GT2017-64636

AN EXPLICIT IMPLICIT TIME INTEGRATION APPROACH FOR FINITE ELEMENT EVALUATION OF ENGINE LOAD FOLLOWING AN FBO EVENT Yiliu Weng AECC Commercial Aircraft Engine Co Ltd Shanghai P R China Lipeng Zheng AECC Commercial Aircraft Engine Co Ltd Shanghai P R China ABSTRACT Engine fan blade off FBO is an extreme event that could well place the flight safety at risk When it happens the engine will experience high velocity impact at first and then enter into a high power stage due to huge unbalance before coming to a steady state called windmilling The analytical process for FBO can be split into two phases one for impact simulation and the other for obtaining the FBO load to pylon Typically explicit method with fine mesh finite elements is used in the first phase and implicit method with coarse meshes is adopted in the second one In most cases the only connection between these two analyses may be the unbalance level caused by FBO More structural responses other than the unbalance level due to fan blade impact are actually ignored in the succeeding implicit analysis Attempts have been made by Boeing GE and MSC to integrate these two processes by adding some features in MD Nastran Yet the intermediate binary files created and the restricted input entries make the integration process quite inflexible This paper introduces an explicit implicit time integration approach for finite element analysis of engine load following an FBO event The proposed method attempts to connect the two stages more closely yet in a more flexible manner In this approach the engine structural response under FBO obtained from explicit analysis is transferred to the implicit analysis together with the unbalance level caused by blade loss The necessity of the approach is discussed and sensitivity analysis is conducted to understand the factors that play significant roles in the approach As the models for explicit and implicit analyses are different in mesh sizes and scales the authors also develop a tool that can interpolate the load information and further smooth it to fit calculation Finally the approach is tested on a full engine model to show its applicability and advantages over the traditional method for load evaluation of FBO event NOMENCLATURE FBO Fan Blade Off Out FE Finite Element FFT Fast Fourier Transformation FHF Fan Hub Frame HHT Hilber Hughes Taylor HPC High Pressure Compressor LPT Low Pressure Turbine TRF Turbine Rear Frame INTRODUCTION Fan blade off during flight is a threatening event to the aircraft engine and the fuselage As the fan blade is designed to be wider and longer for large by pass ratio turbine engine the release energy of a single blade is also getting greater possibly causing more severe damage to the engine There are plenty of information from the actual field events that indicate the danger of the events 1 2 To ensure flight safety the FAA and EASA regulations require that the structural integrity of the engine be maintained after an FBO event 3 4 Therefore evaluation of the ultimate load caused by FBO to the engine structure is necessary in both engine design and certification process A typical FBO process consists of three distinctive phases The beginning phase is the impact of the blade to the fan casing which lasts for only tens of milliseconds Then follows a high power phase during which the engine experience a drastic drop in rotor speed as a result of shut down and a huge unbalance due to loss of fan blades This phase is required to be within 15 seconds The third phase is referred to as windmilling when the non operating engine continues to rotate due to the airflow induced forces on the blades caused by Proceedings of ASME Turbo Expo 2017 Turbomachinery Technical Conference and Exposition GT2017 June 26 30 2017 Charlotte NC USA GT2017 64636 1Copyright 2017 ASME the forward motion of the aircraft and will probably last for several hours The ways to evaluate the dynamic loads in the aftermath of a sudden blade loss include experiments and numerical analysis Full engine FBO tests and various levels of component rig tests have historically been carried out which are extremely expensive and time consuming and sometimes involve risk to the safety of the test equipment and personnel 5 6 In recent years numerical analysis is extensively adopted due to its efficiency and economy Dynamic loads and containment of the engine structure in the first phase are usually evaluated by finite element method with explicit time integration 7 12 The most extensively used program of its kind is LS DYNA Using the central difference method to solve the dynamic equilibrium equation LS DYNA is advantageous in dealing with high velocity impact problem involving strong nonlinearity The impact and contact between engine blades and the casing can be captured with proper meshes and material properties To satisfy the stability condition the time step size for the calculation should be small enough Therefore LS DYNA is usually adopted only in the impact phase of the FBO event The second phase of the FBO process is usually analyzed by finite element method with implicit time integration which adopts larger time step sizes and coarser meshes than the explicit method thus can simulate longer duration of the event Rotor dynamics also need to be explored as the drop of rotor speed in this phase may cause large vibration under resonance However due to the differences in mesh sizes the result of the explicit analysis cannot be directly used in the implicit model as the initial state Typically rotor speed is prescribed in the implicit analysis and unbalance caused by fan blade out is the only input Impact and rub that exist in the second phase is usually not considered and casing flexibility is also difficult to include Therefore the scenario simulated by the implicit method may deviate from the real world case For the third phase as it usually lasts for several hours it is more appropriate to adopt steady state analysis and will not be discussed in this paper Although the explicit and implicit analyses are typically treated separately in FBO analysis due to their distinctive advantages and disadvantages attempts have been made to fill in the gap between these two methods J Husband developed a baseline model to obtain a unified FBO response across all engine components for both impact and imbalance modeling 13 This model is essentially a simplified LS DYNA model and is more suitable for conceptual design Boeing GE and MSC 14 streamlined the FBO simulation process by MD Nastran using the results of the transient FBO calculations as initial conditions for the rotor dynamics analysis However the integration used the internal database of MD Nastran to transfer loads and is not very flexible to use This paper introduces a chained analysis method for load evaluation of an FBO event Figure 1 is the graphical representation of this approach A load transfer tool is designed so that impact rub loads obtained from explicit analysis can be used as input to the implicit analysis The benefits of this method are addressed here and the techniques involved in this chained analysis are also discussed Figure 1 Graphical Representation of the Approach EXPLICIT FINITE ELEMENT ANALYSIS Explicit Time Integration Explicit time integration is often adopted for problems with strong nonlinearity In this research the nonlinear dynamic solver LS DYNA is used for the explicit analysis In LS DYNA the semi discrete equations of motion at time n are 1 where M is the diagonal mass matrix accounts for external and body force loads is the stress divergence vector and is the hourglass resistance 15 The dynamic equation is solved using central difference scheme 2 3 where There is no convergence check in explicit method and the accuracy and stability of the calculation result are ensured by controlling the time step size of the calculation The program automatically determines the minimum time step size based on the characteristic length of element and wave speed to make sure the Courant stability condition is satisfied Elements with reduced integration are widely used in the explicit method e g one point integration element is generally adopted instead of fully integrated elements In this way efficiency of the calculation can be greatly enhanced and shear locking problem induced by fully integrated elements is also avoided However the reduced element will cause another problem called zero energy mode or hourglass mode which is the major source of numerical instability in explicit analysis As a rule of thumb the hourglass energy of each component as well as the whole system should be less than 10 of the internal energy better to be below 5 In LS DYNA the undesirable hourglassing can be resisted by adding a viscous damping or small elastic stiffness the former is referred to as viscous hourglass control and the latter the stiffness hourglass control Efforts should be made on selection of hourglass control type and its coefficient as the effects of the hourglass control are contingent on the calculation cases Despite the methods introduced in LS DYNA the hourglassing instability is best handled by refining the meshes in critical areas Point load 2Copyright 2017 ASME should always be avoided and a concentrated load should be shared by multiple surrounding nodes 16 17 As the explicit time integration does not check convergence for each time step the calculation error would accumulate as the simulation time goes on For a high fidelity FE model with large degrees of freedom it is also very difficult to run the model for a long time without error The explicit method is therefore more suitable for transient problems in this case the impact phase of the whole FBO process FE Model for Explicit Analysis The FE model for the explicit analysis is fine in mesh To capture the impact and rubbing loads the fan blades and the casing are modeled in detail In the model discussed in this paper the fan blades and the casing are modeled by shell elements and the three blades that are most deformed in the FBO process are especially fine in mesh In the impact phase these three blades suffer the most sever loss of material of all the fan blades If the meshes of these blades are too coarse the material loss may not be captured properly which will yield inaccurate unbalance amount Discrepancies in blade meshes will however introduce numerical mistuning of the model and the structure is no longer perfectly cyclic symmetric This is admissible as in the impact phase of FBO the blades will soon become much more deformed making the mistuning caused by mesh difference insignificant The blades are carefully modeled so that the stress distribution under centrifugal load is normal with no highly localized strain energy The meshes for other main structures of the engine should also be fine enough yet not too fine to stagnate the calculation Figure 2 shows the FE model of the whole engine The model consists of over 220 000 elements among which 168 000 are 8 node solid element and 54 000 are 4 node shell elements It takes 19 hours to simulate a process of 0 1 second in high performance computing environment with 8 processors running in parallel Figure 2 Full Engine Explicit FE Model IMPLICIT FINITE ELEMENT ANALYSIS Implicit Time Integration In this paper ANSYS is used for implicit finite element analysis The equation of motion solved by an implicit dynamic analysis is 4 where M is the global mass matrix C is the global damping matrix K is the global stiffness matrix and F t is load vector At any given time t these equations can be thought of as a set of static equilibrium equations that also take into account inertia forces and damping forces In rotordynamic analysis the gyroscopic effect is also included and the equation of motion in a rotational frame of reference becomes 5 where is the spin softening matrix due to the rotation of the structure and G is the global Coriolis matrix 18 Here is the element Coriolis damping matrix and 6 7 where is the angular velocity of the rotation The Coriolis matrix is therefore dependent on the rotational speed The dynamic equation is solved using Newmark approximation or an improved implicit time integration method called HHT 19 The Newmark algorithm updates the displacement and velocity as follows 8 9 where and are Newmark s integration parameters For linear problems the implicit time integration is unconditionally stable and the time step size will vary to satisfy accuracy requirements For nonlinear problems the solution is obtained by a series of linear approximations In each time step there can be many equilibrium iterations Nevertheless the time step size in implicit time integration method is much larger than that in explicit one Therefore a longer result can be achieved by the implicit method FE Model for Implicit Analysis The finite element model for the implicit dynamic analysis is usually coarser in mesh than the explicit one Figure 3 is the implicit model for the engine discussed in this paper Compared with the explicit model the scale of the implicit one is greatly reduced In the model illustrated the rotor of the engine is simplified by beam elements blades and vanes are substituted by mass elements with equivalent masses and inertia and the major stationary parts are modeled by shell elements The element number of the implicit model is over 22 000 among which 18 000 are 4 node shell elements and 4 000 are 1 D beams 3Copyright 2017 ASME Figure 3 Full Engine Implicit FE Model LOAD TRANSFER Due to the significant differences in FE models and time step sizes between the explicit and implicit analyses it is not an easy job to transfer loads from the former to the latter That is why the impact loads in the initial stage of FBO are generally not taken into consideration during the implicit analysis The authors of this paper developed a tool that could transfer the impact loads smoothly and accurately The tool includes an interface for data transform from LS DYNA format to ANSYS format and integrates processes of load mapping time step size matching and unbalance level determination Load Mapping In the approach introduced here the load being processed is resulted from impact and rubbing between the fan blades and the fan casing To capture the impact rub loads in LS DYNA contact groups representing interactions between fan blades and casing are predefined The nodal interface forces on the fan casing formatted as ncforc in LS DYNA are stored in a binary file binout In this way for each one on fan casing there will be a time history curve of nodal force The load transfer tool reads data using a post processing script designed for LS DYNA and exports it in ASCII format so that it can be ready to use by ANSYS The load mapping procedure maps the loads from nodes in a fine mesh model to that in a coarse mesh one The mapping algorithm is so designed that the overall forces being transferred be equivalent while local differences may exist due to discrepancies in meshes Figure 4 is a two dimensional representation of load mapping algorithm Nodes a1 a4 are nodes that in the fine meshed model and b1 b4 are four nodes of a coarser quadrilateral mesh For each node in the finer meshes a direct search is first performed to find n number of neighboring nodes belonging to the coarser meshes In the case illustrated when node a0 is selected and n 4 node b1 b4 are found to be the closest to node a0 The load on node a0 is then distributed to these neighboring nodes The distribution of load is based on the distances between the neighboring nodes to the selected node For each neighboring node bi a weighting factor wi is calculated in this way 10 where is the distance between the jth neighboring node to the selected node The distributed load from the selected node to node bi is calculated as wif The resultant load mapped onto node bi is the summation of distributed loads from all the possible nodes in the finer meshed model after looping over all the concerned nodes In this way local peak loads may be slightly different after mapping but the total forces are conserved The neighboring node number n can be altered by the user according to mesh differences of the two models Figure 5 shows the comparison of the load before curve A and after curve B mapping when n 1 and the resulting loads shows a good agreement with that before mapping Figure 4 2D Representation of Node Search Figure 5 Mapped Load Comparison Time Step Size Matching Because of the severe disparities in time step size between explicit and implicit method it is quite necessary to do time step size matching after load mapping The impact and rubbing load obtained by explicit analysis may have a large number of unrealistic high frequency noises which are undesired in the 4Copyright 2017 ASME implicit analysis The noise is eliminated through implementation of the FFT method Large discontinuity existing in the impact load signal produces high frequency components in the resulting Fourier modes causing an aliasing error To condition the input signal before the transfer a method of windowing is employed Suppose there are N time sequence data sampled with a constant interval k 0 1 2 N 1 11 Windowing is done by multiplying the original input data by a window function as follows j 0 1 2 N 1 12 A typical window function is like this 13 The window function preserves 3 4 of the original input data affecting only the first 1 8 and last 1 8 of the data The discontinuity of the signal can thus be mitigated Unbalance Level Determination During the FBO event the loss of fan blade makes the center of the engine mass deviate significantly from the centerline of the engine In explicit analysis the changes of mass as well as center of mass are tracked and stored in an ASCII file ssstat The load transfer tool reads the ssstat file and extracts unbalance level information The output is then formatted in a table that can