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Research Papers: Contact Mechanics

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

[+] Author and Article Information
Shuangbiao Liu

Technology and Solutions Division, E854 Caterpillar Inc., Peoria, IL 61656-1875liu_jordan@cat.com

Diann Y. Hua

Technology and Solutions Division, E854 Caterpillar Inc., Peoria, IL 61656-1875

J. Tribol 131(2), 021408 (Mar 09, 2009) (8 pages) doi:10.1115/1.3084237 History: Received February 08, 2008; Revised January 27, 2009; Published March 09, 2009

## Abstract

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.

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## Figures

Figure 1

Schematics of the line contact

Figure 2

Schematics of three types of 3D problems: (a) point contact with a confined contact area, (b) nominally flat contact with periodic copies in both directions, and (c) line contact with periodic copies in x2 while with confined contact width in x1

Figure 3

Schematics of periodic padding in the DC-FFTP algorithm before wrap-around order. The displacement at the origin, for example, was caused not only by the pressure inside the target domain but also by the periodic copies around it due to periodic padding. (a) Zero padding in the x1 direction and periodic padding in the x2 direction (see also Fig. 4 in Ref. 34) and (b) periodic padding in both directions.

Figure 4

For the observation point (a) at the center and (b) at the upper-right corner of the target domain, the DC-FFTP algorithm with 1D periodic padding in the x2 direction gives the displacement due to the pressure of two periods distributed along x2 with the observation point as the center

Figure 5

Effects of γ and AL on the von Mises stress along the x1 direction in the surface with μf of 0.5

Figure 6

Textured surface of a cylinder

Figure 7

Contact pressure and von Mises stress with textured surface (μf of 0.25): (a) contact pressure shown in one-quarter, (b) von Mises stress over the central cross section, and (c) counterpart of (b) when the dimple is absent

Figure 8

With μf of 0.25, von Mises stress over the central cross section of (a) the coated half-space with coating of 3 μm thick, (b) the half-space made of the coating material, and (c) the coated half-space as in (a), but with larger depth

Figure 9

Four functions

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