Development of New Method for Calculating Engaged Profiles of Gears

1989 ◽  
Author(s):  
D. Wang ◽  
Z. Qi ◽  
F.-C. T. Shiue
Keyword(s):  
Spline Function ◽  
Gear Tooth ◽  
Cutting Tools ◽  
Computational Procedure ◽  
Grinding Wheels ◽  
Curve Fit ◽  
Manufacturing Accuracy ◽  
Cubic Spline Function ◽  
Parametric Cubic Spline ◽  
General Method

Abstract In investigating the problems of engagement of different gear tooth profiles, the authors have found a generality for these problems. Meanwhile, according to the theory of computational geometry and numerical experiments, a parametric cubic spline function is found as a proper curve-fit technique to represent the tooth profiles of these gears. A general method and its numerical algorithm, based on the generality observed and the spline function chosen, is developed for the calculation of gear cutting tools and mating gears with arbitrary profiles. The cutting tools applied include: gear cutters, grinding wheels, and form milling cutters. The method can also be applied to the inspection of the manufacturing accuracy of the gear or helical screw profiles. A computational procedure is illustrated.

On Numerical Simulations of the Micro-Gears and their Cold Forging Process

2009 ◽  
Vol 419-420 ◽  
pp. 17-20
Author(s):  
Chin Yu Wang ◽  
Hsin Te Wang
Keyword(s):  
Spline Function ◽  
Simulation Software ◽  
Cold Forging ◽  
Design Parameters ◽  
Forging Process ◽  
Gear Design ◽  
Cubic Spline Function ◽  
Corner Filling ◽  
Gear Profile ◽  
Parametric Cubic Spline

In this paper, a parametric cubic spline function for generating gear profile is proposed. The spline function includes new gear design parameters such as pressure angle, number of teeth, module, and tooth tip circle modification. The proposed geometry can improve corner filling condition. Finally, the simulation software DEFORM is used to simulate the cold forging process of the micro-gears with different profiles.

scholarly journals Numerical Method for Solving Nonlinear Equations Arising in Astrophysics

2019 ◽  
Vol 8 (4) ◽  
pp. 1075-1078
Keyword(s):  
Singular Point ◽  
Spline Function ◽  
Linear Problem ◽  
Cubic Spline ◽  
Linear Problems ◽  
Isothermal Gas ◽  
Cubic Spline Function ◽  
Mathematica Software ◽  
The Given ◽  
Parametric Cubic Spline

In this paper, a parametric cubic spline function was used to get the solution of a non-linear problem for an isothermal gas sphere. The quasi-linearization procedure was used to reduce the given problem to a sequence of linear problems, the resulting equations are modified at the singular point and are handled by using parametric cubic spline for determining the numerical results. All computations have been carried out by the Mathematica software program package. The findings of computational outcomes on those astrophysics problems confirmed that the technique is legitimate for the solution of these kinds of equations.

scholarly journals Progress and Regress of Time Dependent Data and Application in Bank Branch

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
F. Hosseinzadeh Lotfi ◽  
Z. Taeb ◽  
S. Abbasbandy
Keyword(s):  
Decision Making ◽  
Commercial Bank ◽  
Spline Function ◽  
Time Dependent ◽  
Malmquist Productivity Index ◽  
Productivity Index ◽  
Dependent Data ◽  
Bank Branch ◽  
Decision Making Unit ◽  
Cubic Spline Function

To evaluate each decision making unit having time dependent inputs and outputs data, a new method has been developed and reported here. This method uses the Malmquist productivity index, and is a very simple function based on Cubic Spline function to determine the progress and regress of that unit. To show the capability of this developed method, the data of 9 branches of a commercial bank has been used, evaluated, and reported.

Power Flow Investigation Using Cubic Spline Function a Case Study

2018 ◽  
Vol 7 (4) ◽  
pp. 1-16 ◽  
Author(s):  
Shabbiruddin ◽  
Karma Sonam Sherpa ◽  
Sandeep Chakravorty ◽  
Amitava Ray
Keyword(s):  
Power Systems ◽  
Power Flow ◽  
Spline Function ◽  
Electrical Power ◽  
Flow Analysis ◽  
Cubic Spline ◽  
Load Flow ◽  
Electrical Power Systems ◽  
Flow Investigation ◽  
Cubic Spline Function

This article presents an approach using cubic spline function to study Load Flow with a view to acquiring a reliable convergence in the Bus System. The solution of the power flow is one of the extreme problems in Electrical Power Systems. The prime objective of power flow analysis is to find the magnitude and phase angle of voltage at each bus. Conventional methods for solving the load flow problems are iterative in nature, and are computed using the Newton-Raphson, Gauss-Seidel and Fast Decoupled method. To build this method, this paper used cubic spline function. This approach can be considered as a ‘two stage' iterative method. To accredit the proposed method load flow study is carried out in IEEE-30 bus systems.

A General Method for Computing Worm Gear Conjugate Mesh Property: Part 2—The Mathematic Model of Worm Gear Manufacturing and Working Processes

1989 ◽  
Vol 111 (1) ◽  
pp. 148-152 ◽  
Author(s):  
Changqi Zheng ◽  
Jirong Lei
Keyword(s):  
Contact Line ◽  
Relative Velocity ◽  
Velocity Vector ◽  
Gear Tooth ◽  
Mathematic Model ◽  
Worm Gear ◽  
Tooth Surface ◽  
Gear Manufacturing ◽  
General Method ◽  
Working Processes

Part 2 of this article is devoted to building a generalized mathematic model of worm gear manufacturing and working processes which can be used for calculating the contact line, the profile, the normal curvature, the conjugate boundary and the angle between the directions of contact line and relative velocity vector for any kind of worm gear tooth surface.

scholarly journals Determination of initial velocities of enzymic reactions from progress curves

1986 ◽  
Vol 237 (3) ◽  
pp. 821-825 ◽  
Author(s):  
R Dagys ◽  
A Pauliukonis ◽  
D Kazlauskas ◽  
M Mankevicius ◽  
R Simutis
Keyword(s):  
Initial Velocity ◽  
Experimental Error ◽  
Spline Function ◽  
Present Communication ◽  
Time Value ◽  
Substrate Conversion ◽  
Novel Method ◽  
Cubic Spline Function ◽  
Large Experimental Error

The present communication describes a novel method for estimating initial velocities (v) of enzyme-catalysed reactions. It is based on an approximation of experimental data obtained by the cubic spline function. The initial velocity of a reaction is calculated as a derivative of the approximating function at a time value equal to zero. The proposed method is usable on a computer with a FORTRAN IV program. The method can be successfully used in such cases as substantial extents of substrate conversion, the inactivation of an enzyme in the course of a reaction, the existence of large experimental error or when the reaction mechanism is unknown.

Grinding of flat glass with Fe- and Cu-based diamond tools

2016 ◽  
Vol 232 (9) ◽  
pp. 1561-1568 ◽  
Author(s):  
Sabri Ozturk
Keyword(s):  
Service Life ◽  
Glass Plant ◽  
Flat Glass ◽  
Cutting Tools ◽  
Grinding Wheels ◽  
Diamond Grit ◽  
Diamond Tools ◽  
Effective Factor ◽  
The Impact ◽  
Cutting Speeds

Preparation of grinding wheels is the most important effective factor in glass machining. This article presents the comparison of the iron- and copper-based grinding tools. The performance of the tools is investigated based on technical and commercial aspects using same cutting speeds, feeds, and sizes of diamond grits. Scanning electron microscope is used in order to observe the microstructures of cutting tools. The service life of the grinding tools is determined on the production line in a flat glass plant. A lifetime of Fe-based diamond tools is longer compared to the copper-based wheels. The impact of metal bond materials on the service life is examined. The results show that the Fe-based tools are more economical and more useful for grinding of glass. The holding of Fe-based bonding to diamond grit is stronger than the copper-based ones.

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