Mesh Theory for Toroidal Drive

2003 ◽  
Vol 126 (3) ◽  
pp. 551-557 ◽  
Author(s):  
Lizhong Xu ◽  
Zhen Huang ◽  
Yulin Yang
Keyword(s):  
Contact Line ◽  
Relative Velocity ◽  
Velocity Vector ◽  
Normal Curvature ◽  
Solid Model ◽  
Contact Lines

In this study, a simpler mesh equation for the toroidal drive is developed. Based on the equation, equations of the contact line, the limit curves, the induced normal curvature between the mating surfaces and the angle of the relative velocity vector to the contact line are introduced. On the basis of the presented equations, the instantaneous contact lines of the planet and the stator or the worm are calculated, the shape of the contact lines and the range of the meshing zone are analyzed, the undercutting of the stator surface and the worm surface is discussed, the induced normal curvature between the planet and the stator or the worm are investigated, and the angles of the relative velocity vector to the contact line are calculated. The solid model of the toroidal drive is presented.

Mesh analysis for toroidal drive with roller teeth

2008 ◽  
Vol 222 (3) ◽  
pp. 473-481
Author(s):  
L Xu ◽  
Z Huang
Keyword(s):  
Contact Line ◽  
Relative Velocity ◽  
Velocity Vector ◽  
Current Paper ◽  
Normal Curvature ◽  
Tooth Surface ◽  
Contact Lines ◽  
Mesh Analysis ◽  
Meshing Equation ◽  
Design And Manufacture

In the current paper, for the toroidal drive with roller teeth, its meshing equation, equations of the contact lines, the limit curves, the induced normal curvature, and the angle of the relative velocity vector to the contact line are determined. Using the equations, contact lines, meshing zones, limit curves, induced normal curvatures, and angles of the relative velocity vector to the contact line are calculated for two kinds of the toroidal drives with roller teeth, respectively. The results are compared with those for the toroidal drive with ball teeth. For the roller tooth surface of the drive, the distribution of the mesh parameters has given. The changes of the mesh parameters along with drive parameters have been investigated. The results are compared with those for the toroidal drive with ball teeth. The results are useful for design and manufacture of the toroidal drive.

A General Method for Computing Worm Gear Conjugate Mesh Property: Part 2—The Mathematic Model of Worm Gear Manufacturing and Working Processes

1989 ◽  
Vol 111 (1) ◽  
pp. 148-152 ◽  
Author(s):  
Changqi Zheng ◽  
Jirong Lei
Keyword(s):  
Contact Line ◽  
Relative Velocity ◽  
Velocity Vector ◽  
Gear Tooth ◽  
Mathematic Model ◽  
Worm Gear ◽  
Tooth Surface ◽  
Gear Manufacturing ◽  
General Method ◽  
Working Processes

Part 2 of this article is devoted to building a generalized mathematic model of worm gear manufacturing and working processes which can be used for calculating the contact line, the profile, the normal curvature, the conjugate boundary and the angle between the directions of contact line and relative velocity vector for any kind of worm gear tooth surface.

scholarly journals Relaxation of a dewetting contact line. Part 1. A full-scale hydrodynamic calculation

2007 ◽  
Vol 579 ◽  
pp. 63-83 ◽  
Author(s):  
JACCO H. SNOEIJER ◽  
BRUNO ANDREOTTI ◽  
GILES DELON ◽  
MARC FERMIGIER
Keyword(s):  
Contact Angle ◽  
Contact Line ◽  
Apparent Contact Angle ◽  
Universal Relation ◽  
Contact Lines ◽  
Viscous Effects ◽  
Solid Plate ◽  
Static Approach ◽  
Critical Capillary Number ◽  
Wetting Liquid

The relaxation of a dewetting contact line is investigated theoretically in the so-called ‘Landau–Levich’ geometry in which a vertical solid plate is withdrawn from a bath of partially wetting liquid. The study is performed in the framework of lubrication theory, in which the hydrodynamics is resolved at all length scales (from molecular to macroscopic). We investigate the bifurcation diagram for unperturbed contact lines, which turns out to be more complex than expected from simplified ‘quasi-static’ theories based upon an apparent contact angle. Linear stability analysis reveals that below the critical capillary number of entrainment, Cac, the contact line is linearly stable at all wavenumbers. Away from the critical point, the dispersion relation has an asymptotic behaviour σ∝|q| and compares well to a quasi-static approach. Approaching Cac, however, a different mechanism takes over and the dispersion evolves from ∼|q| to the more common ∼q2. These findings imply that contact lines cannot be described using a universal relation between speed and apparent contact angle, but viscous effects have to be treated explicitly.

An Experimental Study of the Dynamics of Contact Lines

1995 ◽  
Vol 407 ◽  
Author(s):  
S. Kumar ◽  
M. O. Robbins ◽  
D. H. Reich
Keyword(s):  
Experimental Study ◽  
Capillary Pressure ◽  
Measurement Technique ◽  
Contact Line ◽  
Pressure Measurement ◽  
Differential Pressure ◽  
Contact Lines ◽  
Random Surface ◽  
Depinning Transition ◽  
Surface Disorder

ABSTRACTWe have studied the dynamics of contact lines formed by water-alkane interfaces in capillaries with random surface disorder. We find that the contact-line velocity V scales with the applied capillary pressure P as V∼ (P – Pt)ζ over two decades in V. This is consistent with a critical depinning transition. We obtain this result by using a sensitive ac differential-pressure measurement technique to measure dP/dV. We find that dP/dV αV−0 8 (5) implying that 1/ζ = 0. 20 (5).

scholarly journals Numerical simulation of dynamic contact-line problems

1997 ◽  
Vol 352 ◽  
pp. 113-133 ◽  
Author(s):  
IVAN B. BAZHLEKOV ◽  
PETER J. SHOPOV
Keyword(s):  
Contact Line ◽  
Contact Region ◽  
Outer Region ◽  
Dynamic Contact ◽  
Momentum Conservation ◽  
Phase Region ◽  
Contact Lines ◽  
Three Phase ◽  
Inner Region ◽  
Dynamic Contact Line

The presence of a three-phase region, where three immiscible phases are in mutual contact, causes additional difficulties in the investigation of many fluid mechanical problems. To surmount these difficulties some assumptions or specific hydrodynamic models have been used in the contact region (inner region). In the present paper an approach to the numerical solution of dynamic contact-line problems in the outer region is described. The influence of the inner region upon the outer one is taken into account by means of a solution of the integral mass and momentum conservation equations there. Both liquid–fluid–liquid and liquid–fluid–solid dynamic contact lines are considered. To support the consistency of this approach tests and comparisons with a number of experimental results are performed by means of finite-element numerical simulations.

Surfactant Self-Assemblies Near Contact Lines and their Effect on Wetting by Surfactant Solutions

1994 ◽  
Vol 366 ◽  
Author(s):  
B. Frank ◽  
S. Garoff
Keyword(s):  
Pattern Formation ◽  
Contact Line ◽  
Self Assembly ◽  
Surface Interactions ◽  
Contact Lines ◽  
Dynamic Wetting ◽  
Wetting Behavior ◽  
Wetting Properties ◽  
Surfactant Solutions ◽  
Solid Liquid

ABSTRACTSurfactant self-assembly at the liquid-vapor, solid-liquid, and solid-vapor interfaces controls the wetting behavior of advancing surfactant solutions. While different surfactants exhibit different static and dynamic wetting properties, we show that these behaviors can be understood through an examination of microscopic structures driven by surfactant-surface interactions. We examine surfactant solutions exhibiting complete and partial static wetting as well as spreading by dendritic pattern formation and unsteady, stick-jump behavior. In each case, the observed behavior is related to the structure of the surfactant assemblies in the vicinity of the contact line.

Shear flow over a liquid drop adhering to a solid surface

1996 ◽  
Vol 307 ◽  
pp. 167-190 ◽  
Author(s):  
Xiaofan Li ◽  
C. Pozrikidis
Keyword(s):  
Contact Angle ◽  
Shear Flow ◽  
Contact Line ◽  
Simple Shear ◽  
Liquid Drop ◽  
Contact Angle Hysteresis ◽  
Boundary Integral ◽  
Simple Shear Flow ◽  
Contact Lines ◽  
Transient Deformation

The hydrostatic shape, transient deformation, and asymptotic shape of a small liquid drop with uniform surface tension adhering to a planar wall subject to an overpassing simple shear flow are studied under conditions of Stokes flow. The effects of gravity are considered to be negligible, and the contact line is assumed to have a stationary circular or elliptical shape. In the absence of shear flow, the drop assumes a hydrostatic shape with constant mean curvature. Families of hydrostatic shapes, parameterized by the drop volume and aspect ratio of the contact line, are computed using an iterative finite-difference method. The results illustrate the effect of the shape of the contact line on the distribution of the contact angle around the base, and are discussed with reference to contact-angle hysteresis and stability of stationary shapes. The transient deformation of a drop whose viscosity is equal to that of the ambient fluid, subject to a suddenly applied simple shear flow, is computed for a range of capillary numbers using a boundary-integral method that incorporates global parameterization of the interface and interfacial regriding at large deformations. Critical capillary numbers above which the drop exhibits continued deformation, or the contact angle increases beyond or decreases below the limits tolerated by contact angle hysteresis are established. It is shown that the geometry of the contact line plays an important role in the transient and asymptotic behaviour at long times, quantified in terms of the critical capillary numbers for continued elongation. Drops with elliptical contact lines are likely to dislodge or break off before drops with circular contact lines. The numerical results validate the assumptions of lubrication theory for flat drops, even in cases where the height of the drop is equal to one fifth the radius of the contact line.

scholarly journals Surface textures suppress viscoelastic braking on soft substrates

2020 ◽  
Vol 117 (51) ◽  
pp. 32285-32292
Author(s):  
Martin Coux ◽  
John M. Kolinski
Keyword(s):  
Contact Line ◽  
High Speed ◽  
Solid Phase ◽  
Contact Lines ◽  
Line Geometry ◽  
Moving Contact Line ◽  
Moving Contact ◽  
Cassie State ◽  
Compliant Surfaces ◽  
Gravity Driven

A gravity-driven droplet will rapidly flow down an inclined substrate, resisted only by stresses inside the liquid. If the substrate is compliant, with an elastic modulusG< 100 kPa, the droplet will markedly slow as a consequence of viscoelastic braking. This phenomenon arises due to deformations of the solid at the moving contact line, enhancing dissipation in the solid phase. Here, we pattern compliant surfaces with textures and probe their interaction with droplets. We show that the superhydrophobic Cassie state, where a droplet is supported atop air-immersed textures, is preserved on soft textured substrates. Confocal microscopy reveals that every texture in contact with the liquid is deformed by capillary stresses. This deformation is coupled to liquid pinning induced by the orientation of contact lines atop soft textures. Thus, compared to flat substrates, greater forcing is required for the onset of drop motion when the soft solid is textured. Surprisingly, droplet velocities down inclined soft or hard textured substrates are indistinguishable; the textures thus suppress viscoelastic braking despite substantial fluid–solid contact. High-speed microscopy shows that contact line velocities atop the pillars vastly exceed those associated with viscoelastic braking. This velocity regime involves less deformation, thus less dissipation, in the solid phase. Such rapid motions are only possible because the textures introduce a new scale and contact-line geometry. The contact-line orientation atop soft pillars induces significant deflections of the pillars on the receding edge of the droplet; calculations confirm that this does not slow down the droplet.

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