Thermo-elastohydrodynamic analysis of the inhomogeneous foil bearing with misalignment

Purpose The misalignment is generally inevitable in the process of machining and assembly of rotor systems with gas foil bearings, but the exploration on this phenomenon is relatively less. Therefore, the purpose of this paper is to carry out the thermo-elastohydrodynamic analysis of the foil bearing with misalignment, especially the inhomogeneous foil bearing. Design/methodology/approach The rotor is allowed to misalign in two non-rotating directions. Then the static and dynamic performance of the inhomogeneous foil bearing is studied. The thermal-elastohydrodynamic analysis is realized by combining the Reynolds equation, foil deformation equation and energy equation. The small perturbation method is used to calculate the dynamic coefficients, then the critical whirl ratio is obtained. Findings The gas pressure, film thickness and temperature distribution distort when the misalignment appears. The rotor misalignment can improve the loading capacity but rise the gas temperature at the same time. Furthermore, the rotor misalignment can affect the critical whirl ratio which demonstrates that it is necessary to analyze the misalignment before the rotordynamic design. Originality/value The value of this paper is the exploration of the thermo-elastohydrodynamic performance of the inhomogeneous foil bearing with misalignment, the analysis procedure and the corresponding results are valuable for the design of turbo system with gas foil bearings.

Thermal Characteristics Study of the Bump Foil Thrust Gas Bearing

In this paper, a thermo-hydrodynamic model of the bump foil thrust gas bearing is developed, which solves the coupled gas film three-dimensional energy equation, non-isothermal Reynolds equation, and the foil deformation equation. The effects of bearing speed, thrust load, and external cooling gas on the bearing temperature field are calculated and analyzed. The test rig of foil thrust gas bearing was built to measure the bearing temperature under different working conditions. Both simulation and experiment results show that there exist temperature gradients on the top foil both in the circumferential and radial directions. The simulation results also shows that the top foil side of the gas film has the highest temperature value in the entire lubrication field, and the position of highest temperature moves radially inward on the thrust plate side as the rotor speed increases. The gas film temperature increases with the increasing rotor speed and bearing static load, and rotor speed has greater effects on the temperature variation. Cooling air flow passing through the bump foil is also considered in the simulations, and the cooling efficiency decreases as the mass of gas flow increases.

CONSTITUTIVE MODELING OF DYNAMIC RECRYSTALLIZATION AND PRECIPITATION BEHAVIOR OF Nb AND Ti OF Q1030 HIGH STRENGTH STEEL

The thermal deformation and precipitation behavior at 900-1100℃ and strain rate of 0.1-5s-1 were studied by Gleeble-3800 thermal simulator of Q1030 high strength steel. The activation energy of hot deformation in austenite region was determined by regression method, and the hot deformation equation of the Q1030 high strength steel was established. The critical strain and peak strain of dynamic recrystallization were predicted accurately by fitting the inflection point with cubic polynomial of curve of Q1030 high strength steel, and relationship between critical strain and Z parameter was established. Finally, the precipitation behavior of Nb and Ti particles during low strain rate deformation was studied, the results show that the precipitated phases in steel are rectangular TiN, quadratic (Nb, Ti) (C, N) carbonitride, elliptical (Nb, Ti) C carbide and NbC. Thermodynamic calculation shows that the order of precipitation of the second phase in steel is TiN, TiC, NbC and NbN.

On Symmetrical Deformation of Toroidal Shell with Circular Cross-Section

By introducing a variable transformation $\xi=\frac{1}{2}(\sin \theta+1)$, the symmetrical deformation equation of elastic toroidal shells is successfully transferred into a well-known equation, namely Heun's equation of ordinary differential equation, whose exact solution is obtained in terms of Heun's functions. The computation of the problem can be carried out by symbolic software that is able to with the Heun's function, such as Maple. The Gauss curvature of the elastic toroidal shells shows that the internal portion of the toroidal shells has better bending capacity than the outer portion, which might be useful for the design of metamaterials with toroidal shells cells. Through numerical comparison study, the mechanics of elastic toroidal shells is sensitive to the radius ratio. By slightly adjustment of the ratio might get a desired high performance shell structure.

Model Test and Numerical Study on Surrounding Rock Deformation and Overburden Strata Movement Law of Gob-Side Entry Retaining via Roof Cutting

The effects of roof cutting techniques on the movement law of the overlying strata and deformation features of the surrounding rock in gob-side entry retaining mines were studied using 200 working faces of the Dianping coal mine in Shanxi Province. Using a mechanical analysis, a cantilever beam model formed by roof cutting was used to derive a deformation equation. The physical model test based on the field prototype revealed an asymmetrically distributed displacement curve and reduced collapse displacement when the rock stratum was far from the cutting seam. Outside of the roof cutting height, the collapse of the overlying strata gradually reached a symmetric distribution with increasing height. The deformation of the retained roadway was mainly concentrated on the roof, and the maximum deformation was 14 mm near the roof cutting side. A numerical simulation of the original size of the model test proved that the laws of strata movement and surrounding rock deformation were consistent with the physical test results. Finally, field measurements were performed, which verified the rationality of this study.

On Symmetrical Deformation of Toroidal Shell with Circular Cross-Section

By introducing a variable transformation $\xi=\frac{1}{2}(\sin \theta+1)$, the complicated deformation equation of toroidal shell is successfully transferred into a well-known equation, namely Heun's equation of ordinary differential equation, whose exact solution is obtained in terms of Heun's functions. The computation of the problem can be carried out by symbolic software that is able to with the Heun's function, such as Maple. The geometric study of the Gauss curvature shows that the internal portion of the toroidal shell has better bending capacity than the outer portion, which might be useful for the design of metamaterials with toroidal shell cells.

Hydro-Elastic Oscillations of the Bottom Membrane of a Rectangular Container Filled with Fluid

The analysis of the hydro-elastic interactions of the covering membrane of fluid-filled cavities or containers has a main importance due to the solution of practical problems founded in engineering applications. In this paper the dynamic behaviour of the bottom membrane of a rectangular container filled with a non-viscous and incompressible fluid is analyzed. The fluid velocity potential is obtained first by applying a method of separation of variables and afterwards the pressure field is calculated with the momentum’s linearized equation. Taking into account the deformation equation for the membrane in contact with the fluid and by applying a discretization procedure to the associated generalized work equation, a system is obtained, for the calculus of the membrane frequencies of vibration. The influence of different geometrical parameters such as dimension, aspect ratio, container relative height, relative thickness as well as the fluid density on these frequencies is analysed. Validation of the method is made by comparing the results with those obtained by other authors and theories.

Study on the performance of gas foil thrust bearings with stacked bump foils

Purpose This paper aims to improve the load capacity of gas foil thrust bearing (GFTB) and to introduce and study a novel bearing with stacked bump foils. Design/methodology/approach For the proposed novel GFTB supported by stacked foils, some bump-type gaskets with several partial arches are inserted below the regular bump foil, and the height of each arch can be made differently. These features make the bump foil thickness and height gradually increase, which can bring enhanced support stiffness and convergent film at the trailing edge. Based on a new nonlinear bump stiffness model considering bump rounding and friction force, the finite element and finite difference method were used to solve the coupling Reynolds equation, energy equation and foil deformation equation. Finally, the structural stiffness and static characteristics of the novel GFTB were gained and compared with the traditional bearing. Findings The novel GFTB has an additional convergence effect in the parallel section, which improves the static performance of bearing. The bearing capacity, friction moment, power loss and temperature rise of the novel GFTB are all higher than those of the traditional bearing, and the static characteristics are related to the parameters of stacked bump foils. Originality/value The stacked bump foils bring a fundamental enhancement on the load capacity of GFTB. The results are expected to be helpful to bearing designers, researchers and academicians concerned. Peer review The peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-10-2019-0449/

Focused Ultrasound Ablation for the Treatment of Patients With Localized Deformed Breast Cancer: Computer Simulation

This paper is carried out on the computer simulation of breast cancer treated using a high intensity focused ultrasound (HIFU). The mathematical models consist of the pressure acoustics equation, bioheat equation, heat transfer in a blood vessel, momentum equations in a blood vessel, and mechanical deformation equation. In the numerical simulation, these mathematical models are solved by using an axisymmetric finite element method (FEM) with time-dependent, thermal and acoustic properties to describe the temperature distribution and the total displacement in tissue. The comparison of the simulated results in the model with two sizes of the cancer tumor and two frequencies of ultrasound are also considered in order to approach realistic tissue modeling. The results show that the breast cancer model with deformation, which is the more accurate way to simulate the physical characteristics of therapeutic breast cancer compared to the literature results, hence leads to more useful in the medical approach and this study was conducted to prevent errors caused by inaccurate focal points.

Modified Fourier–Galerkin Solution for Aerospace Skin-Stiffener Panels Subjected to Interface Force and Mixed Boundary Conditions

Aeronautical stiffened panels composed of thin shells and beams are prone to deformation or buckling due to the combined loading, functional boundary conditions and interface forces between joined parts in the assembly processes. In this paper, a mechanical prediction model of the multi-component panel is presented to investigate the deformation propagation, which has a significant effect on the fatigue life of built-up structures. Governing equations of Kirchhoff–Love shell are established, of which displacement expressions are transformed into Fourier series expansions of several introduced potential functions by applying the Galerkin approach. This paper presents an intermediate quantity, concentrated force at the joining interface, to describe mechanical interactions between the coupled components. Based on the Euler–Bernoulli beam theory, unknown intermediate quantity is calculated by solving a 3D stringer deformation equation with static boundary conditions specified on joining points. Compared with the finite element simulation and integrated model, the proposed method can substantially reduce grid number without jeopardizing the prediction accuracy. Practical experiment of the aircraft panel assembly is also performed to obtain the measured data. Maximum deviation between the experimental and predicted clearance values is 0.193 mm, which is enough to meet the requirement for predicting dimensional variations of the aircraft panel assembly.