A Reversed Solution for the Elastic Contacts Between Symmetrical Fourth Order Polynomial Surfaces

2007 ◽  
Author(s):  
E. N. Diaconescu
Keyword(s):  
Numerical Solution ◽  
Pressure Distribution ◽  
Fourth Order ◽  
Contact Area ◽  
Pressure Coefficients ◽  
Order Polynomial ◽  
Fourth Order Polynomial

The paper advances a combined, analytical-numerical solution for the elastic contacts between symmetrical, fourth order polynomial surfaces. This is based on a proposal for contact area and pressure distribution which must generate forth order polynomials for the deformed surface of the halfspace inside contact area. To check this proposal, the normal displacements inside contact area are computed numerically. These agree well with a fourth order polynomial. The effect of contact area and pressure coefficients upon the shape of pressure distribution is evidenced.

Manufacturing Process for Circular-Arc Curvilinear Cylindrical Gears with Predesigned Fourth Order Transmission Error

2010 ◽  
Vol 37-38 ◽  
pp. 623-627 ◽  
Author(s):  
Jin Zhan Su ◽  
Zong De Fang
Keyword(s):  
Fourth Order ◽  
Gear Tooth ◽  
Transmission Error ◽  
Circular Arc ◽  
Cylindrical Gears ◽  
Polynomial Curve ◽  
Order Polynomial ◽  
Tooth Surfaces ◽  
The Stability ◽  
Fourth Order Polynomial

A fourth order transmission error was employed to improve the stability and tooth strength of circular-arc curvilinear cylindrical gears. The coefficient of fourth order polynomial curve was determined, the imaginary rack cutter which formed by the rotation of a head cutter and the imaginary pinion were introduced to determine the pinion and gear tooth surfaces, respectively. The numerical simulation of meshing shows: 1) the fourth order transmission error can be achieved by the proposed method; 2) the stability transmission can be performed by increasing the angle of the transfer point of the cycle of meshing; 3) the tooth fillet strength can be enhanced.

scholarly journals An Improved Analysis for the Harmonic Distortion of MOS Voltage-Controlled-Resistors

1997 ◽  
Vol 19 (4) ◽  
pp. 253-260
Author(s):  
Muhammad Taher Abuelma'atti
Keyword(s):  
Fourth Order ◽  
Harmonic Distortion ◽  
Voltage Characteristic ◽  
Current Voltage Characteristic ◽  
Mos Transistor ◽  
Current Voltage ◽  
Order Polynomial ◽  
Polynomial Expression ◽  
Analytical Expressions ◽  
Fourth Order Polynomial

In this paper, a fourth-order polynomial expression is obtained for the nonlinear current-voltage characteristic of a MOS transistor operating in the triode region. Using this expression, closed-form expressions are obtained for the second-, third- and fourth-harmonic distortion of a MOS voltage-controlled- resistors. The analytical expressions obtained in this paper can be used for a quantitative study of the effect of different parameters of the performance of MOS voltage-controlled-resistors.

ENERGY-LIKE FUNCTIONS FOR SOME DISSIPATIVE CHAOTIC SYSTEMS

2005 ◽  
Vol 15 (08) ◽  
pp. 2507-2521 ◽  
Author(s):  
C. SARASOLA ◽  
A. D'ANJOU ◽  
F. J. TORREALDEA ◽  
A. MOUJAHID
Keyword(s):  
Phase Space ◽  
Dynamic Behavior ◽  
Fourth Order ◽  
Chaotic Systems ◽  
Quantitative Measure ◽  
Energy Functions ◽  
Dissipation Of Energy ◽  
Rossler System ◽  
Order Polynomial ◽  
Fourth Order Polynomial

Functions of the phase space variables that can considered as possible energy functions for a given family of dissipative chaotic systems are discussed. This kind of functions are interesting due to their use as an energy-like quantitative measure to characterize different aspects of dynamic behavior of associated chaotic systems. We have calculated quadratic energy-like functions for the cases of Lorenz, Chen, Lü–Chen and Chua, and show the patterns of dissipation of energy on their respective attractors. We also show that in the case of the Rössler system at least a fourth-order polynomial is required to properly represent its energy.

Elliptical Contact Area Between Elastic Bodies Bounded by High Order Surfaces

2005 ◽  
Author(s):  
Emanuel N. Diaconescu
Keyword(s):  
Analytical Solution ◽  
Pressure Distribution ◽  
Fourth Order ◽  
Contact Area ◽  
High Order ◽  
Normal Displacement ◽  
Hertz Theory ◽  
Elastic Bodies ◽  
Surface Normal ◽  
Elliptical Contact

Hertz theory fails when contacting surfaces are expressed by a sum of even polynomials of higher powers than two. An alternative analytical solution implies the knowledge of contact area. In the case of elliptical domains, there are some published proposals for the correlation between pressure distribution and surface normal displacement. This paper identifies the class of high order surfaces which lead to elliptical contact domains and solves a contact between fourth order surfaces.

scholarly journals Parasupersymmetric Quantum Mechanics and Indices of Fredholm Operators

1997 ◽  
Vol 12 (15) ◽  
pp. 2725-2739 ◽  
Author(s):  
Ali Mostafazadeh
Keyword(s):  
Quantum Mechanics ◽  
Fourth Order ◽  
Classification Scheme ◽  
Algebraic Expression ◽  
Topological Invariants ◽  
Square Root ◽  
Fredholm Operators ◽  
Compatibility Conditions ◽  
Order Polynomial ◽  
Fourth Order Polynomial

The general features of the degeneracy structure of (p = 2) parasupersymmetric quantum mechanics are employed to yield a classification scheme for the form of the parasupersymmetric Hamiltonians. The method is applied to parasupersymmetric systems whose Hamiltonian is the square root of a fourth order polynomial in the generators of the parasupersymmetry. These systems are interesting to study for they lead to the introduction of a set of topological invariants very similar to the Witten indices of ordinary supersymmetric quantum mechanics. The topological invariants associated with parasupersymmetry are shown to be related to a pair of Fredholm operators satisfying two compatibility conditions. An explicit algebraic expression for the topological invariants of a class of parasupersymmetric systems is provided.

Analytical method for locating the secondary instant centres of indeterminate planar linkages

2008 ◽  
Vol 223 (2) ◽  
pp. 491-502 ◽  
Author(s):  
C-M Kung ◽  
L-C T Wang
Keyword(s):  
Fourth Order ◽  
Analytical Method ◽  
Polynomial Equation ◽  
Automated Analysis ◽  
Numerical Examples ◽  
Order Polynomial ◽  
Velocity Information ◽  
Planar Linkages ◽  
Fourth Order Polynomial ◽  
Order Polynomial Equation

This article presents a new analytical method for locating secondary instant centres (SICs) of indeterminate planar linkages. In this method the SICs are first discriminated into three classes according to their level of geometric dependencies. The concepts of instant-centre digraph, instant-centre walk, and instant-centre circuit are then introduced to establish the recursive relationships between the classified instant centres. It is shown that the location of the instant centres within an instant-centre circuit can be evaluated recursively by first solving a second-order polynomial equation. In addition, by combining the recurrence conditions of several related instant-centre walks, the locations of SICs that are not within an instant-centre circuit can be solved analytically from a fourth-order polynomial equation. The proposed method does not rely on any velocity information or graphical techniques; therefore, it can be applied systematically to all types of indeterminate linkages. It can also be implemented on digital computers for automated analysis. Three numerical examples are presented to demonstrate the usage of this method.

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