APPROXIMATION OF INVOLUTE PROFILE BY MOON-SHAPED RING SECTION

In this paper,we study the approximation of involute profile by moor-shaped ring section. By using the minimax method, we find parameter of the best approximation moon-shaped ring section of invelute piofile. The error of approximation is 35% - 70% that of [1] and [2]. Thus the approximation precision of dressing a wheel for involute gear forming-grinding by approximating method has been greatly improved. In order to simplify calculation, the error function is defined according to the implicit equation of curve and its rationalization is proved.     

COMPUTER ALDED DESIGN OF FORMING CUTTER FOR REVISING INVOLUTE HELICAL

In this paper, a calculation method of forming cutter contour of involute helical with arbitrary easement is presented, the segmantal arcs of the best uniform approximation and tolerance to fit smoothly the cutter contour points are used the profile on the cross section of the helical is calculated and the design of the cutter is examined. The method can be used to design precision forming cutter of involute helical with the arbitrary easement. It is valuable in engineering application.     

The Research on Stiffness of Double Involute Gear with Ladder shape Teeth

The stiffness of the tooth with different profile parameters,meshing stiffness and the coefficients of loading distribution allowing for no error are calculated and analyzed on double involute gear with ladder shape teeth for the first time,and the results are made comparison with traditional involute gear;The stiffness of the double involute gear and the meshing stiffness are both increased,and the coefficients of loading distribution are basically unchanged.The energy integration method is also put forth to solve stiffness approximately by linear approximating the tooth profile curve.     

A STUDY OF THE OPTIMIZATION OF CIRCULAR ARC TOOTH PROFILE TRANSMISSION

For the first time, we point out the new idea that we can approximate the involute tooth profile transmission to circular arc tooth profile transmission. Looking upon it as a fourbar linkage we try to minimax the error of the velocity ratio and evaluate the strong-weak point of circular arc tooth profile transmission.     

The Mode and Vibration Response of the Double Involute Gear

From the mathematical model of the double involute gear teeth surface at any corner position,we establish the model of the double involute gear with high precision and parameter in Pro/E,analyze and calculate the influence of natural frequency by the parameter of the double involute gear,analyze the frequency respond elementary.The conclusions reflect the gear's performance of dynamics,and provide the librate characteristic data for the design of double involute gear.     

Corner Point Detection Based on Adaptive Line Approximation

The detection of corner points is one of the basic problems of computer vision. Usually the key question of detecting corner points is how to calculate curvature. This paper presents a novel approach of calculating the backward and forward direction of reference point based on the adaptive line approximation. Our line approximation method objects minimize the distance error and the length of approximation widow adaptively changes with the approximation error. Our adaptive method finds a compromise between the length of approximation widow and the calculation precise. The experiments results show, the method can robustly, effectively and precisely locate corner point for curves with apparent corners with little computation.     

An Exchange Algorithm for the Best Chebyshev Normal Approximation by Quadratic Curves

According to the criterion of measuring profile error,a mathematical model for the best approximation to profile of gear is presented;the characteristic of the best quadratic curve approximation is derived.An algorithm and its convergence are discussed.Finally,the quadratic curve approximations to the profiles of many gears are obtained efficiently by the algorithm.The approximation errors are less than 0.8 micrometers.     

Intensity Comparative Analysis Based on Ideas Between Involute Gear and Double Involute Gear

Modeler and simulation modules in Ideas software are used to build the finite element models on involute gear and double involute gear with accurate tooth shape, and with the same design parameters and under the same loads, finite element contact analysis has been done. At last, the contact stress and bending stress on the two types gear transmission at the different meshing positions are solved out, and comparative analysis and study have been done. At the same time, that the ladder-shape tooth on the double involute gear how to influence contact stress and bending stress is emphatically analysed. All above offer the theoretical foundation that bring the double involute gear with ladder-shape tooth into the industry.     

Process Method of Face-gear Drive with Spur Involute Pinion with the Shaping Machine

In order to research face-gear drives, a face-gear drive with spur involute pinion is considered. The genera, tion of a face gear is based on application of a conventional shaping machine and an involute shaper. The functions of theoretic shaping surface and processing surface about the face gear are deduced. Computer programs are developed for simulation of these surfaces. In shaping time, mutual position of two surfaces, theoretic shaping surface and processing surface, is analyzed by simulation. In the end, the feasibility of the process method is concluded.     

Study on the Nonlinear Vibration System with Slow-changing Parameters

In this paper a posteriori error estimates for Galerkin approximation of general operator equations is firstly presented in the framework of Sobolev spaces. Then a practical posteriori error estimates formula for the adaptive boundary element method solving the acoustic scattering problem with a finite plane screen is obtained by triangulations. The mathematical model of this problem is the three dimensional Neumann boundary value problem of Helmholtz equation with finite plane boundary.     

SOME NEW MACHINING METHODS WITH THE AID OF COMPOUND MOTIONS

The paper describes a new theory and methods for designing hyperbola, degenerate circles, involute and roulette curves which have been applied in grinding convex involute gears, cutting special profiles on a gear shaper, grinding the race-way of ball thrust bearings, form grinding and grinding cyclo-cycloidal gears with an abrasive belt. All these applications have been used in industruy with considerable benefits. The curves are produced by different combinations of straight line and circle motions, Given the curve parameters of the workpieces to be machined, the best approximate curve can be obtained from a computer program designed for this purpose.     

Simulation analysis on stimulation patterns of three-dimension electrical impedance tomography

To solve the lack of information and the error in forward and inverse problem caused by the approximation of actual three-dimensional field from two-dimensional field in electrical impedance tomography (EIT), this article presents a new EIT system. This system improves one-dimensional electrode array to two-dimensional array, and extends the solution domain to the entire three-dimensional field in order to increase the information quantity and eliminate the model error. Based on several current stimulation patterns in EIT which might yield the best sensitiveness for 3-D field, we calculate the forward problem by finite element method and the distinguishability and surface projection image method. The results show that the back electrode pattern has obvious advantages in detecting depth and precision, and has convenience in clinical application. The conclusion of this article can provide reference for the study of 3-D EIT.     

Revival of a well-known, but ignored correction term for χ2 in linkage analysis with small samples

The ‘classical’χ² test is routinely applied in linkage analysis. The values customarily used, however, are only approximations since continuous χ² terms are used instead of discrete multinomial terms. This error becomes increasingly important as the sample becomes small. In this note, a well-known correction term for improvement of this approximation is revived and numerically calculated for some interesting cases from linkage studies.     

VARIABLE METRIC METHODS WITH OPTIMUM DIFFERENCE APPROXIMATIONS OF DERIVATIVES

On the basis of the relation between truncation and rounding errors of difference approximation, the interval formula which can minimize the total error is founded. The method choosing optimum interval is applied to unconstrained VMM(Variable Metric Method), SUMT-DFP, and constrained VMM. Three optimization methods with optimum difference approximations are presented. These methods are very efficient, especially when dealing with complex problem functions.     

Approximating the degrees of freedom for contrasts of genotypes laid out as subplots in an alpha-design in a split-plot experiment

Alpha‐designs have become popular in cultivar trials. Analysis is based on a mixed model. As a result of imbalance, inference tests require approximate methods. This paper investigates the Type I error control of different Satterthwaite approximations for the denominator degrees of freedom of Wald‐type F‐tests and t‐tests in a two‐factorial alpha‐design with cultivars as the subplot factor and management intensities (fertilization, plant protection) as the main plot factor. Simulation results demonstrate good error control for cultivar comparison at the same intensity, with the need for an approximation which diminishes as the number of cultivars increases. By contrast, a comparison of intensities entails a more substantial departure from the nominal significance level, and this is not entirely offset by any of the approximations. The methods are demonstrated using two real data sets.     

Fuzzy adaptive tracking control for MIMO nonlinear time-varying delay systems

A fuzzy adaptive tracking control scheme is proposed for MIMO nonlinear time-varying delay systems. A fuzzy T-S model-based adaptive time-varying delay fuzzy logic systems is developed to approximate the unknown nonlinear time-varying delay functions.Thus, the modeling to nonlinear systems is implemented. The update laws for parameters of the fuzzy logic systems are derived by the tracking error. A Hcompensator is designed to eliminate fuzzy approximation errors and external disturbances. Based on Lyapunov stability theorem, the proposed control scheme can guarantee the stability of the closed loop systems and obtain anticipant Htracking performance as well. Simulation results of the manipulator demonstrate the effectiveness of the control scheme.     

Frequency Estimate Basing on Synergetic Neural Network

This text solves the basic and important frequency estimate problem in communication by synergetic neural network. Basing frequency estimate in satellite communication, concretely studies the frequency estimate about BPSK signal. When the large Doppler frequency is partitioned several smaller area, each order parameter stands for each area. Once get the winner of the order parameters, the smaller frequency is confirmed. The approximation of the adjoint vectors simplify the complexity of arithmetic, but the system error is caused. This method has rapid capture speed, and smaller cost by analyzing and simulation.     

样本正态分布对降低空间抽样数量的重要性

【研究目的】样本总体的分布特征是影响抽样样本数量的主要因素，对于样本总体为非正态分布的情况，正态转换是降低抽样样本数量、提高抽样调查效率的有效手段。【方法】该文采用中国大陆区域2005年耕地空间分布数据，以1:10万地形图图幅框作为抽样单元，统计每个图幅框内耕地面积占比。分别采样1.5次开方、2次开方、2.5次开方、3次开方和4次开方运算的方式对原始数据进行正态转换。在此基础上对比分析了转换前后数据的峰度及偏度、抽样个数及抽样结果误差等。【结果】结果表明，基于2.5次开方运算后的分层抽样可以大大降低抽样率，由92.26%降低为22.55%，耕地面积指数平均值相对误差由7.06%降低为5.66%。利用2015年耕地面积指数进行抽样方法的精度检验，抽样平均值相对误差仅为3.27%。【结论】研究提出的抽样方法具有较高的适用性，同时也表明空间抽样中数据分布正态转换是非常必要的。本研究成果为广大学者在空间抽样调查方面的研究提供了有益的借鉴。     

The machine setting reverse method of spiral bevel gear

The profile error correction of spiral bevel gears is difficult. To solve this problem, the inspected method of spiral bevel gears tooth surface is studied in 3906 gear measuring center. The grids of tooth surface is measured by measurement software. Taking reference tooth surface as the goal, a method of machine setting reverse using approximation algorithms is proposed, and a mathematical model is build. At last, a reverse example based on grinded spiral gear is given. The result shows that the cutting machine setting of bevel gear tooth surface can be exactly calculated.     

Asynchronous Parallel Algorithm for Finding All Zeros of a Polynomial

Parallel Halley iteration method, based on circular arithmetic for finding all zeros of a polynomial, avoids troublesome circular extraction operation,and the approximation with error estimation of all zeros of a polynomial can be obtained at the same time with it, and it has higher convergence rate , while it was synchronous parallel algorithm. The asynchronous parallel algorithm was constructed with circular arithmetic in order to find all zeros of a polynomial, and the convergence theory was established under the similar condition of Halley iteration method. The algorithm not only retain the advantage of Halley iteration method, but has better parallelism.