Abstract
This study focuses on developing physics based fatigue life prediction models for Rolls-Royce (RR) gas turbine (GT) engine components made from varying materials to allow life cycle costing (LCC) of the GT engine. Fatigue lifing has been carried out using data from:
· Assumed slope of S-N data on a log-log plot,
· Stress controlled fatigue rig test data of disc components,
· Stress controlled axial fatigue test data of test coupons and
· Strain controlled rig test data of disc components.
Stochastic fatigue life prediction models have been constructed using a stochastic modelling tool called Decision-Pro (Vanguard). Monte-Carlo simulations (MCS) with a Weibull probability distribution have been performed treating operating temperature and load/stress as random variables to predict the probabilistic fatigue life, which is crucial in deriving a suitable LCC methodology for GT engines. Sentitivity analyses have also been performed to study the effect of changes in model parameters on fatigue life of the components. The probalistic fatigue life thus obtained can be used to estimate the expiration date in terms of flight hours or number of cycles(landings) of all line-replaceable units (LRUs) of the engine. Stochastic fatigue life information will help to: determine optimised maintenance and inspection intervals, facilitate repair or retire decisions of used components, and to explore life extension, remaining life assessment and fitness-for-service concepts, eventually allowing development of a globally optimised LCC tool.
Keywords: Life cycle costing, fatigue, lifing, gas turbine, Monte-Carlo simulation, deterioration mechanisms.
Nomenclature
S - Stress amplitude in MPa
N - Fatigue life in cycles
Nrig - Fatigue life of rig component in cycles
Ncomp -Fatigue life of engine component in cycles
Srig - Rig component stress in MPa
S, Scomp - Engine component stress in MPa
k – A proportionality factor
n – Fatigue life function
T – Temperature in o C
- Polynomial coefficients
R – Load or stress ratio
- Loading frequency in Hz
UTS – Ultimate tensile strength in MPa
Kt - Stress concentration factor
- Percentage of strain amplitude
I. Introduction
Rolls-Royce has a long history of developing pioneering power plant products for aerospace, marine and energy applications. The commercial success of these products is highly dependant on the integrity of components working close to their theoretical limits for long periods of time. The ability to predict performance and life of materials is a key strategic capability. In the recent past companies such as GE, Rolls-Royce and Pratt and Whitney used a business model based on selling engines at low or even negative margins and generating acceptable levels of revenue from sales of spare parts. Intense competition and demands of the market place have led to a dramatic change in the business model for these companies. It is now the norm for customers to seek long-term price and performance guarantees. Various labels have been attached to these commercial agreements including “Power by the Hour”, “Total Care” and “Mission-Ready Management”. The long-term service and support contract with RR won for the Olympus and Tyne gas turbines used in older ships in the British, Belgian, French and Dutch navies and the 12-year, £137M ($244M) contract won from UK’s Ministry of Defence (MoD) in March 2005 are good examples of this. Aftermarket and services now account for more than 50% of total business income [1]. Essentially, these new business models all lead to a fundamental shift in the balance of risk whereby suppliers have to guarantee the long term cost of operation of their products. This presents enormous challenges for manufacturers who now have to:
· Predict performance life very early in the design process
· Gain a deep understanding of complex trade-offs between initial part costs, cost of repair, ease of access, logistics, inspectability etc.
Assessing the Life Cycle Cost(LCC) of a product during the early stages of design and development is crucial for product success [2]. Therefore, the “Total care”-type business relationship needs better tools for LCC which can predict the effect of design decisions on the engine LCC. The prediction of LCC through the new IPAS developed design tools is critical in appraising the impact of design decisions on long-term profitability. LCC is increasingly important in a service world, where LCC risk has moved from the engine operator to the provider of the service.
Running a profitable Total care service or DfLCC (Design for Life Cycle Cost) necessitates reliable estimates of fatigue life of components with LCC implications. Many issues affect LCC of engines. The choice of materials for Gas Turbine (GT) engine applications in the Life-Cycle-Design process takes on strategic importance aimed at minimizing LCC and the environmental impact associated with the engine’s entire life-cycle, while meeting functional, performance and safety requirements [3]. Both civil and military operators look for similar benefits, though their priorities may differ. Civil engine sales have been strongly influenced by initial cost; whereas the military operators tend to favour performance. Nevertheless, such distinctions are blurring and modern military systems are increasingly placing equal importance on performance and LCC [4].
A Life prediction capability that is useful in a design application must address the scatter inherent in material response to fatigue loading [5]. Deterioration of an engine generally results in a lower specific thrust and higher specific fuel consumption (SFC) for the same spool speeds and turbine entry temperatures (TETs). Engines are then run at higher spool speeds and/or TETs to meet the thrust requirement in order to retain the same aircraft performance. As a result, engines experience higher SFC and a shorter life due to the greater creep and fatigue damage incurred [6]. The effect of this on LCC can be minimized by estimating the actual fuel and life consumption and by gaining a better understanding of the effects of each such deterioration on operational performance of engines [7]. Real time life tracking and proactive health management of engine components are instrumental in reducing the cost of ownership. Up to 70% of affordability improvement is attributable to reduced cost of ownership [8].
Deterioration of the exhaust gas temperature (EGT) margin caused mainly by the degradation of high pressure turbine (HPT) components is the primary reason for aircraft engine removal from service [9]. The initial degradation comes from blade tip seal wear and can account for losses in HPT performance of 1% or more. The increased tip clearance accelerates effects of low cycle fatigue and erosion due to increased temperatures in the HPT and degrades the EGT margin and engine life. Once an engine reaches its EGT limit, the engine must come off the wing for maintenance. Maintenance costs for major overhaul of today’s large commercial gas turbine engines can easily exceed $1M [10]. Hot-section life-cycle cost can be reduced significantly through optimal maintenance interval timing, avoidance of non-repairable damage, more effective protective coating systems, materials choice based on customer benefits and improved replacement part designs from the OEM and alternative suppliers [11].
Rolls-Royce have a range of existing cost modelling tools including DMTRADE, PREDICTOR, PREVIEW, and MEAROS. These require a lot of detailed information that is not readily available during the preliminary design stage. Furthermore, these tools do not adequately take account of different component duty and capability (technology) relative to the datum engine. This necessitates the development and implementation of a new methodology to provide tools that can cope with the abstract nature of the design definition at the early concept stage. This work is therefore focused on stochastic fatigue-life prediction of RR engine components to enable LCC of GT engines to be predicted.
II. Fatigue life prediction based on assumed slope
Advanced Propulsion System Design (APSD) is a design organisation within Rolls-Royce responsible for the concept design of new gas turbine systems in order to develop and update the civil aerospace product strategy. APSD involves many stages from concept design through customer support. The key steps involved in this design process are depicted in Fig.1.
Fig.1 Stages in product introduction process [Source: Rolls-Royce]
APSD's objective is to develop a whole engine cycle/architectural solution with the correct mix of attributes to satisfy particular airframe(s) requirements. Throughout all the stages of the design process, LCC models are required, which can vary depending on the point reached in the process. Currently cost assessments in RR are historical points in time that are slow to obtain and are not dynamic enough to use effectively to drive the design. APSD is concerned about the costs associated with primary engine attributes such as fuel burn, unit cost, maintenance cost, landing fees etc. Cost associated with fuel burn is influenced by the engine attributes such as SFC, drag and weight. Unit cost is coupled with interest, depreciation and insurance. Engine maintenance cost is influenced by engine attributes such as reliability, maintainability and operational life. This section therefore discusses fatigue lifing of components for LCC in the preliminary design stage used by APSD where only limited performance design inputs are available.
In stage 1 design, only historical information and knowledge about engines from service experience is available. Complete, specific information about the new engines being introduced are not available at this stage except a few performance and mechanical design inputs which are highlighted as follows: Basic mission profile(s) which primarily dictate the direct operating cost, Engine cycle parameters (temperature and pressure at inportant stations of engine:T30, P30, TET etc), Architecture(eg twin spool or three spool engine, key mechanical parameters (AN2, DN, rim/bore speeds etc), materials of construction of key components, and new technologies.
After a number of discussions with the lifing methods group at Rolls-Royce, Derby, UK, a first order lifing philosophy was developed to predict fatigue life of components in stage 1 APSD design based on historical information and knowledge of RR engines, as detailed below.
If the slope of the S-N curve on the log-log plot is known and it passes through the rig test conditions, lifing of an engine or new component can be done straightforwardly. S-N curves are scaled/interpolated using typical or minimum UTS values of materials used in components. Stresses are scaled with square of component speed as shown in Fig.2 and temperatures scale with TET(in K). Based on an assumed slope of the S-N curve(1.3:4), the fatigue life of a component at a specific feature, is obtained using the temperature dependent UTS values of the relevant materials. The simplistic basis of the lifing is that the fatigue life prediction is essentially stress based and therefore does not account for localised inelastic deformation occuring at stress-critical zones in components. In other words, a stress based, wholly elastic assumption is made for the components in this method, so as to design components with LCC with the few performance and mechanical design inputs available during stage 1 design. The fatigue life generated for a typical RR gas turbine material (Y) at different operating temperatures is shown in Fig.3.
Fig.2 Stress scaling from rig data to obtain engine components’ stress for fatigue lifing.
Fig.3 Fatigue life of Y material at different operating temperatures
III. Lifing based on stress controlled fatigue rig tests
Fatigue life prediction models based on RR stress controlled fatigue test data of spin rig disc components of various materials are discussed in this section. Fig.4 shows fatigue life, as a function of net operating stress and test temperature, of X material at the bore of the disc. The stress quoted is the net peak stress in the component: the sum of global stress due to applied load and residual stress due to forging. The residual stress varies with forging size and shape. It is quite evident from Fig.4 that for a given stress the fatigue life decreases with increase in temperature, though the rate of decrease in life with increase in temperature is greater at a higher stress level.
Fig.4 Fatigue life of disc at the bore as a function of temperature
A 3D analytic response surface for fatigue life as a function of this stress and operating temperature is shown in Fig.5 and has been constructed by least squares fitting of data from Fig.4 to allow further stochastic analyses to be performed. Based on this 3D interpolation, the fatigue life function is given by the following polynomial.
The polynomial coefficients would be different for different stress critical locations or features of disc, even for isotropic metallic disc material. The fatigue life of the disc at a specific feature is then obtained from the life function.
Fig.5 Fatigue life of disc as a function of net stress and operating temperature
Fig.6 Net stress response surface as a function of
life and temperature
Similarly, the analytic response surface which gives the safe net stress as a function of life and temperature at a specific critical material point of the disc component shown in Fig.6 can be obtained by least square fitting of data to work from life targets and the obtained net stress function is given below.
Alternate methods of 3D interpolation are being considered using optimization techniques in Matlab to construct a more accurate life function that also allows for uncertainty in the model interpolation. The generated life function has been coded in a hierarchical stochastic modelling tool called Decision-Pro to carry out a Monte-Carlo simulation. Fig.7 depicts the Vanguard version of fatigue life prediction model based on stress controlled fatigue data of components.