Page 253 - Handbook of Materials Failure Analysis

3 Structural Dynamics Analysis Method of Shovel Front-End Mechanism 249

elements, the suspension ropes with tension cable elements, the rigid revolving frame
with shell elements, and the others with node mass elements. The model does not
include the flexible bucket because the loads generated from three parts are calcu-
lated using a shovel rigid multi-body dynamics model developed by Li and Frimpong
[16]. Here, the loads are applied to hoist rope.
The material properties of the components consist of the elasticity modulus
3
of 206.7 GPa, Poisson’s ratio of 0.3, density of 7820 kg/m , yield strength of
150 MPa and ultimate tensile of 290 MPa. The modal mass, stiffness, and deflection
characteristics are calculated by employing the FEM. A damping ratio of 2-4% is
assigned to modal frequencies between 1 and 20 Hz.
Referring to the shovel operation described in Section 2.2, the model is allowed to
rotate about the y direction at the center O and other five degrees of freedom are
restrained, which are the x, y, and z axial directions, and x and z rotation directions.
The kinematic constraints or forces are applied to boundary nodes to connect two
parts. The motion of flexible bodies is defined by Lagrange equation 10.1 [17].

T
€ _ _ 1 @M ξ _ _ @V g _ T
Mξ + Mξ ξ + Kξ + + Dξ + Ψ λ ¼ Q (10.1)
ξ
2 @ξ @ξ

3.2 DYNAMICS LOADING OF FRONT-END STRUCTURE
Figure 10.6 also contains the local coordinate o (x,y,z) which is attached to the
revolving frame at the center O for loading purposes. The model loading has been
discussed in our early publication [15], which is summarized as:
• Motion loads going into the front-end with the digging, hoisting, swinging,
dumping, and swinging back;
• Structural loads at the hoist ropes;
• Inertia loads due to swing acceleration.

3.3 EQUIVALENT SR AND LIFE ESTIMATION OF FRONT-END
STRUCTURE
The fatigue life of the front-end structure is predicted by employing Palmgren-
Miner’s rule along with a Rainflow cycle-counting procedure. The stress-time
history of each structural element is obtained using transient dynamic analysis.
Figure 10.7 shows a hot spot stress-time history for the front-end structure. It is clear
that SR is variable in amplitude. The equivalent SR used to replace the variable
amplitude SR is required for fatigue investigation, because experimental fatigue test
is built from constant amplitude stress. For getting variable amplitude fatigue, all
recovered structural member stresses are first processed with Rainflow [18] for
cycle-counting the SR of the variable amplitude. The irregular stress-time history
is decomposed into equivalent stress columns. The number of cycles in each column
is recorded in a SR histogram as shown in Figure 10.8.