The Effect of Misalignment on Rotor Vibrations

1998 ◽  
Vol 120 (3) ◽  
pp. 635-640 ◽  
Author(s):  
J. L. Nikolajsen
Keyword(s):  
Steady State ◽  
Dynamic Stiffness ◽  
Instability Threshold ◽  
Influence Coefficient ◽  
Radial Bearing ◽  
Damping Coefficients ◽  
State Bearing ◽  
Optimum Stability ◽  
Bearing Loads ◽  
Stiffness And Damping

Rotors with three or more fluid-film bearings (or fluid seals) have “redundant” supports, and, therefore, interdependent bearing loads that are generally unknown both in magnitude and direction. The steady-state bearing eccentricities and the dynamic stiffness and damping coefficients of the bearings are, therefore, also unknown since both are functions of the bearing loads. Thus, the dynamic behavior of multibearing rotors generally cannot be predicted with good accuracy without access to a procedure for calculating the steady-state bearing loads and eccentricities. This paper outlines such a procedure in terms of both the influence coefficient method, the transfer matrix method, and the finite element method. Radial bearing misalignment and flexibility of the bearing back-up structures are accounted for. Once the eccentricities are available, the bearing stiffness and damping coefficients can be calculated in the usual way and used to predict critical speeds, instability threshold speed, and rotor response to imbalance. A numerical example is presented that illustrates some of the nonlinear effects of bearing support redundancy, notably the large variations in instability threshold speed with radial bearing misalignment. The example shows how the method can be used to determine the level of bearing misalignment that leads to optimum rotor stability. It is concluded that no simple guide lines exist by which optimum stability can be achieved. Neither perfect bearing alignment nor equal load sharing between bearings necessarily lead to optimum stability.

scholarly journals The Effect of Misalignment on Rotor Vibrations

1996 ◽  
Author(s):  
Jorgen L. Nikolajsen
Keyword(s):  
Steady State ◽  
Dynamic Stiffness ◽  
Instability Threshold ◽  
Influence Coefficient ◽  
Radial Bearing ◽  
Damping Coefficients ◽  
State Bearing ◽  
Optimum Stability ◽  
Bearing Loads ◽  
Stiffness And Damping

Rotors with three or more fluid-film bearings (or fluid seals) have ‘redundant’ supports, and therefore interdependent bearing loads which are generally unknown both in magnitude and direction. The steady-state bearing eccentricities and the dynamic stiffness and damping coefficients of the bearings are therefore also unknown, since both are functions of the bearing loads. Thus, the dynamic behaviour of multi-bearing rotors generally cannot be predicted with good accuracy without access to a procedure for calculating the steady-state bearing loads and eccentricities. This paper outlines such a procedure in terms of both the influence coefficient method, the transfer matrix method, and the finite element method. Radial bearing misalignment and flexibility of the bearing back-up structures are accounted for. Once the eccentricities are available, the bearing stiffness and damping coefficients can be calculated in the usual way and used to predict critical speeds, instability threshold speed and rotor response to imbalance. A numerical example is presented which illustrates some of the non-linear effects of bearing support redundancy, notably the large variations in instability threshold speed with radial bearing misalignment. The example shows how the method can be used to determine the level of bearing misalignment which leads to optimum rotor stability. It is concluded that no simple guide lines exist by which optimum stability can be achieved. Neither perfect bearing alignment nor equal load sharing between bearings necessarily lead to optimum stability.

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.

Calculation and Measurement of the Stiffness and Damping Coefficients for a Low Impedance Hydrodynamic Bearing

1997 ◽  
Vol 119 (1) ◽  
pp. 57-63 ◽  
Author(s):  
M. J. Goodwin ◽  
P. J. Ogrodnik ◽  
M. P. Roach ◽  
Y. Fang
Keyword(s):  
Experimental Data ◽  
Dynamic Stiffness ◽  
Perturbation Technique ◽  
The Novel ◽  
Oil Film ◽  
Hydrodynamic Bearing ◽  
Damping Coefficients ◽  
Stiffness And Damping ◽  
Film Stiffness ◽  
Novel Design

This paper describes a combined theoretical and experimental investigation of the eight oil film stiffness and damping coefficients for a novel low impedance hydrodynamic bearing. The novel design incorporates a recess in the bearing surface which is connected to a standard commercial gas bag accumulator; this arrangement reduces the oil film dynamic stiffness and leads to improved machine response and stability. A finite difference method was used to solve Reynolds equation and yield the pressure distribution in the bearing oil film. Integration of the pressure profile then enabled the fluid film forces to be evaluated. A perturbation technique was used to determine the dynamic pressure components, and hence to determine the eight oil film stiffness and damping coefficients. Experimental data was obtained from a laboratory test rig in which a test bearing, floating on a rotating shaft, was excited by a multi-frequency force signal. Measurements of the resulting relative movement between bearing and journal enabled the oil film coefficients to be measured. The results of the work show good agreement between theoretical and experimental data, and indicate that the oil film impedance of the novel design is considerably lower than that of a conventional bearing.

The Surface Roughness Effect on the Dynamic Stiffness and Damping Characteristics of the Hydrostatic Thrust Spherical Bearings: Part 5 of 5 — Clearance Type of Bearings

2007 ◽  
Author(s):  
Ahmad W. Yacout
Keyword(s):  
Surface Roughness ◽  
Capillary Tube ◽  
Dynamic Stiffness ◽  
Dynamic Performance ◽  
Major Effect ◽  
Design Parameters ◽  
Compressibility Effect ◽  
Damping Coefficients ◽  
Stiffness And Damping ◽  
Fluid Compressibility

This study has theoretically analyzed the surface roughness, centripetal inertia and recess volume fluid compressibility effects on the dynamic behavior of a restrictor compensated hydrostatic thrust spherical clearance type of bearing. The stochastic Reynolds equation, with centripetal inertia effect, and the recess flow continuity equation with recess volume fluid compressibility effect have been derived to take into account the presence of roughness on the bearing surfaces. On the basis of a small perturbations method, the dynamic stiffness and damping coefficients have been evaluated. In addition to the usual bearing design parameters the results for the dynamic stiffness and damping coefficients have been calculated for various frequencies of vibrations or squeeze parameter (frequency parameter) and recess volume fluid compressibility parameter. The study shows that both of the surface roughness and the centripetal inertia have slight effects on the stiffness coefficient and remarkable effects on the damping coefficient while the recess volume fluid compressibility parameter has the major effect on the bearing dynamic characteristics. The cross dynamic stiffness showed the bearing self-aligning property and the ability to oppose whirl movements. The orifice restrictor showed better dynamic performance than that of the capillary tube.

Steady-State and Dynamic Behaviour of Multi-Recess Hybrid Oil Journal Bearings

1979 ◽  
Vol 21 (5) ◽  
pp. 345-351 ◽  
Author(s):  
M. K. Ghosh ◽  
B. C. Majumdar ◽  
J. S. Rao
Keyword(s):  
Perturbation Theory ◽  
Steady State ◽  
Theoretical Analysis ◽  
Dynamic Behaviour ◽  
Journal Bearing ◽  
Load Capacity ◽  
Journal Bearings ◽  
Time Dependent ◽  
Damping Coefficients ◽  
Stiffness And Damping

A theoretical analysis of the steady-state and dynamic characteristics of multi-recess hybrid oil journal bearings is presented. A perturbation theory for small vibrations is used to solve an incompressible, finite journal bearing with a time-dependent term. Load capacity, attitude angle, friction parameter, stiffness and damping coefficients are evaluated for a capillary-compensated bearing.

Helical-Grooved Journal Bearing Operated in Turbulent Regime

1970 ◽  
Vol 92 (2) ◽  
pp. 346-357 ◽  
Author(s):  
C. Y. Chow ◽  
J. H. Vohr
Keyword(s):  
Steady State ◽  
Journal Bearing ◽  
Critical Mass ◽  
Reynolds Numbers ◽  
Turbulent Regime ◽  
Damping Coefficients ◽  
Radial Stiffness ◽  
Performance Curves ◽  
Stiffness And Damping ◽  
Laminar And Turbulent Regimes

An analysis for helical bearings operated in turbulent regime, with negligible inertia in an incompressible fluid film, was performed [10, 11]. The analysis is based on the linearised lubrication theory developed by Ng and Pan [4]. The outlines for this analysis and, in particular, the bearing performance data for various helical groovings are given in this paper. The data presented include the bearing performance at the steady state, the stiffness and damping coefficients, and the critical mass of journal in both laminar and turbulent regimes. To facilitate designs, these data are computed for optimal geometries of helical grooved bearings to provide maximum radial stiffness at various Reynolds numbers. In addition, the effect of external pressurized supply of lubricant are shown in the performance curves.

Simple Method for Dynamic Interaction between Two Rigid Foundations

2011 ◽  
Vol 250-253 ◽  
pp. 2225-2228
Author(s):  
Bin Yan ◽  
Ying Hui Lv ◽  
Ping Hu
Keyword(s):  
Dynamic Stiffness ◽  
Dynamic Interaction ◽  
Foundation Soil ◽  
Simple Method ◽  
Damping Coefficients ◽  
The Past ◽  
Calculating Method ◽  
Interaction Factors ◽  
Two Parameters ◽  
Stiffness And Damping

In the past many researchers studied dynamic stiffness and damping coefficients of surface and embedded rigid foundations of arbitrary shapes in the elastic homogenous half space. Dynamic stiffness and damping coefficients were obtained by using regularly shaped foundations instead of arbitrarily shaped ones. Obviously, the calculating methods were not perfect. In addition, the two parameters mentioned above were calculated only in the case of a single foundation. But the cases of two or more foundations were not presented because the interactions between foundations were not considered in all present papers. This paper eliminates two faults named above by using the assumption of the plane strain and of dynamic foundation-soil interaction factors. The calculating method of dynamic impedances presented by the paper proved to be accurate and practical.

Technical Note: Rolling dynamic stiffness and damping characteristics of small-sized pneumatic tyres

2000 ◽  
Vol 214 (3) ◽  
pp. 243-248 ◽  
Author(s):  
V. H. Saran ◽  
V. K. Goel
Keyword(s):  
Normal Load ◽  
Dynamic Stiffness ◽  
Technical Note ◽  
Inflation Pressure ◽  
Laboratory Technique ◽  
Damping Coefficients ◽  
Damping Characteristics ◽  
Stiffness And Damping

In this paper, a laboratory technique for determination of rolling dynamic stiffness and damping coefficients of small-sized, bias-ply tyres has been discussed. The effect of normal load, inflation pressure and speed on four different tyres has been reported. The results show similar trends to those reported by other investigators.

Behavior of Tilting–Pad Journal Bearings With Large Machining Error on Pads

2016 ◽  
Author(s):  
Phuoc Vinh Dang ◽  
Steven Chatterton ◽  
Paolo Pennacchi ◽  
Andrea Vania ◽  
Filippo Cangioli
Keyword(s):  
Static Load ◽  
Dynamic Stiffness ◽  
Maximum Pressure ◽  
Load Direction ◽  
Machining Error ◽  
Damping Coefficients ◽  
Machining Errors ◽  
Tilting Pad ◽  
Stiffness And Damping ◽  
Tilting Pad Journal Bearings

The use of tilting pad journal bearings (TPJBs) has increased in recent years due to their stabilizing effects on the rotor bearing system. Most of the studies addressing steady state and dynamic behaviors of TPJBs have been evaluated by means of thermo-hydrodynamic (THD) models, assuming nominal dimensions for the bearing, (i.e., the physical dimensions of all pads are identical and loads applied along the vertical direction). However machining errors could lead to actual bearing geometry and dimensions different from the nominal ones. In particular, for TPJB the asymmetry of the bearing geometry has not been well-investigated and can lead to an unexpected behavior of the bearing. The asymmetry of the bearing geometry can arise from large machining errors on only one or more pads, as a consequence of a pivot failure or after bad-mounting of the pads during assembly. These conditions can sometimes be detected by high values of the pad temperature, as measured by the temperature probes installed on the bearing pads, or by the abnormal vibration caused by pad-flutter phenomena. In this paper the authors investigate large machining errors on the pad thickness for a five-pad TPJB and analyze their effects on the bearing operating characteristics. Pad thickness errors correspond to a different preload factor or clearance for each pad. A sensitivity analysis was performed for several combinations of pad thickness using a THD model and the behavior of the bearing was analyzed, including dynamic stiffness and damping coefficients, clearance profile, shaft locus, minimum oil-film thickness, power loss, flow rate, and maximum pressure. The experimental case of a five pads TPJB with an intentional large machining error on the thickness of the pads is also described in the paper. The bearing has a nominal diameter of 100 mm, a diameter to length ratio (L/D) equal to 0.7 and can run at up to 3000 rpm. The experimental measurements are compared with the results obtained from the analytical model. The results show that the effects of asymmetry of the bearing geometry are more evident if the direction of the static load applied on the rotor bearing system, which is different from the vertical load, is also considered. For instance, the shape of shaft locus obtained by experimental tests changing the static load direction at a constant speed is an irregular pentagon if it is compared to the case of the nominal bearing. Based on our findings, we concludes that the machining error on the pads has a large influence on the shaft locus, minimum oil-film thickness and maximum pressure on pads, especially at high rotational speed, but has little effect on the flow rate and power loss. In addition, this error significantly affects the dynamic stiffness and damping coefficients, both in terms of rotational speed and load direction.

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