Influence of Flexibly Mounted Rolling Element Bearings on Rotor Response: Part I—Linear Analysis

1970 ◽  
Vol 92 (1) ◽  
pp. 59-69 ◽  
Author(s):  
E. J. Gunter
Keyword(s):  
Equations Of Motion ◽  
Rolling Element Bearings ◽  
Unbalance Response ◽  
Wide Range ◽  
Rolling Element ◽  
Flexible Supports ◽  
Proper Design ◽  
Support Conditions ◽  
Gyroscopic Effects ◽  
Phase Angles

The paper evaluates the influence of damped, linear flexibly mounted rolling-element bearings on dynamic rotor unbalance response. The system analyzed is treated as a general four degree of freedom unbalanced rotor mounted on damped flexible supports and includes rotor gyroscopic effects. The rotor equations of motion are solved for synchronous precession over a wide range of speeds for various support conditions. Rotor performance curves on bearing amplitude, forces transmitted, phase angles as a function of speed for various values of support damping are computer plotted to illustrate rotor and bearing performance over a wide range of speed and operating parameters. Results indicate that forces transmitted to the bearings by the rotor synchronous unbalance response can be dramatically reduced by proper design of the bearing support characteristics.

Dynamics of Rolling-Element Bearings—Part I: Cylindrical Roller Bearing Analysis

1979 ◽  
Vol 101 (3) ◽  
pp. 293-302 ◽  
Author(s):  
P. K. Gupta
Keyword(s):  
Differential Equations ◽  
Normal Force ◽  
Equations Of Motion ◽  
Roller Bearing ◽  
Rolling Element Bearings ◽  
Analytical Formulation ◽  
Rolling Element ◽  
Cylindrical Roller Bearing ◽  
Cylindrical Roller ◽  
Bearing Analysis

An analytical formulation for the roller motion in a cylindrical roller bearing is presented in terms of the classical differential equations of motion. Roller-race interaction is analyzed in detail and the resulting normal force and moment vectors are determined. Elastohydrodynamic traction models are considered in determining the roller-race tractive forces and moments. Formulation for the roller end and race flange interaction during skewing of the roller is also considered. Roller-cage interactions are assumed to be either hydrodynamic or fully metallic. Simple relationships are used to determine the churning and drag losses.

Dynamics of Rolling-Element Bearings—Part II: Cylindrical Roller Bearing Results

1979 ◽  
Vol 101 (3) ◽  
pp. 305-311 ◽  
Author(s):  
P. K. Gupta
Keyword(s):  
Differential Equations ◽  
Power Loss ◽  
Equations Of Motion ◽  
Roller Bearing ◽  
Geometrical Parameters ◽  
Rolling Element Bearings ◽  
Rolling Element ◽  
Cylindrical Roller Bearing ◽  
Cylindrical Roller ◽  
General Motion

Cylindrical roller bearing performance simulations are expressed in terms of the general motion of the bearing elements as derived by integrating the differential equations of motion. Roller skew as induced by relative race misalignment is simulated. It is shown that skidding can be reduced by using a lubricant providing relatively high traction. However, such a fluid results in increased bearing torque and power loss. The influence of geometrical parameters, such as roller/cage, or race/cage clearance and radial preload, on the roller and cage motion is also investigated.

Transient Forward and Backward Whirl of Beam and Solid Rotors With Stiffening and Softening Effects

2011 ◽  
Author(s):  
J. S. Rao
Keyword(s):  
Cross Section ◽  
Variable Cross Section ◽  
Fluid Film ◽  
Variable Cross ◽  
Rolling Element Bearings ◽  
Unbalance Response ◽  
Beam Analysis ◽  
Rolling Element ◽  
Backward Whirl ◽  
Rotor Model

This paper describe the procedure of achieving unbalance response and stability of general accelerating solid rotor model rotors with variable cross-section on fluid film or rolling element bearings and seals with the casings mounted on foundations including stress stiffening and spin softening effects. The solid rotor analysis results are verified with beam analysis results wherever applicable.

Dynamics of Rolling-Element Bearings—Part III: Ball Bearing Analysis

1979 ◽  
Vol 101 (3) ◽  
pp. 312-318 ◽  
Author(s):  
P. K. Gupta
Keyword(s):  
Ball Bearing ◽  
Dynamic Performance ◽  
Equations Of Motion ◽  
Ball Bearings ◽  
Rolling Element Bearings ◽  
Time Simulation ◽  
Rolling Element ◽  
Analytical Development ◽  
Critical Film Thickness ◽  
Bearing Analysis

An analytical formulation for the generalized ball, cage, and race motion in a ball bearing is presented in terms of the classical differential equations of motion. Ball-race interaction is analyzed in detail and the resulting force and moment vectors are determined. The ball-cage and race-cage interactions are considered to be either hydrodynamic or metallic and a critical film thickness defines the transition between the two regimes. Simplified treatments for the drag and churning losses are also included to complete a rigorous analytical development for the real-time simulation of the dynamic performance of ball bearings.

Dynamics of an Improved Inter Shaft Squeeze Film Damper: Theory and Experiment

2007 ◽  
Author(s):  
K. Gupta ◽  
S. Chatterjee
Keyword(s):  
Gas Flow ◽  
Damping Ratio ◽  
Squeeze Film ◽  
Design Parameters ◽  
Radial Clearance ◽  
Rolling Element Bearings ◽  
Squeeze Film Damper ◽  
Wide Range ◽  
Rolling Element ◽  
Theoretical Simulations

Intershaft rolling element bearings are commonly used in aero gas turbine rotors primarily to reduce the length of the engine as well as to avoid obstruction to gas flow path at the turbine end. In order to reduce cross-excitation between the LP and HP shafts of two spool rotor, researchers have proposed introduction of squeeze film in the inter shaft bearing. However, Inter Shaft Squeeze Film Damper (ISSFD) becomes unstable above a threshold operating speeds. In the present work, an improved ISSFD which is inherently stable, is analyzed and tested. It has two rolling element bearings, one each mounted on LP and HP rotor shafts. The two bearings are configured such that the squeeze film is formed between the two non rotating races/surfaces. A centralizing spring between the two races, and a supporting spring between the ground/frame and one of the non rotating races are provided. Two design modifications of this system are analyzed and tested experimentally. Experiments on an improvised two spool rotor setup under unbalance excitation are conducted for all the three designs of ISSFD. In theoretical simulations, various design parameters are varied over a wide range. Theoretical analysis as well as the experiments show that an optimum value of radial clearance exists for a given design to have maximum damping, and a damping ratio of the order of 10% and more is achievable in an ISSFD.

scholarly journals Analysis of Vibration Damping Ability of Deep Cryogenic Treated AISI 4140 Steel Shaft Supported by Rolling Element Bearings

2021 ◽  
Author(s):  
Menderes KAM ◽  
Hamit SARUHAN
Keyword(s):  
Cryogenic Treatment ◽  
Hold Time ◽  
Rolling Element Bearings ◽  
Rotating Shaft ◽  
Deep Cryogenic Treatment ◽  
Tempering Temperature ◽  
Vibration Data ◽  
Damping Behavior ◽  
Wide Range ◽  
Rolling Element

Abstract The main objective of the present study is to experimentally investigate and figure out the effect of deep cryogenic treatment in improving dynamic behaviors in terms of damping of rotating shaft supported by rolling element bearings. An AISI 4140 steel for rotating shaft was selected for experiment because of it is the most widely used material in most industry for a wide range of applications such as machinery components, crankshafts, motor shafts, axle shafts, and railway locomotive traction motor shafts. Untreated, conventionally heat treated, deep cryogenic treated, and deep cryogenic treated and tempered shafts were used for experiments to observe damping behavior changes of the shafts. Deep cryogenic treated and deep cryogenic treated and tempered shafts were cooled from pre-tempering temperature to - 140 oC and holded for temper hold times of 12, 24, 36, and 48 hours. So, ten sets of shafts were employed for the experiment. The vibration data were captured for each of the shafts for five different shaft running speeds 600, 1200, 1800, 2400, and 3000 rpm. The results showed that damping ability of the deep cryogenic treated shaft at hold time of 36 hours was superior to the others shafts.

Dynamics of Rolling-Element Bearings—Part IV: Ball Bearing Results

1979 ◽  
Vol 101 (3) ◽  
pp. 319-326 ◽  
Author(s):  
P. K. Gupta
Keyword(s):  
Differential Equations ◽  
Axial Load ◽  
Ball Bearing ◽  
Equations Of Motion ◽  
Rolling Element Bearings ◽  
Dynamic Simulations ◽  
Rolling Element ◽  
Overall Stability ◽  
The Stability ◽  
General Motion

Dynamic simulations of the performance of a ball bearing are presented in terms of the general motion as obtained by integrating the differential equations of motion of the various bearing elements. It is shown that bearing misalignment significantly influences the ball/cage and race/cage interaction and, hence, the stability of cage motion. The increased radial to axial load ratios promote skidding which couples with the lubricant behavior to impose accelerations on the ball which ultimately influence the ball/cage interactions. Hence, the lubricant behavior and the large load variation on the balls play dominant roles not only in determining the extent of skidding but also in establishing the overall stability of the cage motion.

Vibration damping capacity of deep cryogenic treated AISI 4140 steel shaft supported by rolling element bearings

2021 ◽  
Vol 63 (8) ◽  
pp. 742-747
Author(s):  
Menderes Kam ◽  
Hamit Saruhan
Keyword(s):  
Cryogenic Treatment ◽  
Hold Time ◽  
Damping Capacity ◽  
Rolling Element Bearings ◽  
Deep Cryogenic Treatment ◽  
Tempering Temperature ◽  
Aisi 4140 Steel ◽  
Wide Range ◽  
Rolling Element ◽  
Aisi 4140

Abstract The main objective of the present study is to experimentally investigate and figure out the effect of deep cryogenic treatment in improving dynamic behaviors in terms of damping of a rotating shaft supported by rolling element bearings. An AISI 4140 steel for rotating shafts was selected for the experiments because it is the most widely used material in most industries for a wide range of applications such as machinery components, crankshafts, motor shafts, axle shafts, and railway locomotive traction motor shafts. Untreated, conventionally heat treated, deep cryogenic treated, and deep cryogenic treated and tempered shafts were used for the experiments to observe damping behavior changes of the shafts. Deep cryogenic treated and deep cryogenic treated and tempered shafts were cooled from pre-tempering temperature to -140 °C and held for tempering hold times of 12, 24, 36, and 48 hours. So, ten sets of shafts were employed for the experiment. The vibration data was captured for each of the shafts for five different shaft running speeds 600, 1200, 1800, 2400 and 3000 rpm. The results showed that damping ability of the deep cryogenic treated shaft at a hold time of 36 hours was superior to that of the others shafts.

A Nonlinear Model for Structural Vibrations in Rolling Element Bearings: Part I—Derivation of Governing Equations

1997 ◽  
Vol 119 (1) ◽  
pp. 126-131 ◽  
Author(s):  
J. Datta ◽  
K. Farhang
Keyword(s):  
Nonlinear Model ◽  
Contact Region ◽  
Equations Of Motion ◽  
Rolling Contact ◽  
Rolling Element Bearings ◽  
Structural Vibrations ◽  
Nonlinear Springs ◽  
Rolling Element ◽  
Rolling Elements ◽  
Constituent Elements

This paper, the first of two companion papers, presents a model for investigating structural vibrations in rolling element bearings. The analytical formulation accounts for tangential and radial motions of the rolling elements, as well as the cage, the inner and the outer races. The contacts between the rolling elements and races are treated as nonlinear springs whose stiffnesses are obtained by application of the equation for Hertzian elastic contact deformation. The derivation of the equations of motion is facilitated by assuming that only rolling contact exists between the races and rolling elements. Application of Lagrange’s equations leads to a system of nonlinear ordinary differential equations governing the motion of the bearing system. These equations are then solved using the Runge-Kutta integration technique. Using the formulation in the second part—“A Nonlinear Model for Structural Vibrations in Rolling Element Bearings: Part II—Simulation and Results,” a number of effects on bearing structural vibrations are studied. This work is unique from previous studies in that the model simulates vibration from intrinsic properties and constituent elements of the bearing, and takes into account every contact region within the bearing, representing it by a nonlinear spring.

Sign in / Sign up

Export Citation Format

Share Document