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In mathematics, the moving sofa problem or sofa problem is a two-dimensional idealization of real-life furniture-moving problems and asks for the rigid two-dimensional shape of the largest area that can be maneuvered through an L-shaped planar region with legs of unit width. [1] The area thus obtained is referred to as the sofa constant.
Many practical applications suggest as good practice that the maximum operating speed should not exceed 75% of the critical speed [citation needed]; however, some systems operate above the first critical speed, or supercritically. In such cases, it is important to accelerate the shaft through the first natural frequency quickly so that large ...
Analysis shows that there are well-damped critical speed at lower speed range. Another critical speed at mode 4 is observed at 7810 rpm (130 Hz) in dangerous vicinity of nominal shaft speed, but it has 30% damping - enough to safely ignore it. Analytically computed values of eigenfrequencies as a function of the shaft's rotation speed.
In 1999, the 208-foot (63 m) tall, 2540-tonne Cape Hatteras Lighthouse was moved 2,900 feet (880 m) to protect it from being undermined by beach erosion. When the North Carolina lighthouse was built in 1870, it was over 1,500 feet (460 m) from the sea , but by 1935 the beach had eroded and the waves were only 100 feet (30 m) away.
SFM is a combination of diameter and the velocity of the material measured in feet-per-minute as the spindle of a milling machine or lathe. 1 SFM equals 0.00508 surface meter per second (meter per second, or m/s, is the SI unit of speed). The faster the spindle turns, and/or the larger the diameter, the higher the SFM.
Cutting speed may be defined as the rate at the workpiece surface, irrespective of the machining operation used. A cutting speed for mild steel of 100 ft/min is the same whether it is the speed of the cutter passing over the workpiece, such as in a turning operation, or the speed of the cutter moving past a workpiece, such as in a milling operation.