Analytical Forces Parameters Identification of Hybrid Journal Gas Bearing Based on Transfer Function

Author(s):  
Guang-hui Zhang ◽  
Zhan-sheng Liu ◽  
Gui-long Wang ◽  
Jia-jia Yan

A mathematical model for the flow in the hybrid gas journal bearing is depicted by the transfer function in this paper. The average and modified parameters from the pressure distribution of multi-orifices aerostatic journal bearing are acquired to describe the characteristics accurately. The transient gas film forces of multi-orifices hybrid bearing is derived in the generalized form by analytical means, and then the dynamic characteristics coefficients are got by employing the Laplace transform. It indicates that the obtained forces can calculate the dynamic characteristics coefficients simply, quickly and accurately, which provide an efficient means for designing rotor-bearing systems.

1999 ◽  
Vol 121 (2) ◽  
pp. 301-305 ◽  
Author(s):  
L Q. Liu ◽  
C. Z. Chen

To investigate the dynamic characteristics of gas bearings with holes of tangential supply (TS bearing), drawing on the modified Reynolds equations proposed by Mori, we present new governing equations and their reasonable boundary conditions. Using this mathematical model, the inertia effect of the supplied gas on the aerodynamic film force can be evaluated properly. The governing equations are solved numerically using Finite Element Method (FEM), and the pressure distribution of the gas in the bearing, the critical whirl ratio and so on, are calculated for a typical design. Some results for a cylindrical journal bearing (CJ bearing) and ordinary bearing with holes of radial supply (RS bearing) are also provided for comparison.


2019 ◽  
Vol 8 (2S11) ◽  
pp. 3653-3657

Present paper is designed to compare the distribution of digoxin in three compartment model administered through an intravenous (i.v). These models under consideration is denoted by a system of non-linear ordinary differential equations. The Eigenvalue and the Laplace transform methods were used to solve the system of equations. Digoxin was administered to five subjects through Intravenous then, the serum digoxin concentrations were measured respectively over a period of 72 hours. The transfer coefficients were obtained from observed digoxin concentrations using method of residuals and the variation of digoxin concentration – time curves plotted using MATLAB.


1964 ◽  
Vol 86 (2) ◽  
pp. 405-413 ◽  
Author(s):  
R. J. Wernick ◽  
C. H. T. Pan

The Reynolds equation applicable to a self-acting partial-arc gas journal bearing is perturbed in terms of the compressibility number Λ. The resulting set of equations is then put into a standard form and Galerkin’s method is used to obtain bearing loads and stability derivatives. These results are expressed in a power series in Λ.


2021 ◽  
Vol 2096 (1) ◽  
pp. 012149
Author(s):  
V Kramar

Abstract The paper proposes an approach to constructing a mathematical model of lattice functions, which are mainly used in the study of discrete control systems in the time and domain of the Laplace transform. The proposed approach is based on the assumption of the physical absence of an impulse element. An alternative to the classical approach to the description of discrete data acquisition - the process of quantization in time, is considered. As a result, models of the lattice function in the time domain and the domain of the discrete Laplace transform are obtained. Based on the obtained mathematical models of lattice functions, a mathematical model of the time quantization element of the system is obtained. This will allow in the future to proceed to the construction of mathematical models of various discrete control systems, incl. expanding the proposed approaches to the construction of mathematical models of multi-cycle continuous-discrete automatic control systems


Author(s):  
L. X. Liu ◽  
Z. S. Spakovszky

The high-speed micro hydrostatic gas journal bearings used in the high-power density MIT micro-engines are of very low aspect ratio with an L/D of less than 0.1 and are running at surface speeds of order 500 m/s. These ultra-short high-speed bearings exhibit whirl instability limits and a dynamic behavior much different from conventional hydrostatic gas bearings. The design space for stable high-speed operation is confined to a narrow region and involves singular behavior (Spakovszky and Liu (2003)). This together with the limits on achievable fabrication tolerance that can be achieved in the silicon chip manufacturing technology severely affects bearing operability and limits the maximum achievable speeds of the micro turbomachinery. This paper introduces a novel variation of the axial-flow hydrostatic micro-gas journal bearing concept which yields anisotropy in bearing stiffness. By departing from axial symmetry and introducing biaxial symmetry in hydrostatic stiffness, the bearing’s top speed is increased and fabrication tolerance requirements are substantially relieved making more feasible extended stable high-speed bearing operation. The objectives of this work are: (1) to characterize the underlying physical mechanisms and the dynamic behavior of this novel bearing concept, and (2) to report on the design, implementation and test of this new micro-bearing technology. The technical approach involves the combination of numerical simulations, experiment, and simple, first principles based modeling of the gas bearing flow field and the rotordynamics. A simple description of the whirl instability threshold with stiffness anisotropy is derived explaining the instability mechanisms and linking the governing parameters to the whirl ratio and stability limit. An existing analytical hydrostatic gas bearing model is extended and modified to guide the bearing design with stiffness anisotropy. Numerical simulations of the full non-linear governing equations are conducted to validate the theory and the novel bearing concept. Experimental results obtained from a micro-bearing test device are presented and show good agreement between the theory and the measurements. The theoretical increase in achievable bearing top speed and the relief in fabrication tolerance requirements due to stiffness anisotropy are quantified and important design implications and guidelines for micro gas journal bearings are discussed.


2004 ◽  
Vol 129 (1) ◽  
pp. 177-184 ◽  
Author(s):  
L. X. Liu ◽  
Z. S. Spakovszky

The high-speed microhydrostatic gas journal bearings used in the high-power density MIT microengines are of very low aspect ratio with an L∕D of less than 0.1 and are running at surface speeds of order 500m∕s. These ultra-short high-speed bearings exhibit whirl instability limits and a dynamic behavior much different from conventional hydrostatic gas bearings. The design space for stable high-speed operation is confined to a narrow region and involves singular behavior (Spakovszky and Liu, 2005, “Scaling Laws for Ultra-Short Hydrostatic Gas Journal Bearings,” ASME J. Vibr. Acoust., 127(3), pp. 254–261). This together with the limits on achievable fabrication tolerance, which can be achieved in the silicon chip manufacturing technology, severely affects bearing operability and limits the maximum achievable speeds of the microturbomachinery. This paper introduces a novel variation of the axial-flow hydrostatic micro gas journal bearing concept, which yields anisotropy in bearing stiffness. By departing from axial symmetry and introducing biaxial symmetry in hydrostatic stiffness, the bearing's top speed is increased and fabrication tolerance requirements are substantially relieved making more feasible extended stable high-speed bearing operation. The objectives of this work are: (i) to characterize the underlying physical mechanisms and the dynamic behavior of this novel bearing concept and (ii) to report on the design, implementation, and test of this new microbearing technology. The technical approach involves the combination of numerical simulations, experiment, and simple, first-principles-based modeling of the gas bearing flow field and the rotordynamics. A simple description of the whirl instability threshold with stiffness anisotropy is derived explaining the instability mechanisms and linking the governing parameters to the whirl ratio and stability limit. An existing analytical hydrostatic gas bearing model is extended and modified to guide the bearing design with stiffness anisotropy. Numerical simulations of the full nonlinear governing equations are conducted to validate the theory and the novel bearing concept. Experimental results obtained from a microbearing test device are presented and show good agreement between the theory and the measurements. The theoretical increase in achievable bearing top speed and the relief in fabrication tolerance requirements due to stiffness anisotropy are quantified and important design implications and guidelines for micro gas journal bearings are discussed.


2017 ◽  
Vol 140 (1) ◽  
Author(s):  
Shuyun Jiang ◽  
Shengye Lin ◽  
Chundong Xu

This paper studies the static and dynamic coefficients of an externally pressurized porous gas journal bearing. The finite difference method is used to solve the Reynolds equation of the bearing to obtain the static load capacity. The linear perturbation method is adopted to derive the perturbation equations considering four degrees-of-freedom (4DOF), namely, the translational movements in x and y directions and the rotational movements around x and y directions. The effects of various parameters on the dynamic behaviors of the journal bearing are studied. These parameters include the bearing number, the supply pressure, the feeding parameter, the length-to-diameter ratio, the porosity parameter, the eccentricity ratio, and tilting angles. Simulated results prove that the proposed method is valid in estimating the static and dynamic characteristics of a porous gas journal bearing with 4DOF.


Author(s):  
Krzysztof Czolczynskl

This paper presents an analysis of the dynamic response of the high stiffness gas journal bearing to a harmonic load. The dependence between the frequency of the load, and the amplitude and phase angle of the shaft vibration are estimated from numerical simulation. Results of this simulation enable an attempt of identification of the high stiffness bearing as a linear system with two (or in simplification - one) degrees of freedom, to formulate simple dynamic models of the bearing. Stiffness and damping coefficients are calculated and compared with the simple gas journal bearing. The comparison suggests, that the investigated gas bearing retains high stiffness not only for slow changes of the load which appear in its application to grinding machines, but even when the frequency of the load is equal to several rad/s.


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