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94 Figure 10-11. Reinforced turf material (left) and dog-bone specimen in tensile test jig (right). engineered aggregate concept is to be transitioned into a passing through the material permitted larger particles to be fieldable system. used with negligible decrease in accuracy. 10.4. Modeling Effort 10.4.1.2. Size Distributions The modeling effort sought to replicate the important behav- Section 10.3.1 discussed the particle size variation of the iors of the engineered aggregate arrestor system concept. engineered aggregate, which followed a bounded normal dis- The aggregate and turf simulations were conducted using tribution. This normal distribution was important to repli- the EDEM software, which is a DEM code, as discussed in cate in EDEM because it affects the packing density and the Section 10.2.1. void ratio of the particles. As such, all aggregate simulations used the same normal distribution regardless of size scaling. The turf material was represented using uniformly sized 10.4.1. Particle Sizes and Shapes particles in EDEM. 10.4.1.1. Size Selection In the DEM method, the model particles are often larger 10.4.1.3. Shapes than the actual real-world particles. Because DEM modeling The average maximum-to-minimum diameter ratio of the is a numerical method, various levels of fidelity are possible. aggregate was 1.24, which is close to that of a perfect sphere High fidelity simulations will use a large number of smaller (1.0). As such, all aggregate particles were modeled as simple particles, while low fidelity simulations use a reduced number spheres. The irregularities in shape were essentially accounted of larger particles. If the particles chosen are too large, accu- for through the coefficient of rolling friction for the aggre- racy suffers. Conversely, if the particles are too small, simula- gate, which is discussed further in Section 9.4.2.1. tion times rapidly increase to impractical levels. The general goal for such models is to select a particle size that gives suffi- 10.4.2. Calibration to Physical Tests cient accuracy while keeping simulation times short. During the course of the model development and calibration, The aggregate and turf models were calibrated to match the care was taken to select particle sizes that struck the right bal- physical tests as closely as possible. Properties of density, par- ance of accuracy and time efficiency. For the aggregate models, ticle size distribution, and so on were simply entered into the particle diameters were as small as 0.348 in. (the actual aggre- software. However, the particle interaction properties of the gate size) and as large as 2 in. in diameter. The size required for aggregate and particle bonding properties of the turf required good accuracy was highly dependent on the size of the tire or iterative determination. This section briefly summarizes the structure that was interacting with the material. Larger wheels outcome of the long calibration process.

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95 10.4.2.1. Angle of Repose Figure 10-14 and Figure 10-15 show the pendulum model replicating the high-speed test. The shading indicates the rel- The angle of repose test was replicated in EDEM using a ative particle speeds as the one-wheel bogy passes through the bucket of identical size, filled with particles. The bucket was arrestor bed. Figure 10-16, by contrast, shows the compres- then removed, and the particles were allowed to fall and set- sion force on the particles, indicating the region of high load- tle into a heap (Figure 10-12). Simulations were conducted ing in front of and beneath the wheel. for several scaled particle sizes ranging from the actual size of The pendulum tests were used to calibrate two critical 0.348 in. up to 1 in. in diameter. Each model had nominally parameter sets for the aggregate: the coefficients of restitution 35K particles and 43K particle-to-particle contacts. and the coefficients of static friction. Both parameters must The coefficient of rolling friction for the aggregate was be defined for particle-to-particle and particle-to-surface determined using this method, and it was found to be depen- interactions. These interactions had a substantial effect on the dent on the particle diameter. Therefore, in all subsequent predicted loads for the pendulum strut as it passed through simulations, the coefficient of rolling friction was matched to the aggregate bed. the scaled particle size to ensure accurate results. After calibrating these parameters, the pendulum model The overall accuracy of the predicted angle of repose was matched the test results for both the high- and low-speed tests within 1/2 degree (Figure 10-13). for the dry aggregate bed. Figure 10-17 shows a graphical comparison of the simulation and test data, where the error 10.4.2.2. Hydrostatic Triaxial Tests bars indicate the scatter of the actual test data. The deviations from the true test data for the low- and high-speed tests are The hydrostatic triaxial tests were not replicated in EDEM 3.1% and 3.0%, respectively. due to software limitations. EDEM does not support deform- Recalling the speed dependence manifested during the able structure modeling or pressure load applications. Both physical tests (Figure 10-10), it was important that the aggre- of these features would be required to replicate the elastic gate model be capable of capturing this effect. It was clear membrane that surrounded the triaxial test articles and the from the calibration results in this section that the model did applied hydrostatic pressure. in fact do this with high accuracy. This lends confidence to The hydrostatic triaxial tests nevertheless revealed that the the later predictions made for even faster overrun situations, aggregate performed normally and had no unusual character- at speeds as high as 70 knots (81 mph). istics that might make the use of EDEM inappropriate. The tests also provided data for the shear modulus of the aggre- gate material, which was a parameter required in EDEM. 10.4.2.4. Turf Tests The turf tensile test was replicated in EDEM using a layer 10.4.2.3. Pendulum Tests of particles joined together with a bond contact definition (Figure 10-18). The bonded layer was then pulled apart using An EDEM model was constructed to replicate the pendu- simulated clamps at either end. The geometry of the tensile lum tests and was used to calibrate the remaining aggregate specimen is not an exact match to that of the physical tests material parameters (Figure 10-14). The pendulum strut was due to the rigid geometry limitations of EDEM. However, the simplified in the model to include only the features that inter- loaded area reflects the 8-in. wide region used in the physical acted with the aggregate in the actual test. The aggregate bed test specimens. The model had a total of 946 particles, 2,126 was 16 ft in length, 5 ft in width, and 22.5 in. in depth. The contacts, and 1,937 bonds. model bed width was less than the actual bed width (8 ft) in Figure 10-18 illustrates the tensile loading of the model order to reduce the particle count, but was still wide enough turf. The failure of the specimen is progressive, and as the turf to prevent substantial boundary effects. is stretched an increasing number of inter-particle bonds are The strut followed an arced path approximating that of the broken. The bonds were defined in terms of stiffness and fail- actual strut, with the same 1/2-diameter penetration depth into ure strength, in both normal and shear directions. Iterative the arrestor bed. The wheel was set to a constant rotation rate combinations of these four parameters were tried until the approximating the observed rotation rate of the wheel on test overall turf strength and elongation at failure matched the video. actual test specimens. Other material properties (shear mod- Several particle sizes were attempted, and an error conver- ulus, Poisson's ratio, etc.) were taken from nominal values for gence study was undertaken. It was determined that a 1.0-in. sand or the aggregate model, depending on appropriateness. particle diameter was required for the relatively small pendu- The tensile strength of the model turf was within 1% of the lum strut/wheel assembly. The particle size error was esti- test data average, while the energy absorption was within 11% mated to be less than 6%. The model had a total of 315K of the test data average. However, the spread in the test data particles and 781K particle contacts. itself was +/ 7% and 11% for these quantities, respectively.

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96 Figure 10-12. Angle of repose simulation in EDEM.

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97 Figure 10-13. Angle of repose measurement. Given the highly variable nature of the turf as a material, this model were created with different depths in 6-in. increments, accuracy was deemed sufficient for the needs of the evaluation. from 6 to 36 in. The deeper the bed, the more particles were included. However, the turf layer was always 4.6 in. deep, since this was a fixed layer thickness. All bed depths cited 10.4.3. Tire and Arrestor Simulations include the thickness of the turf layer. Using the calibrated aggregate and turf material models Compared with the pendulum model, this new model was previously described (Section 9.4.2), a large-scale arrestor longer, wider, and deeper, giving a larger overall volume of model was created in EDEM to simulate overruns by aircraft aggregate. As such, larger particles became a practical neces- tires. Figure 10-19 illustrates the model with a 36-in. depth and sity to keep simulation times efficient. A particle size conver- a B737-800 main-gear tire (Goodyear H44.5x16.5) at 50% gence study using the B737 main-gear tire showed that a 2-in. penetration depth. diameter particle could be used with an estimated particle size error of less than 6%. For the 36-in. depth, the model had a total of 149K parti- 10.4.3.1. Arrestor Bed Models cles, including 138K aggregate particles and 11K turf parti- The arrestor bed models for the aircraft tire simulations cles. The particles formed 372K contacts, and the turf layer were 8 ft wide and 25 ft long. Versions of the arrestor bed had 15K inter-particle bonds. Figure 10-14. Overall view of engineered aggregate pendulum model, velocity fringe plot.

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98 Figure 10-15. Side cutaway view of engineered aggregate pendulum model, velocity fringe plot. While most simulations were conducted on a turf-covered were rigid forms that matched the inflated dimensions of the bed, some were also run using an aggregate-only bed. The respective tires. During overruns, the tires maintained this comparison of results is discussed in Section 10.4.4.4. undeformed shape. In reality, the tires would form flat regions on the bottom and front faces, as is shown in the LS-DYNA crushable material models. To account for this discrepancy, 10.4.3.2. Tire Models a corrective calculation was undertaken in the MATLAB EDEM does not inherently support deformable tire model- Arrestor Prediction Code. For the EDEM arrestor models, the ing, which necessitated a different approach be taken than that important measured components were the depth and width of of the LS-DYNA crushable arrestor models. The model tires the rut created, and the corresponding loads that it produced. Figure 10-16. Side cutaway view of engineered aggregate pendulum model, force fringe plot.

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99 Low-Speed Test (8.5 mph) High-Speed Test (17.2 mph) 400 800 300 600 Force (lbf) Force (lbf) 200 400 Test Test 100 200 Simulation Simulation 0 0 g g g g Av Av Av Av ce e ce ce orc or or or XF ZF XF ZF Figure 10-17. Engineered aggregate pendulum model data comparison to test data. Because the tires were non-deforming, the tire library was from the 44.5-in. and 27-in. tire models using width correc- simplified down to three tires instead of the five tires used in tion factors. the crushable models (Table 10-2). The 44.5-in. and 49-in. The tire path through the arrestors was based on a pre- main-gear tires of the B737 and B747 were very close to the scribed motion using a fixed forward speed and rotation rate. same size. Similarly, the 29-in. main-gear CRJ-200 tire and As the tire passed through the bed, a steady-state loading 27-in. nose gear B737 tire were very close to the same size. resulted. The vertical and horizontal loading at this state was The ruts each tire created would, therefore, be similar. As measured. such, predictions for the 49-in. and 29-in. tires were scaled Unlike the LS-DYNA arrestor models, the tire spin could not be released to settle at a steady self-rotation rate in EDEM, Clamp Motion Turf Layer with Bonded Particles Aggregate Layer with Loose Particles Loose Turf Particles After Bonds Broken Loose Turf Particles After Bonds Broken Figure 10-19. Model of combined tire and engineered Figure 10-18. Turf tensile test model showing aggregate arrestor system showing aggregate (light) turf particles (dark) and bonds (light). and turf (dark) particles.

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100 Table 10-2. Tire library simplification for engineered aggregate arrestor models. Aircraft Landing Gear Tire Designation Modeling Method CRJ-200 Main Gear H29x9.0-15 Scaled from H27 Data Nose Gear R18x4.4 Modeled in EDEM B737-800 Main Gear H44.5x16.5-21 Modeled in EDEM Nose Gear H27x7.7-15 Modeled in EDEM B747-400 Main Gear H49x19-22 Scaled from H44.5 Data Nose Gear H49x19-22 Scaled from H44.5 Data since EDEM does not have inherent dynamics calculations tire to travel the required minimum distance. Loading at for the rigid tire parts. Instead, it was held at a constant pre- speeds below 10 knots was based on the extrapolated meta- scribed rate, assumed to be the ideal rate of spin that the tire model data fit.); would have on a hard surface with no slippage at the given Bed depth, from 6 to 36 inches (Figure 10-20); and forward speed. This unfortunate necessity affected the pre- Penetration into the bed, from 10% to 100% of bottom- diction accuracy because the tires can exert a forward "driv- ing depth. ing" type of torque due to their constant rotation rate. The impact of this effect was mitigated by prescribing a low tire-to- Batch simulations for the EDEM arrestor models were aggregate friction of 0.10, which limits any fictitious driving more involved than for the LS-DYNA models because the effects. The impact of such driving was deemed a second-order optimization software, LS-OPT, could not automatically cre- effect in the simulations. ate parameterized variants of the models. Consequently, the Future simulations using the aggregate could potentially input files were created manually prior to running, using link EDEM with a dynamics code for improved accuracy; experimental design points specified by LS-OPT. After the such enhancements were, however, outside the scope of the simulations were finished, the measured load data was then current effort. extracted manually and assembled into a form that could be read back into LS-OPT. The time-consuming nature of this 10.4.4. Batch Simulations manual approach led to a simplified process: simulations were done in batches of 50 for each tire in a single iteration. Using the arrestor bed model, large batches of simulations No additional add-on runs were undertaken, which was often were conducted to generate substantial bodies of data for a done for the LS-DYNA batches in an attempt to increase the wide range of overrun conditions. This data was then assem- accuracy of the final data set. bled into "metamodels" for uploading and use by the APC. 10.4.4.1. Methodology 10.4.4.2. Summary Tables of Metamodels Batch simulations were conducted for each tire with three The output from the batch simulations was assembled and open variables: uploaded into LS-OPT, where metamodels were constructed for the drag and vertical load forces. Metamodeling is analo- Speed, from 10 to 70 knots (Speeds below 10 knots were gous to fitting a curve through experimental data, except it is impractical due to the long simulation times required for a applied to multi-dimensional data sets. Here, the data sets are Penetration Depth Bottoming Depth Bed Depth Figure 10-20. Depth definitions for engineered aggregate bed models.

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101 Table 10-3. Metamodel accuracy summary for engineered aggregate/turf arrestor bed. Experimental Points Tire Response RMS Error R2 Points Used Drag 3.52% 0.999 H44 50 48 Vertical 4.20% 0.996 Drag 4.38% 0.998 H27 50 48 Vertical 8.38% 0.982 Drag 7.59% 0.993 R18 50 48 Vertical 5.00% 0.987 four-dimensional, including speed, depth, penetration, and 10.4.4.3. Parameter Sensitivities load (either vertical or drag). The metamodels used for these responses were RBF networks, which can effectively capture Using the metamodels, it is possible to review how sensitive non-linear behaviors including multiple concavity changes the landing gear loads are to the different variables of speed, across the data set. bed depth, and penetration percentage. The unusual feature Table 10-3 summarizes the fit quality for the metamodels. for the engineered aggregate system is that the response is very The RMS error was typically below 5%, and the R-squared sensitive to forward speed. Practically speaking, this means that value was typically above 0.99, indicating good fit quality with the engineered aggregate system will exert more load on the minimal noise. landing gear when the aircraft is travelling at high speed, and In the table, two outlier points were eliminated from each less at low speed. data set such that the metamodels were constructed using 48 Figure 10-21 shows a surface plot for the metamodel. The of the 50 original experimental design points. Reasons for the drag force in this case becomes stronger (more negative) outliers generally were data measurement issues arising from where the speed increases. For a deep penetration along the a failure of the run to reach steady-state conditions prior to left-front edge of the plot, the loading at 70 knots is 34,700 lbf, the tire exiting the arrestor bed. and at 10 knots it is only 2,400 lbf--a factor of 14 difference. Drag Force (lbf) Speed (knots) Penetration Depth Ratio Figure 10-21. Metamodel drag load surface plot for 44.5-in. tire in an 18-in. deep arrestor/turf bed.

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102 Table 10-4. Comparison of speed velocities are similar in both cases (1,000 in./s), but the vol- sensitivities for engineered aggregate ume of debris appears to be reduced where the turf layer is systems with and without turf cover layer. present. If the ejecta plume is mitigated in this way, it could reduce System Drag Force Vertical Force the risk of ingesting aggregate particles in the aircraft engines. Aggregate/Turf -14 20 However, the reality of this predicted behavior requires con- Aggregate Only -20 23 firmation through physical testing. Percent Advantage for 30% 13% Aggregate/Turf 10.4.4.5. Effects of Penetration Depth The bi-layer construction of the turf-covered aggregate bed The drag load was found to be dependent on speed and speed- can lead to situations where the tire creates a tunnel beneath squared terms: the turf surface. Figure 10-23 illustrates such a situation, where the turf layer is stretched, but not broken, above the Drag = A Speed 2 + B Speed + C small 18-in. diameter tire. In actuality, the landing gear ver- tical strut member would sever the turf layer, preventing a complete tunnel. Additionally, bed designs of this relative 10.4.4.4. Effect of Turf Cover Layer depth would typically not be feasible because they would The presence of the turf cover layer produced a mild overload the landing gear. decrease in the rate sensitivity as compared with a bed of plain aggregate without a cover layer. Table 10-4 compares the rela- 10.4.4.6. Data Transformation tive sensitivities of the two systems to the aircraft speed (H44.5x16.5-22 tire). It may be possible to further enhance this The final metamodel data for each tire was converted for mitigating effect with design improvements to the cover layer. use by the APC. LS-OPT was used to extract nominally 9,000 Another advantage of the turf layer is a predicted reduction data points from each metamodel and export them into tab- in the aggregate ejecta thrown from the tire rut. Figure 10-22 ular form. A MATLAB matrix conversion program was writ- shows a comparison for an 18-in. deep bed with a 44.5-in. tire ten to map this data into multi-dimensional matrix form that at a deep penetration level (99%). In the left-hand illustra- could be quickly accessed by the APC. tion, the aggregate particle flyout is shown with the turf layer For the two tires not explicitly modeled, the appropriate omitted. The right-hand image is the analogous case for a bed response surface data was scaled to produce an approximate with no turf cover layer. The maximum aggregate particle metamodel (Section 10.4.3.2). Figure 10-22. Ejecta plumes of engineered aggregate for beds with (left) and without (right) turf cover layers.