Y.-W. Chen, G.-C. Tsai

concerned on finding the cause of the crack in the blade, and few of papers discussed the dynamic behavior of

the blade systems that have subjected to the cracks in the structure. Therefore, the study about the dynamic be-

havior of the blade with the crack in the root is performed in this report.

The material properties of the blade are obtained through the chemical and mechanical tests. The geometry of

the blade is obtained by applying 3-D measurement system to measure the discarded blade. The measured data

combined with the Auto-CAD computer program to get the exact geometric dimensions. Then apply ANSYS

Pre-processor to read all of the geometric dimensions and create the finite element model of a single blade. The

free -free vibration analysis is applied to obtain the nature frequencies of single blade and compared with the test

results. After these, the finite element model of a group of blades and full system of turbine blade are generated

to investigate the dynamic behavior of blades.

Most of the researches about the dynamic behavior of the turbine blade are concentrated on using one-di-

mensional or two-dimensional models. Therefore, Euler beam was commonly applied in one-dimensional simu-

lation, a few of studies can really consider 3-dimensional turbine blade model. The major reasons came from the

complicated blade geometric dimensions and it is hard to describe by using the mathematical equations. The

other reasons are that the real 3-dimensional geometric data of turbine blade are difficult to get. Therefore, most

of the researches only select the cantilever beam to simulate the rotating dynamic behavior of the turbine blade

and its system (2). In this report, for compensating these gaps, using 3-D type elements creates all of turbine

blade models.

Some turbine blades may have defects due to the manufacture processing and the cracks may have observed

at some locations of high stress area due to the long operation time of turbine blades. The strength and fatigue

life of turbine blades will be reduced as the crack exited at some locations. If the cracks existed at some loca-

tions of turbine blades, the local modes may appear when the turbine blade is in the dynamic status. The local

modes may cause the failure of the whole system; some researches had done these investigations, such as Rizso

(1990), Chen and Chen (1980), and Gwo-ching Tsai (1996). Most of studies proposed by Ben Diksen (1987),

Hodge (1982), Pierre and Dowell (1987), and Wei and Pierre (1988), they selected the beam model to simulate

the vibration behavior of the full blade system, even if the newest researches published by Huang and Kuang [1],

they still used beam model. They all get the same conclusions: the vibration amplitude of the beam near the

crack area is going up and this may cause the failure of the system. But all of these researches didn’t mention the

other effects on the dynamic behavior of full blade systems due to the crack existed in the model. For under-

standing more about the crack effect on the dynamic behavior of the full blade system and the Campbell Dia-

gram, the detailed analyses are performed in this paper. Some papers ([2]-[4]) had pointed out that the full

three -dimensional finite element analyses can really understand the dynamic behavior of the full system because

3-D finite element model can completely simulate the complicated shape and geometry of the blade, shroud, te-

non, blade root, and disk. The 3-D finite element method is approved to be useful in the generation and analyses

of the full system of turbine blade.

2. Free-Free Vibration of Single Blade

The geometric data of a single blade is obtained from a real blade. The material of blade is AISI 403 stainless,

the mechanical properties are the following:

Tensile strength = 786.48 MPa, Yielding stress = 666MPa, Elongation rate = 10.19010.

Young’s modulus = 221,599 MPa. In this report, the unit is mm, therefore, the above material properties can

be transformed to be: Yo ung’s modulus = 2.216 E8kg-mm/s 2/mm2, Density = 7.7E−6 kg/mm, Poisson’s ratio =

0.27.

The finite element model of a single blade is shown in Figure 1. The model has 777 solid45 elements and

1395 nodes. Basically there have three methods to simulate the crack in the blade: the first method is to create

two separate nodes at the same location along the crack surface, this method has no any restrictions between two

neighboring nodes, if the nodes are in separation condition this model can reasonably describe their behavior,

but the solution may make some mistakes as the nodes penetration into the opposite side of body which can not

match with the real conditions. The second method is to apply combination element to simulate the crack. The

combination element basically is spring plus damper. The crack is being simulated by using spring element is

popular and the results are exactly matched with the test data. The third method is that the contact element is ap-

plied to replace the crack. But the contact element is a nonlinear analytical method and it is only available in the

static analysis. The nonlinear characteristic of contact element is not available as the dynamic condition is sus-