scholarly journals FFT-ASSISTED ALGORITHMS FOR 3D LINE-CONTACT PROBLEMS

2021 ◽  
Vol 13 (2) ◽  
pp. 124-129
Author(s):  
Sergiu Spinu ◽  
◽  
Keyword(s):  
Fourier Transform ◽  
Contact Problem ◽  
Fast Fourier Transform ◽  
Contact Area ◽  
Contact Problems ◽  
Contact Length ◽  
The Other ◽  
Line Contact ◽  
Contact Width ◽  
Length Direction

The line-contact is a particular type of contact with a contact length much greater than its width. Such contact scenarios can be treated in the frame of a two-dimensional plane-strain problem if the contacting surfaces can be considered nominally smooth. However, surface irregularities inherent to any manufacturing technique lead to a discontinuous contact area that differs from the one derived on the basis of the smooth profile assumption. It is therefore tantalizing to pursue the solution of a line-contact problem using an intrinsically three-dimensional (3D) model, which can only be numerical due to lack of general analytical solutions in contact mechanics. Considering the geometry of the line-contact, a major challenge in its numerical modelling is that the expected contact area is orders of magnitude larger in one direction compared to the other. This may lead to an unreasonably large number of grids in the contact length direction, which translates to a prohibitive computational burden. An alternative approach, employed in this paper, is to treat the line-contact as non-periodic in the contact width direction, but periodic in the contact length direction, with a period equal to the window required to capture and replicate the surface specific texture. This periodicity encourages the contact problem solution by spectral methods based on the fast Fourier transform (FFT) algorithm. Based on this idea, two methods are derived in this paper from the existing Discrete Convolution Fast Fourier Transform (DCFFT) technique, which was previously developed for purely non-periodic contact problems. A first algorithm variant employs a special padding technique for pressure, whereas a second one mimics the contribution of multiple pressure periods by summation of the influence coefficients over a domain a few times larger than the target domain. Both techniques are validated against the existing analytical Hertz solution for the line-contact and a good agreement is found. The advanced methods seem well adapted to the simulation of contact problems that can be approximated as periodic in one direction and non-periodic in the other.

Three-Dimensional Semiperiodic Line Contact–Periodic in Contact Length Direction

2009 ◽  
Vol 131 (2) ◽  
Author(s):  
Shuangbiao Liu ◽  
Diann Y. Hua
Keyword(s):  
Fourier Transform ◽  
Fast Fourier Transform ◽  
Three Dimensional ◽  
Contact Problems ◽  
Contact Length ◽  
Computational Domain ◽  
Line Contact ◽  
Discrete Convolution ◽  
Length Direction ◽  
Contact Domain

Line contact problems, such as those seen in spur gears and cam-roller follower systems, are often simplified with the plane-strain assumption and thus modeled by two-dimensional equations. However, in order to address the effects of roughness and textured surfaces, three-dimensional modeling is necessary. The challenge arises when the contact domain is several orders of magnitude greater than the grid size needed to properly describe the surface roughness or texture. Considering the surface geometry of a so-called “line contact,” the contact domain is nonperiodic in contact width direction, but it can be treated as periodic in the contact length direction–semiperiodic line contact problem. Thus, only a section of the entire contact domain is used as the computational domain with a much-reduced size. Based on an in-depth investigation of available algorithms, DC-FFTS and DC-CC-FFT algorithms are proposed. The DC-FFTS algorithm is a modified discrete convolution and fast Fourier transform algorithm with superposition of influence coefficients. The DC-CC-FFT algorithm is a hybrid fast Fourier transform based algorithm, which combines the discrete convolution–FFT and the continuous convolution–FFT methods. The proposed algorithms are used to solve three-dimensional displacement, contact pressure, and stresses for line contact problems. The results are compared with the other available algorithms from literature. The accuracy and efficiency of different algorithms are discussed.

On the numerical solution of line contact problems involving bonded and unbonded strips

1988 ◽  
Vol 23 (2) ◽  
pp. 67-77 ◽  
Author(s):  
M J Jaffar ◽  
M D Savage
Keyword(s):  
Contact Problem ◽  
Arbitrary Shape ◽  
Practical Interest ◽  
Contact Problems ◽  
Analytic Solutions ◽  
Line Contact ◽  
Elastic Strip ◽  
Effective Technique ◽  
Contact Width ◽  
Cylindrical Punch

This paper investigates the contact problem in which an elastic strip is indented by a rigid body (punch) of arbitrary shape. Both bonded and unbonded strips are considered. A numerical method due to Gladwell (1)† is shown to be a direct and effective technique for analysing the effect of any punch whose profile is a polynomial of degree n, over a range of a/t (semi-contact width to a depth ratio) which is of practical interest 0 ≤ a/t ≤ 10 for Poisson's ratio 0 ≤ v ≤ 0.5. For the cylindrical punch results are presented and compared with Meijers' asymptotic analytic solutions (2). For small a/t agreement is very good as expected. For a/t large, however, there are some large discrepancies which can be traced to an error in Meijers— expression for pressure distribution when v ≠ 0.5. Results are also presented for both the flat and the linear punch.

Note on the FFT Based Computational Code and Its Application

2008 ◽  
Author(s):  
Xiaoqing Jin ◽  
Leon M. Keer ◽  
Qian Wang
Keyword(s):  
Numerical Simulation ◽  
Fourier Transform ◽  
Fast Fourier Transform ◽  
Toeplitz Matrix ◽  
Contact Problems ◽  
Point Of View ◽  
Fast Fourier Transform Algorithm ◽  
Discrete Convolution ◽  
Mathematical Point ◽  
Computational Code

The discrete convolution based Fast Fourier Transform algorithm (DC-FFT) has been successfully applied in numerical simulation of contact problems. The algorithm is revisited from a mathematical point of view, equivalent to a Toeplitz matrix multiplied by a vector. The nature of the convolution property permits one to implement the algorithm with fewer constraints in choosing the computational domains. This advantageous feature is explored in the present work, and is expected to be beneficial to many tribological studies.

The Contact Problem Studied by Pseudocaustics Formed at the Vicinity of the Contact Zone

1984 ◽  
Vol 106 (3) ◽  
pp. 211-215 ◽  
Author(s):  
P. S. Theocaris ◽  
C. A. Stassinakis
Keyword(s):  
Contact Problem ◽  
Contact Zone ◽  
Contact Area ◽  
The Other ◽  
Tangential Stresses ◽  
Elastic Bodies ◽  
First Case ◽  
Reflected Light ◽  
Spline Polynomial ◽  
Distribution Of Stresses

The method of caustics is applied to formulate the normal and tangential stresses developed in the contact zone of two elastic bodies, and also for one elastic and the other plastic. The stresses are represented by a cubic spline polynomial, its coefficients calculated by pseudocaustics from reflected light around the contact zone. The method is applied to determine the stresses along the boundary of a half-plane and the stresses along the contact area of two disks. The deviation of calculated stresses from the applied ones, in the first case was small, while in the second case it was found that the normal distribution of stresses was similar to a Hertzian distribution. This experimental method can be used to accurately obtain contact stresses.

Analysis of Rubber Friction by the Fast Fourier Transform

1978 ◽  
Vol 6 (2) ◽  
pp. 89-113 ◽  
Author(s):  
R. A. Schapery
Keyword(s):  
Fourier Transform ◽  
Fast Fourier Transform ◽  
Numerical Method ◽  
Plane Strain ◽  
Contact Problems ◽  
Fast Fourier Transform Algorithm ◽  
Periodic Arrays ◽  
Rubber Friction

Abstract A numerical method for solving contact problems is developed and then used to predict friction (without adhesion) between rubber in plane strain and periodic arrays of parabolic and triangular substrate asperities; the numerical method itself, which is based on the fast Fourier transform algorithm, is not limited to these asperity shapes. Also, effects of superposing two and more scales of texture are described. Some generalizations and related applications, such as analysis of tire traction, are then discussed.

scholarly journals An Ultra-Area-Efficient 1024-Point In-Memory FFT Processor

Micromachines ◽  
2019 ◽  
Vol 10 (8) ◽  
pp. 509 ◽  
Author(s):  
Hasan Erdem Yantır ◽  
Wenzhe Guo ◽  
Ahmed M. Eltawil ◽  
Fadi J. Kurdahi ◽  
Khaled Nabil Salama
Keyword(s):  
Fourier Transform ◽  
Fast Fourier Transform ◽  
Current Literature ◽  
Power Efficiency ◽  
Design Principles ◽  
The Other ◽  
Area Efficiency ◽  
Processor Architectures ◽  
Fft Processor ◽  
Area Efficient

Current computation architectures rely on more processor-centric design principles. On the other hand, the inevitable increase in the amount of data that applications need forces researchers to design novel processor architectures that are more data-centric. By following this principle, this study proposes an area-efficient Fast Fourier Transform (FFT) processor through in-memory computing. The proposed architecture occupies the smallest footprint of around 0.1 mm 2 inside its class together with acceptable power efficiency. According to the results, the processor exhibits the highest area efficiency ( FFT / s / area ) among the existing FFT processors in the current literature.

Elastic Fields due to Eigenstrains in a Half-Space

2005 ◽  
Vol 72 (6) ◽  
pp. 871-878 ◽  
Author(s):  
Shuangbiao Liu ◽  
Qian Wang
Keyword(s):  
Fourier Transform ◽  
Fast Fourier Transform ◽  
Half Space ◽  
Numerical Algorithms ◽  
Elastic Field ◽  
Contact Problems ◽  
Fast Fourier Transform Algorithm ◽  
Elastic Fields ◽  
Influence Coefficients ◽  
Residual Strains

Engineering components inevitably encounter various eigenstrains, such as thermal expansion strains, residual strains, and plastic strains. In this paper, a set of formulas for the analytical solutions to cases of uniform eigenstrains in a cuboidal region-influence coefficients, is presented in terms of derivatives of four key integrals. The linear elastic field caused by arbitrarily distributed eigenstrains in a half-space is thus evaluated by the discrete correlation and fast Fourier transform algorithm, along with the discrete convolution and fast Fourier transform algorithm. By taking advantage of both the convolution and correlation characteristics of the problem, the formulas of influence coefficients and the numerical algorithms are expected to enable efficient and accurate numerical analyses for problems having nonuniform distribution of eigenstrains and for contact problems.

scholarly journals Johnson–Kendall–Roberts adhesive contact for a toroidal indenter

2016 ◽  
Vol 472 (2191) ◽  
pp. 20160218 ◽  
Author(s):  
Ivan Argatov ◽  
Qiang Li ◽  
Roman Pohrt ◽  
Valentin L. Popov
Keyword(s):  
Asymptotic Solution ◽  
Contact Problem ◽  
Half Space ◽  
Elastic Properties ◽  
Contact Area ◽  
Adhesive Contact ◽  
Elastic Half Space ◽  
The Other ◽  
Leading Order

The unilateral axisymmetric frictionless adhesive contact problem for a toroidal indenter and an elastic half-space is considered in the framework of the Johnson–Kendall–Roberts theory. In the case of a semi-fixed annular contact area, when one of the contact radii is fixed, while the other varies during indentation, we obtain the asymptotic solution of the adhesive contact problem based on the solution of the corresponding unilateral non-adhesive contact problem. In particular, the adhesive contact problem for Barber’s concave indenter is considered in detail. In the case when both contact radii are variable, we construct the leading-order asymptotic solution for a narrow annular contact area. It is found that for a v-shaped generalized toroidal indenter, the pull-off force is independent of the elastic properties of the indented solid.

Modeling of Finite-Length Line Contact Problem With Consideration of Two Free-End Surfaces

2015 ◽  
Vol 138 (2) ◽  
Author(s):  
Haibo Zhang ◽  
Wenzhong Wang ◽  
Shengguang Zhang ◽  
Ziqiang Zhao
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Fourier Transform ◽  
Contact Problem ◽  
Finite Length ◽  
Line Contact ◽  
Free Boundaries ◽  
Contact Conditions ◽  
Free Surfaces ◽  
Speed Up

Finite-length line contact conditions, existing in applications such as gears or roller bearings, lead to subsurface stress distribution influenced by the free boundaries. This paper presents a semi-analytical method (SAM) for the finite-length line contact problem, based on the overlapping concept and matrix formation, to consider the effect of two free-end surfaces. In order to obtain two free surfaces, three half-spaces with mirrored loads to be solved are overlapped to cancel out the stresses at expected surfaces. The error introduced by this method is analyzed and proven to be negligible. The conjugate gradient method (CGM) is used to solve the pressure distribution, and the fast Fourier transform (FFT) is used to speed up the elastic deformation and stress-related calculation. The model is verified by finite element method (FEM) and shows a high conformity and efficiency. Besides, the line contact situations are discussed to explore the effect of free surfaces.

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