Casting of molten metal is important in many industrial processes. Centrifugal c

Question

Casting of molten metal is important in many industrial processes. Centrifugal casting is used for manufacturing pipes, bearings, and many other structures. A variety of sophisticated techniques have been invented, but the basic idea is as illustrated in the figure below. 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 2.05 cm and outer radius 2.3 cm is to be cast. To eliminate bubbles and give high structural integrity, the centripetal acceleration of each bit of metal should be at least 100g. What rate of rotation is required? State the answer in revolutions per minute.

Explanation / Answer

The period "T" is also equal to rpm = 1/T

The equation for centripetal acceleration is:

a = 4pi^2R/T^2

The centripetal acceleration must equal 100g or 100*9.8m/s^2.

T^2 = 4pi^2*4.35cm/98000cm/s^2

T = 0.04186 seconds

Convert this to minutes:

0.04186s * 1 min/60s = 6.98*10^-4min

RPM = 1 rev/6.98*10^-4min

= 1432.66 RPM

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