Assessing Useful Life Of Turbomachinery Components.

The last four or five decades have seen considerable advancements in the life assessment methods of mechanical components. These methods have been shown to be equally suitable for new as well as used components and even with components with discontinuities. Assessment of life of turbomachinery components has been done with the help of these methods. It will be demonstrated how one can use these methods to determine maintenance schedules. The same concepts also help to facilitate in repair or retire decisions of used components. This tutorial discusses the utility of available and established techniques to perform life assessment of mechanical components. This will include the life assessment on the following basis: • Deterministic type of assessment and • Probabilistic type of estimation. Presentation is arranged on the following topics: • Discussion of common damage mechanisms, • An overview of the concepts and the methods of life estimation, and • Discussion of case histories extended to include the probabilistic aspect. Examples will include components from steam turbines, gas turbines, fluid catalytic cracking (FCC) expanders, and centrifugal compressors mostly taken from the literature where available. INTRODUCTION Traditionally, the reliability assessment of a component is based on the deterministic type of evaluation process. A component is considered reliable when a calculated factor of safety, i.e., implied margin of the design, is above certain predetermined value. Experience has shown that the component will work with these limit values. However, these methods do not provide the following important information. • Most of these margins provide safety based on stress, i.e., the projected stress is kept below certain known material property. Determination about the safe operating life is difficult to ascertain by these numbers. The real issue, however, is to provide an answer to the question “what is the safe life of the component?” 177 ASSESSING USEFUL LIFE OF TURBOMACHINERY COMPONENTS by Murari P. Singh President and Director of Technology Safe Technical Solutions, Inc. Bethlehem, Pennsylvania Bhabesh K. Thakur Senior Structural Analyst and William E. Sullivan Senior Structural Analyst GE Energy Conmec Bethlehem, Pennsylvania • Deterministic methods do not consider variation and uncertainties in the value used for determining the margin. This paper focuses on the discussion of tools that are available today that promise to bring a broader scope of data. This will permit industry to make a more quantifiable decision pertaining to the risk of continuing operation of machines or components. These methods have helped in the process of making a decision about reliability, including retirement decisions and establishing maintenance and inspection intervals for turbomachinery. It will become evident that actual permissible variations rather than average worst case provide a more representative number for reliability. Examples are included to demonstrate the utility of the tools and the concepts. These have the promise to help in the life assessment of turbomachinery components on a logical and a rational basis. Therefore, statistical and probabilistic concepts will be discussed and used to assess the effect of variability present in geometrical dimensions, uncertainty in loads (operations), and variation in material properties. Many of these topics have been presented, analyzed, and discussed by many but it seems prudent to review and discuss briefly some of the theory of probability, damage mechanisms, and concepts even at the risk of being repetitive and being perceived as recycling. DETERMINISTIC TYPE OF ANALYSIS In a deterministic type of analysis the estimated response of a mechanical component is kept below certain preestablished safe limits. The response may be deformation, strain, stress, etc. For example stress is kept below certain mechanical properties of the material of construction. A margin is usually allowed between the applied load (stress) and the established limit (strength of the material). One of such measures is known as “factor of safety.” The desirability for use of the structure is signified by the value of factor of safety to be greater than unity. In the deterministic evaluation of the reliability of a mechanical component, one assumes loads and material properties to be known and to be single valued. This process assumes no variation in them. Of course, the assumption that there is no uncertainty about them is hardly true in most of the practical applications. PROBABILISTIC TYPE OF ANALYSIS Due to uncertainty in the variables, the response is also expected to have scatter in its magnitude. Therefore, the estimated margin or “factor of safety” does not indicate true margin and does not indicate a good measure of safety. The estimation of the occurrence of the violation of the criteria or the “limit” is a measure of probability. Alternatively, the number of times response meets the criteria is a measure of probability of success, i.e., a measure of the reliability of the structure. For example in a high cycle fatigue situation Goodman criterion is applied for reliability evaluation. The factor of safety is shown to depend on mean stress and alternating stress imposed on the component as well as on ultimate strength and fatigue strength of material of the component as it will be discussed in a later section. Uncertainty in the imposed loading and/or variation in the geometrical dimension of the component will be reflected in the magnitude of stress. Thus the stresses should be represented by a statistical distribution. Similarly the observed scatter in the material properties can also be described by statistical distribution. Once the scatter has been established then the chances of the factor of safety having a value larger than a desired value can be calculated, thus providing an estimate of probability. Singh, et al. (2004), used the concept described above to estimate reliability of an impeller in the presence of a discontinuity. It was shown that the reliability of the impeller could be estimated with use of fracture mechanics. However, there are uncertainties or randomness in the parameters that can influence the reliability. For example there is scatter in the material properties and there is always uncertainty about the actual size of the defects. Singh (1991) also with the help of the fracture mechanic’s concept and probabilistic methods evaluated reliability of a weld repaired steam turbine rotor. The life extension, remaining life assessment, and fitness-for-service concepts have evolved to keep plants running beyond design life. This has been achieved either by reassessing the design and/or repairing as needed. Methods using probabilistic concepts have been used to estimate reliability of many structures, e.g., Thacker, et al. (1990), used it for turbopump blades; Singh, et al. (Singh, 1985; Singh and Ewins, 1988; Singh, 1992), demonstrated its use for turbine blades and turbine bladed disk design. The basic assumptions in each probabilistic evaluation are that with inherent variations in stress levels and in properties of the material, it is extremely rare that any particular set of values will occur at once. The limit values of each parameter might not occur at the same time. Once the statistical properties of any parameter influencing safe life of the equipment are known, the method allows us to estimate the probability of reaching a specific number of safe operating cycles. The statistical property of any variable is described by a probability density function (PDF). Area under the curve is the probability of occurrence. By moving from left to right on the PDF, the probability of occurrences of a particular value increases. Obviously, the more information one has on the statistical characteristics of the parameters used in estimating reliability, the better will be the estimate of the probability of reaching a specific number of cycles before failure. Analysis gets more complicated with an increasing number of parameters to be considered. The response of a structure depends on the interaction of applied stress (S) and components’ resistance (R). The deterministic method defines a margin by the ratio R/S, called factor of safety. There are uncertainty in the values of both S and R and these are represented in statistical terms by a PDF. In the probabilistic terms the reliability is estimated as follows: