# Design and Application of Simulating Cutting Experiment System for Drum Shearer
## 2 Simulating Spiral Drum
### Design of the Spiral Drum  
The spiral drum is the cutting device in the cutting process of the shearer, and its practical simulation design is the key to ensuring the similarity between the experimental device and the prototype [10]. This paper takes the drum structure of the shearer as the primary research object and chooses a thin shearer as the prototype. It uses MLT dimensional analysis and similarity criterion derivation to study the cutting mechanism and related movement and structural parameters of the drum during operation [11]. When analyzing, consider the following parameters:  
Drum geometric structure parameters. Drum diameter \(D\). Blade outer edge diameter \(D_{y}\). Drum hub diameter \(D_{g}\). Drum cut depth \(B\). Spiral blade lift angle \(\alpha\). Blade lead \(H\). Blade head number \(Z\). Blade pitch \(S\). Blade hub wrap angle \(\beta\). Pick pitch \(T\). Pick installation angle \(\gamma\). Pick inclination angle \(\lambda\). Material parameters. According to coal and rock identification requirements, the primary consideration is to simulate the compressive strength \(\sigma_{y}\) and material density \(\rho\) of coal and rock materials. Operation parameters. Swing angle range \(\theta\) of the rocker arm, cutting resistance \(F\), cutting power \(P\), rotating speed of drum \(n\), traction speed \(v\). The above parameters will be able to obtain the parameter dimension matrix of the spiral drum, as shown in Table 1.  
On the basis of the second similarity theorem, this paper determined that the number of similarity criteria by the total number of physical quantities and the rank of the dimension matrix. The similarity criterion equation of the system is as follows:  
\[f(D,D_{y},D_{g},B,\alpha,H,Z,S,\beta,T,\gamma,\lambda,\sigma_{y},\rho,g,\theta,F,P,n,v)=0 \tag{2}\]  
There is a total of 20 system parameters. After subtracting the rank 3 of the matrix, the number of similarity criteria is 17. Because it contains 6 dimensionless quantities, it can be regarded as an independent \(\pi\) term. Therefore, the number of similarity criteria to be calculated is 11. Use the exponential method to analyze the dimensions of the system and obtain the linear homogeneous equations of the quality system. \[\left\{ \begin{array}{l}M:a_{13}+a_{14}+a_{17}+a_{18}=0\\ L:a_{1}+a_{2}+a_{3}+a_{4}+a_{6}+a_{8}+a_{10}-a_{13}-3a_{14}+a_{15}+a_{17}+2a_{18 }+a_{20}=0\\ T:-2a_{13}-2a_{15}-2_{17}-3a_{18}-a_{19}-a_{20}=0\end{array} \right. \tag{3}\]  
The similarity criterion for calculating different dimension parameters is:  
\[\left\{ \begin{array}{l}\pi_{1}{=}\;Dn/v,\pi_{2}=D_{y}n/v,\pi_{3}=D_{g}n/v,\pi_ {4}=Bn/v,\pi_{6}=Hn/v,\pi_{8}=Sn/v\\ \pi_{10}=Tn/v,\pi_{13}=\sigma_{y}v^{3}/(Pn^{2}),\pi_{14}=\rho v^{5}/(Pn^{2}), \pi_{15}=g/(nv),\pi_{17}=Fv/P\\ \pi_{5}=\alpha,\pi_{7}=Z,\pi_{9}=\beta,\pi_{11}=\gamma,\pi_{12}=\lambda,\pi_{ 16}=\theta\end{array} \right. \tag{4}\]  
The \(\pi\) term is an invariant, and the similarity index is one according to the first similarity theorem. The similarity coefficient expression is as follows:  
\[\left\{ \begin{array}{l}\frac{C_{0}C_{\pi}}{\zeta_{p}}=1,\frac{C_{D_{g}}C_{ \pi}}{\zeta_{p}}=1,\frac{C_{D_{g}}C_{\pi}}{\zeta_{p}}=1,\frac{C_{g}C_{\pi}}{ \zeta_{p}}=1,\frac{C_{\mu}C_{\pi}}{\zeta_{p}}=1,\frac{C_{g}C_{\mu}}{\zeta_{p}} =1,\frac{C_{\gamma}C_{\pi}}{\zeta_{p}}=1\\ \frac{C_{\gamma}C_{\gamma}^{3}}{C_{\gamma}C_{\gamma}C_{\gamma}^{3}}=1,\frac{C_ {\rho}C_{\gamma}^{5}}{C_{\gamma}C_{\gamma}^{2}}=1,\frac{C_{\rho}}{C_{\gamma} C_{\gamma}}=1,C_{\pi}=1,C_{Z}=1,C_{\beta}=1,C_{\gamma}=1,C_{\lambda}=1\end{array} \right. \tag{5}\]  
Considering the actual design of the simulated shearer, set the similarity coefficient of the drum diameter \(D\) to \(1/4\). The simulated cutting material is made of pulverized coal according to the similar principle, and the similarity coefficient of the material density is set to \(1\)[12, 13]. At the same time, the gravitational acceleration \(g\) value remains unchanged.