Numerical Simulation of Dynamically Loaded Flexible Short Journal Bearings

1985 ◽  
Vol 107 (3) ◽  
pp. 396-401 ◽  
Author(s):  
L. van der Tempel ◽  
H. Moes ◽  
R. Bosma
Keyword(s):  
Numerical Simulation ◽  
Differential Equations ◽  
Numerical Method ◽  
Dynamic Load ◽  
High Speed ◽  
Journal Bearings ◽  
Combustion Engines ◽  
Dynamically Loaded ◽  
Newton Raphson ◽  
Raphson Method

A numerical method is proposed for calculating film thicknesses in flexible short journal bearings under dynamic load. The system of elastohydrodynamic integro-differential equations is discretized directly and solved by a 2-step Newton-Raphson method. The cavitation boundaries are located by a special discretization of the pressure. This type of condition puts practically no restrictions on the boundary alterations. The results for the con rod bearings of medium- and high-speed combustion engines are compared.

Starvation in Dynamically Loaded Flexible Short Journal Bearings

1985 ◽  
Vol 107 (4) ◽  
pp. 516-521 ◽  
Author(s):  
L. van der Tempel ◽  
H. Moes ◽  
R. Bosma
Keyword(s):  
Differential Equations ◽  
Numerical Method ◽  
Dynamic Load ◽  
Journal Bearings ◽  
Important Application ◽  
Combustion Engines ◽  
Connecting Rod ◽  
Supply Pressure ◽  
Continuity Equations ◽  
Medium Speed

A starvation model is incorporated in a previously presented numerical method for calculating film thicknesses inflexible short journal bearings under dynamic load. The system of elastohydrodynamic integro-differential equations is now coupled with continuity equations for the lubricant, considering central circumferential oil grooves and a constant supply pressure. An important application of this method is the connecting rod bearing in medium speed combustion engines. Results for several groove geometries are compared with those for a fully flooded bearing.

Finite Element Analysis of Dynamically Loaded Flexible Journal Bearings: A Fast Newton-Raphson Method

1989 ◽  
Vol 111 (4) ◽  
pp. 597-604 ◽  
Author(s):  
J. D. C. McIvor ◽  
D. N. Fenner
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Computing Time ◽  
Journal Bearings ◽  
Element Analysis ◽  
Dynamically Loaded ◽  
Newton Raphson ◽  
Time Required ◽  
Raphson Method ◽  
Isoparametric Elements

A fast Newton-Raphson method is presented for the finite element analysis of dynamically loaded flexible journal bearings. The method makes use of 8-node isoparametric elements for the lubrication analysis and 20-node isoparametric elements for the structural analysis. Results are presented for the Ruston and Hornsby 6VEB Mk III marine diesel big-end bearing using this method. The computing time required for this analysis is more than two orders of magnitude less than that previously reported for an elastohydrodynamic bearing analysis using a conventional Newton-Raphson method.

scholarly journals Numerical Solution of Nonlinear Equations in Maple

2021 ◽  
Vol 8 (4) ◽  
Author(s):  
Qani Yalda
Keyword(s):  
Numerical Methods ◽  
Numerical Solution ◽  
Numerical Method ◽  
Nonlinear Equations ◽  
Secant Method ◽  
Bisection Method ◽  
Real Roots ◽  
Newton Raphson ◽  
Root Analysis ◽  
Raphson Method

The main purpose of this paper is to obtain the real roots of an expression using the Numerical method, bisection method, Newton's method and secant method. Root analysis is calculated using specific, precise starting points and numerical methods and is represented by Maple. In this research, we used Maple software to analyze the roots of nonlinear equations by special methods, and by showing geometric diagrams, we examined the relevant examples. In this process, the Newton-Raphson method, the algorithm for root access, is fully illustrated by Maple. Also, the secant method and the bisection method were demonstrated by Maple by solving examples and drawing graphs related to each method.

THERMODYNAMIC CALCULATION OF n-COMPONENT EUTECTIC MIXTURES

2004 ◽  
Vol 15 (05) ◽  
pp. 675-687 ◽  
Author(s):  
L. BRUNET ◽  
J. CAILLARD ◽  
P. ANDRÉ
Keyword(s):  
Organic Compound ◽  
Numerical Method ◽  
Melting Temperature ◽  
Nonlinear Problem ◽  
Thermodynamic Calculation ◽  
Eutectic Mixture ◽  
Organic Mixtures ◽  
Eutectic Mixtures ◽  
Newton Raphson ◽  
Raphson Method

This paper presents a simple numerical method to calculate the eutectic mixture composition and melting temperature. Using a Newton–Raphson method to solve the nonlinear problem, the calculation is possible for n-component eutectic. We tested this algorithm on inorganic and organic mixtures. A better correlation between experimental and numerical results has been found for organic compound.

Non-Linear Static Analysis of 2D Steep Wave Riser Under Current Load

2016 ◽  
Author(s):  
Hongdong Qiao ◽  
Weidong Ruan ◽  
Zhaohui Shang ◽  
Yong Bai
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Difference Method ◽  
Shooting Method ◽  
Non Linear ◽  
Newton Raphson ◽  
Raphson Method ◽  
Steep Wave

A new solution combining finite difference method and shooting method is developed to analyze the behavior of steep wave riser subjected to current loading. Based on the large deformation beam theory and mechanics equilibrium principle, a set of non-linear ordinary differential equations describing the motion of the steep wave riser are obtained. Then, finite difference method and shooting method are adopted and combined to solve the ordinary differential equations with zero moment boundary conditions at both the seabed end and surface end of the steep wave riser. The resulting non-linear finite difference formulations can be solved effectively by Newton-Raphson method. To improve iterative efficiency, shooting method is also employed to obtain the initial value for Newton-Raphson method. Results are compared with that of FEM by OrcaFlex, to verify the accuracy and reliability of the numerical method. Finally, a series of sensitivity analyses are also performed to highlight the influencing parameters in the steep wave riser.

Modeling high-speed angular contact ball bearing under the combined radial, axial and moment loads

2013 ◽  
Vol 228 (5) ◽  
pp. 852-864 ◽  
Author(s):  
Wen-Zhong Wang ◽  
Lang Hu ◽  
Sheng-Guang Zhang ◽  
Ling-Jia Kong
Keyword(s):  
Contact Angle ◽  
Contact Force ◽  
High Speed ◽  
Ball Bearing ◽  
Angular Contact Ball Bearing ◽  
Speed Condition ◽  
Newton Raphson ◽  
And Performance ◽  
Angular Displacements ◽  
Raphson Method

In this paper, a method based on coordinate equivalence was presented to investigate the characteristic parameters of angular contact ball bearing such as contact angle and contact force between ball and raceways subjected to the combined radial, axial and moment loads, with considering the effects of centrifugal force and gyroscopic moment in high-speed conditions. The radial, axial and angular displacements are solved based on Newton–Raphson method rather than as the known variables. The method simplifies the procedure involved in determining derivatives for Newton–Raphson method. The results show good agreement with existent model and can be used to analyze the bearing performance, especially for high-speed condition. It was also shown that the inertial loads resulting from the high-speed condition have significant effect on the contact angle and contact force between ball and raceways and have to be considered in the bearing design and performance analysis.

scholarly journals Perbandingan Metode Newton-Raphson & Metode Secant Untuk Mencari Akar Persamaan Dalam Sistem Persamaan Non-Linier

Petir ◽  
2020 ◽  
Vol 13 (1) ◽  
pp. 72-79
Author(s):  
Endang Sunandar ◽  
Indrianto Indrianto
Keyword(s):  
Linear Equation ◽  
Numerical Method ◽  
Equation System ◽  
Elimination Method ◽  
Non Linear Equation ◽  
Linear Equation System ◽  
Non Linear ◽  
Mathematical Problems ◽  
Newton Raphson ◽  
Raphson Method

The numerical method is a technique used to formulate mathematical problems so that it can be solved using ordinary arithmetic operations. In general, numerical methods are used to solve mathematical problems that cannot be solved by ordinary analytic methods. In the Numerical Method, we recognize two types of systems of equations, namely the Linear Equation System and the Non-Linear Equation System. Each system of equations has several methods. In the Linear Equation System between methods is the Gauss Elimination method, the Gauss-Jordan Elimination method, the LU (Lower-Upper) Decomposition method. And for Non-Linear Equation Systems between the methods are the Bisection method, the Regula Falsi method, the Newton Raphson method, the Secant method, and the Fix Iteration method. In this study, researchers are interested in analyzing 2 methods in the Non-Linear Equation System, the Newton-Raphson method and the Secant method. And this analysis process uses the Java programming language tools, this is to facilitate the analysis of method completion algorithm, and monitoring in terms of execution time and analysis of output results. So we can clearly know the difference between what happens between the two methods.

Study on the Distributed and Non-Stationary Dynamic Load Being Transformed into Several Equivalent Centralized Loads for Aerocraft

2011 ◽  
Vol 105-107 ◽  
pp. 965-968
Author(s):  
Xiao Tong Chang ◽  
Yun Ju Yan
Keyword(s):  
Numerical Simulation ◽  
Theoretical Analysis ◽  
Dynamic Load ◽  
High Speed ◽  
Vibration Test ◽  
Feasible Method ◽  
Distributed Load

Missiles always undergo non-stationary and continuously distributed load. However, only some centralized loads can be adopted in the ground for their vibration experiments. In this paper, the theoretical analysis and numerical simulation computations programs are established for the distributed and non-stationary airdynamic load being translated into several equivalent centralized loads for high-speed missile. The researches showed that, under the equivalent rule of structural modal responses, the average responses error in both domains time and frequency is within 1.5dB, so it is possible to provide a feasible method for the vibration test on the ground for missile structures.

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