A Variable Wave Speed Technique for the Steady-State Analysis of Low-Clearance Gas Bearings

1977 ◽  
Vol 99 (3) ◽  
pp. 339-344 ◽  
Author(s):  
J. W. White
Keyword(s):  
Steady State ◽  
Pressure Wave ◽  
Wave Speed ◽  
Numerical Solutions ◽  
Finite Width ◽  
Fluid Viscosity ◽  
Rigid Boundary ◽  
Steady State Analysis ◽  
Gas Bearings ◽  
State Analysis

A method is described which utilizes an artificial fluid viscosity as a means of adjusting the pressure wave speed in asymptotic steady-state analysis of gas bearings. The approach is shown to be useful for producing steady numerical solutions of low-clearance bearings with minimum computation. The technique is first developed for a rigid boundary step bearing of infinite width and then extended to the finite width case by a semi-implicit solution procedure. Last, the method is shown to be useful for the analysis of foil bearings in which case the pressure wave speed is “tuned” to that of the foil wave so as to produce an optimum computational approach to steady state.

Analysis of Single Buffer Random Polling System With State-Dependent Input Process and Server/Station Breakdowns

2018 ◽  
Vol 9 (1) ◽  
pp. 22-50 ◽  
Author(s):  
Thomas Y.S. Lee
Keyword(s):  
Steady State ◽  
Linear Model ◽  
Repair Process ◽  
Polling System ◽  
Steady State Analysis ◽  
Relaxation System ◽  
Polling Model ◽  
State Dependent ◽  
Non Linear ◽  
State Analysis

Models and analytical techniques are developed to evaluate the performance of two variations of single buffers (conventional and buffer relaxation system) multiple queues system. In the conventional system, each queue can have at most one customer at any time and newly arriving customers find the buffer full are lost. In the buffer relaxation system, the queue being served may have two customers, while each of the other queues may have at most one customer. Thomas Y.S. Lee developed a state-dependent non-linear model of uncertainty for analyzing a random polling system with server breakdown/repair, multi-phase service, correlated input processes, and single buffers. The state-dependent non-linear model of uncertainty introduced in this paper allows us to incorporate correlated arrival processes where the customer arrival rate depends on the location of the server and/or the server's mode of operation into the polling model. The author allows the possibility that the server is unreliable. Specifically, when the server visits a queue, Lee assumes that the system is subject to two types of failures: queue-dependent, and general. General failures are observed upon server arrival at a queue. But there are two possibilities that a queue-dependent breakdown (if occurs) can be observed; (i) is observed immediately when it occurs and (ii) is observed only at the end of the current service. In both cases, a repair process is initiated immediately after the queue-dependent breakdown is observed. The author's model allows the possibility of the server breakdowns/repair process to be non-stationary in the number of breakdowns/repairs to reflect that breakdowns/repairs or customer processing may be progressively easier or harder, or that they follow a more general learning curve. Thomas Y.S. Lee will show that his model encompasses a variety of examples. He was able to perform both transient and steady state analysis. The steady state analysis allows us to compute several performance measures including the average customer waiting time, loss probability, throughput and mean cycle time.

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