Deceleration of an Unbalanced Rotor Through a Critical Speed

1967 ◽  
Vol 89 (4) ◽  
pp. 582-585
Author(s):  
W. K. Bodger
Keyword(s):  
Critical Speed ◽  
Degree Of Freedom ◽  
Bending Stress ◽  
Rotor Speed ◽  
Single Degree Of Freedom ◽  
Closed Solution ◽  
Rotor Shaft ◽  
Single Degree ◽  
Unbalanced Rotor ◽  
Maximum Increment

The problem of a single-degree-of-freedom rotor decelerating slowly through its critica speed is solved by an energy approach; a closed solution is obtained. A small discontinuous downward jump of rotor speed across the critical speed is shown to be required, either with or without damping in the system. The maximum increment of deflection, hence bending stress, in the rotor shaft is shown to be small, provided the rotor is carefully balanced and/or the system is sufficiently damped.

The Acceleration of a Single Degree of Freedom System Through its Resonant Frequency

1958 ◽  
Vol 62 (574) ◽  
pp. 752-757 ◽  
Author(s):  
S. Hother-Lushington ◽  
D. C. Johnson
Keyword(s):  
Resonant Frequency ◽  
Critical Speed ◽  
Bessel Functions ◽  
Degree Of Freedom ◽  
Series Solutions ◽  
Mechanical Vibrations ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Method Of Solution ◽  
Simple Integration

It is Sometimes required to find the maximum amplitudes of vibration attained and the speeds at which they occur when a machine is run through its critical speed with different accelerations. The solution of this problem for single degree of freedom systems has been obtained by Lewis and by Ellington and McCallion for mechanical vibrations and by Hok for the equivalent electrical case. These solutions require higher mathematics (contour integration, Fresnel's integrals or series solutions leading to Bessel functions). The purpose of this note is to show how, by using simple integration only, an alternative method of solution can be obtained for both zero and small values of damping.

On the Critical Speed of Continuous Shaft-Disk Systems

1984 ◽  
Vol 106 (1) ◽  
pp. 59-61 ◽  
Author(s):  
H. Nevzat O¨zgu¨ven
Keyword(s):  
Critical Speed ◽  
Degree Of Freedom ◽  
Mass Ratio ◽  
Disk System ◽  
Single Degree Of Freedom ◽  
Single Degree

The critical speed of a shaft-disk system can be approximately determined from a single degree-of-freedom model. The errors in the critical speed predictions obtained from such a model are investigated. The percentage errors are plotted against disk to shaft mass ratio for different bearings and various disk locations.

Kinematic comparison of single degree-of-freedom robotic gait trainers

2021 ◽  
Vol 159 ◽  
pp. 104258
Author(s):  
Jeonghwan Lee ◽  
Lailu Li ◽  
Sung Yul Shin ◽  
Ashish D. Deshpande ◽  
James Sulzer
Keyword(s):  
Degree Of Freedom ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Robotic Gait

Single-Degree-of-Freedom Based Pressure-Impulse Diagrams for Blast Damage Assessment

2014 ◽  
Vol 567 ◽  
pp. 499-504 ◽  
Author(s):  
Zubair Imam Syed ◽  
Mohd Shahir Liew ◽  
Muhammad Hasibul Hasan ◽  
Srikanth Venkatesan
Keyword(s):  
Damage Assessment ◽  
Structural Response ◽  
Blast Loading ◽  
Computational Effort ◽  
Degree Of Freedom ◽  
Negative Phase ◽  
Single Degree Of Freedom ◽  
Pressure Impulse ◽  
Single Degree ◽  
Structural Resistance

Pressure-impulse (P-I) diagrams, which relates damage with both impulse and pressure, are widely used in the design and damage assessment of structural elements under blast loading. Among many methods of deriving P-I diagrams, single degree of freedom (SDOF) models are widely used to develop P-I diagrams for damage assessment of structural members exposed to blast loading. The popularity of the SDOF method in structural response calculation in its simplicity and cost-effective approach that requires limited input data and less computational effort. The SDOF model gives reasonably good results if the response mode shape is representative of the real behaviour. Pressure-impulse diagrams based on SDOF models are derived based on idealised structural resistance functions and the effect of few of the parameters related to structural response and blast loading are ignored. Effects of idealisation of resistance function, inclusion of damping and load rise time on P-I diagrams constructed from SDOF models have been investigated in this study. In idealisation of load, the negative phase of the blast pressure pulse is ignored in SDOF analysis. The effect of this simplification has also been explored. Matrix Laboratory (MATLAB) codes were developed for response calculation of the SDOF system and for repeated analyses of the SDOF models to construct the P-I diagrams. Resistance functions were found to have significant effect on the P-I diagrams were observed. Inclusion of negative phase was found to have notable impact of the shape of P-I diagrams in the dynamic zone.

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