scholarly journals Interference Torque of a Gas-Dynamic Bearing Gyroscope Subject to a Uniform Change of the Specific Force and the Carrier Angular Velocity

Sensors ◽  
2020 ◽  
Vol 20 (23) ◽  
pp. 6852
Author(s):  
Yan Li ◽  
Desheng Zhang ◽  
Fuhai Duan
Keyword(s):  
Steady State ◽  
Angular Velocity ◽  
Degrees Of Freedom ◽  
Reynolds Equation ◽  
Hysteresis Effect ◽  
Specific Force ◽  
Change Rate ◽  
Gas Dynamic ◽  
Bearing Force ◽  
Uniform Change

The work is devoted to an analysis of interference torque of a gas-dynamic bearing gyroscope, while a condition with uniformly changed specific force and carrier angular velocity are taken into account. A five-degrees-of-freedom (5-DOF) model is established considering the translation and tilt of the rotor, which solves dynamic rotor equations and the Reynolds equation simultaneously. The model makes it possible to obtain the rotor trajectory under time-transient specific force and carrier angular velocity. The interference torque of the gyroscope is analyzed based on the rotor trajectory. Results indicate that the gas-dynamic bearings show a significant hysteresis effect with a perturbation of bearing force or bearing moment, which indicates the necessity of transient research. Interference torque is large when the carrier angular velocity starts to change or stops to change, and when the specific force stops to change. When the specific force change rate is less than 8.4 km/s3 with no change of the carrier angular velocity, the condition could be simplified as a steady state, which is consistent with the previous study.

Static error model of a three-floated gyroscope with a rotor supported on gas-lubricated bearings

2017 ◽  
Vol 232 (16) ◽  
pp. 2850-2860 ◽  
Author(s):  
Yan Li ◽  
Fuhai Duan ◽  
Liang Fan ◽  
Ying Yan
Keyword(s):  
Regression Analysis ◽  
Angular Velocity ◽  
Degrees Of Freedom ◽  
Axial Direction ◽  
Error Model ◽  
Specific Force ◽  
Static Error ◽  
Rapid Prediction ◽  
Bearing Force ◽  
Three Degrees Of Freedom

Three-floated gyroscope with the advantages of high accuracy has been widely used in platform inertial navigation system. To investigate the influence of specific force on the measured angular velocity of a gyroscope with a rotor supported on gas-lubricated bearings, a static error model considering three-degrees-of-freedom displacement of the rotor is proposed through numerical computation. Firstly, the conical Reynolds equation incorporated with the Fukui and Kaneko’s slip model is adopted and solved by the finite difference method, and the bearing force, caused by specific force, are obtained for each rotor displacement. Secondly, the error of gyroscope measured angular velocity is calculated from bearing force and rotor displacement. Finally, the relationship between the error and specific force is obtained by regression analysis, and the static error model of the gyroscope is proposed. To simplify the ternary regression analysis to binary, two intermediate parameters, radial interference torque and circumferential angle between interference torque and specific force, are introduced. Numerical results show that interference torque is approximately π/2 ahead of specific force in circumferential direction with fz > 0, and π/2 behind specific force with fz < 0, and that a large interference torque is produced when the specific force in radial and axial direction are both large. The error model provides a rapid prediction of the error caused by rotor displacement by three-degrees-of-freedom specific force.

Stability of Ring-Type MEMS Gyroscopes Subjected to Stochastic Angular Speed Fluctuation

2017 ◽  
Vol 139 (4) ◽  
Author(s):  
Samuel F. Asokanthan ◽  
Soroush Arghavan ◽  
Mohamed Bognash
Keyword(s):  
Angular Velocity ◽  
Degrees Of Freedom ◽  
Microelectromechanical Systems ◽  
Damping Ratio ◽  
Operating Conditions ◽  
System Stability ◽  
System Response ◽  
Ring Type ◽  
Mems Gyroscopes ◽  
The Stability

Effect of stochastic fluctuations in angular velocity on the stability of two degrees-of-freedom ring-type microelectromechanical systems (MEMS) gyroscopes is investigated. The governing stochastic differential equations (SDEs) are discretized using the higher-order Milstein scheme in order to numerically predict the system response assuming the fluctuations to be white noise. Simulations via Euler scheme as well as a measure of largest Lyapunov exponents (LLEs) are employed for validation purposes due to lack of similar analytical or experimental data. The response of the gyroscope under different noise fluctuation magnitudes has been computed to ascertain the stability behavior of the system. External noise that affect the gyroscope dynamic behavior typically results from environment factors and the nature of the system operation can be exerted on the system at any frequency range depending on the source. Hence, a parametric study is performed to assess the noise intensity stability threshold for a number of damping ratio values. The stability investigation predicts the form of threshold fluctuation intensity dependence on damping ratio. Under typical gyroscope operating conditions, nominal input angular velocity magnitude and mass mismatch appear to have minimal influence on system stability.

An Improved Airborne Single Observer Passive Location

2012 ◽  
Vol 157-158 ◽  
pp. 1533-1536
Author(s):  
Yong Wang ◽  
Chang Qiang Huang ◽  
Zheng Wang ◽  
Wang Xi Li
Keyword(s):  
Angular Velocity ◽  
Phase Difference ◽  
Measurement Problem ◽  
Doppler Frequency ◽  
Original Method ◽  
Parameter Measurement ◽  
Frequency Change ◽  
Passive Location ◽  
Change Rate ◽  
Domain Information

Using phase difference change rate’s augmentation to angular velocity, an improved passive location is developed,which solves the high precision parameter measurement problem of angular velocity in passive location and tracking via spatial-frequency domain information. The simulation shows that this method can reduce the difficulties of parameter measurement. The ranging error is mainly affected by the measurement error of phase difference change rate and doppler frequency change rate. Compared with the original method, it has higher passive location precision.

An Assessment of the Value of Theory in Predicting Gas-Bearing Performance

1961 ◽  
Vol 83 (2) ◽  
pp. 195-200 ◽  
Author(s):  
S. Cooper
Keyword(s):  
Steady State ◽  
Slip Velocity ◽  
Reynolds Equation ◽  
Energy Equation ◽  
Experimental Methods ◽  
Experimental Results ◽  
Theoretical Investigations ◽  
Gas Bearing ◽  
Theoretical Results

The object of the paper is to indicate the value of theoretical investigations of hydrodynamic finite bearings under steady-state conditions. Methods of solution of Reynolds equation by both desk and digital computing, and methods of stabilizing the processes of solution, are described. The nondimensional data available from the solutions are stated. The outcome of an attempted solution of the energy equation is discussed. A comparison between some theoretical and experimental results is shown. Experimental methods employed and some difficulties encountered are discussed. Some theoretical results are given to indicate the effects of the inclusion of slip velocity, stabilizing slots, and a simple case of whirl.

Beam-Vibration Analysis With the Electric-Analog Computer

1950 ◽  
Vol 17 (1) ◽  
pp. 13-26
Author(s):  
G. D. McCann ◽  
R. H. MacNeal
Keyword(s):  
Steady State ◽  
Vibration Analysis ◽  
Degrees Of Freedom ◽  
Analog Computer ◽  
Accurate Solution ◽  
Rotary Inertia ◽  
Beam Vibration ◽  
Lumped Constant ◽  
Electric Analog

Abstract The authors have developed a true dynamic analogy which has been used with the Cal Tech electric-analog computer for the rapid and accurate solution of both steady-state and transient beam problems. This analogy has been found well suited to the study of beams having several coupled degrees of freedom, including torsion, simple bending, and bending in a plane. Damping and effects such as rotary inertia may be handled readily. The analogy may also be used in the study of systems involving combined beams and “lumped-constant” elements.

The Effect of Lubricant Inertia in Journal-Bearing Lubrication

1957 ◽  
Vol 24 (4) ◽  
pp. 494-496
Author(s):  
J. F. Osterle ◽  
Y. T. Chou ◽  
E. A. Saibel
Keyword(s):  
Reynolds Number ◽  
Steady State ◽  
Reynolds Equation ◽  
Journal Bearing ◽  
Journal Bearings ◽  
Hydrodynamic Theory ◽  
Simple Relationship ◽  
Inertia Effect ◽  
Laminar Regime ◽  
Steady State Operation

Abstract The Reynolds equation of hydrodynamic theory, modified to take lubricant inertia into approximate account, is applied to the steady-state operation of journal bearings to determine the effect of lubricant inertia on the pressure developed in the lubricant. A simple relationship results, relating this “inertial” pressure to the Reynolds number of the flow. It is found that the inertia effect can be significant in the laminar regime.

A Theoretical Analysis of Floating Bush Journal Bearing With Axial Oil Film Rupture Being Considered

2002 ◽  
Vol 124 (3) ◽  
pp. 494-505 ◽  
Author(s):  
Kiyoshi Hatakenaka ◽  
Masato Tanaka ◽  
Kenji Suzuki
Keyword(s):  
Steady State ◽  
Reynolds Equation ◽  
Speed Ratio ◽  
Shaft Speed ◽  
Film Rupture ◽  
State Behavior ◽  
Oil Film ◽  
Rotordynamic Coefficients ◽  
The Stability ◽  
Very High

A new modified Reynolds equation is derived with centrifugal force acting on the hydrodynamic oil film being considered. This equation, together with a cavitation model, is used to obtain the steady-state equilibrium and calculate the rotordynamic coefficients of lightly loaded floating bush journal bearings operating at very high shaft speeds. The bush-to-shaft speed ratio and the linear cross-coupling spring coefficients of the inner oil film is found to decrease with the increase in shaft speed as the axial oil film rupture develops in the inner oil film. The present model can give reasonable explanation to the steady-state behavior and the stability behavior of the bearing observed in actual machines.

Effects of Suspension Design on the Attitudes of a Car during Braking and Acceleration

1973 ◽  
Vol 187 (1) ◽  
pp. 787-794
Author(s):  
J. R. Ellis
Keyword(s):  
Steady State ◽  
Linear Systems ◽  
Degrees Of Freedom ◽  
Coupled Systems ◽  
Two Degrees Of Freedom ◽  
Simulation Techniques ◽  
Non Linear ◽  
Non Linear Systems ◽  
Effort Distribution

Two degrees of freedom models of a car are employed to demonstrate the effects of the suspension derivative ∂ x/∂ z on the pitch and bounce attitudes during braking or accelerating. The work equation is employed to show that brake effort distribution between the axles has a significant effect on the attitudes when anti-dive suspension characteristics are utilized. The steady-state positions in both pitch and bounce are developed for linear systems of typical suspensions that may be either standard or coupled systems. Non-linear systems are considered using simulation techniques. A description of some simulation circuits is contained in an appendix.

Periodic Steady State Response and Fatigue Analysis of a Nonlinear City Bus Model

2009 ◽  
Author(s):  
George Valsamos ◽  
Christos Theodosiou ◽  
Sotirios Natsiavas
Keyword(s):  
Steady State ◽  
Degrees Of Freedom ◽  
Nonlinear Models ◽  
Equations Of Motion ◽  
High Stress ◽  
Direct Determination ◽  
Accurate Information ◽  
Steady State Response ◽  
State Response ◽  
Periodic Steady State

Dynamic response related to fatigue prediction of an urban bus is investigated. First, a quite complete model subjected to road excitation is employed in order to extract sufficiently reliable and accurate information in a fast way. The bus model is set up by applying the finite element method, resulting to an excessive number of degrees of freedom. In addition, the bus suspension units involve nonlinear characterstics. A step towards alleviating this difficulty is the application of an appropriate coordinate transformation, causing a drastic reduction in the dimension of the final set of the equations of motion. This allows the application of a systematic numerical methodology leading to direct determination of periodic steady state response of nonlinear models subjected to periodic excitation. Next, typical results were obtained for excitation resulting from selected urban road profiles. These profiles have either a known form or known statistical properties, expressed by an appropriate spatial power spectral density function. In all cases examined, the emphasis was put on investigating ride response. The main attention was focused on identifying areas of the bus suspension and frame subsystems where high stress levels are developed. This information is based on the idea of a nonlinear transfer function and provides the basis for applying suitable criteria in order to perform analyses leading to prediction of fatigue failure.

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