## 3 Materials and Methods
### Analysis of Natural Frequencies for the Bucket Wheel Arm  
To analyse the influence of corrosion on the natural frequencies on the metal structures of the mining equipment in the lignite quarries [34], we considered the equipment that is most commonly used: a wheel excavator with type ERc 1400-30/7 buckets (Figure 9). We also conducted tests on the bucket wheel arm of the ARS assembly (the excavator itself) (1). The bucket ladder is connected to the machine tower through the joint (9), which allows it to rotate in the vertical plane. At the other end is the battery of pulleys (2'), over which the lifting and lowering cables (2) pass. The cables are type Warrington-Seale 40M-6\(\times\)36-1760/BG-s/z, with metal cores. According to Figure 8, we have: the support for the bucket wheel mechanism (8); and the clamping support (6) of the bucket wheel reducer (5), which is attached to the shaft. The reducer acts through a bucket wheel shaft (4). Also attached to the top is the wheel guard with cups. From the excavator, through the connecting bridge (10), the connection is made with the deposition truck on the front belt. Figure 8: Material deposits on the ERC1400-30/7 excavator bucket wheel arm: (**a**) lower part of the bucket wheel arm; (**b**) belt conveyor detail on bucket wheel arm, bottom side; (**c**) corner corrosion detail, cup holder wheel arm metal construction; (**d**) cup wheel drive group holding beam. Figure 9: ERc1400-30/7 Excavator type, part of ARS—the excavator itself. The substructure modelling of the bucket wheel arm is carried out using beam and plate finite elements, in accordance with the technical specifications established for this type of mining equipment. Beam elements can be standard, but can also include composite sections or welded sections as shown in Figure 10a. The discretisation of plate-type elements (2'), (6), (8), and (9) will be done with second-order plate elements, especially in the joint area (9), where the structure presents curved elements as illustrated in Figure 10a,b. The transition from beam to plate elements and the connection between the support and the shaft reducer are realised with rigid link-type elements, as shown in Figure 10b, position (5) [33]. An implicit solver was used for both static and dynamic analysis, suitable for both linear and nonlinear problems. The implicit solver provides good accuracy and is an efficient tool for analysing natural frequencies and vibration modes. To complete the finite element analysis of the bucket wheel arm (bucket ladder), we must also consider the masses associated with the subassemblies, which were not included in the finite element modelling. For example, the bucket wheel guard (3) illustrated in Figure 9 will have mass distributed over its attachment points on the bucket wheel reducer, which is not represented directly in our model. These masses will be considered concentrated or distributed masses on the structure and will be included in the calculation of natural frequencies to obtain a more accurate assessment of the vibration behaviour of the bucket wheel arm under operating conditions. Inputs in the FE analysis:  
1. Geometry of the structure: The complete structural model of the bucket wheel arm, including all major components and structural discontinuities, including the bucket ladder support cables, position 2 in Figure 10, was simulated using truss elements. 2. Materials: The material properties, including the modulus of elasticity, density, and Poisson's ratio. 3. Boundary conditions: These are the fixing and support conditions of the structure, such as joints and attachment points. In the bucket ladder joint, position 9 in Figure 10b, only rotation around the OY axis is considered, as shown in Figure 10a. 4. Loads: Types of loads applied to the structure, including static loads (LC1-LC14) and dynamic loads (the masses of the structural elements and mechanisms). LC1: Self-weight. LC2: Load from the mass of the reducer. LC3: Maximum output moment of the reducer. LC4: Load from the mass of mechanisms.