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

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.