Dynamic Stability of Mechanical Structures Containing Externally Pressurized Gas-Lubricated Thrust Bearings

1988 ◽  
Vol 110 (2) ◽  
pp. 271-278 ◽  
Author(s):  
P. Plessers ◽  
R. Snoeys
Keyword(s):  
Frequency Response ◽  
Stability Criterion ◽  
Feedback Loop ◽  
Response Functions ◽  
Thrust Bearings ◽  
Supporting Structure ◽  
Nyquist Criterion ◽  
The Stability ◽  
Stability Limits ◽  
Gas Bearing

A stability criterion is presented to evaluate instability phenomena in mechanical systems containing externally pressurized gas bearings. For this criterion, the gas bearing films and the supporting structure are characterized separately by means of frequency response functions. The overall system may be considered as a feedback-loop for which the Nyquist criterion will define stability limits. The analysis demonstrates the interaction between the dynamics of the supporting structure and the air gap. The stability criterion is generalized for systems containing more than one gas film. The stability criterion is verified experimentally.

Dynamic Stability of a Motorized High Speed Machine Tool Spindle Supported on Bearings

2014 ◽  
Vol 612 ◽  
pp. 29-34
Author(s):  
Jakeer Hussain Shaik ◽  
J. Srinivas
Keyword(s):  
Machine Tool ◽  
Frequency Response ◽  
High Speed ◽  
Stability Boundary ◽  
Second Phase ◽  
Element Formulation ◽  
Machining Parameters ◽  
Response Functions ◽  
Frequency Response Functions ◽  
The Stability

Dynamic behaviour of spindle system influences chatter stability of machine tool considerably. Self-excited vibrations of the tool results in unstable cutting process which leads to the chatter on the work surface and it reduces the productivity. In this paper, a system of coupled spindle bearing system is employed by considering the angular contact ball bearing forces on stability of machining. Using Timoshenko beam element formulation, the spindle unit is analyzed by including the gyroscopic and centrifugal terms. Frequency response functions at the tool-tip are obtained from the dynamic spindle model. In the second phase, solid model of the system is developed and its dynamic response is obtained from three dimensional finite element analysis. The works on analysis of the stability of milling processes focus on calculating the stability boundary of the machining parameters based on the dynamic models characterizing the milling processes. The stability lobe diagrams are generated from frequency response functions (FRF’s) lead to an stability limit prediction for the system at high speed ranges.

Dynamic Identification of Convergent Externally Pressurized Gas-Bearing Gaps

1988 ◽  
Vol 110 (2) ◽  
pp. 263-270 ◽  
Author(s):  
P. Plessers ◽  
R. Snoeys
Keyword(s):  
Frequency Response ◽  
Response Function ◽  
Frequency Response Function ◽  
Dynamic Stiffness ◽  
Test Procedure ◽  
Dynamic Identification ◽  
Thrust Bearings ◽  
Stiffness And Damping ◽  
Air Film ◽  
Gas Bearing

The dynamic behavior of externally pressurized gas bearings is described by means of frequency response functions, from which dynamic stiffness and damping coefficients are derived. A numerical method is presented to calculate the frequency response function for plane circular thrust bearings with convergent gap geometry. A test procedure is described for measuring the frequency response function of an air film in order to verify computational, results. The comparison reveals a fairly good agreement between measured and calculated frequency responses. Finally, the effect of bearing parameters on the frequency response function of the air film is investigated.

Rotordynamic Evaluation of Centrifugal Compressor Using Electromagnetic Exciter

2011 ◽  
Author(s):  
Naohiko Takahashi ◽  
Yohei Magara ◽  
Mitsuhiro Narita ◽  
Haruo Miura
Keyword(s):  
High Pressure ◽  
Frequency Response ◽  
Damping Ratio ◽  
Practical Method ◽  
Magnetic Bearing ◽  
Response Functions ◽  
Mathematical Operation ◽  
Frequency Response Functions ◽  
Calculation Results ◽  
The Stability

Since heavier gases exert larger effects on rotordynamic stability, stability evaluation is important in developing or designing high-pressure compressors. To evaluate the rotor stability during operation, an excitation test using a magnetic bearing is the most practical method. In stability analysis, labyrinth seals can produce significant cross-coupling forces, which particularly reduce the damping ratio of the first forward mode. Therefore, forward modes should be distinguished from backward modes in the excitation test. One method that excites only the forward modes, not the backward modes (and vice versa), is the use of a rotating excitation. In this method, the force is simultaneously applied to two axes to excite the rotor in circular orbits. Two trigonometric functions, i.e., cosine and sine functions, are used to generate this rotation force. Another method is the use of a unidirectional excitation and a mathematical operation to distinguish the forward whirl from the backward whirl. In this method, a directional frequency response function that separates the two modes in the frequency domain is obtained from four frequency response functions by using a complex number expression for the rotor motion. In this study, the latter method was employed to evaluate the rotor stability of a high-pressure compressor. To obtain the frequencies and damping ratios of the eigenvalues, the curve fitting based on system identification methods, such as the prediction error method, was introduced for the derived frequency response functions. Firstly, these methods were applied to a base evaluation under a low-pressure gas operation, in which the stability mainly depends on the bearing property. Using the obtained results, the bearing coefficients were estimated. Next, the same methods were applied to stability evaluations under high-pressure gas operations. The destabilizing forces were also estimated from the test results and compared with the calculation results.

Stability Criterion for Spiral Grooved Thrust Gas Bearings

1990 ◽  
Vol 112 (4) ◽  
pp. 734-737 ◽  
Author(s):  
V. N. Constantinescu ◽  
S. Galetuse
Keyword(s):  
Pressure Distribution ◽  
Dynamic Stability ◽  
Small Perturbation ◽  
Perturbation Analysis ◽  
Stability Criterion ◽  
Analytical Procedure ◽  
Previous Analysis ◽  
Unconditionally Stable ◽  
Thrust Bearings ◽  
Gas Bearing

A previous analysis of dynamic stability for a blocked center inward pumping spiral grooved thrust gas bearing is extended to two other types of similar bearings, namely annular thrust bearings with either inward or outward pumping. Both a numerical small perturbation analysis and an analytical procedure are used, the latter one being based on an approximate shape of the pressure distribution. The analysis provides a critical compressibility number up to which the bearings is unconditionally stable.

scholarly journals The Basics of Time-Domain-Based Milling Stability Prediction Using Frequency Response Function

2020 ◽  
Vol 4 (3) ◽  
pp. 72 ◽  
Author(s):  
Zoltan Dombovari ◽  
Markel Sanz-Calle ◽  
Mikel Zatarain
Keyword(s):  
Frequency Response ◽  
Response Function ◽  
Time Domain ◽  
Impulse Response Function ◽  
Stationary Solutions ◽  
Milling Process ◽  
Response Functions ◽  
Objective Functions ◽  
Convergence Properties ◽  
The Stability

This study presents the fundamentals of the usage of frequency response functions (FRF) directly in time-domain-based methods. The methodology intends to combine the advantages of frequency- and time-domain-based techniques to determine the stability of stationary solutions of a given milling process. This is achieved by applying the so-called impulse dynamic subspace (IDS) method, with which the impulse response function (IRF) can be disassembled to separated singular IRFs that form the basis of the used transformation. Knowing the IDS state, the linear stability boundaries can be constructed and a measure of stability can be determined using the Floquet multipliers via the semidiscretization method (SDM). This step has a huge importance in parameter optimization where the multipliers can be used as objective functions, which is hardly achievable using frequency-domain-based methods. Here we present the basic idea of utilizing the IDS method and analyze its convergence properties.

Rotordynamic Evaluation of Centrifugal Compressor Using Electromagnetic Exciter

2012 ◽  
Vol 134 (3) ◽  
Author(s):  
Naohiko Takahashi ◽  
Yohei Magara ◽  
Mitsuhiro Narita ◽  
Haruo Miura
Keyword(s):  
High Pressure ◽  
Frequency Response ◽  
Damping Ratio ◽  
Practical Method ◽  
Magnetic Bearing ◽  
Response Functions ◽  
Mathematical Operation ◽  
Frequency Response Functions ◽  
Calculation Results ◽  
The Stability

Since heavier gases exert larger effects on rotordynamic stability, stability evaluation is important in developing or designing high-pressure compressors. To evaluate the rotor stability during operation, an excitation test using a magnetic bearing is the most practical method. In stability analysis, labyrinth seals can produce significant cross coupling forces, which particularly reduce the damping ratio of the first forward mode. Therefore, forward modes should be distinguished from backward modes in the excitation test. One method that excites only the forward modes, not the backward modes (and vice versa), is the use of a rotating excitation. In this method, the force is simultaneously applied to two axes to excite the rotor in circular orbits. Two trigonometric functions, i.e., cosine and sine functions, are used to generate this rotation force. Another method is the use of a unidirectional excitation and a mathematical operation to distinguish the forward whirl from the backward whirl. In this method, a directional frequency response function that separates the two modes in the frequency domain is obtained from four frequency response functions by using a complex number expression for the rotor motion. In this study, the latter method was employed to evaluate the rotor stability of a high-pressure compressor. To obtain the frequencies and damping ratios of the eigenvalues, the curve fitting based on system identification methods, such as the prediction error method, was introduced for the derived frequency response functions. Firstly, these methods were applied to a base evaluation under a low-pressure gas operation, in which the stability mainly depends on the bearing property. Using the obtained results, the bearing coefficients were estimated. Next, the same methods were applied to stability evaluations under high-pressure gas operations. The destabilizing forces were also estimated from the test results and compared with the calculation results.

Stability Criterion of Linear Control Systems with Time Delay

1970 ◽  
Vol 3 (3) ◽  
pp. 86-87 ◽  
Author(s):  
F. L. N-Nagy ◽  
M. N. Al-Tikriti
Keyword(s):  
Control System ◽  
Time Delay ◽  
Control Systems ◽  
Stability Criterion ◽  
Feedback Loop ◽  
Linear Control ◽  
Linear Control Systems ◽  
Loop Gain ◽  
Nyquist Stability ◽  
The Stability

The paper outlines the Nyquist stability criterion linear control systems with time delay, using frequency response results. The variation of the loop-gain and time delay are investigated when the time delay occurs in the forward-loop or the feedback-loop or both. The stability condition of a simple control system is used to illustrate the method.

Stability as a constraint in sagittal plane human force exertion modeling

1998 ◽  
Vol 1 (1) ◽  
pp. 23-39
Author(s):  
Carter J. Kerk ◽  
Don B. Chaffin ◽  
W. Monroe Keyserling
Keyword(s):  
Muscle Strength ◽  
Ankle Joint ◽  
Coefficient Of Friction ◽  
Sagittal Plane ◽  
Biomechanical Model ◽  
Whole Body ◽  
The Stability ◽  
Joint Center ◽  
Static Conditions ◽  
Stability Limits

The stability constraints of a two-dimensional static human force exertion capability model (2DHFEC) were evaluated with subjects of varying anthropometry and strength capabilities performing manual exertions. The biomechanical model comprehensively estimated human force exertion capability under sagittally symmetric static conditions using constraints from three classes: stability, joint muscle strength, and coefficient of friction. Experimental results showed the concept of stability must be considered with joint muscle strength capability and coefficient of friction in predicting hand force exertion capability. Information was gained concerning foot modeling parameters as they affect whole-body stability. Findings indicated that stability limits should be placed approximately 37 % the ankle joint center to the posterior-most point of the foot and 130 % the distance from the ankle joint center to the maximal medial protuberance (the ball of the foot). 2DHFEC provided improvements over existing models, especially where horizontal push/pull forces create balance concerns.

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