A CAE-BASED STUDY OF REDUCTION OF CRASH AGGRESIVITY OF PICKUP TRUCKS A Thesis by Vikram Krishnamurthy B.E., Bangalore University, 2001 Submitted to the Department of Mechanical Engineering and the faculty of the Graduate School of Wichita State University in partial fulfillment of the requirements for the degree of Master of Science December 2005 A CAE-BASED STUDY OF REDUCTION OF CRASH AGGRESIVITY OF PICKUP TRUCKS I have examined the final copy of this thesis for form and content and recommend that it be accepted in partial fulfillment of the requirements for the degree of Master of Science with a major in Mechanical Engineering. __________________________________ Hamid M. Lanakarani, Committee Chair We have read this thesis and recommend its acceptance: ___________________________________ Kurt Soschinske, Committee Member ___________________________________ Gamal Weheba, Committee Member ii DEDICATION To my Parents iii You say the hill's to steep to climb, climbing you say you'd like to see me try, climbing you pick the place and I'll choose the time and I'll climb the hill in my own way just wait a while for the right day and as I rise above the tree-line and the clouds I look down, hearing the sounds of the things you've said today …… “Fearless” -- Meddle Pink Floyd When someone is seeking ...it happens quite easily that he only sees the thing that he is seeking; that he is unable to find anything, unable to absorb anything ...because he is obsessed with his goal. Seeking means: to have a goal; but finding means: to be free, to be receptive, to have no goal." Chapter 12, Page 113 Siddhartha Hermann Hesse There is a road, no simple highway, between the dawn and the dark of night, and if you go, no one may follow, that path is for your steps alone. Jerry Garcia iv ACKNOWLEDGEMENTS I would like to thank Dr. Hamid Lankarani for advising and guiding me through my graduate education at Wichita State University. Thank you Dr.Lankarani. I would also like to thank my committee members, Dr. Kurt Soschinske and Dr. Gamal Weheba, for giving their time in support of this thesis. I would also like to take this opportunity to extend my deepest gratitude to Natesan and his loving family for all their support and encouragement. Finally, I need to thank all my friends who have supported, encouraged, and inspired me throughout my life. v ABSTRACT During the past few years, the disparity in the structural design of light trucks and vans (LTVs) and passenger cars and the number of fatalities involved in these vehicles has become a growing concern among automobile manufacturers. In order to characterize the problem of compatibility, the National Highway Transport Safety Authority (NHTSA) has defined an aggresivity metric (AM) as the ratio of driver fatalities in the collision partner to the number of crashes of the subject vehicle. The aggresivity metric did prove that the sport utility vehicle (SUV) and LTV class of vehicles were substantially more aggressive than the rest of the class of vehicles but failed to highlight the main factor(s) responsible for it. Current research has established that the aggresivity of vehicles involved in frontal crashes is mainly affected by geometric interaction, vehicle stiffness, and vehicle mass. The present study describes a methodology to reduce the aggresivity of pickup trucks using a Computer—Aided Engineering (CAE) combined with a Design of Experiments (DOE) approach. Computer—aided crash simulations using finite element models of an average pickup truck and a small car using LS-DYNA (an explicit finite element program) and MAthematical DYnamic MOdelling (MADYMO, a multi-body occupant simulation program) are used to study the vehicle structural deformation and the occupant’s injury responses. Categorical responses of small car: intrusion, combined injury index and internal energy ratio are observed by varying the mass, stiffness, and overlap between the energy absorbing structures of the vehicles. The variation was modeled to approximately represent an entire fleet of pickup trucks. Statistical analyses showed that mass is one of vi the major factors influencing the overall aggresivity of pickup trucks. Regression equations showed good correlation to the actual tests and can be used to predict responses for factor variation within the design space. The overlay plots reveal that reduction in mass leads to increase in optimum region. vii TABLE OF CONTENTS Chapter 1. INTRODUCTION ...................................................................................................1 1.1 1.2 1.3 2. 2.5 2.6 2.7 History of Vehicle Safety.............................................................................6 Automotive Structure...................................................................................7 Occupant Safety ...........................................................................................8 Crash Induced Injuries .................................................................................9 2.4.1 Injury Criteria...................................................................................9 2.4.2 Tolerance to Injuries ......................................................................14 Crashworthiness.........................................................................................16 Vehicle Safety Tests ..................................................................................17 2.6.1 FMVSS 208 ..................................................................................18 2.6.2 NCAP............................................................................................19 2.6.3 IIHS Offset Test............................................................................20 2.6.4 Effect of Safety Tests....................................................................20 Compatibility .............................................................................................21 2.7.1 Aggresivity and Aggresivity Metric ..............................................23 SYSTEM SETUP...................................................................................................27 3.1 3.2 3.3 3.4 4. Motivation....................................................................................................1 Literature Review.........................................................................................2 Objective ......................................................................................................5 BACKGROUND .....................................................................................................6 2.1 2.2 2.3 2.4 3. Page Formulation................................................................................................28 3.1.1 Validation......................................................................................31 Selection of Design Variables....................................................................34 3.2.1 Mass ...............................................................................................34 3.2.2 Stiffness..........................................................................................35 3.2.3 Overlap...........................................................................................38 3.2.4 Constant Variables .........................................................................40 3.2.5 Response Variables........................................................................40 Design of Experiment ................................................................................41 3.3.1 Factorial Design .............................................................................42 3.3.2 Optimization Methodology............................................................43 Simulations ................................................................................................44 RESULTS ..............................................................................................................45 4.1 Finite Element Simulations........................................................................45 viii 4.2 4.3 4.4 5. Response Surface ......................................................................................51 4.2.1 Pair-Wise Comparison ...................................................................51 Regression Analysis...................................................................................57 Optimization ..............................................................................................57 DISCUSSION .......................................................................................................61 5.1 5.2 Conclusions................................................................................................61 Future Research .........................................................................................61 LIST OF REFERENCES...................................................................................................67 ix LIST OF TABLES Table Page 1. Summary of Recommended Injury Criteria for the Final Rule ................................15 2. Chevy C1500 and Geo Metro Model Definition ......................................................29 3. Range of Mass Selected for the Study ......................................................................35 4. Range of Stiffness Selected for the Study.................................................................37 5. Selected Response Variables ....................................................................................40 6. Stat Ease Design Matrix............................................................................................43 7. Effects List for Dashboard Intrusion.........................................................................52 8. ANOVA Results for Dashboard Intrusion................................................................52 9. Effects List for Internal Energy Ratio.......................................................................54 10. ANOVA Results for Internal Energy Ratio ..............................................................55 11. Effects List for Combined Injury Index (Pcomb) ........................................................56 12. ANOVA Results for Combined Injury Index (Pcomb) ...............................................57 13. Comparison of Regression and Actual Results.........................................................58 x LIST OF FIGURES Figure Page 1. Car occupant fatalities during 2000-03.......................................................................1 2. Different vehicle structural designs ............................................................................8 3. Neck injury criteria1 .................................................................................................11 4. Deaths per 1,000 crash injuries by age and sex ........................................................15 5. Injuries per 1,000 AIS 2—6 injuries (moderate to maximum).................................15 6. Different crash configurations ..................................................................................17 7. Vehicle to barrier tests (reproduced from www.safecarguide.com) .........................18 8. Front-end profiles of an LTV, a passenger car a small car.......................................22 9. Mass and stiffness values from NCAP tests .............................................................23 10. U.S. sales and registrations of LTV and cars............................................................24 11. Overall aggresivity metric ........................................................................................25 12. Aggresivity metric frontal-frontal.............................................................................26 13. Driver fatalities for frontal-frontal in LTV-car crashes ............................................26 14. Adopted methodology ..............................................................................................27 15. Finite element models of Chevy C1500 (left) and Geo Metro (right) ......................28 16. MADYMO interior model of Geo Metro .................................................................30 17. Inflation of airbag .....................................................................................................30 18. Head and chest acceleration validation for the MADYMO model ..........................31 19. NCAP rigid barrier test setup for C1500 ..................................................................32 20. Placement of accelerometers in C1500.....................................................................32 xi 21. Acceleration and velocity profiles for C1500 (simulation-blue, actual-red) ............32 22. Post test view for C1500 (simulation-left, actual-right) ...........................................32 23. NCAP rigid barrier test setup for Metro ...................................................................33 24. Placement of accelerometers in Metro......................................................................33 25. Acceleration and velocity profiles for Metro (simulation-blue, actual-red).............33 26. Post test view for Metro (simulation-left, actual-right) ............................................33 27. Mass-stiffness plot for determining the zone of consideration.................................34 28. Force-deflection of 35 mph NCAP test ....................................................................36 29. Stiffness calculation at 240 mm of crush..................................................................37 30. Energy distribution and percentage for Chevy C1500 in NCAP test .......................38 31. Parts selected for the stiffness variation ...................................................................38 32. Baseline model and the two levels of overlap ..........................................................39 33. Parts used to calculate nodal displacements .............................................................41 34. Model configuration at 0 milliseconds .....................................................................45 35. Crash simulation representing M, S, and O variable levels......................................46 36. Intrusion levels..........................................................................................................47 37. Normalized intrusion levels ......................................................................................48 38. Percentage energy absorbed......................................................................................49 39. Normalized IE ratio ..................................................................................................49 40. Pcomb index ................................................................................................................50 41. 3D plot of the dashboard intrusion at stiffness low (left) and high (right) ...............53 42. 3D plot of the dashboard intrusion at stiffness mass (low) ......................................53 43. Cube plot of the dashboard intrusion........................................................................53 xii 44. Pair-wise comparison of internal energy ratio..........................................................55 45. Factor effects on Pcomb, Pair-wise (left), mass effect (right) .....................................57 46. Optimal region based on constraints at mass (low) ..................................................59 47. Optimal region based on constraints at mass (medium-top, high-bottom)...............60 xiii LIST OF ABBREVIATIONS AIS Abbreviated Injury Scale AM Aggresivity Metric ATD Anthromorphic Test Dummy CAE Computer—Aided Engineering CTI Combined Thoracic Injury DOE Design of Experiments FARS Fatal Accident Reporting System FE Finite Element FMVSS Federal Motor Vehicle Safety Standards GES General Estimates System GSI Gadd Severity Index HIC Head Injury Criteria IARV Injury Assessment Reference Values IE Internal Energy IIHS Insurance Institute of Highway Safety LS-DYNA Explicit Finite Element Software developed by LSTC LTV Light Truck and Van MADYMO MAthematical DYnamic MOdelling MPH Miles Per Hour NASS National Accident Sampling System NCAC National Crash Analysis Center NCAP New Car Assessment Program xiv NHTSA National Highway Transport Safety Authority NPRM Notice of Proposed Rule Making and Order SUV Sport Utility Vehicle xv CHAPTER 1 INTRODUCTION 1.1 MOTIVATION In 2003, Sport Utility Vehicles (SUVs) accounted for 20 percent of registered passenger vehicles, up from 13 percent. Meanwhile, during the same time, the percentage of cars dropped to 58 percent from 68 percent, in a decade. This highlights a serious issue in the present crash environment because the increasing fatalities in collisions between car and a light pickup truck (LTV) are not only due to the aggressive behavior of LTVs but also due to the increasing number of stiffer and incompatible structures involved in collisions. Figure 1 shows car occupant fatalities during 2000-03 [1]. The fatalities in car-LTVs accounted for nearly 18 percent of fatalities and are the highest in the vehiclevehicle category. The aggresivity metric (AM) as defined by National Highway Transport Safety Administration (NHTSA), ranges from 69.27 for large pickups, 30.62 for large SUVs, 14.09 for large cars, and 5.45 for minicars [2]. This vast variation must be carefully studied to evaluate the possible factors affecting aggresivity. In the case of vehicle—to—vehicle collisions among different classes of vehicles, a fine balance needs to be maintained when attempting to effectively alter the aggresivity of vehicles. 42 Single Car Car-Car Car-Big Truck 15 16 7 Car-PU Car-SUV 11 9 Car- 2+ Figure 1. Car occupant fatalities during 2000-03. 1 Reduction of aggresivity may or may not correspond to increased crashworthiness. The predictive power of computer—aided engineering can be utilized to form a tool to predict the aggresivity of not only newly introduced vehicles but also vehicles that are still in the conceptual stage. 1.2 LITERATURE REVIEW Since the problem of compatibility was first addressed, several institutions, individual researchers, and automobile manufacturers have explored different facets in this field. This section, presents some of the research which mainly deals with analytical and experimental methods used to study the issues of compatibility and aggresivity. Summers etal. [2] are some of the pioneers who identified the growing concern of SUV sales in the United States, the increasing fatality rates in car-LTV crashes. They also introduced the aggresivity metric (AM) and calculated the relative metric for different classes of vehicles and also sub-divided those into different crash configurations. They also describe experimental tests conducted using pickups, passenger cars, minivans, and SUVs. Their results were then correlated into the aggresivity metric. Brown etal [3] focused on the effectiveness of combining Design of Experiments (DOE) techniques with conventional Finite Element (FE) analysis and using these methods to understand the behavior of incompatible structures. They describe principles that must be followed while designing an experiment. The public domain model of a Ford Taurus was used in a Taurus-Taurus crash configuration with a 40% offset configuration. Design variables were selected: mass, front—end stiffness, and available crush length for each vehicle; and the longitudinal relative height and the vehicle closing speed. Ten response variables: B post acceleration, footwell intrusion, A pillar intrusion, longitudinal 2 average load and the longitudinal crush for each vehicle were studied. One of the most significant factors—the time taken to build a model based on the selected combination of design variables was also considered while deciding upon the DOE matrix. The DOE model allowed the interrelationships between mass, stiffness, and height to be studied in detail. It was concluded that closing speed was one of the most influential factors. Occupant injuries were not considered for this study. Lee etal [4] used robust parametric studies and structural optimization methodologies to study the complex design parameters and geometric changes. Study Wizard, a software tool specifically designed for conducting parametric analytical studies was used for this study. The main objective of the paper was to identify how vehicle safety may be improved by structural changes that are designed to interact better during the crash and by restraint systems that are designed to act properly in the secondary collision for each. They used oblique offset vehicle to vehicle crash tests to study the relationship between aggresivity and injuries. Their paper provides an excellent resource on response surface optimization for crash problems. This DOE study is followed by an optimization study, the former of which acts as a screening study for the factors considered using four parameters: engine position, front member inner thickness, sub frame thickness, and dash lower panel thickness. The results of the DOE show that the engine position and sub frame have more effect on both deceleration and displacement responses. The final results of the optimization study were not reported in this paper. Barbat etal. [5] described a CAE—based optimization methodology for a fullfrontal vehicle-to-vehicle configuration using the finite element models of an average SUV and an average full-size passenger vehicle. Four variables of the SUV selected for 3 this study included the following: mass, fore rail thickness, fore rail length, and fore rail height were selected for this study. Latin Hypercube sampling technique was used to form the simulation matrix. Dash intrusions in the passenger vehicle and the absorbed collision energy in both the vehicles were response variables. Prediction equations were developed based on the response surfaces for the selected response variables. Results indicated that aligning front-end structures has a greater effect on the responses than mass and stiffness variables. Additionally, the effect of thickness was observed to be greater than that of mass on maximum dash intrusion. The optimal SUV configuration showed that the minimum dash intrusion was obtained with the aligned fore rail, reduced mass, and fore rail thickness, which can be translated to the lightest, least— stiff and best—aligned SUV. Some important factors like the effect of reduced stiffness on the SUV’s crashworthiness and occupant responses were not considered in this study. Kuchar [6] explains a methodology consisting of a parametric three-dimensional kinematic simulation of crash events. The response was simulated using computational models that are one—dimensional lumped-parameter systems, with three discrete masses representing the occupant compartment, engine, and wheels. The models were simulated and developed using the Structural Impact Simulation And Model Extraction (SISAME) program. Head and chest injury results for each case were converted to harm vectors in terms of probabilistic Abbreviated Injury Scale (AIS) distributions based on previously defined risk analyses. This methodology was applied to single—and two—vehicle frontal collisions among passenger cars and light trucks. The model was validated against injury field data and found to accurately reflect the trends in distribution of injury severity. The model 4 was used for variable sensitivity analyses, wherein changes in LTV/car population mix and other parameters were evaluated in terms of their effect on occupant harm within the subset crash environment. 1.3 OBJECTIVE The solution for developing a compatible fleet is a very tedious process and more so because the existing safety standards reflect only the crashworthiness of vehicles and not their compatibility with the rest of the fleet. This study aims to find an optimum solution for the aggresivity of a pickup truck using CAE based optimization techniques. 5 CHAPTER 2 BACKGROUND In 1889, New York City recorded the first motor vehicle fatality. This event is believed to have led to the birth of the field of automotive safety. The past decade has seen an increase in awareness about vehicle safety from not only consumers but also manufacturers who started to regard safety as a core design objective. This chapter will briefly discuss the history of automotive safety and introduce few definitions that were used throughout this study. 2.1 HISTORY OF VEHICLE SAFETY Automotive historians have identified three distinct periods in the development of automotive safety [7]. The first period from the start of the century to early 1935 saw the development of understanding of the complex process of vehicle collisions. Some of the basic improvements such as a reduction of tire blowouts, introduction of the self starter, headlamps for better visibility, laminated glass, and adopting an all-steel body structure were carried out during this period. The first full-scale crash test was carried out with car—to—barrier and rollover simulations. The estimated fatality rate in 1935 was approximately 17 per million. The second period from 1935 to 1965 was the intermediate safety period. Collision avoidance systems like turn signals, improved headlamps, and dual windshield wipers were introduced by manufacturers. Tests simulating the head impacting the instrument panel were carried out, and GM conducted the first car-to-barrier frontal crash test. Vehicles were evaluated according to the observed deformation in the vehicle. One 6 of the most significant safety devices introduced during this era were seat belts as an option in 1956. The third period started in 1966, with the creation of the NHTSA. Federal Motor Vehicle Safety Standards (FMVSS) were introduced and dealt with several aspects of the vehicle development process. Over the past seven decades, vehicle safety improvements have focused on crash avoidance technology, structural crashworthiness, and occupant protection devices, which did show a significant decrease in fatality rates. Today, the automotive industry is focused on not only the above factors but also driver performance, driver behavior, ergonomics, highway or road construction, and accident avoidance systems. Current legislation also has a strong influence on safety. The third period saw safety become a competitive item for medical, technical scientists, legislators, and more importantly to automotive engineers. There was an added effect by consumer advocates such as Ralph Nader, who championed the need for automobile manufacturers being held responsible for not only faulty designs but also for fatalities that vehicles caused to their occupants. The increasing number of consumer information reports, such as crashworthiness rating reports issued by institutes like Insurance Institute for Highway Safety (IIHS), Highway Loss Data Institute, has made more information available to the public about the performance of vehicles. This has led to consumers ranking safety features as extremely or very important when buying new cars. 2.2 AUTOMOTIVE STRUCTURE The first patent in the field of vehicle body design relating to safety was published in 1952 by Bela Bareny. In this patent, he described how structural strength should be 7 greatest in the vehicle compartment and that the front and rear of the vehicle should less resistant to crushing and capable of absorbing energy during a crash [8]. The evolution of automotive structure design has been subject to the need to satisfy consumers and many constraints like materials and energy availability, safety regulations, competition and manufacturing capabilities. Figure 2 (a), (b), and (c) shows the body-over frame, unitbody design and the ladder frame, respectively. The type of materials used in the construction has been traditionally steel but current trends have shifted to aluminum and composites for body panels both of which provide excellent weight reduction. (c) (a) (b) Figure 2. Different vehicle structural designs. 2.3 OCCUPANT SAFETY The field of vehicle safety, which focuses on the protection, provided to passengers a vehicle in a collision, either from the interiors, the restraint system or the vehicle structure itself, is termed occupant safety. Typical safety systems include 8 collapsible steering systems, safety windshields, belt restraints, and airbags. It is now common knowledge that belt restraints and airbags have become the two most important safety devices that reduce the fatality rates considerably. 2.4 CRASH INDUCED INJURIES This section briefly discusses some common terminology relating to the structure of the human body and injuries [9]. Anatomy is defined as the study of the body’s structure, and describing the shape and location of various parts of the body. Usually the body is referenced according to subdivisions like the head, neck, upper extremities, lower extremities, and torso. The torso can be further subdivided into upper region, thorax and lower region, or abdomen. Vehicle-related injuries may occur to various body regions. Head injuries may be due to injuries to the skin, bones, or the contents of the skull, or combination. Injuries to the chest might occur due to a blunt impact (e.g., with the steering wheel), which will result in compression of the ribcage or even fracture in a severe case. In the lower extremities, the pelvis might fracture or displace. When a person is seated, bones in the lower extremities like the femur, tibia, and fibula, may be fractured upon impact with the vehicle interiors, such as knee bolster. 2.4.1 INJURY CRITERIA Injury criteria have been developed to address the mechanical responses of crash test dummies in terms of risk to life or injury to a living human. The different injury criteria developed for the NHTSA’s FMVSS 208 frontal crash protection program are presented in this section [10]. 9 2.4.1.1 HEAD Injuries to the head are responsible for 50,000 deaths and nearly one million hospitalizations per year in the United States. Motor vehicle crashes are responsible for nearly half of these head injuries. Head injury continues to be a leading cause of death and disability [10]. A relationship known as the Wayne State Tolerance Curve (WSTC) between the acceleration level and impulse duration with respect to head injury indicated a decreasing tolerable level of acceleration as duration increased. WSTC has become the foundation upon which most currently accepted indexes of head-injury tolerance are based. The original data only covered a time duration range of 1 to 6 milliseconds but was later extended to durations above 6 milliseconds. The WSTC data was plotted by Gadd on log paper and an approximate straight— line function was developed for the weighted impulse criterion that eventually became known as the Gadd Severity Index (GSI). In response to a study of the analysis of the relationship between the WSTC and the GSI by Versace in 1971, a new parameter, the Head Injury Criterion (HIC), was defined by NHTSA in 1972. The HIC is currently used to assess head injury potential in automobile crash test dummies. It is based on the resultant translational acceleration rather than the frontal axis acceleration of the original WSTC. HIC is computed as (2.1) 10 where t2 and t1 are any two arbitrary times during the acceleration pulse. HIC is unique among FMVSS 208 injury criteria in that the HIC limit of 1,000 was not based on tests where HIC was measured and injuries observed. The HIC has no specific meaning in terms of injury mechanism. The NHTSA proposed time interval was reduced to 15 milliseconds from 36 milliseconds but it limited the maximum time interval to 36 milliseconds with acceleration rising to a limit of 60 g. The analyses of data from the New Car Assessment Program (NCAP) and FMVSS No.208 showed that almost all the vehicles had a value of HIC15 ≤ 700, and the average HIC values for the driver was 222. 2.4.1.2 NECK The concept that a composite neck injury indicator based on a linear combination of axial tension loads and extension (rearward) bending moments was developed in 1984 by Prasad and Daniel [10] using their results from experimental tests on porcine subjects. Based on their formulation for a three—year old dummy, the allowable region in the tension/extension quadrant of the plot becomes the shaded area shown in Figure 3. Figure 3. Neck injury criteria. 11 Any test falling above the diagonal line in this plot would exceed the tolerance levels suggested by Prasad and Daniel and was expanded to include the four major classifications of combined neck—loading modes, namely, tension-extension, tensionflexion, compression-extension, and compression-flexion. Proposed critical intercept values for tension load, compression load, extension moment, and flexion moment were established. The resulting criteria are referred to as Nij, where “ij” represents indices for the four injury mechanisms: namely NTE, NTF, NCE, and NCF. The first index represents the axial load (tension or compression) and the second index represents the sagittal plane bending moment (flexion or extension). The intercept values shown are those proposed for the Hybrid III mid-sized male dummy. The proposed neck injury criteria can thus be written as the sum of the normalized loads and moments as (2.2) where FZ is the axial load, Fint is the corresponding critical intercept value of load used for normalization, MY is the flexion/extension bending moment computed at the occipital condyles, and Mint is the corresponding critical intercept value for moment used for normalization. 2.4.1.3 CHEST Classic work by Stapp, Mertz and Gadd led to the development of the injury threshold for chest acceleration of 60 g. The first injury assessment recommendation for the rib cage and underlying organs using chest deflection was developed by Neathery et al. [10] for blunt frontal loading. They recommended a chest injury assessment value of three inches maximum sternal compression for a 50th percentile male in blunt frontal 12 impact. This recommendation represented a 50 percent risk of an AIS 4+ thoracic injury for a 45— year—old human. An injury criteria using chest deflection alone may not have predicted the correct injury level under such circumstances as well as the linear combination of deflection and acceleration. It is believed that the linear combination model using Dmax and As is the most appropriate injury criteria for assessing thoracic trauma. However, since only one deflection measurement is available on most dummies, the central chest deflection will be used with this formulation. The equation of the 50 percent probability of injury line using the deflections adjusted for skin thickness is mathematically equivalent to a line that has intercepts on the vertical and horizontal axes of Dint = 103 mm and Aint = 90 g, respectively. Thus, the combined thoracic injury criteria, CTI, is defined as (2.3) where Amax is the maximum value of 3 ms clip spinal acceleration (As), Dmax is the maximum value of the dummy deflection (D), and Aint and Dint are the respective intercepts as defined above. In order to harmonize with the Injury Assessment Reference Values (IARV) used by Transport Canada, the chest deflection limit for the 50 percent male was taken to be 63 mm (2.5 inches), and a 3-msec clip value of resultant chest acceleration limit was taken to be 60 g. Therefore, the recommended performance limits are Ac = 60 g and Dc = 63 mm for the 50 percent male. The proposed CTI injury criteria from the Notice of Proposed Rule Making and Order (NPRM) will be used for estimating the probability of injury. 13 2.4.1.4 FOOT AND LOWER EXTREMITIES A vast amount of research is currently being conducted to better understand the complex mechanisms of foot and ankle injuries. The existing IARV for femur load used in FMVSS 208 is 10 KN for the 50th percentile male. The tibia index was originally proposed by Mertz [10] as an injury tolerance criterion for the leg which combines the bending moment and axial compressive loads on the leg, as measured by the Hybrid III tibia load cell. The modified version of the tibia index (TI) adopted by EEVC is given by (2.4) where F is the measured compressive axial force (kN) in the superior-inferior direction and M is the resultant moment of the medial-lateral and anterior-posterior moments. 2.4.2 TOLERANCE TO INJURIES It has been observed that the age of the driver has a very strong influence on tolerance to injuries. Younger drivers tend to get into more severe collisions; older drivers are more likely to die from their injuries [12]. Evans [13] found that the risk of fatal injuries increased three times at age 70 than at 20. Drivers from about age 30 to 60 have the lowest involvement rates. As age decreases below 30, rates increase at an increasing rate but for ages greater than 60, the rates increase much less rapidly. The risk of crashes is higher among the 16 to19—year—olds than any other age group. In fact, per mile driven, a 16-year-old driver is seven times more likely to crash than a driver 25 to 29 years old. Drivers 65 and older have higher crash death rates per mile than all others, except teen drivers [14]. See Figures 4 and 5 [15]. To control for this age effect during 14 the initial analysis, only drivers of ages 26 to 55 were selected for calculating the aggresivity metric. Figure 4. Deaths per 1,000 crash injuries by age and sex. Figure 5. Injuries per 1000 AIS 2-6 injuries (Moderate to Maximum). TABLE 1 Summary of Recommended Injury Criteria for the Final Rule [16] Large Sized Male MidSized Male Small Sized Male Head Injury Criteria: HIC (15msec) 700 700 Neck Criteria: Nij In position Critical Intercept Values Tension (N) Compression (N) Flexion (N) Extension (N) Peak Tension (N) Peak Compression (N) 1.0 1.0 8216 7440 415 179 5030 4830 N/A 6806 6160 310 135 4170 4000 N/A 4287 3880 155 67 2620 2520 Recommended Criteria Neck Criteria: Nij Out-of- Position Tension (N) Compression (N) Flexion (N) Extension (N) Peak Tension (N) Peak Compression (N) Thoracic Criteria 1. Chest Acceleration (g) 2. Chest Deflection (mm) Lower Ext. Criteria Femur Load (KN) 6 YO Child 3 YO Child 1 YO Infant 700 700 700 700 1.0 N/A N/A N/A 1.0 1.0 1.0 1.0 3880 3880 155 61 2070 2800 2800 93 37 1490 2120 2120 68 27 1130 1460 1460 43 17 780 2520 1820 1380 960 55 70 (2.8 in) 60 63 (2.5 in) 60 52 (2.0 in) 60 40 (1.6 in) 55 34 (1.4 in) 50 30 (1.2 in) 12.7 10.0 6.8 NA NA NA 15 2.5 CRASHWORTHINESS Crashworthiness is a qualitative measure used to define the ability of the structure to protect its occupants in collisions. The present automotive structure designs seek to mitigate two adverse effects of a crash: 1) rapid deceleration of the passenger compartment, and (2) crush of the passenger compartment survival space, which must be minimized. The front-end of vehicles are designed to crumple in a controlled manner in a collision. These progressive crush zones absorb the kinetic energy. But in a severe collision, the intrusions may extend into the passenger compartment causing injuries. The goal of all vehicle designers is an optimized structure that can absorb the crash energy by controlled vehicle deformations while maintaining adequate space so that any residual crash energy can be managed by the restraint systems. In the real world vehicles can collide with vehicles of a similar or different size or mass or they might collide with a stationary structure like a tree or pole, or they may experience a single or multiple collisions. Almost all collisions can be classified into four different types, based on the manner in which the collision happens: frontal, side, and rear as shown in Figure 6. The constraints that designers and engineers face when designing a new vehicle are that the structure be crashworthy, be light to improve efficiency and increase mileage, and be economically mass producible. Another real concern that engineers have is the safety of the occupant, so that decelerations transmitted to occupants are well within human tolerance limits. A crash deceleration pulse with an early peak in time and a gradual decay reduces the potential of injury to restrained occupants. 16 Manufacturers employ a variety of methods to assess the vehicle’s performance before the vehicle is manufactured. The earliest safety evaluation was started by General Motors in 1934, where they launched a vehicle into a rigid barrier. Frontal (Head-On) Collision Oblique/Angled Collision Side Collision Rear-end Collision Figure 6. Different crash configurations. 2.6 VEHICLE SAFETY TESTS The two organizations: NHTSA and Insurance Institute for Highway Safety (IIHS) use crash testing to determine the crashworthiness of vehicles. Beginning in the 1960’s, both the organizations began examining at automobile safety when the public became more aware of the issue as a result of the book, Unsafe at Any Speed, in which author Ralph Nader revealed the safety issues associated with the Chevrolet Corvair. In 1967, the first safety regulation, the Federal Motor Vehicle Safety Standards (FMVSS), No.209 was introduced. The federal standards, now, range from how bright the turn signal bulbs must be to the crash-testing requirements. NHTSA only started conducting 17 crash tests in 1978, and the IIHS, which is supported by automobile insurance companies, didn't begin its crash testing for consumers until 1995. Currently, NHTSA and the IIHS perform both frontal and side crash testing, the tests however differ from each other. Following is a brief description of the different frontal crash tests conducted in the U.S. 2.6.1 FMVSS 208 The FMVSS No. 208 defines the requirements for occupant protection in a frontal crash with the use of restraints and airbags. Testing is conducted with a full-scale vehicle impacting a rigid barrier from 0 to 30 mph and impact angles from 0 to 30 degrees, as shown in Figure 7 [17]. Figure 7. Vehicle to barrier tests. Occupant responses are calculated using an anthropomorphic test dummy (ATD). This standard originally specified the type of occupant restraints (i.e., seat belts) required. It was amended to specify performance requirements for ATDs seated in the front outboard seats of passenger cars and of certain multi—purpose passenger vehicles, trucks, and buses, including active and passive restraint systems. The purpose of the standard is to reduce the number of fatalities and the number and severity of injuries to occupants involved in frontal crashes. 18 2.6.2 NCAP NCAP was initiated in 1978 with the primary purpose of providing consumers with a measure of the relative safety potential of vehicles in frontal crashes. Side—crash rating results were added to the program beginning with model year 1997 vehicles, and more recently rollover ratings were added beginning with model year 2001 vehicles. The ultimate goal of NCAP is to improve occupant safety by providing market incentives for vehicle manufacturers to voluntarily design their vehicles to better protect occupants in a crash and be less susceptible to rollover, rather than by regulatory directives [17]. Testing is similar to FMVSS 208, except for the increased impact speed of 35 mph and the use of restraints in addition to airbags. The rigid barrier test is equivalent to a head-on collision between two similar vehicles, each moving at 35 mph. NHTSA rates the cars based on how likely the occupants are to be injured during a crash and gives the vehicle a star rating based on the percent chance of serious injury to the head and chest. A serious injury is one requiring immediate hospitalization and may be life threatening. NHTSA's star ratings are as follows: = 10% or less chance of serious injury = 11% to 20% chance of serious injury = 21% to 35% chance of serious injury = 36% to 45% chance of serious injury = 46% or greater chance of serious injury 19 2.6.3 IIHS OFFSET TEST The frontal test that the IIHS conducts is offset, meaning that only one side of the vehicle's front end is hit. The vehicle being tested strikes a deformable barrier on the driver side at 40 mph, which means the forces are similar to a frontal offset crash between two vehicles of the same weight that are each traveling at just under 40 mph. About 40 percent of the front end of the vehicle is impacted. The IIHS ranks the vehicles it tests in one of four positions: Good, Acceptable, Marginal, or Poor. Ratings do not correlate to a chance of injury as in the government's test, because the IIHS is assessing more than just occupant injury. It is also looking at how well the vehicle structure performs and the movement of the dummy, such as a partial ejection from the vehicle. 2.6.4 EFFECT OF SAFETY TESTS Even though the different safety tests have a common goal of increasing the safety of occupants in a vehicle, the effect of these tests on fatality rates had not been studied till recently. It was observed [18] that the NCAP scored have improved steadily since the inception of the program, with the greatest improvement in the early years. By now, most of the passenger cars meet FMVSS No. 208 criteria in the 35 mph NACP test. A 20 to 25 percent reduction in the fatality risk for belted drivers in actual head-on collisions between passenger cars has been observed. In 1998, an issue was raised by the vehicle manufacturers about the need to design stiffer LTV structures due to the NCAP tests, which in turn led to increased aggresivity. A study [19] conducted by NHTSA involving the frontal crash test results of 175 LTVs concluded that the total crush of the LTVs has increased, the peak deceleration 20 has decreased, and the time duration of the crash pulse has increased. This correlates to the overall reduction in the total stiffness of frontal structures of LTVs. When considering the NCAP and the IIHS tests, it would seem that they are measuring basically the same issues, but actually, the tests are conducted very differently, which means that the results tend to be quite different. Both organizations feel their respective frontal tests are complements to each other, not competitive. Nathaniel Beuse, division chief of NHTSA's New Car Assessment Program, says that consumers should use the results from both tests "together to assess overall frontal crash test safety in terms of the effectiveness of restraint systems and the integrity of the occupant compartment." More importantly, both tests can only be used to get an idea of how the vehicle would perform in a collision with a vehicle of similar size and weight or in a singlevehicle collision, which results in essentially the same forces as a collision with a similarly sized vehicle. They cannot be used to assess how a vehicle would fare if it collides with a vehicle that is significantly different in size. Since the rating reflects a crash between two similar vehicles, vehicles from the same weight class, plus or minus 250 pounds, should be compared when looking at frontal crash star ratings. 2.7 COMPATIBILITY In general terms, compatibility may be described as the capability of vehicles to protect occupants in case of collision and at the same time, offer as little aggressiveness as possible to crash partner vehicles. Figure 8 shows the geometric incompatibility between different classes of vehicles. The definition can be further specified to state that regardless of the accident circumstances, both vehicles should have almost the same probability of injury. The traffic environment includes cars, trucks, pedestrians, and two- 21 C 1500 Ford Taurus Geo Metro Figure 8. Front-end profiles of an LTV, a passenger car, and a small car. wheelers and injuries can occur from to collisions with similar or different vehicles or even single fixed objects. Naturally, the problem of compatibility is global and requires careful understanding of the crash mechanism. The main aspects of the problem of compatibility have been identified as follows: Mass ratio of the colliding vehicles. Ride height or the front end geometry of the vehicles. Force deflection or stiffness of the front end structures of the vehicles. Other factors that have been observed to effect compatibility are the location, size, and mass of the powertrain and more importantly the stiffness of the occupant cell itself. These factors can be broadly classified as mass incompatibility, stiffness incompatibility and geometrical incompatibility. The issue of vehicle compatibility has been known since the 1960’s but no organized research had been done until recently by NHTSA and other agencies worldwide. The trend of increasing mass and stiffness for pickup trucks is as shown in Figure 9. 22 Mass, Stiffness vs Model Year 2500.00 2000.00 1500.00 1000.00 500.00 Stiffness Mass Power (Mass) Power (Stiffness) 0.00 82 84 86 88 90 Model Year 92 94 96 98 Figure 9. Mass and stiffness values from NCAP tests [20]. The compatibility concerns were condensed into two vehicle categories—SUV and LTV—not only because of their increasing market share in the past decade but also because these vehicles are generally designed heavier, stiffer, and with a higher ground clearance than passenger cars. 2.7.1 AGGRESIVITY AND AGGRESIVITY METRIC The NHTSA’s vehicle aggresivity and compatibility program was established to address this serious issue. The initial focus of the program was to identify and characterize compatible vehicle designs that would result in significant reductions in crash—related injuries. The group’s major concern was the effect of the structural modifications that were being done by vehicle manufacturers in response to frontal offset crash testing. Modifications caused the strengthening of the structures to reduce intrusions into the passenger compartment, but these in turn caused the vehicle structure to become stiffer. When the sales trend of the vehicle fleet was studied an interesting 23 pattern emerged. In the United States, the class of light trucks and vans (LTVs) as shown in Figure 10, account for nearly one-third of the new vehicle purchases. TRUCK CAR Figure 10. U.S sales and registrations of LTV and cars [4]. Aggresivity is a term used to define how fatal a vehicle is to its partner vehicle’s occupants in a two—or multi-vehicle collision; in other words aggresivity is a relative measure of the level of incompatibility. Since 1993 NHTSA conducted studies to investigate the crash compatibility of passenger cars and LTVs in vehicle—to—vehicle collisions. Crash compatibility is typically evaluated either by crash testing or analysis of accident data like the Fatality Analysis Reporting System (FARS) and General Estimates System (GES). These provided an indisputable record of the safety performance of a vehicle but by nature are only an historical record and cannot predict the compatibility or aggresivity behavior of new vehicle models. In order to characterize the compatibility problem, NHTSA defined an aggresivity metric based on the FARS and GES crash involvements, defined as: 24 Aggresivity = Fatalities in Collision Partner Number of Crashes of the Subject Vehicle The fatality rates were normalized to include the fatalities in the collision partner per the number of the crashes in which the subject vehicle was involved, which accounted for the different vehicle populations and driver demographics. Only two vehicle crashes where both vehicles were less than 10,000 pounds and had model years 1980 and newer were included because the earlier analyses showed that these vehicles showed lower aggresivity metrics than the entire model years combined. Only fatalities of the drivers with ages between 26 and 55 were considered, in order to remove any injury tolerance shown by younger and older drivers, as discussed in Section 2.4.2. The vehicle categories studies were LTVs which are a subset of the LTV vehicle categories provided by FARS and GES and passenger cars which were categorized using the NCAP vehicle weight ranges. The computed aggresivity metric included all the three different modes of crashes – front, side and rear. The overall aggresivity metric and front—front crashes are shown in Figure 11 and 12, respectively. The driver fatalities for frontal crashes between LTV—car is shown in Figure 13. Figure 11. Overall aggresivity metric. 25 Figure 12. Aggresivity metric frontal-frontal. Figure 13. Driver fatalities for frontal-frontal in LTV—car crashes. About four percent of all two-vehicle crashes were accounted for by frontalfrontal crashes, but 4300 average fatalities were recorded between 1995 and 1999. The metrics for the frontal-frontal category are much higher than for all two-vehicle crashes, but the relative rankings of the vehicle categories remain the same. 26 CHAPTER 3 SYSTEM SETUP The problem of vehicle compatibility and aggresivity led to an attempt to optimize the aggresivity of a common pickup truck by considering a worst-case scenario involving a vehicle-vehicle collision involving a common small car. This section will describe the system formulation and the methodology, as shown in Figure 14, used for the optimization study. System Formulation Model and Configuration Selection Selection of Parameters Selection of Experimental Design Optimization Design of Experiment Matrix Intrusions LS-DYNA Crash Simulations Acceleration Internal Energy MADYMO Occupant Simulations Combined Injury Index Injury Criteria - HIC, Chest Acc Figure 14. Adopted methodology. 27 3.1 FORMULATION NHTSA and National Crash Analysis Center (NCAC) have developed finite element models of different vehicles which have been validated against the rigid barrier NCAP tests and are commonly used for crash studies. The 1994 Chevy Pickup C1500 and the 1997 Geo Metro models for a full—frontal, collinear crash configuration were selected. Figure 15 shows the two different vehicle models. Table 2 summarizes the model definitions. Figure 15. Finite element models of Chevy C1500 pickup (left) and Geo Metro (right). TABLE 2 Chevy C1500 and Geo Metro Model Definition Chevy C1500 Geo Metro Parts 226 211 Nodes 62681 19543 Shell Elements 51324 15374 Solid Elements 3554 522 Beam Elements 171 4 28 The system was setup under the assumption that the Geo Metro represents an average small passenger car. A baseline vehicle-vehicle model was constructed by combining the two vehicle models to represent a full—frontal crash scenario. The closing velocity was calculated to be 50 mph, which would effectively result in a change of velocity of 35 mph. This change in velocity represents the 35 mph rigid—barrier NCAP test. To be able to study the effect of the main parameters on aggresivity, only the three parameters of the pickup truck were varied, keeping that of the Geo Metro unchanged. Variation in the parameters, discussed in Section 3.2.1, was used to effectively encompass the entire fleet of pickup trucks. The MAthematical DYnamic Model, or MADYMO as it commonly known was used to simulate the dynamic behavior of mechanical systems. Although originally developed for studying passive safety, MADYMO is being increasingly used for active safety and also biomechanics study. Its unique facility of combining finite element (FE) and multi-body allows it to be used for a multitude of problems. To study the occupant kinematics and their injury parameters, the occupant compartment was modeled in MADYMO, as shown in Figure 16. The occupant compartment of the Geo Metro was modeled using the measurements from the FE model and actual test data. To simulate occupants, ATDs have been used and in this study a 50th Hybrid III Dummy was used. The Hybrid III represents an average U.S adult male. The model of the dummy consists of 69 bodies, with six left and right ribs. The reference joint is chosen in the lower torso. Accelerometers and load cells are appended in the dummy database to study the injury parameters. The occupant compartment is modeled using planes, ellipsoids, and cylinders. Measurements are obtained from the actual rigid barrier 29 test data. The airbag is modeled using the finite element capabilities of MADYMO. Figure 17 shows inflation of the airbag. The triggering conditions are used to activate the airbag inflation at a specified time. The dummy is restrained using shoulder and lap seat restraints. They are modeled using a combination of seat belt segments and finite elements. Appropriate contact definitions are provided to define contact between the belts and the dummy parts. Friction between ellipsoids, planes, and finite element nodes are also taken into account. Figure 16. MADYMO interior model of Geo Metro. Figure 17. Inflation of airbag. 30 3.1.1 VALIDATION The FE models used in this study, developed by NCAC were validated with respective NCAP tests conducted by NHTSA. Model validation is an integral part of any study, because the developed models are generic models and the experimenter(s) must ensure that they correlate to the actual full—scale vehicles. Figure 18 shows validation graphs for the MADYMO vehicle interior model. The simulation was based on the NCAP test of the Geo Metro, NHTSA test number 2239. The head acceleration and chest acceleration are plotted against time and show good correlation to the actual test (red line) data. The Chevy pickup C1500 model was validated against test number 1741, conducted by NHTSA under the New Car Assessment Program (NCAP) [20]. Figure 19 shows the 35 mph rigid—barrier test setup. The acceleration calculated through the accelerometers placed in the vehicle, as shown in Figure 20, shows good correlation to the actual test results, shown in Figure 21. The post —test view shows similar crush patterns as shown in Figure 19. Figures 22 to 26 show similar results for the Geo Metro [21]. Figure 18. Head and chest acceleration validation for the MADYMO model. 31 Figure 19. NCAP rigid barrier test setup for Chevy 1500. Figure 20. Placement of accelerometers in Chevy C1500. Figure 21. Acceleration and velocity profiles for Chevy C1500 (simulation- blue, actual -red). Figure 22 Post—test view for Chevy C1500 (simulation—left, actual—right). 32 Figure 23 NCAP rigid barrier test setup for Geo Metro. Figure 24 Placement of accelerometers for Geo Metro. Figure 25 Acceleration and velocity profiles for Geo Metro (simulation- blue, actual -red). Figure 26 Post—test view for Geo Metro (simulation—left, actual—right). 33 3.2 SELECTION OF DESIGN VARIABLES As mentioned earlier, the three main factors affecting the aggresivity of a vehicle, are the mass, stiffness, and height of the vehicle. A brief description of how the variables and the levels were introduced into the FE models is presented in the following sections. 3.2.1 MASS One of the most important variables is the mass of the pickup truck. The stiffness and the mass values from the NCAP tests were obtained [22] and plotted. Figure 27 shows the zone of consideration for this study. Stiffness vs Mass (MY 83-97) 3000 Zone of Consideration Stiffness 2500 2000 1500 1000 500 1350 1550 1750 1950 2150 2350 2550 2750 Mass Figure 27. Mass-stiffness plot for determining the zone of consideration. It can be observed from Figure 27 that the mass of pickup trucks typically varies from 1,400 Kg to approximately 2,500 Kg, and the range selected for the study was 1403 Kg to 2422 Kg, representing the low and the high values. Since a difference in mass was 34 observed between the FE model and the actual NCAP test vehicle, the range was scaled to account for the discrepancy. Table 3 depicts the selected variables. TABLE 3 The Range of Mass Selected for the Study LOW HIGH Difference from Original Model 0.82 1.2 Mass in Kg 1194 2055 In order to vary the mass, the pickup truck mass was varied by changing the material properties of some of its structural parts, while minimizing the change in the center of gravity of the model. 3.2.2 STIFFNESS The stiffness of the pickup truck was modeled using only one parameter - the thickness of the front—end structural parts. Previous work [3, 5] has modeled the stiffness change using two parameters: the thickness of the fore rails and length of the fore rail. Additional members like the bumper system and radiator were translated by amounts corresponding to the change in fore rail length. This method not only increases the model preparation time but also increases the number of factors considered, former of which was not considered to be practical, when considering a design of experiment study. Therefore, in this study, the method was simplified to include only the variation of thickness of the structural members. Figure 28 shows the comparison plot of force—deflection for the simulation and the actual test of the 35 mph NCAP test. Beuse, N. et al. [23] evaluated the methods of 35 calculating stiffness from the 1982-2001 NCAP crash test data and concluded that the desirable characteristics were the following: Good correlation of linear fit (R2). Emphasis on the initial deformation of the vehicle. Reflection of the overall slope. Allowance for non-zero intercepts. Figure 28. Force—deflection of 35 mph NCAP test. It was decided that the correlation should begin within the first 200 mm of deflection in order to reflect the overall slope; linear stiffness had to correlate for a minimum distance of 150 mm. The linear fit showed good correlation (R2) at 241 mm of crush and the stiffness was calculated to be 778.88 KN/m, as shown in Figure 29. To effectively simulate the entire pickup truck population, stiffness values for the chosen levels are shown in Table 4. 36 350000 NCAP Test V 1741 300000 250000 200000 Forc e (N) Test V 1741 Linear Approximation (0-241mm) y = 1058.5x - 24015 150000 R2 = 0.8659 100000 FE Simualtion 50000 FE Linear Approximation (0-241mm) y = 778.88x - 15472 R2 = 0.8691 0 0 50 100 241 mm 150 200 25 -50000 Displacement (mm) Figure 29. Stiffness calculation at 240 mm of crush. Table 4 The Range of Stiffness Selected for the Study LOW HIGH Difference from Original Model 0.54 1.89 Stiffness in KN/m 450 1512 Initial simulations with variation of thickness of only the fore rails did not correspond well to the change in stiffness. To better understand the crash and energy— absorption characteristics, the frontal structure was analyzed for the 35 mph rigid— barrier test. Figure 30 shows the percentage of energy that is absorbed by the front end of 37 Chevy pickup and Figure 31 shows the structural parts that were selected. Out of the total energy absorbed during the NCAP test, approximately 53 percent was absorbed by these parts. Bumper, 10.8 Hood, 5.8 Fender, 4.5 Fore Rail, 31.6 Figure 30. Energy distribution and percentage for Chevy C1500 in NCAP test. Fenders Hood Fore Bumper and Mounting Figure 16 Energy distribution and percentage Chevy C1500 in a 35 mph NCAP test Figure 31. Parts selected for the stiffness variation. 38 3.2.3 OVERLAP The variation of the ride height or overlap of the LTV was modeled by changing the Z-coordinates of the entire model. Since there were no available databases to determine the range of the ride height of pickup trucks, the variation was simplified to overlap the front—end structural members. Similar to mass and stiffness, the height also was varied in two levels as shown in Figure 32. Baseline Model 100 % Overlap No Overlap Figure 32. Baseline model and the two levels of overlap. 39 3.2.4 CONSTANT VARIABLES The variables that were kept constant were the closing speed and the processor. Closing speed is defined as the difference in the initial velocities in a vehicle-vehicle crash simulation. For this study, the closing speed was determined to be 50 mph. To remove noise in the simulations arising from different processors and even platforms, these factors were kept the same for all simulations. 3.2.5 RESPONSE VARIABLES The responses that were chosen to be studied fall into two categories: (a) structural intrusions and (b) occupant injury levels, as listed in Table 5. Table 5 Selected Response Variables Structural Intrusions Occupant Injury Dashboard / Instrument Panel Combined Injury Index (Pcomb) Internal Energy Ratio The structural intrusions were found by calculating the nodal X and Y displacements of the parts shown in Figure 33. The observed occupant injury: Head Injury Criteria (HIC) and Chest Acceleration are combined to form a single index, Combined Injury Index (Pcomb). The HIC and Chest Acceleration are calculated by using multi-body models of dummy and the vehicle interior. Only the driver-side intrusions were calculated; intrusions affecting the passenger and the lower extremities injuries are beyond the scope of this study. 40 Figure 33. Parts used to calculate the nodal displacements. 3.3 DESIGN OF EXPERIMENTS A Design of Experiments (DOE) is a carefully organized series of trials, based on sound mathematically theory, where the responses are measured for set combinations of the variables. This is a highly cost—effective solution for conducting parametric studies that are then used to develop a statistical model of the system. The model thus created allows for prediction of various responses by relating them to the variables, either individually and/or in combination. The DOE model has the following features: • Variables - These are the primary factors of interest that are believed to affect the responses and in this study, include the mass, stiffness, and height of the pickup truck. 41 • Outputs or Responses - These are the responses required from the system under consideration and in this study, include the intrusions, injury parameters, and absorbed energy ratio. Usually the system behaves as a non-linear system, and the variables interact in a very complex manner, which give rise to the need for good interpretation of these interactions. Several graphic methods are employed to visualize these interactions. 3.3.1 FACTORIAL DESIGN Factorial designs are used in experiments involving several factors where it is necessary to observe the joint effect of the factors on the response [24]. The most important of these are the k factors, each at two levels. The levels might be qualitative or quantitative, or the high and low levels of a factor. One of the major assumptions considered in this type of design is that since there are only levels of factor, the response varies linearly over their range. This is often desired in factor—screening experiments which are primarily used to study the process or system. A single replicate 2k design was selected for this study. The logical explanation behind this is that the replication of a finite element simulation will not result in variability in the response as long as the other variables are held constant. Table 6 shows the experimental design developed using Design-Expert©. The experimental design shows the three factors, each at two levels, which in turn produce eight runs. 42 Table 6 Stat Ease Design Matrix Std A: Mass B: Stiffness C: Overlap Order Kg KN/m 1 1194 684.27 0 2 2055 684.27 0 3 1194 2009 0 4 2055 2009 0 5 1194 684.27 1 6 2055 684.27 1 7 1194 2009 1 8 2055 2009 1 3.3.2 OPTIMIZATION METHODOLOGY The engineering of structural design is a challenge to determine the best one through an iterative process where a series of structural changes regarded as reasonable trials show off different responses. Optimization and FE simulation tools can be used to change the design parameters and obtain the efficient search for the right combination of design parameters for a certain design. Parametric study and optimization can be usefully combined to investigate and optimize the behavior of a model. Response surface methods can handle just a few design variables, since otherwise, the computational effort is too high. For this study the following procedure was followed: Possible numerical errors that affect the responses were excluded. Design parameters chosen were proven [4, 9, 10, 11] to be the major factors influencing the responses. The DOE method is used to understand the factorial effects. 43 A second—order Response surface model is made up with the design parameters and is used to optimize the system. 3.4 SIMULATIONS The crash simulations were conducted using LS-DYNA, a general purpose explicit finite element code used to analyze non-linear dynamic response of structures. Its fully automated contact analysis capability and error-checking features help solve complex crash, impact, and forming problems. Each numerical simulation was run on a WIN32 (PCWIN), OS Level-Windows XP, with single precision (I4R4), 2GB RAM, using two Xeon processors and LS-Dyna 970. The termination time for each simulation was 130 milliseconds and they ran for approximately seven hours each. MADYMO simulations were run using MADYMO 6.2 on a UNIX platform. Each simulation took approximately ten minutes. 44 CHAPTER 4 RESULTS The results from the LS-DYNA and MADYMO simulations are presented in this section. The statistical analysis using Design-Expert, along with optimization solution is also provided. The prediction equations developed from the statistical data are tested using original model. 4.1 FINITE ELEMENT SIMULATIONS The simulation shown in Figure 34 represents the Geo Metro and Chevy C1500 in a frontal-frontal crash configuration. The response variables calculated from the eight simulations are shown in Figure 35. Figure 34. Model configuration at 0 milliseconds. 45 Time: 15 Milliseconds Time: 30 Milliseconds Time: 45 Milliseconds Time: 60 Milliseconds Time: 75 Milliseconds Time: 90 Milliseconds Time: 105 Milliseconds Time: 120 Milliseconds Figure 35. Crash simulation representing M, S, and, O variable levels. 46 Figure 36 shows the intrusions that were calculated from the eight runs. It can be observed that the toe pan intrusions were lower than the baseline model for all runs. The graph also shows that the intrusion caused variation in the results with the number of runs. This is a good indication of the fact that the variables considered for this study had a significant effect on the intrusions and also that there is a possibility of interaction between the variables. The normalized intrusion which was calculated based upon that of the baseline simulation is shown in Figure 37. On the average, the toe pan and the B pillar intrusion were reduced, while the footwell, dashboard, and A pillar showed an increase. Runs 5 and 6 specifically showed a significant reduction in overall intrusions, while Runs 7 and 8 showed an overall increase. Comparing Runs 7 and 8 shows a reduction in the intrusions in the latter, with the exception of toe pan intrusion. INTRUSIONS Toepan Dashboard A pillar Footwell 100 90 80 70 P ercen ta ge 60 50 40 30 20 10 0 Original Run1 Run2 Run3 Run4 Run5 Figure 36. Intrusion levels. 47 Run6 Run7 Run8 25 20 15 Toepan B Pillar 10 Footwell 5 Dashboard 0 A pillar -5 -10 -15 A pillar Dashboard -20 Footwell Run1 Run2 Run3 B Pillar Run4 Run5 Run6 Toepan Run7 Run8 Figure 37. Normalized intrusion levels. A very interesting pattern is observed when the percent of internal energies were plotted as shown in Figure 38. The internal energies closely relate to the variation in stiffness values as shown previously in Table 6. Comparing two adjacent runs, Run 1 and 2 for example, the energy absorbed by the Geo Metro increased marginally by an increase in mass of the Chevy C1500. From a primary overview, overlap does not seem to affect the energy absorption characteristics of either vehicle. The normalized percent internal energy (IE) ratio is plotted in Figure 39. The IE ratio is the ratio between the energy absorbed by the Geo Metro and the Chevy C1500. This graph also shows a similar pattern, but the difference between Runs 2, 3 and 4, 5 was very large. 48 % C15 % MET 100 90 80 70 60 50 40 30 20 10 0 Run 1 Run 2 Run 3 Run 4 Run 5 Run 6 Run 7 Run 8 C15-ME Figure 38. Percentage energy absorbed. Internal Enery Ratio vs Runs 1.00 0.80 0.60 0.40 0.77 0.82 0.58 0.20 0.34 0.00 -0.15 -0.20 -0.38 -0.17 -0.36 -0.40 Figure 39. Normalized IE ratio. 49 Figure 40 shows the combined injury index Pcomb that was used to calculate the combined effect of the head and chest injury criteria values is observed for the different runs. As can be seen, there are sharp peaks and corresponding valleys. The initial high and low points in the curve correlate exactly to the variation in the mass of the pickup truck. The difference between them is decreased when the stiffness is increased. The increase in overlap leads to lower probability of injury, the lowest value corresponding to decreased mass and stiffness and increased overlap. The Pcomb value is equal to the baseline model when the mass, stiffness, and overlap are increased. Pcomb 0.24 0.22 0.20 Probability 0.18 0.16 0.14 0.12 0.10 Run 1 Run 2 Run 3 Run 4 Run 5 Run 6 Figure 40. Pcomb index. 50 Run 7 Run 8 Org 4.2 RESPONSE SURFACE The 2k factorial design can be used to express the responses in terms of a regression model. These equations show the dependency of the design variables to the selected responses. The coefficient R2 was used to measure the model’s ability to fit the response data. The obtained regression was used to generate the response surface plots. The fitted plots are planar because the regression model is first-order. Design-Expert, a statistical software package was used for the ANalysis Of VAriance (ANOVA). 4.2.1 PAIR-WISE COMPARISONS Pair-wise comparisons, as the name suggests, is a means of visualizing the relative importance of each factor on the responses. This section will discuss the pairwise comparison of the dashboard intrusion, internal energy ratio, HIC, and chest acceleration. 4.2.1.1 DASHBOARD INTRUSION Table 7 shows the effects list for dashboard intrusion and Table 8 shows the ANOVA results. It is clear that all three factors—mass, stiffness, and overlap—had a significant effect on the dashboard intrusion, overlap being the highest. The two-factor interactions had a marginal effect on the intrusion. A comparison of mass and overlap, shown in Figure 41, indicates a strong relationship between intrusion levels and overlap and stiffness, which were major factors causing intrusion. When overlap and stiffness are compared, a similar pattern is seen, as shown in Figure 42. The cube plot shows that the lowest intrusion was observed at low mass, stiffness, and height as shown in Figure 43. 51 TABLE 7 Effects List for Dashboard Intrusion Term Effect SumSqr % Contribution Require Intercept Model A 10.25 210.125 16.39 Model B 9.75 190.125 14.83 Model C 19.75 780.125 60.86 Error AB 0.75 1.125 0.09 Model AC 4.75 45.125 3.52 Model BC 5.25 55.125 4.30 Error ABC 0.25 0.125 0.01 TABLE 8 ANOVA Results for Dashboard Intrusion Response: Dash Intrusion ANOVA for Selected Factorial Model Sum of Squares DF Mean Square F Value Prob > F Model 1280.6 5 256.125 409.8 0.0024 A 210.13 1 210.125 336.2 0.0030 B 190.13 1 190.125 304.2 0.0033 C 780.13 1 780.125 1248.2 0.0008 AC 45.125 1 45.125 72.2 0.0136 BC 55.125 1 55.125 88.2 0.0111 Residual 1.25 2 0.625 Cor Total 1281.9 7 Source Std. Dev. 0.791 R-Squared 0.999 Mean 18.625 Adj R-Squared 0.997 C.V. 4.245 Pred R-Squared 0.984 PRESS 20.000 Adeq Precision 58.059 52 significant DESIGN-EXPERT Plot DESIGN-EXPERT Plot Dash Intrusion X = A: Mass Y = C: Overlap Dash Intrusion X = A: Mass Y = C: Overlap Actual Factor B: Stiffness = 684.27 Actual Factor B: Stiffness = 2009.00 28.5 43.5 34.6875 22.3125 25.875 Da sh In tru sio n Dash Intrusion 16.125 17.0625 9.9375 3.75 1.00 1.00 2055.00 0.75 8.25 1839.75 0.50 C: Overlap 2055.00 0.75 1839.75 1624.50 0.25 1409.25 0.50 A: Mass C: Overlap 0.00 1194.00 1624.50 0.25 1409.25 A: Mass 0.00 1194.00 Figure 41. 3D plot of the dashboard intrusion at stiffness low (left) and high (right). DESIGN-EXPERT Plot DESIGN-EXPERT Plot Dash Intrusion X = B: Stif fness Y = C: Overlap Dash Intrusion X = A: Mass Y = B: Stiff ness Z = C: Overlap Actual Factor A: Mass = 1624.50 Cube Graph Dash Intrusion 28.5 43.5 36 28.625 B+ 8.25 13.75 6.5 B: Stiffness Dash Intrusion 21.25 13.875 13.5 28.5 1.00 C: Overlap 2009.00 0.75 1677.82 0.50 C: Overlap B- 1346.64 A- 0.25 1015.45 3.75 9.25 CA+ A: Mass B: Stiffness 0.00 684.27 Figure 42. 3D plot of the dashboard intrusion at mass (low). C+ Figure 43. Cube plot of the dashboard intrusion. 53 4.2.1.2 INTERNAL ENERGY The effects list in Table 9 suggests that stiffness is the biggest factor affecting energy absorption. The effect of the interaction between stiffness and overlap is also significant but the effect of mass and the other two-factor interaction is very negligible. An inverse transformation was applied to the model to increase the accuracy. Table 10 shows the ANOVA results for the IE ratio. The response surface plot shown in Figure 44 shows that a decrease in overlap causes an increase in energy absorption by the Geo Metro, when the stiffness was high. The internal energy ratio decreased as overlap increased and also the difference between the maximum and minimum values increased as the overlap increased. The change in IE ratio was reduced when the stiffness was reduced. The mass effects were negligible at either of the levels. The peak values were observed when there was no overlap between the engaging structures and stiffness was highest. Similarly, the lowest ratio was observed when the stiffness was lowest and there was no overlap. TABLE 9 Effects list for Internal Energy Ratio Term Effect SumSqr % Contribution Require Intercept Error A -0.048 4.555E-03 0.19 Model B -1.00 2.00 84.60 Model C -0.21 0.087 3.68 Error AB -0.029 1.631E-03 0.069 Error AC -3.511E-04 2.466E-07 1.04E-05 Model BC 0.36 0.26 11.18 Error ABC -0.058 6.753E-03 0.29 54 TABLE 10 ANOVA Results for Internal Energy Ratio Response: I E Ratio Transform: Inverse ANOVA for Selected Factorial Model Sum of Squares DF Mean Square F Value Model 2.35 3 0.78 242.58 < 0.0001 B 2.00 1 2.00 619.03 < 0.0001 C 0.087 1 0.087 26.91 0.0066 BC 0.26 1 0.26 81.81 000008 Residual 0.013 4 3.235E-03 Cor Total 2.37 7 Source Prob > F significant Std. Dev. 0.057 R-Squared 0.9945 Mean 1.18 Adj R-Squared 0.9904 C.V. 4.84 Pred R-Squared 0.9781 PRESS 0.052 Adeq Precision 33.925 DESIGN-EXPERT Plot 1.0/(I E Ratio) X = B: Stif f ness Y = C: Overlap Actual Factor A: Mass = 1624.50 1.67463 1.38342 I E Ratio 1.09222 0.80101 0.509804 2009.00 1.00 1677.82 0.75 1346.64 0.50 1015.45 0.25 C: Overlap B: Stiffness 0.00 684.27 Figure 44. Pair-wise comparison of internal energy ratio. 55 4.2.1.3 Pcomb The effects of the factors on the combined injury index are shown in Table 11. As can be observed, mass and overlap were the most significant factors. The effect of the two-factor interaction between mass and overlap was also significant. Overlap and the two-factor interaction between stiffness and overlap had a very low effect on Pcomb. To increase the accuracy of the model, a power transformation was applied. The ANOVA results are tabulated in Table 12. From the response surface plots shown in Figure 45, it was observed that the Pcomb value increased when the stiffness was reduced, and there was no overlap between the engaging structures. The peak values are observed in this region. The minimum value of Pcomb was observed when each, stiffness was reduced and overlap were increased. The effect of overlap diminished when stiffness was increased. Increase in mass caused two percent increase in Pcomb values. TABLE 11 Effects List for Combined Injury Index (Pcomb) Term Effect SumSqr % Contribution Require Intercept Model A -1.200 2.881 13.222 Model B -0.392 0.307 1.410 Model C 2.262 10.229 46.951 Error AB 0.290 0.168 0.770 Error AC 0.392 0.307 1.408 Model BC -1.984 7.870 36.121 Error ABC -0.114 0.026 0.119 56 TABLE 12 ANOVA Results for Combined Injury Index (Pcomb) Response: P Comb Transform: Power Lambda: -1.2, Constant: 0 ANOVA for Selected Factorial Model Sum of Squares DF Mean Square F Value Prob > F Model 21.286 4.000 5.322 31.916 0.0086 A 2.881 1.000 2.881 17.276 0.0253 B 0.307 1.000 0.307 1.842 0.2677 C 10.229 1.000 10.229 61.349 0.0043 BC 7.870 1.000 7.870 47.198 0.0063 Residual 0.500 3.000 0.167 Cor Total 21.786 7.000 Source significant Std. Dev. 0.408 R-Squared 0.977 Mean 8.758 Adj R-Squared 0.946 C.V. 4.663 Pred R-Squared 0.837 PRESS 3.557 Adeq Precision 16.868 DESIGN-EXPERT Plot DESIGN-EXPERT Plot (P Comb)^-1.2 X = B: Stiffness Y = C: Overlap (P Comb)^-1.2 One Factor Plot 0.23 X = A: Mass 0.201651 Actual Factors B: Stiffness = 1346.64 C: Overlap = 0.50 0.184937 0.205 P Comb 0.168224 0.15151 P Co m b Actual Factor A: Mass = 1624.50 0.134796 0.18 0.155 2009.00 1677.82 0.13 0.00 1346.64 0.25 B: Stiffness 0.50 1015.45 1194.00 1409.25 1624.50 1839.75 0.75 684.27 1.00 C: Overlap A: Mass Figure 45. Factor effects on Pcomb, pair-wise (left), mass effect (right). 57 2055.00 4.3 REGRESSION ANALYSIS The regression equations obtained from ANOVA analyses are shown in Table 13. and R2 values suggest that these equations can be used to predict the responses within the design space. Mass, stiffness, and overlap were represented as M, S, and O, respectively. TABLE 13 Comparison of Regression and Actual Values Regression Simulation Dashboard Intrusion = -6.20159 + 6.38792E-003 * M + 3.39692E-003 * S - 8.84784 * O + 0.011034 * M * O + 7.92614E-003 * S * O 11.84 17.00 I E Ratio = 1/ [+2.66629 – 1.02994E-003 * S - 0.94818 * O + 5.49195E-004 * S * O] 0.82 0.88 Pcomb =[+8.27308 - 1.39385E-003*M + 1.20153E-003 * S + 6.29438 * O - 2.99477E-003 * S * O]^1.2 11.67 17 The responses observed in the baseline simulation were compared with the values obtained from regression equations. Regression values show good correlation to baseline simulation but also show that values were under—predicted. 4.4 OPTIMIZATION From the selected responses an overlay plot was created to develop the design space that would yield the most optimum design. Constraints were based on the obtained responses and the rigid—barrier tests. The constraint condition was defined as; Dash Board Intrusion: 6 -17 cm Pcomb: ≤ 20 IE Ratio: 0.85 -1.2 58 The upper limit of the dashboard intrusion corresponds to the intrusion level observed in the rigid—barrier test. The NCAP rates the vehicles according to the probability of serious injury (AIS 4 +). Therefore, Pcomb was restricted to 20 percent to account for a four—to five—star NCAP rating. The IE ratio was limited to 0.85 and 1.2 to create a balanced design space, which would not only increase the energy absorbed by the pickup truck but also that of the Geo Metro. The overlay plot as shown in Figure 46 revealed that reduction in mass led to increase in the optimum region (shaded lighter). DESIGN-EXPERT Plot Overlay Plot 1.00 Overlay Plot Design Points X = B: Stif f ness Y = C: Overlap 0.75 Actual Factor A: Mass = 1194.00 C: Overlap Dash Intrusion: 17 I E Ratio: 0.85 I E Ratio: 1.2 0.50 0.25 Dash Intrusion: 6 0.00 684.27 1015.45 1346.64 1677.82 2009.00 B: Stiffness Figure 46. Optimal region based on constraints at mass (low). Overlap ranged from 0 to 84 percent with reduced stiffness, and 0 to 55 percent with increased stiffness. Stiffness values for this condition were found to be more than NCAP values. Thus, considering that increase in stiffness was a constant trend, reduction in mass of the pickup trucks caused a significant reduction in the aggresivity. However, the optimum region reduced as mass was increased, as shown in Figure 47. The area 59 reduction was observed to be due to reduction in the overlap or height of optimum area but the width, or stiffness remained constant. DESIGN-EXPERT Plot Overlay Plot 1.00 Overlay Plot X = B: Stiff ness Y = C: Overlap Actual Factor A: Mass = 1624.50 C: Overlap 0.75 I E Ratio: 1.2 I E Ratio: 0.85 0.50 Dash Intrusion: 17 0.25 0.00 684.27 1346.64 1015.45 1677.82 2009.00 B: Stiffness DESIGN-EXPERT Plot Overlay Plot 1.00 Overlay Plot Design Points X = B: Stif fness Y = C: Overlap 0.75 C: Overlap Actual Factor A: Mass = 2055.00 I E Ratio: 0.85 I E Ratio: 1.2 0.50 Dash Intrusion: 17 0.25 P Comb: 0.2 0.00 684.27 1015.45 1346.64 1677.82 2009.00 B: Stiffness Figure 47. Optimal region based on constraints at mass medium (top) and high (bottom). 60 CHAPTER 5 DISCUSSION 5.1 CONCLUSION The disturbing trend of increasing number of aggressive vehicles and the difference between aggresivity of different classes of vehicles is a growing concern among manufacturers and consumers, alike. This study gave a glimpse into the mechanisms behind crash—related aggresivity of pickup trucks. Public domain FE models of Chevy C1500 pickup and Geo Metro were used. LS-DYNA was used to simulate actual vehicle collisions and MADYMO was used to study the occupant responses. The effect of variation of the mass, stiffness, and overlap between the energy— absorbing structures of the pickup truck was used to observe the intrusion, energy absorption, and the injury criteria in the Geo Metro. DOE was used to observe the combined effect of the factors on the responses and Design-Expert was used to develop the simulation matrix and to analyze the responses. The statistical analyses showed that intrusion was most affected by change in overlap and to some extent by change in mass and stiffness. The combined injury index was largely affected by change in mass and overlap, whereas internal energy ratio was directly related to stiffness variation. Regression equations obtained from the ANOVA analyses showed that these equations could be used for prediction but a trend of under— prediction was also observed. Overlay plots were created by constraining response values to values observed in NCAP and baseline simulations. They revealed that the region used 61 to form compatible fleets is very narrow. Reduction in mass led to a significant reduction in response values. When mass was increased, a reduction in the optimum region was observed which was mainly due to reduction in overlap. This suggested that if mass of pickup trucks was increased, only a small area corresponding to increased stiffness and decreased overlap would decrease the aggresivity of pickup trucks. A wider area bounded by increased stiffness and overlap but with decreased mass meant that manufacturers had a wider choice for designing compatible fleets. 5.2 FUTURE RESEARCH The scope of this study was to evaluate a means of reducing the aggresivity of pickup trucks with respect to small cars. Similar studies can be conducted using different classes of vehicles. Recent research has shown that similar optimization studies can be conducted efficiently, and that a more accurate model can be developed by conducting similar studies in MADYMO or through the use of lumped-mass systems. The distinct advantage is that a more diverse group of vehicles can be used. Once these models reveal a general trend, the FE method can be used to further refine the system parameters. The use of DOE combined with either of the above—mentioned systems could be developed into a powerful system that can be used to predict the aggresivity of future vehicle designs. 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