The Effect of Spin Upon the Rolling Motion of an Elastic Sphere on a Plane

1958 ◽  
Vol 25 (3) ◽  
pp. 332-338
Author(s):  
K. L. Johnson
Keyword(s):  
Thrust Bearing ◽  
Theoretical Estimate ◽  
Leading Edge ◽  
Small Extent ◽  
Partial Slip ◽  
Elastic Plane ◽  
Rolling Motion ◽  
Elastic Sphere ◽  
Quantitative Measurements ◽  
Wide Range

Abstract The motion and deformation of an elastic sphere rolling on an elastic plane are examined for the case when the sphere, in addition to its straight rolling motion, has an angular velocity of “spin” Ω about an axis normal to the plane. The action of spin is to twist the area of contact. Surface tractions resulting from this rotation are found, which demonstrate the necessity of partial slip in the area of contact. Previous investigations suggest that this slip cannot occur at the leading edge of the contact circle, so that a system of tractions is found which corresponds to zero stress at the leading point. It is shown that such a system of tractions gives rise to a transverse creep of the sphere in the direction of its rotation Ω. The magnitude of this creep is calculated for small values of Ω, when slip occurs to only a small extent. Experiments have been performed using a simple thrust bearing with plane parallel races. As the bearing rotates, the balls creep radially outward in the predicted manner. Quantitative measurements of this creep agree with the theoretical estimate over a wide range.

The Effect of a Tangential Contact Force Upon the Rolling Motion of an Elastic Sphere on a Plane

1958 ◽  
Vol 25 (3) ◽  
pp. 339-346
Author(s):  
K. L. Johnson
Keyword(s):  
Tangential Force ◽  
Elastic Plane ◽  
Rolling Motion ◽  
Elastic Sphere ◽  
Normal Contact ◽  
Ball Rolling ◽  
Slip Region ◽  
Flat Steel ◽  
Normal Contact Pressure ◽  
Theoretical Results

Abstract The motion and deformation of an elastic sphere rolling on an elastic plane under a normal contact pressure N have been studied for the case where a tangential force T is also sustained at the point of contact. Provided that T < μN (μ = coefficient of friction), the sphere rolls without sliding but exhibits a small velocity relative to the plane, termed “creep.” Following the work of Mindlin and Poritsky, it is shown that creep arises from slip over part of the area of contact, and further, that this slip takes place toward the trailing edge of the contact area. On the assumption of a locked region in which no slip occurs, of circular shape, tangential to the circle of contact at its leading point, surface tractions are found which satisfy the condition of no slip within the locked region and are approximately consistent with the laws of friction in the slip region. The variation of creep velocity with tangential force is thereby determined. Experimental measurements of the creep of a steel ball rolling on a flat steel surface are in reasonable agreement with the theoretical results.

Experimental Studies of Leading Edge Contouring Influence on Secondary Losses in Transonic Turbines

2012 ◽  
Author(s):  
Ranjan Saha ◽  
Jens Fridh ◽  
Torsten Fransson ◽  
Boris I. Mamaev ◽  
Mats Annerfeldt
Keyword(s):  
Gas Turbine ◽  
Guide Vane ◽  
Experimental Studies ◽  
Three Dimensional ◽  
Leading Edge ◽  
Secondary Flows ◽  
Noticeable Effect ◽  
Flow Angle ◽  
Wide Range ◽  
Contour Plots

An experimental study of the hub leading edge contouring using fillets is performed in an annular sector cascade to observe the influence of secondary flows and aerodynamic losses. The investigated vane is a three dimensional gas turbine guide vane (geometrically similar) with a mid-span aspect ratio of 0.46. The measurements are carried out on the leading edge fillet and baseline cases using pneumatic probes. Significant precautions have been taken to increase the accuracy of the measurements. The investigations are performed for a wide range of operating exit Mach numbers from 0.5 to 0.9 at a design inlet flow angle of 90°. Data presented include the loading, fields of total pressures, exit flow angles, radial flow angles, as well as profile and secondary losses. The vane has a small profile loss of approximately 2.5% and secondary loss of about 1.1%. Contour plots of vorticity distributions and velocity vectors indicate there is a small influence of the vortex-structure in endwall regions when the leading edge fillet is used. Compared to the baseline case the loss for the filleted case is lower up to 13% of span and higher from 13% to 20% of the span for a reference condition with Mach no. of 0.9. For the filleted case, there is a small increase of turning up to 15% of the span and then a small decrease up to 35% of the span. Hence, there are no significant influences on the losses and turning for the filleted case. Results lead to the conclusion that one cannot expect a noticeable effect of leading edge contouring on the aerodynamic efficiency for the investigated 1st stage vane of a modern gas turbine.

Calculation and Simulation Azimuth Hydrostatic Thrust Bearing of a Large Alt-Azimuth Telescope

2013 ◽  
Vol 364 ◽  
pp. 28-32
Author(s):  
Long Huang ◽  
Wen Li Ma ◽  
Jin Long Huang
Keyword(s):  
Thrust Bearing ◽  
Structure Parameter ◽  
Tracking Accuracy ◽  
Low Friction ◽  
Element Analysis ◽  
Hydrostatic Bearing ◽  
Wide Range ◽  
And Performance ◽  
Large Telescopes ◽  
Main Factor

The use of hydrostatic bearing for support of telescope offers a number of potential performance advantages, but the structure parameter of bearing is the main factor which influence the bearing. The temperature rise of bearing is also important for the stiffnees of the telescope mount.In addition to the known benefit of mount stiffness and tracking accuracy from exceedingly low friction, the hydrostatic bearing provides a wide range of geometric possibilities for large telescopes [1].This paper analyzes various familiar hydrostatic bearing for the azimuth and elevation axes of telescope.Theoretical calculation and simulation show that the performance of bearing meets telescope’s design requirements.The principle and process of this work and Finite Element Analysis (FEA) are introduced in detail. According to the CFX result, the structure parameter and performance of bearing ,temperature field and pressure distribution have obtained.

Static Characteristics of a Rectangular Hydrostatic Thrust Bearing With a Self-Controlled Restrictor Employing a Floating Disk

1993 ◽  
Vol 115 (2) ◽  
pp. 307-311 ◽  
Author(s):  
S. Yoshimoto ◽  
Y. Anno ◽  
M. Fujimura
Keyword(s):  
Flow Rate ◽  
Applied Load ◽  
Thrust Bearing ◽  
Static Characteristics ◽  
Hydrostatic Bearing ◽  
Supply Pressure ◽  
Wide Range ◽  
Bearing Stiffness ◽  
New Type ◽  
Very High

This paper proposes a new type of a self-controlled restrictor which can achieve a very high bearing stiffness in hydrostatic bearings. This self-controlled restrictor employs a floating disk to control the mass flow rate of the oil entering the bearing clearance according to changes of the applied load. Furthermore, a hydrostatic bearing with this restrictor can theoretically achieve an infinite stiffness when the mass of a floating disk is assumed to be zero. The static characteristics of a rectangular hydrostatic thrust bearing with this self-controlled restrictor are theoretically and experimentally investigated. It was consequently shown that the proposed hydrostatic thrust bearing can achieve a very high stiffness (nearly infinite stiffness) in a very wide range of applied load independent of supply pressure.

Influence of Pre-History and Leading Edge Contouring on Aero-Performance of a 3D Nozzle Guide Vane

2013 ◽  
Author(s):  
Ranjan Saha ◽  
Boris I. Mamaev ◽  
Jens Fridh ◽  
Björn Laumert ◽  
Torsten H. Fransson
Keyword(s):  
Guide Vane ◽  
Three Dimensional ◽  
Leading Edge ◽  
Stagnation Line ◽  
Wide Range ◽  
Nozzle Guide Vane ◽  
Turbine Vane ◽  
Loss Coefficients ◽  
Exit Mach Number ◽  
Nozzle Guide

Experiments are conducted to investigate the effect of the pre-history in the aerodynamic performance of a three-dimensional nozzle guide vane with a hub leading edge contouring. The performance is determined with two pneumatic probes (5 hole and 3 hole) concentrating mainly on the endwall. The investigated vane is a geometrically similar gas turbine vane for the first stage with a reference exit Mach number of 0.9. Results are compared for the baseline and filleted cases for a wide range of operating exit Mach numbers from 0.5 to 0.9. The presented data includes loading distributions, loss distributions, fields of exit flow angles, velocity vector and vorticity contour, as well as, mass-averaged loss coefficients. The results show an insignificant influence of the leading edge fillet on the performance of the vane. However, the pre-history (inlet condition) affects significantly in the secondary loss. Additionally, an oil visualization technique yields information about the streamlines on the solid vane surface which allows identifying the locations of secondary flow vortices, stagnation line and saddle point.

Improved compensation for a reduction stepper to meet the challenges for advanced packaging applications

2013 ◽  
Vol 2013 (1) ◽  
pp. 000814-000819 ◽  
Author(s):  
James E Webb ◽  
Steven Gardner ◽  
Elvino DaSilveira
Keyword(s):  
Leading Edge ◽  
Image Features ◽  
Wafer Level ◽  
Projection Lens ◽  
Wafer Level Packaging ◽  
Alignment System ◽  
Wide Range ◽  
Advanced Packaging ◽  
Volume Production ◽  
Mix And Match

Advanced packaging manufacturers require steppers that will provide solutions for the challenges encountered with new advances in wafer-level packaging technologies such as TSV, eWLB, silicon and glass interposers being utilized in leading edge mobile devices. Step and repeat photolithography systems capable of finer imaging with tighter overlay are being introduced to meet the challenging manufacturing requirements associated with the mix and match needed for volume production on larger wafers. A 2X reduction stepper with unique features incorporated that extend the range of compensation is necessary to achieve the tighter specifications needed for many advanced packaging applications printed on 300 to 450mm wafers. A high throughput projection optical system is used to expose circuit patterns from a reticle mask onto a substrate to image features with the optimal fidelity required for advanced packaging technologies. The camera incorporates 350–450nm light from a mercury arc lamp that is transmitted through the mask containing circuit patterns. The imaging field prints a large 52mm × 66mm area in a single exposure. These features enable a system to process wafers in fewer shots which result in higher throughput using lower power. Substrates are positioned with a precise X, Y, Θ stage by locating marks using an off-axis, bright field alignment system with fully trainable mark feature capability. The approach results in precisely placed features within a layer and from layer to layer without directly referencing the reticle. The integrated metrology and precision positioning subsystem technologies are combined with a low distortion projection lens and a wide range of adjustments, allowing the stepper to be integrated into a production line in a mix and match setup with other lithography systems. This equipment can be used to image critical layers on substrates while ensuring grid registration and alignment with other lithography systems that are also printing images in the same process line. Several important global and intra-field image placement relationships for devices requiring multiple layer patterning have been combined in the stepper matching correction software. Further adjustment to the tool can be made to improve overlay when incorporated with fab-wide yield management software for automated, real-time process control. The types of adjustments needed and techniques that can be applied to compensate for image placement errors over large areas are discussed.

Recent progress in flapping wings for micro aerial vehicle applications

2020 ◽  
pp. 095440622091742
Author(s):  
Naeem Haider ◽  
Aamer Shahzad ◽  
Muhammad Nafees Mumtaz Qadri ◽  
Syed Irtiza Ali Shah
Keyword(s):  
Leading Edge ◽  
Flapping Wing ◽  
Flapping Wings ◽  
Structural Flexibility ◽  
Micro Aerial Vehicles ◽  
Flexible Wings ◽  
Performance Variables ◽  
Aerial Vehicles ◽  
Wide Range ◽  
Wing Geometry

Micro aerial vehicles using flapping wings are under investigation, as an alternative to fixed-wing and rotary-wing micro aerial vehicles. Such flapping-wing vehicles promise key potential advantages of high thrust, agility, and maneuverability, and have a wide range of applications. These applications include both military and commercial domains such as communication relay, search and rescue, visual reconnaissance, and field search. With the advancement in the computational sciences, developments in flapping-wing micro aerial vehicles have progressed exponentially. Such developments require a careful aerodynamic and aeroelastic design of the flapping wing. Therefore, aerodynamic tools are required to study such designs and configurations. In this paper, the role of several parameters is investigated, including the types of flapping wings, the effect of the kinematics and wing geometry (shape, configuration, and structural flexibility) on performance variables such as lift, drag, thrust, and efficiency in various modes of flight. Kinematic variables have a significant effect on the performance of the flapping wing. For instance, a high flap amplitude and pitch rotation, which supports the generation of the strong leading-edge vortex, generates higher thrust. Likewise, wing shape, configuration, and structural flexibility are shown to have a large impact on the performance of the flapping wing. The wing with optimum flexibility maximizes thrust where highly flexible wings lead to performance degradation due to change in the effective angle of attack. This study shows that the development of the flexible flapping wing with performance capabilities similar to those of natural fliers has not yet been achieved. Finally, opportunities for additional research in this field are recommended.

Sting-free measurements on a magnetically supported right circular cylinder aligned with the free stream

2008 ◽  
Vol 596 ◽  
pp. 49-72 ◽  
Author(s):  
HIROSHI HIGUCHI ◽  
HIDEO SAWADA ◽  
HIROYUKI KATO
Keyword(s):  
Circular Cylinder ◽  
Shear Layer ◽  
Free Stream ◽  
Aerodynamic Force ◽  
Cross Flow ◽  
Leading Edge ◽  
Magnetic Suspension ◽  
Recirculation Region ◽  
Mean Velocity ◽  
Wide Range

The flow over cylinders of varying fineness ratio (length to diameter) aligned with the free stream was examined using a magnetic suspension and balance system in order to avoid model support interference. The drag coefficient variation of a right circular cylinder was obtained for a wide range of fineness ratios. Particle image velocimetry (PIV) was used to examine the flow field, particularly the behaviour of the leading-edge separation shear layer and its effect on the wake. Reynolds numbers based on the cylinder diameter ranged from 5×104 to 1.1×105, while the major portion of the experiment was conducted at ReD=1.0×105. For moderately large fineness ratio, the shear layer reattaches with subsequent growth of the boundary layer, whereas over shorter cylinders, the shear layer remains detached. Differences in the wake recirculation region and the immediate wake patterns are clarified in terms of both the mean velocity and turbulent flow fields, including longitudinal vortical structures in the cross-flow plane of the wake. The minimum drag corresponded to the fineness ratio for which the separated shear layer reattached at the trailing edge of the cylinder. The base pressure was obtained with a telemetry technique. Pressure fields and aerodynamic force fluctuations are also discussed.

Prediction of Cavitation Erosion: An Energy Approach

1998 ◽  
Vol 120 (4) ◽  
pp. 719-727 ◽  
Author(s):  
F. Pereira ◽  
F. Avellan ◽  
Ph. Dupont
Keyword(s):  
Energy Spectrum ◽  
Prediction Model ◽  
Cavitation Erosion ◽  
Threshold Energy ◽  
Leading Edge ◽  
Generation Process ◽  
Efficiency Coefficient ◽  
Volume Data ◽  
Vapor Cavity ◽  
Wide Range

The objective is to define a prediction and transposition model for cavitation erosion. Experiments were conducted to determine the energy spectrum associated with a leading edge cavitation. Two fundamental parameters have been measured on a symmetrical hydrofoil for a wide range of flow conditions: the volume of every transient vapor cavity and its respective rate of production. The generation process of transient vapor cavities is ruled by a Strouhal-like law related to the cavity size. The analysis of the vapor volume data demonstrated that vapor vortices can be assimilated to spherical cavities. Results are valid for both the steady and unsteady cavitation behaviors, this latter being peculiar besides due to the existence of distinct volumes produced at specific shedding rates. The fluid energy spectrum is formulated and related to the flow parameters. Comparison with the material deformation energy spectrum shows a remarkable proportionality relationship defined upon the collapse efficiency coefficient. The erosive power term, formerly suggested as the ground component of the prediction model, is derived taking into account the damaging threshold energy of the material. An erosive efficiency coefficient is introduced on this basis that allows to quantify the erosive potential of a cavitation situation for a given material. A formula for localization of erosion is proposed that completes the prediction model. Finally, a procedure is described for geometrical scale and flow velocity transpositions.

scholarly journals Stagnation Region Heat Transfer Augmentation at Very High Turbulence Levels

2015 ◽  
Author(s):  
J. E. Kingery ◽  
F. E. Ames
Keyword(s):  
Heat Transfer ◽  
Leading Edge ◽  
Reynolds Numbers ◽  
Bypass Transition ◽  
Stagnation Region ◽  
Heat Transfer Augmentation ◽  
Wide Range ◽  
High Turbulence ◽  
Very High ◽  
Turbulence Generator

A database for stagnation region heat transfer has been extended to include heat transfer measurements acquired downstream from a new high intensity turbulence generator. This work was motivated by gas turbine industry heat transfer designers who deal with heat transfer environments with increasing Reynolds numbers and very high turbulence levels. The new mock aero-combustor turbulence generator produces turbulence levels which average 17.4%, which is 37% higher than the older turbulence generator. The increased level of turbulence is caused by the reduced contraction ratio from the liner to the exit. Heat transfer measurements were acquired on two large cylindrical leading edge test surfaces having a four to one range in leading edge diameter (40.64 cm and 10.16 cm). Gandvarapu and Ames [1] previously acquired heat transfer measurements for six turbulence conditions including three grid conditions, two lower turbulence aero-combustor conditions, and a low turbulence condition. The data are documented and tabulated for an eight to one range in Reynolds numbers for each test surface with Reynolds numbers ranging from 62,500 to 500,000 for the large leading edge and 15,625 to 125,000 for the smaller leading edge. The data show augmentation levels of up to 136% in the stagnation region for the large leading edge. This heat transfer rate is an increase over the previous aero-combustor turbulence generator which had augmentation levels up to 110%. Note, the rate of increase in heat transfer augmentation decreases for the large cylindrical leading edge inferring only a limited level of turbulence intensification in the stagnation region. The smaller cylindrical leading edge shows more consistency with earlier stagnation region heat transfer results correlated on the TRL (Turbulence, Reynolds number, Length scale) parameter. The downstream regions of both test surfaces continue to accelerate the flow but at a much lower rate than the leading edge. Bypass transition occurs in these regions providing a useful set of data to ground the prediction of transition onset and length over a wide range of Reynolds numbers and turbulence intensity and scales.

Sign in / Sign up

Export Citation Format

Share Document