Optimization of Self-Acting Gas Bearings for Maximum Static Stiffness

1990 ◽  
Vol 57 (3) ◽  
pp. 758-761 ◽  
Author(s):  
Michel P. Robert
Keyword(s):  
Finite Element ◽  
Film Thickness ◽  
Calculus Of Variations ◽  
Two Dimensional ◽  
Final Solution ◽  
Static Stiffness ◽  
Finite Element Technique ◽  
Minimum Film Thickness ◽  
Element Technique ◽  
Gas Bearing

The gap profile of a two-dimensional self-acting gas bearing is determined such that the static stiffness it can achieve is maximum. Three fundamental profiles are obtained according to the stiffness mode to be considered: normal, pitch, or roll. The optimization process takes place within the framework of the compressible lubrication theory among all the profiles having a given minimum film thickness. The method proposed here is based on the calculus of variations and uses a finite element technique coupled with an iterative mapping to converge to the final solution. As an example, the case of a square bearing is treated and the three fundamental gap profiles, along with their optimum characteristics, are plotted to illustrate the solutions.

scholarly journals Two-Dimensional, Time-dependent Modelling of an Arbitrarily Shaped Ice Mass with the Finite-Element Technique

1985 ◽  
Vol 31 (109) ◽  
pp. 350-359 ◽  
Author(s):  
Steven M. Hodge
Keyword(s):  
Finite Element ◽  
Numerical Models ◽  
Basis Functions ◽  
Time Dependent ◽  
Small Computer ◽  
Two Dimensional ◽  
Maximum Increase ◽  
Steady State Condition ◽  
Finite Element Technique ◽  
Element Technique

AbstractThe two-dimensional, time-dependent flow of an arbitrarily shaped ice mass can be successfully modeled with the finite-element technique on a small computer. Methods developed for automatically generating the mesh data greatly simplify the data preparation and optimize the numerical simulations. Using quadratic basis functions permits the flow to be approximated quite adequately by only two element rows (five nodes vertically). Mixed-order basis functions, however, must be used so that numerical oscillations do not set in, and the ends of the ice mass, where the thickness tends to zero, must be treated carefully. Time simulations to a steady-state condition are necessary to test such numerical models adequately.South Cascade Glacier, Washington, is currently close to equilibrium. A bedrock sill dominates the bed topography in the lower half of the glacier, rising to a height of about 20% of the ice thickness. This sill produces a maximum increase in the overall thickness of about 6–7% compared to what the thickness would have been if the sill were not present. Finally, this glacier does not appear to be sliding much, if at all, despite its maritime alpine environment. This could help explain the difficulties encountered when trying to measure sliding and basal water pressures on the same glacier (Hodge, 1979), or it could imply that drag exerted by the valley walls has a significantly greater effect than conventional shape-factor concepts imply.

scholarly journals Two-Dimensional, Time-dependent Modelling of an Arbitrarily Shaped Ice Mass with the Finite-Element Technique

1985 ◽  
Vol 31 (109) ◽  
pp. 350-359 ◽  
Author(s):  
Steven M. Hodge
Keyword(s):  
Finite Element ◽  
Numerical Models ◽  
Basis Functions ◽  
Time Dependent ◽  
Small Computer ◽  
Two Dimensional ◽  
Maximum Increase ◽  
Steady State Condition ◽  
Finite Element Technique ◽  
Element Technique

AbstractThe two-dimensional, time-dependent flow of an arbitrarily shaped ice mass can be successfully modeled with the finite-element technique on a small computer. Methods developed for automatically generating the mesh data greatly simplify the data preparation and optimize the numerical simulations. Using quadratic basis functions permits the flow to be approximated quite adequately by only two element rows (five nodes vertically). Mixed-order basis functions, however, must be used so that numerical oscillations do not set in, and the ends of the ice mass, where the thickness tends to zero, must be treated carefully. Time simulations to a steady-state condition are necessary to test such numerical models adequately.South Cascade Glacier, Washington, is currently close to equilibrium. A bedrock sill dominates the bed topography in the lower half of the glacier, rising to a height of about 20% of the ice thickness. This sill produces a maximum increase in the overall thickness of about 6–7% compared to what the thickness would have been if the sill were not present. Finally, this glacier does not appear to be sliding much, if at all, despite its maritime alpine environment. This could help explain the difficulties encountered when trying to measure sliding and basal water pressures on the same glacier (Hodge, 1979), or it could imply that drag exerted by the valley walls has a significantly greater effect than conventional shape-factor concepts imply.

scholarly journals COMPUTATION OF COMBINED REFRACTION - DIFFRACTION

1972 ◽  
Vol 1 (13) ◽  
pp. 23 ◽  
Author(s):  
J.C.W. Berkhoff
Keyword(s):  
Differential Equation ◽  
Finite Element ◽  
Small Parameter ◽  
Source Distribution ◽  
Harmonic Waves ◽  
Two Dimensional ◽  
Distribution Method ◽  
Finite Element Technique ◽  
Element Technique

This paper treats the derivation of a two-dimensional differential equation, which describes the phenomenon of combined refraction - diffraction for simple harmonic waves, and a method of solving this equation. The equation is derived with the aid of a small parameter development, and the method of solution is based on the finite element technique, together with a source distribution method.

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