As one of the main components of the belt conveyor, the design of the transmission roller often uses the empirical formula method, and adopts a higher safety factor to ensure the reliability of the roller. The disadvantage of this method is that the roller structure is too large, the mass is increased, and the cost is greatly increased. This paper uses Ansys software to analyze the roller assembly model, find out the stress-strain distribution law, and analyze the stress-strain cloud map to facilitate the optimization of the roller.

1 3D modeling of roller assembly
The transmission roller consists of roller shell, spoke plate and wheel hub, sleeve and roller shaft. According to its load-bearing capacity, it can be divided into three categories: light roller, medium roller and heavy roller. According to the surface structure of the roller, it can be divided into smooth roller and ceramic roller, etc. According to the function, it can be divided into transmission roller, redirection roller, surface increase roller and unloading roller. The roller type in this paper is a heavy transmission roller. The spoke plate and the wheel hub are cast and welded into one. The roller shaft and the wheel hub are connected by expansion sleeves, which can withstand greater loads and are easy to disassemble and assemble.
There are two ways to model the roller assembly. One is to create a model in 3D software and then import it into Ansys software through the interface between Ansys and 3D software; the other is to model directly in Ansys. This paper adopts the latter modeling method. The roller shaft, expansion sleeve, spoke plate and wheel hub, roller shell, etc. are modeled from bottom to top in Ansys software, as shown in Figure 1. In order to improve the calculation rate and accuracy, the following simplifications were performed when establishing the model:
1) The expansion sleeve was regarded as a unified solid body without considering the internal structure;
2) Some small features such as chamfers and fillets of each component were ignored;
3) The constraint of the bearing seat on the roller shaft was simplified to a simply supported beam form;
4) Minor components such as the bearing seat, screws used for pre-tightening the expansion sleeve, and screw holes were omitted.

Figure 1 3D model of transmission roller

The main parameters of the transmission roller are: roller diameter D = 1,250 mm, conveyor belt width B = 1,800 mm, roller length L = 2,000 mm, cylinder thickness t = 25 mm, shaft length 3,000 mm, shaft diameter at the expansion sleeve is 400 mm, shaft diameter at the bearing is 360 mm, expansion sleeve type and size are ZT9300×375, and the wrap angle is 210°.

2 Finite element model of roller and definition of contact pairs
The roller solid model is meshed, different parts are assigned different unit types and unit properties, and different parts are meshed differently. In this paper, the surface of the shaft is firstly meshed intelligently using Mesh 200, and then the Solid 185 unit is used to rotate to obtain the meshing of the shaft. The other parts are all meshed by sweeping, but the number of units for meshing is set differently. Since the shaft is the main force-bearing component, the meshing is relatively fine. After the meshing is completed, contact pairs are established between the shaft and the expansion sleeve, and between the expansion sleeve and the hub. The analysis of the shaft and the expansion sleeve, and between the expansion sleeve and the hub belongs to nonlinear analysis. This paper takes this part into consideration to obtain more reliable results. The finite element model of the roller is shown in Figure 2, and the contact pairs established between the roller shaft and the expansion sleeve are shown in Figure 3. The finite element analysis of the contact pairs between the expansion sleeve and the hub is similar.

Figure 2 Finite element model of transmission drum

Figure 3 Contact pairs established between the roller shaft and the expansion sleeve

3. Applying constraints
After dividing the mesh, the loads must be set before applying the loads to the finite element model. The loads in the finite element include boundary constraints, displacement constraints, and force constraints. Generally, loads are divided into 6 categories: freedom constraints, force loads, surface loads, volume loads, inertia forces, and coupled field loads. This paper applies constraints at the bearings to limit the axial (Z axis) and radial (X axis) degrees of freedom of movement of the shaft. At the same time, the shaft is also restricted by the coupling, and the degree of freedom of rotation of the torque input end of the transmission roller shaft around the axis must be set.

4 Determination of load
The force analysis of the drive roller is shown in Figure 4. The drive roller is the main component for transmitting power. In order to transmit the necessary traction, there must be sufficient friction between the conveyor belt and the roller. According to the Euler formula S in ≤ S out eμα

Where: Sin is the tension of the conveyor belt at the winding end, Sout is the tension of the conveyor belt at the winding end, e is the base of the natural logarithm, and μ is the friction factor between the conveyor belt and the roller.
In the Euler formula, the ratio of Sin/Sout must be less than or equal to eμα. Less than means that the wrap angle is not fully utilized, so there must be a utilization arc α N of the wrap angle.

Figure 4 Force analysis of the driving roller

Using arcs to express Euler’s formula

The tension diagram of the conveyor belt along the arc expressed in polar coordinates is based on the spiral logarithm, as shown in Figure 5. For any φ ＜α N, the general expression is

The static arc represents a reserve of circumferential force, which is used to overcome the resistance and unestimated resistance that occurs during starting. Therefore, it can also be regarded as a safety factor. The static arc generally occurs when the conveyor is stable. If S in and S out reach their maximum values, the static arc disappears, and the entire wrap angle is used for power transmission. At this time, S in = S out eμα.
According to the friction drive theory, the winding end and the winding end of the roller follow the Euler formula. The wrap angle of the roller is 230°, the static arc is 30°, and the utilization arc is 200°. In the static arc, there is no sliding between the conveyor belt and the roller, but there is static friction. The utilization arc is completely different. In this arc segment, the force on the roller conforms to the Euler formula from the winding end to the winding end and gradually increases, that is, the tension of the conveyor belt changes along the circumferential direction on the roller surface, which conforms to the Euler formula. At the same time, it is also subject to the friction force tangent to the roller surface, which
is simulated by the surface unit. According to theoretical analysis, the force on the axial roller surface is not constant, but distributed in a semi-sine function. In order to simplify the calculation, this paper assumes that the force on the roller along the axial direction is constant, which has little effect on the results.

Figure 5 Load application

5 Solving and post-processing analysis of the stress condition of the transmission drum
After completing the previous series of work, the drum is solved and post-processed in the Ansys solution and post-processing module, and the stress distribution diagram of the drum shell and the deformation diagram of the drum shell are obtained as shown in Figures 6 and 7. In theory, after the transmission drum is subjected to the force of the conveyor belt, the main stress-bearing parts are the shaft and bearing, the expansion sleeve and the hub, and the contact part between the spoke plate and the inner wall of the drum. The solution of Ansys can list the stress components, principal stresses, displacements, etc. of the unit nodes, and can also use other methods to display displacements and stresses. These can describe the distribution of the transmission drum model as a whole and determine which part is subjected to the greatest stress and which part is the most dangerous.

Figure 6 Stress cloud diagram

Figure 7 Strain cloud diagram

The analysis of the heavy-duty transmission roller in this paper takes into account the nonlinear analysis of the roller shaft and the expansion sleeve, as well as the nonlinear analysis of the hub and the expansion sleeve. Through the analysis of the stress deformation cloud map, it can be seen that the maximum displacement coordinates are (300.86, 412.89, 1 688.91), which appears in the middle of the transmission roller shell. The maximum value is 0.342 3. From the stress distribution diagram of the transmission roller, it can be seen that the actual force of the roller is almost the same as the force of the theoretical analysis, that is, they all appear at the contact point between the shaft and the bearing, with coordinates of (136.08, 25.430,
880.72), and the maximum stress is 43.23 MPa. According to the strength theory, the shaft is made of 45# steel, and the allowable strength can reach 65 MPa after quenching and tempering. The transmission roller meets the strength requirements, and the allowable strength of the shaft is much greater than the actual stress of the shaft, so there is still a lot of room for optimization.

6 Conclusion
1) Use Ansys software to better judge the stress condition of the transmission roller, view the results from the deformation diagram and stress diagram, and provide a better basis for optimization.
2) Analyze the deformation diagram and stress distribution diagram of the roller, and obtain the actual stress and deformation of the roller. The roller has a small deformation and its strength is much smaller than the actual bearing strength of the shaft. It can be seen that the size and quality of the roller can also be optimized.
3) This article simplifies the modeling process. The actual roller stress condition may be more complicated. Due to limited conditions, the actual roller modeling analysis was not performed.