Special Issue "Friction and Lubrication of Bearings"

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A special issue of Lubricants (ISSN 2075-4442).

Deadline for manuscript submissions: closed (30 October 2014)

Special Issue Editors

Guest Editor
Dr. Romeo P. Glovnea (Website)

Department of Engineering and Design, University of Sussex, Falmer, Brighton BN1 9QT, UK
Fax: +44 127 367 8399
Interests: lubrication; machine elements; mechanical transmissions; fluid rheology
Guest Editor
Dr. Michel Fillon (Website)

Pprime Institute, CNRS - University of Poitiers - ISAE-ENSMA, Department of Mechanical Engineering and Complex Systems, SP2MI - Téléport 2, 11 Boulevard Marie et Pierre Curie, BP 30179, F86962 FUTUROSCOPE CHASSENEUIL Cedex, France
Fax: +33 549 496 504
Interests: thermal effects in hydrodynamic journal and thrust bearings; non-laminar regime; transient effects; risk of bearing seizure; misalignment effects; thermal and mechanical deformations; dynamically loaded bearings; mixed lubrication; lubrication of textured surfaces and wear of hydrodynamic bearings; PTFE and PEEK layered journal and thrust tilting pad bearings; theoretical analyses and numerical simulations under THD or TEHD regime and experimental analyses

Special Issue Information

Dear Colleagues,

Every year, billions of bearings of all kinds are working worldwide. Without exaggeration, bearings are by far the most common machine elements. From miniature bearings used in watches to rolling bearings used in cars, and to huge sliding bearings used in hydro turbines, bearings are present in almost every possible aspect of our lives.

The role of bearings is to guide and support surfaces in relative motion and at the same time, to reduce friction. At a first glance, this may seem a simple task. However, not only does this task involve complex, physical, chemical, mechanical, and energetic phenomena, this role is of paramount importance in our current efforts to increase the efficiency of machines, to extend their working lives, and to protect the environment.

The significant research into all aspects of bearing operations has been extensive in the last century. However, the drive for better quality and longer-lasting bearings and the use of new materials, designs, and lubricants enable continuous research and add new knowledge to engineering science. The current Special Issue is aimed at the latest developments concerning lubrication mechanisms and lubricants and the effect of working parameters upon their functionality and the modelling of their behavior.

Dr. Romeo P. Glovnea
Dr. Michel Fillon
Guest Editors

Submission

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. Papers will be published continuously (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are refereed through a peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Lubricants is an international peer-reviewed Open Access quarterly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. For the first couple of issues the Article Processing Charge (APC) will be waived for well-prepared manuscripts. English correction and/or formatting fees of 250 CHF (Swiss Francs) will be charged in certain cases for those articles accepted for publication that require extensive additional formatting and/or English corrections.


Keywords

  • bearing
  • rolling
  • sliding
  • modeling
  • hydrodynamic lubrication
  • hydrostatic lubrication,
  • journal bearings
  • thrust bearings
  • materials
  • lubricants

Published Papers (15 papers)

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Research

Jump to: Review

Open AccessArticle Friction Reduction and Reliability for Engines Bearings
Lubricants 2015, 3(3), 569-596; doi:10.3390/lubricants3030569
Received: 10 July 2015 / Revised: 10 July 2015 / Accepted: 16 July 2015 / Published: 23 July 2015
Cited by 2 | PDF Full-text (2824 KB) | HTML Full-text | XML Full-text
Abstract
Friction reduction is necessary in order to decrease engine emissions, so bearing friction needs to be reduced but with the constraint that low friction solutions should not affect bearing reliability. To meet this target of low friction and high reliability bearings, several [...] Read more.
Friction reduction is necessary in order to decrease engine emissions, so bearing friction needs to be reduced but with the constraint that low friction solutions should not affect bearing reliability. To meet this target of low friction and high reliability bearings, several technical solutions are reviewed. Particular attention is paid to evaluating friction reduction performance for each solution. Damage risks relating to customer uses are also presented in order to check that these risks are negligible with low friction solutions. Full article
(This article belongs to the Special Issue Friction and Lubrication of Bearings)
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Open AccessArticle Probability of Face Contact for a High-Speed Pressurised Liquid Film Bearing Including a Slip Boundary Condition
Lubricants 2015, 3(3), 493-521; doi:10.3390/lubricants3030493
Received: 29 January 2015 / Revised: 18 May 2015 / Accepted: 11 June 2015 / Published: 24 June 2015
PDF Full-text (479 KB) | HTML Full-text | XML Full-text
Abstract
An initial deterministic mathematical model for the dynamic motion of a simple pressurised liquid film bearing is derived and utilised to evaluate the possibility of bearing contact for thin film operation. For a very thin film bearing the flow incorporates a Navier [...] Read more.
An initial deterministic mathematical model for the dynamic motion of a simple pressurised liquid film bearing is derived and utilised to evaluate the possibility of bearing contact for thin film operation. For a very thin film bearing the flow incorporates a Navier slip boundary condition as parametrised by a slip length that in general is subject to significant variability and is difficult to determine with precision. This work considers the formulation of a modified Reynolds equation for the pressurised liquid flow in a highly rotating coned bearing. Coupling of the axial motion of the stator is induced by prescribed axial oscillations of the rotor through the liquid film. The bearing gap is obtained from solving a nonlinear second-order non-autonomous ordinary differential equation, via a mapping solver. Variability in the value of the slip length parameter is addressed by considering it as a random variable with prescribed mean and standard deviation. The method of derived distributions is used to exactly quantify the impact of variability in the slip length with a parametric study investigating the effect of both the deterministic and distribution parameters on the probability of contact. Additionally, as the axial rotor oscillations also have a random aspect due to possible varying excitations of the system, the probability of contact is investigated for both random amplitude of the periodic rotor oscillations and random slip length, resulting in a two parameter random input problem. The probability of contact is examined to obtain exact solutions and evaluate a range of bearing configurations. Full article
(This article belongs to the Special Issue Friction and Lubrication of Bearings)
Open AccessArticle Experiment and Numerical Study of Wear in Cross Roller Thrust Bearings
Lubricants 2015, 3(2), 447-458; doi:10.3390/lubricants3020447
Received: 31 December 2014 / Revised: 13 April 2015 / Accepted: 22 May 2015 / Published: 29 May 2015
PDF Full-text (892 KB) | HTML Full-text | XML Full-text
Abstract
Bearings are essential parts used in machine tools where high precision is required. It is important to understand bearing failure in order to replace a bearing before it affects the quality of precision. Bearing failure appears as a run-out in some applications, [...] Read more.
Bearings are essential parts used in machine tools where high precision is required. It is important to understand bearing failure in order to replace a bearing before it affects the quality of precision. Bearing failure appears as a run-out in some applications, which is a critical factor for precision. However, previous studies have only focused on failure mechanisms, such as spalling. In this study, two types of wear models were used to predict the thrust bearings run-out: Linear and non-linear mechanisms. In order to validate the models, wear experiments of cross roller thrust bearings were performed. The average difference between the experiment and simulation run-out result was 16%. Then, the wear of different sized cross roller bearings was predicted by using a simulation. This was compared with the experiment result and showed up to a 6% difference. The suggested wear models are expected to be used to predict the failure/life of bearings. Full article
(This article belongs to the Special Issue Friction and Lubrication of Bearings)
Open AccessArticle Relationship between Supplied Oil Flow Rates and Oil Film Thicknesses under Starved Elastohydrodynamic Lubrication
Lubricants 2015, 3(2), 365-380; doi:10.3390/lubricants3020365
Received: 12 December 2014 / Revised: 31 March 2015 / Accepted: 8 April 2015 / Published: 28 April 2015
PDF Full-text (2497 KB) | HTML Full-text | XML Full-text
Abstract
Many studies have already considered starved lubrication. However, there have been no reports on the oil film thicknesses under steady starved EHL (elastohydrodynamic lubrication), where the ultra-low volume of oil supplied per unit time is uniform. The present study examined the relationship [...] Read more.
Many studies have already considered starved lubrication. However, there have been no reports on the oil film thicknesses under steady starved EHL (elastohydrodynamic lubrication), where the ultra-low volume of oil supplied per unit time is uniform. The present study examined the relationship between the supplied oil flow rate and oil film thickness under steady starved lubrication. A ball-on-disk testing machine was used in experiments to measure the oil film thickness by means of optical interferometry. A microsyringe pump was used to accurately control the supplied oil flow rate. The supplied oil flow rate was kept constant, and the minimum oil film thickness was measured for 1 h after the start of the tests to determine the relationship between the supplied oil flow rate and oil film thickness. Full article
(This article belongs to the Special Issue Friction and Lubrication of Bearings)
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Open AccessArticle Nonlinear Dynamic Response of an Unbalanced Flexible Rotor Supported by Elastic Bearings Lubricated with Piezo-Viscous Polar Fluids
Lubricants 2015, 3(2), 281-310; doi:10.3390/lubricants3020281
Received: 1 November 2014 / Revised: 11 January 2015 / Accepted: 22 January 2015 / Published: 16 April 2015
PDF Full-text (790 KB) | HTML Full-text | XML Full-text
Abstract
On the basis of the V. K. Stokes micro-continuum theory, the effects of couple stresses on the nonlinear dynamic response of the unbalanced Jeffcott’s flexible rotor supported by layered hydrodynamic journal bearings is presented in this paper. A nonlinear transient modified Reynolds’ [...] Read more.
On the basis of the V. K. Stokes micro-continuum theory, the effects of couple stresses on the nonlinear dynamic response of the unbalanced Jeffcott’s flexible rotor supported by layered hydrodynamic journal bearings is presented in this paper. A nonlinear transient modified Reynolds’ equation is derived and discretized by the finite element method to obtain the fluid-film pressure field as well as the film thickness by means of the implicit Euler method. The nonlinear orbits of the rotor center are determined by solving the nonlinear differential equations of motion with the explicit Euler’s scheme taking into account the flexibility of rotor. According to the obtained results, the combined effects of couple stresses due to the presence of polymer additives in lubricant and the pressure dependent viscosity on the nonlinear dynamic response of the rotor-bearing system are significant and cannot be ignored or overlooked. As expected, these effects are more noticeable for polymers characterized by higher length molecular chains. Full article
(This article belongs to the Special Issue Friction and Lubrication of Bearings)
Open AccessArticle Rolling Friction Torque in Ball-Race Contacts Operating in Mixed Lubrication Conditions
Lubricants 2015, 3(2), 222-243; doi:10.3390/lubricants3020222
Received: 5 October 2014 / Revised: 2 December 2014 / Accepted: 16 February 2015 / Published: 13 April 2015
Cited by 1 | PDF Full-text (511 KB) | HTML Full-text | XML Full-text
Abstract
Based on a theoretical model and an experimental methodology for defining the friction torque for lubricated conditions in a modified thrust ball bearing having only three balls, the authors experimentally investigated the influence of the lubricant parameter Λ on friction torque for [...] Read more.
Based on a theoretical model and an experimental methodology for defining the friction torque for lubricated conditions in a modified thrust ball bearing having only three balls, the authors experimentally investigated the influence of the lubricant parameter Λ on friction torque for mixed IVR (isoviscous rigid) and EHL (elastohydrodynamic) lubrication conditions. The experiments were conducted using ball diameters of 3 mm, 3.97 mm and 6.35 mm loaded at 0.125 N, 0.400 N and 0.633 N. Two oils of viscosity 0.08 Pa·s and 0.05 Pa·s were used and rotational speed was varied in the range 60–210 rpm to obtain a lubricant parameter Λ varying between 0.3 and 3.2. The experiments confirmed that the measured friction torque can be explained using hydrodynamic rolling force relationships respecting the transition from an IVR to an EHL lubrication regime. Full article
(This article belongs to the Special Issue Friction and Lubrication of Bearings)
Open AccessArticle Thermo-Hydrodynamic Analysis of a Plain Journal Bearing on the Basis of a New Mass Conserving Cavitation Algorithm
Lubricants 2015, 3(2), 256-280; doi:10.3390/lubricants3020256
Received: 6 January 2015 / Revised: 25 March 2015 / Accepted: 30 March 2015 / Published: 13 April 2015
Cited by 2 | PDF Full-text (1769 KB) | HTML Full-text | XML Full-text
Abstract
Accurate prediction of cavitation is an important feature in hydrodynamic bearing modeling. Especially for thermo-hydrodynamic modeling, it is crucial to use a mass-conservative cavitation algorithm. This paper introduces a new mass-conserving Reynolds cavitation algorithm, which provides fast convergence and easy implementation in [...] Read more.
Accurate prediction of cavitation is an important feature in hydrodynamic bearing modeling. Especially for thermo-hydrodynamic modeling, it is crucial to use a mass-conservative cavitation algorithm. This paper introduces a new mass-conserving Reynolds cavitation algorithm, which provides fast convergence and easy implementation in finite element models. The proposed algorithm is based on a variable transformation for both the pressure and mass fraction, which is presented in the form of a complementary condition. Stabilization in the streamline and crosswind direction is provided by artificial diffusion. The model is completed by including a simple and efficient thermal model and is validated using the numerical values of a reference plain journal bearing experiment under steady-state conditions. In addition, a transient analysis is performed of a journal bearing subjected to a harmonic load. It is shown that the proposed cavitation algorithm results are in good agreement with the reference measurement results. Moreover, the algorithm proves to be stable and requires only a small number of iterations to convergence in the Reynolds-based finite element model. Full article
(This article belongs to the Special Issue Friction and Lubrication of Bearings)
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Open AccessArticle Running Torque of Slow Speed Two-Point and Four-Point Contact Bearings
Lubricants 2015, 3(2), 181-196; doi:10.3390/lubricants3020181
Received: 4 November 2014 / Revised: 8 December 2014 / Accepted: 15 December 2014 / Published: 9 April 2015
PDF Full-text (2460 KB) | HTML Full-text | XML Full-text
Abstract
A decoupled slow speed friction torque model has been developed to predict the running torque of a double-arched angular contact bearing when operating as a four-point, as well as a two-point contact bearing. The load distribution model from Amasorrain et al. (2003) [...] Read more.
A decoupled slow speed friction torque model has been developed to predict the running torque of a double-arched angular contact bearing when operating as a four-point, as well as a two-point contact bearing. The load distribution model from Amasorrain et al. (2003) and the kinematics model developed by Leblanc and Nelias (2007) have been combined after ignoring centrifugal and gyroscopic effects, a valid assumption for slow speed operation. Results from the model are compared with previous literature data, as well as with tests done on a specially-developed friction torque rig. The comparison with the literature results was done for two specific cases: (i) when only one out of the two contact lines in the four-point contact bearing is active (effectively creating a two-point contact bearing); and (ii) where both contact lines in the four-point contact bearing are active. Further, the comparison was done with a custom-built friction torque rig with FAG QJ309 bearings, again for two cases: (i) bearings mounted with a specific clearance (two-point contact); and (ii) bearings mounted with larger size balls to obtain interference (four-point contact). All tests were performed at low speeds. The sliding friction, which is an important input to the friction torque model, is carefully measured on ball-on-plate test using the same interface roughness, speed and contact pressure conditions as seen in the QJ309 friction test. The model comparison with experimental results is covered. The comparison is found to be encouraging, with the RMS difference being less than 7% between the model and experimental data for a four point contact. Full article
(This article belongs to the Special Issue Friction and Lubrication of Bearings)
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Open AccessArticle Experimental Measurements of Journal Bearing Friction Using Mineral, Synthetic, and Bio-Based Lubricants
Lubricants 2015, 3(2), 155-163; doi:10.3390/lubricants3020155
Received: 24 November 2014 / Revised: 17 February 2015 / Accepted: 25 February 2015 / Published: 3 April 2015
Cited by 1 | PDF Full-text (480 KB) | HTML Full-text | XML Full-text
Abstract
The environmental impact of many industrial and naval applications is becoming increasingly important. Journal bearings are crucial components related with the reliable, safe and environmentally friendly operation of rotating machinery in many applications, e.g., in hydroplants, ships, power generation stations. The maintenance [...] Read more.
The environmental impact of many industrial and naval applications is becoming increasingly important. Journal bearings are crucial components related with the reliable, safe and environmentally friendly operation of rotating machinery in many applications, e.g., in hydroplants, ships, power generation stations. The maintenance activities in certain cases also have considerable environmental impact. Fortunately, it is relatively easy to reduce the impact by changing the way lubricants are being used. Selecting the proper lubricant is important to sharply reduce long-term costs. The best-fit product selection can mean longer lubricant life, reduced machine wear, reduced incipient power losses and improved safety. Suitable basestocks and additives reduce environmental impact. In this paper, three types of lubricants are used in order to examine their effects on the tribological behavior of journal bearings. A mineral oil, a synthetic oil and a bio-based lubricant are experimentally and analytically examined for several configurations of load and journal rotational velocity. The friction forces and the hydrodynamic friction coefficients are calculated and compared. This investigation can assist the correct choice of lubricant in journal bearings with minimized environmental footprint. Full article
(This article belongs to the Special Issue Friction and Lubrication of Bearings)
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Open AccessArticle Frictional Characteristics of a Small Aerostatic Linear Bearing
Lubricants 2015, 3(2), 132-141; doi:10.3390/lubricants3020132
Received: 2 February 2015 / Revised: 9 March 2015 / Accepted: 16 March 2015 / Published: 2 April 2015
PDF Full-text (599 KB) | HTML Full-text | XML Full-text
Abstract
Frictional characteristics of a small aerostatic linear bearing are accurately evaluated by means of a method, in which the force acting on the moving part of the bearing is measured as the inertial force. An optical interferometer is newly developed to measure [...] Read more.
Frictional characteristics of a small aerostatic linear bearing are accurately evaluated by means of a method, in which the force acting on the moving part of the bearing is measured as the inertial force. An optical interferometer is newly developed to measure the Doppler shift frequency of the laser light reflected on the small moving part. From the measured time-varying Doppler shift frequency, the velocity, the position, the acceleration and the inertial force of the moving part are numerically calculated. It is confirmed that the dynamic frictional force acting inside the bearing is almost proportional to the velocity of the moving part and is similar to the theoretical value calculated under the assumption that the flow inside the bearing is the Couette flow. Full article
(This article belongs to the Special Issue Friction and Lubrication of Bearings)
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Open AccessArticle Analysis of the Journal Bearing Friction Losses in a Heavy-Duty Diesel Engine
Lubricants 2015, 3(2), 142-154; doi:10.3390/lubricants3020142
Received: 15 January 2015 / Revised: 27 February 2015 / Accepted: 9 March 2015 / Published: 2 April 2015
Cited by 2 | PDF Full-text (925 KB) | HTML Full-text | XML Full-text
Abstract
Internal combustion engines (ICE) for the use in heavy-duty trucks and buses have to fulfil demanding requirements for both vehicle efficiency as well as for emission of greenhouse gases. Beside the piston assembly the journal bearings are among the largest contributors to [...] Read more.
Internal combustion engines (ICE) for the use in heavy-duty trucks and buses have to fulfil demanding requirements for both vehicle efficiency as well as for emission of greenhouse gases. Beside the piston assembly the journal bearings are among the largest contributors to friction in the ICE. Through a combination of measurements and validated simulation methods the journal bearing friction losses of a state-of-the-art heavy-duty Diesel engine are investigated for a large range of real world operating conditions. To this task recently developed and extensively validated simulation methods are used together with realistic lubricant models that consider the Non-Newtonian behaviour as well as the piezoviscous effect. In addition, the potential for further friction reduction with the use of ultra-low viscosity lubricants is explored. The results reveal a potential of about 8% friction reduction in the journal bearings using a 0W20 ultra-low viscosity oil with an HTHS-viscosity (The HTHS-viscosity is defined as the dynamic viscosity of the lubricant measured at 150 °C and at a shear rate of 106 s Full article
(This article belongs to the Special Issue Friction and Lubrication of Bearings)
Open AccessArticle Survey of Damage Investigation of Babbitted Industrial Bearings
Lubricants 2015, 3(2), 91-112; doi:10.3390/lubricants3020091
Received: 28 October 2014 / Revised: 9 March 2015 / Accepted: 9 March 2015 / Published: 1 April 2015
Cited by 1 | PDF Full-text (1143 KB) | HTML Full-text | XML Full-text
Abstract This survey collects the efforts to understand the sources and consequences of damage to babbitted industrial bearings, which operate by means of a hydrodynamic, or hydrostatic, film. Major individual damage types are discussed in the context of major damage categories. Full article
(This article belongs to the Special Issue Friction and Lubrication of Bearings)
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Open AccessArticle Experimental Performance Study of a High Speed Oil Lubricated Polymer Thrust Bearing
Lubricants 2015, 3(1), 3-13; doi:10.3390/lubricants3010003
Received: 30 October 2014 / Accepted: 23 December 2014 / Published: 21 January 2015
Cited by 1 | PDF Full-text (449 KB) | HTML Full-text | XML Full-text
Abstract
With the demand for turbomachinery to operate at higher speeds, loads, and power, fluid film bearings that support turbomachinery must be capable of operating in these more demanding applications. Thrust bearings operating at high speeds and loads can experience high surface temperatures [...] Read more.
With the demand for turbomachinery to operate at higher speeds, loads, and power, fluid film bearings that support turbomachinery must be capable of operating in these more demanding applications. Thrust bearings operating at high speeds and loads can experience high surface temperatures and thin fluid film thickness. Typically, babbitt (white metal) is the bearing lining material for most turbomachinery bearings but is limited in operating temperature and allowable film thickness. Polymer based materials are alternative materials that can operate at high temperatures and with thin films and have been in use for many decades in high load applications, such as electric submersible pumps (ESP). Test results of polymer lined thrust bearings subjected to modern turbomachinery speeds and loads are presented and compared to babbitt lined bearings of the same design and under similar conditions. The test results show polymer lined thrust bearings can operate at higher bearing unit loads than babbitt. Full article
(This article belongs to the Special Issue Friction and Lubrication of Bearings)

Review

Jump to: Research

Open AccessReview Friction and Lubrication of Large Tilting-Pad Thrust Bearings
Lubricants 2015, 3(2), 164-180; doi:10.3390/lubricants3020164
Received: 28 November 2014 / Revised: 6 February 2015 / Accepted: 11 March 2015 / Published: 3 April 2015
Cited by 1 | PDF Full-text (1007 KB) | HTML Full-text | XML Full-text
Abstract
Fluid film bearings have been extensively used in the industry because of their unbeatable durability and extremely low friction coefficient, despite a very low coefficient of friction dissipation of energy being noticeable, especially in large bearings. Lubricating systems of large tilting pad [...] Read more.
Fluid film bearings have been extensively used in the industry because of their unbeatable durability and extremely low friction coefficient, despite a very low coefficient of friction dissipation of energy being noticeable, especially in large bearings. Lubricating systems of large tilting pad thrust bearings utilized in large, vertical shaft hydrogenerators are presented in this paper. A large amount of heat is generated due to viscous shearing of the lubricant large tilting pad thrust bearings, and this requires systems for forced cooling of the lubricant. In the dominant bath lubrication systems, cooling is realized by internal coolers or external cooling systems, with the latter showing some important advantages at the cost of complexity and also, potentially, lower reliability. Substantial losses in the bearings, reaching 1 MW in extreme cases, are a good motivation for the research and development aimed at reducing them. Some possible methods and their potential efficiency, along with some effects already documented, are also described in the paper. Full article
(This article belongs to the Special Issue Friction and Lubrication of Bearings)
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Open AccessReview On the Characteristics of Misaligned Journal Bearings
Lubricants 2015, 3(1), 27-53; doi:10.3390/lubricants3010027
Received: 29 January 2015 / Revised: 28 February 2015 / Accepted: 3 March 2015 / Published: 16 March 2015
PDF Full-text (446 KB) | HTML Full-text | XML Full-text
Abstract
Journal bearing misalignment arise generally from the shaft deformation under load, deflection of the shaft, manufacturing and assembly errors, improper installation, and asymmetric loading. During operations, misalignment has a considerable effect on the static and dynamic performances. It could cause wear, vibration [...] Read more.
Journal bearing misalignment arise generally from the shaft deformation under load, deflection of the shaft, manufacturing and assembly errors, improper installation, and asymmetric loading. During operations, misalignment has a considerable effect on the static and dynamic performances. It could cause wear, vibration and even system failure. In this article, a literature review of misalignment of the journal bearings is presented. The basic theory for the misalignment and some results for the circular journal bearing are also presented to show the general trends of the misalignment. Full article
(This article belongs to the Special Issue Friction and Lubrication of Bearings)

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