On some special ruled surfaces

Generating Parametric Gn Blending Surface with Some Constraints

Asymmetrical rail grinding in sharp-radius curves could reduce the side wear of railheads and enhance curve capacity of rail vehicles. The wheel/rail contact performance and curve capacity could be further improved by the optimization of the asymmetrical rail grinding target profile. In order to modify the target profile smoothly, the nonuniform rational B-spline curve with adjustable weight factors is used to establish a parameterized model of railhead curves in the asymmetrical grinding region. The indices of contact performance and curve capacity for different weight factors are obtained using experiment design and service performance simulation. Two Kriging surrogate models are proposed, in which the design variables are the adjustable weight factors, and the response parameters are the indices of contact performance and curve capacity, respectively. The multi-objective optimization model of the target profile is established, in which the objective functions are the two Kriging surrogate models of contact performance and curve capacity. The optimized weight factors are sought using a nondominated sorting genetic algorithm II, and the corresponding optimal target profile is obtained. The wheel/rail service performance simulation before and after optimization indicates that the contact performance and curve capacity are improved significantly.

Contact curvature plays a pivotal role in the Young’s modulus determination and mechanical response of a particle. This paper presents the sensitivity analysis of a particle morphology to contact curvature and its influence on the Young’s modulus determination during the elastic deformation of a particle. X-ray computed micro-tomography (μCT) was conducted to obtain the prototype of a single particle. The digital information of the scanned particle, including 2D slices and 3D rendering was processed and the variation of contact curvature of the particle was examined using the circular (spherical at 3D) and polynomial fitting methods. The fitting sections of the particle are taken into account. The effect of contact curvature on Young’s modulus determination was investigated and it was found that Young’s modulus changed substantially from global fitting to local fitting. Young’s modulus is highly related to the surface roundness, which exerts a significant influence on the determination of Young’s modulus.

A metamodel considering material plasticity is presented for computationally efficient prediction of wheel–rail normal contact in railway switches and crossings (S&C). The metamodel is inspired by the contact theory of Hertz, and for a given material, it computes the size of the contact patch and the maximum contact pressure as a function of the normal force and the local curvatures of the bodies in contact. The model is calibrated based on finite element (FE) simulations with an elasto-plastic material model and is demonstrated for rail steel grade R350HT. The error of simplifying the contact geometry is discussed and quantified. For a moderate difference in contact curvature between wheel and rail, the metamodel is able to accurately predict the size of the contact patch and the maximum contact pressure. The accuracy is worse when there is a small difference in contact curvature, where the influence of variation in curvature within the contact patch becomes more significant. However, it is shown that such conditions lead to contact stresses that contribute less to accumulated plastic deformation. The metamodel allows for a vast reduction of computational effort compared to the original FE model as it is given in analytical form.

The influences of machining and misalignment errors play a very critical role in the performance of the anti-backlash double-roller enveloping hourglass worm gear(ADEHWG). However, a corresponding efficient method for eliminating or reducing these errors on the tooth profile of the ADEHWG is seldom reported. The gear engagement equation and tooth profile equation for considering six different errors that could arise from the machining and gear misalignment are derived from the theories of differential geometry and gear meshing. Also, the tooth contact analysis(TCA) is used to systematically investigate the influence of the machining and misalignment errors on the contact curves and the tooth profile by means of numerical analysis and three-dimensional solid modeling. The research results show that vertical angular misalignment of the worm wheel(Δβ) has the strongest influences while the tooth angle error(Δα) has the weakest influences on the contact curves and the tooth profile. A novel efficient approach is proposed and used to minimize the effect of the errors in manufacturing by changing the radius of the grinding wheel and the approaching point of contact. The results from the TCA and the experiment demonstrate that this tooth profile design modification method can indeed reduce the machining and misalignment errors. This modification design method is helpful in understanding the manufacturing technology of the ADEHWG.

In this article, the design of a nonrelative sliding gear mechanism for parallel axes transmission is presented. First, the general meshing line functions were actively designed for the nonrelative sliding transmission between parallel axes. The parametric equations of contact curves on the driving and driven gears were deduced by the coordinate transformations of function-oriented design of meshing line functions. The meshing between two contact curves on driving and driven gears follows the principle of space curve meshing. Based on two types of motion equations of meshing points, the parametric equations of driving and driven tooth surfaces were deduced according to the helical motion along the calculated contact curves. According to the calculation equations, two pairs of numerical examples were designed and material prototype samples were fabricated to experimentally validate the kinematic performances. After the two types of meshing line motion functions for nonrelative sliding meshing for parallel axes transmission were analyzed, a tooth contact comparative analysis was carried out between the nonrelative sliding gears with uniform motion of meshing points and involute gears, exhibiting better performances. This article introduces a new design method of nonrelative sliding gear mechanism for parallel axes transmission based on function-oriented design of meshing line functions.

This article presents the results of the study of roll contact curves in two-roll modules. The shapes of the contact curves of the rolls in the generalized two-roll module are modeled in the case when the nature of the deformation of the contacting bodies is described by empirical formulas. It was revealed that the previously obtained mathematical models, considering the ratio of deformation of contacting bodies to be equal to the ratio of their deformation rates, describe a particular case of interaction in a two-roll module. Expressions are found that determine the ratio of the deformation rates in a two-roll module, which make it possible to determine the shape of the roll contact curves.

Pseudo-holomorphic curves in nearly Kähler [formula omitted

Computer-Aided Modelling of the Fluting Process for Twist Drill Design and Manufacture

Generating [formula omitted] parametric blending surfaces based on partial reparameterization of base surfaces

A method of generating n-sided (n=3, 5, 6) G2 blending surfaces (except that the 3-sided blending surface is C0 continuous at the three vertexes and the 5-sided blending surface is C0 continuous at a vertex) is presented in this paper. When this method is used to generate n-sided (n=3, 5, 6) G2 blending surfaces between the base surfaces, the base surfaces are expressed as n-sided (n=3, 5, 6) by reparameterising the base surfaces; then the n-sided (n=3, 5, 6) G2 blending surfaces are convex combinations of the base surfaces expressed as n-sided (n=3, 5, 6) surfaces. When the contact curves are arbitrary curves in the base surfaces, the regions near the contact curves in the base surfaces are reparameterised and expressed as n-sided (n=3, 5, 6) surfaces; then the n-sided (n=3, 5, 6) G2 blending surfaces are convex combinations of the reparameterised local base surfaces expressed as n-sided (n=3, 5, 6) surface styles. The shape of the n-sided (n=3, 5, 6) blending surfaces can be adjusted by changing the size of the reparameterised local base surfaces and the combination weights. An example of a 5-sided surface generated between an aerofoil, the body and the fringe surface of a missile is given.

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.

Irreducible contact curves via graph stratification

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.

We report on the investigation of the resistive switching (RS) in the ultrathin (≈5 nm in thickness) yttria-stabilized zirconia (YSZ) films with single layers of Au nanoparticles (NPs) by conductive atomic force microscopy (CAFM). Besides the butterfly-type hysteresis loops in the current-voltage (I-V) curves of the contact of the CAFM probe to the investigated film surface corresponding to the bipolar RS, the negative differential resistance (NDR) has been observed in the I-V curves of the AFM probe contact to the YSZ films with Au NPs in the conductive (“ON”) state. The NDR has been related to the resonant tunneling of electrons through the size-quantized energy states in the ultrafine (1 to 2 nm in diameter) Au NPs built in the conductive filaments in the YSZ films.