Analytical and Low-Order Numerical Modeling of Ball-to-Ball Contact Friction in Linear Ball Bearings and Ball Screws

2019 ◽  
Vol 141 (7) ◽  
Author(s):  
Bo Lin ◽  
Molong Duan ◽  
Chinedum E. Okwudire
Keyword(s):  
Case Studies ◽  
Numerical Models ◽  
Experimental Studies ◽  
Point Contact ◽  
Ball Screw ◽  
Contact Friction ◽  
Ball Bearings ◽  
Friction Behavior ◽  
Ball Contact ◽  
Low Order

Analytical and low-order numerical models are very useful for studying friction behavior of rolling element machine components like ball bearings and ball screws. This is because they provide generalizable insights into friction behavior at much lower computational costs compared with high-order numerical models like finite element analysis (FEA). While analytical and low-order numerical models in the literature are mainly focused on ball-to-groove contact friction, experimental studies have shown that ball-to-ball contact friction is also very important. This is especially true for linear ball bearings/guideways and ball screws which, unlike rotary ball bearings, do not typically make use of caged balls to prevent ball-to-ball contact. Therefore, in this paper, low-order numerical models for ball-to-ball contact friction in linear ball bearings and ball screws are developed. Furthermore, an analytical model for ball-to-ball contact friction in four-point contact linear ball bearing is derived by making simplifications to its low-order numerical model. Compared with ball-to-ball friction predictions from FEA models developed in ansys, the proposed numerical models are shown in case studies to be accurate within 7%, while computing at least three orders of magnitude faster. Moreover, case studies are used to demonstrate how the developed models can be used in practice, e.g., for the mitigation of ball-to-ball contact friction in linear ball bearings and the prediction of friction variation during the operation of a ball screw.

An Improved Analytical Model of Friction and Ball Motion in Linear Ball Bearings With Application to Ball-to-Ball Contact Prediction

2018 ◽  
Author(s):  
Bo Lin ◽  
Molong Duan ◽  
Chinedum E. Okwudire ◽  
Jason S. Wou
Keyword(s):  
Analytical Model ◽  
Analytical Formula ◽  
Point Contact ◽  
Friction Model ◽  
Linear Velocity ◽  
Contact Forces ◽  
Ball Bearings ◽  
Friction Behavior ◽  
Rolling Ball ◽  
Ball Contact

The friction behavior of rolling ball machine components like linear ball bearings is very important to their functionality. For instance, differences in linear velocity of balls induces ball-to-ball contact in certain circumstances, resulting in significant increases and variations in friction. In this paper, an improved analytical formula for determining the linear velocity of balls in four-point-contact linear ball bearings is derived as a function of contact angle deviations and contact forces. The analytical formula is validated against a comprehensive friction model in the literature and shown to be in good agreement, while an oversimplified analytical model proposed by the authors in prior work is shown to be inaccurate. A case study is presented where insights gained from the derived analytical formula are used to mitigate velocity difference of balls in a linear ball bearing which otherwise would experience ball-to-ball contact.

Validation of Numerical Models Used for Designing the Composite Blade for ILX-27 Rotorcraft

2019 ◽  
Vol 2019 (4) ◽  
pp. 23-31
Author(s):  
Jakub Wilk ◽  
Radosław Guzikowski
Keyword(s):  
Epoxy Composite ◽  
Numerical Models ◽  
Experimental Studies ◽  
Strength Analysis ◽  
Laminate Glass ◽  
Composite Blade ◽  
Real Objects ◽  
Validation Procedure ◽  
Research Objects ◽  
Comparison Of The Results

Abstract The paper presents the validation procedure of the model used in the analysis of the composite blade for the rotor of the ILX-27 rotorcraft, designed and manufactured in the Institute of Aviation, by means of numerical analyses and tests of composite elements. Numerical analysis using finite element method and experimental studies of three research objects made of basic materials comprising the blade structure – carbon-epoxy laminate, glass-epoxy composite made of roving and foam filler – were carried out. The elements were in the form of four-point bent beams, and for comparison of the results the deflection arrow values in the middle of the beam and axial deformations on the upper and lower surfaces were selected. The procedure allowed to adjust the discrete model to real objects and to verify and correct the material data used in the strength analysis of the designed blade.

Droughts, floods and freshwater ecosystems: evaluating climate change impacts and developing adaptation strategies

2011 ◽  
Vol 62 (3) ◽  
pp. 223 ◽  
Author(s):  
Allison Aldous ◽  
James Fitzsimons ◽  
Brian Richter ◽  
Leslie Bach
Keyword(s):  
Climate Change ◽  
Case Studies ◽  
Management Practices ◽  
Climate Adaptation ◽  
Numerical Models ◽  
Climate Change Impacts ◽  
Freshwater Ecosystems ◽  
Adaptation Strategies ◽  
South Eastern ◽  
Eastern Australia

Climate change is expected to have significant impacts on hydrologic regimes and freshwater ecosystems, and yet few basins have adequate numerical models to guide the development of freshwater climate adaptation strategies. Such strategies can build on existing freshwater conservation activities, and incorporate predicted climate change impacts. We illustrate this concept with three case studies. In the Upper Klamath Basin of the western USA, a shift in land management practices would buffer this landscape from a declining snowpack. In the Murray–Darling Basin of south-eastern Australia, identifying the requirements of flood-dependent natural values would better inform the delivery of environmental water in response to reduced runoff and less water. In the Savannah Basin of the south-eastern USA, dam managers are considering technological and engineering upgrades in response to more severe floods and droughts, which would also improve the implementation of recommended environmental flows. Even though the three case studies are in different landscapes, they all contain significant freshwater biodiversity values. These values are threatened by water allocation problems that will be exacerbated by climate change, and yet all provide opportunities for the development of effective climate adaptation strategies.

scholarly journals Synergism of coupled subsarcolemmal Ca2+ clocks and sarcolemmal voltage clocks confers robust and flexible pacemaker function in a novel pacemaker cell model

2009 ◽  
Vol 296 (3) ◽  
pp. H594-H615 ◽  
Author(s):  
Victor A. Maltsev ◽  
Edward G. Lakatta
Keyword(s):  
Cell Model ◽  
Numerical Models ◽  
Experimental Studies ◽  
Cardiac Pacemaker ◽  
Critical Dimension ◽  
Pacemaker Cell ◽  
Pumping Rate ◽  
Rate Modulation ◽  
Wide Scale ◽  
Fail Safe

Recent experimental studies have demonstrated that sinoatrial node cells (SANC) generate spontaneous, rhythmic, local subsarcolemmal Ca2+ releases (Ca2+ clock), which occur during late diastolic depolarization (DD) and interact with the classic sarcolemmal voltage oscillator (membrane clock) by activating Na+-Ca2+ exchanger current ( INCX). This and other interactions between clocks, however, are not captured by existing essentially membrane-delimited cardiac pacemaker cell numerical models. Using wide-scale parametric analysis of classic formulations of membrane clock and Ca2+ cycling, we have constructed and initially explored a prototype rabbit SANC model featuring both clocks. Our coupled oscillator system exhibits greater robustness and flexibility than membrane clock operating alone. Rhythmic spontaneous Ca2+ releases of sarcoplasmic reticulum (SR)-based Ca2+ clock ignite rhythmic action potentials via late DD INCX over much broader ranges of membrane clock parameters [e.g., L-type Ca2+ current ( ICaL) and/or hyperpolarization-activated (“funny”) current ( If) conductances]. The system Ca2+ clock includes SR and sarcolemmal Ca2+ fluxes, which optimize cell Ca2+ balance to increase amplitudes of both SR Ca2+ release and late DD INCX as SR Ca2+ pumping rate increases, resulting in a broad pacemaker rate modulation (1.8–4.6 Hz). In contrast, the rate modulation range via membrane clock parameters is substantially smaller when Ca2+ clock is unchanged or lacking. When Ca2+ clock is disabled, the system parametric space for fail-safe SANC operation considerably shrinks: without rhythmic late DD INCX ignition signals membrane clock substantially slows, becomes dysrhythmic, or halts. In conclusion, the Ca2+ clock is a new critical dimension in SANC function. A synergism of the coupled function of Ca2+ and membrane clocks confers fail-safe SANC operation at greatly varying rates.

Mechanical Power Losses of Ball Bearings: Model and Experimental Validation

2021 ◽  
pp. 1-29
Author(s):  
Ahmet Dindar ◽  
Amit Chimanpure ◽  
Ahmet Kahraman
Keyword(s):  
Dynamic Model ◽  
Point Contact ◽  
Elastohydrodynamic Lubrication ◽  
Mechanical Power ◽  
Ball Bearings ◽  
Power Losses ◽  
Euler Parameters ◽  
Surface Shear ◽  
Axial Forces ◽  
Set Up

Abstract A tribo-dynamic model of ball bearings is proposed to predict their load-dependent (mechanical) power losses. The model combines (i) a transient, point contact mixed elastohydrodynamic lubrication (EHL) formulation to simulate the mechanics of the load carrying lubricated ball-race interfaces, and (ii) a singularity-free dynamics model, and establishes the two-way coupling between them that dictates power losses. The dynamic model employs a vectoral formulation with Euler parameters. The EHL model is capable of capturing two-dimensional contact kinematics, velocity variations across the contact as well as asperity interactions of rough contact surfaces. Resultant contact surface shear distributions are processed to predict mechanical power losses of example ball bearings operating under combined radial and axial forces. An experimental set-up is introduced for measurement of the power losses of rolling-element bearings. Sets of measurements taken by using the same example ball bearings are compared to those predicted by the model to assess its accuracy in predicting mechanical power loss of a ball bearing within wide ranges of axial and radial forces.

Experimental Studies Using Response Surface Methodology for Condition Monitoring of Ball Bearings

2010 ◽  
Vol 132 (4) ◽  
Author(s):  
M. S. Patil ◽  
Jose Mathew ◽  
P. K. Rajendrakumar ◽  
Sumit Karade
Keyword(s):  
Response Surface Methodology ◽  
Response Surface ◽  
Interaction Effect ◽  
Damage Identification ◽  
Experimental Studies ◽  
Design Procedure ◽  
Defect Size ◽  
Ball Bearings ◽  
Box Behnken Design ◽  
Outer Race

The presence of defect in the bearing (outer race, inner race, or ball) results in increased vibrations. Time domain indices such as rms, crest factor, and kurtosis are some of the important parameters used to monitor the condition of the bearing. Radial load and operating speed also have an important role in bearing vibrations. The interaction between the defect size, load, and speed helps to study their effect on vibrations more effectively. Response surface methodology (RSM) is a combination of statistical and mathematical techniques to represent the relationship between the inputs and the outputs of a physical system. But so far, the literature related to its application in bearing damage identification is scarce. The proposed study uses RSM to study the influence of defect size, load, and speed on the bearing vibrations. Kurtosis is used as response factor. Experiments are planned using Box Behnken design procedure. Experiments are performed using 6305 ball bearings and the results have been presented. MINITAB statistical software is used for analysis. It is seen from the analysis of the experimental results that the defect size, interaction effect of defect size and load, and interaction effect of defect size and speed are significant. Response surface method using Box Behnken design and analysis of variance has proved to be a successful technique to assess the significant factors related to bearing vibrations.

scholarly journals MHD-waves in the geomagnetic tail: A review

10.12737/7168 ◽  
2015 ◽  
Vol 1 (1) ◽  
pp. 4-22 ◽  
Author(s):  
Анатолий Леонович ◽  
Anatoliy Leonovich ◽  
Виталий Мазур ◽  
Vitaliy Mazur ◽  
Даниил Козлов ◽  
...  
Keyword(s):  
Numerical Models ◽  
Experimental Studies ◽  
Low Frequency ◽  
Detailed Comparison ◽  
Mhd Waves ◽  
Theoretical Studies ◽  
Geomagnetic Tail ◽  
Magnetopause Oscillations ◽  
Experimental And Theoretical Studies ◽  
Theoretical Results

This article presents the review of experimental and theoretical studies on ultra-low-frequency MHD oscillations of the geomagnetic tail. We consider the Kelvin–Helmholtz instability at the magnetopause, oscillations with a discrete spectrum in the “magic frequencies” range, the ballooning instability of coupled Alfvén and slow magnetosonic waves, and “flapping” oscillations of the current sheet of the geomagnetic tail. Over the last decade, observations from THEMIS, CLUSTER and Double Star satellites have been of great importance for experimental studies. The use of several spacecraft allows us to study the structure of MHD oscillations with high spatial resolution. Due to this, we can make a detailed comparison between theoretical results and those obtained from multi-spacecraft studies. To make such comparisons in theoretical studies, in turn, we have to use the numerical models closest to the real magnetosphere.

Theoretical and experimental studies of the oil film in lubricated point contact

1966 ◽  
Vol 291 (1427) ◽  
pp. 520-536 ◽  
Keyword(s):  
Surface Layer ◽  
Film Thickness ◽  
Strong Evidence ◽  
Experimental Studies ◽  
Point Contact ◽  
Elastohydrodynamic Lubrication ◽  
Experimental Results ◽  
Point Contacts ◽  
Previous Theory ◽  
Oil Film

A technique using Newton’s rings for mapping the oil film of lubricated point contacts is described. A theoretical value for the film thickness of such contacts in elastohydrodynamic lubrication is derived. The experimental results give the exit constriction predicted by previous theory but never shown in detail. The comparison of theoretical and experimental oil film thicknesses, which is satisfactorily accurate, gives strong evidence for a viscous surface layer some 1000Å thick. This film agrees with the known ‘lubricating power’ of the various oils tested.

scholarly journals Recent advances in understanding Antarctic climate evolution

2008 ◽  
Vol 20 (4) ◽  
pp. 313-325 ◽  
Author(s):  
Martin J. Siegert ◽  
Peter Barrett ◽  
Robert DeConto ◽  
Robert Dunbar ◽  
Colm Ó Cofaigh ◽  
...  
Keyword(s):  
Case Studies ◽  
Numerical Models ◽  
Full Range ◽  
Ice Sheet ◽  
Geological Evidence ◽  
Last Glacial ◽  
Recent Advances ◽  
Climate Evolution

AbstractGeological evidence shows that the ice sheet and climate in Antarctica has changed considerably since the onset of glaciation around 34 million years ago. By analysing this evidence, important information concerning processes responsible for ice sheet growth and decay can be determined, which is vital for appreciating future changes in Antarctica. Geological records are diverse and their analyses require a variety of techniques. They are, however, essential for the establishment of hypotheses regarding past Antarctic changes. Numerical models of ice and climate are useful for testing such hypotheses, and in recent years there have been several advances in our knowledge relating to ice sheet history gained from these tests. This paper documents five case studies, employing a full range of techniques, to exemplify recent insights into Antarctic climate evolution from modelling ice sheet inception in the earliest Oligocene to quantifying Neogene ice sheet fluctuations and process-led investigations of recent (last glacial) changes.

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