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.

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.

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 The Equation of the Contact Line of the Involute Curvilinear-Tooth Cylindrical Gear Pump for the Agricultural Tractor

2014 ◽  
Vol 8 (1) ◽  
pp. 879-884 ◽  
Author(s):  
Yi-Qiang Jiang ◽  
Li Hou ◽  
Yong Zhao
Keyword(s):  
Contact Line ◽  
Helical Gear ◽  
Tooth Surface ◽  
Gear Pump ◽  
Mathematical Software ◽  
Coordinate Systems ◽  
Cylindrical Gear ◽  
Face Width ◽  
Meshing Equation ◽  
Agricultural Tractor

In order to derive the equation of the contact line of the involute curvilinear-tooth cylindrical gear pump for the agricultural tractor, the tooth surface of the involute curvilinear-tooth cylindrical gear is firstly generated as that of the spur or helical gear. Then the equation of the tooth surface is derived from changing the settings and orientations of the coordinate systems after the equation of the tooth profile in an arbitrary radial section is calculated by the methods of differential geometry. Based on the equation of the tooth surface, the meshing equation of the two gears is further acquired and then the equation of the contact line. Finally, the tooth surface and the contact line are simulated with mathematical software. The results suggests that the contact line between two curvilinear-tooth cylindrical gears is an arc line in the surface of action; and this line, shaped as an arc line in the generating plane of the tooth surface, is longer than that of the spur or helical gear with the same face width.

Analysis of Contact Lines on Corrected Planar Double-Enveloping Worm Wheel

2011 ◽  
Vol 341-342 ◽  
pp. 124-127
Author(s):  
Yue Min Zhang ◽  
Xiao Lin Wang ◽  
Xiao Ru Hao
Keyword(s):  
Contact Line ◽  
Worm Gear ◽  
New Method ◽  
Tooth Surface ◽  
Contact Lines ◽  
Matlab Software ◽  
Worm Wheel ◽  
Tooth Surfaces

The tooth-surfaces of corrected planar double-enveloping worm wheel were established by programming in MATLAB with the theory of spatial engagement. The contact lines were analyzed, and the contact styles were classified with given parameters. A new method of judging the types of contact lines was brought out. Based on the theory of spatial engagement, the re-machined planar double-enveloping worm gear is established by programming with MATLAB software. The contact lines on the worm wheel tooth-surface are analyzed and given the method of the contact line kind judgment.

The Study of Meshing Performance for Single Screw Compressor Based on Contact Analysis

2009 ◽  
Vol 16-19 ◽  
pp. 259-263
Author(s):  
Ke Wang ◽  
Bin Zhao
Keyword(s):  
Contact Line ◽  
Contact Analysis ◽  
Tooth Surface ◽  
Screw Compressor ◽  
Contact Lines ◽  
Surface Equation ◽  
Single Screw ◽  
Distribution Rules ◽  
Screw Rotor ◽  
Transition Surface

In order to increase transmission performance and lubricating condition for meshing pair of the single screw compressor, the contact analysis for the single screw compressor is analyzed. The equations of the former tooth surface of the gate rotor, the back tooth surface of the gate rotor, the top tooth surface of the gate rotor and transition surface between two tooth of gate rotor are constructed respectively. The tooth surface equation of the screw rotor is deduced through using the tooth surface equation of the gate rotor and transform matrix depending on conjugated theory, the contact line equation is moreover acquired. The calculation formula of inducing method curvature is deduced, the inducing method curvature of some points on contact line with the rotation degree of the gate rotor changing is calculated. The computing results show that the contact surface is osculating, which is favor to increase contact strength of the tooth surface. The distribution rules for contact lines of the former tooth surface and back tooth surface of gate rotor is gained through calculation, which provide theory basis for manufacturing screw rotor.

Normal Method for Tooth Surface Generation of Helical Gear

2014 ◽  
Vol 945-949 ◽  
pp. 836-839
Author(s):  
Jing Lin ◽  
Ru Qiong Li ◽  
Hui Shen
Keyword(s):  
Helical Gear ◽  
Surface Generation ◽  
Tooth Surface ◽  
Normal Vector ◽  
Logical Method ◽  
Tooth Surfaces ◽  
Basic Parameters ◽  
General Mathematical Model ◽  
Normal Method ◽  
Design And Manufacture

a general mathematical model for describing tooth surfaces of a helical gear. Normal vector of tooth surface are introduced to deal with the model. The tooth surface of a helical gear could be generated directly by giving two basic parameters and . It is believed that the model may provide a simple logical method for the design and manufacture of helical spur gears.

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.

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