Experimental Study on the Influence of Rotational Speed on Grinding Efficiency for the Vertical Stirred Mill

Abstract

The rotational speed of the agitator is one of the important parameters that affect the grinding efficiency of the vertical stirred mill. Increasing the speed will improve the grinding effect, but it will increase energy consumption, and determining a reasonable speed setting is a system issue. The effects of different speeds on energy consumption, product particle size, and grinding efficiency were analyzed in this study. An experimental vertical stirred mill was used to grind iron ore, and five different speed parameters from 175 rpm to 350 rpm were set as variables. It was found that increasing the rotational speed will increase the grinding effect, but it will trigger more energy consumption. A new evaluation index to comprehensively reflect the grinding efficiency of the mill, which was defined as the ability of a mill to grind the same product per unit of time and energy consumption, was proposed. The grinding efficiency was calculated when the particle size of iron ore powder decreased to −45, −38, and −28 μm at different speeds. It can be seen that the growth rate of energy consumption is faster than that of the percentage of particle size, which leads to a continuous decrease in grinding efficiency with the increase in rotational speed. If high processing capacity is pursued within a certain period of time, high speed can be chosen, but it will result in energy loss. On the contrary, the low speed can be chosen, if considering grinding economy.

1. Introduction

Milling is one of the most energy intensive processes in industry, contributing 2% of all global energy usage [1]. As the reserves of many nonrenewable mineral resources around the world are decreasing year by year, and the resource occurrence grade is low, the particle size is fine, and the composition is complex, a large amount of poor fine impurities and difficult-to-process ores are problematic to comprehensively utilize due to outdated grinding equipment, high energy consumption, and low efficiency [2]. A vertical stirred mill is a type of energy-saving ultrafine milling equipment that mainly works by friction grinding. Compared to traditional horizontal ball mills, it can reduce production energy consumption for coarse grinding by up to 30% [3] and has the advantages of low energy consumption, low noise, and a small footprint. It is widely used in mineral processing [4].

During the operation of the vertical stirred mill, the motor drives the agitator to rotate, which in turn drives the circular reciprocating motion of the grinding media and slurry inside the cylinder. Under the continuous squeezing, collision, and shearing of the grinding spheres, the micro-sized ore particles in the slurry are refined [5,6,7]. There is a multiphase material coupling effect between the agitator, slurry, and grinding spheres inside the cylinder, and the motion law is very complex. Different operating parameters, structural parameters, and process parameters will result in different grinding efficiencies [8,9]. The local grinding media concentration, velocity profiles, grinding media collisions, and stress energies were compared for varied total grinding media fillings and stirrer speeds by Fragnière et al. [10]. Rhymer et al. explored the fundamental dynamics of vertical stirred mills when using multiple sizes of grinding media by employing the discrete element method (DEM) [11], and the grinding performance was evaluated from five aspects: media segregation, media velocity, media force, contact energy, and power draw. A HIGmill, operated on a copper regrind circuit, was sampled under different operating conditions, i.e., tip speeds, solids contents, and media filling, and the influence on grinding efficiency was studied by Altun et al. [12]. The influence of different operating parameters on the temperature of a stirred mill was studied by Guner et al. [13], and a power number correlation was established to calculate the power under any milling condition, which determines the heat generation rate. The effects of agitator shape, including tower mill and pin mill, and the shape of the grinding media on grinding efficiency were studied by Sinnott et al. [14,15]. Therefore, reasonable parameter settings can improve the grinding efficiency of a vertical stirred mill.

The rotational speed of the agitator is one of the important parameters affecting the grinding efficiency. Several researchers found that the increase in speed resulted in an increase in fineness and specific surface area of the product [16,17]. Oliveira et al. [18] proposed that the speed had a very significant effect on predicted apparent breakage rates, increasing approximately in proportion to the mill’s specific power. Such variation was mainly due to the increase in collision frequency with speed. Increase in speed also resulted in an increase in fineness of the apparent breakage function. Fadhel et al. [19] emphasized that increasing the speed of the stirrer would increase the collision force of the grinding spheres and also increase the number of collisions. The grinding efficiency is the highest when the collision energy of the grinding spheres reaches just enough to overcome the particle crushing energy. Mankosa et al. [16,20] proposed that when the rotational speed reaches 7 m/s, vortices will form in the chamber of gravity-induced mills, which will reduce the grinding efficiency. Low speed can actually reduce the influence of vortices and improve grinding efficiency [21]. Rhymer et al. [1] mentioned that higher rotational speeds can improve grinding efficiency, but this comes at the cost of increased power consumption, and the two are conflicting. It is necessary to find a reasonable rotational speed to balance the effectiveness and efficiency of the mill. From this, it can be seen that the rotational speed has a significant impact on the grinding efficiency. Increasing the speed will improve the grinding effect, but it will increase energy consumption. There is still controversy over whether to choose high or low speeds for the mill.

Simulation and experimentation are the main means of studying the operating parameters of a vertical stirred mill [22,23,24]. The early application of DEM was used to simulate the motion law and wear behavior of grinding spheres in dry stirred mills [25,26]. Subsequently, computational fluid dynamics (CFD) was developed to simulate slurry, which belongs to the fluid phase, and the DEM–CFD method was widely used in wet stirred mills [27,28]. In order to improve the computational efficiency of coupling simulation between slurry and grinding media, the smoothed particle hydrodynamics (SPH) method was developed to model the slurry [29]. Then, the DEM–SPH method was widely used in wet vertical stirred mills [30,31]. Furthermore, the coupled particle finite element method (PFEM), finite element method (FEM), and DEM models were used to simulate the mechanical behavior of a stirred mill [32,33,34]. Although these simulation methods can reflect grinding behavior through power, force, energy, wear, etc., they cannot truly provide information on product particle size and processing capacity. On the contrary, experiments can provide information such as grinding time and product particle size, which is still the preferred research method for studying grinding efficiency [35,36,37].

In this study, a vertical spiral stirred mill was taken as the research object, and the effects of different speeds on energy consumption and product particle size were experimentally studied. The purpose of this study is to obtain the influence of speed on energy consumption and product particle size and to establish an evaluation index to comprehensively reflect the grinding efficiency at different speeds, providing a basis for selecting the speed of the mill. The sections are organized as follows. The experimental setup and parameters are introduced in Section 2. The grinding results are provided from two aspects, energy consumption and product size, in Section 3. A new evaluation index of grinding efficiency is established, and the grinding efficiency at different rotational speeds is calculated in Section 4. Finally, some important conclusions are presented in Section 5.

2. Experiment Setup

2.1. Experimental Equipment

In this study, the CSM-2.2 vertical stirred mill (CITIC Heavy Industries Co., Ltd., Luoyang, China), shown in Figure 1, is selected as the experimental equipment, and the grinding effect at different speeds could be determined through batch grinding experiments. The operating power of the motor is 2.2 kW, and it is connected to the spiral agitator through a coupling. A torque and speed tester is installed on the upper end of the coupling to obtain the real-time operating speed and torque of the spiral agitator.

The mill specifications are shown in

Table 1. Mill specifications.

Parameter	Value
Installed mill motor power (kW)	2.2
Rotational range of the spiral agitator (r/min)	173–350
Outer diameter of the cylinder (mm)	300
Height of the cylinder (mm)	500
Outer diameter of the spiral agitator (mm)	220
Net volume (m3)	0.036

. The agitator speed is 173–350 (r/min); the outer diameter and height of the cylinder are 300 mm and 500 mm, respectively. Its effective volume is 36 L, and the material is 316 stainless steel. The agitator is manufactured by Q355B, with a maximum outer diameter of 220 mm and a pitch of 175 mm. The feed slurry to the chamber is pumped via the top. After being subjected to the combined action of the agitator and the grinding media inside the cylinder for a period of time, samples can be taken from the overflow port at the upper end.

2.2. Feed Particle Size

In this study, Donganshan hematite ore is used for grinding experiments. The samples were collected from Liaoning Province, China. The mineral structure is mainly manifested as the automorphic crystal structure of hematite, the semi automorphic crystal structure of magnetite, and the alternating structure between two or more minerals. The chemical composition was detailed separately in

Table 2. Chemical composition of the samples (wt%).

Number	TFe	FeO	SiO2	MgO	Al2O3	CaO	P	S
Content	33.42	4.81	46.92	0.49	0.86	0.56	0.043	0.026

. TFe refers to total Fe, which includes iron elements in various compounds such as iron carbonate, iron oxide, etc. Its content was measured using the photometric titration method, according to the Chinese National Standard GB/T 6730.73 [38]. The FeO, other oxides, and elements were measured using the wet analysis methods according to standard GB/T 6730.71 [39]. The TFe grade in the ore is 33.42%, the FeO content is 4.81%, the SiO₂ content is 46.92%, and the main vein mineral is quartz. The density is 3400 kg/m³, and the Brinell hardness coefficient is 15.

Before the experiment, 11.2 kg of iron ore powder and 6.72 L of water are mixed to obtain a slurry with a mass concentration of 62.5% and a density of 1957.4 kg/m³. The particle size distribution of the feed sample measured by a laser particle size analyzer (Malvern Panalytical Mastersizer, Malvern, England) is shown in Figure 2.

2.3. Experimental Parameters

Grinding experiments were performed in a wet stirred mill with varying rotational speeds. The steel spheres with a diameter of 8 mm were added inside the cylinder, with a total filling amount of 49 kg, accounting for 48.5% of the cylinder volume. Five agitator speeds were set, as shown in

Table 3. Agitator speed and test number.

Number	A	B	C	D	E
Speed (r/min)	175	215	260	300	350

, including 175, 215, 260, 300, and 350 r/min, corresponding to test numbers A, B, C, D, and E, respectively. After starting the motor, the torque of the agitator was recorded every 10 min, and samples were obtained from the overflow port. A laser particle size analyzer was used to measure the content of −45, −38, and −28 μm in the samples.

3. Experiment Results

3.1. Energy Consumption

Each experiment lasted for 30 min, and the torques of the agitator were measured. Figure 3 shows the torque variation pattern of Group A. It can be seen that the torque fluctuates greatly in the initial stage (t = 0–1 min). After running for 1 min, the torque fluctuates within a certain range, indicating that the mill is operating in a stable phase. The time points with significant fluctuations in torque values are excluded, and the average torque during the stable phase is selected as the torque for that time period, corresponding to the first 10 min, second 10 min, and third 10 min, respectively. It can be seen that in the same set of experiments, there is only a small difference in the torque values of the three sampled values, indicating that the vertical stirred mill has reached a stable stage during sampling.

Comparing the average torque of each speed with the three sampled values, the trend of its variation is shown in Figure 4. It can be seen that as the speed increases, the torque value of the agitator increases continuously.

The energy consumption of the mill is not only related to torque, but also to operating speed. The energy consumption E can be calculated by multiplying power P and time t. The relationship between power P and torque T is shown in Equation (1) [40], and the results are shown in Figure 5.

$$P={\displaystyle \frac{T\times n}{9550}}$$

(1)

where n represents rotational speed.

It can be seen from Figure 5a that at the same rotational speed, energy consumption increases linearly with time. Figure 5b shows that energy consumption increases nonlinearly with speed, and the rate of energy consumption increase is greater with the increase in speed, which can be obtained from the slope in the graph.

3.2. Particle Size of the Product

The particle size of the product can reflect the actual grinding effect of the mill under a set of given experimental parameters. During the experiment, samples are taken from the overflow port every 10 min, and the particle percentage of −45, −38, and −28 μm in the samples is measured using a laser particle size analyzer. The particle size at P₈₀ is analyzed.

The experimental results are shown in

Table 4. Percentage of particle size at different times and speeds.

Number	−45 μm Particle Size Percentage (%)	−38 μm Particle Size Percentage (%)	−28 μm Particle Size Percentage (%)	Particle Size of P80 (μm)
A10	71.51	64.42	52.44	54.52
A20	83.63	76.83	63.53	41.07
A30	92.45	87.52	75.44	31.15
B10	77.32	70.02	57.24	47.83
B20	90.42	84.95	72.50	33.43
B30	96.34	92.90	82.65	26.21
C10	81.26	74.17	60.84	43.58
C20	93.24	88.80	77.63	29.63
C30	99.35	97.45	88.99	22.59
D10	83.32	76.61	63.50	41.33
D20	95.05	91.29	80.78	27.44
D30	99.60	97.96	90.41	21.44
E10	87.63	81.09	67.68	37.09
E20	96.89	93.39	83.32	25.75
E30	99.96	99.52	95.03	19.41

. Among them, the number A10 represents the sampling data of Group A at 10 min, and other numbers are used in sequence. The variation law of product percentage with speed is shown in Figure 6.

From Figure 6a–c, it can be seen that at the same rotational speed, as the grinding time increases, the percentage of the same product particle size in the screened material continues to increase. For example, in group A with a speed of 175 r/min, the product percentage of −45 μm after grinding for 10 min is 71.51%. After grinding for 20 min, it increases to 83.63%, and then it increases to 92.45% at 30 min. The variation law of the particle size of other products with grinding time at the same speed follows this law.

Further analysis shows that under the same grinding time, as the agitator speed increases, the percentage of the same product particle size in the screened material also increases continuously. For example, in Group A, with a speed of 175 r/min, the product percentage of −38 μm in Group A10 is 64.42% after grinding for 10 min, and the speed increased sequentially; the product percentages of −38 μm in groups B10, C10, D10, and E10 are 70.02%, 74.17%, 76.61%, and 81.09%, respectively.

The size of P₈₀ is calculated to reflect the particle size of the product with a percentage of 80% after grinding for a certain period of time under different parameters. As shown in Figure 6d, at the same rotational speed, the particle size of P₈₀ continuously decreases with the increase in grinding time. For example, in Group A with a speed of 175 r/min, the particle sizes of P₈₀ after grinding for 10, 20, and 30 min are 54.52, 41.07, and 31.15 μm, respectively. On the other hand, under the same grinding time, as the agitator speed increases, the particle size of P₈₀ continuously decreases. For example, in Groups A30, B30, C30, D30, and E30, the particle sizes of P80 are 31.15, 26.21, 22.59, 21.44, and 19.41 um, respectively, after 30 min. From the above analysis, it can be seen that at the same rotational speed, the grinding effect increases with the increase in grinding time. Under the same grinding time, the grinding effect increases with the increase in rotation speed.

After grinding at different speeds for a certain period of time, the energy consumption of the particle size to reach the same percentage is measured. The energy consumption when the percentage of −45, −38, and −28 μm reaches 90%, 80%, and 80% is shown in

Table 5. Energy consumption when percentage of −45, −38, and −28 μm reaches 90%, 80%, and 80%.

Number	−45 μm (90%)	−38 μm (80%)	−28 μm (80%)
A	0.1263	0.1020	0.1821
B	0.1331	0.1079	0.1837
C	0.1447	0.1174	0.2041
D	0.1593	0.1341	0.2305
E	0.1742	0.1441	0.2579

. The variation law of energy consumption with speed is shown in Figure 7.

It can be seen that the energy consumption increases with the increase in rotational speed when the particle size of the same product reaches the same proportion. For example, when the particle percentage of −45 μm reaches 90%, the energy consumption in Group A with a speed of 175 r/min is 0.1263 kWh. As the speed increases, the energy consumption of Groups B, C, D, and E increases sequentially to 0.1331, 0.1447, 0.1593, and 0.1742 kWh, respectively. From this, it can be seen that increasing the rotational speed will increase the grinding effect, but it will trigger more energy consumption. This results is consistent with the results obtained by Rhymer et al. [1], who mentioned that higher rotational speeds will lead to increased effectiveness, but it also comes at a cost of increased power draw, and a compromise would need to be made between effectiveness and efficiency. Some similar conclusions can also be found in References [17,18]. Therefore, the evaluation of grinding efficiency requires the comprehensive consideration of grinding time, energy consumption, and product particle size.

4. Comprehensive Evaluation of Grinding Efficiency

4.1. Evaluation Index

A new evaluation index to comprehensively reflect the grinding efficiency of the mill is proposed in this study. Firstly, for the same sample, the grinding efficiency is influenced by the combined effects of grinding time, product particle size, and energy consumption. The grinding efficiency η can be defined as the ability of a mill to grind the same product per unit of time and energy consumption, which can be calculated by Equation (2). η is a dimensionless evaluation index, and the value is a relative quantity rather than an absolute quantity. For the same group of grinding experiments, a larger value indicates higher grinding efficiency. If the value is normalized, the highest grinding efficiency is 1.

$${\eta }_{vt}={\displaystyle \frac{{\omega }_{vt}}{\raisebox{1ex}{$E_{vt}$}\!\left/ \!\raisebox{-1ex}{$\overline{E_t}$}\right.}}$$

(2)

where v is the rotational speed, η_vt represents the grinding efficiency at a certain speed v and grinding time t, ω_vt is the product percentage, and E_vt is the energy consumption. $\overline{E_t}$ is the average energy consumption.

4.2. Result Analysis

The energy consumption and the particle percentage of −45, −38, and −28 μm have been shown in Figure 5 and Figure 6. By substituting the above data into the Equation (2), the grinding efficiency can be calculated, and the results are shown in

Table 6. Grinding efficiency of −45 μm at different speeds.

Number	A	B	C	D	E
10 min	1.44	1.10	0.83	0.68	0.55
20 min	1.67	1.29	0.96	0.78	0.61
30 min	1.85	1.37	1.02	0.81	0.63

,

Table 7. Grinding efficiency of −38 μm at different speeds.

Number	A	B	C	D	E
10 min	1.30	1.00	0.76	0.62	0.51
20 min	1.54	1.21	0.91	0.74	0.58
30 min	1.75	1.32	1.00	0.80	0.62

and

Table 8. Grinding efficiency of −28 μm at different speeds.

Number	A	B	C	D	E
10 min	1.06	0.82	0.62	0.52	0.42
20 min	1.27	1.03	0.80	0.66	0.52
30 min	1.51	1.17	0.91	0.74	0.60

.

By plotting the data in the table into Figure 8, the variation of grinding efficiency with grinding time and speed can be obtained. It can be seen that for the same product particle size, the grinding efficiency decreases continuously with the increase in rotation speed at the same time.

Taking the −45 μm particle size after 10 min of grinding as an example, the changes in energy consumption, percentage of particle size, and grinding efficiency with respect to rotational speed were comprehensively compared. The energy consumption, percentage of particle size, and grinding efficiency under this setup were normalized to [0,1], as shown in

Table 9. The normalized energy consumption, percentage of particle size, and grinding efficiency for −45 μm.

Number	A10	B10	C10	D10	E10
Energy consumption	0.31	0.44	0.61	0.77	1.00
Percentage of particle size	0.82	0.88	0.93	0.95	1.00
Grinding efficiency	1.00	0.76	0.58	0.47	0.38

. Their variation with rotational speed is shown in Figure 9.

It can be seen that with the increase in time, both energy consumption and percentage of particle size continue to increase with the increase in speed, and the growth rate of energy consumption is faster than that of the percentage of particle size. But the grinding efficiency decreases continuously with the increase in rotational speed. If high processing capacity is pursued within a certain period of time, high speed can be chosen, but it will result in energy loss. On the contrary, the low speed can be chosen if considering the grinding economy.

There is an intersection point between grinding efficiency and energy consumption in Figure 9, which is the critical speed selection point, and the corresponding agitator speed is around 260 rpm. If the speed is lower than this, the energy consumption of the mill is relatively small and the grinding efficiency is high. On the contrary, if the speed is higher than this, the energy consumption of the mill is relatively high, and the grinding efficiency is low.

5. Conclusions

The rotational speed of the agitator is one of the important parameters that affect the grinding efficiency of the vertical stirred mill. The effects of different speeds on energy consumption, product particle size, and grinding efficiency are analyzed in this study. An experimental vertical stirred mill with 2.2 kW operating power was used to grind iron ore. Five different speed parameters (175, 215, 260, 300, 350 rpm) are set. The torque of the agitator and product particle size are recorded every 10 min. Some important results and conclusions have been obtained.

Firstly, the energy consumption of the mill at different speeds and times is measured and calculated. At the same rotational speed, the energy consumption increases linearly with time, and the energy consumption also increases continuously as the rotational speed increases during the same time period.

Then, the particle percentages of −45, −38, −28 μm and the particle size at P₈₀ in the samples are studied at different speeds and times. It was found that at the same rotational speed, the percentage of the same product particle size in the screened material continues to increase as the grinding time increases. It also increases as the agitator speed increases under the same grinding time. In addition, the particle size of P₈₀ continuously decreases with the increase in grinding time at the same rotational speed, or the agitator speed increases under the same grinding time. After grinding at different speeds for a certain period of time, the energy consumption for the particle size to reach the same percentage is measured. It was found that the energy consumption increases with the increase in rotational speed when the particle size of the same product reaches the same proportion. From the above analysis, it can be concluded that increasing the rotational speed will increase the grinding effect, but it will trigger more energy consumption. The evaluation of grinding efficiency requires comprehensive consideration of grinding time, energy consumption, and product particle size.

Next, a new evaluation index to comprehensively reflect the grinding efficiency of the mill is proposed in this study. The grinding efficiency η can be defined as the ability of a mill to grind the same product per unit of time and energy consumption, which is a dimensionless evaluation index, and the larger its value, the higher the grinding efficiency. It was found that for the same product particle size, the grinding efficiency decreases continuously with the increase in rotation speed at the same time.

Finally, the changes in energy consumption, percentage of particle size, and grinding efficiency with respect to rotational speed are comprehensively compared. It was found that with the increase in time, both energy consumption and the percentage of particle size continue to increase with the increase in speed, and the growth rate of energy consumption is faster than that of the percentage of particle size, but the grinding efficiency decreases continuously with the increase in rotational speed. If high processing capacity is pursued within a certain period of time, high speed can be chosen, but it will result in energy loss. On the contrary, the low speed can be chosen if considering the grinding economy. In future research, different ore materials and feed particle sizes should be considered as evaluation indicators of grinding efficiency, which will improve the universality of the results.