Calibration and Experimental Validation of Contact Parameters in a Discrete Element Model for Tobacco Strips

Abstract

To study the contact parameters of the tobacco strips during redrying, in this study, the funnel stacking test is used to determine the stacking angle, and the discrete element method is used to simulate the formation process of the stacking angle, to calibrate and verify the physical and contact parameters of tobacco strips. The Placket–Burman test was used to screen out the parameters that had significant effects on the stacking angle. The regression response surface model between the stacking angle and contact parameters was established by Central Composite Design using the stacking angle from physical tests as the response index. The test results show that static and rolling friction coefficients between tobacco strips have significant effects on the test results, so these two parameters must be accurately calibrated. Finally, the accuracy and validity of the calibrated tobacco strips contact parameters were verified by comparing the stacking angle and void ratio of physical and simulation experiments. The calibration results can provide basic parameters for studying the interaction and motion of the tobacco strips in the redrying process using simulation methods.

1. Introduction

Redrying is an important link in the tobacco industry chain [1]. At present, the adjustment of redrying control parameters of tobacco strips depends on experience entirely, which is manual setting and modification, and the control effect varies from person to person [2]. This leads to unstable quality of redrying tobacco strips, which makes some of the redrying finished products decline in quality or become moldy during storage and fermentation, bringing huge economic losses to tobacco factories [3,4].

The interactions between tobacco strips as well as between tobacco strips and equipment during the redrying process are very complex. The discrete element method (DEM) is used to numerically simulate the interaction and motion law between tobacco strips as well as between tobacco strips and equipment [5,6,7,8], which is helpful to capture the mechanism of interaction between tobacco strips, and then realize the automatic adjustment of relevant equipment process parameters [9,10,11]. However, before using the DEM for simulation tests, the simulation parameters (physical properties parameters, contact parameters between materials) of the material to be studied need to be determined, and it is important to use an accurate and reliable method to determine these simulation parameters [12]. Determining the simulation parameters of the tobacco strips by the method of parameter calibration is helpful to improve the accuracy in studying the interaction mechanism and motion law between tobacco strips using the DEM [13,14,15].

At present, parameter calibration by stacking angle is the main method to obtain simulation parameters of DEM, and the stacking angle of the study object can be obtained by the split cylinder method, tilt method, side plate lifting method, and inclined plane method [12]. Using these methods, researchers have conducted more studies on the calibration of simulation parameters of DEM such as seeds, straws, fertilizers, and soils. Cao et al. [16] calibrated the parameters of the rapeseed DEM model by stacking angles, and it was verified using a metering device test. Zhou et al. [17] calibrated the contact parameters between corn seeds by stacking angle and “self-flow screening” tests. Liu et al. [18] proposed a flexible wheat straw model based on the DEM to establish a flexible bending model of wheat straw, and the bonding parameters of the model were investigated. Liao et al. [19] calibrated the contact parameters of the fodder rape crop discrete element model through stacking angle tests, factor significance screening, and response surface tests. Xie et al. [20] used a combination of physical and simulation tests to develop a quadratic regression response surface model of the stacking angle and related parameters by the Box–Behnken test, using the measured stacking angle as the optimization index and deriving the results of the calibration parameters of organic fertilizer pellets. Wen et al. [12] proposed a friction factor calibration method based on the overall characteristics of the granular material, and the calibration parameters of urea particles were obtained by combining simulation tests with physical tests. Mudarisov et al. [21] evaluated the importance of particle contact parameters by the DEM, and they combined field tests and model tests to derive a nomogram for selecting contact model parameters based on moisture and soil type. Stahl et al. [22] proposed a numerical simulation method for the generation and calibration of stabilized soil with geogrid based on particles and studied the simulation of biaxial geogrid with specific particle and parallel bond models. In summary, the tobacco strip is a flake material and irregular in shape, and its material properties are different from existing research materials, and there are fewer related studies and a lack of similar materials for reference.

In this study, EDEM software was used as the simulation software, and the tobacco strips with different sizes and curls in the redrying stage were selected as the research object. The stacking angle of the physical test and simulation test were obtained by physical measurement and image processing technology. Through the significance test, the significant parameters affecting the stacking angle of the tobacco strips were determined, including the interval value of significance parameters through the steepest ascent test and the static friction coefficient and rolling friction coefficient between tobacco strips by the Central Composite Design. The fitting equation of the stacking angle is established, and the optimal stimulation parameters are obtained. Finally, the accuracy of calibration parameters is verified by the stacking angle test and void ratio test.

2. Materials and Methods

2.1. Tobacco Strips Material and Physical Test of Stacking Angle

The tobacco strips used in this study were C3F tobacco from Yuxi in 2021 (Figure 1), and the tobacco strips selected in the test were irregularly shaped flakes. Randomly measure the thickness of the 10 groups (each group is the thickness of 10 overlapping layers) of tobacco strips, take the average value, and the thickness of the tobacco strips is about 0.20 mm. The sizes and proportions of different sizes of tobacco strips are shown in

Table 1. Different sizes and proportions of tobacco strips.

Category	Size (mm)	Proportion
Large tobacco strips	>25.4	10%
Medium tobacco strips	12.7–25.4	80%
Small tobacco strips	6.35–12.7	10%

.

In this study, a method similar to the alfalfa straw stacking angle test measurement [23] was used for the tobacco strips stacking angle test. The test setup consisted of a funnel, a stand, and a material tray (Figure 1). During the experiment, the tobacco strips fall from the center of the upper entrance of the funnel, and the feeding amount is 600 strips. The tobacco strips were fed evenly to avoid blocking the funnel, and finally, the tobacco strips formed a tobacco strips pile on the material tray. The pile angle of the tobacco strips pile was the stacking angle. After repeating the test 10 times, the average value of the stacking angle was 40.37°. Referring to the similar material in the literature [24], it can be seen that the stacking angle obtained from the test is reasonable.

2.2. Tobacco Strips Simulation Model

Combined with the existing related studies [9,14,19], the curl of tobacco strips, the interaction between tobacco strips, and the interaction between tobacco strips and stainless steel are important factors that affect the simulation results in this study. Therefore, to balance the realism of the simulation results and the simulation efficiency when performing the parameter calibration, five types of tobacco strips models were established by combining the dimensional parameters such as the contour size and curl degree of the tobacco strips (Figure 2).

To better characterize the contour size and curl degree of the tobacco strips, this study obtained the geometry information of the tobacco strips by the image method, the curl degree of the tobacco strips by measurement, and finally, the discrete element model of the tobacco strips by using the multi-sphere model [25]. In building the model, according to the geometry and curl degree, the particle template of the tobacco strips model is built in UG; then, the particle template is imported into EDEM, the particles fall freely above the particle template, and the particle template is filled with particles. After the particles are filled in the particle template, the coordinates of the filled particles are derived in EDEM using post-processing, and then, the particle model of the tobacco strips is constructed in EDEM using the API modeling method. The Hertz–Mindlin model was used between the particles, the diameter of the particles was 0.20 mm (thickness of the tobacco strips), and the discrete element model of the tobacco strips obtained was rigid.

The measured curl of tobacco strips ranged from 5% to 22%, and when the curl is <9%, it could be regarded as no curl. Five models were established according to the geometry and curl of tobacco strips, and the types and proportions of tobacco strips corresponding to the five models are shown in

Table 2. Curl degree, size, and proportion of five tobacco strips models.

Category	Category Code	Curl	Size (mm)	Particles Count	Proportion
Large tobacco strips	a	20%	27	3682	10%
Medium tobacco strips I	b	16%	23	1702	30%
Medium tobacco strips II	c	0%	20	1216	20%
Medium tobacco strips III	d	12%	15	777	30%
Small tobacco strips	e	0%	8	140	10%

.

2.3. Simulation Parameters Determination

The material parameter ranges of the discrete element model for tobacco strips were determined based on the relevant literature [19,26,27]; pre-test and pre-simulation, they were as shown in

Table 3. Parameter settings for tobacco strips stacking angle simulation tests.

Parameter	Value	Source
Tobacco strips density (kg/m${}^3$)	280	[27]
Tobacco strips Poisson’s ratio	0.25–0.35	[27]
Tobacco strips shear modulus (Pa)	2.4 × ${10}^7$–3.5 × ${10}^7$	[27]
Stainless steel density (kg/m${}^3$)	7850	[19,26]
Stainless steel Poisson’s ratio	0.3	[19,26]
Stainless steel shear modulus (Pa)	7.94 × ${10}^1$${}^0$	[19,26]
Collision recovery coefficient between tobacco strips	0.01–0.10	[26]
Static friction coefficient between tobacco strips	0.4–1.0	Laboratory measurement
Rolling friction coefficient between tobacco strips	0.01–0.10	Laboratory measurement
Collision recovery coefficient between tobacco strips and stainless steel	0.02–0.20	[26]
Static friction coefficient between tobacco strips and stainless steel	0.35–0.50	Laboratory measurement
Rolling friction coefficient between tobacco strips and stainless steel	0.01–0.05	Laboratory measurement

. The particle generation method is dynamic, the generation rate of tobacco strips is 200 strips/s, the total number of tobacco strips is 600 strips, the time step is 0. 01 s, the grid size is 10R (R is the diameter of tobacco strips filled particles), and the simulation time is 4 s. Tobacco strips fall freely from the upper opening of the funnel through the funnel.

2.4. Tobacco Strips Stacking Angle Measurement for Physical Experiments

In the physical test, the tobacco strips pile can be considered as a uniformly distributed cone, as shown in Figure 3. The bottom diameter D and height H of the tobacco strips pile are measured several times in different orientations, and the average value of multiple measurements is used. Then, the stacking angle of the tobacco strips is calculated by the following equation:

$$tan{\theta }_1=\frac{2H}{D}$$

(1)

where ${\theta }_1$ is the stacking angle measured by the physical test of tobacco strips, (°); H is the stacking height of tobacco strips pile, mm; D is the diameter of the bottom of tobacco strips pile, mm.

In the simulation test, the stacking angles were obtained by image processing techniques [28,29]. (i) Obtain the stacking images in EDEM in the X and Y directions of the tobacco strips pile, and segment the images symmetrically to form four unilateral images of X+, X−, Y+, and Y− (Figure 4a); (ii) Extract the contour coordinates of the unilateral images in MATLAB (Figure 4b); (iii) Select the slope contour coordinates of the unilateral images and perform a linear fit in Origin to obtain the slope k of the fitted equation (Figure 4c). Then, the unilateral stacking angle can be calculated by Equation (2), and finally, the average value of the four unilateral stacking angles is taken as the stacking angle of the tobacco strips pile.

$$tan{\theta }_2=\mid k\mid$$

(2)

where ${\theta }_2$ is the stacking angle measured by the tobacco strips simulation test, (°); k is the slope of the linear fitting equation for the profile curve of the simulated tobacco strips pile.

3. Results and Discussion

3.1. Calibration and Analysis of Contact Parameters

3.1.1. Screening and Analysis of Significant Parameters

To reduce the number of tests and obtain the determined combinations of simulation parameters such as static and rolling friction coefficient, and collision recovery coefficient as soon as possible, the Plackett–Burman test design was carried out by applying Design-Expert software, and the parameters with significant effects on the simulation test results were selected by using the physical test measurements of the stacking angle as the response values. The Plackett–Burman experimental design was performed for the eight uncertain parameters in Table 3, and the minimum and maximum values of the eight parameters were coded as −1 and +1 levels [23], respectively, according to the already determined parameter ranges, and the results are shown in

Table 4. Plackett–Burman test parameters.

Parameters	Symbols	Level
		Low Level (−1)	High Level (+1)
Tobacco strips Poisson’s ratio	$X_1$	0.25	0.35
Tobacco strips shear modulus (Pa)	$X_2$	2.4 × ${10}^7$	3.5 × ${10}^7$
Collision recovery coefficient between tobacco strips	$X_3$	0.01	0.10
Static friction coefficient between tobacco strips	$X_4$	0.40	1.00
Rolling friction coefficient between tobacco strips	$X_5$	0.01	0.10
Collision recovery coefficient between tobacco strips and stainless steel	$X_6$	0.02	0.20
Static friction coefficient between tobacco strips and stainless steel	$X_7$	0.35	0.50
Rolling friction coefficient between tobacco strips and stainless steel	$X_8$	0.01	0.05

.

The stacking angle of the tobacco strips pile is obtained by measuring the stacking angle of the four one-sided images of the tobacco strips pile. The Plackett–Burman experimental design and results are shown in

Table 5. Plackett–Burman test design and results.

No.	${\mathit{X}}_1$	${\mathit{X}}_2$	${\mathit{X}}_3$	${\mathit{X}}_4$	${\mathit{X}}_5$	${\mathit{X}}_6$	${\mathit{X}}_7$	${\mathit{X}}_8$	${\mathit{\theta }}_2$ (°)
1	1	1	−1	−1	−1	1	−1	1	30.80
2	1	−1	−1	−1	1	−1	1	1	43.13
3	−1	−1	−1	1	−1	1	1	−1	45.63
4	1	−1	1	1	−1	1	1	1	42.75
5	1	−1	1	1	1	−1	−1	−1	69.97
6	−1	1	1	−1	1	1	1	−1	47.51
7	1	1	1	−1	−1	−1	1	−1	28.71
8	1	1	−1	1	1	1	−1	−1	64.36
9	−1	−1	1	−1	1	1	−1	1	45.23
10	−1	1	−1	1	1	−1	1	1	50.66
11	−1	−1	−1	−1	−1	−1	−1	−1	37.45
12	−1	1	1	1	−1	−1	−1	1	49.87

.

The results of Table 5 were analyzed by ANOVA, and the influence effect of each parameter was obtained, which is shown in

Table 6. Significance analysis of Plackett–Burman test parameters.

Parameters	Sum of Squares	Mean Square	F-Value	p-Value
$X_1$	0.9464	0.9464	0.0658	0.8142
$X_2$	12.51	12.51	0.8692	0.4199
$X_3$	12.02	12.02	0.8355	0.4281
$X_4$	681.16	681.16	47.35	0.0063 **
$X_5$	611.33	611.33	42.49	0.0073 **
$X_6$	1.03	1.03	0.0714	0.8067
$X_7$	128.64	128.64	8.94	0.0581
$X_8$	81.07	81.07	5.64	0.0982

Note, ** indicates an extremely significant effect (p < 0.01).

. The significant p-value determines the influence level of the parameter on the stacking angle. As can be seen from Table 6, the effects of $X_4$ and $X_5$ on the stacking angle of the tobacco strips were extremely significant with p-values of 0.0063 and 0.0073, respectively, while the effects of other factors were small. To improve the efficiency and accuracy of the simulation test, the significance test level was set as 0.01, the generally significant influencing factors were excluded, and the two factors $X_4$ and $X_5$ were focused and calibrated by the simulation test. The remaining parameters were taken by referring to the method of the literature [26] ($X_1$ = 0.30, $X_2$ = 2.95 × ${10}^7$, $X_3$ = 0.055, $X_6$ = 0.11, $X_7$ = 0.425, $X_8$ = 0.03).

3.1.2. The Optimal Range for Significant Parameters

Based on the results of the Plackett–Burman test, the steepest ascent test allows for the determination of the optimal range of simulation parameters for the significance parameters [19], and the design scheme and results are shown in

Table 7. The steepest ascent test design scheme and results.

Test Level No.	${\mathit{X}}_4$	${\mathit{X}}_5$	${\mathit{\theta }}_2$ (°)	Relative Error /%
1	0.4	0.010	33.22	17.71%
2	0.5	0.025	38.15	5.50%
3	0.6	0.040	43.44	7.60%
4	0.7	0.055	50.13	24.18%
5	0.8	0.070	54.38	34.70%
6	0.9	0.085	56.08	38.91%
7	1.0	0.100	56.56	40.10%

. The results show that the stacking angle of tobacco strips increases with the increase of coefficients $X_4$ and $X_5$, and the relative error of stack angle first decreases and then increases. At Test level 2 and level 3, the relative error is the minimum value. The stacking angle at Test level 2 is smaller than the test value, and the stacking angle at Test level 3 is larger than the test value. It can be seen that the optimal value interval is between Test levels 2 and 3, so the range around Test levels 2 and 3 was selected for the Central Composite Design.

3.1.3. Results and Analysis of Central Composite Design

Based on the results of the steepest ascent test, $X_4$ was determined to range from 0.5 to 0.6, and $X_5$ was 0.025 to 0.040. $X_4$ and $X_5$ were coded for the simulation test parameters before using Design-Expert software for Central Composite Design, and the factor coding results are shown in

Table 8. Level coding table for simulation parameters.

Level Coding	Parameters
	${\mathit{X}}_{\mathbf{4}}$	${\mathit{X}}_{\mathbf{5}}$
−1.414	0.479	0.0219
−1	0.50	0.025
0	0.55	0.0325
1	0.60	0.040
1.414	0.621	0.0431

.

Design-Expert software was applied for generic Central Composite Design. $X_4$ and $X_5$ were the simulation test factors, and the stacking angle measured by physical experiments was the response index. Thirteen sets of simulation tests were designed according to the test requirements, of which five sets were central level repetition simulation tests, and the results are shown in

Table 9. Central Composite Design and results.

No.	${\mathit{X}}_4$	${\mathit{X}}_5$	${\mathit{\theta }}_2$ (°)	Relative Error /%
1	1.41421	0	42.51	5.30%
2	0	0	40.17	0.50%
3	1	1	43.62	8.05%
4	0	0	40.26	0.27%
5	0	0	40.03	0.84%
6	0	0	40.12	0.62%
7	0	1.41421	39.92	1.11%
8	0	0	40.15	0.54%
9	−1.41421	0	39.97	0.99%
10	0	−1.41421	38.31	5.10%
11	−1	−1	38.22	5.32%
12	−1	1	40.25	0.30%
13	1	−1	37.64	6.72%

.

The regression equation between $X_4$, $X_5$, and the stacking angle ($\theta$) is established from the data in Table 9. As shown in Equation (3).

$$\begin{array}{cc}\hfill \theta =& 0.9017X_4+0.5750X_5+0.9875X_4{X}_5-0.55582X_4^2-0.5260X_5^2\hfill \\ \hfill & +1.43X_4^2{X}_5-0.2096X_4{X}_5^2-0.2456X_4^2{X}_5^2+40.15\hfill \end{array}$$

(3)

The ANOVA for Central Composite Design test results was performed using the Analysis module of the Design-Expert software, and the results are shown in

Table 10. ANOVA for Central Composite Design test results.

Source	Sum of Squares	df	Mean Square	F-Value	p-Value
Model	31.07	8	3.88	560.42	<0.0001	significant
$X_4$	3.23	1	3.23	465.48	< 0.0001
$X_5$	1.3	1	1.3	187.02	0.0002
$X_4{X}_5$	3.9	1	3.9	562.86	< 0.0001
$X_4^2$	1.71	1	1.71	246.72	< 0.0001
$X_5^2$	1.52	1	1.52	219.12	0.0001
$X_4^2{X}_5$	4.03	1	4.03	582.16	< 0.0001
$X_4{X}_5^2$	0.087	1	0.087	12.56	0.0239
$X_4^2{X}_5^2$	0.1182	1	0.1182	17.06	0.0145
Pure Error	0.0277	4	0.0069
Cor Total	31.1	12
$R^2$ = 0.9991	$Adjusted{R}^2$ = 0.9973		$C.V.$ = 0.2076%		$AdeqPrecision$ = 86.3346

. The F-value of the regression model is 560.42 > 21.35, indicating that the model is significant; and all p-values are less than 0.05, indicating that each item in the mode is important. In this case, $X_4$, $X_5$, $X_4{X}_5$, $X_4^2$, $X_5^2$, $X_4^2{X}_5$, $X_4{X}_5^2$, and $X_4^2{X}_5^2$ are significant model terms. It shows that this test is reasonable and effective, and all factors that have a significant effect on the stacking angle have been taken into account. The coefficient of determination $R^2$ = 0.9991 and the corrected coefficient of determination $Adjusted{R}^2$ = 0.9973, which both tend to be close to 1, indicate that the model fits well with the actual test. The coefficient of variation ($C.V.$) is 0.2076%, which indicates that the test has high reliability. The test accuracy ($AdeqPrecision$) is 86.3346 > 4, indicating that the model has good accuracy [30].

The response surface of the stacking angle of tobacco strips is shown in Figure 5. As can be seen from Figure 5, the response surface curves of $X_4$ and $X_5$ are both steep and have different trends, indicating that both factors have a significant effect on the stacking angle, but not to the same extent. At the same time, the contours are denser along with $X_4$ than along $X_5$, indicating that the effect of $X_4$ on the stacking angle is more significant than that of $X_5$.

The Optimization-Numerical module of Design-Expert software is used to make the simulation results closest to the experimentally obtained tobacco strips stacking angle, and the regression model is solved optimally with the constrained objective (Equation (4)).

$$\left\{\begin{array}{c}\theta (X_4,X_5)=40.37\\ 0.500\le X_4\le 0.600\\ 0.025\le X_5\le 0.040\end{array}\right.$$

(4)

The optimization results are obtained from Equations (3) and (4), and Figure 5: the coefficient of static friction between tobacco strips ($X_4$) is 0.560, and the coefficient of rolling friction between tobacco strips ($X_5$) is 0.033, at which time the stacking angle simulation results satisfy the response index.

3.2. Validation and Analysis of Contact Parameter Calibration Results

3.2.1. Verification and Analysis by the Stacking Angle Test

To verify the reliability and authenticity of the simulation parameters of the calibrated discrete element model, the parameters determined above were used as the EDEM simulation parameters, and three simulation tests were conducted to obtain the stacking angles of 40.32${}^{°}$, 40.46${}^{°}$, and 40.66${}^{°}$ for the tobacco strips pile, respectively, the two-sample equal variance t-test was performed on the stacking angle of this sample and the physical test, and p = 0.73 > 0.05 was obtained, which showed that there was no significant difference between the stacking angle obtained from the physical test and the simulation test. The mean value of the stacking angle of the physical test is 40.37${}^{°}$, the mean value of the stacking angle of the simulation test is 40.48${}^{°}$, and the relative error between them is only 0.27%, which verified the reliability and authenticity of the simulation test. The test comparison is shown in Figure 6.

3.2.2. Verification and Analysis by the Void Ratio Test

In the study of simulation parameter calibration tests using stacking angle, in addition to using the stacking angle test to verify the accuracy of the simulation parameters, other physical tests are usually used to verify the simulation parameters, such as the electromagnetic hopper vibration verification test [30], the corn seed stacking density verification test [31], and the corn seed reversal verification test [32]. The basic principle of these validation tests is based on the stacking density of the material, which can reduce the error caused by the material shape and other factors. The light mass, curl, and irregular shape of tobacco strips make it difficult to measure the stacking density directly. In this study, based on the above characteristics of tobacco strips, the void ratio test was used to validate the calibrated discrete element simulation parameters of tobacco strips. The void ratio is the ratio of the total volume of tobacco strips to the total volume of the tobacco strips pile in the formed tobacco strips pile.

The results of the three simulation tests in Section 3.2.1 were used to calculate the tobacco strips pile stack void ratio. The physical test tobacco strips pile stack void ratio was measured by the ideal gas method [33], and the experimental setup is shown in Figure 7. In Figure 7, container A and container B are equal volume and not deformed pressure vessels, container B is filled with tobacco strips (free fall filling); open gas pipe a, close gas pipe b, add gas to container A with gas pump, when the pressure gauge reaches the appropriate value close gas pipe a, record the value of the pressure gauge $P_0$ (relative air pressure value). According to the ideal gas law, there are:

$$(P_0+P_a)V_A+P_a{V}_B=nRT$$

(5)

where $V_A$ is the volume of gas in container A, m${}^3$; $V_B$ is the volume occupied by the gas in container B, m${}^3$; $P_a$ is the atmospheric pressure at the location of the test chamber, Pa; T is the temperature, K; n is the amount of substance of the gas, mol; R is the molar gas constant, J/(mol.K).

Open the gas pipe b and wait until the barometer value is stable to record the pressure gauge value $P_1$. According to the ideal gas law, there are:

$$(P_1+P_a)(V_A+V_B)=nRT$$

(6)

According to Equations (5) and (6), there are:

$$\frac{V_B}{V_A}=\frac{P_0-P_1}{P_1}$$

(7)

The stacking void ratio $\epsilon$ of tobacco strips is the ratio of the volume occupied by gas in container B to the volume occupied by gas in container A. According to Equation (7), the void ratio $\epsilon$ can be expressed as:

$$\epsilon =\frac{P_0-P_1}{P_1}\times 100\%$$

(8)

After three simulation tests, the voids ratio of the tobacco strips pile were 65.72%, 63.37%, and 61.18%, respectively. A two-sample equal variance t-test was performed for this sample, and the physical test stacking angle and p = 0.86 > 0.05 was obtained. The results showed that there was no significant difference between the void fraction obtained from the physical test and the simulation test. The mean value of the void ratio of the physical test is 62.28%, the mean value of the void ratio of the simulation test is 63.42%, and the relative error of both is 1.83%. The reliability and authenticity of the simulation test were further verified.

4. Conclusions

Based on a combination of physical and simulation tests, a discrete element simulation model of tobacco strips was developed using EDEM software, and the relevant parameters were calibrated using the physical experimental stacking angle as the response index. The conclusions are as follows:

(1)

The results of the significant factor screening test showed that among the parameters of the simulation model, the static friction coefficient between tobacco strips ($X_4$) and the rolling friction coefficient between tobacco strips ($X_5$) had an extremely significant effect on the stacking angle (p < 0.05). The results of the steepest ascent test showed that the tobacco strips stacking angle increased with the increase of the two significantly influencing parameters.

(2)

Based on the results of Central Composite Design, a regression equation between $X_4$, $X_5$, and stacking angle was established, and the response surface finding a solution to the regression equation was carried out using the physical test stacking angle of tobacco strips as the response index. The optimal combination of the significant parameters was obtained as the static friction coefficient between tobacco strips ($X_4$) is 0.560, and the rolling friction coefficient between tobacco strips ($X_5$) is 0.033.

(3)

The simulation test is carried out under the optimal combination of significant parameters. The average value of the stacking angle for the three simulations was 40.48${}^{°}$, with a relative error of 0.27% compared to the actual physical test stacking angle. The mean value of the void ratio for the three simulations was 63.42%, with a relative error of 1.83% compared to the actual physical void ratio results. The accuracy and validity of the simulation parameters of the discrete element model for tobacco strips were demonstrated.