The Effect of Support Flexibility and Damping on the Synchronous Response of a Single-Mass Flexible Rotor

1972 ◽  
Vol 94 (1) ◽  
pp. 221-232 ◽  
Author(s):  
R. G. Kirk ◽  
E. J. Gunter
Keyword(s):  
Steady State ◽  
Equations Of Motion ◽  
Optimization Procedure ◽  
Dynamic Vibration Absorber ◽  
Steady State Analysis ◽  
Transient Motion ◽  
Unbalance Response ◽  
Single Mass ◽  
Effect Of Support ◽  
State Analysis

This paper deals with the dynamic unbalance response and transient motion of the single-mass Jeffcott rotor in elastic bearings mounted on damped, flexible supports. A steady-state analysis of the shaft and the bearing housing motion was made by assuming synchronous precession of the system. The conditions under which the support system would act as a dynamic vibration absorber at the rotor critical speed were studied and plots of the rotor and support amplitudes, phase angles, and forces transmitted were evaluated by the computer and the performance curves were plotted by an automatic plotter unit. Curves are presented on the optimization of the support housing characteristics to attenuate the rotor synchronous unbalance response. The complete transient motion including rotor unbalance was examined by integrating the equations of motion numerically using a modified 4th-order Runge–Kutta procedure and the resulting whirl orbits were plotted by an automatic plotter unit. The results of the transient analysis are discussed with regard to the design optimization procedure derived from the steady-state analysis.

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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