a b s t r a c tThis study presents crack initiation, propagation and coalescence at or near pre-existing open cracks or flaws in a specimen under uniaxial compression. The flaw geometry in the specimen was a combination of a horizontal flaw and an inclined flaw underneath. This flaw geometry is different from those reported in the previous studies, where a pair of parallel flaws was used. Three materials were used, PMMA (Poly Methyl MethAcrylate), Diastone (types of molded gypsum), and Hwangdeung granite. Crack initiation and propagation showed similar and different patterns depending on the material. In PMMA, tensile cracks initiated at the flaw tips and propagated to the tip of the other flaw in the bridge area. The cracks then coalesced at a point of the inclined flaw, which is affected by the flaw inclination angle. For Diastone and Hwangdeung granite, tensile cracks were observed followed by the initiation of shear cracks. Coalescence occurred mainly through the tensile cracks or tensile and shear cracks. Crack coalescence was classified according to the crack coalescence types of parallel flaws for overlapping flaw geometry in the past works. In addition, crack initiation and coalescence stresses in the double-flawed specimens were analyzed and compared with those in the single-flawed specimen. Numerical simulations using PFC 2D (Particle Flow Code in two dimensions) based on the DEM (Discrete Element Method) were carried out and showed a good agreement with the experimental results in the coalescence characteristics in Hwangdeung granite. These experimental and numerical results are expected to improve the understanding of the characteristics of cracking and crack coalescence and can be used to analyze the stability of rock and rock structures, such as the excavated underground openings or slopes, tunneling construction, where pre-existing cracks or fractures play a crucial role in the overall integrity of such structures.

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Since the slot opening is large in the uniform slot machine, the torque ripple generated by overlapping or misaligning with the rotor cavity is remarkably large in the case of interior permanent magnet (IPM) machine. In this work, it is observed that the magnitude of torque ripple depends strongly on the phase difference between air-gap field harmonics: The ripple is minimized when the two dominant harmonic components cancel each other. Based on this fact, a condition is developed to minimize torque ripple by adjusting the q-flux channel width and d-flux barrier width. The torque ripple minimizing solution is found from a level chart made by subdomain time-stepping analysis. Finite element analysis (FEA) also gives a very similar minimizing solution. A prototype machine is manufactured, and its performances are validated through experiments.

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