Ball Mill Steel Ball Disorder Phenomenon

During work, we frequently receive inquiries about the disorder of grinding-media balls inside the mill and about reverse grading. Because these questions often arise unexpectedly, we can only provide impromptu answers, which are often inadequate and may even appear to be mere perfunctory responses. This paper offers a preliminary analysis of the causes of this phenomenon, along with preventive measures and troubleshooting methods, with the aim of sharing these insights with employees at Conch Group. Given the author’s limited expertise, any shortcomings are welcome to be pointed out.

I. Overview

Nowadays, ball mills are predominantly used for the final grinding of cement. As the material is ground from the mill inlet to the outlet, its particle size progressively decreases. Based on the comminution characteristics of the material, the steel grinding media within the mill should also be graded from coarse at the inlet to fine at the outlet.

To meet the aforementioned requirements, ball mills are typically divided into multiple chambers along the axis to establish a corresponding relationship between the grinding media and the material. However, due to numerous constraints, the number of chambers cannot be increased indefinitely; in practice, mills are usually configured with only two or three chambers. Consequently, after chamber division, the steel balls only roughly satisfy the intended size distribution. Within each chamber, fluctuations in material filling and operational conditions often result in an uneven or even reverse distribution of ball sizes, making it difficult to achieve the desired correspondence between ball diameter and particle size.

Following the introduction of classification liners, grinding mills—beyond simply dividing the mill into chambers—often install classification liners in the longer chambers as well. These liners help distribute the grinding media within the mill according to optimal specifications, thereby achieving the best possible grinding performance.

To better illustrate the issues of steel-ball size distribution disorder and reverse grading, we will begin by examining the grading principle underlying the classification liners in grinding mills, and then jointly explore the root causes of these problems as well as appropriate remedial measures, with the aim of preventing their recurrence in the future.

II. Grading Principle of Graded Lining Plates

1. Rotational and抛落 motion of steel balls

As shown in Figure 1, due to the rotation of the mill, the steel ball located at the lower portion of the mill’s cross-section (point A in Figure 1) experiences a downward-directed centrifugal force (P in Figure 1) generated by the mill’s rotation, which, together with its own gravitational weight, acts vertically on the liner. (For analytical convenience, the additional gravitational forces exerted by other steel balls above the surface layer are disregarded.) This results in a certain frictional force between the liner and the steel ball (for simplicity, we temporarily set aside the direct thrust effects arising from the irregularly shaped liners with sharp edges). When the mill speed is relatively high, this frictional force is sufficient to keep the steel ball nearly synchronized with the mill liner; under the action of friction, the steel ball is gradually lifted. As the lifting height increases (to point B in Figure 1), the vertical component of the steel ball’s gravitational force acting on the liner (G1 in Figure 1) progressively decreases. Moreover, after the steel ball reaches the horizontal diameter of the mill, its motion reverses and becomes opposite to the direction of the centrifugal force (points C and D in Figure 1). When the steel ball attains the top of the mill shell, the vertical component of gravity reaches its maximum value—equal to the steel ball’s own weight. If the steel ball’s self-weight is less than or equal to the centrifugal force, the ball will simply follow the mill shell in synchronous circular motion, thereby failing to provide effective grinding. To address this, the design reduces the mill shell’s rotational speed so that the vertical component of gravity equals the centrifugal force before the steel ball reaches its highest point; this point is defined as the ball’s drop point. Once the steel ball reaches the drop point and continues moving forward, the vertical component of gravity exceeds the centrifugal force and becomes dominant. Under the combined influence of inertia and gravity, the steel ball then follows a parabolic trajectory (points E and F in Figure 1), thus achieving a dropping motion of the steel balls across the mill’s cross-section. The trajectories of steel balls in different layers when they are piled up are similar to the analysis above; however, since this is not the main focus of the present paper, further details are omitted. In addition, the threshold for friction varies in response to changes in the vertical component of gravity acting on the liner; likewise, the equilibrium relationship between friction and the component of gravity parallel to the liner is also outside the scope of this paper and will not be discussed in detail here.

P — centrifugal force acting on the steel ball as it rotates during grinding; G — gravitational force on the steel ball.

G1—The component of gravity perpendicular to the mill shell; G2—The component of gravity parallel to the tangent.

2. Classification Mechanism

Along the axial direction of the mill, to ensure that the steel balls are graded from large at the mill head to small at the mill tail—thus matching the particle size distribution of the material being processed—we commonly employ graded liners.

Figure 2: Axial Cross-Sectional Diagram of Gravitational Force Decomposition on the Classification Liner for Steel Balls

g — gravitational force on the steel ball; g₁ — component of the gravitational force along the inclined plane in the axial cross-section (lateral force);

g 2—component of gravity acting perpendicular to the liner;

As shown in Figure 2, the grading liner forms an inclined plane in the axial cross-section of the mill, with its high end at the discharge end and its low end facing the feed end. On this inclined surface, the gravitational force acting on a steel ball can be resolved into two components: one perpendicular to the incline, which is supported by the incline itself (denoted as g₂ in Figure 2), and the other, referred to as the lateral force (denoted as g₁ in Figure 2), which is parallel to the incline and directed toward the bottom of the slope. Under the action of this lateral force, the steel ball tends to move toward the feed end. However, as long as the ball is still rotating along the inner wall of the mill and has not yet reached the point of free fall, the lateral force is effectively constrained by the balls on its left side and thus exerts no net effect; the ball can only follow the standard local circumferential motion dictated by the rotation of the mill shell. Once the ball enters the free-fall zone, though, the constraint imposed by the lateral force is lifted, allowing the force to pull the ball and deflect its trajectory toward the feed end. Consequently, with each revolution of the mill, the ball’s impact point shifts progressively toward the feed end relative to the initial cross-sectional plane—meaning that, in the absence of any other restraining factors, the grading liner causes the balls to advance in a helical path toward the feed end. In this way, all the balls that come into contact with the grading liner are drawn toward the feed end; constrained by the available space within the mill and by friction among the balls, they ultimately form a slightly inclined accumulation surface that is higher at the feed end and lower at the discharge end. Because larger balls have greater inertia than smaller ones, they are better able to occupy the positions they seek, forcing the smaller balls to yield and thereby achieving a size-segregated arrangement in which larger balls predominate at the head of the charge.

Another important factor is the wind-classification effect. The action of wind causes the smaller balls to move toward the mill’s discharge end more readily than the larger balls. This is because, during the ballistic fall of the steel balls, the wind force is directly proportional to the ball’s cross-sectional area and inversely proportional to its inertial force. The cross-sectional area is proportional to the square of the ball diameter, while the inertial force is proportional to the ball’s mass—and thus to the cube of the ball diameter. Consequently, the influence of wind force is inversely proportional to the ball diameter: the smaller the ball, the greater the driving force that propels it toward the mill’s discharge end.

Wind force ∝ cross-sectional area Wind force ∝ sphere diameter squared Wind force ∝ 1

Inertial force Ball diameter 3 Ball diameter

III. Mechanism of Gradation Disruption and Inverse Grading

During normal operation and running of the mill, despite the presence of disturbances such as feed material, the trajectories and overall patterns of the grinding media within the mill remain essentially unchanged.

When the following circumstances arise, the situation will undergo a trend-based shift. For the sake of clarity, the author divides this developmental trend into four stages in the following discussion.

Phase 1: Temporary Gradation Disruption

During operation, if material is fed in too rapidly in a single batch—whether at startup or during running—the filling effect of the material causes a localized, short-term slope within the mill, with a higher grinding head and lower grinding tail. This phenomenon is analogous to the classification principle of the classifier lining; in this region, the steel balls inside the mill will undergo reverse classification, leading to slight disruption of the gradation.

If the mill’s throughput remains adequate, as the material fill level within the mill gradually becomes more uniform along the axial direction, the sloping surface will either disappear or flatten out, allowing the mill to establish a new equilibrium at a consistent ball-to-material interface and thereby achieve operational stability. Furthermore, as the mill runs for longer periods, the back-rolling steel balls will progressively realign under the action of the classification liners. If we open the mill for inspection before this realignment has fully occurred, we can readily detect evidence of a disordered ball-size distribution.

Phase 2: Moderate Gradation Disturbance

The above operational errors, if they exceed the mill’s self-restoring limit for balance, will cause the mill to drift toward overfilling. At this point, as the material level inside the mill rises, the height difference in the lifting of the grinding balls decreases, and the ballistic motion transitions to a cascading or tumbling motion, virtually eliminating the classification function of the grading liners (as previously discussed, the grading liners are effective only during the ballistic phase of the grinding balls). Consequently, the sloping material surface accelerates the tendency for grade distribution to become disordered. Upon opening the mill for inspection, one finds large and small balls mixed together or distributed in a random pattern.

Phase 3: Severe Gradation Disturbance

If no operational intervention is implemented after the onset of the second stage, the mill will operate under conditions of overgrinding. Under these circumstances, the motion of the grinding media and the material will shift from cascading to tumbling and sliding; driven by the sloping accumulation of material, segregation will become dominant, and the distribution of grinding balls within the mill will rapidly evolve from a disordered state toward a reverse grading pattern. Upon opening the mill for inspection, one observes segregated accumulations of large and small balls, yet without any consistent or predictable pattern.

Phase Four: Reverse Grading

In the third stage, the phenomenon recurs: frequent, abrupt additions of feed followed by intensive grinding, which ultimately leads to reverse grading. Upon opening the mill for inspection, steel balls of similar size are found clustered in distinct bands, resembling zebra stripes or a reverse grading pattern.

IV. Common Causes of Steel Ball Disorder During Operation and Corresponding Countermeasures

Reverse grading is an extreme manifestation of ball segregation, whereas in production practice, grade segregation is more common. The underlying causes can be summarized as follows:

1. Feeding is too rapid at the start of grinding; likewise, excessive feeding during operation can easily lead to overfilling and resulting gradation disruption. It is recommended to feed in small, frequent increments, gradually increasing to the target feed rate. The author suggests establishing a feed-rate curve and adhering to it rigorously. At the same time, the tail-end ventilation rate should be synchronized with the feed rate throughout the operation.

2. When feeding is interrupted for any reason and feed is then added too rapidly, this situation is even less given due attention in production practice. Therefore, after a feed interruption, feed addition must still be carried out in accordance with the feed-in curve.

3. Feed supply is unstable, fluctuating unpredictably and causing material surges; in severe cases, amplitude-modulated oscillations may occur. It is recommended to standardize on-site operations and ensure consistent operational practices across all three shifts.

4. During operation, repeatedly pushing the mill to its production-capacity limit causes the mill’s operating conditions to oscillate between a partially loaded state and normal operation; this phenomenon is the most common occurrence in production. Each time such a push is attempted, the ball-size distribution becomes increasingly disrupted, grinding efficiency declines, and, due to back-classification or ball segregation, large particles readily bypass the partition plates in large quantities, thereby reducing both internal ventilation and material throughput and accelerating the deterioration of mill performance. Yet each time a bold push fails, operators often simply revert to the previous “normal” operating point—unaware that yesterday’s “normal” is no longer today’s “normal.” This stopgap approach only exacerbates the deterioration, ultimately leading to a steady decline until the mill’s performance can no longer be maintained. Bold experimentation and exploration are essential in production if higher performance is to be achieved; however, when a push fails, it is crucial to adopt a corrective strategy that overcompensates to restore stability: first reduce the mill’s output slightly below the pre-push level to establish a stable operating platform, then fine-tune the ball-size distribution before returning to the previously attained near-maximum operating point. Following thorough analysis and reflection, a new target and action plan for the next push should be formulated.

5. Wear failure and installation errors of graded liners require no further elaboration.

In the foregoing brief discussion, each factor was analyzed in isolation for the sake of clarity; however, in actual production, these factors rarely act independently. Rather, they typically interact synergistically—sometimes reinforcing one another, sometimes exhibiting a primary–secondary relationship, sometimes shifting over time, and sometimes changing as their intensity evolves. Nevertheless, as long as the principal underlying issue is identified, the fundamental nature of the problem remains constant, allowing for timely mitigation or resolution.

Conclusion:

1. Adding the charge too rapidly in a single batch is the primary cause of ball-size distribution disruption.

2. Overfilling of the mill, which weakens the function of the classification liners, is another common cause of grade distortion.

3. Repeated instances of overfeeding, leading to overgrinding, are the root cause of reverse classification in the mill.