derive the expression of critical speed for a standard ball mill

ball mill critical speed

ball mill critical speed

A Ball Mill Critical Speed(actually ball, rod, AG or SAG) is the speed at which thecentrifugal forces equal gravitational forces at the mill shells inside surface and no balls will fall from its position onto the shell.

The mill speed is typically defined as the percent of the Theoretical Critical Speed, often abbreviated as %Cs. The Theoretical Critical Speed (Cs) of rotation is the speed (in RPM) at which an infinitely small particle will cling to the inside of the liners for a complete revolution. The percent of critical speed is the ratio (expressed as a percentage) of the actual mill speed and the Theoretical Critical Speed of that mill. The critical speed of a rotating mill is the RPM at which a grinding medium will begin to centrifuge, namely will start rotating with the milland therefore cease to carry out useful work.

Ball and SAG Mills are driven in practice at a speed corresponding to 60-81% of the critical speed, the choice of speed being influenced by economical considerations. Within that range the power is nearly proportional to the speed.

mill critical speed formula derivation - grinding & classification circuits - metallurgist & mineral processing engineer

mill critical speed formula derivation - grinding & classification circuits - metallurgist & mineral processing engineer

When the ball mill rotates at the critical speed the theoretical trajectory of the charge is such that it would fall outside the shell as centrifuging occur at this stage and the medium is carried around in a fixed position against the shell. The formula to calculate critical speed is given below.

In practice Ball Mills are driven at a speed of 50-90% of the critical speed, the factor being influenced by economic consideration. Mill capacity can be increased by increasing speed but there is very little increase in efficiency (i.e kWht-1) when the mill is operated above about 40-50% of the critical speed

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