Energy Efficiency Measurement of Mechanical Crushing Based on Non-Contact Identification Method

Abstract

The efficiency of mechanical crushing is a key metric for evaluating machinery performance. However, traditional contact-based methods for measuring this efficiency are unable to provide real-time data monitoring and can potentially disrupt the production process. In this paper, we introduce a non-contact measurement technique for mechanical crushing efficiency based on deep learning algorithms. This technique utilizes close-range imaging equipment to capture images of crushed particles and employs deeply trained algorithmic programs rooted in symmetrical logical structures to extract statistical data on particle size. Additionally, we establish a relationship between particle size and crushing energy through experimental analysis, enabling the calculation of crushing efficiency data. Taking cement crushing equipment as an example, we apply this non-contact measurement technique to inspect cement particles of different sizes. Using deep learning algorithms, we automatically categorize and summarize the particle size ranges of cement particles. The results demonstrate that the crushing efficiencies of ore crushing particles, raw material crushing particles, and cement crushing particles can respectively reach 80.7%, 70.15%, and 80.27%, which exhibit a high degree of consistency with the rated value of the samples. The method proposed in this paper holds significant importance for energy efficiency monitoring in industries that require mechanical crushing.

1. Introduction

Mechanical crushing equipment holds a pivotal position in industrial production, finding widespread application in various sectors such as building materials, chemicals, metallurgy, and mining [1,2,3,4]. As global awareness of energy conservation and emission reduction continues to grow, enhancing the crushing efficiency of mechanical grinding equipment, reducing energy consumption, and mitigating environmental pollution have emerged as focal points for various industries [5]. The crushing efficiency of mechanical crushing equipment not only concerns the control of production costs for enterprises but also has profound implications for the sustainable development of society [6]. Therefore, effectively evaluating the energy efficiency of mechanical grinding equipment is crucial for promoting energy conservation and emission reduction efforts.

Mechanical crushing energy pertains to the energy expended by a crushing unit in the process of breaking down rock, which is a crucial parameter in optimizing the efficiency of crushing motors and minimizing energy usage in practical applications. The fundamental aspect of crushing theory revolves around investigating the variations in the degree of impact crushing from the standpoint of crushing energy. This primarily involves establishing a quantitative correlation between the crushing energy and the parameters that define the crushing degree. For instance, Narayanan and Whiten [7] established a correlation between particle size based on drop hammer test data. Banini [8] conducted comprehensive drop hammer tests on eight ore types, including gold, copper, lead-zinc ore, and quarry materials, encompassing a range of eight sizes and nine specific energy levels. From this, a crushing model was proposed that incorporates the impact of particle size, building upon the original Bourgeois model. Furthermore, Vogel and Peukert [9] formulated a fracture probability model rooted in Weibull statistics’ fracture mechanics model, outlining the material properties’ influence and the method for determining model parameters. Tavares [10] devised a particle impact crushing model grounded in continuous loss mechanics, examining particle breakage under cyclic loading and analyzing the resulting particle size distribution. The current advancements in crushing energy research provide a robust basis for evaluating the crushing energy efficiency of mechanical equipment.

Currently, there are numerous commonly used methods for evaluating the energy efficiency of mechanical crushing [11,12]. The energy consumption indicator method assesses the energy efficiency of crushing equipment by measuring its energy consumption during the crushing process, which illustrates that the crushing and grinding of particles per unit mass into different particle sizes have an energy efficiency of varying degrees. This approach typically involves recording indicators such as electrical energy consumption or fuel consumption during the operation of the crushing equipment and then comparing them with the crushing effectiveness of the processed materials for analysis [13]. The crushing efficiency indicator method determines the energy efficiency of crushing equipment by evaluating its crushing effect on raw materials. This method realized that the efficiency generally maintains a value between 56.5–70%. The energy efficiency modeling method usually establishes an energy efficiency model based on the characteristics of the crushing process and derives the energy efficiency parameters of the equipment through simulation and calculation [14]. The experimental testing method evaluates the energy efficiency by conducting crushing experiments on standardized samples. In these experiments, various parameters, such as material properties and crushing equipment settings, can be controlled to accurately assess the energy efficiency performance of the equipment [15]. However, the existing methods primarily rely on contact-based measurement techniques for evaluating energy efficiency parameters. This approach not only prevents real-time monitoring of energy efficiency during the crushing process but also has a certain impact on the production process.

The image recognition functionality powered by machine learning has been extensively utilized across various fields, including industrial applications, healthcare, security, and autonomous driving [16]. Notably, machine learning algorithms possess the ability to learn features and patterns from extensive training data, enabling accurate identification of target objects in images [17]. In the context of grinding equipment, by employing deep learning on training samples of different particle sizes, these algorithms can effectively recognize particles of varying diameters [18]. Deeply trained image recognition algorithms exhibit rapid processing and real-time monitoring capabilities, capturing image information in real-time during the production process and swiftly analyzing and identifying the particle size with precision [19]. This real-time monitoring functionality facilitates the prompt detection and adjustment of any abnormalities in the production process, thereby enhancing production efficiency and product quality [20]. Furthermore, machine learning algorithms possess a certain degree of adaptability, allowing them to adjust and optimize based on factors such as lighting and angles in different environments, thus adapting to diverse production scenarios and working conditions [21]. Once a machine learning model is thoroughly trained and optimized, it typically requires minimal human intervention, automatically performing image acquisition, recognition, and analysis processes. This reduces human resource costs and minimizes the possibility of human error [22]. Due to the inherent characteristics of machine learning algorithms, they can continuously optimize and improve their models by collecting additional data and feedback, enhancing their performance in practical applications over time [23,24,25].

In this paper, we introduce machine learning algorithms to the assessment of mechanical crushing energy efficiency. The close-range imaging equipment is employed to capture crushed particle images, and the deeply trained algorithms are utilized to extract particle size statistics based on the symmetrical logical structure. Through experimental analysis, we establish a correlation between particle size and crushing energy, enabling the computation of efficiency data. Using cement crushing equipment as a case study, our non-contact measurement technique inspects particles of various sizes. Deep learning algorithms categorize and summarize particle size ranges, facilitating non-contact monitoring and energy efficiency evaluation of grinding equipment without disrupting production. This approach offers a smarter, more efficient solution for energy efficiency parameter assessment.

2. Theoretical Analyses

2.1. Deep Learning Algorithms

In deep learning algorithms, the surface image of a sample is read using OpenCV’s imread function, and the original image is converted into a grayscale image. Adaptive threshold (AT) is then applied for image binarization, followed by morphological denoising, dilation, and erosion to extract the boundaries of particulate matter. The convolution kernel for morphological denoising is fine-tuned, and the image is filtered using the Fast Fourier Transform. Sobel operators and image fusion techniques are utilized along with semantic segmentation to classify the original image into particulate regions. Selected regions from the classified areas are manually annotated to create training and testing sets for deep learning. TensorFlow is then employed to train a recognition model for the specific category of particulate matter. This model is applied to identify samples in the testing set, automatically extracting the particulate matter from the images. Each individual particle is binarized using OpenCV, and the bounding rectangle or circumcircle of the particle is determined. After reading the diameters of all particles, they are summarized. The gradient operator for image segmentation is defined as follows [26]:

$$G(x,y)=\sqrt{{\nabla }_x{f}^2(x,y)+{\nabla }_y{f}^2(x,y)}.$$

(1)

To reduce the computational complexity, Equation (1) can be approximated by considering the absolute values

$$G(x,y)\cong \left|{\nabla }_{x}f(x,y)\left|+\right.\right.\left|{\nabla }_{y}f(x,y)\right|.$$

(2)

In image segmentation, we use gradients to express the variations of gray levels of pixels. In our theory, the Roberts operator obtained the highest efficiency, so we chose this algorithm to represent the gradients of the images. We originate from a 3 × 3 matrix in the pixel space shown in Figure 1 to calculate the gradients.

The Roberts operator could be expressed as

$$d_x=\left[\begin{array}{cc}-1& 0\\ 0& 1\end{array}\right], d_y=\left[\begin{array}{cc}0& -1\\ 1& 0\end{array}\right],$$

(3)

According to Equation (3), the diagonal Robert operator of image discretization is obtained by using difference as

$$\left\{\begin{array}{l}{\nabla }_{x}f(x,y)=f(x,y)-f(x-1,y-1),\\ {\nabla }_{y}f(x,y)=f(x-1,y)-f(x,y-1).\end{array}\right.$$

(4)

Thus, the gradient of the operator’s pixel center point P5 is

$$\left\{\begin{array}{l}{g}_x=\frac{\partial f}{\partial x}=P9-P5,\\ g_y=\frac{\partial f}{\partial y}=P8-P6.\end{array}\right.$$

(5)

After segmentation processing, the blocks are manually annotated to summarize the databases for the front and back sides, respectively. These databases are then used for training to obtain standard values corresponding to different particle diameters. Subsequently, a standard particle size database is established.

For the research on the relationship between the crushing energy and particle size of products, due to the working characteristics of the high-pressure roller mill, the material is only subjected to compressive force in the compression zone. Therefore, the corresponding force-bearing area is the upper half of the pressure roller. Consequently, the compressive force F of the pressure roller is calculated as

$$F=1000P\frac{D}{2}L,$$

(6)

where F represents the compressive force exerted by the pressure roller on the material, P stands for the working pressure of the pressure roller, L is the length of the pressure roller, and D denotes the diameter of the roller. The torque T caused by the compressive force F in the vertical direction is calculated as

$$T=F\sin (\beta )\frac{D}{2},$$

(7)

where β is half of the angle at which laminated crushing occurs. Since the roller mill has two pressure rollers, the total power is twice the product of the compressive force F in the vertical direction and the linear velocity v of the pressure roller. Therefore, the power P is calculated as

$$P=2F\sin (\beta )\nu .$$

(8)

Therefore, the unit energy consumption W_i of the roller mill is calculated as

$$W_i=\frac{P}{d_i},$$

(9)

where d_i is the average diameter of the product.

2.2. Mechanical Crushing Energy

In the determination of mechanical crushing energy, the energy absorbed by particles during the mechanical crushing process is [10]

$$W_S=W_d+W_k+W_0.$$

(10)

where W_d is the energy used to extend the original crack and to generate the new crack. W_k is the projectile kinetic energy that is carried when the rock is broken. W₀ is other energy such as acoustic energy and radiation energy. According to the calculation of kinetic energy under the high-speed camera, the ratio of the kinetic energy W_k is

$$\frac{W_k}{W_0}=\frac{(0.69v_0+0.22)}{100},$$

(11)

where v₀ is the impact velocity of the punch. The calculated value of kinetic energy is mostly within 10% of the total crushing energy, and the absorption energy is mainly composed of the energy dissipation under the impact loading. As a result, the speed impact loading can be used to minimize the kinetic energy, and then the crushing energy of particles can be expressed as

$$W_s=W_d.$$

(12)

Considering the size difference between the particles, the crushing energy density is a more objective parameter to reflect the energy consumption of the rock, which is the crushing energy of unit volume particles

$$w_d=\frac{W_d}{V_S}.$$

(13)

where V_S is the volume of particles.

3. Experimental Method

During the experimental procedure, we introduced three distinct particle samples: crushed ore particles (large particles spanning 1mm to 12mm), raw material crushed particles (small particles ranging from 65 μm to 80 μm), and cement powder ground particles (microparticles below 45 μm). According to the product specifications, approximately 80% of the crushed ore particles’ total mass falls within the 1–12 mm size range; similarly, 72% of the raw material grinding particles’ mass is distributed between 65 μm and 80 μm, while 80% of the cement powder particles’ mass measures less than 45 μm. We then separately screened these three batches of particles using traditional manual methods and non-contact measurement techniques, respectively.

For the manual measurement method, we prepared two sieve mesh sizes (1mm and 12mm) for the large particles, as depicted in Figure 2. The second layer of the sieve mesh retained particles with sizes between 1mm and 12mm. For the small particles, we utilized sieves with pore sizes of 65 μm and 80 μm, and the second layer filtered out particles in the 65–80 μm range. For the microparticles, we employed a sieve with a 45 μm pore size. We then agitated the sieve device to screen the particles. Finally, we weighed the selected, qualified particles, determining their proportion when compared to the original weight of qualified particles obtained through traditional screening techniques.

Next, we delved into the correlation between crushing energy and particle size, specifically examining the mechanical crushing energy efficiency parameters (which represent the energy efficiency necessary to reduce particles per unit mass to a specific size). Our experimental setup for studying this relationship comprises two key components: A particle crushing system and a data acquisition system. The particle crushing system incorporates upper and lower pressure rods along with a precision pressure sensor. These rods exert pressure on the particles with a displacement accuracy of 0.001 mm, a load accuracy of not more than 0.5%, and a testing speed ranging from 0.001 to 1000 mm/min, boasting a speed accuracy of no more than 0.3%. The pressure sensor primarily tracks variations in the compressive load generated during the compression of the samples. It has a measurement range for compressive loads spanning from 0.2% to 100%FS and a deformation measurement range of 0.1% to 100%FS. The data acquisition system, meanwhile, consists of a video microscope and a photoelectric displacement encoder, which together capture crucial data during the experimentation.

To address the challenges of low efficiency, significant random errors, and the inability to conduct online inspections in manual detection of particle size and shape for hydraulic fracturing quartz sand proppants, the introduction of dynamic image detection methods not only allows for simultaneous measurement of particle size and shape but also opens up new avenues for online proppant inspection. The system primarily comprises a sampler, vibrating feeder, parallel backlight source, telecentric lens, industrial camera, and other components. Given the high concentration of cement particles in the transportation pipeline, a sampling system is utilized to extract the cement particles from the pipeline. After photographing and sampling, the powder is returned to the original pipeline through a return air system. To ensure that the collected cement samples are representative, the inlet at the front end of the sampling probe is placed at the center of the cement transportation pipeline.

The primary objective of installing a lens window in the camera setup is to protect the camera and lens from erosion by cement particles. Additionally, to maintain the cleanliness of the window, a protective gas is continuously purged over it during operation. The main process involves the sampling system extracting cement particles from the operating cement transportation pipeline at the site and transporting them through a pipeline into a feeding tray. Through the vibration of the vibrating feeder, the cement particles are dispersed and fed into the sampling pipeline. Due to gravity, the particles further disperse and descend towards the lens. The camera captures real-time images of the cement particles by exposing them to a background light source and taking pictures at the set frame rate. The image data are then transmitted to a computer, where it is analyzed using visual image processing algorithms to detect the particle size information of that particular batch, thus enabling non-contact detection of crushing particles.

The captured images are segmented and manually annotated. Machine learning is then employed to categorize and train a database of positive and negative samples, summarizing their features and generating a decision model for the given sample. This process establishes a standard particle size database. Subsequently, the surface images of standard cement samples are cropped to create regions suitable for evaluation by machine vision algorithms. After obtaining the image scale, a machine vision algorithm is utilized to automatically classify the particle size range based on the standard particle size database. The image acquisition diagram is shown in Figure 3.

4. Results and Discussion

The image processing framework adopted is OpenCV. To convert the original image into a grayscale image, opening operations with circular structuring elements of different diameters are applied to the particle images, achieving image smoothing. The Roberts operator utilizes local differential operators to detect edges, providing high edge localization accuracy. However, it can easily miss some edges and lacks the ability to suppress noise. This operator performs well on images with steep edges and minimal noise, especially those with numerous edges oriented at positive and negative 45 degrees. Nevertheless, its positioning accuracy is relatively poor. As shown in Figure 4, experimental tests were conducted using five different diameters of structuring elements, and it was found that a diameter of 6 pixels matrix yielded the best results.

A grayscale image comprises 256 brightness levels, and a binarized image can be obtained through the selection of an appropriate threshold. This process not only reduces the amount of image data but also preserves the overall characteristics of the image while enhancing its boundary features, thus highlighting the target contours. By employing this model to identify the sample set for recognition, particles in the image are automatically extracted and binarized again using OpenCV, as illustrated in Figure 5. The circumscribed rectangle or circumscribed circle of the particle is then determined.

Based on the above particle size identification and statistical methods, a batch of qualified ore-crushing particles, raw material-crushing particles, and cement-crushing particles have been selected as the experimental samples.

Table 1. Actual percentage of eligible particle sizes present in the measured pellets.

Particles	Crushed Ore Particles	Raw Material Grinding Particles	cement Milling Particles
Size range (μm)	1000–1200	65–80	<45 μm
Percentage (%)	80	72	80

provides a detailed breakdown of the actual percentage of eligible particle sizes present in the measured pellets within these batches.

After photographing and sampling these particles, the images of ore-crushing product particles, raw material-crushing particles, and cement-crushing equipment particles are identified and statistically analyzed. At the same time, traditional manual particle size detection methods were used as a control to generate the particle size distribution comparison chart in Figure 6a, raw material crushing equipment products in Figure 6b, and cement crushing equipment products in Figure 6c. From the above analysis, it can be seen that the accuracy of this machine vision recognition technology is closer to the accurate, true value compared to traditional measurement methods. For example, regarding cement crushing particles, the proportion of particles measured using traditional methods within the range of 3–45 μm is around 60%, while the proportion measured using this machine vision recognition technology is 80.7%, which is very close to the actual sample particle proportion. The comparison with actual statistical content demonstrates the accuracy of machine vision recognition technology in identifying cement particles. This not only provides an effective method for evaluating the results of crushing equipment but also offers optimization suggestions for cement production processes.

After the machine vision recognition technology has precisely determined the particle sizes, we can deduce the crushing energy from the established correlation between crushing energy and particle size outlined in Section 3. This effective energy can then be benchmarked against the motor’s energy consumption during the same period, serving as a crucial indicator for evaluating the efficiency of the crushing process. As evident in

Table 2. The relationship between particle size and energy consumption.

Particle Size (μm)	>12,000	12,000–1000	1000–200	200–80	80–65	65–45	<45
Effective energy (J)	5.89	24.77	22.76	35.27	76.98	51.15	3.78
Motor energy (J)	6.984	35.424	35.532	58.5	139.46	82.116	6.696
Efficiency (%)	84.2	69.9	64.2	60.3	55.2	62.3	56.5

, when the particle crushing size aligns with the cement production process’s requirements, 80% of ore crushing equipment products exhibit particle sizes within the acceptable 1–12 mm range, with a minimum power consumption of 24.77 J and an efficiency of 69.9%. Similarly, 72% of raw material crushing equipment products achieve particle sizes less than 80 μm, consuming a minimum of 76.98 J and achieving 55.2% efficiency. Besides, 80% of cement crushing equipment products yield particle sizes under 45 μm, consuming 3.78 J and maintaining 56.5% efficiency. In contrast to existing technologies, this experiment pioneers the detection of characteristic particle sizes in crushing particles through a non-contact optical imaging approach. By capturing pixel information of individual particles from standard cement samples, we establish a particle size standard database to accurately determine the size of cement particles under test. This methodology automatically summarizes the particle size characteristics of crushing particles, providing invaluable data for analyzing characteristic particle sizes and detecting cement quality. We compared particle size measurements using non-contact measurement methods with commercial measurement methods. When measuring particles larger than 38 μm, the measurement results obtained by the non-contact method differ by 0.07% from commercial methods. The results obtained by commercial methods for particles smaller than 38 μm are 2.83% worse than those obtained by non-contact recognition methods [27,28]. Furthermore, the use of machine learning techniques enables automatic recognition and classification of crushing particle sizes into their respective ranges.

5. Conclusions

In this paper, the mechanical crushing energy efficiency of the commonly used crushing equipment is investigated. Through simulating and calculating the relationship between the crushing pressure and particle diameters, a corresponding relationship between the useful work of the crushing equipment and the particle size is found, thereby establishing a relationship between the energy consumption of the crushing equipment and the particle size. Aiming at the acquisition of particle size parameters, a particle size recognition and summation system based on machine vision is proposed. The collected particle image parameters are recognized and summarized through deep learning of machine vision, real-time recognition, statistical summation, and evaluation of product particle sizes for different crushing products. Finally, the efficiency evaluation parameters of the crushing equipment are obtained by combining the particle size information of the crushing products and the relationship between the particle size and equipment energy consumption. When applying this technology to particle detection and energy efficiency testing during the cement production process, the results obtained are consistent with the actual particle size distribution and energy consumption of the crushing products. It is expected to become a novel method for detecting particle sizes of mechanical crushing products and obtaining energy efficiency parameters.