How to Determine Power Input in Laboratory Ball Mill

In the study of ball mill grinding at the International Experiment Station of the United States Bureau of Mines at Salt Lake City, Utah, it was desirable to measure the work input to a ball mill at the mill itself so that consideration of motor efficiency and transmission losses would be eliminated.

The device adopted is essentially that used by Prof. H. E. T. Haultain in measuring wore input to rolls. The mechanism was changed only so as to adapt it to a ball mill.

Description of Equipment

Figure 1 is a diagrammatic sketch of the apparatus.

The pulley which rotates the mill is loose on the mill shaft and is equipped with ball bearings. This pulley is connected by means of three tangential springs to the driving plate, which is solid on the mill shaft. Power applied to the loose pulley is transmitted to the driving plate, and hence to the mill, by the three springs; the greater the resistance of the mill, the greater the spring extension. The extension of the springs is transmitted by the steel extension tape to the differential integrating meter.

The integrating meter is operated by two friction wheels in contact with the integrator disk, which revolves at a definite ratio of speed to that of the mill. The friction wheels are held in contact with the disk by the spring suspension of the integrator and are connected to a differential gear cage, the revolutions of which are recorded on a counter such as is used in gas meters. Due to the differential gears the cage is stationary when the two friction wheels revolve at the same speed in opposite directions; this condition exists when the integrator is centered on the disk and corresponds to no load or to a zero spring extension, as the load is applied, the springs extend and move the integrator from the center or zero point, resulting in a difference of speed between the two friction wheels. Due to the revolution of the differential cage this change in speed is transmitted to the counter. The integrator and extension tape system is kept taut by means of a light spring attached to the integrator, the spring having just enough tension to assure that the integrator returns to zero when the load becomes zero.

The integrator does not give direct readings of the work input, as the readings increase with speed or revolutions per minute and the spring extension is not in direct proportion to the load or pull. The integrator reading is, however, a true product of speed and pull, a given pull always results in the same, spring extension and a given pull per revolution always gives the same reading, irrespective of speed. The relation between horsepower-hours per revolution and integrator-reading-per revolution can thus be expressed by a calibration curve from which the work input can be obtained when time of running and number of revolutions are known.

Calibration of the Integrator

The spring extension and the displacement of the integrator from the zero point are increased as the work input increases, so that the revolutions of the differential gear are a measure of work input.

To convert the meter readings to work input the apparatus was calibrated at various speeds with a Prony brake and also by means of a static load.

The static method was particularly useful as a check on the Prony brake measurements and for those loads where the Prony brake readings were not steady enough for the required accuracy.

Calibration With the Prony Brake

A Prony brake was made to fit the mill shell, and readings were obtained with different loads and at different speeds, by plotting the horsepower-hours per revolution against the integrator-reading per revolution, the data for all speeds can be used to establish a single curve. This has been done in Figure 2.

The mill was run at a definite speed and the belt then removed. A known weight was suspended from the driving pulley at a distance of 10 1/8 inches from its center. The disk was then run at the speed which corresponded to the particular mill speed and integrator readings were obtained.

The results of the static measurements plotted similarly to those obtained with the Prony brake are given in Figure 2. It will be seen that the Prony brake and the static method give essentially the same results. This curve is used for the determination of work input when springs of the same strength are used.

Use of the Calibration Curve

To determine the work input to the mill, it is only necessary to know the mill revolutions and the integrator readings for definite periods of time. The figure obtained from the curve multiplied by the revolutions per minute gives the horsepower-hours per minute input delivered at the mill irrespective of motor efficiency, transmission losses, or belt slip.

The only place in which belt slip affects the results is in the transmission to the mill or to the integrating disk, thus altering the speed ratio between these two from that obtaining during calibration.

Speed counters are used both on the mill and on the integrator disk so that any variation in the speed ratio can be noted and a correction applied, the integrator readings being directly proportional to the disk speed.

The curve may be considered as accurate for readings from 0.000015 to 0.000085 horsepower-hours per revolution. For readings below this the accuracy of results obtained with the springs used in the calibration may be questioned. For work input measurements below 0.000015 horsepower-hours per revolution, weaker springs are used, which was done in obtaining no-load figures. However, in either case the curves obtained do not go through zero as they theoretically should unless the curve be bent sharply. The explanation of this lies in the fact that a certain pull is necessary before the springs begin to extend. Furthermore, a certain force is necessary to overcome the pull of the tension spring which keeps the extension tape taut. This does not affect the range in which the ball-mill experiments are made.