The One-Dimensional Optimum Hydrodynamic Gas Slider Bearing

1968 ◽  
Vol 90 (1) ◽  
pp. 281-284 ◽  
Author(s):  
C. J. Maday
Keyword(s):  
Film Thickness ◽  
Load Capacity ◽  
Maximum Load ◽  
Slider Bearing ◽  
Compression Process ◽  
One Dimensional ◽  
One Step ◽  
The Difference ◽  
The One ◽  
Bearing Number

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.

The Optimum Rayleigh Bearing in Terms of Load Capacity or Friction for Non-Newtonian Lubricants

1985 ◽  
Vol 107 (1) ◽  
pp. 59-67 ◽  
Author(s):  
P. Bourgin ◽  
B. Gay
Keyword(s):  
Film Thickness ◽  
Load Capacity ◽  
Maximum Load ◽  
Slider Bearing ◽  
Generalized Newtonian Fluid ◽  
Newtonian Viscosity ◽  
One Dimensional ◽  
Minimum Film Thickness ◽  
The One ◽  
Numerical Program

Pontryagin’s Maximum Principle is used to show that the configuration of the one-dimensional slider bearing which carries the maximum load for a specified minimum film thickness, is a modified Rayleigh bearing. The lubricant may be any Generalized Newtonian Fluid. Having selected two optimization criteria (1: maximum load capacity for a given minimum film thickness—2: minimum friction force for a specified load), a numerical program allows one to determine the optimal step bearing associated with the lubricant non-Newtonian viscosity. Several examples are worked out, showing that significant gains are expected, in comparison with the results obtained for the classical (Newtonian) Rayleigh bearing.

A Bounded Variable Approach to the Optimum Slider Bearing

1968 ◽  
Vol 90 (1) ◽  
pp. 240-242 ◽  
Author(s):  
C. J. Maday
Keyword(s):  
Film Thickness ◽  
Load Capacity ◽  
Inequality Constraints ◽  
Maximum Load ◽  
Slider Bearing ◽  
Lagrange Equations ◽  
Variable Approach ◽  
Pressure Dependent Viscosity ◽  
One Step ◽  
Dependent Viscosity

Contemporary methods for treating inequality constraints in the calculus of variations are employed to determine the maximum load-capacity one-dimensional slider bearing using a lubricant with pressure-dependent viscosity. A lower bound on the minimum film thickness is put into equational form to facilitate the use of the Euler-Lagrange equations, the corner conditions, and the Weierstrass E-function. It is found that, for typical lubricants, the slider bearing contains only one step separting two values of the film thickness. It is shown also that there exist cases for which a solution cannot be obtained to describe a real situation.

Rayleigh Step Journal Bearing, Part II—Incompressible Fluid

1969 ◽  
Vol 91 (4) ◽  
pp. 641-650 ◽  
Author(s):  
B. J. Hamrock ◽  
W. J. Anderson
Keyword(s):  
Theoretical Analysis ◽  
Film Thickness ◽  
Journal Bearing ◽  
Load Capacity ◽  
Maximum Load ◽  
Single Step ◽  
Thickness Ratio ◽  
Infinite Length ◽  
One Step ◽  
Bearing Part

A theoretical analysis of the pressure distribution, load, capacity, and attitude angle for a single-step concentric as well as a multistep infinite length eccentric Rayleigh step journal bearing is performed. The results from the single-step concentric analysis indicated that the maximum load capacity is obtained when the film thickness ratio is 1.7 and the ratio of the angle subtended by the ridge to the angle subtended by the pad is 0.35. The results from the infinite length eccentric analysis indicated that one step placed around the journal was optimal. For eccentricity ratios greater than or equal to 0.2 the maximum load occurred for a bearing without a step or a Sommerfeld bearing. For eccentricity ratios less than 0.2 the optimal film thickness ratio is 1.7 while there are three optimal ratios of angle subtended by the ridge to the angle subtended by the pad of 0.4, 0.45, and 0.5 depending on whether load capacity or stability or both load capacity and stability is more important in the application being considered.

A Variational Principle Applied to the Plane Slider Bearing

1965 ◽  
Vol 87 (4) ◽  
pp. 1081-1082
Author(s):  
Clarence J. Maday
Keyword(s):  
Variational Principle ◽  
Film Thickness ◽  
Power Loss ◽  
Minimum Principle ◽  
Slider Bearing ◽  
One Dimensional ◽  
Dimensional Plane ◽  
Minimum Film Thickness ◽  
The One ◽  
Made In

A minimum principle from hydrodynamics is applied to the one-dimensional plane slider bearing which is provided with a self-seeking pivot mechanism. An analysis was made in which a certain integral was minimized subject to the constraint that the load, speed, and viscosity were held fixed. This analysis showed that this corresponded exactly to that combination of minimum film thickness and inclination which would minimize the power loss subject to the above-mentioned constraint. It was also found that, in order to satisfy the minimum principle, there exists a definite numerical ratio between the slider inclination and the nondimensional minimum film thickness. This, in turn, fixed the pivot location relative to the length of the slider.

The Maximum Principle Approach to the Optimum One-Dimensional Journal Bearing

1970 ◽  
Vol 92 (3) ◽  
pp. 482-487 ◽  
Author(s):  
C. J. Maday
Keyword(s):  
Maximum Principle ◽  
Film Thickness ◽  
Journal Bearing ◽  
Maximum Load ◽  
Load Direction ◽  
One Dimensional ◽  
The Maximum Principle ◽  
Minimum Film Thickness ◽  
Constant Viscosity ◽  
The One

Pontryagin’s Maximum Principle is used to determine the journal bearing which supports the maximum load for a given minimum film thickness and a specified load direction. The one-dimensional configuration which uses a constant-viscosity, incompressible lubricant is considered. Comparison shows that the optimum bearing carries a load about 13.5 percent greater than the maximum carried by the usual full-Sommerfeld bearing and about 121 percent greater than that carried by the half-Sommerfeld unit. The problem is formulated subject to the constraints of a fixed load direction and a specified minimum film thickness while the only boundary condition imposed is that the pressure must vanish at the inlet and at the outlet. The actual extent of the bearing is determined in the optimization process and it is shown that this extent is 360 deg. Further, the bearing is stepped with only two regions of different but constant film thickness.

Effect of leakage and blockage on the acoustic behavior of particle filters

2019 ◽  
Vol 67 (6) ◽  
pp. 483-492
Author(s):  
Seonghyeon Baek ◽  
Iljae Lee
Keyword(s):  
Transfer Matrix ◽  
Particle Filters ◽  
Acoustic Analysis ◽  
Transmission Loss ◽  
One Dimensional ◽  
Filter System ◽  
The Difference ◽  
The One ◽  
Analytical Approaches ◽  
Good Agreement

The effects of leakage and blockage on the acoustic performance of particle filters have been examined by using one-dimensional acoustic analysis and experimental methods. First, the transfer matrix of a filter system connected to inlet and outlet pipes with conical sections is measured using a two-load method. Then, the transfer matrix of a particle filter only is extracted from the experiments by applying inverse matrices of the conical sections. In the analytical approaches, the one-dimensional acoustic model for the leakage between the filter and the housing is developed. The predicted transmission loss shows a good agreement with the experimental results. Compared to the baseline, the leakage between the filter and housing increases transmission loss at a certain frequency and its harmonics. In addition, the transmission loss for the system with a partially blocked filter is measured. The blockage of the filter also increases the transmission loss at higher frequencies. For the simplicity of experiments to identify the leakage and blockage, the reflection coefficients at the inlet of the filter system have been measured using two different downstream conditions: open pipe and highly absorptive terminations. The experiments show that with highly absorptive terminations, it is easier to see the difference between the baseline and the defects.

An Accurate Solution of the Gas Lubricated, Flat Sector Thrust Bearing

1977 ◽  
Vol 99 (1) ◽  
pp. 82-88 ◽  
Author(s):  
I. Etsion ◽  
D. P. Fleming
Keyword(s):  
Film Thickness ◽  
Thrust Bearing ◽  
Load Capacity ◽  
Thickness Distribution ◽  
Maximum Load ◽  
Accurate Solution ◽  
Operating Conditions ◽  
Thrust Bearings ◽  
Practical Design ◽  
Minimum Film Thickness

A flat sector shaped pad geometry for gas lubricated thrust bearings is analyzed considering both pitch and roll angles of the pad and the true film thickness distribution. Maximum load capacity is achieved when the pad is tilted so as to create a uniform minimum film thickness along the pad trailing edge. Performance characteristics for various geometries and operating conditions of gas thrust bearings are presented in the form of design curves. A comparison is made with the rectangular slider approximation. It is found that this approximation is unsafe for practical design, since it always overestimates load capacity.

Limit theorems and absorption problems for quantum radom walks in one dimension

2002 ◽  
Vol 2 (Special) ◽  
pp. 578-595
Author(s):  
N. Konno
Keyword(s):  
Random Walks ◽  
Limit Theorems ◽  
The Other ◽  
One Dimension ◽  
Unitary Matrices ◽  
Quantum Random Walks ◽  
One Dimensional ◽  
The Difference ◽  
The One

In this paper we consider limit theorems, symmetry of distribution, and absorption problems for two types of one-dimensional quantum random walks determined by $2 \times 2$ unitary matrices using our PQRS method. The one type was introduced by Gudder in 1988, and the other type was studied intensively by Ambainis et al. in 2001. The difference between both types of quantum random walks is also clarified.

Relation Between Surface Crystallography and Surface Electron Structure of the Superlattice

2003 ◽  
Vol 10 (02n03) ◽  
pp. 195-199 ◽  
Author(s):  
I. Bartoš ◽  
T. Strasser ◽  
W. Schattke
Keyword(s):  
Energy Distribution ◽  
Surface State ◽  
Electron Structure ◽  
Surface Electron ◽  
One Dimensional ◽  
One Step ◽  
Surface Brillouin Zone ◽  
Topmost Layer ◽  
The One ◽  
Periodic Crystal

Profound gradual changes of surface state energies were predicted for varying surface terminations of the periodic crystal potential in one-dimensional models.1 This situation can be realized in superlattices with different thicknesses of topmost layers. For the ideally terminated (100) surface of a very thin superlattice (GaAs)2(AlAs)2, the shift of the energy of the surface state over the whole minigap in the lower part of the valence band has been found for different terminations of the topmost layer. In the center of the surface Brillouin zone the surface state shift follows model trends. The changes of the energy distribution of photoemitted electrons as determined from the one-step photoemission calculation2 indicate that experimental observation by the surface-sensitive technique of angle-resolved photoemission should be feasible, and preliminary data indicate this. The results show a straigthforward tuning of surface electron structure by geometrical means.

scholarly journals Influence of the calibration on experimental UV index at a midlatitude site, Granada (Spain)

2010 ◽  
Vol 3 (6) ◽  
pp. 5645-5670
Author(s):  
M. Antón ◽  
J. E. Gil ◽  
A. Cazorla ◽  
J. M. Vilaplana ◽  
F. J. Olmo ◽  
...  
Keyword(s):  
Calibration Method ◽  
Conversion Factors ◽  
Uv Index ◽  
Calibration Methods ◽  
One Step ◽  
The Difference ◽  
Mean Differences ◽  
Experimental Values ◽  
The One

Abstract. The ultraviolet (UV) index is the variable most commonly used to inform the general public about the levels and potential harmful effects of UV radiation incident at Earth's surface. This variable is derived from the output signal of the UV radiometers applying conversion factors obtained by calibration methods. This paper focused on the influence of the use of two of these methods (called one-step and two-steps methods) on the resulting experimental UV Index (UVI) as measured by a YES UVB-1 radiometer located in a midlatitude station, Granada (Spain) for the period 2006–2009. In addition, it is also analyzed the difference with the UVI values obtained when the calibration factors provided by the manufacturer are used. For this goal, the detailed characterization of the UVB-1 radiometer obtained in the first Spanish calibration campaign of broadband UV radiometers at the "El Arenosillo" INTA station in 2007 is used. In addition, modeled UVI data derived from the LibRadtran/UVSPEC radiative transfer code are compared with the experimental values recorded at Granada for cloud-free conditions. The absolute mean differences between the measured and modeled UVI data at Granada are around 5% using the one-step and two-steps calibration methods. This result indicates the excellent performance of these two techniques for obtaining UVI data from the UVB-1 radiometer. In contrast, the application of the calibration factor supplied by the manufacturer produces a high overestimation (~14%) of the UVI values. This fact generates unreliable alarming high UVI data in summer when the manufacturer's factor is used. Thus, days with an extreme erythemal risk (UVI higher than 10) increase up to 46% of all cases measured between May and September at Granada when the manufacturer's factor is applied. This percentage is reduced to a more reliable value of 3% when the conversion factors obtained with the two-steps calibration method are used. All these results report about the need of a sound calibration of the broadband UV instruments in order to obtain reliable measurements.

Sign in / Sign up

Export Citation Format

Share Document