A Comparison between a Classical and a Modified Root Fillet

The main purpose of this paper consists in improving the rigidity of the gear tooth by applying various root fillet forms that differ from the classical 0.38m radius circle arc. During the research the necessity of the re-formulation of the undercut appeared. It appears much later in case of applying rounded addendum edge planing comb as in case of using a classic generating profile tool. Therefore, the limits of the profile shifting can be significantly extended without weakening the tooth dedendum. The paper presents the stress repartitions under equal load, which occur on classic teeth, and on teeth having a modified root fillet. In this last case, the modified root fillet is the envelope of the curve family constituted by the rounded edge curves, in the relative motion of the comb related to the cut gear.

An alternative capacity in metric measure spaces

A new condenser capacity $\CMp(E,G)$ is introduced as an alternative to the classical Dirichlet capacity in a metric measure space $X$. For $p>1$, it coincides with the $M_p$-modulus of the curve family $\Gamma(E,G)$ joining $\partial G$ to an arbitrary set $E \subset G$ and, for $p = 1$, it lies between $AM_1(\Gamma(E,G))$ and $M_1(\Gamma(E,G))$. Moreover, the $\CMp(E,G)$-capacity has good measure theoretic regularity properties with respect to the set $E$. The $\CMp(E,G)$-capacity uses Lipschitz functions and their upper gradients. The doubling property of the measure $\mu$ and Poincar\'e inequalities in $X$ are not needed.

A Novel Condition to the Harmonic of the Velocity Vector Field of a Curve in Rn

In this paper, a condition is obtained for the harmonic of the velocity vector field in the curve family passing through the fixed p and q points in Rn. It shows that the condition can be expressed in terms of the curvature functions. Finally, we give an example which provides the mentioned condition in this work and illustrates it with figures.

Moduli of curve families and (quasi-)conformality of power-law entropies

We present aspects of the moduli of curve families on a metric measure space which may prove useful in calculating, or in providing bounds to, non-additive entropies having a power-law functional form. We use as paradigmatic cases the calculations of the moduli of curve families for a cylinder and for an annulus in [Formula: see text]. The underlying motivation for these studies is that the definitions and some properties of the modulus of a curve family resembles those of the Tsallis entropy, when the latter is seen from a micro-canonical viewpoint. We comment on the origin of the conjectured invariance of the Tsallis entropy under Möbius transformations of the non-extensive (entropic) parameter. Needing techniques applicable to both locally Euclidean and fractal classes of spaces, we examine the behavior of the Tsallis functional, via the modulus, under quasi-conformal maps. We comment on properties of such maps and their possible significance for the dynamical foundations of power-law entropies.

A Practical Approximate Method to Predict Adjusting Performance of a Centrifugal Compressor Stage With Inlet Guide Vane

This paper has proposed a method for predicting an adjusting performance curve family of a centrifugal compressor stage with the inlet guide vane (IGV). The method can be separated into two steps. In the first step, a centrifugal compressor model stage is selected as a basic model stage to build the basis of prediction. Both the ordinary performance curve of the model stage without IGV and the adjusting performance curve family of the model stage at various setting angles of the IGV are obtained by experiments. Then, using the ordinary performance curve as a criterion, a non-dimensional mathematical relationship is set up between the ordinary performance curve and each curve in the adjusting performance curve family. In the second step, based on the relationship established above, a prediction is made for the adjusting performance curve family of another centrifugal compressor stage with an IGV. For this prediction, two conditions must be satisfied: 1) The adjustment must be done using the IGV of the same type as used in the first step; 2) The ordinary performance curve of the predicted model stage must have been obtained experimentally. By applying the method, a prediction was carried out for the IGV adjusting performance curve family of a centrifugal compressor stage. Comparison between the predicted results and experimental results shows that although there is relatively great discrepancy between the basic model stage and the predicted stage under the mechanical geometric construction and operating conditions, the two results agree well in most of the areas of the adjusting performance curve family. There are only greater errors of predicted results in areas of large IGV setting angle. Although the current method has some deficiencies, it still possesses some strength featuring simplicity, convenience and reliability, thus providing a practical approximate prediction method available for the centrifugal compressor manufacturers that have the model stage database, but lack the APCF for the model stages with IGV.

Approximation and Analytical Studies of Inter-clustering Performances of Space-Filling Curves

International audience A discrete space-filling curve provides a linear traversal/indexing of a multi-dimensional grid space.This paper presents an application of random walk to the study of inter-clustering of space-filling curves and an analytical study on the inter-clustering performances of 2-dimensional Hilbert and z-order curve families.Two underlying measures are employed: the mean inter-cluster distance over all inter-cluster gaps and the mean total inter-cluster distance over all subgrids.We show how approximating the mean inter-cluster distance statistics of continuous multi-dimensional space-filling curves fits into the formalism of random walk, and derive the exact formulas for the two statistics for both curve families.The excellent agreement in the approximate and true mean inter-cluster distance statistics suggests that the random walk may furnish an effective model to develop approximations to clustering and locality statistics for space-filling curves.Based upon the analytical results, the asymptotic comparisons indicate that z-order curve family performs better than Hilbert curve family with respect to both statistics.