An Experimental Investigation of the Dynamic Characteristics of an Axial Spline Coupling in High-Speed Rotating Machinery

1993 ◽  
Author(s):  
James F. Walton ◽  
C.-P. Roger Ku ◽  
Jorgen W. Lund
Keyword(s):  
Experimental Investigation ◽  
Dynamic Characteristics ◽  
High Speed ◽  
Rotating Machinery ◽  
Experimental Measurements ◽  
Bending Moments ◽  
Damping Coefficients ◽  
Spline Coupling ◽  
Stiffness And Damping ◽  
Internal Rotor

Abstract This paper presents the results of the second part of an investigation of the dynamic characteristics of an axial spline coupling in high-speed rotating machinery. In the experimental method described herein, the bending moments and angular deflections transmitted across the axial spline coupling were measured while the nonrotating shaft was excited by an external shaker. The effects of external force and frequency on the angular stiffness and damping coefficients were investigated. The angular stiffness and damping coefficients were used to perform a linear steady-state rotordynamics stability analysis, and the unstable natural frequency was calculated and compared to experimental measurements. In addition, the mechanism and source of internal rotor friction instability caused by the axial spline couplings was studied.

Dynamic Coefficients of Axial Spline Couplings in High-Speed Rotating Machinery

1994 ◽  
Vol 116 (3) ◽  
pp. 250-256 ◽  
Author(s):  
C. P. Roger Ku ◽  
J. F. Walton ◽  
J. W. Lund
Keyword(s):  
High Speed ◽  
Experimental Measurements ◽  
Viscous Damping ◽  
Bending Moments ◽  
Equivalent Viscous Damping ◽  
Damping Coefficients ◽  
Dynamic Coefficients ◽  
Test Conditions ◽  
Spline Coupling ◽  
Stiffness And Damping

This paper provided the first opportunity to quantify the angular stiffness and equivalent viscous damping coefficients of an axial spline coupling used in highspeed turbomachinery. The bending moments and angular deflections transmitted across an axial spline coupling were measured while a nonrotating shaft was excited by an external shaker. A rotordynamics computer program was used to simulate the test conditions and to correlate the angular stiffness and damping coefficients. The effects of external force and frequency were also investigated. The angular stiffness and damping coefficients were used to perform a linear steady-state rotordynamics stability analysis, and the unstable natural frequency was calculated and compared to the experimental measurements.

A Theoretical Approach to Determine Angular Stiffness and Damping Coefficients of an Axial Spline Coupling in High-Speed Rotating Machinery

1993 ◽  
Author(s):  
C.-P. Roger Ku ◽  
James F. Walton ◽  
Jorgen W. Lund
Keyword(s):  
Data Reduction ◽  
High Speed ◽  
Sensitivity Analyses ◽  
Rotating Shaft ◽  
Equivalent Viscous Damping ◽  
Damping Coefficients ◽  
Test Methodology ◽  
Test Conditions ◽  
Spline Coupling ◽  
Stiffness And Damping

Abstract This paper provided the first opportunity to quantify the angular stiffness and equivalent viscous damping coefficients of an axial spline coupling used in high-speed turbomachinery. A unique test methodology and data reduction procedures were developed. The bending moments and angular deflections transmitted across an axial spline coupling were measured while a non-rotating shaft was excited by an external shaker. A rotordynamics computer program was used to simulate the test conditions and to correlate the angular stiffness and damping coefficients. In addition, sensitivity analyses were performed to demonstrate that the accuracy of the dynamic coefficients do not rely on the accuracy of the data reduction procedures.

Static and dynamic characteristics and stability analysis of high-speed water-lubricated hydrodynamic journal bearings

2021 ◽  
pp. 135065012110270
Author(s):  
Bo Xu ◽  
Hun Guo ◽  
Xiaofeng Wu ◽  
Yafeng He ◽  
Xiangzhi Wang ◽  
...  
Keyword(s):  
Stability Analysis ◽  
Dynamic Characteristics ◽  
High Speed ◽  
Load Capacity ◽  
Journal Bearings ◽  
Operating Conditions ◽  
Inertia Effect ◽  
Static And Dynamic Characteristics ◽  
Damping Coefficients ◽  
Stiffness And Damping

The purpose of this paper is to analyze the influence of turbulent, inertia, and misaligned effects on the static and dynamic characteristics and stability of high-speed water-lubricated hydrodynamic journal bearings. Based on the Navier–Stokes equation, the mixing-length theory, and the essential assumption that the velocity profile is not strongly affected by inertia force, the fluid lubrication model with turbulent, inertia, and misaligned effects is established, and then the stability analysis of bearings is carried out based on the equation of motion with four degrees of freedom. The model is solved by the finite difference method and the numerical results are compared under different operating conditions. The results show that the turbulent effect greatly increases the load capacity, power consumption, stiffness and damping coefficients, and stability of bearings, and the inertia effect significantly increases the volume flow rate of bearings, and the misaligned effect increases the load capacity, stiffness and damping coefficients, and stability of bearings. In high rotary speed and moderate eccentricity ratios, the influence of the inertia effect on the load capacity, stiffness coefficients, and stability cannot be neglected.

Ball bearing turbocharger vibration management: application on high speed balancer

2020 ◽  
Vol 21 (6) ◽  
pp. 619
Author(s):  
Kostandin Gjika ◽  
Antoine Costeux ◽  
Gerry LaRue ◽  
John Wilson
Keyword(s):  
Dynamic Behavior ◽  
High Speed ◽  
Internal Combustion Engines ◽  
Ball Bearing ◽  
Squeeze Film ◽  
Design And Technology ◽  
Squeeze Film Damper ◽  
Damping Coefficients ◽  
Bearing Loads ◽  
Stiffness And Damping

Today's modern internal combustion engines are increasingly focused on downsizing, high fuel efficiency and low emissions, which requires appropriate design and technology of turbocharger bearing systems. Automotive turbochargers operate faster and with strong engine excitation; vibration management is becoming a challenge and manufacturers are increasingly focusing on the design of low vibration and high-performance balancing technology. This paper discusses the synchronous vibration management of the ball bearing cartridge turbocharger on high-speed balancer and it is a continuation of papers [1–3]. In a first step, the synchronous rotordynamics behavior is identified. A prediction code is developed to calculate the static and dynamic performance of “ball bearing cartridge-squeeze film damper”. The dynamic behavior of balls is modeled by a spring with stiffness calculated from Tedric Harris formulas and the damping is considered null. The squeeze film damper model is derived from the Osborne Reynolds equation for incompressible and synchronous fluid loading; the stiffness and damping coefficients are calculated assuming that the bearing is infinitely short, and the oil film pressure is modeled as a cavitated π film model. The stiffness and damping coefficients are integrated on a rotordynamics code and the bearing loads are calculated by converging with the bearing eccentricity ratio. In a second step, a finite element structural dynamics model is built for the system “turbocharger housing-high speed balancer fixture” and validated by experimental frequency response functions. In the last step, the rotating dynamic bearing loads on the squeeze film damper are coupled with transfer functions and the vibration on the housings is predicted. The vibration response under single and multi-plane unbalances correlates very well with test data from turbocharger unbalance masters. The prediction model allows a thorough understanding of ball bearing turbocharger vibration on a high speed balancer, thus optimizing the dynamic behavior of the “turbocharger-high speed balancer” structural system for better rotordynamics performance identification and selection of the appropriate balancing process at the development stage of the turbocharger.

Internal Rotor Friction Induced Instability in High-Speed Rotating Machinery

1993 ◽  
Author(s):  
James F. Walton ◽  
Michael R. Martin
Keyword(s):  
Internal Friction ◽  
Natural Frequency ◽  
High Speed ◽  
Critical Speed ◽  
Rotating Machinery ◽  
Rotor System ◽  
Analytical Models ◽  
Interference Fit ◽  
Internal Rotor

Abstract Results of a program to investigate internal rotor friction destabilizing effects are presented. Internal-friction-producing joints were shown to excite the rotor system first natural frequency, when operating either below or above the first critical speed. The analytical models used to predict the subsynchronous instability were also confirmed. The axial spline joint demonstrated the most severe subsynchronous instability. The interference fit joint also caused subsynchronous vibrations at the first natural frequency but these were bounded and generally smaller than the synchronous vibrations. Comparison of data from the two test joints showed that supersynchronous vibration amplitudes at the first natural frequency were generally larger for the interference fit joint than for the axial spline joint. The effects of changes in imbalance levels and side loads were not distinguishable during testing because amplitude-limiting bumpers were required to restrict orbits.

Modal Frequency Response of a Four-Pad Tilting Pad Bearing With Spherical Pivots, Finite Pivot Stiffness and Different Pad Preloads

2010 ◽  
Author(s):  
Timothy W. Dimond ◽  
Amir A. Younan ◽  
Paul E. Allaire ◽  
John C. Nicholas
Keyword(s):  
Frequency Response ◽  
High Speed ◽  
Degrees Of Freedom ◽  
Natural Frequencies ◽  
Theoretical Calculations ◽  
Leading Edge ◽  
Damping Coefficients ◽  
Tilting Pad ◽  
The Subject ◽  
Stiffness And Damping

Tilting pad journal bearings (TPJBs) provide radial support for rotors in high-speed machinery. Since the tilting pads cannot support a moment about the pivot, self-excited cross-coupled forces due to fluid-structure interactions are greatly reduced or eliminated. However, the rotation of the tilting pads about the pivots introduces additional degrees of freedom into the system. When the flexibility of the pivot results in pivot stiffness that is comparable to the equivalent stiffness of the oil film, then pad translations as well as pad rotations have to be considered in the overall bearing frequency response. There is significant disagreement in the literature over the nature of the frequency response of TPJBs due to non-synchronous rotor perturbations. In this paper, a bearing model that explicitly considers pad translations and pad rotations is presented. This model is transformed to modal coordinates using state-space analysis to determine the natural frequencies and damping ratios for a four-pad tilting pad bearing. Experimental static and dynamic results were previously reported in the literature for the subject bearing. The bearing characteristics as tested are considered using a thermoelastohydrodynamic (TEHD) model. The subject bearing was reported as having an elliptical bearing bore and varying pad clearances for loaded and unloaded pads during the test. The TEHD analysis assumes a circular bearing bore, so the average bearing clearance was considered. Because of the ellipticity of the bearing bore, each pad has its own effective preload, which was considered in the analysis. The unloaded top pads have a leading edge taper. The loaded bottom pads have finned backs and secondary cooling oil flow. The bearing pad cooling features are considered by modeling equivalent convective coefficients for each pad back. The calculated bearing full stiffness and damping coefficients are also reduced non-synchronously to the eight stiffness and damping coefficients typically used in rotordynamic analyses and are expressed as bearing complex impedances referenced to shaft motion. Results of the modal analysis are compared to a two degree-of-freedom second-order model obtained via a frequency-domain system identification procedure. Theoretical calculations are compared to previously published experimental results for a four-pad tilting pad bearing. Comparisons to the previously published static and dynamic bearing characteristics are considered for model validation. Differences in natural frequencies and damping ratios resulting from the various models are compared, and the implications for rotordynamic analyses are considered.

Structural and Rotordynamic Force Coefficients of a Shimmed Bump Foil Bearing: An Assessment of a Simple Engineering Practice

2015 ◽  
Vol 138 (1) ◽  
Author(s):  
Luis San Andrés ◽  
Joshua Norsworthy
Keyword(s):  
Loss Factor ◽  
High Speed ◽  
Static Load ◽  
Low Cost ◽  
Mechanical Energy ◽  
Excitation Frequency ◽  
Engineering Practice ◽  
Force Coefficients ◽  
Damping Coefficients ◽  
Stiffness And Damping

High speed rotors supported on bump-type foil bearings (BFBs) often suffer from large subsynchronous whirl motions. Mechanically preloading BFBs through shimming is a common, low cost practice that shows improvements in rotordynamic stability. However, there is an absence of empirical information related to the force coefficients (structural and rotordynamic) of shimmed BFBs. This paper details a concerted study toward assessing the effect of shimming on a first generation BFB (L = 38.1 mm and D = 36.5 mm). Three metal shims, 120 deg apart, are glued to the inner surface of the bearing cartridge and facing the underside of the bump foil strip. The shim sets are of identical thickness, either 30 μm or 50 μm. In static load tests, a bearing with shims shows a (nonlinear) structural stiffness larger than for the bearing without shims. Torque measurements during shaft acceleration also demonstrate a shimmed BFB has a larger friction coefficient. For a static load of 14.3 kPa, dynamic loads with a frequency sweep from 250 Hz to 450 Hz are exerted on the BFB, without and with shims, to estimate its rotordynamic force coefficients while operating at ∼50 krpm (833 Hz). Similar measurements are conducted without shaft rotation. Results are presented for the original BFB (without shims) and the two shimmed BFB configurations. The direct stiffnesses of the BFB, shimmed or not, increase with excitation frequency, thus evidencing a mild hardening effect. The BFB stiffness and damping coefficients decrease slightly for operation with rotor speed as opposed to the coefficients when the shaft is stationary. For frequencies above 300 Hz, the direct damping coefficients of the BFB with 50 μm thick shims are ∼30% larger than the coefficients of the original bearing. The bearing structural loss factor, a measure of its ability to dissipate mechanical energy, is derived from the direct stiffness and damping coefficients. The BFB with 50 μm thick shims has a 25% larger loss factor—average from test data collected at 300 Hz to 400 Hz—than the original BFB. Further measurements of rotor motions while the shaft accelerates to ∼50 krpm demonstrate the shimmed BFB (thickest shim set) effectively removes subsynchronous whirl motions amplitudes that were conspicuous when operating with the original bearing.

Numerical Analysis on Dynamic Characteristics of Cryogenic Hydrostatic Journal Bearing

1999 ◽  
Vol 121 (4) ◽  
pp. 879-885 ◽  
Author(s):  
Hiroyuki Yoshikawa ◽  
Terukazu Ota ◽  
Kazuyuki Higashino ◽  
Shunichiro Nakai
Keyword(s):  
Numerical Analysis ◽  
Dynamic Characteristics ◽  
Rotational Speed ◽  
Frequency Ratio ◽  
Journal Bearing ◽  
Liquid Hydrogen ◽  
Transport Systems ◽  
Rocket Engines ◽  
Damping Coefficients ◽  
Stiffness And Damping

Dynamic characteristics of a two row staggered recess cryogenic hydrostatic journal bearing used in the liquid hydrogen turbopump of rocket engines for space transport systems are numerically analyzed. Effects of the rotational speed and the shaft eccentricity are studied in the analysis. Their effects on the stiffness and damping coefficients and the whirl frequency ratio are clarified. Moreover, effects of the orifice parameter, the distance between two recess rows, and the number of recesses on these dynamic characteristics are investigated.

scholarly journals Effect of groove texture on the dynamic characteristics of water-lubricated thrust bearing

2018 ◽  
Vol 213 ◽  
pp. 01003
Author(s):  
Huihui Feng ◽  
Liping Peng
Keyword(s):  
Dynamic Characteristics ◽  
Reynolds Equation ◽  
Thrust Bearing ◽  
Water Film ◽  
Geometrical Parameters ◽  
Damping Coefficients ◽  
Rotary Speed ◽  
Stiffness And Damping ◽  
Groove Texture ◽  
Film Lubrication

In this study, the effects of groove texture on the dynamic characteristics of water-lubricated thrust bearing are theoretically investigated. The turbulent Reynolds equation and its perturbation equations for water-film lubrication are derived and solved by using finite difference method. Dynamic characteristics including the stiffness and damping coefficients of the bearing are calculated. The effects of rotary speed, film clearance and geometrical parameters including groove texture depth and circumferential angle on the dynamic characteristics of the bearing have been investigated.

Compressibility Effects on the Static and Dynamic Characteristics in Stepped Thrust Gas Film Bearings

1999 ◽  
Author(s):  
Hiromu Hashimoto ◽  
Masayukl Ochiai
Keyword(s):  
Dynamic Characteristics ◽  
High Speed ◽  
Simple Structure ◽  
Friction Torque ◽  
Static And Dynamic Characteristics ◽  
Load Carrying ◽  
Minimum Film Thickness ◽  
Stiffness And Damping ◽  
Compressibility Effects ◽  
Theoretical Results

Abstract Hydrodynamic gas film bearings are used for supporting high-speed, lightly loaded rotating machinery. Stepped type gas film bearings are often used for such machinery because of their simple structure, high stability and load carrying capacity. This paper describes the measurements of compressibility effects on the static and dynamic characteristics of stepped thrust gas film bearings. In the experiments, the minimum film thickness, friction torque on the bearing surface and stiffness and damping coefficients of gas films are measured for a range of rotational speed from 10,000 rpm to 20,000 rpm under a constant stator mass and a fixed step height. The measured data are compared with the theoretical results and the gas film compressibility effects on the static and dynamic characteristics of the bearings are discussed. The experimental results agree well with the predicted results based on the compressible lubrication theory.

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