Abstract:High performance oil-free turbomachinery implements gas foil bearings (FBs) to improve mechanical efficiency in compact units. FB design, however, is still largely empirical due to its mechanical complexity. The paper provides test results for the structural parameters in a bump-type foil bearing. The stiffness and damping (Coulomb or viscous type) coefficients characterize the bearing compliant structure. The test bearing, 38.1mm in diameter and length, consists of a thin top foil supported on bump-foil strip… Show more
“…It is important to note that the static force coefficients depend on static eccentricity and rotational speed, whereas the dynamic bearing coefficients are governed by the zeroth order pressure distribution plus excitation frequency, which might be different from the shaft rotational frequency. Kim and San Andrés [17] account for mechanical dissipation losses generated by Coulomb friction between the foils via a structural loss coefficient, c. Typical bump-type foil bearings yield empirical structural loss coefficients ranging from 0.05 to 0.2 for nondimensional static loads of 0.028 to 0.14 [28]. The foil bearing under investigation is composed of a singleleaf top foil that is loosely laid upon a bump foil.…”
Experimental evidence in the literature suggests that foil bearing-supported rotors can suffer from subsynchronous vibration. While dry friction between top foil and bump foil is thought to provide structural damping, subsynchronous vibration is still an unresolved issue. The current paper aims to shed new light onto this matter and discusses the impact of various design variables on stable foil bearing-supported rotor operation. It is shown that, while a time domain integration of the equations of motion of the rotor coupled with the Reynolds equation for the fluid film is necessary to quantify the evolution of the rotor orbit, the underlying mechanism and the onset speed of instability can be predicted by coupling a reduced order foil bearing model with a rigid-body, linear, rotordynamic model. A sensitivity analysis suggests that structural damping has limited effect on stability. Further, it is shown that the location of the axial feed line of the top foil significantly influences the bearing load capacity and stability. The analysis indicates that the static fluid film pressure distribution governs rotordynamic stability. Therefore, selective shimming is introduced to tailor the unperturbed pressure distribution for improved stability. The required pattern is found via multiobjective optimization using the foil bearing-supported rotor model. A critical mass parameter is introduced as a measure for stability, and a criterion for whirl instability onset is proposed. It is shown that, with an optimally shimmed foil bearing, the critical mass parameter can be improved by more than two orders of magnitude. The optimum shim patterns are summarized for a variety of foil bearing geometries with different L/D ratios and different degrees of foil compliance in a first attempt to establish more general guidelines for stable foil bearing design. At low compressibility (Λ < 2), the optimum shim patterns vary little with bearing geometry; thus, a generalized shim pattern is proposed for low compressibility numbers.
“…It is important to note that the static force coefficients depend on static eccentricity and rotational speed, whereas the dynamic bearing coefficients are governed by the zeroth order pressure distribution plus excitation frequency, which might be different from the shaft rotational frequency. Kim and San Andrés [17] account for mechanical dissipation losses generated by Coulomb friction between the foils via a structural loss coefficient, c. Typical bump-type foil bearings yield empirical structural loss coefficients ranging from 0.05 to 0.2 for nondimensional static loads of 0.028 to 0.14 [28]. The foil bearing under investigation is composed of a singleleaf top foil that is loosely laid upon a bump foil.…”
Experimental evidence in the literature suggests that foil bearing-supported rotors can suffer from subsynchronous vibration. While dry friction between top foil and bump foil is thought to provide structural damping, subsynchronous vibration is still an unresolved issue. The current paper aims to shed new light onto this matter and discusses the impact of various design variables on stable foil bearing-supported rotor operation. It is shown that, while a time domain integration of the equations of motion of the rotor coupled with the Reynolds equation for the fluid film is necessary to quantify the evolution of the rotor orbit, the underlying mechanism and the onset speed of instability can be predicted by coupling a reduced order foil bearing model with a rigid-body, linear, rotordynamic model. A sensitivity analysis suggests that structural damping has limited effect on stability. Further, it is shown that the location of the axial feed line of the top foil significantly influences the bearing load capacity and stability. The analysis indicates that the static fluid film pressure distribution governs rotordynamic stability. Therefore, selective shimming is introduced to tailor the unperturbed pressure distribution for improved stability. The required pattern is found via multiobjective optimization using the foil bearing-supported rotor model. A critical mass parameter is introduced as a measure for stability, and a criterion for whirl instability onset is proposed. It is shown that, with an optimally shimmed foil bearing, the critical mass parameter can be improved by more than two orders of magnitude. The optimum shim patterns are summarized for a variety of foil bearing geometries with different L/D ratios and different degrees of foil compliance in a first attempt to establish more general guidelines for stable foil bearing design. At low compressibility (Λ < 2), the optimum shim patterns vary little with bearing geometry; thus, a generalized shim pattern is proposed for low compressibility numbers.
“…The sharp amplitude increases at the shut-down stage of Cases C and D can be attributed to the small damping of HGFB, and the resonant vibration caused by the friction between the rotor and the bearing surface. 20 Both the conventional HGFB and the new DPGFB can achieve stable performance of high speed operation in the experiments. At the same speed, the HGFB with 0Cr18Ni9 and the DPGFB shows better damping performance than that of the HGFB with QBe1.7.…”
Section: Resultsmentioning
confidence: 93%
“…21 The quick increase of the synchronous amplitude at 90° could validate the prediction of Rubio. 20 Figure 8.Phase angle of synchronous vibration as a function of rotation speed.…”
In this paper, the hydrodynamic performance of a new double-layered protuberant gas foil journal bearing (DPGFB) was experimentally studied in a high-speed turbo-expander and compared with the conventional Hydresil foil journal bearing (HGFB). The material properties of supporting foils are important for the bearing performance such as load capacity and frictional damping. In both DPGFBs and HGFBs, two types of materials, stainless steel (0Cr18Ni9) and beryllium bronze (QBe1.7), have been used as supporting foil materials, and their effects on the bearing performance were discussed. A stable operation of turbo-expander with rotational speed up to 70,000 rpm was achieved in the tests of both of two types of bearings. Due to the larger stiffness of the foil layer, the DPGFBs had larger lift-off speed and larger gas film friction torque than HGFBs at high speed when the same foil material was used. The comparison showed that the bearings using 0Cr18Ni9 had a larger life-off friction torque. The synchronous vibration amplitudes of the rotors during the high speed operation and the shut-down process were smaller for DPGFBs than HGFBs, which indicated that the DPGFBs had a better damping performance than HGFBs.
“…These dynamic instabilities, also called stick-slip motion result in self-excited vibrations and drastic decreases in performance of some machine parts. Oscillating systems excited by dry friction are frequently encountered in many practical applications, including for instance brake systems [2,3], hydraulic cylinders [4], gears [5] or bearing [6]. Therefore the extensive analysis of these non-smooth dynamic systems to detect instabilities is a crucial point in engineering design.…”
Parametric studies for dynamic systems are of high interest to detect instability domains. This prediction can be demanding as it requires a refined exploration of the parametric space due to the disrupted mechanical behavior. In this paper, an efficient surrogate strategy is proposed to investigate the behavior of an oscillator of Duffing's type in combination with an elasto-plastic friction force model. Relevant quantities of interest are discussed. Sticking time is considered using a machine learning technique based on Gaussian processes called kriging. The largest Lyapunov exponent is proposed as an efficient indicator of non-regular behavior. This indicator is estimated using a perturbation method. A dedicated adaptive kriging strategy for classification called MiVor is utilized and appears to be highly proficient in order to detect instabilities over the parametric space and can furthermore be used for complex response surfaces in multi-dimensional parametric domains.
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