**6. Virtual shovel prototype simulation**

A virtual 3D prototype of the rope shovel is built in AutoCAD-2012 as shown in **Figure 5**. The dimensions of the shovel front-end assembly are chosen to represent the dimensions of the P&H 4100XPC shovel and are measured from a scaled model [19]. The front-end geometry is simplified to avoid unnecessary geometric complications. The model consists of one revolute and two prismatic joints that control the motion of the dipper into the formation. The boom and saddle are modeled as rigid bodies. The boom is considered fixed to the ground. Both joints are constrained; the revolute joint allows rotation only in the z-axis, and the prismatic joints allow motion only in the x-axis. The resistive forces of the formation are applicable as a remote force available at the teeth. The material force is also modeled as a remote force acting on the dipper. The revolute joint is given a fixed rotation at every time step to ensure the completion of the digging cycle in 3 s. The contacts and boundary conditions are shown in **Figure 6**. The dipper body is modeled using brick elements with a minimum of three elements through the thickness of the dipper.

The dipper trajectory is given as an input function to the shovel simulation process in MAT-LAB/SIMULINK. The dipper traverses the known trajectory, and the reverse kinematic model is used to determine the crowd-arm extension (d2) and rotation (θ1) requirements to achieve this trajectory. These two output parameters from the numerical simulation process are used as inputs for the shovel prototype. Together, these two inputs define the dipper trajectory. Similarly, the resistive forces computed during the shovel dynamic simulation are modeled as higher order polynomial in MATLAB and are fed into the system as time functions. The payload also exerts a force on the dipper side walls. This force is modeled using the earth pressure at-rest theory [20] and is considered to be acting uniformly over the side wall.

**Figure 5.** Simplified 3D model of cable shovel and dipper.

**5.** *Digging resistive forces f3 and f4*: The resistive forces, f3 and f4, are combined as a single cutting force (Fr) and calculated using Eq. (1) [11]. The cutting force (Fr) acts along the tangent of the trajectory at the dipper tip. This force is resolved into its rectangular components, one along the dipper base and the other normal to it. These tangent and normal components

**6.** *The main model and numerical simulation*: The dynamic model of the dipper-teeth assembly is solved in the main model. The outputs from all the sub-models, along with system constants and time steps are fed into the main model as inputs. The main model then numerically solves the mathematical model and generates the desired outputs. Two of the important results or outputs from this solution are the hoisting force (F1) and crowd-arm

During this numerical simulation process, four of the six resistive forces (f1, f3, f4, f6) are computed as separate subsystems, while the other two resistive forces (f2 and f5) are set to zero. The resistive force f2 is set to zero by selecting an appropriate trajectory of the dipper [6]. The excavation trajectory is selected in such a way that the dipper stays clear off the material and does not compress the material. This assumption is reasonable in the sense that it involves proper bench geometric design and operator skill. An improper bench geometric design would lead to undue stresses on the shovel, which must be avoided during the excavation process. The force f5 represents the dipper and payload inertia. This force can be set to zero if the dipper moves through the material with a constant velocity and hence with zero acceleration. For this research, it is assumed that the dipper moves through the bench with a constant velocity and hence a zero acceleration. This assumption is consistent with the field observations [17] for

A virtual 3D prototype of the rope shovel is built in AutoCAD-2012 as shown in **Figure 5**. The dimensions of the shovel front-end assembly are chosen to represent the dimensions of the P&H 4100XPC shovel and are measured from a scaled model [19]. The front-end geometry is simplified to avoid unnecessary geometric complications. The model consists of one revolute and two prismatic joints that control the motion of the dipper into the formation. The boom and saddle are modeled as rigid bodies. The boom is considered fixed to the ground. Both joints are constrained; the revolute joint allows rotation only in the z-axis, and the prismatic joints allow motion only in the x-axis. The resistive forces of the formation are applicable as a remote force available at the teeth. The material force is also modeled as a remote force acting on the dipper. The revolute joint is given a fixed rotation at every time step to ensure the completion of the digging cycle in 3 s. The contacts and boundary conditions are shown in **Figure 6**. The dipper body is modeled using brick elements with a minimum of three elements

and Fn) of the resistive force (Fr) are computed at every trajectory point in this sub-

(Ft

120 Lagrangian Mechanics

model.

torque (T1).

hoist rope extension.

**6. Virtual shovel prototype simulation**

through the thickness of the dipper.

**Figure 6.** Boundary conditions and external forces on shovel front end.
