AIST finds ellipsoidal balls are optimal for "ball mills" — 10% higher grinding efficiency

The National Institute of Advanced Industrial Science and Technology (AIST) has revealed that the balls used for grinding in the pulverization device known as a "ball mill" achieve approximately 10% higher grinding efficiency when shaped as irregular forms resembling slightly distorted ellipsoids, rather than the traditionally used spheres. If practical applicability can be confirmed in industrial settings, these balls could replace the conventional spherical balls in mineral beneficiation processes for extracting valuable minerals from ores and in cement manufacturing.

A ball mill is a device that places hard balls and materials inside a rotating cylinder, performing pulverization and mixing of materials through impact and friction. While widely used for grinding ores, ceramics, pigments, and chemical feedstocks, most of the input energy used to rotate the cylinder is lost as heat and vibration. To improve grinding efficiency, proposals have been made to use balls shaped like bullets, among others. However, there have been reports that reproduction experiments failed to achieve results exceeding those of spheres, and the traditional use of spherical balls has continued for over 100 years.

Senior Researcher Takao Ueda in Mineral Resources Engineering at AIST, hypothesized that balls with larger contact areas for trapping and grinding target materials would improve grinding efficiency. Using "spherical harmonics" — the three-dimensional equivalent of Fourier series — he created numerous three-dimensional shapes without holes. He excluded shapes that were impractical for use, such as those with extreme spikes that would cause excessive wear.

For the remaining 5,500 shapes, he performed calculations such as randomly rotating each shape 10,000 times and measuring the contacting parts, then calculated the average contact area. When comparing the average values for each shape, the contact area was largest for a shape resembling a fava bean—like an ellipsoid distorted slightly asymmetrically.

To verify whether the optimal shape determined through numerical analysis could actually grind more efficiently than spherical shapes, 10 spherical and 10 fava-bean-shaped balls (OPTIPSE) were fabricated by cutting alumina, and grinding experiments were conducted in a small mill with a diameter of 10 cm and depth of 12 cm.

In the experiments, conditions such as mill rotation speed and time were kept constant, and approximately 80 grams each of silica sand and limestone were grinded with each type of ball. After grinding, fine particles with diameters of 90 micrometers (micro = one millionth) or less were collected and weighed. The weight ratio of fine particles increased by 7-16% with OPTIPSE compared with spherical balls, indicating better grinding efficiency.

Simulations of conditions inside the ball mill revealed more frequent contact with grinding targets and greater impact forces. "While not quite as flat as a fava bean, the irregular shape, which doesn't roll straight. appears to be involved," said Ueda.

Ueda plans to verify whether similar effects can be obtained when balls are fabricated from iron, which is actually used, and aims to conduct demonstration experiments at actual scale. The results were published online in the international journal Minerals Engineering on November 8.