7.6 An Engineering Case Study

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In this section, we illustrate the procedure for the vibration analysis of a gearbox housing, shown in

Figure 7.3. The vibration analysis was performed using ANSYS [5].

7.6.1 Objectives

The chief aim of the vibration analysis is to ensure that the gearbox housing is not subject to a dangerous

resonant condition during the full range of operation. Specifically, the natural vibration frequencies of

the gearbox housing have to be widely separated from the rotating speeds of the shafts. Hence, natural

vibration analysis is required for this purpose. Furthermore, there are concerns about the strength of the

gearbox, and so a static stress analysis is also required.

7.6.2 Modeling Strategy

The gearbox housing shown in Figure 7.3 contains the following three subparts: the vertical cylinder,

the front housing, and the rear housing, which are welded together. Because the FEA model has to be

built up with the considerations of both vibration analysis and static stress analysis, some detailed

Vibration Modeling and Software Tools 7-19

© 2005 by Taylor & Francis Group, LLC

geometries such as filets are not deleted but modeled with fine meshes. In addition, a sufficient level of

attention is paid to the interconnections between different sections. To achieve a balance between the

accuracy of the results and the size of finite element model, quadratic elements (midsize nodes) are

used for both shell elements and solid elements. These usually yield better results at less expense than

linear elements.

Three types of finite elements are used to model the different parts:

1. The front cylinder plate, side plates and bottom plate: shell elements with variable thickness;

8 nodes, 6 DoF per node.

2. The ribs and fringes: solid elements; 20 nodes, 3 DoF per node.

3. The gears, shafts, clutch, and bearings: lumped mass elements; 1 node, 6 DoF per node.

Because of the discrepancy in the DoF between the shell elements and the solid elements, the nodal

rotating freedoms around the edges that connect shell elements and solid elements together are not

constrained, and consequently each rotating freedom needs to be constrained by two nodal translation

freedoms on solid elements near the edge, but not on the edge.

The total numbers of nodes, shell elements, and solid elements are given in Table 7.1, and the complete

finite element model is shown in Figure 7.3.

FIGURE 7.3 Finite element model of the gearbox housing. (Courtesy of Pacific Rim Engineered Products, Surrey,

British Columbia.)

TABLE 7.1 Total Size of the Finite Element Model of the Gearbox Housing

Nodes 36,523

Shell elements 4,060

Solid elements 3,760

7-20 Vibration and Shock Handbook

© 2005 by Taylor & Francis Group, LLC

7.6.3 Boundary Conditions

The four mountings on each side are constrained completely and the front edge of the cylinder is also

completely constrained.

7.6.4 Material

The mechanical properties of the material are given in Table 7.2.

7.6.5 Results

The first 10 natural frequencies and the associated mode shapes are calculated with a Lanczos algorithm.

They are listed in Table 7.3.

The first and the fifth mode shapes are shown in Figure 7.4 and Figure 7.5, respectively.

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