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Application of Short and Long (Enhanced Vlasov's) Solutions for Cylindrical Shell on Example of Concentrated Radial Force

2020 ◽  
Vol 143 (1) ◽  
Author(s):  
Andrii Oryniak ◽  
Igor Orynyak
Keyword(s):  
Cylindrical Shell ◽  
Efficient Solution ◽  
Radial Force ◽  
Circumferential Direction ◽  
Axial Line ◽  
Eighth Order ◽  
Concentrated Force ◽  
Accuracy Of Results ◽  
Analytical Approaches ◽  
Asme Paper

Abstract Analytical approaches for cylindrical shell are mostly based on expansion of all variables in Fourier series in circumferential direction. This leads to eighth-order differential equation with respect to axial coordinate. Here it is approximately treated as a sum of two fourth-order biquadratic equations. First one assumes that all variables change more quickly in circumferential direction than in axial one (long solution), while the second (short) one is based on opposite assumption. The accuracy and applicability of this approach were demonstrated (Orynyak, I., and Oryniak, A., 2018, “Efficient Solution for Cylindrical Shell Based on Short and Long (Enhanced Vlasov's) Solutions on Example of Concentrated Radial Force,” ASME Paper No. PVP2018-85032) on example of action of one or two concentrated radial forces and compared with finite element method results. This paper is an improvement of our previous work (Orynyak, I., and Oryniak, A., 2018, “Efficient Solution for Cylindrical Shell Based on Short and Long (Enhanced Vlasov's) Solutions on Example of Concentrated Radial Force,” ASME Paper No. PVP2018-85032). Two amendments are made. The first is insignificant one and use slightly modified expressions for bending strains, while the second one relates to the short solution. Here we do not consider any more that circumferential displacement is negligible as compared with radial one. Eventually this improves the accuracy of results, as compared with previous work. For example, for cylinder with radius, R, to wall thickness, h, ratio equal to 20, the maximal inaccuracy for radial displacement in point of force application decreases from 5% to 3%. For thinner cylinder with R/h = 100, this inaccuracy decreases from 2.5% to 1.25%. These inaccuracies are related to larger terms in Fourier expansion, the significance of which decrease when length or area of outer loading becomes greater. The last conclusion is demonstrated for the case of distributed concentrated force acting along short segment on axial line.

Experimental Rotordynamic Force Coefficients for a Diffusion Bonded Compliant Hybrid Journal Gas Bearing Utilizing Fluid-Filled Hermetic Dampers

2020 ◽  
Vol 142 (4) ◽  
Author(s):  
Keith Gary ◽  
Bugra Ertas
Keyword(s):  
Dynamic Testing ◽  
Companion Paper ◽  
Squeeze Film ◽  
Dynamic Force ◽  
Force Coefficients ◽  
Squeeze Film Dampers ◽  
Lower Excitation ◽  
Excitation Frequencies ◽  
Gas Bearing ◽  
Asme Paper

Abstract Dynamic force coefficients are presented from experimental results of a radial gas bearing with hermetically sealed squeeze film dampers (HSFDs) in the bearing support. HSFDs are a relatively new technology aimed to increase damping levels in gas bearings while sustaining an oil-free bearing sump. Past HSFD designs proved bulky and contained many components making it difficult to employ in size-limited environments such as jet engines, while the diffusion bonded bearing discussed in this paper provides a compact integral design. Details of the design are found in a companion paper by Ertas (Ertas, B. H., 2019, “Compliant Hybrid Gas Bearing Using Integral Hermetically-Sealed Squeeze Film Dampers,” ASME Paper No. GT2018-76312). Test results for a 3 in. (76.2 mm) diameter bearing using a test rig providing static loads up to 80 lbs (356 N), controlled-dynamic orbital motion, and speeds up to 27 krpm are shown. Results include frequency- and speed-dependent direct and cross-coupled rotordynamic force coefficients. Dynamic testing showed little dependence on rotor speed or static load and exhibited frequency dependency at lower excitation frequencies. Cross-coupled terms are generally an order of magnitude lower than direct terms. Results show the direct stiffness coefficients increasing with frequency, while direct damping decays radically with frequency. Comparison of the overall gas bearing coefficients with the companion paper (Ertas, B. H., 2019, “Compliant Hybrid Gas Bearing Using Integral Hermetically-Sealed Squeeze Film Dampers,” ASME Paper No. GT2018-76312), showing bearing support coefficients, reveals a drastic reduction in damping when engaging the gas film. The results also indicate that the bearing can withstand vibration levels representative of a large rotor system critical speed at lower excitation frequencies.

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