Third-Order Surface Application to Determine the Tooth Contact Pattern of Hypoid Gears

1986 ◽  
Vol 108 (2) ◽  
pp. 263-269 ◽  
Author(s):  
Koichi Takahashi ◽  
Norio Ito
Keyword(s):  
Higher Order ◽  
Second Order ◽  
Contact Pattern ◽  
Trial And Error ◽  
Conventional Theory ◽  
Third Order ◽  
Hypoid Gears ◽  
Surface Application ◽  
Tooth Surfaces ◽  
Order Surface

In the conventional theory for hypoid gears tooth surfaces are represented by second-order surfaces. However, for developing an excellent tooth bearing, this theory is not accurate enough because higher-order surfaces are required. This paper presents a new theory using third-order tooth surfaces instead of the conventional second-order surfaces. The results are useful for drawing accurate patterns of the tooth bearing and eliminating the need for trial-and-error methods to improve the tooth bearing.

How to Obtain the Formal Tooth Bearing Pattern Between Hypoid Gear and the Conjugate Pinion

2000 ◽  
Author(s):  
Norio Ito ◽  
Koichi Takahashi
Keyword(s):  
Conventional Method ◽  
Analytical Method ◽  
Second Order ◽  
Tooth Surface ◽  
Gear Pair ◽  
Hypoid Gear ◽  
Third Order ◽  
Hypoid Gears ◽  
Gear Cutting ◽  
Tooth Surfaces

Abstract In this paper, the relationships between the conjugate tooth surfaces of hypoid gears and the formal tooth bearing pattern are presented. First, we introduce the tooth surface elements necessary for the tooth bearing. Next, the tooth bearing pattern, which changes according to the generating condition of the pinion, is introduced. The hypoid gear pair is a formate gear and the pinion generated to run with such a gear. The conventional method for analyzing the tooth bearing pattern has been developed by the motion of generation between second-order tooth surfaces. In this paper, the tooth surface is expressed by the original third-order tooth surface, and the tooth bearing pattern is analyzed by the meshing motion of the tooth surface. The tooth bearing pattern obtained from such an analytical method becomes the formal tooth bearing. Therefore, the machine settings for accurate gear cutting become possible, and the desired tooth bearing pattern can be obtained beforehand without a trial cutting.

Validity of Higher-Order Ability Constructs in Structure-of-Intellect Tests All Involving Semantic Content and Operations of Cognition or Evaluation: A Confirmatory Maximum Likelihood Factor Analysis

1985 ◽  
Vol 45 (2) ◽  
pp. 353-359 ◽  
Author(s):  
David E. Mace ◽  
William B. Michael ◽  
Dennis Hocevar
Keyword(s):  
Factor Analysis ◽  
Maximum Likelihood ◽  
Semantic Content ◽  
Higher Order ◽  
Second Order ◽  
Third Order ◽  
Maximum Likelihood Factor Analysis ◽  
Practical Standpoint ◽  
Order Factor ◽  
Structure Of Intellect

Through use of confirmatory maximum likelihood factor analysis in conjunction with the LISREL V computer program devised by Jöreskog and Sörbom, an evaluation was made of the validity of higher-order ability constructs in structure-of-intellect tests all containing semantic content and operations of cognition or evaluation. The hypothesized first-, second-, and third-order factors were all reproducible with every one of the estimated factor loadings being significant beyond the .01 level. Although the first- and second-order factors were shown to be reproducible and statistically separable, the high intercorrelations among the six first-order product factors and the two second-order operations factors would suggest from a practical standpoint that the single third-order factor of semantic content would constitute a plausible alternative for accounting for much of the covariance among the test variables.

scholarly journals Improved Approximations for the Aggregate Claims Distribution in the Individual Model

1986 ◽  
Vol 16 (2) ◽  
pp. 89-100 ◽  
Author(s):  
Christian Hipp
Keyword(s):  
Error Bounds ◽  
Absolute Error ◽  
Higher Order ◽  
Second Order ◽  
Third Order ◽  
Individual Model ◽  
Concentration Functions ◽  
Aggregate Claims ◽  
The Individual ◽  
Stop Loss

AbstractKornya-type higher order approximations are derived for the aggregate claims distribution and for stop loss premiums in the individual model with arbitrary positive claims. Absolute error bounds and error bounds based on concentration functions are given. In the Gerber portfolio containing 31 policies, second order approximations lead to an accuracy of 3 × 10−4, and third order approximations to 1.7 ×10−5.

scholarly journals Higher Order Elastic Constants, Gruneisen Parameters and Lattice Thermal Expansion of Trigonal Calcite

2005 ◽  
Vol 2 (4) ◽  
pp. 207-217
Author(s):  
Thresiamma Phlip ◽  
C. S. Menon ◽  
K. Indulekha
Keyword(s):  
Elastic Constants ◽  
Deformation Theory ◽  
Elastic Stiffness ◽  
Higher Order ◽  
Second Order ◽  
Model Approximation ◽  
Third Order ◽  
Third Order Elastic Constants ◽  
Grüneisen Parameters ◽  
Gruneisen Parameters

The second- and third-order elastic constants of trigonal calcite have been obtained using the deformation theory. The strain energy density derived using the deformation theory is compared with the strain dependent lattice energy obtained from the elastic continuum model approximation to get the expressions for the second- and third-order elastic constants. Higher order elastic constants are a measure of the anharmonicity of a crystal lattice. The seven second-order elastic constants and the fourteen non-vanishing third-order elastic constants of trigonal calcite are obtained. The second-order elastic constants C11, which corresponds to the elastic stiffness along the basal plane of the crystal is greater than C33, which corresponds to the elastic stiffness tensor component along the c-axis of the crystal. First order pressure derivatives of the second-order elastic constants of calcite are evaluated. The higher order elastic constants are used to find the generalized Gruneisen parameters of the elastic waves propagating in different directions in calcite. The Brugger gammas are evaluated and the low temperature limit of the Gruneisen gamma is obtained. The results are compared with available reported values.

On higher-order wave theory for submerged two-dimensional bodies

1969 ◽  
Vol 38 (2) ◽  
pp. 415-432 ◽  
Author(s):  
Nils Salvesen
Keyword(s):  
Free Surface ◽  
Wave Theory ◽  
Order Theory ◽  
Wave Drag ◽  
Higher Order ◽  
Second Order ◽  
Two Dimensional ◽  
Third Order ◽  
Free Surface Waves ◽  
Body Shapes

The importance of non-linear free-surface effects on potential flow past two-dimensional submerged bodies is investigated by the use of higher-order perturbation theory. A consistent second-order solution for general body shapes is derived. A comparison between experimental data and theory is presented for the free-surface waves and for the wave resistance of a foil-shaped body. The agreement is good in general for the second-order theory, while the linear theory is shown to be inadequate for predicting the wave drag at the relatively small submergence treated here. It is also shown, by including the third-order freesurface effects, how the solution to the general wave theory breaks down at low speeds.

scholarly journals 02. Social Pathologies, Reflexive Pathologies, and the Idea of Higher-Order Disorders

2015 ◽  
Author(s):  
Arto Laitinen
Keyword(s):  
Social Reality ◽  
Social Criticism ◽  
Higher Order ◽  
Second Order ◽  
Third Order ◽  
First Order ◽  
The Third ◽  
The Social ◽  
Order Reflection

This paper critically examines Christopher Zurn’s suggestion mentioned above that various social pathologies (pathologies of ideological recognition, maldistribution, invisibilization, rationality distortions, reification and institutionally forced self-realization) share the structure of being ‘second-order disorders’: that is, that they each entail ‘constitutive disconnects between first-order contents and secondorder reflexive comprehension of those contents, where those disconnects are pervasive and socially caused’ (Zurn, 2011, 345-346). The paper argues that the cases even as discussed by Zurn do not actually match that characterization, but that it would be premature to conclude that they are not thereby social pathologies, or that they do not have a structure in common. It is just that the structure is more complex than originally described, covering pervasive socially caused evils (i) in the social reality, (ii) in the first order experiences and understandings, (iii) in the second order reflection as discussed by Zurn, and also (iv) in the ‘third order’ phenomenon concerning the pre-emptive silencing or nullification of social criticism even before it takes place 

Higher-order terms in the dielectric constant of ionic crystals

1959 ◽  
Vol 252 (1269) ◽  
pp. 217-235 ◽  
Keyword(s):  
Dielectric Constant ◽  
Dipole Moment ◽  
Higher Order ◽  
Second Order ◽  
Static Dielectric Constant ◽  
Order Moment ◽  
Ionic Crystals ◽  
Third Order ◽  
The Third ◽  
Infra Red

The infra-red absorption of ionic crystals differs in important details from the predictions of the theory based on first approximations. It is known that this discrepancy may be due to two effects which are neglected in such a theory, namely, to the anharmonic terms in the potential energy and to those terms in the dipole moment which are of higher order than the first in the displacement co-ordinates. These higher-order terms in the dipole moment arise from the deformation of the electron shells. The present paper develops in a systematic way the influence of these higher-order effects on the static dielectric constant. Because of the dispersion relations, the terms occurring in the static dielectric constant must also appear in the infra-red absorption spectrum . It is found that the third- and the fourth-order potential, the second- and the third-order dipole moment, and cross-terms between the second-order moment and the third-order potential, all con­tribute terms in the same order to the static dielectric constant. It is also found that the third-order potential contains important contributions from the long-range dipolar inter­action. These dipolar contributions are proportional to the product of the first- and second-order dipole moments, and it follows that in ionic crystals a large second-order moment automatically results in a large third-order potential. It is suggested that these dipolar contributions to the third-order potential may be responsible for the fact that in the infra-red spectra of different ionic crystals not only the intensity of the side band but also the width of the main band varies in the same way as the deformability of the electron shells.

Second- and higher-order logics

2018 ◽  
Author(s):  
Shaughan Lavine
Keyword(s):  
Predicate Logic ◽  
Higher Order ◽  
Second Order ◽  
Order Logic ◽  
First Order Logic ◽  
Third Order ◽  
First Order ◽  
Proof Systems ◽  
The Universe ◽  
Second Order Logic

In first-order predicate logic there are symbols for fixed individuals, relations and functions on a given universe of individuals and there are variables ranging over the individuals, with associated quantifiers. Second-order logic adds variables ranging over relations and functions on the universe of individuals, and associated quantifiers, which are called second-order variables and quantifiers. Sometimes one also adds symbols for fixed higher-order relations and functions among and on the relations, functions and individuals of the original universe. One can add third-order variables ranging over relations and functions among and on the relations, functions and individuals on the universe, with associated quantifiers, and so on, to yield logics of even higher order. It is usual to use proof systems for higher-order logics (that is, logics beyond first-order) that include analogues of the first-order quantifier rules for all quantifiers. An extensional n-ary relation variable in effect ranges over arbitrary sets of n-tuples of members of the universe. (Functions are omitted here for simplicity: remarks about them parallel those for relations.) If the set of sets of n-tuples of members of a universe is fully determined once the universe itself is given, then the truth-values of sentences involving second-order quantifiers are determined in a structure like the ones used for first-order logic. However, if the notion of the set of all sets of n-tuples of members of a universe is specified in terms of some theory about sets or relations, then the universe of a structure must be supplemented by specifications of the domains of the various higher-order variables. No matter what theory one adopts, there are infinitely many choices for such domains compatible with the theory over any infinite universe. This casts doubt on the apparent clarity of the notion of ‘all n-ary relations on a domain’: since the notion cannot be defined categorically in terms of the domain using any theory whatsoever, how could it be well-determined?

Higher order rogue waves for the(3 + 1)-dimensional Jimbo–Miwa equation

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Mohammed K. Elboree
Keyword(s):  
Symbolic Computation ◽  
Fourth Order ◽  
Bilinear Form ◽  
Rogue Waves ◽  
Higher Order ◽  
Second Order ◽  
Third Order ◽  
First Order ◽  
Hirota Bilinear Form ◽  
Hirota Bilinear

Abstract Based on the Hirota bilinear form for the (3 + 1)-dimensional Jimbo–Miwa equation, we constructed the first-order, second-order, third-order and fourth-order rogue waves for this equation using the symbolic computation approach. Also some properties of the higher-order rogue waves and their interaction are explained by some figures via some special choices of the parameters.

Robust Optimization of the Loaded Contact Pattern in Hypoid Gears With Uncertain Misalignments

2010 ◽  
Vol 132 (4) ◽  
Author(s):  
M. Gabiccini ◽  
A. Bracci ◽  
M. Guiggiani
Keyword(s):  
Optimization Problems ◽  
Optimization Procedure ◽  
Target Area ◽  
Contact Pattern ◽  
Trial And Error ◽  
Unified Framework ◽  
Hypoid Gears ◽  
Contact Patterns ◽  
Unconstrained Nonlinear Optimization ◽  
The One

This paper presents an automatic procedure to optimize the loaded tooth contact pattern of face-milled hypoid gears with misalignments varying within prescribed ranges. A two-step approach is proposed to solve the problem: in the first step, the pinion tooth microtopography is automatically modified to bring the perturbed contact patterns (as the assembly errors are varied within the tolerance limits) match a target area of the tooth while keeping them off the edges; in the second step, a subset of the machine-tool settings is identified to obtain the required topography modifications. Both steps are formulated and solved as unconstrained nonlinear optimization problems. While the general methodology is similar to the one recently proposed by the same authors for the optimization at nominal conditions, here, the robustness issues with respect to misalignment variations are considered and directly included in the optimization procedure: no a posteriori check for robustness is therefore required. Numerical tests show that nominally satisfactory and globally robust hypoid pairs can be designed by a direct process and within a unified framework, thus avoiding tiresome trial-and-error loops.

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