A Detailed Discussion of Steel Balls (Part 4) — The Influence of Mill Operating Conditions on Steel Ball Wear

The wear, breakage, and out-of-roundness of grinding balls are influenced not only by their intrinsic quality but also by the grinding process conditions and the operating conditions of the mill. This lecture will primarily explore the impact of mill operating conditions on grinding-ball wear from the perspectives of mill specification parameters and in-mill process parameters.

I. Operating Conditions of the Mill

1. The inner diameter of the mill affects

The larger the mill’s internal diameter, the greater the impact force exerted by the grinding media upon falling; under otherwise identical conditions, the wear of the steel balls also increases accordingly. H.E. Lous’ research findings indicate that the relative wear coefficient Kd of the steel balls can be expressed as a function of the ratio between the mill’s internal diameter D and the maximum diameter d of the steel balls, according to the following equation:

Kd = 0.356 (D/d)^0.15
 
Effect of the Ratio of Mill Inner Diameter to Maximum Steel Ball Diameter, D/d, on Steel Ball Wear

When D/d ≤ 5, the wear of the steel balls increases most significantly, exhibiting a linear increase.

When the D/d ratio is between 5 and 10, the wear of the steel balls increases gradually.

When D/d ≥ 10, the wear of the steel balls exhibits minimal variation and approximates a slightly inclined straight line.

The wear of steel balls in small mills is high; in industrial applications, the typical mill diameter-to-ball-diameter ratio (D/d) is generally ≥15, indicating that increasing the mill diameter has only a limited impact on ball wear.

2. The Influence of Mill Rotational Speed on Steel Ball Wear

According to the research results, the relative wear coefficient Kd of steel balls increases approximately in direct proportion to the specific rotational speed of the mill, where the specific rotational speed is defined as the ratio of the mill cylinder’s rotational speed n to the critical rotational speed no.

Effect of Mill Rotational Speed on Steel Ball Wear

The higher the mill speed, the more severe the wear on the grinding balls; therefore, small mills typically operate at higher speeds and exhibit greater ball wear, while large mills operate at lower speeds and experience less ball wear. Currently, the specific speed of domestic mills generally falls within the range of 0.7 to 0.8, and empirical evidence indicates that a design with n/no = 0.77 is the most optimal.

3. Influence of Steel Ball and Material Filling Ratio

The figure shows the relationship curve between the steel-ball filling ratio ψ and steel-ball wear. When ψ = 60%, steel-ball wear is at its maximum. For various mills used in the cement industry, the typical filling ratio generally falls within the range of 25%–35%, corresponding to a steel-ball wear coefficient Kd of 0.75–0.84; this pattern is consistent with variations in mill power. The steel-ball filling ratio ψ and the material filling ratio V are two distinct concepts, yet they are closely related. An excessive amount of steel balls loaded can lead to increased ball wear; conversely, reducing the steel-ball filling ratio ψ and decreasing the number of balls results in less ball–material friction, thereby lowering wear—but output may fail to meet specifications. In practice, factories assess the rationality of the ball-mixing scheme by observing the following under normal mill operating conditions: the feed and discharge material flows are balanced and stable, with high and consistently uniform production; the product fineness is both qualified and uniform. During routine shutdown inspections, the observed conditions are as follows: in the first chamber, the material level essentially covers the steel balls or exposes about half of each ball; in the second chamber, the material just barely covers the balls or the segment surfaces; the material level in the first chamber is 20–50 mm higher than that in the second chamber; in the fine-grinding chamber, the steel balls should be covered by a 10–20 mm layer of material; and there should be minimal adhesion on the steel balls, steel segments, lining plates, and the feed and discharge grates.

The relationship between the material filling ratio and steel-ball wear is as follows: when the material filling ratio is approximately half of the void space between the steel balls, i.e., V = 0.6, steel-ball wear is at its maximum, with a relative wear coefficient Kd = 1. When the material completely fills the void space between the steel balls, i.e., V = 1, steel-ball wear decreases by 45%. When the material filling ratio exceeds twice the void space between the steel balls, i.e., V = 2, the wear is only about one-tenth of that observed at V = 0.6.

The ball-size distribution in a grinding mill is closely related to the clearances between the balls; therefore, the appropriateness of the ball-size distribution and the feed rate significantly affects ball wear.

Effect of Mill Filling Ratio on Steel Ball Wear

Thus, we have outlined, from a technical standpoint, the factors that influence steel-ball wear and other failure modes—knowledge that we believe will prove beneficial in your day-to-day work. Yet it is crucial to remember: technology itself is static, whereas real-world phenomena are dynamic and ever-changing; they are alive. In many cases, we must approach problems with a comprehensive, systematic, and dialectical mindset—observing, analyzing, and thinking through them holistically. The column’s author once encountered a rather intriguing incident: several years ago, during winter, the CEO of a steel-ball manufacturer from northern China sought me out, eager to discuss his challenges. After being shown into my office and offered tea, he wasted no time in launching into his predicament. It turned out that the company had been producing steel balls for more than a decade, and its products enjoyed a solid reputation among local customers. Following the company’s restructuring, the newly appointed CEO boldly pursued market expansion, propelling the business to rapid growth and widespread success. However, a series of relatively large-scale incidents involving steel-ball spalling dealt a severe blow, leaving the ambitious leader momentarily stunned. He promptly organized an internal team of engineers to review production records and investigate the root causes, while also engaging a renowned professor specializing in wear-resistant materials from a leading university to conduct a joint diagnostic assessment. Despite several rounds of exhaustive investigation, no clear cause could be identified; two batches of defective balls were scrapped, yet the outcome remained unchanged—much like “shining a lantern at one’s own reflection.” The CEO was understandably frantic. I looked up at this man before me, his eyes bloodshot, and quickly reassured him: “There’s no need to rush; we’ll surely solve this problem.” After carefully examining the chemical-composition reports, mechanical-property test reports, metallographic micrographs, and even a dark, unpolished sample of the actual product he had brought along, I also gained a thorough understanding of the company’s equipment, instrumentation, raw materials, workforce qualifications, quality-management system, and even inquired about salary and bonus practices. Yet despite all this scrutiny, no obvious weaknesses or anomalies emerged. Frowning slightly, I shifted my focus to the operating conditions. Soon, the CEO provided a detailed account of how the product was being used by the customer: a φ4.6 × 13.5 m intermediate-discharge drying mill at a plant in Northeast China, where hot air temperatures sometimes exceeded 200°C. Moreover, the plant was still in the trial-production phase, with unstable operations and frequent shutdowns and restarts of the mill. Upon hearing this, a lightbulb went off in my mind: a cursory glance at the material composition revealed a single, seemingly insignificant element that immediately raised red flags…

The real culprit was quickly identified: at the time, molybdenum ferroalloy prices were extraordinarily high, so the company adopted a high-chromium air-quenching process. However, the steel balls’ hardenability was insufficient, prompting the addition of extra manganese to improve it. Using manganese in place of molybdenum is a technique that was already mastered in East Germany in the 1970s and subsequently refined by numerous domestic firms in the 1980s—nothing particularly surprising in itself. The problem arose when the increased manganese content led to a corresponding rise in residual austenite. Under normal operating conditions for wear-resistant components, this would not normally be a major issue; the crux, however, was that the mill was blown with hot air reaching over 200°C at times, and during the trial-production phase the operation was frequently started and stopped, subjecting the material to repeated thermal cycling. As the residual austenite transformed into martensite upon cooling, its volume expanded—much like free calcium hydrating and expanding within cement paste, causing concrete to crack. In the same way, the steel balls began to spall off one after another…

The root cause was finally identified, and the solution turned out to be remarkably straightforward: the forum moderator helped him make minor adjustments to the material composition and also optimized his heat-treatment process, after which the problem was quickly and completely resolved. Years later, at a conference last year, that CEO ran into me again. He grabbed both my hands—his warmth and enthusiasm were simply beyond words. By evening, after a few drinks, we began sharing our heartfelt thoughts, which was truly moving…