**11. Conclusions**

of

may also be implemented based on field operating conditions or using the crack-growth

The crack-growth curve for the dipper bottom plate is shown in **Figure 12**. It is observed that the crack-propagation rates become very high after a certain crack length. A critical length1

100 mm is set for this crack. As illustrated in this figure, the estimated life for a 50 mm bottomplate crack is 38 days. However, once the crack grows to 75 mm, the remaining life is only 16

**Figure 12.** Critical crack length and remaining life expectancy for an initial length of 50 mm.

The research underlying this chapter is a pioneering effort for understanding electric rope shovel dipper stress analysis using dynamic resistive forces. The research results contribute to the existing body of knowledge on health and longevity of shovel dipper-teeth assembly. It advances shovel reliability, maintainability, and availability, which influence surface mining productivity. Previous research generally ignored the dynamic forces due to the weight of the dipper and payload. Given the size of current large shovels with 100+ tons per pass, these forces must be accounted for in any meaningful and comprehensive dynamic model. The research models provide detailed information on the forces and torques for all joints and links within the shovel front-end assembly. This research is also the first attempt to model the fatigue life of the shovel dipper-teeth assembly. It lays a foundation for understanding dipper fatigue failure resulting from high stress intensity, crack initiation, and propagation for rope shovel front-end assembly. Research shows that dipper-related breakdowns are among the highest for shovel excavation downtimes [4]. The current maintenance practice for the shovel frontend assembly is based on experience rather than science. This chapter lays a foundation for

Crack length in this text (and in literature) is always referred as half of the total length of crack. A critical length of

curves.

128 Lagrangian Mechanics

days for the same crack.

**10. Significant contributions**

100 mm would be 200 mm total length of the crack.

1

Estimating electric rope shovel health and longevity is a complicated task and requires a thorough understanding of the shovel digging process. Thus far, the shovel front-end assembly repair model is based on experience and judgment rather than science. Shovel kinematic and dynamic models provide a scientific basis for shovel repair and fatigue failure modeling. The shovel dynamic model requires a good estimation of shovel digging forces. Current rope shovels have large dipper capacities, and their digging resistive forces can be significant. Shovel payload is a dynamic and significant contributor of these digging forces. The dynamic forces result in stress loading of shovel front-end components. The maximum stress values can be as high as 282 MPa and can be higher than the lower yield strength limits for low, medium, and high carbon steel. Material flaws, high stresses, and other environmental factors can initiate cracks on the dipper. Under severe stress loading conditions, these cracks can propagate to critical lengths in no time. The estimated life for a 50 mm bottom-plate crack was found to be 38 days. However, once the crack grows to 75 mm, the remaining life can be as low as 16 days only. This chapter lays a foundation for the fatigue failure analysis of dipper-teeth assembly. The virtual prototype is a scaled and simplified model. It is recommended that the work be extended for real full-scale virtual prototype for the actual steel materials used.

#### **Nomenclature**



da/dN crack-growth rate per cycle as defined by Paris' law


L(x) straight-line function representing the bench face
