Summary：In order to reduce the wear and tear of impact crusher blow bars and prolong its service life, according to Rabnowicz equation, the material content of the impact crusher blow bar was optimized by taking the load on the impact crusher blow bar as the evaluation criterion of its wear and tear. The physical measurement of LT1213 impact crusher and copper ore is carried out. The UG model of LT1213 impact crusher is established and imported into EDEM software. The particle model of copper ore is analyzed. The quadratic regression orthogonal rotary combination test design is adopted. The load of the impact plate is tested by the discrete element software EDEM. The regression equation of each test factor is obtained by SPSS software, and the three-dimensional contour map is drawn by matlab, and the influence rule of each parameter on the performance index is determined. The optimum combination of parameters is obtained by optimizing the test factors. When TiC content is 3.58% , TaC content is 2.77% , and Ni content is 0. 33% , the load on the blow bars of the impact crusher is 24. 76 kN. The influence trend of TaC and TiC content on the wear of the blow bars of LT1213 impact crusher was obtained through experiments, and the simulation conclusion was verified. The results provide a theoretical basis for optimizing the blow bars of the impact crusher, reducing its wear and prolonging its service life.
The blow bar is one of the key working parts of the impact crusher, and its working conditions are harsh and complex, and it is prone to wear, deformation and other failure forms . The adoption of corresponding methods to reduce the wear amount of the impact plate and improve the wear resistance is of great significance for extending its service life and reducing production costs. EDEM is a kind of application software of discrete element method, which is very suitable for the study of motion behavior and mechanical behavior between discontinuous particle populations, and has many prospective applications and researches in different engineering environments .
In this paper, the process of crushing copper ore with LT1213 impact crusher is studied by discrete element method. On this basis, the wear amount of blow bar of impact crusher is analyzed, and the quadratic orthogonal rotation combination test is carried out by discrete element software EDEM, aiming to obtain the optimal composition combination of blow bar of impact crusher with certain calculation methods.
Establishment of model
Discrete element theory model
In the discrete element method proposed in this study, the interaction between particles is mainly radial force and normal force, and the normal force can be expressed as:
![\[ F_{\mathrm{n}}=\frac{4}{3} E^{*}\left(R^{*}\right)^{1 / 2} \alpha^{3 / 2} \]](https://qimingcasting.oss-us-west-1.aliyuncs.com/wp-content/ql-cache/quicklatex.com-b7a37fa6b90b720463c178a58e9ced5b_l3.png "Rendered by QuickLaTeX.com")
In the above formula, 
is the mean of the radius of all particles, 
is the range of contact of particles and 
is the mean of the elastic modulus of all particles, expressed as:
![\[ \frac{1}{E^{*}}=\frac{1-\nu_{1}^{2}}{E_{1}}+\frac{1-\nu_{2}^{2}}{E_{2}} \]](https://qimingcasting.oss-us-west-1.aliyuncs.com/wp-content/ql-cache/quicklatex.com-f72d91538679b7de9a74883661c57359_l3.png "Rendered by QuickLaTeX.com")
In the form above,
form is the elastic modulus of one particle, and 
form is the Poisson’s ratio of one particle. The 
and 
in the same expression.
Radial force can be expressed as:
![\[ F_{\mathrm{t}}=-8 G^{*} \sqrt{R^{*} \alpha} \eta \]](https://qimingcasting.oss-us-west-1.aliyuncs.com/wp-content/ql-cache/quicklatex.com-8d3f1d1fb0a2b614b7539220d4680622_l3.png "Rendered by QuickLaTeX.com")
In the above formula, η is the area of overlap between interacting particles and 
is the modulus translated from particles.
Therefore, it can be analyzed that in the study of the discrete element method, the forces on the particles and objects contacted by the particles are closely related to their modulus of elasticity, Poisson’s ratio, shear modulus, etc., and the values of these parameters are inextricably linked to the type of material.
The establishment of particle model and geometric model
Rabnowicz equation:
![\[ \frac{V}{S}=K_{\mathrm{abr}} \frac{W}{H} \]](https://qimingcasting.oss-us-west-1.aliyuncs.com/wp-content/ql-cache/quicklatex.com-d7811118dac97fdf1acfd42fd421b542_l3.png "Rendered by QuickLaTeX.com")
is the wear coefficient, 
is the abrasive wear amount (mm),
is the wear distance(mm); 
is the load(kN); 
is the material hardness(MPa).
Therefore, in the process of operation of the impact crusher, generally in the case of 
and , the working parts of the impact crusher (such as: crusher blow bars, impact plate) wear is related to the load it receives.
The internal materials of the impact plate of LT1213 impact crusher were analyzed by energy spectrum analyzer (FIG. 1), and combined with relevant literature, it was found that the main material components that had a greater impact on the wear of the blow bars were TiC, TaC, Ni, etc. TaC, TiC and NIwere selected to conduct simulation tests. Quadratic regression orthogonal rotation combination design was used in the experiment.
In the study of the discrete element method in mining engineering, no matter what kind of ore is crushed, the external geometric characteristics of the ore have an important impact on the calculation results of the discrete element method. Therefore, in this study, the geometric size of copper ore (FIG. 2) is analyzed, its geometric characteristics are measured by laser scanner, and the scope and law of its size distribution are analyzed. According to the analysis results, the corresponding discrete element model of copper ore is established in EDEM for subsequent simulation research.
In the simulation calculation of discrete elements, it is not necessary to establish a complete external model, but only the parts in contact with particles need to be modeled. Therefore, the UG model of the crusher is relatively simplified in EDEM (Figure 3).
Design and optimization of auxiliary parameters based on EDEM
EDEM software simulation
The resting Angle is measured according to the collapse experiment (FIG. 4) and combined with the literature, the physical characteristics between copper ore and impact crusher are shown in Table 1.
| Table.1 Simulation Parameters | ||||||
| Materials | density (kg·m ³) | Poisson’s ratio | Shear modulus /Pa | Coefficient of restitution | Static friction coefficient | Kinetic friction coefficient |
| Copper ore | 2520 | 0.245 | 2.5×10⁸ | 0.4 | 0.45 | 0.02 |
| Steel | 7800 | 0.3 | 7×10¹⁰ | 0.5 | 0.85 | 0.06 |
| TiC | 4930 | 0.3 | 7.9×10⁹ | 0.6 | 0.8 | 0.07 |
| TaC | 5650 | 0.33 | 8.3×10¹⁰ | 0.6 | 0.8 | 0.07 |
| Ni | 8902 | 0.27 | 2.2×10¹¹ | 0.65 | 0.9 | 0.09 |
Due to the non-adhesion effect of copper ore surface and the above research on discrete element model, it is known that Hertz-MindLin(no slip) built-in is chosen as the simulation contact model.
Simulation test factors and indexes
Based on the analysis of Rabnowicz equation above, the load (Z) on the impact plate is taken as the evaluation index. According to the above-mentioned theoretical analysis and the actual operation requirements of LT1213 impact crusher, the variation range of test factors is reasonably controlled, each test is repeated 7 times, and the average value is taken as the test result, the factor level code is shown in Table 2, and the test plan and results are shown in Table 3.
| Encoding | Table 2. Factor horizontal coding | ||
| TiC Content/% | Tac Content/% | Ni Content/% | |
| X₁ | X₂ | X₃ | |
| 1.682 | 4.4 | 3.2 | 1.05 |
| 1 | 3.93 | 2.92 | 0.90 |
| 0 | 3.25 | 2.5 | 0.68 |
| -1 | 2.57 | 2.08 | 0.46 |
| -1.682 | 2.1 | 1.8 | 0.31 |
| Table 3 Test scheme and results | ||||
| Series | TiC Content/% | TaC Content/% | Ni Content/% | Wear Parts load/% |
| 1 | 1 | 1 | 1 | 25.79 |
| 2 | 1 | 1 | -1 | 24.8 |
| 3 | 1 | -1 | 1 | 24.66 |
| 4 | 1 | -1 | -1 | 26.11 |
| 5 | -1 | 1 | 1 | 29.03 |
| 6 | -1 | 1 | -1 | 27.22 |
| 7 | -1 | -1 | 1 | 31.60 |
| 8 | -1 | -1 | -1 | 31.80 |
| 9 | 1.682 | 0 | 0 | 26.01 |
| 10 | -1.682 | 0 | 0 | 30.84 |
| 11 | 0 | 1.682 | 0 | 26.17 |
| 12 | 0 | -1.682 | 0 | 32.71 |
| 13 | 0 | 0 | 1.682 | 25.02 |
| 14 | 0 | 0 | -1.682 | 24.99 |
| 15 | 0 | 0 | 0 | 25.28 |
| 16 | 0 | 0 | 0 | 25.13 |
| 17 | 0 | 0 | 0 | 24.67 |
| 18 | 0 | 0 | 0 | 26.39 |
| 19 | 0 | 0 | 0 | 25.32 |
| 20 | 0 | 0 | 0 | 26.08 |
| 21 | 0 | 0 | 0 | 24.79 |
| 22 | 0 | 0 | 0 | 24.71 |
| 23 | 0 | 0 | 0 | 25.80 |
Test results and analysis
Wear parts load
Spss data analysis software was used to conduct regression analysis on the load test results of the counterattack plate in Table 3, and the regression equation test data were shown in Table 4.
| Table 4 Test table of regression equation for wear parts load | ||||
| Source | Sum of squares | Degree of freedom | Mean square | F-value |
| regression | 16575.89 | 10 | 1657.59 | 2334.63 |
| Residual error | 9.233 | 13 | 0.71 | |
| Before correction | 16585.13 | 23 | ||
| After correction | 143.77 | 22 | ||
See Table F.₀ ₀₁(10,13)=4.10,F=2334.63>F₀. ₁(10,13),Therefore, the regression equation is highly significant, and the quadratic regression equation model is as follows:
![\[ \begin{array}{l}A=142.296-23.028 X_{1}-56.088 X_{2}- \\3.209 X_{3}+2.184 X_{1}{ }^{2}+7.969 X_{2}{ }^{2}-3.902 X_{3}{ }^{2}+ \\2.854 X_{1} X_{2}-1.585 X_{1} X_{3}+5.624 X_{2} X_{3}\end{array} \]](https://qimingcasting.oss-us-west-1.aliyuncs.com/wp-content/ql-cache/quicklatex.com-56eecf5ff305cb538bfcb98567963a47_l3.png "Rendered by QuickLaTeX.com")
Use Matlab to draw 3D contour map, as shown in Figure 5.
The analysis of FIG. 5 shows that when TiC content is at zero level, with the increase of TaC content, the impact plate load shows a trend of first decreasing and then increasing. When TaC content is at zero level, with the increase of TiC content, the impact plate load shows a slow decline trend. When the TiC content is at zero level, the change of Ni has little effect on the impact plate load. When the Ni content is at the zero level, with the increase of the TiC content, the impact plate load shows a sharp decline and then a slight increase. When TaC content is at zero level, the impact plate load decreases slightly with the increase of Ni content, but has little effect on it. When the Ni content is at zero level, with the increase of TiC, the impact plate load shows a sharp decline and then a slow rise trend. In addition, it can be seen from the regression equation and three-dimensional contour map that three factors have significant effects on the impact plate load within the test range: TaC content, TiC content and Ni content.
Impact crusher blow bars optimization
According to the optimization mathematical model and the regression equation of each performance evaluation index of the impact crusher, the nonlinear optimization fmincon function in Matlab is used, and the optimization process is carried out under the condition of Fₘᵢₙ=Z, that is, the minimum load. The proposed constraint function is as follows:
![\[ \begin{array}{l}F_{\min }=Z \\\text { s.t. }\left\{\begin{array}{l}2.1 \% \leqslant X_{1} \leqslant 4.4 \% \\1.8 \% \leqslant X_{2} \leqslant 3.2 \% \\0.31 \% \leqslant X_{3} \leqslant 1.05 \%\end{array}\right.\end{array} \]](https://qimingcasting.oss-us-west-1.aliyuncs.com/wp-content/ql-cache/quicklatex.com-1a240422a5ec7745f930149cd1ce98c4_l3.png "Rendered by QuickLaTeX.com")
The optimal treatment results are as follows: TiC content is 3.58%,TaC content is 2.77%, Ni content is 0.33%. Under this condition, the simulation test shows that the impact crusher wear parts load of the impact crusher is 24.76 kN.
Test verification
In order to carry out the test reasonably, and due to the requirements of the accuracy of the material preparation instrument, when the Ni content is 0.3%, The UMT-3 wear measuring instrument was used to test and analyze the wear of the crusher blow bars with different TaC content (1.8%, 2%, 2.5%, 3%, 3.2%) and different TiC content (2.1%, 2.6%, 3.2%, 3.8%, 4.3%), and the test was repeated 10 times in each case. The wear amount of the crusher blow bar obtained by the test is shown in Figure 6.
From Fig. 6, when the TiC content is the same, with the increase of TaC content, the wear of the impact crusher blow bars gradually decreases, and when the TaC content reaches 2.5%, the wear of the impact crusher blow bars reaches the lowest, and then with the increase of TaC content, the wear of the impact crusher blow bars gradually increases. When the TaC content is the same, TiC content is different, except in TaC content of 1.8%, TiC content of 3.8% wear is greater than the TiC content of 2.6% wear, the rest of the test results reflect that the wear of the impact plate from small to large corresponding to the TaC content are: 3.2%, 3.8%, 2.6%, 4.3%, 2.1%, respectively. The trend of the effect of TaC and TiC content on the impact plate wear of the impact crusher is the same as that of the simulation results.
Conclusion
- By using EDEM as virtual crushing test of orthogonal copper ore, the regression equation based on the force of counter plate is established by quadratic regression orthogonal rotating combination test. Using Matlab to draw the contour map of the investigation index, the influence trend of the test factors on the force of the blow bar was obtained, and the main and secondary factors affecting the force of the blow bar were determined as TaC content, TiC content and Ni content.
- The optimal parameter combination to reduce the wear component of the impact plate of LT1213 impact crusher is determined. When the TiC content is 3.58%, TaC content is 2.77%, Ni content is 0.33%, the blow bar wear is the least, and the load on the blow bar of the impact crusher is 24.76 kN.
- The influence trend of TaC and TiC content on the blow bar wear of impact crusher is obtained through experiments, which shows the correctness of analyzing the impact plate by discrete element method.
