Contact Curves Research Articles

Contact line treatment with the sharp interface method

A technique to handle contact points in a sharp interface method based on the level set method is presented. The contact points are tracked explicitly. The coupling between the contact points and the zero level set is enforced by boundary conditions during reinitialisation of the distance function. For sharp interface methods an accurate approximation of the curvature is important. However, this cannot be obtained by using the conventional central difference methods adjacent to walls since the level set functions are not defined therein. Therefore we propose to use the tracked contact point and the intersection points of the first two grid lines parallel to the wall with the zero contour line of the signed distance function to approximate the contact angle and curvature adjacent to the walls. The method is verified using a capillary rise and a gravity driven two phase channel flow.

Sawing performance comparison of brazed and sintered diamond wires

Great attention has been paid on fabricating diamond wire by using the brazing diamond because of its strong chemical bonding strength and controllability of grits distribution. Although several serving performances of brazed diamond wire have been reported, seldom do these studies refer to its process characteristics. Sawing performances of a brazed diamond wire are investigated and compared with those of a sintered diamond wire on a wire saw machine. The surface topographies of beads selected from the two wires are micro observed before sawing. The sawing tests are carried out in constant feed rate feeding(CFF) and constant normal force feeding(CNFF). In CFF test, sawing force, power, and the cut depths of positions on contact curve are measured. Then, coupled with the observations of beads topographies, sawing force and its ratio, relations of power against material removal rate, and contact curve linearity are compared and discussed. In CNFF test, the sawing rates of the two wires are investigated. The results indicate that the brazed wire performs with lower sawing force(less 16% of tangential force and 28% of normal force), more energy efficiency(nearly one-fifth of sawing power is saved), at a higher sawing rate (the rate is doubled) and with better contact curve linearity as compared with the sintered wire. This proposed research experimentally evaluates the sawing performances of brazed diamond wire from the aspect of process parameters, which can provide a basis for popularizing the brazed diamond wire.

Characteristics of grasping movements in a laboratory and in an everyday-like context

To understand the principles of motor control, it is useful to know whether movements with the same physical constraints can be governed by different rules depending on the behavioral context. We therefore have recently introduced a paradigm in which subjects grasp from the same starting position to the same final object, once as a typical laboratory task and once as part of everyday-like behavior. In the laboratory context, grasping was repetitive, externally triggered and purposeless; in the everyday-like context, it was embedded in a complex activity, intentionally initiated, and served a purpose. Here we present a comprehensive analysis of data from that paradigm. Among 38 response parameters that reflected hand transport, grip shaping and object manipulation, 20 differed significantly between groups. Factor analysis further reduced them to four orthogonal factors: response speed, finger-object contact, response variability, and hand path curvature. This shows, for the first time, that behavioral context influences the execution of grasping movements in four independent ways, possibly reflecting four distinct functional modules in the motor system. This fits well with the view – derived from neurological data – that grasping is controlled by a set of interconnected brain areas which are differentially recruited to achieve different behavioral goals.

Design of an optimised wheel profile for rail vehicles operating on two-track gauges

This article sets out an optimum synthesis methodology for wheel profiles of railway vehicles in order to secure good dynamic behaviour with different track configurations. Specifically, the optimisation process has been applied to the case of rail wheelsets mounted on double-gauge bogies that move over two different gauges, which also have different types of rail: the Iberian gauge (1668 mm) and the International Union of Railways (UIC) gauge (1435 mm). Optimisation is performed using Genetic Algorithms and traditional optimisation methods in a complementary way. The objective function used is based on an ideal equivalent conicity curve which ensures good stability on straight sections and also proper negotiation of curves. To this end, the curve is constructed in such a way that it is constant with a low value for small lateral wheelset displacements (with regard to stability), and increases as the displacements increase (to facilitate negotiation of curved sections). Using this kind of ideal conicity curve also enables a wheel profile to be secured where the contact points have a larger distribution over the active contact areas, making wear more homogeneous and reducing stresses. The result is a wheel profile with a conicity that is closer to the target conicity for both gauges studied, producing better curve negotiation while maintaining good stability on straight sections of track. The article shows the resultant wheel profile, the contact curves it produces, and a number of dynamic analyses demonstrating better dynamic behaviour of the synthesised wheel on curved sections with respect to the original wheel.

Numerical investigation of bubble nucleation process using the lattice Boltzmann method

In this paper, the state of metastable equilibrium and the state of unstable equilibrium of water at a certain temperature are explored using an exact difference lattice Boltzmann model and the conditions of bubble (droplet) formation are investigated in the isothermal phase transition processes. From these simulation results, it is found that the model predictions are in good agreement with analytical results. Based on these works, a new model, which is based on exact difference lattice Boltzmann model and extended with an energy transfer equation to model heat transfer, is proposed to describe liquid-vapor phase transition process. The effects of the wall-fluid interaction strength on the bubble nucleation process in a pit are investigated using this new heterogeneous phase transition model. Simulation results accurately reproduce the characteristics of three stages of the bubble nucleation process. The changes of the contact angle, curvature radius, and volume with the bubble nucleation process are explored, and the relationship curve between curvature and bubble volume from the simulations is in qualitative agreement with the previous results.

Design of Space-Curve Meshing-Wheels with Unequal Tine Radii

In some recent papers a new gear mechanism named Space-Curve Meshing-Wheel (SCMW) has been proposed by the present authors. However the research there presented was limited in the equal tine radius case. This paper presents a method to solve the SCMW design with unequal tine radii. As a consequence, with a pair of contact curves, the tine radii of the driving and driven wheels can be selected independently according to actual need. A design example is illustrated in detail and testified in both simulation and practical experiment. This method provides a design fundamental for the SCMWs to optimize the tine shapes according to strength conditions, and therefore it can extend their application in industrial.

Almost contact curves in normal almost contact 3-manifolds

We study almost contact curves in normal almost contact metric 3-manifolds satisfying \({\triangle{H} = \lambda{H}}\) or \({\triangle^\bot {H} = \lambda{H}}\) . Moreover we study almost contact curve of type AW(k) in normal almost contact metric 3-manifolds. We give natural equations of planar biminimal curves.

Efficient solution to the 3D problem of automatic wall paintings reassembly

This paper introduces a new approach for the automated reconstruction- reassembly of fragmented objects having one surface near to plane, on the basis of the 3D representation of their constituent fragments. The whole process starts by 3D scanning of the available fragments. The obtained representations are properly processed so that they can be tested for possible matches. Next, four novel criteria are introduced, that lead to the determination of pairs of matching fragments. These criteria have been chosen so as the whole process imitates the instinctive reassembling method dedicated scholars apply. The first criterion exploits the volume of the gap between two properly placed fragments. The second one considers the fragments’ overlapping in each possible matching position. Criteria 3,4 employ principles from calculus of variations to obtain bounds for the area and the mean curvature of the contact surfaces and the length of contact curves, which must hold if the two fragments match. The method has been applied, with great success, both in the reconstruction of objects artificially broken by the authors and, most importantly, in the virtual reassembling of parts of wall paintings belonging to the Mycenaic civilization (c.1300 BC.), excavated in a highly fragmented condition in Tyrins, Greece

A Simple Verification Test for Nonlinear Flow Calculations Around a Ship Hull Steadily Advancing in Calm Water

Simple analytical relations that can readily be applied to verify a critical aspect of numerical predictions of fully nonlinear free-surface flows around ship hulls steadily advancing in calm water are given. The relations do not involve the flow field equations; that is, they are only based on the boundary conditions at the ship hull surface and at the free surface. These boundary conditions have a predominant influence on free-surface flows around advancing ship hulls. The analytical relations are exact for inviscid flows, and can be applied to numerical methods that solve either the Laplace equation (potential-flow methods) or the Euler flow equations (CFD Euler-flow methods). They provide a simple test to verify if numerical predictions given by nonlinear potential-flow or Euler-flow methods correctly satisfy the hull-surface and free-surface boundary conditions along the contact curve between the hull surface and the free surface. The relations might also be used to verify CFD methods that solve the RANS equations if they are applied at the edge of the viscous boundary layer. The analytical test can identify an inconsistency, which might point to a "method issue" related to a feature of a numerical method (e.g., a numerical-differentiation scheme) or an "implementation issue" in the implementation of the method (e.g., a poor discretization). For purposes of illustration, the test is applied to predictions of flows around the Wigley parabolic hull given by two CFD methods that solve the Euler equations with fully nonlinear boundary conditions at the free surface. This illustrative example demonstrates that the test can indeed be useful to identify numerical inaccuracies. The analytical relations can also be used to determine experimental values of the flow velocity at a ship wave profile that correspond to measurements of the wave profile.

Parametric Study of Meshing Characteristics With Respect to Different Meshing Rollers of the Antibacklash Double-Roller Enveloping Worm Gear

Roller shapes play a very critical role in the performance of antibacklash double-roller enveloping hourglass worm (ADEHW) gears; however, their influence is seldom reported in the literature. Based on the theories of differential geometry and gear meshing, this paper presents generic models of meshing characteristics for ADEHW gears, including both the contact curve and the tooth profile. We present different meshing functions and their derivatives with respect to each drive type and their associated roller shapes. We also compare the effects of contact curve, tooth profile, tooth undercutting, lubrication angle, induced normal curvature, and autorotation angle in order to design the most optimal tooth profile for the ADEHW gear. Finite element analysis was also conducted in order to minimize the contact stresses as a function of the roller type. Our results show that a spherical roller has the smallest value among the three available meshing roller shapes but is the most difficult design to procure. A cylindrical roller, however, incurs the greatest contact stress.

Differential Contact Path and Conjugate Properties of Planar Gearing Transmission

This paper presents a general conjugation model based on the intrinsic kinematical properties of the contact path. The model is truly general for any planar transmission through contact curves, such as gearing. The effectiveness of the method is not affected by the type of centrodes or motion and path of contact. With the method, for any given centrodes and any chosen path of contact, the corresponding conjugate curves can be identified and the geometric properties of the conjugation can be determined even before the conjugate curves are found. The method is demonstrated with straight, circular, and polynomial paths of contact in both circular and noncircular gears. The versatility of the theory and the outstanding features of the method become obvious with treating arbitrary centrodes or any planar motion transmission. The freedom of selecting contact path suggests the possibility of optimal conjugation design.

Connection Theory of Conical Worm Gear Drives

We worked out a mathematical modell for the production geometry and mathematical analysis of spiroid worm gear drives. This modell is adapted for analysis of spiroid worm gear drives with random profile. Using this modell it could be possible for defining of the equations of cog surfaces, the surface normal vector, contact curves and connection surface in one concrete case.

An experiment investigation on dual rotary fretting of medium carbon steel

Abstract A test rig of dual rotary fretting, which combined with the torsional and rotational fretting modes has been developed, based on a low-speed reciprocating rotary motor system. As two extreme cases for the dual rotary fretting, when the tilt angle ( α ) equals 0° or 90°, the fretting transforms to simple mode of torsional fretting or rotational fretting, respectively. The dual rotary fretting tests of medium carbon steel (LZ50) flats against AISI52100 steel balls have been carried out under normal load of 50 N, varied tilt angles ( α = 5°, 10°, 20°, 40°) and varied angular displacement amplitudes ( θ = 0.125°, 0.25°, 0.5°, 1°, 2°, 10°). Kinetic analyses of the fretting running behaviours have been performed in combination with microscopic examinations through optical microscopy, surface profilometer, scanning electric microscopy (SEM) and energy dispersive analysis of X-ray (EDX). The results showed that the running and damage behaviours of the dual rotary fretting were mainly dependent upon the tilt angle α , the angular displacement amplitude θ and the number of cycles, which were obviously different from the two simple fretting modes. The evolutions of the kinetic curves, fretting running regimes, tangential force against normal load curves of contact interfaces and asymmetric morphologies of wear scars as a function of the tilt angle α and the angular displacement amplitude θ have been discussed in detail. Finally, the wear mechanism was summarized.

On the 7th order ODE with submaximal symmetry

We find a general solution to the unique 7th order ODE admitting a ten-dimensional group of contact symmetries. The integral curves of this ODE are rational contact curves in P 3 which give rise to rational plane curves of degree six. The moduli space of these curves is a real form of the homogeneous space Sp ( 4 ) / SL ( 2 ) .

A Darboux-Frame-Based Formulation of Spin-Rolling Motion of Rigid Objects With Point Contact

This paper investigates the kinematics of spin-rolling motion of rigid objects. This paper does not consider slipping but applies a Darboux frame to develop kinematics of spin-rolling motion, which occurs in a nonholonomic system. A new formulation of spin-rolling motion of the moving object is derived in terms of contravariant vectors, rolling velocity, and geometric invariants, including normal curvature, geodesic curvature, and geodesic torsion of the respective contact curve. The equation is represented with geometric invariants. It can be readily generalized to suit both arbitrary parametric surface and contact trajectory and can be differentiated to any order. Effect of the relative curvatures and torsion on spin-rolling kinematics is explicitly presented. The translation velocity of an arbitrary point on the moving object is also derived based on the Darboux frame.

On the fundamental group of the complement of linear torus curves of maximal contact

In this paper, we compute the fundamental group of the complement of linear torus curves of maximal contact and we show that it is isomorphic to that of generic linear torus curves. As an application, we give new two Zariski triples.

Conformal quaternionic contact curvature and the local sphere theorem

A tensor invariant is defined on a quaternionic contact manifold in terms of the curvature and torsion of the Biquard connection involving derivatives up to third order of the contact form. This tensor, called quaternionic contact conformal curvature, is similar to the Weyl conformal curvature in Riemannian geometry and to the Chern–Moser tensor in CR geometry. It is shown that a quaternionic contact manifold is locally quaternionic contact conformal to the standard flat quaternionic contact structure on the quaternionic Heisenberg group, or equivalently, to the standard 3-Sasakian structure on the sphere iff the quaternionic contact conformal curvature vanishes.

Pseudo-holomorphic curves in nearly Kähler [formula omitted

We study pseudo-holomorphic curves in the nearly Kähler 6-manifold CP 3 . First, we introduce two classes of pseudo-holomorphic curves, called horizontal and null-torsion, respectively. We show that both classes are in one to one correspondence with contact holomorphic curves studied by Bryant in the Kähler manifold CP 3 . The correspondence between horizontal curves and contact curves can be seen from their definitions. The correspondence between null-torsion and contact curves needs a double fibration to describe. Borrowing Bryant's results, we show that both classes allow Weierstrass representations. Second, we completely characterize pseudo-holomorphic 2-spheres. It is shown that if they are neither vertical nor horizontal, they must have null torsion.

A load distribution model for hypoid gears using ease-off topography and shell theory

A computationally efficient load distribution model is proposed for both face-milled and face-hobbed hypoid gears produced by Formate and generate processes. Tooth surfaces are defined directly from the cutter parameters and machine settings. A novel methodology based on the ease-off topography is used to determine the unloaded contact patterns. The proposed ease-off methodology finds the instantaneous contact curve through a surface of roll angles, allowing an accurate unloaded tooth contact analysis in a robust and accurate manner. Rayleigh-Ritz based shell models of teeth of the gear and pinion are developed to define the tooth compliances due to bending and shear effects efficiently in a semi-analytical manner. Base rotation and contact deformation effects are also included in the compliance formulations. With this, loaded contact patterns and transmission error of both face-milled and face-hobbed spiral bevel and hypoid gears are computed by enforcing the compatibility and equilibrium conditions of the gear mesh. The proposed model requires significantly less computational effort than finite elements (FE) based models, making its use possible for extensive parameter sensitivity and design optimization studies. At the end, comparisons to the predictions of a FE hypoid gear contact model are also provided to demonstrate the accuracy of the model under various load and misalignment conditions.

Five-axis tool path generation for a flat-end tool based on iso-conic partitioning

Traditionally, for the flat-end tool, due to the intertwined dependence relationship between its axis and reference point, most 5-axis tool-path generation algorithms take a decoupled two-stage strategy: first, the so-called cutter contact (CC) curves are placed on the part surface; then, for each CC curve, tool orientations are decided that will accommodate local and/or global constraints such as minimum local gouging and global collision avoidance. For the former stage, usually simplistic “offset” methods are adopted to determine the cutter contact curves, such as the iso-parametric or iso-plane method; whereas for the latter, a common practice is to assign fixed tilt and yaw angle to the tool axis regardless the local curvature information and, in the case of considering global interference, the tool orientation is decided solely based on avoiding global collision but ignoring important local machining efficiency issues. This independence between the placement of CC curves and the determination of tool orientations, as well as the rigid way in which the tilt and yaw angle get assigned, incurs many undesired problems, such as the abrupt change of tool orientations, the reduced efficiency in machining, the reduced finishing surface quality, the unnecessary dynamic loading on the machine, etc. In this paper, we present a 5-axis tool-path generation algorithm that aims at alleviating these problems and thus improving the machining efficiency and accuracy. In our algorithm, the CC curves are contour lines on the part surface that satisfy the iso-conic property — the surface normal vectors on each CC curve fall on a right small circle on the Gaussian sphere, and the tool orientations associated to a CC curve are determined by the principle of minimum tilt (also sometimes called lead) angle that seeks fastest cutting rate without local gouging. Together with an elaborate scheme for determining the step-over distance between adjacent CC curves that seeks maximum material removal, the presented algorithm offers some plausible advantages over most existing 5-axis tool-path generation algorithms, particularly in terms of reducing the angular velocity and acceleration of the rotary axes of the machine. The simulation experiments of the proposed algorithm and their comparison with a leading commercial CAM software toolbox are also provided that demonstrate the claimed advantages.