Comparison Between a Meshless Method and the Finite Difference Method for Solving the Reynolds Equation in Finite Bearings

2013 ◽  
Vol 135 (4) ◽  
Author(s):  
Rodrigo Nicoletti
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Meshless Method ◽  
Reynolds Equation ◽  
Normal Force ◽  
Basis Functions ◽  
Structured Meshes ◽  
The Finite Difference Method ◽  
Better Than

Meshless methods are an alternative procedure for solving partial differential equations in opposition to the numerical methods that require structured meshes. In this work, the meshless method with radial basis functions (MMRB) is compared to the finite difference method (FDM) for solving the Reynolds equation applied to lubricated finite bearing applications. The performance of these two methods is compared based on the precision of estimating the normal force applied to the sliding surface of the bearing. Different mesh families are tested for different bearing configurations. Results show that the MMRB is better than the FDM for nonrectangular geometries with coarser meshes. For rectangular domains without discontinuities, the FDM is still the best choice for solving the problem.

Heat Diffusion in Heterogeneous Bodies Using Heat-Flux-Conserving Basis Functions

1988 ◽  
Vol 110 (2) ◽  
pp. 276-282 ◽  
Author(s):  
A. Haji-Sheikh
Keyword(s):  
Heat Flux ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Diffusion Equation ◽  
Difference Method ◽  
Solution Method ◽  
Basis Functions ◽  
Heat Diffusion ◽  
Simple Geometry ◽  
The Finite Difference Method

The generalized analytical derivation presented here enables one to obtain solutions to the diffusion equation in complex heterogeneous geometries. A new method of constructing basis functions is introduced that preserves the continuity of temperature and heat flux throughout the domain, specifically at the boundary of each inclusion. A set of basis functions produced in this manner can be used in conjunction with the Green’s function derived through the Galerkin procedure to produce a useful solution method. A simple geometry is selected for comparison with the finite difference method. Numerical results obtained by this method are in excellent agreement with finite-difference data.

Averaging effect on pitch errors in hydrostatic lead screws considering helical recess layout and nut misalignment

2017 ◽  
Vol 232 (9) ◽  
pp. 1181-1192
Author(s):  
Yongtao Zhang ◽  
Changhou Lu ◽  
Yunpeng Liu
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Radial Displacement ◽  
Continuity Equation ◽  
Reynolds Equation ◽  
Spatial Frequencies ◽  
The Finite Difference Method ◽  
Low Speeds ◽  
Flank Surface

The hydrostatic nut usually has different helical recess layouts and the nut misalignment (including radial displacement and tilt) may occur during movement, which will influence the averaging effect on pitch errors, i.e. the motion accuracy of the hydrostatic nut. This paper researches the averaging effect on pitch errors in capillary compensated hydrostatic lead screws, under low speeds and considering the helical recess layout and the nut misalignment. Based on the equivalent plane of the flank surface of threads, whose normal clearance is calculated by vector operations, the Reynolds equation and the flow continuity equation are solved using the finite difference method. The results show that (a) the averaging coefficient presents bulges at corresponding spatial frequencies for the hydrostatic nut with discontinuous helical recesses, (b) the positions of the first and second periodical fluctuations of the averaging coefficient are the same for the hydrostatic nut with symmetric continuous helical recesses, symmetric discontinuous helical recesses, or asymmetric continuous helical recesses, and (c) The nut misalignment has little influence on the averaging coefficient.

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