On stresses of an isotropic elastic disc in the form of a cardioid rotating steadily in its plane

1955 ◽  
Vol 6 (2) ◽  
pp. 136-139 ◽  
Author(s):  
Debendranath Mitra
Keyword(s):  
Elastic Disc

3-D elastic coupling vibration and acoustical radiation characteristics of cracked gear under elastic support condition

2015 ◽  
Vol 23 (9) ◽  
pp. 1548-1568 ◽  
Author(s):  
Shao Renping ◽  
Purong Jia ◽  
Xiankun Qi
Keyword(s):  
Dynamic Response ◽  
Support System ◽  
Three Dimensional ◽  
Elastic Support ◽  
Dynamic Responses ◽  
Tooth Root ◽  
Support Condition ◽  
Elastic Boundary ◽  
Root Crack ◽  
Elastic Disc

According to the actual working condition of the gear, the supporting gear shaft is treated as an elastic support. Its impact on the gear body vibration is considered and investigated and the dynamic response of elastic teeth and gear body is analyzed. On this basis, the gear body is considered as a three-dimensional elastic disc and the gear teeth are treated as an elastic cantilever beam. Under the conditions of the elastic boundary (support shaft), combining to the elastic disk and elastic teeth, the influence of three-dimensional elastic discs on the meshing tooth response under an elastic boundary condition is also included. A dynamic model of the gear support system and calculated model of the gear tooth response are then established. The inherent characteristics of the gear support system and dynamics response of the meshing tooth are presented and simulated. It was shown by the results that it is correct to use the elastic support condition to analyze the gear support system. Based on the above three-dimensional elastic dynamics analysis, this paper set up a dynamics coupling model of a cracked gear structure support system that considered the influence of a three-dimensional elastic disc on a cracked meshing tooth under elastic conditions. It discusses the dynamic characteristic of the cracked gear structure system and coupling dynamic response of the meshing tooth, offering a three-dimensional elastic body model of the tooth root crack and pitch circle crack with different sizes, conducting the three-dimensional elastic dynamic analysis to the faulty crack. ANSYS was employed to carry out dynamic responses, as well as to simulate the acoustic field radiation orientation of a three-dimensional elastic crack body at the tooth root crack and pitch circle with different sizes.

scholarly journals EIGENVALUES EVALUATION OF GENERALLY DAMPED ELASTIC DISC BRAKE MODEL LOADED WITH NON-CONSERVATIVE FRICTION FORCE

2020 ◽  
Vol 60 (1) ◽  
pp. 81-87
Author(s):  
Juraj Úradníček ◽  
Miloš Musil ◽  
Michal Bachratý
Keyword(s):  
Friction Force ◽  
Degrees Of Freedom ◽  
Positive Real Part ◽  
System Stability ◽  
Positive Real ◽  
Disk Brake ◽  
Double Eigenvalues ◽  
Time Domain Response ◽  
Coulomb Friction Force ◽  
Elastic Disc

This paper deals with the evaluation of eigenvalues of a linear damped elastic two-degrees-of-freedom system under a non- onservative loading. As a physical interpretation of a proposed mathematical model, a simplified disk brake model is considered. A spectral analysis is performed to predict an eigenvalues bifurcation, known as the Krein collision, leading to double eigenvalues, one of them having a positive real part causing a vibration instability of the mechanical systems. This defective behaviour of eigenvalues is studied with respect to a magnitude of non-conservative Coulomb friction force, through the variation of the friction coefficient. The influence of a proportional versus general damping on the system stability is further analysed. The generalized non-symmetric eigenvalue problem calculation is employed for spectral analyses, while a modal decomposition is performed to obtain a time-domain response of the system. The analyses are compared with an experiment.

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