Shearer parameter optimization and low energy consumption mining based on 3D point cloud characterization of coal wall

To achieve efficient and low energy consumption mining under different cutting depths of a shearer, a multiparameter coupling optimization method for the shearer based on three‐dimensional (3D) characterization of the coal wall was proposed. First, a seven‐axis absolute articulated arm measuring machine was used to obtain 3D point cloud data of the coal wall, and then the 3D of the coal wall surface was reconstructed by using segmentation, filtering, and stitching processing, thereby obtaining the average thickness of different coal wall areas. Second, through the quadratic rotation regression orthogonal combination experiment, the optimal combination of drum speed, traction speed, and cutting depth was obtained, further obtaining the order of primary and secondary influences, and the regression model. Moreover, a particle swarm optimization algorithm was used to obtain the optimal drum speed and finally, the laboratory and field test experiments were conducted to verify the effectiveness of the proposed optimization algorithm in reducing the cutting energy consumption of shearer. The experiment results show that the given optimization algorithm can adaptively optimize the traction speed and drum speed based on the corresponding cutting depth, which significantly reduces the cutting specific energy consumption of the shearer. Thus, it provided an important technical means for the shearer to achieve low energy consumption and efficient mining.


| INTRODUCTION
During the mining process of a shearer in a fully mechanized mining face, the traction speed and drum speed are generally controlled by the operators based on the observed and heard mining conditions.However, the illumination of a fully mechanized mining face is poor, the dust concentration is quite large when the shearer cutting coals, and the mining process is accompanied by obvious mechanical noise.Thus, it is difficult for a shearer driver to determine the actual working condition of mining accurately in real time.Especially, affected by mining and free caving, the surface of the coal wall to be mined is usually uneven, namely, the cutting depth of the shearer will constantly change with the different cutting positions.Thus, to ensure the high efficiency and low energy consumption of a shearer, it is necessary to adjust the traction speed and drum speed in real time according to the actual cutting depth.
Among the existing multiparameter coupling optimization methods of a shearer, a variety of qualitative analysis methods were mainly used to study the coupling relationship between drum speed, traction speed, and cutting depth, and the simulation is carried out by means of force analysis, discrete element method and finite element modeling.Qin et al.  analyzed the variation law of different coal mining performance indexes with drum motion parameters, established a multi-objective optimization model with different performance indexes as subobjectives, and then obtained the motion parameters with the best comprehensive performance under different coal seam hardness by using particle swarm optimization (PSO) algorithm. 1Combined with a fuzzy control algorithm, radial basis function neural network, and proportional-integral-derivative control, Liang enables the parameters of the controller to be adjusted adaptively according to different environments, so as to provide a better speed regulation scheme for realizing intelligent, efficient, and high-quality mining. 2 Sun designed a new automatic speed control system of drum shearer based on strain sensor to realize the automatic speed control. 3Chen et al. proposed a speed collaborative optimization control method based on the dual machine energy consumption model, which can effectively reduce the energy consumption of the dual machine system of shearer and scraper conveyor. 4The EDEM, a discrete element simulation software, was used by Zhao et al. to establish the coupling model of spiral drum and coalcontaining gangue.By analyzing the influence of shearer traction speed, drum speed, spiral angle of blade, and cutting depth on the shearer's loading rate, lump coal rate, and specific energy of cutting, the parameters were optimized with genetic algorithm for back propagation neural network, which is capable to realize the efficient mining of a shearer. 5,6Gao et al. used the modeling test method to obtain the coupling relationship of the key factors affecting the loading ratio of drum. 7Ge et al. established a multi-objective optimization model of shearer cutting performance by studying the cutting performance indexes of the shearer when mining and used a genetic algorithm to optimize the optimal traction-cutting motion parameters with changes in cutting impedance under normal coal seam, gangue seam, and rock fault circumstances, realizing safe operation and efficient mining of coal mining equipment under diverse cut-off working situations. 8Zhang et al. used the iterative method to establish a multi-parameter coupled optimization matching model for the optimal control of dust reduction in shearers, combined with the experimentally set final index, to determine the iterative termination conditions and obtain the results of optimizing the multi-cut parameters of shearers based on the lowest coal dust production. 9Feng created a rolling prediction model based on an Elman neural network and used the shearer operating speed, the amount of fallen coal, the scraper conveyor's operating speed, and the maximum load in the experimental process as samples for continuous optimization training to achieve cooperative control of the shearer and scraper conveyor. 10Li established the relationship between cutting depth and cutting load by analyzing the speed regulation mode of shearer-cutting operations and formulating a corresponding speed adjustment control scheme to increase the speed of the mining operation of shearer-cutting operations. 11Liu et al. used wavelet packet decomposition theory and a back propagation neural network to identify cutting resistance in the cut-off process and a PSO algorithm to optimize motion parameters such as traction speed and drum speed to achieve adaptive control of a shearer by establishing the adaptive control system model. 12Hu et al. proposed a drum speed control strategy and a joint traction-drum speed control strategy to adapt to different abrupt load conditions, as well as established and analyzed a cutting drive system model that not only effectively reduces dynamic load but also achieves efficient coal mining under abrupt load conditions. 13owever, in the above study, the simulation is only carried out under ideal conditions, due to the complex environment of a fully mechanized mining face, it is difficult to obtain an accurate three-dimensional (3D) characterization of the coal wall in time, which will lead to deviations between the simulation model and the actual cutting condition, and then the drum speed and traction speed of the shearer cannot be adjusted effectively and accurately.The research on adaptive speed regulation of shearers using experimental methods combined with actual cutting conditions and mining environments can realize efficient mining of shearers, but it has not yet taken into account the uncertain random coal wall thickness distribution, and it has not yet cut at the optimal traction speed and drum speed WANG ET AL.
| 737 before cutting, which will then affect the stability and mining efficiency of the entire shearer.Therefore, it is necessary to study the influence of coal wall thickness characteristics on the shearer when cutting and adjust the drum speed and traction speed of the shearer in realtime according to the average thickness of the coal wall to be cut to achieve mining with low energy consumption, high efficiency, and high-quality shearers.In this paper, a new method was proposed to optimize the coupling of cutting parameters of the shearer based on the 3D reconstruction of the coal wall surface, which is capable to achieve the optimal joint speed regulation of drum speed and traction speed.First, a multiple point cloud data algorithm was used to process the point cloud data, then calculate the average thickness of the coal wall accurately to improve the preperception ability of the coal mining machine on the surface of the coal wall before mining.Next, a regression model was constructed for the relationship between drum speed, traction speed, average coal wall thickness, and cutting energy consumption.Finally, a PSO algorithm was used to obtain the optimal drum speed and traction speed under random average thickness, further improving the mining efficiency and enhancing the stability of the shearer.

| Coal cutting test-bed
The actual structure and mining principle of the shearer should be comprehensively considered while building the cutting test-bed.In this paper, we mainly study the coupling optimization method of multicutting parameters of a shearer based on coal walls with different thicknesses, thus, the walking and cutting functions of the shearer were mainly considered.The built coal cutting test-bed is composed of the mechanical system, the control system, data acquisition, and the analysis system, as shown in Figure 1.A detailed experimental procedure is shown in Figure 2.
As seen in Figure 1, the selected cutting motor of the test-bed is the three-phase asynchronous motor, the rated power is 0.75 kW and the rated speed is 1400 r/min.The worm gear reducer was used to reduce the rotating speed of the drum and increase the load torque of the drum, and its reduction ratio is 38:1.The cutting diameter of the drum is 300 mm, and the minimum speed of the drum is 24 r/min.The type of the traction motor is 5IK120RGN- CF, the rated power is 120 W, the rated speed is 75 r/min, and the reduction ratio of the reducer is 20K:1.The length of the slide rail is 1000 mm, and the distance between two slide rails is 800 mm.The RACO-Elektrozylinders are used to provide pressure for fixing the coal wall.Moreover, the three-phase electricity parameter acquisition module and the present acquisition module of the traction motor are used to monitor the electrical signals of cutting motor and traction motor in real time.

| Cutting performance of shearer
The specific energy of cutting, namely, the value of the energy consumed by the shearer to obtain the unit volume of coal, 14 is the Key economic indexes of shearer in the process of cutting the coal wall, which is capable to characterize the utilization rate of energy during mining.The smaller the value of cutting specific energy consumption is, the smaller the energy loss and the higher the cutting efficiency of the shearer will be.To obtain the specific energy of cutting, the powers of cutting motor and traction motor were acquired to calculate the cutting energy consumption, and then calculate the specific energy of cutting according to Equation (1).
where A denotes the cutting resistance, namely, the hardness characteristics of the coal wall, N/mm.K is the coefficient of correction, 2.78.b is the width of the pick's notched edge, mm.φ denotes the angle of break, rad.n is the speed of the drum, r/min, and v is the traction speed, m/min.m is the number of picks on each section of the drum.Obviously, from Equation ( 1), the shearer needs to carry out the simulated cutting experiment at high traction speed and low drum speed, which can obtain the minimum specific energy of cutting and improve the cutting efficiency of the shearer.
In this paper, the specific energy of cutting is the total power of cutting motor and traction motor when cutting a unit volume of coal, thus, the mathematical relationship model of cutting energy consumption and specific energy of cutting is shown in Equation ( 2).The cutting energy consumption needs to sum the cutting power and feeding power within a certain period, and then divide it by the volume of the cut coal to finally obtain the value of the specific energy of cutting.
where H w is the specific energy of cutting, kW h/m 3 .W H is the total cutting energy consumption of the shearer in a certain time, kWh.P t ( ) is the instantaneous power of cutting drum and traction motor, kW.K b is the loose coefficient of coal wall specimen during crushing, 1.2.B is the cutting depth, m.H is the average mining height of shearer, m. v ¯is the average traction speed of the test-bed, m/min.t is the cutting time, s.
From Equation ( 2), the cutting energy consumption is positively correlated with the specific energy of cutting.
When the traction speed and cutting depth are constant, the power decreases with the decrease of drum speed.Moreover, when the drum speed and cutting depth are constant, the higher the traction speed is, the smaller the power will be.

| Boundary conditions of parameters
In the mining process of a shearer, the main parameters affecting the specific energy of cutting are drum speed, traction speed and cutting depth.According to the size parameters of the cutting test-bed and the actual cutting conditions of the shearer, the boundary conditions of drum speed, traction speed, and cutting depth need to be preset. 15) Boundary condition of drum speed The higher the set value of drum speed is, the smaller the cutting amount of the shearer will be, which leads to an increase in the unit energy consumption of the shearer while cutting coal walls in a certain period. 16According to the adjustment range of drum speed in the actual mining process of the shearer, the boundary condition is set as follows: (2) Boundary condition of traction speed The traction speed directly affects the vibration amplitude of the ranging arm when the shearer cuts the coal wall.With the increase of the traction speed, the vibration displacement of each part of the shearer increases significantly.If the vibration is too large, it will affect the stability of the shearer. 17But the cutting efficiency will be affected if the traction speed is too small.Therefore, combined with the actual speed regulation range of the shearer, the boundary condition of traction speed is set as follows: (3) Boundary condition of cutting depth With the increase of cutting depth, the mean stress of the pick will increase continuously, accelerating the cutting energy consumption of the shearer. 18The maximum cutting depth of the test-bed's drum is 80 mm, and comprehensively considering the cutting amount of the drum, the boundary condition of cutting depth is set as follows: (5) 3 | THREE-DIMENSIONAL POINT CLOUD CHARACTERIZATION OF COAL WALL

| Three-dimensional point cloud model of coal wall
To obtain the average thickness of the coal wall, the 3D point cloud data of the coal wall's surface should be measured first.Thus, a seven-axis absolute articulated arm measuring machine was used to obtain the 3D point cloud data of the coal wall.The parameters of the seven-axis absolute articulated arm measuring machine are shown in Table 1.
Two coal specimens with stepwise changes in the average thickness were poured for the verification experiment. 19By using the seven-axis absolute articulated arm measuring machine, the 3D point cloud data were measured as shown in Figure 3 and the final point cloud images of two coal specimens are shown in Figure 4.

| Point cloud data processing
To obtain the 3D point cloud data in areas with different thicknesses, the 3D point cloud segmentation algorithm based on region growth is used for point cloud segmentation.The segmentation algorithm gathers point clouds with similar properties in the same area, and then uses the growth of seeds to expand and screen the region.First, select the initial seed point of the area, and judge the properties of nearby seeds according to the normal vector or curvature during seed growth.Next, determine whether the seeds have similar properties, if they meet the characteristics of growth, they will be merged into the area where the initial seeds are located.At the same time, the new seeds will continue to grow around and determine the range of seeds that can be merged.While expanding the position that does not meet the set value, the present seed growth area is finally determined. 20The specific steps of the algorithm are as follows.
Step 1: Select the initial seed point and seed area.average thicknesses as the initial seed point, and set the area where the seed point is located as the initial seed area.
Step 2: Search for adjacent areas.
Set the initial seed point cloud sequence of the coal wall specimen as an empty set, select the initial seed points from the known point cloud sequence, and add them to the set.Next, search the field points near the area to determine whether the field space meets the point cloud curvature of the coal wall specimen.If so, it can be used as the growth area of the seeds.
Step 3: Judgment of similarity criterion.
Compare the angle between the neighborhood point cloud data with different average thicknesses and the normal of the present seed point.If the angle is less than the calculated smoothing threshold of the point cloud of the coal specimen, the present area is added to the present seed area.If the curvature of the neighborhood point cloud data is less than the curvature threshold, add that to the seed set.
Repeat steps 1-3 until the obtained seed sequence is empty.
The segmented 3D point cloud images of the coal wall are shown in Figure 5. 21

| Average thickness calculation of coal specimens
In a spatial coordinate system, to calculate the average value of different thicknesses of coal specimens, it is necessary to determine the present number of point clouds and the distance from each point cloud data to the standard plane, namely, the coordinate information in the Z-direction.Accumulate the z-axis coordinates of all point cloud data in each region, and then divide by the total number of point clouds.Finally, the actual average thickness of each coal specimen can be calculated, as shown in Table 2.
The error comparison between the calculated coal sample thickness based on the 3D point cloud model and the actual coal sample thickness is shown in Figure 6.Obviously, the maximum error between the calculated thickness of the scanned average coal wall and the actual thickness is merely 0.06 mm, which proves the accuracy of the proposed calculation method in this paper.

| Preparation of standard coal specimens
To test the cutting energy consumption of the shearer under different cutting depths, drum speed, and traction speed, and combined with the boundary condition of cutting depth, five kinds of coal specimens suitable for different cutting depths were poured, the size of the specimens is 600 mm × 450 mm × 120 mm, as seen in Figure 7.The coal specimens were poured with coals, cement, and adhesive, 22 the proportion of each material is shown in Table 3, and the material properties of the poured coal specimens are shown in Table 4.

| Quadratic rotation orthogonal combination experiment
The drum speed, traction speed, and cutting depth significantly impact the cutting efficiency of the shearer, thus, the quadratic rotation orthogonal combination method was used to carry out the cutting experiment.

Specimen-I (mm)
Specimen-II (mm) According to the experimental results, the variance, significance, and main parameter effect were analyzed, meanwhile, the primary and secondary influence and interaction of each parameter were clarified.Finally, the optimal combination of parameters of each influencing parameter was obtained.
The cutting experiment uses three factors and five levels.Considering the determined boundary conditions of drum speed, traction speed, and cutting depth, the horizontal factor coding table of quadratic rotation orthogonal combination experiment with three factors and five levels was defined, as seen in Table 5.
According to the horizontal factor coding table, 23 combinations need to be tested in total, as seen in Table 6.Next, using Design-Expert mathematical statistical software, as well as taking the specific energy consumption of shearer cutting as the experimental evaluation index, the 23 groups of experiments were carried out.The experimental process of coal specimens with different cutting depths and the test results of the actual cutting depth are shown in Figure 8. Obviously, the actual cutting depth of each specimen is consistent with the set value.

| Analysis of experimental results
According to the test results in Table 6, by using the quadratic rotation regression analysis, the regression equations of drum speed, traction speed, and cutting depth on the specific energy of cutting are established as below. 23 The variance and significance analyses of the experimental results are shown in Table 7, the mismatch value p of the model is less than 0.0001, which indicates that the regression equation has high significance and a good fitting degree.
Combined with the mismatch value p, the influence of drum speed, traction speed, and cutting depth on the specific energy of cutting can be judged.As seen in Table 6, the influence of the shearer's parameters on , x 2 x 3 , x 1 x 3, and x 1 x 2 .Among them, the mismatch values of x 1 x 3 and x 1 x 2 are greater than 0.1, which indicates not significant.Thus, x 1 x 3 and x 1 x 2 , namely, the interaction terms of drum speed and traction speed, as well as drum speed and cutting depth, were merged into residual terms for further analysis of The influence laws of a single parameter on the specific energy of cutting are shown in Figure 7, from Figure 9A, when the traction speed and cutting depth are constant, the specific energy of cutting is positively correlated with the drum speed, namely, the specific energy of cutting increases with the increase of drum speed.From Figure 9B, when the drum speed and cutting depth are constant, the specific energy of cutting is negatively correlated with the traction speed.Similar to Figure 9B, when the drum speed and traction speed are constant, the specific energy of cutting is also negatively correlated with the cutting depth, as shown in Figure 9C.Moreover, processing the data to obtain the response surface of significant interaction among drum speed, traction speed, and cutting depth to the specific energy of cutting, as shown in Figure 10.
From Figure 10A, when the cutting depth is constant and the drum speed is in the range of 24-29 r/min, the specific energy of cutting is negatively correlated with the traction speed.When the cutting depth is constant and the traction speed is in the range of 2.6-3.1 m/min, the specific energy of cutting is positively correlated with the drum speed, as shown in Figure 10B.When the traction speed is constant and the cutting depth is in the range of 40-60 mm, the specific energy of cutting decreases with the decrease of drum speed.
Combined with the influence trend of drum speed, traction speed, and cutting depth on specific energy of cutting in Figure 9 and the interaction between any two parameters in Figure 10, the optimal drum speed range is 24-29 r/min, the optimal traction speed range is 2.6-3.1 m/min, and the optimal cutting depth range is 40-60 mm.
According to the analysis results, the constraint conditions of each parameter are determined as 34, 1.7 3.5, 40 60.
According to the constraint conditions in Equation ( 8), the actual effects of drum speed, traction speed, and cutting depth on the specific energy of cutting can be obtained, as shown in Figure 11.Obviously, the specific energy of cutting decreased significantly with greater traction speed, smaller cutting depth, and cutting speed.
According to the value range of each parameter in Equation ( 8), limit the drum speed, traction speed, and cutting depth, and then obtain the optimal combination of cutting speed, cutting depth, and traction speed with the target of minimum specific energy of cutting, as shown in Table 8.  of particle location information is d, the characteristics of each particle are as follows 24 : (1) Present location of particles: (2) Historical optimal location of particles: (3) Velocity of particles: In Equations ( 9)-( 11), i = 1, 2, …, N, compare the present location of particle i with the historical optimal location, if the present location is better than the historical optimal location of particle, a new iteration is realized to complete a self-update. 25Next, combined with the update formulas of velocity and position, calculate the present location of particle i + 1.Moreover, compare and iterate with the historical optimal location, determine each optimal location repeatedly, and record them in the set.The update formulas of velocity and location are as below.
The velocity update is given by and the location update is given by where v id k is the present velocity of the ith particle in ddimensional location space, v id k+1 is the update velocity of the ith particle in d-dimensional location space, pbest id k is an individual historical optimal location of the ith particle in d-dimensional location space, gbest d k is the historical optimal location of the entire population in ddimensional location space, x id k is the present position of a particle, c 1 and c 2 are the acceleration factors and a nonnegative constant, the value of them is 1.
where w is the weight coefficient.The parameter optimization process of PSO is shown in Figure 12.
According to the established regression model and experimental results, we found that the values of drum speed, traction speed, and cutting depth can directly affect the cutting energy consumption of the shearer.However, the change of cutting depth is limited by the actual distribution of the coal wall surface, thus, it is necessary to adjust the drum speed and traction speed according to the change of the thickness of the coal wall.Considering the complexity of the coal wall surface distribution, the average thickness of the coal wall was defined as the independent variable, and the drum speed and traction speed were defined as the dependent variable. 27ouring two specimens with thickness changes as shown in Figure 13, according to the installation method of specimens on the test-bed and the installation position of the drum, the cutting depths of different thickness areas of the two specimens are obtained by using a sevenaxis absolute articulated arm measuring machine, as shown in Table 9.
According to the cutting depth of two specimens in Table 9, a PSO algorithm based on dynamic weights was used to optimize the drum speed and traction speed corresponding to the minimum cutting specific energy consumption of the shearer, which the constructed mathematical regression model as a fitness function.The optimization results are shown in Table 10, and the corresponding optimization iteration curve is shown in Figure 14.

| Experimental analysis of optimal parameters
Table 10 shows the theoretical optimal drum speed and traction speed for different cutting depths.However, in actual cutting experiments, the optimal drum speed, traction speed, and cutting depth obtained from the quadratic rotation regression orthogonal combination model need to be used for cutting.Thus, the initial drum speed, traction speed, and cutting depth are determined to be 24.71r/min, 3.07 m/min, and 46 mm.When the cutting depth changes, Compare the optimal cutting depth to calculate the optimal drum speed and traction speed corresponding to the current cutting depth.The cutting experiments of two specimens with different cutting depths are shown in Figures 15 and 16, respectively.
To verify the effectiveness of the proposed optimization method, we obtained the cutting specific energy consumption for the following three situations separately.
(1) the theoretical optimal cutting specific energy consumption; (2) the cutting specific energy consumption based on optimal parameters; (3) the cutting specific energy consumption using constant speeds, where the drum speed is 24.71 r/ min and traction speed is 3.07 m/min.
For the above three situations, the cutting specific energy consumption under different cutting depths is shown in Figure 17.
As shown in Figure 17, obviously, regardless of the cutting depth, when the feed speed and drum speed remain constant, the cutting specific energy consumption is significantly higher than that of two parameters optimized F I G U R E 13 Specimens with random thickness.
T A B L E 9 Cutting depth of two specimens.

Specimen-I (mm)
Specimen-II (mm) with changes in cutting depth.Especially, when the cutting depth is 71.986 mm, the maximum deviation in cutting specific energy consumption reached 0.48 kW h/m 3 , with an increase of 85.87%.Although the cutting specific energy consumption using optimized parameters is still higher than that of the theoretical optimal, it is mainly due to losses during the mechanical assembly and transmission process of the test-bed.cutting specific energy consumption under different hardness conditions of coal, and analyzing the impact law of the coal's hardness on the cutting specific energy consumption.In addition, the given method optimized the parameters of drum speed and traction speed based on cutting depth, so further consideration can be given to collaborative optimization of cutting depth, traction speed, and drum speed based on the surface characteristics of the coal wall, ensuring the lowest cutting specific energy consumption during the mining process.

T A B L E 1
Parameters of seven-axis absolute articulated arm measuring machine.
Calculate the curvature value of point cloud data with different average thicknesses on the same coal wall specimen to determine the point cloud sequence, then set the minimum curvature value of point cloud data with different F I G U R E 3 Point cloud data acquisition process.F I G U R E 4 Point cloud images of specimens.(A) Specimen-I and (B) Specimen-II.

F I G U R E 5
Segmented three-dimensional point cloud images.(A) Specimen-I and (B) Specimen-II.T A B L E 2 Average thickness of coal specimens.

6 4
Error Comparison.(A) Error comparison of Specimen-I and (B) error comparison of Specimen-II.F I G U R E 7 Five kinds of coal specimens.T A B L E 3 Proportion of materials.Material properties of coal specimens.

F I G U R E 8
Cutting experiments with different cutting depths: (A) 43 mm, (B) 50 mm, (C) 60 mm, (D) 70 mm, and (E) 77 mm.variance, which is capable to optimize the regression equation.The final optimized regression equation is shown below.

1 |
Analysis of cutting parameters based on PSOAssuming the number of particles generated in this optimization experiment is n, and the spatial dimension

F I G U R E 9
Influence of single parameter on specific energy of cutting.(A) Drum speed, (B) traction speed, and (C) cutting depth.F I G U R E 10 Interaction between parameters.(A) Drum speed and traction speed, (B) drum speed and cutting depth, and (C) cutting depth and traction speed.

F I G U R E 11 12
Influence trend of parameters on specific energy of cutting.T A B L E 8 Optimal combination of parameters.Parameters Drum speed n (r/min) Traction speed v (m/min) Cutting depth H (mm) Parameter optimization process of particle swarm optimization.

F
I G U R E 14 Iterative curve of optimization.Cutting depth is (A) 54.929 mm, (B) 58.030 mm, (C) 68.970 mm, and (D) 71.986 mm.F I G U R E 15 Specimen-I.Cutting depth is (A) 46 mm, (B) 58.030 mm, and (C) 71.986 mm.
Where x 1 denotes the drum speed, x 2 denotes the traction speed, and x 3 denotes the cutting depth. Note: 5, and rand k 1 and rand k 2 produce pseudo-random values between [0, 1].Additionally, by considering that a basic PSO can easily become trapped within a locally optimal value, the weight coefficient w was used to balance the global and local search capabilities of the PSO.The global search capability is stronger with a larger w, and conversely, the local search capability is stronger with a smaller w.The updated formulas are given below.