Analysis of motion and vibration characteristics of elastic composite cylindrical roller bearing

Abstract

To investigate the motion characteristics and vibration characteristics of elastic composite cylindrical roller bearings (ECCRBs), a simulation model of the ECCRB is established in ABAQUS software. The influences of filling degrees and working conditions on motion characteristics of the ECCRB are compared, and the modal characteristics and harmonic response of the ECCRB are analyzed. Calculation results show that when the filling degree increases from 0% to 60%, there is a nonlinear relationship between the filling degree and the slip rate of cage, the natural frequency of each order decreases, and the vibration displacement of ECCRB increases under the excitation load; increasing the rotation speed and decreasing the radial load reasonably is beneficial to the motion stability of the ECCRB. At the same time, with the increase of the excitation load, the vibration displacement of the ECCRB increases. The analysis results can present some theoretical basis for the structural optimization of the ECCRB.

Keywords

Elastic composite cylindrical roller bearing motion characteristics harmonic response analysis slip rate vibration

Introduction

Cylindrical roller bearings (CRBs) are essential supporting components, which mainly use the rolling contact between the inner ring, outer ring, cage, and rolling elements to transfer load and motion. CRBs are widely used in rotating machinery such as aero-engine spindles and speed change devices because of their strong radial bearing capacity, large radial stiffness, and small friction factor. The motion and vibration characteristics of CRBs have an essential influence on the working performance and reliability of bearings.

Patra et al.¹ developed a dynamic model of the CRB and analyzed theoretically the influence of the rotation speed on the dynamic characteristics of the CRB under balanced and unbalanced conditions. Cui et al.² built a dynamic analysis model considering the cage dynamic unbalance to investigate the influence of the cage dynamic unbalance on the dynamic characteristics. Han et al.³ presented a nonlinear dynamic model of the CRB and the influences of different working conditions on the motion characteristics of the CRB considering actual working conditions were studied. Rubio et al.⁴ used Algor to analyze the dynamic characteristics of the CRB, ignoring the contact impact of the cage. Chen et al.⁵ developed a dynamic model of a high-speed CRB to investigate the influences of four aviation lubricants on the centroid trajectory of the cage, and used the Poincaré diagram to analyze the running stability of the cage. Hao et al.⁶ built a finite element model of the shaft-CRB-bearing pedestal system considering temperature effects and clearance changes. The dynamic characteristics of the bearing were systematically studied. Considering the roller angular misalignment, the geometric interference model of the cylindrical contact pair was established by Wu et al.⁷ to study the contact characteristics of the cylindrical roller with these two logarithmic profiles. Ma et al.⁸ developed a theoretical method for calculating roller-pocket oil film pressure and film thickness, and the influences of working conditions and structural parameters on roller-pocket oil film performance were analyzed. Tong⁹ presented a quasi-static model with four degrees of freedom of Double-row Cylindrical roller bearings (D-CRBs), and investigated the influences of structural parameters on dynamic characteristics and fatigue life of the D-CRB.

The above studies are all based on traditional solid CRBs. However, when the solid CRBs are under load, the phenomenon of stress concentration on the edges of the rolling elements often occurs. The centrifugal force of the rolling elements is significant when the bearing is running at high speed, which leads to contact fatigue and surface wear of the inner ring, the rolling elements and outer ring. To overcome the above shortcomings, some scholars have done a lot of studies on the structure of rolling elements. A new cylindrical roller model with the logarithmic profile was proposed by Cui.¹⁰ The contact stress of the bearing and the modified reference rating life of the bearing were analyzed. Liu¹¹ established a dynamic model of the CRB with hollow rollers considering lubrication and analyzed the impacts of different working conditions and hollow roller percentage on bearing vibrations. Solanki¹² proposed a layered cylindrical hollow rolling element, and studied the effects of different hollowness percentages on contact pressure. Yao et al.^13,14 investigated the effect of the rolling element of filling degree on dynamic equivalent stress and inner wall bending stress of the ECCRB.

Based on the above research, to study the motion and vibration characteristics of the ECCRB, according to the complex nonlinear dynamic contact relationship between the bearing parts, a finite element model of the ECCRB is built in ABAQUS software. The dynamic and vibration characteristics of the ECCRB are studied. The results can give some theoretical guidance for the engineering application of the bearing.

Theoretical foundation

Cage slip rate

As an evaluation criteria for the motion stability of the bearing, the cage slip rate is used to represent the relative error between the theoretical rotation speed and the actual rotation speed of the cage.¹⁵ Assuming that the rollers do not slip, the theoretical rotation speed can be calculated by the kinematic theory of the rolling bearing. Under a given working condition, the actual rotation speed of the cage can be calculated by using the central difference algorithm in ABAQUS software. In the calculation, it is assumed that the inner ring and outer ring of the bearing rotate at the same time. The contact angle α of the rolling elements to the inner and outer rings is the same. Equation (1) is used to represent the linear speed $V_{c}$ of the contact point between the outer raceway and rolling element, and equation (2) is used to represent the linear speed $V_{m}$ of the contact point between the rolling element and the inner raceway, which is as follows:

V_{c} = \frac{π}{60} n_{c} (1 + \frac{D}{d_{o}} \cos α)

(1)

V_{m} = \frac{π}{60} n_{m} (1 - \frac{D}{d_{o}} \cos α)

(2)

Where

n_{c}

is the outer ring rotation speed;

n_{m}

is the inner ring rotation speed;

d_{o}

is the pitch diameter; D is the rolling element diameter. If the rolling element doesn’t slip, the linear speed of the cage is equal to the average linear speed of the raceway of the inner ring and outer ring. The cage linear speed

V_{e}

is given as equation (3):

V_{e} = \frac{1}{2} (V_{c} + V_{m})

(3)

The cage linear velocity can be expressed as equation (4):

V_{e} = \frac{ω_{e} d_{o}}{2}

(4)

Combining equations (1)–(4), the theoretical angular velocity $ω_{e}$ of the cage is obtained as equation (5):

ω_{e} = \frac{π}{120} [n_{c} (1 + \frac{D}{d_{o}} \cos α) + n_{m} (1 - \frac{D}{d_{o}} \cos α)

(5)

The calculation formula of slip rate S of the cage is written as equation (6)

S = \frac{| ω_{a} - ω_{e} |}{ω_{e}}

(6)

In equation (6), $ω_{a}$ is the actual speed of the cage.

Mechanical vibration theory

Mode is the evaluation index for the vibration characteristic of a structure as well as a natural property of a structure. When the natural frequency of a structure approaches the excitation frequency, the structure will be damaged by resonance. Through the modal vibration analysis of the ECCRB, the natural frequency of the bearing can be obtained, which is helpful to avoid resonance effectively.¹⁶

Equation (7) is used to calculate the vibration equation of a linear system with n degrees of freedom as follows

[M] {\ddot{a} (t)} + [C] {\dot{a} (t)} + [K] {a (t)} = P (t)

(7)

In equation (7),

[M]

represents the quality matrix of the system;

[C]

represents the damping matrix of the system;

[K]

is the stiffness matrix of the system;

a (t)

is the displacement vector;

P (t)

is the load vector.

Neglecting damping and external loads, the vibration equation of the system can be expressed as equation (8):

[M] {\ddot{a} (t)} + [K] {a (t)} = {0}

(8)

Where

{0}

represents the zero vector. Equation (9) is used to express the general solution of equation (8) as follows:

{a (t)} = {A} \sin (ω t + φ)

(9)

Where

ω

is the natural frequency of the system, and

φ

represents the initial phase of displacement. Substituting equation (9) into equation (8) can get equation (10)

([K] - ω^{2} [M]) {A} = P (t)

(10)

Since ${A}$ is not a zero vector, the vibration equation can be transformed as equation (11)

([K] - ω^{2} [M]) = 0

(11)

Equation (11) can be expanded to obtain the nth degree equation about the frequency $ω^{2}$ . Suppose the matrices in equation (11) are positive definite matrices, the natural frequency $ω_{k}$ (k = 1, 2,…,n) of the system and displacement vector ${A}_{k}$ can be obtained. The vector ${A}_{k}$ corresponding to $ω_{k}$ represents the mode shape, and one natural frequency conforms to one mode shape.

Harmonic response analysis

Harmonic response analysis is the theoretical method to study the vibration displacement of a linear system under excitation load with different frequencies, and obtain the frequencies with the significant influence on the vibration displacement. The equation of motion is determined as equation (9).

In equation (9), the force vector $P (t)$ and the displacement vector $a (t)$ are simply harmonic, both of their frequencies are $ω$ . By twice deriving the harmonic response displacement vector $a (t)$ , The harmonic response motion equation of the system is given as equation (12):

- ω^{2} [M] + i [C]) + [K] ({a_{1}} + i {a_{2}}) = ({P_{1}} + i {P_{2}})

(12)

Where

P_{1}

is the real part of the force;

P_{2}

is the imaginary part of the force;

a_{1}

is the real part of the displacement;

a_{2}

is the imaginary part of the displacement.

Analysis of bearing motion characteristics

The establishment of finite element model

The ECCRB is mainly composed of the outer ring, inner ring, elastic composite rolling elements and a cage. The elastic composite rolling element comprises a filling body and a hollow cylindrical roller. The filling degree of the rolling element is defined as the ratio of the filling body diameter d to the outer diameter D of the hollow cylindrical roller, which is represented by the symbol K. Taking the N2208 CRB as the research object, the specific structural dimensions of the bearing are recorded in Table 1.

Table 1.

Structure dimensions of N2208 roller bearings.

Parameters	Values
Outer ring diameter D_i/mm	80
Inner ring diameter D_o/mm	40
Bearing width b/mm	18
Rolling element diameter D/mm	10
Effective length of rolling elements l/mm	10
Number of rolling elements	13
Guide clearance c/mm	0.55

According to the parameters, a three-dimensional model is established in SolidWorks software and imported into ABAQUS software, and the material parameters of each component are set in ABAQUS software. To fit the deformation of all parts during the actual bearing operation, all aspects of the bearing are set as elastomers. The materials of hollow cylindrical rollers and inner and outer rings are bearing steel, which the elastic modulus is 2.0 × 10⁵ MPa as well as the density is 7800 kg/m³, and the Poisson’s ratio is 0.3; The cage is made of nylon, with an elastic modulus of 2600 MPa, a density of 1200 kg/m³ and a Poisson’s ratio of 0.35; The filling body is made of PTFE, with an elastic modulus of 280 MPa, a density of 2200 kg/m³ and a Poisson’s ratio of 0.4. Considering the accuracy and efficiency of calculation, the element type of each bearing component adopts hexahedral element, and the type of hexahedral element is C3D8R.¹⁷ The finite element model of the ECCRB with a filling degree of 50% is shown in Figure 1.

Figure 1.

Mesh generation of bearing with a filling degree of 50%.

When a bearing works, there are complex contacts and motion relationships between the bearing components, so select ABAQUS-Explicit as the solution tool for the finite element model. To simulate the dynamic relationship between the bearing components as realistically as possible, the contact between the surfaces of the bearing components is established in the interaction module and the contact properties are set, as shown in Table 2.¹⁸ The inner surface of the inner ring and outer surface of the cage are coupled to their midpoints, through which the load and boundary conditions can be applied to the inner ring and cage, and binding constraints are set between the filling body and hollow cylindrical roller.

Table 2.

Setting of contact properties of bearing parts.

Contact pair	Rolling elements with inner and outer rings	Cage with other parts
Friction coeff	0.05	0.1
Contact properties	Surface to surface contact, normal behavior is hard contact, tangential behavior is penalty contact
Sliding formulation	Finite sliding

The application of bearing load and speed is completed in the load unit. Due to the way in which the studied bearing is guided by the inner ring, the outer ring in the boundary conditions is steady. In addition to the X, Y direction of the translational degree of freedom and the rotational degree of freedom in the Z direction, the other directions of the cage and the inner ring are limited. The inner ring is applied with rotation speed in the Z direction and radial load in the Y direction, and the gravitational acceleration of y-direction with a magnitude of 9.8 m/s² is applied to the whole model. The smooth step is chosen as load amplitude curve and speed amplitude curve.

Validation of the model

In order to ensure the calculation accuracy of the above finite element model, the parameters of the ECCRB in the literature¹⁴ are selected, and the parameters are listed in Table 3. The finite element models of the ECCRB with filling degrees of 0%, 40%, 50% and 65% are established, and the maximum vibration amplitudes in the Y direction of the center point of the bearing inner ring are extracted and compared with the maximum experimental amplitudes, which is shown in Figure 2.

Table 3.

Structure dimensions of N310E roller bearings.

Parameters	Values
Outer ring diameter D_i/mm	110
Inner ring diameter D_o/mm	50
Bearing width b/mm	27
Rolling elements diameter D/mm	15
Effective length of rolling elements l/mm	13.5
Number of rollers	12

Figure 2.

Comparison of vibration displacement of experimental value and simulation value.

According to the analysis in Figure 2, the average relative error between the finite element simulation value and the experimental value is 5.71%, and the maximum relative error is 8.69%. The change rule of the two is similar, which verifies the correctness of the established finite element model to a certain extent.

The simulation values of the inner ring and cage velocity of the bearing with a filling degree of 50% is extracted and compared with the theoretical value, as shown in Table 4. As can be seen from the table, the relative error between the simulation value and the theoretical value of the inner ring and cage velocity of the bearing with a filling degree of 50% is 0.28% and 0.88%, respectively. The error between the finite element calculation results and the theoretical value is small, which further verifies the accuracy of the finite element dynamic analysis model of CRB established in this paper.

Table 4.

Comparison between simulation value and theoretical value of part velocity.

Part	Simulation value/mm·s⁻¹	Theoretical value/mm·s⁻¹	Relative error, %
Inner race	5250.80	5235.99	0.28
Cage	2451.80	2430.37	0.88

Computational results and analysis

With a filling degree K of 50% and guide clearance c of 0.55 mm, under the working conditions in which the radial load Fr is 2500 N, and the bearing rotation speed n is 2000 r/min, the dynamic response of the ECCRB is calculated and gained.

On the finite element model, node No. 558 on the outer diameter surface of the cage, node No. 235 on the inner ring raceway, and node No. 445 on the end face of the rolling element are selected respectively. The displacements of the cage, the inner ring raceway and the rolling element are shown in Figures 3 and 4 displays the node velocity of the cage. It can be obtained from the figures that at 0.015 s, the displacements of the node No. 558, No. 235 and No. 445 gradually increase, and the velocity of the node No. 445 gradually increases, which means that at this time, the inner ring starts to rotate and the rolling element starts to move driven by the inner ring. The displacements of node No. 558, node No. 235 and node No. 445 change sinusoidally with time. The node displacement period of the inner ring is about 0.03 s, and that of the rolling element and cage node is about 0.0736 s. The node velocity of the rolling element changes sinusoidally with time. The peak represents the velocity when the node touches the inner raceway, and the trough represents the velocity when the node touches the outer raceway. The velocity change period of the rolling element is about 0.01 s, and the average amplitude is about 5.5 m/s.

Figure 3.

Node displacements of inner ring, rolling element and cage.

Figure 4.

Node velocity of the rolling element.

Effects of the filling degree on cage stability

When the radial load Fr is 2500 N, the rotation speed of inner ring n is 2000 r/min, and the guide clearance c is 0.55 mm, the finite element models of the ECCRBs with filling degrees of 0%, 40%, 50% and 60% are established respectively. The actual angular velocity and the average value of the slip ratio of the cage are calculated and displayed in Figures 5 and 6.

Figure 5.

Angular velocity of the cage with different filling degrees. (a) K = 0%; (b) K = 40%; (c) K = 50%; (d) K = 60%.

Figure 6.

Average slip rate of the cage with different filling degrees.

It can be discovered from Figures 5 and 6 that there is a nonlinear relationship between the filling degree and the average value of cage slip rate. When the filling degree is less than 50%, with the increase of filling degree, the fluctuation range of angular velocity decreases and the average value of the cage slip rate decreases; as the filling degree increases from 50% to 60%, the fluctuation range of angular velocity and the average value of the cage slip rate increases. That is because as the filling degree increases, the mass and stiffness of rolling element decreases, the centrifugal force of rolling element is reduced and the inner ring’s drag effect on the roller is enhanced, which enhances the motion stability of the rolling element. When the filling degree is more than 50%, the stiffness and bearing capacity of the rolling element decrease sharply, which reduces the motion stability of the rolling element.

Influence of rotation speed on cage stability

Under the working conditions in which the radial load Fr is 2500 N, with the filling degree K of 50% and the guide clearance value c of 0.55 mm, the finite element models with the inner ring rotation speeds which are set as 1000 r/min, 2000 r/min, 3000 r/min, and 4000 r/min are established respectively. The actual angular velocity and the average value of the slip ratio of the cage are calculated, as shown in Figures 7 and 8.

Figure 7.

Angular velocity of the cage with different rotation speeds. (a) n = 1000 r/min; (b) n = 2000 r/min; (c) n = 3000 r/min; (d) n = 4000 r/min.

Figure 8.

Average slip rate of the cage with different rotation speeds.

Combined with Figures 7 and 8, it can be found that reducing the rotation speed is helpful to suppress the sliding of the cage. As the inner ring rotation speed decreases from 4000 r/min to 1000 r/min, the fluctuation range of angular velocity of the cage is reduced by 27.97 rad/s, and the average value of the slip rate decreases is reduced by 1.09%. The reason for this phenomenon is that as the inner ring rotation speed increases, the rolling element centrifugal force gradually increases. Therefore, the traction of the inner ring acting on the rolling elements is gradually weakened, and the impact frequency between roller and cage increases, leading to the decrease in the overall motion stability of the bearing.

Influence of radial load on cage stability

With the conditions that the inner ring rotation speed n is 2000 r/min, the filling degree K is 50% and the guide clearance c is 0.55 mm, the finite element models with different radial loads are established respectively. The actual angular velocity and the average value of the slip ratio of the cage are calculated, as displayed in Figures 9 and 10.

Figure 9.

Angular velocity of the cage with different radial loads. (a) Fr = 1500 N; (b) Fr = 2500 N; (c) Fr = 3500 N (d) Fr = 4500 N.

Figure 10.

Average slip rate of the cage with different radial loads.

Figures 9 and 10 has revealed that the relationship between the bearing motion stability and the radial load acting on the ECCRB is monotonically decreasing. With the increase of the radial load, the cage fluctuation range of angular velocity cage is reduced by 3.52 rad/s, and the average value of the slip rate decreases is reduced by 1.01%. This is because following the increase of radial load, the traction on the rolling element increases, and the movement of the roller tends to be stable, which inhibits the bad impact between roller and cage. As a consequence, the overall operation of the bearing becomes stable.

Analysis of bearing vibration characteristics

The establishment of finite element model

Modals of ECCRB with filling degrees of 0%, 40%, 50% and 60% are established and material properties are set in ABAQUS software, and the specific material parameters are shown in Table 1. Then a modal analysis step is created. The Block Lanczos method is selected to calculate, and the numerical method is used to select the number of eigenvalues requested.¹⁹ Considering that the natural frequency corresponding to the higher-order mode is large, which has little influence on the vibration of the bearing, the first 12 orders of free mode of the bearing are extracted as reference results. The contact between the parts of the bearing is established in the interaction module, and binding constraints are set between the filling body and the hollow cylindrical roller.

Based on the above modal analysis, a harmonic response analysis step is established, and the excitation frequency is set. According to the actual load condition of the bearing, with coupling the inner surface of inner ring to center point of the inner surface, the excitation load is exerted at the bearing center point, and outer surface of the outer ring is fixed. Because the shapes of the bearing components are relatively regular, the mesh of each part of the bearing is divided into a hexahedral mesh with the element type C3D8R.

Modal calculation results and analysis

The finite element models of ECCRBs with filling degrees of 0%, 40%, 50% and 60% are solved by modal solutions, and the natural frequencies of the first 12 orders of each bearing are calculated, as listed in Table 5.

Table 5.

Natural frequencies of the first 12 orders.

Order number	Natural frequency/Hz
Order number	0%	40%	50%	60%
1–6	0	0	0	0
7	5166.7	5139.5	5135.2	5113.4
8	5167.8	5140.1	5136.7	5114.7
9	5432.9	5416.5	5346.2	5218.2
10	5434.6	5416.7	5346.7	5218.8
11	8240.7	8207.2	8122.2	7784.5
12	12161	12142	11281	11252

From this table, it can be detected that the natural frequencies at the first six orders of the bearing in the free mode are 0, which is called the rigid mode. A higher-order mode of each bearing tends to correspond to a larger frequency. In addition, the data in the table shows that as the filling degree increases, the natural frequencies of each order of the ECCRB decrease.

Figure 11 shows the seventh-order modal vibration shapes of the ECCRB with different filling degrees, and vibration modal shapes of different orders of the ECCRB with a filling degree of 50% are shown in Figure 12. It can be discovered that for the vibration modal shape of the same order, as the filling degree increases, the vibration displacement of the bearing increases slightly. Each vibration modal shape of the bearing is different.

Figure 11.

Vibration modal shape of the seventh order with different filling degrees.

Figure 12.

Vibration modal shape of bearings with a filling degree of 50%.

Harmonic response analysis results

Analysis of bearing harmonic response under variable filling degree

To explore the effect of filling degree on vibration of bearing under excitation load, the same nodes of the cage and the rolling element of each finite element model are selected for comparative analysis, as shown in Figure 13. When the excitation load F is 2500 N, the vibration responses of ECCRBs with the filling degrees of 0%, 40%, 50% and 60% are calculated and compared.

Figure 13.

Node selection of the bearing finite element model.

Figures 14 and 15 show the vibration displacement of the cage node with excitation frequency and the vibration displacement of the rolling element node with excitation frequency respectively. It can be found from the figures that there are two peaks in the vibration displacements of the cage node and the rolling element node with different filling degrees. The change curve of the node displacement is as follows: increases from 0 to the maximum value at the beginning, then decreases rapidly, soon afterwards increases rapidly to the second peak value, and finally decreases slowly. The maximum peak values and the corresponding frequencies are shown in Table 6.

Figure 14.

Vibration displacement of cage node with different filling degrees.

Figure 15.

Vibration displacement of rolling element node with different filling degrees.

Table 6.

Maximum peak values and the corresponding frequencies.

Filling degree	The cage node		The rolling element node
Filling degree	Frequency/Hz	Displacement/mm	Frequency/Hz	Displacement/mm
K = 0	14103.5	0.00546	14103.5	0.00249
K = 40%	6663	0.00608	6663	0.00288
K = 50%	6578.4	0.00644	6578.4	0.00312
K = 60%	6337.9	0.00701	6337.9	0.00369

It is obvious to see from the table that the relationship between filling degree and vibration displacement is monotonically increasing. This is because the increase of filling degree would lead to the decrease in rolling element stiffness. The frequency corresponding to the peak displacement of the cage node is the same as that of the rolling element node, and the vibration displacement of the cage node is greater than that of the rolling element node. The reason is that the cage material has a smaller elastic modulus and a lower density compared with the rolling element, resulting in the larger elastic deformation of the cage under the excitation load.

Analysis of bearing harmonic response under variable excitation load

With a filling degree of 50%, the vibration response of the ECCRB under different excitation loads F of 1500 N, 2500 N, 3500 N, and 4500 N are carried out respectively. The vibration displacements at the same node of the cage and the rolling element with excitation load are obtained, as shown in Figures 16 and 17.

Figure 16.

Vibration displacement of cage node with different excitation loads.

Figure 17.

Vibration displacement of rolling element node with different excitation loads.

From the Figures 16 and 17, it is clear to know that the vibration displacements of the cage node and the rolling element node are consistent with the excitation frequency. At frequencies of 6578.4 Hz and 7214.7 Hz, the vibration displacement of the cage node and the rolling element node reaches the maximum value and the second peak. As the excitation load increases, the node vibration displacement increases. By comparison with the cage node, the vibration displacement of the rolling element node is smaller than that of the cage node, which shows that the excitation load plays a crucial effect on the vibration of the cage.

Conclusions

On the basis of kinematic theory and modal vibration theory, the finite element model of the ECCRB is established, and the influences of different filling degrees and different working conditions on the motion characteristics of the bearing are studied. The modal analysis and harmonic response analysis of the bearing are carried out. The conclusions are as follows:

1. There is a nonlinear relationship between the filling degree and the cage rate, as the filling degree increases, the bearing motion stability increases at the beginning and then decreases. Bearing inner ring speed and radial load affect significantly on the cage rate. Reasonable decrease of rotational speed and increase of radial force could enhance stability of the ECCRB.

2. The relationship between the filling degree and the natural frequency of the ECCRB is monotonically decreasing, and the decrease of the filling degree could decrease the vibration displacement of the ECCRB. With the increase in the excitation load, the vibration displacement of the ECCRB increases.

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: The authors would like to thank the Major scientific and technological projects in Shanxi Province (20201102003), Shanxi coal based low carbon joint fund (No. U1610118), National Natural Science Foundation of China (No. 51375325), National Key R&D Program of China (2018YFB1308701), Henan Province Science and Technology Research Project (No. 222102240017) for their support to this research.

ORCID iD

Chunjiang Zhao

Appendix

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