# Research on Material Viscoelasticity and Its Influence on Indentation Rolling Resistance
## 1 Introduction  
Belt conveyors account for 30% of the total installed power of coal mines and consume 60% of the energy in coal mining operations, making them the main energy consuming equipment in coal mines [1]. One approach to reduce energy consumption is to intelligently monitor and adjust the operating status of belt conveyors. Another strategy involves fundamentally reducing energy consumption through design and manufacturing improvements aimed at enhancing machine performance and reducing operating resistance. Under stable operation, the operating resistance of a belt conveyor mainly comprises the following components: main resistance, additional resistance, special resistance, and lifting resistance [2]. The main resistance of the conveyor encompasses the rotational resistance of the rollers, the indentation rolling resistance generated by the relative movement between the conveyor belt and the rollers, and the bending resistance produced when the conveyor belt repeatedly bends under the action of the driving roller [3].  
The proportion of indentation rolling resistance exceeds half of the overall operating resistance [4]. This resistance is generated by the rolling of a rigid roller on the surface of a viscoelastic material, such as the conveyor belt cover surface. The process of deformation and recovery of viscoelastic materials occurs gradually over time, leading to strain lagging behind stress [5]. When a rigid cylinder rolls on the surface of a viscoelastic material, the contact area between the conveyor belt and the roller is asymmetric relative to the center of the roller. This results in an asymmetric distribution of the contact stress, generating resistance that hinders the movement of the conveyor belt, known as collapse rolling resistance [6]. When the transportation distance of the belt conveyor is increased, it requires more rollers to support its weight, leading to a greater accumulation of collapse rollingresistance [7]. In summary, the formation of indentation rolling resistance is attributed to the inherent characteristics of the material. Therefore, it is imperative to explore the characterization method of viscoelastic materials using the relaxation model (relaxation modulus function) and evaluate the relationship between the model and the indentation rolling resistance. The Maxwell model is used to characterize the viscoelastic properties of materials and establish the relaxation modulus function. However, the three-element Maxwell model, commonly used as an engineering characterization method, can only roughly provide an approximate characterization of the materials [8]. In practical scenarios, material structures are more intricate, rendering the three-element model too simple to characterize them. The generalized Maxwell model, a theoretical representation method, offers a more comprehensive characterization of the viscoelasticity of materials [9]. However, its applicability is limited by the actual testing time range. In this study, we address this limitation by modifying and streamlining the generalized Maxwell model. Subsequently, the model is integrated into the collapse rolling resistance formula to evaluate the collapse rolling resistance.