Load–Displacement Relationship of a Ball Bearing With Axial, Radial, and Angular Displacements for Both the Inner and Outer Rings

2016 ◽  
Vol 139 (1) ◽  
Author(s):  
Hiroyuki Ohta ◽  
Tomoya Sakaguchi ◽  
Masaharu Uchiumi
Keyword(s):  
Radial Displacement ◽  
Ball Bearing ◽  
Angular Displacement ◽  
Axial Displacement ◽  
Outer Ring ◽  
Ball Bearings ◽  
Outer Race ◽  
Load Displacement ◽  
Angular Displacements ◽  
Relationship Of

This paper deals with the load–displacement relationship of a ball bearing with axial, radial, and angular displacements for both the inner and outer rings. First, the expressions for the load–displacement relationship of ball bearings with any number of balls under the combined axial, radial, and moment loads were presented by using a system in which both the inner and outer rings are allowed to move in the axial, radial, and angular directions. Second, the presented expressions were compared with Jones' expressions (which are typical conventional expressions for the load–displacement relationship), then the range of application of Jones's expressions were elucidated. Third, the relative axial displacement, the relative radial displacement, and the relative angular displacement of a miniature ball bearing type 692 under the combined axial, radial, and moment loads were calculated. Finally, it was shown that the relative angular displacement in the case with no inner ring angular displacement is Ri/Ro times the relative angular displacement in the case with no outer ring angular displacement, in which Ri and Ro are the radii of the inner and outer race curvature center loci.

Carriage Drift in Linear-Guideway Type Roller Bearings

2015 ◽  
Vol 137 (2) ◽  
Author(s):  
Hiroyuki Ohta ◽  
Taiki Kato ◽  
Soichiro Kato ◽  
Hideyuki Tajimi
Keyword(s):  
Ball Bearing ◽  
Roller Bearing ◽  
Experimental Results ◽  
Ball Bearings ◽  
Roller Bearings ◽  
Angular Displacements ◽  
Return Process

This study deals with carriage drift (which is the differences of the carriage displacements or angular displacements at a certain position on a rail during a forward and return process) in linear-guideway type roller bearings. First, the displacements and angular displacements of the carriage of the “nonrecirculating” linear roller and ball bearings under a reciprocating operation were measured. The experimental results showed that carriage drift (in the horizontal, vertical, yaw, and pitch directions) occurred in the roller bearing and not in the ball bearing. Next, in relationship to roller skew, the generating mechanism of carriage drift in roller bearings was examined by a multibody analysis (MBA), then the generating mechanism of carriage drift was explained. Finally, to reduce carriage drift by restricting the roller skew, an antiskewing brace (ASB) was developed.

Vibrations of the All-Ceramic Ball Bearing

2002 ◽  
Vol 124 (3) ◽  
pp. 448-460 ◽  
Author(s):  
Hiroyuki Ohta ◽  
Shinya Satake
Keyword(s):  
Natural Vibration ◽  
Ball Bearing ◽  
Axial Direction ◽  
Outer Ring ◽  
Ball Bearings ◽  
Ceramic Ball ◽  
Vibration Spectra ◽  
All Ceramic ◽  
Hybrid Ceramic ◽  
Mass Type

All-ceramic ball bearings with silicone nitride balls and silicone nitride rings were tested and the vibration characteristics were compared with those of hybrid ceramic ball bearings and conventional steel ball bearings. The vibration measurement results showed that the overall vibratory velocity levels of the all-ceramic ball bearings are influenced by rotational velocities, and do not change with axial loads. Under a given axial load and rotational velocity, the overall vibratory velocity level of the all-ceramic ball bearing is the lowest, and the hybrid ball bearing the highest. The frequencies of main peaks in the measured vibration spectra of the all-ceramic ball bearing are higher than the frequencies of the corresponding main peaks for the hybrid ceramic ball bearing and the steel ball bearing. To explain the main peaks, modal analysis was done and the relationship between peak and natural vibration was analyzed. The results of the analyses showed that the main peaks are caused by: (1) the mass-type natural vibration of the outer ring in the vertical direction, (2) the bending natural vibration of the outer ring in the radial direction, (3) the moment of inertia-type natural vibration of the outer ring in the angular direction, (4) the mass-type natural vibration of the outer ring in the axial direction, and (5) the bending natural vibration of the outer ring in the axial direction. We also discuss the generating mechanism of the vibration and present the calculation method of the vibration spectra. As a result, it is clear that the vibration spectra of the all-ceramic ball bearing are determined by the amplitude of the waviness of the raceways and ball surface, the mobility, and the non-linear spring constant associated with the contact between the raceways and balls.

Discovering Irregular Diagnostic Proper Orthogonal Decomposition Signatures in Healthy Marine Ball Bearings

2012 ◽  
Author(s):  
Ioannis T. Georgiou ◽  
Nikolaos Kintzios
Keyword(s):  
Spatial Distribution ◽  
Ball Bearing ◽  
Flexible Structures ◽  
Ball Bearings ◽  
Radial Acceleration ◽  
Outer Race ◽  
Structural Health ◽  
Proper Orthogonal ◽  
The Impact ◽  
Acceleration Signals

Presented is a structural health condition diagnosis based on optimal space-time decompositions of ensembles of acceleration signals developed in the complex physical domain of marine ball bearings when interrogated by a set of diagnostic impulsive forces. Ensembles of diagnostic forces and ensembles of collocated responses acceleration signals are decomposed into proper orthogonal modes. Typical inner and ensembles of nondestructive impact diagnostic forces covering three times the inner and outer races are strongly dominated by a single POD mode with uniform spatial distribution and a sharp pulse time modulation. There exist high order modes with very small amount of energy. This indicates that the impact response of the suspended ball bearing depends slightly on the impact location. Diametrically opposite, the typical ensemble of radial acceleration signals collected at a point on the outer race has a very broad POD energy spectrum. All POD modes have energy fractions of the same order and irregular (no periodic) space modulations. Despite this spatial irregularity, all POD spatial modulations have astonishingly common statistical properties: nearly zero mean values, and nearly identical standard deviations at the value level of the uniform spatial distribution of the dominant POD mode of the ensembles of diagnostic forces. The result is that the healthy ball bearing spreads nearly evenly the energy of collocated acceleration signals to a large number of POD modes. The analysis aims at gaining a basic understanding of the behavior of collocated acceleration signals developed in the complex domains of multi-body flexible structures with applications in structural health monitoring of marine-aeronautical machinery critical elements such as propellers, bearings, brakes, clutches and gearboxes.

scholarly journals Tongue Rehabilitation Device for Dysphagic Patients

Sensors ◽  
2019 ◽  
Vol 19 (21) ◽  
pp. 4657 ◽  
Author(s):  
Mario Milazzo ◽  
Andrea Panepinto ◽  
Angelo Maria Sabatini ◽  
Serena Danti
Keyword(s):  
Mechanical Model ◽  
Ball Bearing ◽  
Point Of Care ◽  
Angular Displacement ◽  
Force Sensor ◽  
Pressure Force ◽  
Sensor Device ◽  
Speech Therapist ◽  
Angular Displacements ◽  
Dysphagic Patients

Dysphagia refers to difficulty in swallowing often associated with syndromic disorders. In dysphagic patients’ rehabilitation, tongue motility is usually treated and monitored via simple exercises, in which the tongue is pushed against a depressor held by the speech therapist in different directions. In this study, we developed and tested a simple pressure/force sensor device, named “Tonic Tongue (ToTo)”, intended to support training and monitoring tasks for the rehabilitation of tongue musculature. It consists of a metallic frame holding a ball bearing support equipped with a sterile disposable depressor, whose angular displacements are counterbalanced by extensional springs. The conversion from angular displacement to force is managed using a simple mechanical model of ToTo operation. Since the force exerted by the tongue in various directions can be estimated, quantitative assessment of the outcome of a given training program is possible. A first prototype of ToTo was tested on 26 healthy adults, who were trained for one month. After the treatment, we observed a statistically significant improvement with a force up to 2.2 N (median value) in all tested directions of pushing, except in the downward direction, in which the improvement was slightly higher than 5 N (median value). ToTo promises to be an innovative and reliable device that can be used for the rehabilitation of dysphagic patients. Moreover, since it is a self-standing device, it could be used as a point-of-care solution for in-home rehabilitation management of dysphasia.

Investigation of Dynamic Processes in Ball Bearings with Defects

2013 ◽  
Vol 198 ◽  
pp. 651-656 ◽  
Author(s):  
Marijonas Bogdevičius ◽  
Viktor Skrickij
Keyword(s):  
Mathematical Model ◽  
Ball Bearing ◽  
Dynamic Processes ◽  
Experimental Investigations ◽  
Ball Bearings ◽  
Outer Race ◽  
Rolling Element ◽  
Inner Race

The paper considers the dynamics of ball bearings with defects. A mathematical model of a ball bearing with defects is offered. The performed theoretical and experimental investigations of ball bearings with defects are described. Five cases of various defects are investigated, including the defective outer race, the defective inner race, the defective rolling element, the defective inner and outer races, the rolling element and a separator, the worn-out ball bearing.

scholarly journals Performance of 75-Millimeter Bore Arched Outer-Race Ball Bearings

1977 ◽  
Vol 99 (3) ◽  
pp. 346-352 ◽  
Author(s):  
H. H. Coe ◽  
B. J. Hamrock
Keyword(s):  
Experimental Data ◽  
Computer Program ◽  
Analytical Study ◽  
Ball Bearing ◽  
Ball Bearings ◽  
Shaft Speed ◽  
Operating Characteristics ◽  
Outer Race ◽  
Deep Groove ◽  
Deep Groove Ball Bearing

An investigation was performed to determine the operating characteristics of 75-mm bore, arched outer-race bearings, and to compare the data with those for a similar, but conventional, deep groove ball bearing. Further, results of an analytical study, made using a computer program developed previously, were compared with the experimental data. Bearings were tested up to 28,000 rpm shaft speed with a load of 2,200 N (500 lb). The amount of arching was 0.13, 0.25, and 0.51 mm (0.005, 0.010, and 0.020 in.). All bearings operated satisfactorily. The outer-race temperatures and the torques, however, were consistently higher for the arched bearings than for the conventional bearings.

Numerical investigation of the oil–air distribution inside ball bearings with under-race lubrication

2021 ◽  
pp. 135065012110105
Author(s):  
Le Jiang ◽  
Yaguo Lyu ◽  
Wenjun Gao ◽  
Pengfei Zhu ◽  
Zhenxia Liu
Keyword(s):  
High Speed ◽  
Ball Bearing ◽  
Volume Fraction ◽  
Volume Flow Rate ◽  
Ball Bearings ◽  
Outer Race ◽  
Rotating Speed ◽  
Oil Distribution ◽  
Hole Configuration ◽  
Inner Race

Oil distribution inside the under-race lubricated bearing is crucial for lubrication and cooling of high-speed ball bearings. An under-race lubricated ball bearing is modeled to numerically investigate the effects of operating parameters and feed hole configuration on the distribution behavior of lubricant oil. The results of the numerical simulation indicate that the average oil volume fraction changes with a convex trend as the outer race rotating speed increases, while it changes monotonically with the inner race rotating speed, oil volume flow rate, and oil temperature. The extent of oil spreading on the outer race, cage, ball, and inner race decreases successively. Optimizing the feed hole configuration according to the average oil volume fraction is helpful to achieve precise lubrication of the under-race lubricated ball bearing.

Radial Stiffness of Thrust Ball Bearings

2011 ◽  
Vol 490 ◽  
pp. 257-264
Author(s):  
Andrzej Raczyński ◽  
Jaroslaw Kaczor
Keyword(s):  
Computer Program ◽  
Radial Displacement ◽  
Ball Bearing ◽  
Ball Bearings ◽  
Radial Stiffness ◽  
Wear And Tear ◽  
Radial Strength ◽  
Calculation Results ◽  
Special Computer Program ◽  
Bearing System

The paper presents the unusual question of determining the dependency between the radial strength applied to the thrust ball bearing against the radial displacement of one ring to another. Contrary to appearances, the shift may occur in a standard bearing system and consequently it may lead to its premature wear and tear. The article depicts a method of determining this dependency (called ‘radial stiffness’) and shows the examples of calculation results obtained through a special computer program.

Analysis of Deep Groove Ball Bearing Design for Assembly

2013 ◽  
Vol 633 ◽  
pp. 77-86
Author(s):  
Radivoje Mitrovic ◽  
Aleksandar Subic ◽  
Ivana Atanasovska
Keyword(s):  
Ball Bearing ◽  
Experimental Testing ◽  
Theory Of Elasticity ◽  
Outer Ring ◽  
Ball Bearings ◽  
Element Analysis ◽  
Thin Ring ◽  
Deep Groove ◽  
Deep Groove Ball Bearing ◽  
Slight Deformation

This paper presents a comprehensive analysis of the assembly processes for single-row ball bearings. There are two different types of assembly processes, which depend on ball numbers and ball bearing ring designs. In the case of deep groove ball bearings, assembly is usually undertaken through slight deformation of the outer ring to increase clearance for insertion of the final ball. As a result, the outer ring takes an elliptical instead of a circular shape and requires deformation to be below a critical level to avoid fracture. Causal analysis of outer ring fracture during assembly is the main goal of the presented analysis, based on the expressions of the Theory of Elasticity for the thin ring exposed to bending, as well as Finite Element Analysis (FEA). The theoretical and numerical results have been verified by experimental testing.

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