Introduction
Crushing is a set of operations carried out to fragment blocks of ore of various sizes, and can be segmented into stages, such as primary and secondary. The machines most commonly used during crushing are crushers, which come in different types, such as gyratory, jaw, impact and roller crushers.
This article deals with one of Kot's success stories, in which the failure analysis of the driven shaft of a roller crusher (Figure 1 shows the fractured shaft) was carried out. The system in question consists of a set of 9 rotors, each made up of three teeth, and the shaft in turn is driven by an electric motor system connected to a hydrodynamic coupling.
Figure 1: Fractured crusher shaft.
In order to determine the causes of the failure, Kot carried out a structural assessment of the axle, using visual inspections, laboratory analysis and computer analysis using the Finite Element Method (FEM).
Methodology used
The activity began with the as-built model of the crusher shaft, using a 3D scan of the fractured structure, as well as a dimensional survey. The scanned shaft model can be seen in Figure 2.
Figure 2: 3D scan of the fractured shaft. SOURCE: Kot Collection.
The finite element model was generated using specific software. A combination of second-order tetrahedral and hexahedral solid elements was used to generate the mesh. The shaft failure region was modeled with greater mesh refinement, in order to obtain a better ratio of computational cost and precision for calculating the field of acting stresses. Figure 3 shows the finite element model.
Figure 3: Finite element model of the crusher shaft. SOURCE: Kot Collection.
As well as correctly determining the discretization of the continuous medium, applying the boundary conditions is also crucial to obtaining results that are true to the reality of the simulated object, especially in a failure analysis. Restrictions were applied to the model to represent the contact of the shaft with the radial bearings and the contact of the splined part with the gearbox of the drive system. The loads generated by the contact between the teeth and the material to be crushed were applied as remote loads to calculate the bending and torsional moments.
Various operating conditions were simulated in order to cover the widest range of forces acting during a rotation of the shaft, as well as accounting for the various load cycles that the equipment is exposed to during its useful life. The variation in tooth positions and load magnitudes considered allows for a fatigue analysis with a load spectrum that is closer to reality. Figure 4 illustrates the boundary conditions for one of the simulated operating situations.
Figure 4: Boundary conditions and loads applied to the computer model. SOURCE: Kot Collection.
Resultados
After building the computer model, static analyses were carried out using the Finite Element Method. For all situations, including the maximum torque (see Figure 5), the axle structure has a safety factor higher than that considered appropriate for the type of application, indicating that the structure can withstand the static forces acting on it.
Figure 5: Results of the static analysis using the finite element method. SOURCE: Kot Collection.
The second stage of the failure analysis was to check for shaft fatigue. Based on the motor current history recorded by the automation system, the load cycles were counted using the rainflow methodology recommended by international standards.
Depending on how the crusher operates, a non-reversible multi-axial stress state is generated, requiring the use of a specific fatigue analysis methodology. The classic S-N diagram shows a constant plateau after106 cycles, but according to an international standard, steels in components subject to a high number of cycles do not have such a plateau. The angular coefficient of the S-N curve after106 cycles was therefore altered to reflect this behavior, as can be seen in Figure 7. Based on the S-N curve and the number of cycles the shaft was subjected to before its failure, a safety factor higher than the recommended one was also obtained, indicating that fatigue failure of the shaft was not expected.
Figure 7: S-N diagram for the crusher shaft. SOURCE: Kot Collection.
In order to better understand what caused the failure, a detailed analysis of the fracture surface was carried out, which revealed the presence of several cracks close to the keyway, resulting from previous maintenance work on the shaft. The coalescence of these cracks generated a macro crack, which propagated due to fatigue and compromised a percentage of the shaft's cross-section before failure. This led to the possibility of an overload failure during operation.
In order to understand the magnitude of the load that generated the failure, a Linear Elastic Fracture Mechanics analysis was carried out, in which a crack with dimensions similar to those seen on the fracture surface was introduced into a finite element computer model. This allows the Stress Intensity Factor (SIF) at the crack front to be calculated and this parameter to be compared with the material's Fracture toughness (KIC).
Based on the simulations carried out, it was observed that stresses equivalent to the maximum torque of the drive motor were capable of causing the combined FIT for the tensile and torsional modes to equal the KIC of the material, culminating in the fracture of the shaft. Figure 8 illustrates the distribution of the Stress Intensity Factor in front of the crack inserted into the computer model.
Figure 8: Stress Intensity Factor obtained from the computer model. SOURCE: Kot Collection.
Conclusion
Based on the analysis carried out, it was concluded that the design of the shaft was suitable for the forces acting on it. However, due to the inclusion of defects resulting from shaft maintenance interventions, a crack was generated which propagated steadily due to fatigue until, during an overload event, the material reached its fracture toughness, culminating in the shaft's brittle rupture.
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