных и построенных в различные периоды, их, как и всю дорожную сеть, необходимо поддерживать в состоянии, соответствующем нормативам, а для этого проводить ремонт с использованием элементов усиления несущих конструкций. При качественном возведении и надлежащем уходе высокая степень сохранности мостов позволяет продлить срок их службы путем решения ряда конструктивных вопросов, наиболее актуальным из которых считают обеспечение нормативной грузоподъемности. Усиление с целью повышения грузоподъемности эксплуатируемых мостов достигается путем добавления элементов внешних или внедренных в состав существующего конструктива в зависимости от типа сооружения, его состояния и доступной технологии производства. Однако не только грузоподъемность, но и подверженность конструкций деформациям определяет транспортно-эксплуатационные параметры сооружения, характеризующие послеремонтное состояния моста. Цель настоящего исследования – анализ известного и широко востребованного способа усиления железобетонных балок внешним армированием как обеспечивающего минимальное вмешательство в существующие основные конструкции, технологичного и доступного в исполнении. Впервые дана оценка влияния стадийности включения в работу элементов усиления на общие деформации – прогибы главных балок. Ключевые слова: главная балка, грузоподъемность, усиление, внешняя арматура, свободная затяжка, стадийность работы, относительная деформация, прогиб. Currently, there are quite a lot of road bridges in operation, designed and built in different periods. It is necessary to maintain the road network including bridge structures in a condition that meets up-to-date standards, and for this repair should be carried out using reinforcing elements of the supporting structures. With high-quality construction and proper maintenance, a high degree of safety of bridges allows to extend their service life by solving a number of design issues, the most important of which is considered to be the provision of standard load capacity. Strengthening in order to increase the carrying capacity of operated bridges is achieved by adding elements external or incorporated into the existing structure, depending on the type of structure, its condition and available production technology. However, not only the carrying capacity, but also the susceptibility of structures to deformations determines the transport and operational parameters of the structure, which characterize the post-repair state of the bridge. The purpose of this study is to analyze the well-known and widely demanded method of reinforcing reinforced concrete beams with external reinforcement as providing minimal interference with the existing basic structures, technological and affordable in execution. For the first time, an assessment of the influence of the staging of the inclusion of reinforcement elements in the work on the general deformations – deflections of the main beams. Keywords: main beam, carrying capacity, reinforcement, external reinforcement, free rod, staging of work, relative deformation, deflection.


Author(s):  
J. K. Patrick ◽  
N. N. S. Chen

This paper presents the results of an extensive experimental investigation into the performance of a short multi-grooved bearing subjected to a range of static and alternating loads. Lubricating oil was supplied, at pressures of up to 2000 lb/in2, to capillary type restrictors connected to 10 closed-end axial grooves in the bearing. The bearing had a length/diameter ratio of 1/3 and operated with a journal speed and load frequency of 327 c/min. Measured load capacity, stiffness, and flow characteristics indicate that bearings of this type have a significant load-carrying capacity at zero journal speed and that the load capacity is increased by journal rotation. A feature of the journal behaviour under alternating loads is the movement of the journal centre along a straight line coincident with the load plane. The extensive oil film pressure surveys indicate for the first time the pressure distribution within narrow hydrostatic bearings and provide a basis for a realistic theoretical analysis of this type of bearing.


2008 ◽  
Vol 130 (2) ◽  
Author(s):  
John Tichy ◽  
Benyebka Bou-Saïd

The Phan-Thien and Tanner (PTT) model is one of the most widely used rheological models. It can properly describe the common characteristics of viscoelastic non-Newtonian fluids. There is evidence that synovial fluid in human joints, which also lubricates artificial joints, is viscoelastic. Modeling the geometry of the total hip replacement, the PTT model is applied in spherical coordinates for a thin confined fluid film. A modified Reynolds equation is developed for this geometry. Several simplified illustrative problems are solved. The effect of the edge boundary condition on load-carrying normal stress is discussed. Solutions are also obtained for a simple squeezing flow. The effect of both the relaxation time and the PTT shear parameter is to reduce the load relative to a Newtonian fluid with the same viscosity. This implies that the Newtonian model is not conservative and may overpredict the load capacity. The PTT theory is a good candidate model to use for joint replacement lubrication. It is well regarded and derivable from molecular considerations. The most important non-Newtonian characteristics can be described with only three primary material parameters.


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