Development of Stochastic Methods for Helicopter Crash Simulation

Transcription

1 Development of Stochastic Methods for Helicopter Crash Simulation Dr G Pearce; Mr J Page*; Mr J Kealy University of New South Wales, Sydney, Australia *j.page@unsw.edu.au Abstract. A research project has been initiated with the ultimate goal of simulating the entire crash scenario including; normal flight conditions, significant failures, pilot response, impact and occupant injury metrics. To this end an integrated flight simulation and finite element modelling methodology was developed which can capture both the flight dynamics during the emergency and the structural dynamics of the crash. It is envisaged that with the introduction of this technology, piloting and vehicle design strategies can be developed to improve harm minimisation under a range of crash scenarios. This paper proposes that the current deterministic approach to crash simulation is inappropriate. The chaotic nature of the crash process makes it impossible to rely on a small number of highly computationally intensive simulation results to drive design, as critical crash cases can be easily missed. Instead, a computationally cheap modelling approach with acceptable accuracy coupled with stochastically derived input parameters provides a much better simulation framework for capturing and designing for the critical crash cases. This paper investigates the application of stochastic methods to the helicopter crash simulation methodology including both the flight simulation and crash simulation. The results illustrate the benefit of the stochastic approach, as correlations can be established between occupant loads and the critical input variables. Occupant harm was found to be most closely linked to vertical impact velocity, as expected, but the relationship was not linear. In cases tending to greater crash energies, the correlation of variables was weaker and the influence of input parameters on the crash outcomes could only be derived from stochastic analysis. 1. INTRODUCTION The major obstacle that must be overcome to allow simulation-driven design of aircraft is the validation of crash simulations with experimental data for the general crash case. This challenge has not yet been achieved for two distinct reasons. Firstly, the expense of crash testing aircraft, as opposed to automobiles, is prohibitive for all but a small set of predefined critical loads cases (Fasanella and Jackson 2002). Consequently, experimental data is only available for a small subset of possible crash conditions. (Maia 2005) identifies that the main deficiency in the current simulation approach lies in the lack of information to adequately determine the uncertainty in the experimental data. Secondly, although it is improving, crash simulation fidelity has not yet reached the critical level at which it can reliably and robustly model all the structural response and occupant loads during a crash event (Jackson et al. 2009; Annett 2010). There are some authors (Hemez and Doebling 2001) who question the validity of treating a crash simulation as predictive when it was matched with only one set of test data. Such a model, they claim, would not be useful for scenarios not represented by that test data. Hemez and Doebling contend that the focus of research into model validation should be shifted from validating deterministic models to validating statistically accurate models. Such an approach would allow for variability and uncertainties in the testing environment. 2. STOCHASTIC METHOD Uncertainty and scatter exist to some degree in all physical system properties under realistic conditions. As a result, no two physical systems will behave identically, even under precisely controlled conditions. In some systems, the degree of this variability is small and the relationship between system inputs and system response can be easily determined. These systems can be dependably modelled with deterministic tools. In other systems where the degree of scatter is large, the system response can only be related to the system inputs using a statistical approach. A vehicle crash is an excellent example of such a system; the event is chaotic in nature and small input perturbations can lead to large variability in outputs. Randomly sampling such a system, i.e. conducting a single vehicle crash, provides little information about the system response. To determine the statistical system response, the system must be sampled many times, which is unfeasible using large-scale crash testing. Simulation has the potential to probe complex system behaviour quickly and cheaply. Sahlin et al. (2003) suggests using a Monte-Carlo approach, as illustrated in Figure 1. Randomly sampled input shots are processed by the complex system simulation in order to generate a system response cloud.

2 Input Variables x 1 x 2 y 1 y 2 Response Variables A Robinson R22 helicopter was chosen as a platform for this research. The R22 has simple flight and control characteristic as well as simple structural geometry, making it an ideal choice for pilot studies in this area. The popularity and roles of the R22 also ensure that it appears regularly in the NTSB accident database, providing comparison data to augment the simulation studies. Response y1 x 3 x m y Integrated Flight and Crash Simulation This study forms part of a larger pilot study into the integration of flight simulation, pilot emergency response and crash simulation, previously reported in Pearce et al. (2011). The schematic architecture of the integrated approach is shown in Figure 3. The current paper focuses on the stochastic nature of each simulation methodology. A Monte-Carlo approach was used to explore the correlations between input and response for the two simulation tools used. Emergency Flight Parameters Airspeed, Altitude, Attitude, Rotor Speed Input x 1 Figure 1: Monte-Carlo simulation approach (Sahlin et al. 2003) The relationship strength of the correlation between input, x, and output, y, variables can be found using the Pearson correlation coefficient. r = x y xy n ( x) ( y) y x n n Pearson coefficients of +1 and -1 represent perfect correlation and inverse correlation respectively while a value of 0 indicates an independent relationship. 3. SIMULATION METHODOLOGY 3.1 Vehicle Selection Figure 3: Current simulation methodology 3.3 Flight Simulation Flight Simulation and Emergency Response Impact Conditions Velocity, Rotational Velocity, Orientation, Lift Crash Simulation Severity Determination Acceleration, Head Impact, Restraint Loads Figure 2: Robinson R22 Figure 4: R22 X-Plane model

3 X-Plane flight simulator was used for this research. X- Plane is a powerful simulator used by air forces, aircraft manufacturers and defence contractors for applications ranging from design, testing and training. The R22 model was selected from the X-Plane database of over 4000 aircraft. The model was awarded Best Helicopter Award by x-plane.org and is shown in Figure 4. The flight simulation study was conducted using the stochastic approach shown in Figure 5. Total engine failure was simulated followed by an attempted autorotation landing following procedures outlined in the 2007 US Army Field Manual. It should be noted that the attempted landing in this study were performed by an untrained pilot with only simulator experience. The simulation results could be considered representative of the response of a trainee pilot undertaking the autorotation manoeuvre. Stochastic Flight Parameters Flight Simulation Simulate Engine Failure Attempt Autorotation Stochastic Impact Conditions Figure 5: Stochastic approach for flight simulation Six baseline flight cases were selected to study, as shown in Table 1. Cases 1-3 were considered marginally safe autorotation cases as defined by the Height vs Velocity curves for the R22 (Cantrell 2011) while cases 4-6 were considered unsafe. Table 1: Baseline flight parameters at engine failure Case Number Altitude (ft) Air Speed (kts) Hover Hover Hover 6 50 Hover 3.4 Crash Simulation LS-Dyna was used as an explicit Finite Element (FE) analysis solver for this research. The computational cost of running stochastic explicit FE impact simulations is still very high so efforts must be made to simplify the crash models as much as possible. The R22 crash model was reduced to a beam-mass model as shown in Figure 6. The airframe was considered to be impacted rigid ground. Masses were added for the engine, systems and missing structure but the placement of theses masses was not exact and the structural members connecting to large point masses, such as the engine and occupant, were not accurately represented. Figure 6: Beam-mass R22 model with rigid ground The input conditions for the crash simulation were determined from the results of the flight simulation studies. The impact conditions predicted by the flight simulation were found to follow a normal distribution. Two input data sets were generated that matched the statistical properties of the safe autorotation simulations and the unsafe autorotation simulations. The input parameters considered for each case were vertical speed, ground speed, pitch angle, roll angle, pitch rate, roll rate and yaw rate. The input parameters were applied to the centroid of the model as initial conditions prior to the model being released to impact the ground. The airframe mesh was constructed with beam elements with a constant tubular cross-section of 30mm OD and 2mm wall thickness. The mesh was assigned bi-linear elasto-plastic steel properties with a yield strength of 630 MPa. The non-linear material ensured that the structure absorbed some energy from the crash event and that it was not all stored in elastic strain energy. The model used was not intended as a predictive tool. The fidelity of the model was very poor and many simplifying assumptions were made at this early stage. It was representative of helicopter vehicle structure however, and was suitable for comparative studies. The fidelity of this model can be expanded in future to provide a more realistic structural response if the added computational costs are warranted or if more detailed structural information is attained. 4. RESULTS 4.1 Flight Simulation The flight simulation was conducted for three safe and three unsafe autorotation cases shown in Table repetitions of each case were run for a total of 600 manually attempted autorotation landings. There was no stochastic variation of the input parameters but the complex non-linear response of the flight simulation

4 coupled with small input variations from the pilot ensured that the system response was random in nature Safe Autorotations It was found for all the safe autorotation cases that autorotation could be achieved even for an untrained pilot and that vertical impact velocities of under 1.5 m/s could be achieved in most cases. There was significant variability in the results however, as shown in Figure 7. The state of the vehicle immediately prior to impact is summarised in Table 2. This variability is critical knowledge when designing training helicopters that will be regularly landed in this manner. Figure 7: Vertical vs horizontal impact velocity for safe simulation case 1 Table 2: Safe autorotation impact conditions Variable Mean Standard Deviation Vertical Velocity (m/s) Indicated Velocity (m/s) Ground Speed (m/s) Pitch (deg) Roll (deg) Q (rad/s) P (rad/s) R (rad/s) Unsafe Autorotations For the unsafe autorotation cases it was not possible to develop true autorotation landings. It was shown however that vertical impact velocity could be minimised with increased forward velocity, as shown in Figure 8. The correlation between these two variables was expected from physical principles because the greater the forward speed the greater the lift generated by the autorotating blades. Application of the stochastic simulation added to the physical understanding by establishing the variability of the response. It would be feasible to trial different autorotation protocols rapidly using this technique. It could be determined how robust or repeatable the different protocols were in the face of stochastically varying input conditions. Figure 8: Vertical vs horizontal impact velocity for unsafe simulation case 2 Table 3: Unsafe autorotation impact conditions Variable Mean Standard Deviation Vertical Velocity (m/s) Indicated Velocity (m/s) Ground Speed (m/s) Pitch (deg) Roll (deg) Q (rad/s) P (rad/s) R (rad/s) Crash Simulation The inputs for the crash simulation were generated stochastically from the impact conditions derived from the flight simulations given in Table 2 and Table random variations each were generated for both the safe and unsafe autorotation data sets, known as Monte- Carlo Simulation (MCS) 1 and MCS2 respectively. A 75kg mass was added to the base of the seat and the acceleration of this mass during the crash event was recorded. Four key system outputs were measured during the simulation based on the maximum acceleration of the occupant in each of four different directions. The coordinate system for the occupant acceleration is shown in Figure 9. Figure 9: Occupant acceleration coordinate system The results for MCS2 were of more interested as they represented the most energetic crash events likely to cause injury. The occupant accelerations as a function of vertical impact velocity are shown in Figure 10. It is sensible that these loads increase as the vertical impact velocity increases. The interesting result achieved by the stochastic approach is the degree of variability. For instance, the case with the largest vertical impact velocity actually experienced less than half the

5 maximum acceleration of the worst case simulation. It is clear from these results that a single deterministic simulation would yield very little information about the system response. DISCUSSION AND CONCLUSION The aim of this project was to investigate the application of stochastic analysis to flight and crash simulation. It is part of a broader study into the benefits of integrating flight simulation with crash simulation to determine occupant injury metrics from real emergency scenarios. The flight simulation study examined a large number of cases, and found the flight performance of the X-Plane simulator to be realistic. Statistical analysis of the results allowed assessment of the variability of the landing/impact conditions depending on small variations induced by the emergent simulation behaviour and the pilot inputs. This information can be using to improve design guidelines for crashworthiness as well as possibly developing more robust response protocols to various in-flight emergency scenarios. The crash study utilised Monte Carlo Simulation to analyse two sample sets of 100 cases based on the statistical information derived from the flight simulation. The Pearson correlation coefficients for all input and output variables are shown in Table 4. The correlation between the vertical impact velocity and the vertical accelerations is moderately strong whereas the other correlations were quite weak or insignificant. This leads to the conclusion that the crash event is very chaotic and that a stochastic approach is definitely needed. Occupant harm was found to be most closely linked to vertical impact velocity, as expected, but the relationship was not linear. In cases tending to greater crash energies, the correlation of variables was weaker and the influence of input parameters on the crash outcomes could only be derived from stochastic analysis. Figure 10: Occupant acceleration experienced as a function of vertical impact velocity Table 4: Pearson correlation matrix for unsafe autorotation crash cases

6 5. FUTURE WORK 5.1 Improvements to Flight Simulation The emergency and crash scenarios considered in this paper were highly simplified cases intended to illustrate the stochastic methodology. The input conditions were deterministic and represented simple emergency scenarios. Two key extensions are planned to flight simulation. Firstly, more representative emergency scenarios will be investigated with stochastic inputs. Secondly, and more challengingly, an automated emergency response protocol will be included in the flight simulation phase to include the response of the pilot and onboard crash mitigation systems. Rapid stochastic investigation of emergency response protocols will allow for robust protocols to be developed and will open new avenues for pilot training or design improvements. 5.2 Improvements to Crash Simulation The crash simulation used for this research was subject to many simplifications to facilitate rapid solutions. The simulation complexity needs to be incrementally increased in order to capture more of the physics involved in a true crash event. Key areas of simulation improvement already considered vital are: Improved structural models (e.g. non-linear materials, inclusion of skin panels, better internal mass distribution). Improved ground models (e.g. soft and hard soil models) Occupant modelling to extract more realistic and representative occupant loads. Extra simulation complexity can lead to dramatically longer solution times, especially when stochastic analyses are performed. Future extensions to the FE solution will be carefully scrutinised to ensure that a practical balance between solution time and accuracy is maintained. 6. REFERENCES Annett, M. S. (2010). LS-DYNA Analysis of a Full- Scale Helicopter Crash Test. 11th International LS-DYNA Users Conference. Dearborn, MI, United States. Cantrell, R. (2011). "Height versus Velocity Curves." from ve.html. Fasanella, E. L. and K. E. Jackson (2002). Best Practices for Crash Modeling and Simulation. Hampton, Virginia, USA, U.S. Army Research Laboratory and NASA. Hemez, F. M. and S. W. Doebling (2001). "Model validation and uncertainty quantification." Modal Analysis 2000: 1-6. Jackson, K. E., Y. T. Fuchs and S. Kellas (2009). "Overview of the National Aeronautics and Space Administration Subsonic Rotary Wing Aeronautics Research Program in Rotorcraft Crashworthiness." Journal of Aerospace Engineering 22(3): Maia, L. G. (2005). "A Review of Finite Element Simulation of Aircraft Crashworthiness." SAE International Technical Paper Series Pearce, G., J. Page, P. Sammons, R. Subbaramaiah and G. Prusty (2011). Crash Investigation using Integrated Flight Simulation and Finite Element Modelling. Asia-Pacific Simulation and Training Conference and Exhibition Melbourne, Australia: Sahlin, P., C. Jimenez, A. Kuhn and T. Riedenbauer (2003). Implementing Stochastic Multidisciplinary Design Improvement Examples and Implications. NAFEMS Seminar: Use of Stochastics in FEM Analyses. Wiesbaden, Germany.