Casting of molten metal is important in many industrial processes. Centrifugal casting is used for manufacturing pipes, bearings, and many other structures. A cylindrical enclosure is rotated rapidly and steadily about a horizontal axis. Molten metal is poured into the rotating cylinder and then cooled, forming the finished product. Turning the cylinder at a high rotation rate forces the solidifying metal strongly to the outside. Any bubbles are displaced toward the axis, so unwanted voids will not be present in the casting. Sometimes it is desirable to form a composite casting, such as for a bearing. Here a strong steel outer surface is poured, followed by an inner lining of special low-friction metal. In some applications, a very strong metal is given a coating of corrosion-resistant metal. Centrifugal casting results in bonding between the layers.
Suppose that a copper sleeve of inner radius 2.04 cm and outer radius 2.26 cm is to be cast. To eliminate bubbles and give high structural integrity, the centripetal acceleration of each bit of metal should be 100g. What rate of rotation is required? State the answer in revolutions per minute.
w = √(a/r)
RPM = 60w/2π = 60√(a/r)/2π
Since the angular speed is a function of the radius, the rpm for a particular radius and acceleration is unique; only the metal at that exact radius will experience the specified acceleration. Using the smaller radius,
RPM = 60*√(98000/2.04)/2π = 2093
w = √(a/r)
RPM = 60w/2π = 60√(a/r)/2π
Since the angular speed is a function of the radius, the rpm for a particular radius and acceleration is unique; only the metal at that exact radius will experience the specified acceleration. Using the smaller radius,
RPM = 60*√(98000/2.04)/2π = 2093
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