Grinding balls are essential mechanical components in ball and semiautogenous (SAG) mills. Their function is crushing and grinding ore rocks weighing up to 45 kg (100 lb) preparatory to recovery of valuable minerals, from lead through rare earth elements, which are essential to the approaching 21st century technological society. Their design, manufacture, and selection deserve careful attention.

Motors convert electrical energy to mechanical torque to rotate ball and SAG mills so their ore/ball charges cascade continuously. During each revolution, each individual ball’s quantum of kinetic energy is delivered, through rapid deceleration impacts, on ore fragments to break them in preparation for mineral recovery.

Critical ball design features include new size and mass, worn size distribution, chemistry, hardness, microstructure, toughness, internal stress, and stability of microstructure. These factors determine how effectively and economically the balls grinding mission will be performed. These features, therefore, must be carefully designed, specified, and maintained.

Seemingly small deviations from design, or small deficiencies in properties or quality, have large effects on grinding performance and economics.

Ball manufacturers have made remarkable improvements in ball manufacturing, properties, quality, and price to provide the mining industry with a wide selection for ball sizes and types. These allow selection of custom designed balls appropriate for each specific application. The mill operator who does not exploit this cornucopia of ball types may forfeit thousands or even millions of dollars in annual ball costs, lost tonnage, and percent recovery.

This paper shows that among the ball designs available from several excellent sources, there exists one or more design combination that is closest to being right for each application. Analysis and service testing can narrow the field and provide insight to aid in selection. The experiences of the Henderson and Climax molybdenum mines are offered as examples showing the potential savings that result from careful ball selection and quality control.

Ball Design Factors

Size and Mass

Importance of size: Taggart (1927) stated “Size of balls should be proportional to the work to be done, i.e. the size of the particle that must be broken by impact, hence coarse feed and hard ores require larger balls than finer feeds and softer ores.” The 9 to 10 m (30 to 33 ft) SAG mills now in wide use and the 127 mm (5 in.) balls they require to break primary crusher products testify to the validity of Taggart’s work of 60 years ago.

An empirical relationship relating ball size to ore properties and mill size has been developed by Azzaroni (1981).

F80 = feed size, 80% passing, microns
Wi = Bond Work Index, metric tons
N = Mill revolutions/minute
D = Mill diameter, meters

Large rock breakage has been investigated by Mayera et al. (1982) as it relates to use of hydraulic impactors to break large boulders. They conclude that the minimum specific energy required to break a boulder is an exponential function of the average dimension of the boulder.

The kinetic energy (KE) of falling ball is the product (mass x velocity² ÷ 2). Maximum KE is attained by top sized balls falling about 0.5 mill diameter, with actual distance depending on charge level, critical speed, and liner shape designs. Ball mass varies and is a function of material density, soundness, and ball size. New ball sizes vary widely compared to nominal theoretical size and weight.

The Azzaroni equation size predictions agree well with ball sizes found to be effective for grinding Henderson 203 mm (<8 in.) SAG mill feed and Climax 9.5 mm (0.37 in.) ball mill feeds. There, 127 mm (5 in.) and 76 mm (3 in.) balls, respectively, were selected upon the basis of mill performance in long term tests (Hinken, 1982; Born, Bender, and Keihn, 1975).

Required ball weight/mass should be determined from actual operating mill or pilot plant tests. They should be specified for the individual plant and be maintained by the vigilance of both manufacturer and user. Manufacturing size variations, density variations, and breakage are prime enemies of ball weight/mass.

Ball size availability: Given the importance of weight/mass, in an ideal world, ideal ball size could be selected from an infinite size range. Presently, in many cases, only two ball sizes are available for a given milling operation -too big and too small.

The weight increments between ball sizes are too large to allow precise selection. Ball users would benefit if size increments of about 6 mm (0.25 in.) were available between 50 to 101 mm (2 and 4 in.) sizes, and steps of 3 mm (0.1 in.) were offered in sizes 101 to 152 mm (4 to 6 in.).

Control of Ball Weight: The specified weight should be maintained in all shipments by minimizing variations from nominal weight. This is the manufacturers job.

There is wide variation in weight between manufacturer’s balls and between balls from different lots of balls currently being made. A light ball is actually a defective ball.

Nominal 76 mm (3 in.) balls received at the Climax mine weighed between 1.75 and 2 kg (3.85 and 4.40 lb) depending on source and lot. In 127 mm (5 in.) balls received at the Henderson mill, weights of 7.9 and 8.8 kg (17.4-19.5 lb) have been recorded.

Where a specific mill feed requires a certain minimum ball weight to grind effectively, lighter balls of the same nominal size reduce grinding effectiveness.

Effect of Low New Weight: Light subnominal weight balls have a detrimental effect on mill grinding capacity and on ball consumption. Balls consistently lighter than nominal deprive the mill charge of all the individual balls having kinetic energy between theoretical nominal and actual values. Ore fragments requiring the higher levels of energy are less effectively broken by more, lower energy blows of smaller balls.

The boulder breaking study by Mayera et al concluded that to break a given boulder it is more efficient to increase the (single) blow energy than the total power (number of blows). If a nominal ball is made 1 kg (2.2 lb) lighter than another type, it has instantaneously “lost” over 10% of its theoretical maximum weight and thus 10% of the maximum kinetic energy it can deliver in SAG mill operation. Variations of this magnitude have been seen in balls at the Henderson mill.

Effect of Breakage: If a 127-mm (5-in.) ball splits into halves it is no longer a 127-mm (5-in.) ball, it is two poor 101 mm (4 in.) “balls,” neither of which may have required KE to do the work intended for the 127 mm (5 in.) ball. Similar penalties apply to smaller ball sizes, used in ball mills.

An allegedly “small” number of split balls can cause significant losses of mill grinding capacity with attendant increases in ball consumption because of the inefficiency of each day’s charge ration in breaking the ore fragments requiring top size balls.

A typical day’s ration of 127 mm (5 in.) balls for a Henderson 8.5 m (28 ft) SAG mill, 6.2 t (6.8 st) of balls, contains about 745 127 mm (5 in.) balls. Some manufacturers state 4% to 5% breakage is normal. Five percent broken balls represents 37 broken balls daily, each worth $5, a waste of nearly $ 185 a day per unit and $740 a day for four units.

Worse, the effect of 5% breakage is to decrease by 5% the entire population of balls in the mill having minimum or greater energy needed to break the larger ore fragments in the mill feed for which 127 mm (5 in.) balls were selected.

Five percent breakage increases the population of sub critical energy balls by 10% if balls break into halves, by 20% if they split into quarters. These nearly useless fragments then consume volume, allowable mill charge weight, and energy to lift them each mill revolution for the remainder of their life while they do little or no useful work. At the Henderson mill, the disastrous effects of “small” amounts of ball spalling, splitting, or fragmentation have been recorded several times during long-term comparisons of two or more ball types.

During startup tests and early operation at the Henderson mill, it was found that the 8.5 m (28 ft) SAG mills could grind about 91 t/h (100 stph) autogenously, using no balls. Successively higher tonnages were achieved with 76 and 101 mm (3 and 4 in.) balls. The mills really hit their stride using 127 mm (5 in.) balls, the present standard (MacPherson, 1978). Tests using 140 mm (5.5 in.) balls showed these might perform even better but concern for liner breakage with the 11.2 kg (24.7 lb) balls prevailed against their use. It is probably significant that the lowest sustained ball consumption rate ever attained was achieved using balls weighing 8.5 to 8.8 kg (18.5 to 19.5 lb), up to 5% heavier than nominal weight.

Henderson milling experience, recorded in long-term concurrent mill comparisons, showed that undersized 127 mm (5 in.) balls weighing 8.2 to 8.4 kg (18.1 to 18.5 lb) and having a tendency to split off 1 kg (2 lb) “caps” caused a 12% to 15% ball consumption increase. Increased power consumption was also noted, up 2%, and 6% loss of mill t/h rate compared to performance recorded with use of the heavier, sounder balls.

The ineffective fragments of broken balls occupy mill volume. Their weight must be lifted during each mill revolution regardless of their inability to perform useful work during the charge cascade part of the cycle. This weight and volume should be devoted to ore and full size balls if breakage can be eliminated.

Broken ball fragments plug grates and wedge between mill liners, making changes difficult. Their sharp edges also cut rubber liners in pipes, cyclones, and pumps before they go on to accumulate in sumps and launders.

Detecting ball breakage: Casual inspections may not reveal the true extent of breakage. A “few” splits in a truckload of new balls can be a symptom of more extensive breakage inside the mill.

Mill charges are segregated by size when at rest and require slow tumbling by stages until the charge core, composed of small balls and fragments, comes to view.

Ideally, all worn balls should be intact, round, or cubic system polyhedrons. If the core of smaller sizes contains many halves, quarters, caps, disks, flakes, or other junk, it is evidence of serious breakage. The nature of these shards will show how and when they form.

A decline in mill production, efficiency, product size, or an increase in ball consumption or energy consumption may signal onset of ball breakage or changes in ball properties not easily seen in new ball shipments or mill charge inspections.

Ball manufacturing practice and quality can change almost over night, causing mill performance to start declining within a week.

If breakage develops, the manufacturer should be told immediately. “Modest” breakage can quickly build up a large residual volume of useless fragments in a total mill charge starved of the large size balls needed for good ore breakage. It can take months to rid the mill of this harmful junk unless means exist to purge the mills. Performance will suffer until the scrap is worn out.

Causes of ball breakage: Before breakage can be attributed to ball deficiencies, the mill operator should assure himself that operational factors are not at fault. Some of these include: mill speed change, liner profile change, ball charge rate errors, ball charge level change, mill solids change, feed size change, feed rate change, rough ball handling, mill grindouts feed rate transients, and feed weightometer error.

Where operational factors can be absolved, ball breakage may be caused by design, manufacturing,or quality control changes including: chemical composition, heat treatment, hydrogen cracking, delayed austenite transformation, residual stress, deformation stress, ductile-brittle transition, pre-existing defects, and quality control.

Weight loss by breakage: Ball breakage radically reduces maximum ball weight. Designing balls to prevent breakage is the province of the manufacturer. The mill operator can do much to prevent breakage during handling and mill operation.

Breakage takes several forms, from spalling coin-sized flakes to bursts and splits of new balls during transport.

Causes of ball breakage are many. Internal stress resulting from delayed austenite to martensite transformation, induced by exposure to cold temperatures or by impact adds to existing residual stress to burst balls in storage or during service. Migration of dissolved hydrogen atoms to voids where they form larger hydrogen (H2) molecules unable to migrate through steel creates pressures able to split balls. Low impact toughness of the steel and changes in ductility at low temperature break balls. Pre-existing flaws such as quench cracks, gas and shrink cavities, centerline shrink in continuous cast bar before forging, and cold laps in surfaces serve as stress concentrators to break balls.

The ball manufacturer has primary control over breakage through design of alloy/casting/forging/heat-treating processes and through quality control practices that prevent, detect, and cull out flawed or crack prone balls.

The ball user can minimize breakage by avoiding rough handling new balls. Even short drops of a few feet develop severe Hertzian compressive stress during ball-on-ball collisions.

Grinding mill operation should be done only with an adequate “cushion” of coarse ore in mills to prevent ball-on- ball impacts that occur during low feed rate operation or grind outs.

Ball-on-ball impacts develop subsurface Hertzian stresses exceeding any steel’s ultimate strength. Stresses of 4050 MPa (587,000 psi) can be generated by 127 mm (5 in.) balls impacting bare liners in 8.5 m (28 ft) SAG mills (Dunn, 1976).

Microstructures containing the decomposition products of martensite like ferrite (soft iron) and pearlite (platelets of iron carbide and ferrite in alternating laminations) are softer, more deeply indented, and more easily cut away by sharp ore.

Being softer, the lower hardness structures respond to excessive stress by deformation instead of cracking. Since they are the decomposition products of a metastable structure, they can decompose no further and thus do not undergo transformations that create internal stress as does martensite.

Hardness

Effect on abrasion resistance: Hardness is resistance to indentation, a necessary event for abrasion of steel, cast iron, or porcelain. Sharp, hard ore penetrates the harder metals less deeply than softer ones and, therefore, less metal is cut away during lateral relative movement between ball surface and ore particle.

Hardness in steel and cast iron balls is obtained by rapid cooling from high critical temperature, typically about 871° C (1600° F) for steels, and 982° C (1800° F) for cast iron.

In steels, austenite transforms to martensite, a metastable, super-saturated solid solution of carbon atoms in a body- centered tetragonal crystal lattice. In alloy cast irons, a martensite matrix, containing hard Fe, Cr, and Mo M7C type carbides is formed. Martensite, at up to 700HB, and M7C3 carbides are about as hard as, or harder, than most ore minerals including quartz.

The relationship between composition, hardness, and wear rate is one of increasing wear resistance with increases in hardness and carbon content (Norman and Hall, 1969). This has been demonstrated many times in marked ball wear tests and mill liner wear tests in production ball and SAG mills at the Climax and Henderson operations (Albright and Dunn, 1983; Dunn, 1985).

Hardness Effect on Toughness: Hardness itself does not cause brittleness. But rapid quenching required to obtain high hardness produces transient thermal stress that causes quench cracks. Variations in metal microstructure with depth below ball surfaces cause high residual stress due to differences in density between martensite and pearlite.

Delayed transformation of martensite started by low temperature or impact deformation creates internal stress that may add to existing residual stress. The sums of stresses can exceed ball strength and break balls.

Dissolved hydrogen migrating to voids and generating H2 gas pressure can split balls. Many steels show a transition from ductile to brittle behavior at temperatures of 4° C (40° F) and below and respond to stress by breaking instead of deforming.

These phenomena may be perceived as brittleness and are sometimes attributed to hardness. They often accompany hardness and they undeniably break balls.

Hardness profile: Microstructure transformation rates are strongly time dependant. Small balls of less than 76 mm (3 in.) have small variations in microstructure and hardness, surface to center, because their small volume permits rapid cooling during quenching. Larger balls greater than 76 mm (3 in.) with greater radial distance for heat to dissipate through, cool too slowly to produce a fully martensitic structure unless alloy content is very high, as in high chrome cast iron alloys.

Larger steel balls with greater radial heat path for cooling develop pronounced gradients of hardness and microstructure.

A hardness and structure gradient is usually viewed as undesirable because of faster wear of softer constituents. But the hardness gradient can be exploited to manipulate the ball size distribution of the ball charge to produce better mill grinding capacity and lower ball consumption than is obtained using a ball with harder interior metal.

This unexpected phenomenon is believed to be caused by accelerated wear on the soft interior ball cores. At 42 HRC, compared to 60 HRC surface metal, the soft interior has a relative wear rate measured at 29% higher than that of 60 HRC surface material in marked ball wear tests (Dunn, 1985).

The soft core ball grinds Henderson ore more efficiently and can perform its task using fewer balls added daily than can a hard core design. Reduced weight of small, worn balls makes room and frees up mill energy to accommodate additional volumes of ore, itself grinding media in SAG milling.

This unique relationship of ball hardness profile to mill grinding performance may not hold true at other mines milling different types of ore. In fact, ball producers offer several types of hardness profiles in large SAG mill balls to suit the varied needs of diverse milling operations.

It is important to recall that the majority of grinding balls in SAG mills are ore rocks whose size distribution and competence determine their effectiveness as well as the need for and properties of steel balls to be added as a grinding aid.

In ball mills, balls take up most of charge volume and are the major ore grinding components. The balls do most of the ore size reductions, unlike SAG mills where large ore fragments do most of the size reduction. The missions of the two types of balls are different and the properties required to perform those missions are different.

Hardness profile and size distribution: Many mills exhibit ball wear rates that are constant in terms of ball diameter loss per unit of time. Climax and Henderson ball and SAG mills show this type of wear (Dorfler, Lorenzetti, and Dunn, 1981).

In such mills, balls that have uniform microstructure and hardness, surface to center, lose diameter at a constant rate and produce a seasoned ball charge of daily cohorts whose diameters vary by one day’s diameter loss.

If structure and hardness vary, surface to center, the size distribution will be skewed. Typical 127 mm (5 in.) martensitic balls are hard on the exterior, softer in the center. Their older cohorts lose diameter more rapidly. The resultant charge size distribution contains fewer small balls and fewer older cohorts of balls than are found in a charge of balls with no hardness gradient, surface to center.

This phenomenon is being exploited to improve mill productivity and ball consumption in the Henderson SAG mills.

The opposite effect occurs in Climax 3 and 4 m (9.5 and 13 ft) ball mills. These grind less than 9.5 mm (0.3 in.) ore that requires 76 mm (3 in.) top size balls. The size distribution resulting from use of martensitic steel balls with softer centers was found to be less effective than a charge of uniform hardness but softer carbon steel balls (Dunn, 1976). The softer balls produced a 6% better mill t/h rate but did so at 29% ball consumption penalty.

A cost saving solution was found by dosing the daily charge of hard martensitic steel balls with 50% (weight basis) 51 mm (2 in.) martensitic balls to produce seasoned mill ball charge artificially skewed towards the small size end of the spectrum. This allowed the ball mills to retain the higher tonnage rates characteristic of 76 mm (3 in.) soft, uniform hardness, pearlitic steel balls while obtaining the 29% lower wear rate benefit of hard martensitic steel balls (Dorfler, Lorenzetti. and Dunn, 1981).

Ball quality control for mill operators

Ball manufacturers perform continuous quality control on balls produced. However, variations in composition, heat treatment, and other variables occur and their effects on service performance are not always predictable.

Ball users can improve ball performance and cost by monitoring ball quality and service performance.

Suggested ball QC programs: Since annual ball costs reach millions of dollars for many users, a routine program of quality control is an investment that can pay good dividends in ball cost and mill production. Elements of an effective ball quality-control program include ball properties monitoring— inspection of shipments, hardness tests, weight determinations, and manufacturer’s QC reports.

Ball performance monitoring includes mill charge inspections, ball scrap discard inspections, continuous mill performance monitoring, two or more types in comparable mills, comparison with historical data, and service testing various sizes and types.

Ball shipments should be inspected to reveal cracked or broken balls and irregularities not acceptable to the particular milling operation.

Small balls 76 mm (3 in.) or smaller can be prepared by wet grinding small flats, 180° apart, sufficiently deep to expose metal not decarburized, for Rockwell C hardness tests.

Large balls should be sectioned using a water cooled abrasive cutoff saw to produce half diameter slabs upon which surface-to-center hardness traverses are made using Rockwell C scale test equipment. These are time consuming preparations that can only spot check against manufacturer’s test reports.

Manufacturer’s test reports should include chemistry, weight, hardness, test profiles — surface-to-center, and heat numbers for every heat shipped.

Mill charges should be inspected frequently to catch occurrences of breakage as quickly as possible. This is to preclude a large build-up of broken balls in the mills taking perhaps months to wear out.

If worn balls are routinely culled out for discard or reuse, these are invaluable sources of information on ball wear and breakage and should be monitored frequently.

Continuous monitoring of mill production data, especially t/h, kWh/t, balls/t, and fineness of grind is essential. Unexplainable changes may be the result of sudden onset of ball breakage or changes in as-received properties.

Continuous comparison, where possible, with other ball types, provides a relative basis of comparison of ball performance. Testing of ball types, sizes, and size-mix ratio will eventually indicate the best type of new balls to use and thus guarantee best mill production and economic performance.

Conclusions

• Mill performance is affected strongly by ball design and properties.
• Mill performance and operation costs can be improved by selection of balls most nearly optimal for a given grinding circuit.
• Large variations exist between balls produced by various manufacturers and between production lots of balls.
• Undersize balls and balls that break endanger mill productivity and cost of mineral production.
• Ball quality-control measures pay large dividends in mill productivity and production cost savings and should be a feature of all milling operations.