Research on the Relationship between Multi-Component Complex Ore and Its Component Minerals’ Grinding Characteristics under Abrasion Force

Abstract

The relationship between the grinding characteristics of polymetallic complex ore and its component minerals, pyrrhotite, sphalerite, and quartz, under the action of abrasion was studied, based on batch grinding experiments and theoretical analysis methods of selective grinding. The results show that when the polymetallic complex ore was subjected to the action of abrasion, the crushing effect of ore was enhanced by the existence of sphalerite, that is, sphalerite plays a positive role in the crushing effect of ore. The crushing effect of ore was reduced by the existence of pyrrhotite and quartz, that is, pyrrhotite and quartz plays a negative role in the crushing effect of ore. In addition, the sphalerite had a more prominent effect on the grinding characteristics of the ore. The grinding speed of ore and its component minerals decreased exponentially with the grinding time, and the instantaneous grinding speed of 0 min was negatively correlated with the feed sizes. The rapidly decreasing trend of the grinding speed reached the threshold when the grinding time reached 4 min. The results can provide some theoretical guidance for the study of grinding characteristics of multi-component complex ores in subsequent grinding process.

1. Introduction

Grinding is the last stage of grinding operation and is also a process to provide qualified materials for subsequent separation operations. Grinding operation is not only an essential unit of mineral processing, but is also widely used in metallurgy, building materials, electronics, and the pharmaceutical and chemical industries [1,2,3,4,5]. The literature shows [6,7] that the energy consumption of grinding operations is about 50%~70% of that of ore dressing plants, and the consumption of steel is huge. The annual consumption of steel is over 600,000 tons, accounting for 40%~45% of the cost, however, the energy efficiency of grinding process is extremely low. Therefore, optimizing grinding operations, improving grinding efficiency, and reducing grinding costs have always been the focus and difficulty of mineral processing workers.

The ball mill has been widely used in industrial production since its appearance because of its simple structure, easy adjustment, reliability, and safety [8,9]. The grinding power, the steel ball consumption, and the grinding production index are directly affected by the ball mill internal medium movement state. A set of systematic grinding theories has been proposed by Davis [10]. Since the early 1920s, a lot of research has also been carried out by relevant researchers, and the theory of the motion state of different grinding mediums had also been proposed. Among them, there are three more typical motion states of grinding medium, namely, cascading type, throwing type, and centrifugal type, as shown in Figure 1.

When the ball mill is started, the grinding medium is gradually moved upward with the rotation of the wall of the mill. When the rotation speed of the mill is too low, the grinding medium is not able to be pushed to a higher place by the friction force generated. At this time, the grinding medium will slide down along the inner surface of the ball mill and the state is called the cascading type, as shown in Figure 1A. When the rotation speed of the mill is increased, the friction force generated by the internal surface of the ball mill on the medium is also increased, which can push the medium higher. When the rotating speed is high enough to throw the medium, this state is called throwing type, as shown in Figure 1B. When the rotation speed of the ball mill is too high, such as greater than the critical rotation speed, the medium is sufficiently pushed to the highest point by the generated frictional force, and then performs circular motion. The state is called centrifugal type, as shown in Figure 1C. Among them, the throwing state is based on impact as the main action, so as to realize the grinding of the material. For the ball mill medium in the throwing state, relevant researchers have conducted a lot of research [11,12,13,14,15] and the relevant theoretical formula can be used for the corresponding quantitative description and analysis. The motion state and force of the grinding medium can be quantitatively analyzed by applying mathematical methods, which provide theoretical support for grinding practice. In the cascading state, abrasion is the main force used to achieve material grinding. It can be seen that it is quite different from the motion form of the medium in the throwing state, and the two are not related to the grinding mechanism of the material. Therefore, so far, the movement of the medium in the ball mill in the cascading state has only stayed at the level of qualitative description [16]. In addition, the previous studies were mostly biased towards a single mineral [17,18,19], but there were few reports on the link between actual complex ore and its component minerals.

2. Materials and Methods

In view of the above problems, the polymetallic complex ore and its main component minerals pyrrhotite, sphalerite and quartz were taken as the research objects in this paper. Based on the theoretical formula, the frequency converter is used to adjust the grinding speed to the cascading state. Grinding characteristic indicators, such as breakage rate, grinding speed, parameter of products t₁₀, were used for characterization, and the theoretical analysis was based on the principle of selective grinding. The relationship between the grinding characteristics of the polymetallic complex ore and its component minerals was preliminarily explored when the medium in the mill was in the cascading state. The results can provide some theoretical guidance for the study of grinding characteristics of multi-component complex ore in subsequent grinding process.

2.1. Materials

The test samples were taken from a polymetallic complex ore in Guangxi, and its main component minerals were pyrrhotite, sphalerite, cassiterite, mica, and quartz, etc. Among them, pyrrhotite, sphalerite, and quartz account for more than 90% of the ore content [14,20]. In order to ensure the representativeness and simplicity of the test, considering the mineral content of ore composition, the complex polymetallic ore is simplified as consisting of pyrrhotite, sphalerite, and quartz, which is conducive to discussing the relationship between complex ore and component minerals. The component minerals of the selected ore were pure minerals purchased from a company in Guangzhou. The surface of the ore and component minerals to be used are first cleaned and sun-dried, and then crushed, screened, mixed, and reduced. They were prepared into size fractions of 4 single samples, such as −4.75 + 3.35 mm, −3.35 + 2.36 mm, −2.36 + 1.70 mm, −1.70 + 1.18 mm.

2.2. Methods

2.2.1. Construction of the Cascading Grinding State

The test equipment is a (XMQ-ϕ240 × 90 A) conical ball mill. The material is mainly subjected to the abrasion force when the grinding medium is in the cascading state. The research shows that [7], when the outermost medium of the mill is in the cascading state, all the inner layers are in the state of falling when the mill working. The movement trajectory of the outermost medium when the mill is working is shown in Figure 2.

In the Figure 2, point A is the detachment point of the outermost medium; Point B is the highest point of the parabolic motion of the outermost medium; Point C is the fall back point of the outermost medium for parabolic motion; Point D is the point at which the outermost layer of media reaches the mill liner in parabolic motion; v is the linear velocity of the medium moving from point A to point B; m/s; R₁ is the distance between the medium layer and the center of the mill cylinder; mm; α₁ is the shedding Angle, (°); n is the rotation rate of the mill, %. When the diameter of the ball mill medium is D = 25 mm, it can be obtained from the theoretical formula [19,21] that means the mill speed n ≤ 12.43 r/min in this test and the medium in the mill can be in the cascading state.

2.2.2. Breakage Rate

The crushing degree of the material can be represented by the breakage rate of the material. In this paper, the breakage rate is used to compare and study the grinding resistance of ore and component minerals and the relationship between them under different grinding test conditions. The formula for calculating the breakage rate of materials is shown in Equation (1) below [22]:

$$\mathrm{Breakage} \mathrm{rate}=\frac{ \begin{array}{c}\mathrm{Mass} \mathrm{of} \mathrm{particles} \mathrm{of} \mathrm{specified} \mathrm{particle}\\ \mathrm{sizes} \mathrm{of} \mathrm{sample} \mathrm{before} \mathrm{grinding}\end{array}-\begin{array}{c}\mathrm{Mass} \mathrm{of} \mathrm{particles} \mathrm{of} \mathrm{specified} \mathrm{particle}\\ \mathrm{sizes} \mathrm{of} \mathrm{sample} \mathrm{after} \mathrm{grinding}\end{array} }{ \begin{array}{c}\mathrm{Mass} \mathrm{of} \mathrm{particles} \mathrm{of} \mathrm{specified} \mathrm{particle}\\ \mathrm{sizes} \mathrm{of} \mathrm{sample} \mathrm{before} \mathrm{grinding}\end{array}}$$

(1)

2.2.3. Grinding Speed

The meaning of grinding dynamics is that the disappearance rate of a certain particle size in the ball mill is proportional to the content of this particle sizeand its expression is as follows [23]:

$$\frac{dR}{dt}=-kR$$

(2)

After integrating Equation (2), the first-order grinding dynamics expression can be obtained as follows:

$$R=R_0{e}^{-kt}$$

(3)

However, in the actual production process, the expression of n-order grinding dynamics is more consistent with the actual situation and its mathematical expression is as follows [24]:

$$R=R_0{e}^{-k{t}^n}$$

(4)

Taking the derivative of the n-order grinding dynamic Equation (4) with respect to time, the grinding velocity can be expressed as follows:

$$V=\frac{dR}{dt}=\frac{d\left(R_0{e}^{-k{t}^n}\right)}{dt}=-R_{0}k{t}^{n-1}n{e}^{-k{t}^n}$$

(5)

where V is the grinding speed at the grinding time, %/min; R₀ is the production rate of the feeding ore larger than a certain particle size, %; R is the output of the ore grinding products larger than a certain particle size after the t time, %; k and n are grinding kinetic parameters. Negative sign indicates coarse fraction reduction.

2.2.4. t₁₀ Parameter

The parameter t_xx means the cumulative yield under the sieve of the feed size 1/xx grinding product. The t₁₀ is the cumulative yield under sieve of grinding products with a feed size of 1/10, which can represent the fineness of grinding products. The larger the parameter t₁₀ is, the finer the grinding product is. The t₁₀ is also often used as an important parameter for grinding modeling in grinding process research [25,26]. The literature shows that [27,28,29] t₁₀ is the only parameter related to the particle size distribution of grinding products. The t₁₀–t_xx relation curve is only related to the nature of the material. If the parameter t₁₀ can be obtained, the t_xx family curve can be obtained. The t₁₀–t_xx relation curve can represent a complete product particle size distribution, so parameter t₁₀ can represent the particle size characteristics of grinding products.

2.2.5. Evaluation Method for the Relationship between Complex Ore and Component Minerals

In the actual grinding process, the component minerals in the multi-component complex ore have different physical, chemical, and mechanical properties, so the materials will show different grinding characteristics when they are subjected to grinding action [30,31]. This is the phenomenon of selective grinding. Component minerals with low hardness, high toughness, and many structural defects are easier to be ground and the opposite are more difficult to be ground. This difference of component minerals in the ore leads to the interaction of component minerals during grinding. This is the negative grinding effect of hard minerals on soft minerals and the positive grinding effect of soft minerals on hard minerals [32,33,34,35]. In order to further study the relationship between the grinding characteristics of polymetallic composite ore and its component minerals, this paper introduces the above principles and preliminarily discusses the relationship between the polymetallic composite ore and its component minerals under grinding action. The specific evaluation method is explained as follows: if the degree of fragmentation of a component mineral is less than the degree of ore, it means that the component mineral is a hard mineral relative to the ore. In this case, this component mineral is defined as a negative effect against the fragmentation of complex ore. On the contrary, it is considered that this component mineral plays a positive role in this complex ore breakage.

3. Results and Discussion

3.1. Comparative Test of Breakage Rate

According to Equation (1), the breakage rate of polymetallic complex ore and its component minerals under different feeding particle sizes was calculated based on the grinding test data, and the relation diagram of its change with grinding time was made. The results are shown in Figure 3.

It could be seen from Figure 3a–d that the change rule of the breakage rate of component minerals was similar to that of ore. With the extension of the grinding time, the more sufficient abrasion force was applied to the ore and component minerals, and the breakage rate of different materials gradually increased. At the same time, comparing the slope of the breakage rate curve of different materials could be known. At the early stage of grinding, the breakage rate of materials with different feed sizes increased greatly, and began to decrease slowly when the grinding time reached 4 min. According to the analysis of Figure 3a–d, it can also be seen that the breakage rate of fine particle size grain is higher than that of coarse particle size grain, that is, the breakage rate of material is negatively correlated with the feed sizes. The reason for this phenomenon is that the specific surface area of fine particle size material is larger than that of coarse particle size material when materials with the same properties are subjected to abrasion force. That is to say, as the feed particle size becomes smaller, the contact area between the material and the medium in the mill was larger. That is, the greater the “effective area” in contact, the greater the abrasion force on the whole material. Therefore, the breakage rate of fine particle size is higher than that of coarse particle size.

In order to further analyze the relationship between the breakage rate of ore and its component minerals in the cascading state during grinding, with the change of grinding time, the breakage rate of different materials with the same feeding size was comparatively analyzed and studied and the results are shown in Figure 4.

According to the analysis in Figure 4a–d, the breakage rate of the ore and its component minerals is positively correlated with the grinding time. The comparative analysis of the breakage rate curve of the ore and its component minerals showed that under the same feed size and different grinding times, the breakage rate of sphalerite was the largest, followed by ore, then pyrrhotite, and then quartz. Therefore, when the material is subjected to abrasion force, the order of abrasion force on its component minerals is sphalerite > ore > pyrrhotite > quartz. By analyzing Figure 4a–d again, it could be seen that the breakage rate curve of the ore was always “sandwiched” between the breakage rate curve of its component minerals pyrrhotite and sphalerite under the conditions of different feed sizes, and the breakage rate curve of the component mineral quartz was always below the breakage rate curve of the ore. According to the theoretical analysis in Section 2.2.5., when the ore is subjected to grinding, the crushing effect of ore is enhanced by the existence of the component sphalerite, that is, sphalerite plays a positive role in the crushing effect of ore. The crushing effect of ore was reduced by the existence of the components pyrrhotite and quartz, that is, pyrrhotite and quartz play a negative role in the crushing effect of ore.

3.2. Comparative Test of Grinding Speed

The grinding kinetic equation of n-order was built by the applying Equation (4) and the MATLAB curve fitting toolbox. The grinding kinetic parameters n and k of the four single particle size materials can be directly calculated. The parameters n and k are shown in

Table 1. Grinding kinetic parameters n and k of different size fraction.

Size Fraction /mm	Ore		Pyrrhotite		Sphalerite		Quartz
	n	k	n	k	n	k	n	k
−4.75 + 3.35	0.3011	0.2391	0.3168	0.1915	0.3855	0.2950	0.5454	0.1170
−3.35 + 2.36	0.3747	0.2820	0.3700	0.2589	0.4036	0.3284	0.3404	0.2029
−2.36 + 1.70	0.3278	0.3278	0.3986	0.2699	0.3881	0.3649	0.3736	0.2438
−1.70 + 1.18	0.2834	0.4845	0.4073	0.3132	0.3058	0.5154	0.4252	0.2608

. By substituting the obtained grinding kinetic parameters n and k into Equation (5), the grinding velocities of polymetallic complex ore and its component minerals can be calculated under different feed sizes and different grinding times when the grinding medium is in the cascading state. The instantaneous grinding speed of the material at the grinding time of 0 min was calculated by applying the interpolation approximation method in the MATLAB curve fitting toolbox. The changing relationship between the grinding speed of different feed sizes on ore and its component minerals with the grinding time was shown in Figure 5.

By comparing Figure 5a–d, it can be seen that when the grinding medium was in the cascading state, the grinding speed of the ore and its component minerals decreases exponentially. At the same time, the instantaneous grinding speed was negatively correlated with the feed sizes at the grinding time of 0 min. When the grinding time of the ore and its component minerals reached 4 min, the grinding speed reached the threshold of a rapid downward trend. The main reason for this phenomenon was that with the prolongation of grinding time and the continuous decrease in feed sizes, the fine particle size material gradually increased. In other words, the probability of acting on the coarse particle size would be gradually reduced by the grinding medium with the extension of the grinding time and the fine particle size material generated at the same time will also be formed into a particle bed so that the grinding effect of the medium on the material would be weakened [36]. Therefore, the grinding speed of the material decreases gradually after the grinding time reaches 4 min.

In order to further analyze the relationship between the grinding speed of ore and its component minerals, the grinding speed of different materials with the same feed particle size was comparatively studied with time and the results were shown in Figure 6.

According to the analysis of Figure 6a–d, the grinding velocity curves of the ore and its component minerals are tight on the right and loose on the left. That is, the distance between the grinding velocity curves of ore and its component minerals becomes smaller and smaller with the grinding time. At the same time, it could also be found that the left opening of the grinding velocity curve gradually closes with the decrease in the feed sizes. That is, when the grinding time is 0 min, the gap in instantaneous grinding speed of different materials gradually decreases with the decrease in feed sizes. The reason is that with the decrease of feed size, the contact area between material and medium in the mill gradually approaches saturation [37,38]. The abrasion forces of different materials gradually became close to each other and the situation in which the particles could not be effectively sandwiched between the medium and the cylinder wall of the mill was reduced. Therefore, in addition to the differences in the properties of different materials, when subjected to the same abrasion force, the difference in the instantaneous grinding speed of different materials gradually decreases when the grinding time was 0 min.

3.3. Comparison of Particle Size Characteristics of Grinding Products

Based on the grinding test data, the respective product parameter t₁₀ of the material was calculated, so that the relation curve between t₁₀ and grinding time was drawn, and the result was shown in Figure 7.

By comparing the analysis of Figure 7a–d, it could be seen that when the mill medium was in the cascading state, the grinding product t₁₀ of fine particle size was larger than that of coarse particle size. That is, the grinding crushing degree of fine particle size is larger than that of coarse particle size. By observing the overall slope of the t₁₀ curve of grinding minerals with different particle sizes of different materials, it can be seen that the slope of this curve gradually increases with the decrease in feed particle size. It could be seen that when the material was subjected to abrasion action and the finer the feeding particle size, the more adequate the abrasion action. This was consistent with the analysis results of the change law of material breakage rate. By comparing the smoothness of the grinding product t₁₀ curve of different materials, it could be found that there seems to be some linear relationship between grinding products’ t₁₀ and grinding time when materials were subjected to grinding action. In order to further analyze the relationship between the particle size characteristics of grinding products of ore and its component minerals under abrasion action, the comparative study was conducted on the relationship between product parameter t₁₀ of different materials with the same feed size and the change of time, and the results are shown in Figure 8.

According to the analysis in Figure 8a–d, it can be seen that under the conditions of the same feed size and the same grinding time, the t₁₀ curve of the grinding product of the ore was always “sandwiched” between sphalerite, pyrrhotite, and quartz, and the t₁₀ curve of the grinding product of sphalerite was above the ore, while the t₁₀ curve of the grinding product of pyrrhotite and quartz was below the ore. The analysis shows that the anti-crushing capacity of ore and component minerals is: sphalerite < ore < pyrrhotite < quartz. When the ore was subjected to abrasion force, based on the theoretical analysis of 2.2.5, it could be seen that the ore crushing effect was enhanced by the existence of sphalerite. That is, sphalerite plays a positive role on the ore breakage effect, and the ore crushing effect was reduced by the existence of pyrrhotite and quartz, which is consistent with the breakage rate analysis results. It can also be seen from Figure 8a–d that the overall slope of the t₁₀ curve of the material grinding product was larger with the decreases of feed sizes. This showed that the smaller the feed particle size was, the faster the t₁₀ growth rate of the grinding product of the material, and the better the grinding effect of the material. Based on the above analysis, when the material was subjected to abrasion force, the change law of grinding product t₁₀ of component minerals significantly affects the change law of grinding product t₁₀ of ore, and the change curve of grinding product t₁₀ of component sphalerite was more similar to that of ore. It could be seen that component sphalerite has a more prominent influence on the grinding characteristics of ore. The results can provide some theoretical guidance for the study of grinding characteristics of multi-component complex ores in subsequent grinding processes.

4. Conclusions

• The breakage rate of ore and its component minerals has a positive correlation with grinding time and a negative correlation with feed sizes. When the material is subjected to abrasion force, the order of abrasion force on its component minerals is sphalerite > ore > pyrrhotite > quartz. The crushing effect of ore was enhanced by the existence of the component sphalerite, that is, sphalerite plays a catalytic role in the crushing effect of ore. The crushing effect of ore was reduced by the existence of the components pyrrhotite and quartz, that is, pyrrhotite and quartz play a negative role in the crushing effect of ore.
• The grinding speed of ore and its component minerals decreases exponentially with the grinding time. The instantaneous grinding speed of 0 min was negatively correlated with the feed sizes, and the decreasing trend of the grinding speed reached the threshold when the grinding time reached 4 min.
• The grinding products t₁₀ of the ore and its component minerals were positively correlated with the grinding time and negatively correlated with the feed sizes. The t₁₀ curve of the grinding products of the ore was always “sandwiched” between the t₁₀ curve of the grinding products of the component minerals at the same feed size. It is consistent with the results of breakage rate analysis, that is, the sphalerite plays a positive role in the crushing effect of ore, while the pyrrhotite and the quartz play a negative role in the crushing effect of ore. When the ore is subjected to abrasion force, sphalerite has a more prominent influence on the grinding characteristics of the ore. The results can provide some theoretical guidance for the study of grinding characteristics of multi-component complex ore in subsequent grinding processes.