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"source": [
"# Fluid-flow: Wear Bearing"
]
},
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"metadata": {},
"source": [
"**WEAR BEARINGS**\n",
"\n",
"Although lubrication reduces the friction between the metal surfaces of the bearing, these structures usually suffer wear after a long operating period or else due to a certain number of repetitions of the starting cycles.\n",
"\n",
"![alt text](../_static/img/img_examplo_ff_wear.png)\n",
"\n",
"\n",
"\n",
"\n",
"The wear geometry that will be used in the FluidFlow has been adapted from the version presented by MACHADO; CAVALCA (2015) [1]. To include wear in the geometry, it is necessary to make some adaptations to the stator radius. Considering that the fault starts at the angular position $\\theta = \\theta_{s}$ and ends at $\\theta = \\theta_{f}$, the stator description from the origin is defined as:\n",
"\n",
"$$R_o^* = R_o + d_{\\theta}$$\n",
"\n",
"where \n",
"$$d_{\\theta} =\\begin{cases} \n",
" 0 \\text{,} \n",
" &\\text{if} \n",
" \\quad 0 \\leq \\theta \\leq \\theta_s\\text{,} \\quad\n",
" \\theta_f \\leq \\theta \\leq 2\\pi \\\\ \n",
" d_0 - F \\left(1 + \\cos{\\left(\\theta - \\pi/2\\right)} \\right) \\text{,} \n",
" &\\text{if} \n",
" \\quad \\theta_s < \\theta < \\theta_f\n",
"\\end{cases}$$\n",
".\n",
"\n",
"In $\\theta_{s}$ and $\\theta_{f}$, the wear depth is zero, so the location of the edges can be defined as follows:\n",
"\n",
"$$\\theta_s = \\pi/2 + \\cos^{-1}{\\left(d_0/F -1\\right)} + \\gamma \\nonumber\\\\\n",
" \\theta_f = \\pi/2 - \\cos^{-1}{\\left(d_0/F -1\\right)} + \\gamma $$"
]
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