National Academies Press: OpenBook

Developing Improved Civil Aircraft Arresting Systems (2009)

Chapter: Appendix F - Tire Models

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Page 184
Suggested Citation:"Appendix F - Tire Models." National Academies of Sciences, Engineering, and Medicine. 2009. Developing Improved Civil Aircraft Arresting Systems. Washington, DC: The National Academies Press. doi: 10.17226/14340.
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Suggested Citation:"Appendix F - Tire Models." National Academies of Sciences, Engineering, and Medicine. 2009. Developing Improved Civil Aircraft Arresting Systems. Washington, DC: The National Academies Press. doi: 10.17226/14340.
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Suggested Citation:"Appendix F - Tire Models." National Academies of Sciences, Engineering, and Medicine. 2009. Developing Improved Civil Aircraft Arresting Systems. Washington, DC: The National Academies Press. doi: 10.17226/14340.
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Suggested Citation:"Appendix F - Tire Models." National Academies of Sciences, Engineering, and Medicine. 2009. Developing Improved Civil Aircraft Arresting Systems. Washington, DC: The National Academies Press. doi: 10.17226/14340.
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184 In order to predict landing gear loads effectively, computer models were required for both the arrestor materials and the tires of the three subject aircraft. This appendix discusses the tire model development, while Chapters 9 through 12 discuss the modeling of the candidate arrestor systems. F.1. Subject Tires Modeled Manufacturer references give the tire sizes, pressures, and load limits for the three aircraft of interest (60). Table F-1 lists the main- and nose-gear tires for each aircraft, and Table F-2 provides specifications for the tires. The tire designations give three numbers, referring to the diameter, width, and ply rat- ing, respectively. The leading “H” appearing in some tires indicates a bias-ply tire designed for high deformations. Goodyear supplied load-deflection curves for the tires listed, which were used for later tire calibration and validation. F.2. Tire Modeling Approach Tire modeling can be a highly detailed process, involving discrete representation of the treads, carcass material, reinforc- ing fiber layers, the tire–rim interface, inflation pressures, and so on. Modeling these facets is required for accurate prediction of stresses within the tire, oscillatory behavior, tread wear, and so on. However, for arrestor bed modeling, such detail did not necessarily offer added value. A number of these facets would constitute higher order (and lower importance) effects when applied to the simulation of crushable material interactions. A tire model was needed that could produce a realistic rut through an arrestor bed. A realistic rut would feature the cor- rect penetration depth and cross-sectional shape. Since the energy dissipation is largely based on the crushed volume of material, a rut of the correct dimensions would tend to pro- duce the correct energy dissipation and hence the correct drag load. Under a static vertical load with steady forward motion, this means that the tire would deform and settle to a steady-state depth in the material, producing a rut of the cor- rect depth and width for that loading condition. For a tire model to create such a rut, it would have to repli- cate two critical behaviors: 1. Correct deformation shape under loading, and 2. Correct interface loading (ground pressure) against the arrestor material. After a review of available tire modeling methods and mechanical phenomena, the tire model priorities were set per Table F-3. F.2.1. Tire Dimensions The tire models needed to accurately represent the gross dimensions of the actual aircraft tires. Ensuring such a match was actually more complicated than it appeared. During infla- tion, the tire model stretched, which altered its original gross dimensions. Therefore, the dimensional criterion applied to the match of the inflated model tire with the inflated actual tire. F.2.2. Ground Pressure The ground pressure that the tire produced strongly depended on its inflation pressure and governed the penetra- tion of the tire into the arrestor material. Provided that the gross dimensions were correct and the load-deflection performance matched, the model would produce a ground pressure that would be sufficiently accurate for the soft-ground interaction. F.2.3. Load-Deflection Performance Goodyear provided load versus deflection curves, both in quasi-static and dynamic loading regimes. The load-deflection performance is analogous to a spring deflection curve. Typi- cal efficiencies for a tire are slightly less than an ideal spring, A P P E N D I X F Tire Models

at nominally 45 to 47%, a quasi-linear behavior that applies to the bulk of the loading domain (14). This linear behavior ceases during very high “bottoming” loading of the tire, when the deflection is high enough to allow the wheel rim to “bot- tom out.” Bottoming loads are most likely during hard land- ing impacts, but do not occur in an aircraft in a steady roll with properly inflated tires. As such, replication of the tire performance during bottoming was deemed non-essential to this research. The domain of concern was limited to 80% of bottoming loads for each tire (Figure F-1). F.3. Model Construction F.3.1. Modeling Methods Finite element tire models for each aircraft were con- structed in LS-DYNA. The tire models were developed using a simple tire carcass with a smeared-property orthotropic material (61). The smeared properties represented the com- bination of all materials in the actual tire: tread, bulk rubber, reinforcement plies, and so on. This approach was attractive due to its simplicity, and it produced correct deformation within the loading range of interest. It was also practical since little detail was known about the inner construction of the actual tires: proprietary manufacturer data would be required to effectively model the various components individually. The tire model used two-dimensional shell elements for the carcass in order to obtain the best computational efficiency. For a full tire, the carcass contained 4,608 shell elements in 2.5-degree increments; usually a quarter- or half-symmetry version was used, with the element count reduced accordingly (Figure F-2). A constant pressure was applied to the inner surface of the tire to simulate pneumatic pressure. When loaded vertically, the tire models deflected realistically, forming an increasingly large flat contact area with the ground (Figure F-3). F.3.2. Model Calibration In using a smeared approach, the material properties of the tire carcass required calibration, such that the load-deflection behavior of the model matched that of the actual tire. Using LS-OPT, this calibration was accomplished in a systematic fashion. Two optimization criteria were defined: 1. Match the load-deflection curve for the actual tire as closely as possible, and 185 Aircraft Tire Tire Designation Main Tire H29x9.0-15 CRJ-200 Auxiliary Tire 18x4.4 Main Tire H44.5x16.5-21 B737-800 Auxiliary Tire 27x7.75R15 Main Tire H49x19.0-22 B747-400 Auxiliary Tire H49x19.0-22 Table F-1. Tires for subject aircraft. Tire Designation 18x4.4 27x7.75R15 H29x9.0-15 H44.5x16.5-21 H49x19-22 Units Rated Speed 210 225 210 225 235 mph Rated Load 4,350 9,650 14,500 44,700 56,600 lbf Rated Inflation Pressure 225 200 196 214 205 psi Maximum Bottoming Load 13,000 28,950 39,200 121,000 152,800 lbf Table F-2. Data for subject aircraft main-gear tires (60). Aspects to Replicate Aspects to Neglect • Tire dimensions • Ground pressure • Load versus vertical deflection performance • Correct mode of deformation • Computational efficiency • Internal tire stresses • Heat generation • Tread features • Ground traction and slip • Lateral loading deformations • High frequency effects, noise, vibration Table F-3. Aspects of tire dynamics for inclusion and exclusion.

Many simulations were conducted in batches over multiple iterations. Using a sequential response surface methodology (SRSM), the design parameters were gradually narrowed until LS-OPT had determined an optimum set of material proper- ties (62). These best-case properties produced the closest over- all match between the model and the actual tire performance. Table F-4 summarizes the tire calibration results. As shown in the lower half of the table, nearly all the criteria were met to within 2% of the objective values. The RMSE values indicate how closely the load-deflection curves match the real tires (Fig- ure F-4). The inflated dimension error represents how closely the final tire diameter matched the actual tire. Practically speak- ing, these values indicate that the tires have the correct shape and respond with the correct loading as the tire is compressed. F.4. Summary of Tire Model Development The selected tire modeling approach struck a balance between accuracy and efficiency. The orthotropic smeared- property method neglected details required for nuanced tire design models, but it still replicated the overall tire deformation and loading pertinent to arrestor simulation. When compared with the prior state-of-the-art in arrestor modeling—the radial spring tire model—the FEM approach adopted herein offers an increase in fidelity. This three- dimensional model does not depend on ellipsoid contact sur- face assumptions and includes lateral tire bulging. The five tires developed in this task replicate the main- and nose-gear tires of the three subject aircraft. Each mimics the actual tire performance well, typically with less than 2% error for inflated dimensions and load-deflection behavior. The iterative optimization process using LS-OPT made this accu- rate calibration possible. 186 Vertical Load Vertical Deflection Energy Absorbed in Compression ~47% Efficiency Linear Spring Performance Bottoming Domain of Matching for Model: 0% to 80% of Bottoming Load Bottoming Load Figure F-1. Tire load curve and modeling domain of interest. Figure F-2. 44.5-in. tire model. 2. Match the inflated dimensions for the actual tire as closely as possible. The load-deflection objective was defined by the mean- squared-error (MSE) between the load curves of the simulated and actual tires. The inflated dimensions were compared by measuring the tire just after the inflation process completed.

187 Figure F-3. Quarter symmetry 44.5-in. tire model undergoing vertical deflection. Tire 18x4.4 27x7.75R15 H29x9- 15 H44.5x16.5- 21 H49x19- 22 RSM Type Quadratic Quadratic Quadratic Linear Linear Open Variables 3 3 2 3 3 Simulations Per Iteration 16 16 10 7 7 Number of Iterations (Pre Final) 10 20 4 5 7 Simulation Parameters Total Simulations 161 321 41 36 50 RMSE for Load-Deflection Curve Match 1.6% 7.4% 2.0% 2.0% 1.7% Quality of Optimized Design Error for Targeted Inflation Dimensions 2.65% 1.1% 2.2% 1.9% 0.08% Table F-4. Summary of tire calibration. Normalized Vertical Deflection A A A A B B B B B A Target (TireLCF) History comparison for MSE (Experiment 8.1) B Computed (Force_Dist) N or m al iz ed L oa d Figure F-4. Sample load-deflection curve comparison to 80% of bottoming load (units omitted).

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TRB’s Airport Cooperative Research Program (ACRP) Report 29: Developing Improved Civil Aircraft Arresting Systems explores alternative materials that could be used for an engineered material arresting system (EMAS), as well as potential active arrestor designs for civil aircraft applications. The report examines cellular glass foam, aggregate foam, engineered aggregate, and a main-gear engagement active arrestor system.

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