A computer solution for the dynamic load, lubricant film thickness and surface temperatures in spiral bevel gears

A complete analysis of spiral bevel gear sets is presented. The gear profile is described by the movements of the cutting tools. The contact patterns of the rigid body gears are investigated. The tooth dynamic force is studied by combining the effects of variable teeth meshing stiffness, speed, damping, and bearing stiffness. The lubrication performance is also accomplished by including the effects of the lubricant viscosity, ambient temperature, and gear speed. A set of numerical results is also presented

Models for Lateral Dynamic Interaction of High-Speed Trains and Bridges

In this work a methodology for analysing the lateral coupled behavior of large viaducts and high-speed trains is proposed. The finite element method is used for the structure, multibody techniques are applied for vehicles and the interaction between them is established introducing wheel-rail nonlinear contact forces. This methodology is applied for the analysis of the railway viaduct of the R´ıo Barbantino, which is a very long and tall bridge in the north-west spanish high-speed line

Multibody approach for railway dynamic analysis

In the work presented, a computational tool used for the dynamic simulation of railway vehicle systems was developed using multibody systems formulations. The model based on the multibody techniques developed by Shabana. With respect to other exciting methodologies the proposed one make use of a combined frame of references that permit the use of independent coordinates, with out the possibility to have singularity configurations depending on the rotation sequence. The combined frame of references used as a base for the formulation and modeling of wheel-rail contact problem with high precision. The program was designed for considering with a flexible form the different configuration of railway vehicles. The main structure of the program has the ability of making changes for enhancement of the wheel-rail contact model or the implementation of dynamic structure of the track, which considered to be future aspects for a PHD dissertation. The model used was applied to make a simulation for single bogie , also for a complete vehicle with two bogies. The obtained results of the dynamic response for a defined track composed of, tangent segment, transition curve which take the form of a clothoid curve, and finally circular curve with constant radius. The calculations were made for different velocities, lower than the critical in which the vehicle responded in stable form, and higher than the critical at which the instability of the vehicle was studied.Elsayed Abdel Hameed Amer Shaltout, R. (2010). Multibody approach for railway dynamic analysis. http://hdl.handle.net/10251/13763Archivo delegad

Constructing geometrical models of spherical analogs of the involute of a circle and cycloid

The common properties of images on a plane and a sphere are considered in the scientific works by scientists-designers of spherical mechanisms. This is due to the fact that the plane and the sphere share common geometric parameters. They include constancy at all points of the Gaussian curve, which has a zero value for a plane and a positive value for a sphere. Figures belonging to them can slide freely on both surfaces. With unlimited growth of the radius of the sphere, its limited section approaches the plane, and the spherical shape transforms into a plane. Thus, a loxodrome that crosses all meridians at a constant angle is transformed into a logarithmic spiral that intersects at a constant angle the radius vectors that come from the pole. The tooth profile of cylindrical gears is outlined by the involute of a circle. A spherical involute is used for the corresponding bevel gears. Other spherical curves are also known, which are analogs of flat ones. The formation of a cycloid and an involute of a circle are associated with the mutual rolling of a line segment with each of these figures. If the segment is fixed and the circle rolls along it, then the point of the circle describes the cycloid. In the case of a stationary circle along which a segment is rolled, the point of the segment will execute the involute. To move to the spherical analogs of these curves, it is necessary to replace the circle with a cone, and the straight line with a plane. The spherical prototype of the cycloid will be the trajectory of the point of the base of the cone, which rolls along the plane, that is, along the sweep of the cone. The sweep of a cone is a sector, the radius of the limiting circle of which is equal to the generating cone. If this sweep, like a section of a plane, is rolled around a fixed cone, when its top coincides with the center of the sector, then the point of the limiting radius of the sector will execute a spherical involute. This paper analytically implements these two motions and reports the parametric equations of the spherical analogs of the circle involute and the cycloi

The homotopy type of spaces of locally convex curves in the sphere

A smooth curve \gamma: [0,1] \to \Ss^2 is locally convex if its geodesic curvature is positive at every point. J. A. Little showed that the space of all locally convex curves $\gamma$ with $\gamma(0) = \gamma(1) = e_1$ and $\gamma'(0) = \gamma'(1) = e_2$ has three connected components $L_{-1,c}$, $L_{+1}$, $L_{-1,n}$. The space \cL_{-1,c} is known to be contractible. We prove that \cL_{+1} and \cL_{-1,n} are homotopy equivalent to (\Omega\Ss^3) \vee \Ss^2 \vee \Ss^6 \vee \Ss^{10} \vee \cdots and (\Omega\Ss^3) \vee \Ss^4 \vee \Ss^8 \vee \Ss^{12} \vee \cdots, respectively. As a corollary, we deduce the homotopy type of the components of the space \Free(\Ss^1,\Ss^2) of free curves \gamma: \Ss^1 \to \Ss^2 (i.e., curves with nonzero geodesic curvature). We also determine the homotopy type of the spaces \Free([0,1], \Ss^2) with fixed initial and final frames.Comment: 47 pages, 13 figure

Conformal cartographic representations

Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2017, Director: Francesc Xavier Massaneda Clares[en] Maps are a useful tool to display information. They are used on a daily basis to locate places, orient ourselves or present different features, such as weather forecasts, population distributions, etc. However, every map is a representation of the Earth that actually distorts reality. Depending on the purpose of the map, the interest may rely on preserving different features. For instance, it might be useful to design a map for navigation in which the directions represented on the map at a point concide with the ones the map reader observes at that point. Such map projections are called conformal. This dissertation aims to study different conformal representations of the Earth. The shape of the Earth is modelled by a regular surface. As both the Earth and the flat piece of paper onto which it is to be mapped are two-dimensional surfaces, the map projection may be described by the relation between their coordinate systems. For some mathematical models of the surface of the Earth it is possible to define a parametrization that verifies the conditions E = G and F = 0, where E, F and G denote the coefficients of the first fundamental form. In this cases, the mapping problem is shown to reduce to the study of conformal functions from the complex plane onto itself. In particular, the Schwarz-Christoffel formula for the mapping of the upper half-plane on a polygon is applied to cartography