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44 5.1 Introduction This chapter provides details of the vehicle encroachment simulations performed under this project. These simulations were performed to determine the influence of various roadside and encroachment parameters on the kinematics of the vehicles as they traverse the sloped terrains. The chapter has been divided in various sections. These include discussions on the selection of appropriate simulation tools, development of vehicle models, details of a wrapper program that generates simulation inputs and manages the vehicle dynamics simulations and their outputs, various sensitivity studies performed to determine the appropriate values of different parameters used in the simulations, evaluation of the friction ellipse model to incorporate soil furrowing forces, the simulation matrix used for this research, and the results of the simulation analyses performed. 5.2 Simulation Tools For many years, computer codes have been used to simulate vehicle handling, vehicle impacts with roadside objects, and encroachments over roadside geometric features such as slopes, ditches, and driveways. In these studies, researchers have utilized varying levels of vehicle model sophistication ranging from simple lumped masses, springs and dampers, to detailed finite element model representations using thousands of elements. Generally speaking, all computer codes and models have limitations and they all incorporate different levels of assumptions. It was therefore crucial that the codes and models selected for use in this study be capable of accurately modeling relevant characteristics of the vehicle, terrain, and the interactions among them. Various issues that were considered in making the final selection of such codeâmodel combinations are presented below. 5.2.1 Vehicle Characteristics 1. Vehicular mass and mass distribution of the vehicle. The inertia of the vehicle and the mass moments of inertia play a major role in the behavior of the vehicle and must therefore be accurately quantified and modeled. This is because inertial forces are key factors in any dynamic vehicle maneuver. 2. Suspension system. The suspension sub-system of the vehicle provides the linkage between the sprung and unsprung mass. It is important to have an accurate representation of the suspension system because it affects the dynamic response of the vehicle to a given maneuver such as traversing a slope or ditch. 3. Tires. Tires are the linkage between the vehicle (through the suspension system) and the ground. They are the source of all disturbance forces that are applied to the vehicle under C H A P T E R 5 Simulation Analysis
Simulation Analysis 45 normal operation (except for aerodynamic forces). Although their functional description is quite simple, the mechanism of the interaction between tires and the road is very complex. 4. Steering linkages. A simulation model has to account for steering the vehicle in order to accurately capture the motion of the vehicle during slope traversal. Driver reaction is one of the most significant factors that can affect the likelihood of vehicle rollover during slope traversal. The code selected for the simulation must have the capability to define driver reaction in terms of steering angle, braking force, and acceleration, if needed. 5.2.2 Terrain Modeling The geometry of the terrain is an important aspect. Roadway, shoulders, and slide slopes should be appropriately accounted for in the simulation model. 5.2.3 Vehicle and Terrain Contact The selected simulation code should be capable of modeling the interaction between the vehicle and the ground, which includes the frictional contact between the tires and terrain features. Vehicle body contact with terrain can also influence vehicle dynamics for roadside encroachments. The vehicle body-to-terrain contact may not be as crucial while the vehicle is traversing the foreslope. However once the vehicle reaches the bottom of the slope, it is expected to encounter a sudden change in slope, which may result in vehicle body-to-terrain contact. The ability of the selected simulation package to model this contact is useful in evaluating the effect of sudden changes in the slope of the terrain. Available simulation codes capable of modeling vehicle traversals of sloped terrains can be divided into two broad categories: 1. Multi-rigid-body vehicle dynamics codes (e.g., CarSim, ADAMS, HVOSM, HVE) 2. Non-linear finite element analysis codes (e.g., LS-DYNA, ANSYS, NASTRAN) Bases on all considerations, the researchers used the vehicle dynamics code instead of the finite element analysis code. And among the vehicle dynamics codes, the researchers used CarSim. A detailed discussion of the reasons for this selection is presented next. 5.2.4 Vehicle Dynamics Codes versus Finite Element Analysis Codes 126.96.36.199 Computational Time In addition to the ability of a particular simulation code to model vehicle traversing different terrains, it is important to evaluate the computational resources needed and the scale of the simulation study. Generally speaking, finite element analysis codes require significantly large computation time to complete each simulation. A finite element simulation of a sufficiently detailed vehicle model performing a driving maneuver on a foreslope for about 3 to 5 s may require several days of computations. In contrast, a similar simulation performed using a vehicle dynamics code typically completes the computations in less than 3 to 5 s. This is because the large number of degrees of freedom involved in finite element analysis codes like LS-DYNA requires longer computation time to simulate a vehicle encroachment event. In a vehicle dynamics code, however, the model has a much smaller number of degrees of freedom and thus vehicle handling and encroachment events can be simulated with minimum computation time. Because of the significantly larger degrees of freedom in the model, the finite element analysis codes have the ability to calculate deformations and stresses in the vehicle or the soil/terrain they are traversing. This feature is not available in vehicle dynamics codes, and hence finite
46 Guidelines for Traversability of Roadside Slopes element analysis codes are extremely popular in crash simulations and other types of analyses requiring determination of loads and deformations. In this research, however, such levels of detail for the vehicle or the terrain were not needed. Furthermore, the size of the simulation matrix was expected to be very large in order to incorporate the many variables associated with evaluating the vehicleâs traversability on slopes. Use of a finite element analysis code (such as LS-DYNA or others) was therefore impractical because of the time needed to complete each simulation. Use of the finite element analysis code would have required a dramatic decrease in the number of design parameters and their combinations that could be evaluated. 188.8.131.52 Accuracy Using a finite element analysis code does not necessarily render greater accuracy for the types of slope traversal simulations that were anticipated in this research. The researchers, in a previous study, compared the use of both LS-DYNA and CarSim in simulating the encroachment of a 2000P Chevrolet C2500 pickup truck and an 820C Geo Metro car on a 1V:6H foreslope (35). As shown in Figure 5.1, the trajectory of the vehicles obtained from CarSim closely matched the trajectory of the vehicles obtained from LS-DYNA. A single-core processor required 0.8 s to simulate each event in CarSim. An 8-core processor, on the other hand, required 2 h (i.e., 16 h of CPU time) to simulate the same event in LS-DYNA. Thus, considering the large number of parametric runs needed to address the variables of interest, use of a vehicle dynamics code like CarSim was considered to be most suitable. 184.108.40.206 Vehicle Model Development The development of a vehicle model for a finite element analysis code, such as LS-DYNA, requires significant resources. A limited number of vehicle finite element models are available in the public domain. Under funding from FHWA, the National Crash Analysis Center had developed public domain finite element models of a 5000-lb pickup truck and a 2425-lb small passenger car. The National Crash Analysis Center had developed several vehicle models but the overall number of vehicle models in the public domain remain limited. More importantly, these vehicle models were developed with a focus on impact analyses and they are not sufficiently validated for slope traversals. Proper modeling and validation of steering and suspension link- ages, joints, and springs and dampers properties is needed for these models. (a) (b) 0 2 4 6 8 10 12 14 16 -30 -20 -10 0 10 20 30 40 50 60 Lateral Offset (ft) B um pe r T op H ei gh t ( in ch ) CARSIM: Chevy2500; 62.5 mi/h; 25 deg. LS-DYNA: Chevy2500; 62.5mi/h; 25 deg. 6:1 Roadside Slope Profile 0 5 10 15 20 25 30 -60 -40 -20 0 20 40 60 Lateral Offset (ft) B um pe r T op H ei gh t ( in ch ) CARSIM: 820C GM; 62.5mi/h; 20 deg. LS-DYNA: 820C GM; 62.5mi/h; 20 deg. 6:1 Roadside Slope Profile Figure 5.1. Comparison of CarSim and LS-DYNA in simulating (a) a pickup truck and (b) a passenger car encroachment events on a slope.
Simulation Analysis 47 On the other hand, CarSim, which is a vehicle dynamics code, has about 30 pre-built vehicle models in different vehicle classes. These pre-built vehicle models can be modified with considerably less effort to represent different vehicle makes and models. In CarSim, geometric dimensions and inertia properties of the existing vehicle model can be modified with ease to match those of any desired vehicle type. Accurate suspension properties can also be incorporated as needed. Thus, use of CarSim enabled the researchers to simulate encroachment events for any vehicle type deemed necessary for this research. 220.127.116.11 Soil Furrowing Both finite element analysis codes and vehicle dynamics codes have limitations in modeling soil-tripped rollover that results from the tires digging into the soil as the vehicle slides laterally. For example, both LS-DYNA and CarSim do not have the capability to model tire blowout or debeading, which may occur in the actual lateral vehicle sliding event. Similarly, digging and furrowing of tires in soil cannot be modeled explicitly in either of the codes. Although the soil can be modeled explicitly at a cost of large computation time in LS-DYNA, unavailability of reliable soil properties and limitations on mesh distortion during soil furrowing event, make it difficult to accurately capture the vehicle behavior. Hence, in both CarSim and LS-DYNA, the soil-tire interaction can be best represented by defining a high lateral drag coefficient for tire-to-terrain contact. In LS-DYNA, the same drag coefficient is used for the tire-terrain interface in the longitudinal and lateral directions. CarSim, on the other hand, can be modified using custom subroutines to allow user-defined friction formulation with different coefficients in the longitudinal and lateral directions. This allows defining a higher coefficient of friction in the lateral direction to accommodate the forces resulting from soil furrowing. This technique of modeling soil furrowing has been previously used in most of the simulation studies using vehicle dynamics codes that incorporated soil tripping. Thus using CarSim allows incorporation of soil furrowing effects in the analyses, which cannot be easily incorporated using finite element codes such as LS-DYNA. 18.104.22.168 Driver Input Driver input was one of the most important parameters in this study. Driver response in terms of steering and braking can significantly affect the dynamics of a vehicle traversing a foreslope. Some of the current public domain LS-DYNA vehicle models have steering linkages defined; however, the steering system response has not been evaluated and validated so far. Most of these models have been developed with an impact scenario in mind where the vehicle impacts an object almost immediately at the start of the simulation. Thus the available public domain finite element models generally lack the fidelity in the steering system needed to âdriveâ a vehicle on a terrain using some steering input. Similarly, the public domain LS-DYNA finite element models do not have any braking systems incorporated in them. Brakes are generally non-functional in these models and are only incorporated to account for the mass and geometry of the brake parts. While it is possible to apply certain braking input using torque load on the wheels, this method is significantly rudimentary for this research. Most vehicles now come with ABS. Without a well-defined braking model, use of finite element analysis codes such as LS-DYNA would be further problematic. In contrast, CarSim has the ability to model ABS brakes, which can have a significant influence on vehicle control and kinematics once brakes are applied in a panic mode. 22.214.171.124 Body-to-Terrain Contact Most of the foreslope traversal simulations to be performed in this research were not expected to result in a contact between the vehicle body and the terrain. However, it was expected that
48 Guidelines for Traversability of Roadside Slopes for some of the more severe foreslope configurations with steeper foreslopes and flat bottom, such a contact may occur. If a contact between the vehicle body and the terrain occurs during an encroachment event, it can significantly change the dynamics of the vehicle. Unlike a finite element analysis code like LS-DYNA, most commercially available vehicle handling codes cannot model vehicle body-to-terrain contact. These multi-rigid-body dynamic analysis codes are only capable of modeling the interaction between the tire and ground. Among the vehicle dynamics codes, HVOSM has a customized TTI version (HVOSM V3) that has a limited capability to model vehicle body-to-terrain contact. This contact was built into the original version of HVOSM by TTI researchers in one of the previous studies (36). However, HVOSM is an old public domain code that has not been updated or improved to incorporate changes in vehicle design features of the newer vehicle fleet. In contrast to HVOSM, CarSim vehicle models have ABS, a library of tire models, and better suspension system models that account for suspension compliance effects. Furthermore, a major advantage of using CarSim was the availability of a large number of predetermined vehicle parameters and properties for the current vehicle fleet. These properties could be used for building new vehicle models under this project with relative ease and without requiring to build the models from scratch. To incorporate a vehicle body-to-terrain contact, TTI researchers have developed a user subroutine for the commercial CarSim package. This subroutine checks if the vehicleâs body is getting in contact with the terrain during the simulation run time. If a contact is detected, the subroutine applies the contact forces to the vehicle to account for the terrain reaction. The contact subroutine uses a contact formulation previously used in the TTIâs version of HVOSM (36). The algorithm tracks several user-defined points on the body of the vehicle and determines if any of those points have penetrated the local terrain. If penetration is detected for a specific point, corrective forces are applied to the vehicle. For a penetrated point P on the vehicleâs body (see Figure 5.2), the contact algorithm calculates the penetration TP âââ normal to the terrain. Using the penetration amount, vehicleâs velocity, and the penetrated point Pâs direction of travel, the contact subroutine applies a normal force Fn to remove the penetration. A friction force Ff is also applied tangent to the local terrain surface in the direction opposite to the travel of point P. The normal and tangential forces are defined as follows: Normal Force: Fn = K_total â¢ n Tangential Force: Ff = K_total â¢ U â¢ T Figure 5.2. Body-to-terrain contact forces.
Simulation Analysis 49 Where, K_total = K_terrain â¢ TPâââ â¢ [1 + Mu â¢ Vn], K_terrain = stiffness coefficient of the terrain, Mu = damping coefficient of the terrain for normal penetration of point P, Vn = velocity of point P normal to the terrain surface, n = unit vector normal to the terrain surface penetrated by point P, U = friction coefficient of the body-to-terrain interface, and T = tangential unit vector in the direction of the sliding point P on the terrain surface. Terrain properties for the contact algorithm were kept the same as those used in the HVOSM contact. The stiffness coefficient of the terrain (K_terrain) was set at 4000 lb/inch, which was based on soil subgrade modulus of 40 lb/inch3 and a contact area of 100 inch2. The damping coefficient of the terrain for normal penetration (Mu) was set at 0.001 lb-s/inch. And the coefficient of friction of the vehicle body-to-terrain interface was set at 0.25. While these values were used in previous studies using TTIâs version of HVOSM, they were not recommended as default because terrain properties can change significantly depending on surface conditions, type of soil, and other factors. The contact subroutine written for CarSim has the option to adjust these parameters if needed. Using the same contact algorithm and contact parameters, the researchers have replicated the contact features that were previously only available in TTIâs version of HVOSM. This version of the HVOSM was previously validated in various studies using full-scale crash testing with vehicles traversing sloped terrains and ditches (37, 38). Based on the factors discussed above, the researchers selected CarSim as the simulation tool for this research. In summary, the key advantages of using CarSim are the availability of a library database of pre-assembled vehicle models and sub-systems, short run durations that allow the performance of a large number of simulations, the availability of new vehicle design features such as ABS braking and advanced suspension properties, the ability to apply reliable steering and braking inputs, and the ability to batch a large number of simulation cases. Furthermore, TTI has developed a user subroutine that can be incorporated with CarSim to apply body-to- terrain contact. 5.3 Vehicle Models In this research, simulation analysis was performed using four vehicle types. These vehicles represent four different vehicle classes. Two of these were the MASH 2270P pickup truck and the 1100C small passenger car vehicles. The remaining two vehicles types were selected based on the results of the crash data analysis performed at the start of this research (see Chapter 3). One of these non-MASH vehicles was the compact utility vehicle, which has a high RR of rollover, as shown in Table 3.7. The crash data analysis showed that the 2002 Ford Explorer had the highest number of rollovers in the range analyzed, which included vehicles newer than year 2001 (Table 3.8). For this reason, the 2002 Ford Explorer was selected as one of the vehicles for the simulation analysis. The crash data indicated that the 4-door sedan also had a large number of rollovers (Table 3.7). While the RR of a 4-door sedan is less than that of a pickup truck or a utility vehicle, due to the large number of rollovers and a high percentage of sales, it was deemed important that this vehicle class should be included in the development of the traversability guidelines. The crash data analysis showed that the 2004 Honda Accord had the highest number of rollovers in the range analyzed (Table 3.8). Therefore, the 2004 Honda Accord was initially selected for further simulation analysis.
50 Guidelines for Traversability of Roadside Slopes After selecting the vehicle makes and models, the research team proceeded with develop- ing vehicle dynamics models of these vehicles. A problem faced by the research team was the unavailability of these vehicles for taking the non-destructive measurements for developing the vehicle dynamics model. These vehicles could not be rented as they were old enough to be unavailable in most rental fleets. They could also not be purchased under this project due to budgetary limitations. The researchers were able to arrange a 2002 Ford Explorer for taking measurements for model development. Unfortunately, a 2004 Honda Accord could not be arranged. Results of the crash data analysis presented in Table 3.8 also showed that the second highest number of rollovers of a 4-door sedan were for the 2001 Ford Taurus. This vehicle was available to the researchers for taking measurements. The researchers compared some of the main vehicle properties of a 2001 Ford Taurus and a 2004 Honda Accord published in the literature (31). This comparison was made for properties that are most relevant in developing a CarSim vehicle dynamics model. As shown in Figure 5.3, the two vehicles are very similar to each other. The suspension types are the same and most vehicle properties are very closely matched for the two vehicles. Because of the similarities of the two vehicles and the availability of the 2001 Ford Taurus for taking measurements, the 2001 Ford Taurus was used to develop a CarSim model of a midsize 4-door sedan. TTI has previously developed a CarSim model for the 2270P pickup truck model under NCHRP Project 16-05. This is a model for a 5000-lb Dodge Ram pickup truck that meets the MASH design criteria for the 2270P vehicle. The researchers used this model for the pickup truck simulations performed in this research. The researchers developed vehicle dynamics models of the MASH 1100C (2425-lb) small passenger car, the 2002 Ford Explorer, and the 2001 Ford Taurus. Presented next is a brief description of the process used to develop the vehicle dynamics model of the 2006 Kia Rio, which meets the MASH 1000C vehicle criteria and is commonly used in roadside safety hardware testing. The Ford Explorer and the Ford Taurus models were also developed using the same process. An evaluation of the âpre-setâ vehicle models included with the CarSim software was per- formed to select a base model which closely resembles the 2006 Kia Rio. This evaluation was based on factors including vehicle mass, weight distribution, dimensions (wheelbase, wheel center height, and vehicle length), CG location, and various engine specifications. Researchers determined that CarSimâs Class-B vehicle model (shown in Figure 5.4) was the closest to the Kia Rio passenger car and thus selected it as the base model for making further changes. The 2006 Kia Rio vehicle that the researchers used for developing the model was being used by the TTI Proving Ground facility for an imminent full-scale crash test. Various dimensions and properties of this vehicle were measured for use in developing the CarSim vehicle model. Roll, pitch, and yaw moments of inertia values of the base model were modified to match those Vehicle 2001 Ford Taurus 2004 Honda Accord Variation (%) Curb Weight (lb) 3331 3137 -6.2 Wheel Base (in) 109.1 107.9 -1.1 Track Width (in) 61.8 61.0 -1.3 CG Height (in) 22.0 22.4 1.7 Suspension Type Independent Front and Back Independent Front and Back - Figure 5.3. Comparison of vehicle properties between 2001 Ford Taurus and 2004 Honda Accord.
Simulation Analysis 51 of the Kia Rio model. These values were taken from the 4N6XPRT vehicle database described in Chapter 4. The researchers also raised the Kia Rio vehicle and determined the coordinates of seven âhard pointsâ underneath the vehicle. Hard points are relatively stiff structural locations under- neath the vehicle. If these come in contact with the terrain, it is expected that significant ground to vehicle forces will be applied that can influence the trajectory of the vehicle. TTIâs user subroutine for incorporating the contact between the terrain and the vehicle uses these hard points for applying contact forces to the vehicle if penetration in the ground is detected during a simulation. Figure 5.5 shows the locations of the selected hard points for the Kia Rio model with respect to the centerline and front axle of the vehicle. As mentioned previously, the researchers developed CarSim vehicle models for the 2002 Ford Explorer and 2001 Ford Taurus using the same approach as described above. This included using most of the vehicle properties from the pre-assembled CarSim vehicle models and then incorporating geometric and inertial properties that were determined from existing literature or by measurements from the actual vehicles. The âhard pointsâ for vehicle body-to-terrain contact were also measured for each vehicle type. 5.4 Wrapper Program The researchers developed a wrapper program using Visual Basic programming language. This program had the objectives of generating various input files for the CarSim solver, running CarSim in batch mode to perform analysis of all simulation cases, and generating the needed output. Figure 5.4. CarSimâs Class-B vehicle model was used as the base model for making changes. Kia Rio Points Description X Y Z Driver Side Bottom of Front Bumper 838.20 508 262.5 Passenger Side Bottom of Front Bumper 838.20 -508 262.5 Driver Side Middle of Vehicle -1480 682.5 200 Passenger Side Middle of Vehicle -1480 -682.5 200 Driver Side Bottom of Rear Bumper -3252.45 619 400 Passenger Side Bottom of Rear Bumper -3252.45 -619 400 Coordinate System Figure 5.5. Locations of hard points underneath Kia Rio (in mm).
52 Guidelines for Traversability of Roadside Slopes Prior to discussing the details of the wrapper program, it will be helpful to have an overview of how various inputs are organized for running a CarSim analysis. There are five main com- ponents of a CarSim input (for each simulation case). These are the road file, event file, vehicle model, run file, and simfiles. A brief description of each input file is presented below. â¢ Road File. This contains all geometric information about the terrain and associated terrain friction coefficients. â¢ Event File. Events or procedures are inputs that âdriveâ the vehicle on the terrain. This file contains the vehicleâs initial orientation, initial speed, initial yaw rate, driver steering, and braking inputs as functions of time and others such inputs. â¢ Vehicle Model. This contains vehicle properties and related inputs needed to define the vehicle model. â¢ Run File. The run file combines the road, event, and vehicle model files. This gets submit- ted to the Carsim solver. â¢ Simfiles. These files have additional information such as solver path, animation file path, results file path for each simulation case. To automate the process of generating inputs and running a large number of simulation cases, the wrapper program needs to generate the above mentioned files for each case in the simulation matrix. The wrapper program performs the following functions: 1. Determines the types of CarSim inputs that need to be generated by the wrapper program and the types that will be provided by the user; 2. Generates the needed CarSim input files, which may include road/terrain profiles and event files (containing information such as the vehicleâs encroachment speed, angle, and rate, and the driverâs steering, braking, and throttle); 3. Runs CarSim in loop to perform analysis for all simulation cases and in doing so checks for vehicle body-to-terrain penetration using TTIâs contact algorithm; 4. Applies soil furrowing forces to the vehicle model if it determines that the vehicle is side- slipping while traversing on a wet-soil terrain that has been marked to apply soil furrowing forces; 5. Manages each simulation run time and terminates simulation based on various termination criteria (such as the vehicle returns to the road, travels too far, overturns); and 6. Generates output logs for all simulation cases, recording key simulation outcomes for further use in data analysis of the simulation outcomes. The following is an overview of the structure of the TTIâs wrapper program and a generalized description of the tasks it performs. 5.4.1 Wrapper Program Structure and Overview A high-level flowchart of the TTIâs wrapper program is shown in Figure 5.6. The program starts by reading a user input file which directs the wrapper program on the tasks the users want to perform. For greater flexibility, the researchers have coded the wrapper program with several options. The program can be run to generate most CarSim road/terrain, event, and final inputs that include the vehicle model and all other commands needed to run the CarSim solver. The program can then run each simulation case, one after another, and log results of the analyses. In addition to running the entire matrix, the program can be run to perform selective tasks. For instance, the program can be run to generate selected input files only, such as the road file or the event file. It can also be run to generate all inputs, including the final assembled input files for submission to the CarSim solver, but quit without performing the analyses. And similarly,
Figure 5.6. TTIâs CarSim wrapper program main flowchart.
54 Guidelines for Traversability of Roadside Slopes the program can be run to perform CarSim analyses with user provided input files, skipping input generation altogether. This flexibility was built into the program to allow running various selective small-scale studies to evaluate the effects of the different parameters, such as terrain friction, driver perception- reaction time (PRT). Additionally, this flexibility allows researchers to make small changes to road, event, or other files and analyze selective cases instead of performing analyses for the entire matrix each time. After reading the initial user input file, the program determines if CarSim input generation is needed. If needed, it enters into an inputs generation module, as shown in Figure 5.6. After generating the needed inputs (if needed), the program determines if analysis needs to be performed. If analysis is not needed, the program quits. Otherwise, the program sequentially loads each simulation case and submits it to the CarSim solver, applies contact forces and soil furrowing forces as needed during run time, until all the simulations have been performed. While performing each simulation, the wrapper program exchanges the coordinates of several points on the vehicleâs body with the CarSim solver to track and check for penetration with the terrain. Coordinates of these points are exchanged between the TTIâs wrapper program and the CarSim solver at each time step of the simulation. The wrapper program checks if a tracked vehicle body point has penetrated the local terrain, and if penetration is detected, it calculates the appropriate contact force needed to remove the penetration. The wrapper pro- gram submits the contact forces to the CarSim solver for applying to the vehicle body points being tracked using the CarSim solver exchange variables. The wrapper program also evaluates the extent of the vehicleâs side-slip angle for each tire during a simulation run. Similar to the contact algorithm, the wrapper program exchanges information about the tire side-slip angle at each time step of the simulation and applies appropriate lateral tire forces. The wrapper program also writes the outputs needed for post- processing the results of the simulation. 5.4.2 Inputs Generation Module If the user provides a table listing all of the simulation input files (simfiles) for the CarSim solver, the main program skips the inputs generation module. Otherwise, the module deter- mines the types of inputs the user is providing (in CarSimâs PARSFILE format for submitting directly to solver) and generates the rest based on other input parameters provided by the user. The overall flowchart of the inputs generation module is shown in Figure 5.7. There are four possible cases for inputs generation. Case 1. In this case, the user provides a table for all the road and events input files (PARSFILE) that need to be simulated using CarSim. The wrapper program does not create any of these files. It simply assembles all the final simulation files (simfiles) for each case, referencing appropriate road, event, and vehicle model files for final submission to the CarSim solver. Case 2. In this case, the user provides a table of all the event files and the wrapper program generates the road files and a table containing a list of all the road files generated. The pro- gram then assembles all simulations files (simfiles) for each case, referencing appropriate road, event, and vehicle model files for final submission to the CarSim solver. Case 3. In this case, the user provides a table of all the road/terrain files and the wrapper program generates the events files and a table containing a list of all the files generated. The program then assembles all simulations files (simfiles) for each case, referencing appropriate road, event, and vehicle model files for final submission to the CarSim solver. Case 4. In this case, the wrapper program generates all road and event files. It then assembles all simulations files (simfiles) for each case.
Figure 5.7. TTIâs CarSim wrapper program inputs generation module flowchart.
56 Guidelines for Traversability of Roadside Slopes The road files are generated by a separate subroutine in TTIâs wrapper program. The flowchart of this subroutine is shown in Figure 5.8a. The subroutine starts by reading a user input file containing information about the terrain/road parameters. These include information such as road length, vertical slope, widths and slopes of roadway, shoulders, foreslopes, ditch bottoms, and backslopes. Information on different types of surface coefficients is also read in this step. The subroutine then calculates the total number of road profiles needed based on the input parameters. It then generates these road profiles in the format needed by the CarSim solver. Similarly, the event files are generated by a separate subroutine in the wrapper program. Its flowchart is shown in Figure 5.8b. The subroutine starts by reading a user input file containing information about the different vehicle encroachment speeds, angles, and yaw rates. The informa- tion on different driver inputs to be used in generating the event files are also read at this point. (a) (b) Figure 5.8. Flowcharts for generating (a) terrain/road and (b) event inputs in TTIâs CarSim wrapper program.
Simulation Analysis 57 The subroutine then calculates the total number of event files needed based on the number of parameters read. It then generates these event files in a format needed by the CarSim solver. After generating the road and event files, the program generates or assembles a master simulation file (simfile) which contains links to all the road, event, and vehicle model files, along with other information needed for the analysis, such as start time, stop time, integration time step. This master file is what eventually gets submitted to the CarSim solver. After generating these input files, the control is returned to the main wrapper program, which, if requested, proceeds with the CarSim analyses as described earlier. The flowchart of TTIâs contact module is shown in Figure 5.9. While performing a simula- tion, the wrapper program interfaces with the CarSim solver to get the coordinates of all the vehicle body points being tracked for possible terrain penetration. It also gets the coordinates of the local terrain for these points and determines if a tracked vehicle point has penetrated. If no penetration is detected, no contact force is applied. However, if a vehicle body point penetrates the terrain, the program determines the contact forces needed to remove the penetration. The program determines the contact forces in the direction normal and tangent to the terrain. These forces are communicated to the CarSim solver, which applies them to the vehicle in the next integration time step. 5.4.3 Simulation Stopping Conditions The researchers coded several conditions for determining if a simulation should be stopped after the outcome of an encroachment case has been determined. This prevents the simulation from running longer than needed and saves time when a large number of simulations need to be performed. A simulation is stopped if any of the following conditions is met: 1. Vehicleâs CG comes back to its initial lateral position, indicating that the vehicle has returned to the roadway. 2. Vehicle travels beyond a specified lateral offset (set at 105 ft from the roadside edge of the travel lane). 3. Vehicleâs speed reduces below a specified minimum (set at 5 mph). 4. Vehicle rolls more than a specified maximum roll (set at 65 degrees). The vehicle is considered to have overturned at this point. 5. Vehicle pitches more than a specified maximum pitch (set at 90 degrees). The vehicle is considered to have overturned at this point. 6. Vehicle has traveled for more than 10 s without any other significant outcome occurring. In addition to the stopping conditions, the researchers also programmed several conditions that flag a simulation without stopping it. This can assist in evaluating the influence of different parameters on the overall stability of the vehicle, even if an overturn does not occur. These flagging conditions include the following: 1. Vehicle has rolled more than 55 degrees. 2. Vehicle has pitched more than 55 degrees. 3. Vehicle spins out (i.e., the forward velocity of the vehicle becomes zero or negative while it still has lateral velocity). 4. Vehicle has side slipped more than 20 degrees. 5.4.4 Simulation Outputs CarSim generates detailed output for each simulation case that includes calculated values for a large number of vehicle parameters as a function of time. In addition to this detailed
58 Guidelines for Traversability of Roadside Slopes Figure 5.9. Flowchart of TTIâs code for applying body-to-terrain contact with CarSim.
Simulation Analysis 59 simulation output for each case, there was a need to generate an overall simulation output table with key outcomes recorded for each simulation case and the associated terrain and driver input parameters. The output module of the wrapper program was coded to generate this aggregate output table that facilitates the use of bulk simulation results in further statistical analysis. The output module logs each run the terrain profile, driver input type, stopping condition that caused the simulation to terminate, vehicleâs maximum roll, maximum pitch, maximum lateral sliding velocity, and any flags described above. Table 5.1 shows the types of outputs recorded. Additionally, terrain and driver input are also logged. See Appendix C for more details. As mentioned previously, CarSim generates outputs for a large number of parameters for each individual simulation. Because most of these vehicle parameters are not of any interest to this research, the researchers use a separate program (available with CarSim) to extract more relevant output parameters. These include the vehicle CGâs path, velocity, acceleration, slip angle, roll, pitch, yaw, tire forces, tire side-slip angles, and others, as a function of time. Table 5.2 shows the list of output parameters extracted for each simulation case (more parameters can be extracted if needed). The researchers have prepared a standalone user guide for TTIâs wrapper program that pro- vides lists of these inputs and outputs, along with a description of the reported parameters and their units (presented in Appendix C). The user guide also describes some of the key criteria used by the wrapper program in running the simulation analyses. This guide was useful in commu- nicating simulation results between researchers generating simulation results and those using the results for further analysis. 5.5 Soil Furrowing Forces The default CarSim tire model determines lateral force on each tire using the vertical load and the side-slip angle of the tire. Tire properties include a series of graphs plotting the lateral tire force as a function of the slip angle of the tire for different values of vertical load (see Figure 5.10). These plots are provided by CarSim and are generated using a known friction Label Description Run No. Simulation case number. Unique for a single-vehicle type only. Termination Describes if the simulation terminated normally, or if the simulation crashed. It has values of âNormalâ or âERRORâ. Outcome Stopping condition that caused the run to stop. It has the following values: - Time Exceeded - Returns - Stops - Gone Far - Overturns Description A brief description of the outcome. High Roll Flag for high roll (> 55 degrees). It has value of 1 or 0 (1 = high roll). Max Roll Maximum vehicle roll during simulation (degree). High Pitch Flag for high pitch (> 55 degrees). It has value of 1 or 0 (1 = high pitch). Max Pitch Maximum vehicle pitch during simulation (degree). Side-slip Flag for side slipped vehicle (> 20 degrees). It has value of 1 or 0 (1 = vehicle sideslips). Max Slip Maximum side-slip angle during simulation (degree). Spinout Flag for vehicle spinout. It has value of 1 or 0 (1 = vehicle spins out). Max Lat Vel (km/h) Maximum lateral vehicle velocity during simulation (km/h). Max Lat Travel (m) Maximum distance vehicle travels laterally from edge of roadway (m). Xcg at Sim Stop (m) X-coordinate of the vehicleâs sprung mass CG when simulation stops (m). Ycg at Sim Stop (m) Y-coordinate of the vehicleâs sprung mass CG when simulation stops (m). Table 5.1. Simulation outcomes logged in the aggregate simulation results table.
60 Guidelines for Traversability of Roadside Slopes Label Description Time Simulation time (s) XCG_SM X-coordinate of the vehicleâs sprung mass CG in global coordinates (m) YCG_SM Y-coordinate of the vehicleâs sprung mass CG in global coordinates (m) ZCG_SM Z-coordinate of the vehicleâs sprung mass CG in global coordinates (m) VxBf_SM X-component velocity for vehicleâs sprung mass CG in body-fixed coordinate system (km/h) VyBf_SM Y-component velocity for the vehicleâs sprung mass CG in body-fixed coordinate system (km/h) VzBf_SM Z-component velocity for the vehicleâs sprung mass CG in body-fixed coordinate system (km/h) AxBf_SM X-component acceleration for the vehicleâs sprung mass CG in body-fixed coordinate system (g) AyBf_SM Y-component acceleration for the vehicleâs sprung mass CG in body-fixed coordinate system (g) AzBf_SM Z-component acceleration for the vehicleâs sprung mass CG in body-fixed coordinate system (g) Pitch Vehicleâs Euler pitch (degree) Roll_E Vehicleâs Euler roll (degree) Yaw Vehicleâs Euler yaw (degree) YawLocal Vehicleâs Euler yaw offset to zero at start of simulation (degree) Beta Side-slip angle of vehicle based on Vx and Vy (degree) Alpha_L1 Tire L1 lateral slip (L/R is Left/Right, 1/2 is front/rare axle) (degree) Alpha_L2 Tire L2 lateral slip (degree) Alpha_R1 Tire R1 lateral slip (degree) Alpha_R2 Tire R2 lateral slip (degree) Fx_L1 Tire L1 longitudinal force (N) Fx_L2 Tire L2 longitudinal force (N) Fx_R1 Tire R1 longitudinal force (N) Fx_R2 Tire R2 longitudinal force (N) Fy_L1 Tire L1 lateral force (N) Fy_L2 Tire L2 lateral force (N) Fy_R1 Tire R1 lateral force (N) Fy_R2 Tire R2 lateral force (N) Fz_L1 Tire L1 vertical force (N) Fz_L2 Tire L2 vertical force (N) Fz_R1 Tire R1 vertical force (N) Fz_R2 Tire R2 vertical force (N) Table 5.2. Simulation output data saved for each simulation case. Figure 5.10. Tire properties in CarSim (lateral force is plotted as a function of the slip angle for different vertical tire loads).
Simulation Analysis 61 coefficient between the tire and the tire testing machineâs surface. During a simulation, the absolute lateral friction force from the test plots is adjusted based on the local terrain friction coefficient before being applied to the vehicle. While the default method of applying lateral forces to the tires is adequate for most surfaces and conditions, the researchers added a capability to apply soil furrowing forces using higher lateral friction force. This accounts for prolonged side-slipping of the vehicle when it is not on the roadway and therefore has a potential for soil-tripped rollover due to soil furrowing. Using an increased lateral friction coefficient as a surrogate for soil furrowing in a vehicle dynamics model is somewhat complicated. As the vehicle starts to side-slip on soil, the fur- rowing forces build up gradually. The amount of lateral force applied on the vehicle due to soil furrowing is a function of many factors, and their relationship is not completely understood at this time. Among these factors are the properties of the soil (dry/wet, well compacted/loose, etc.), vehicle mass distribution and CG, vehicle side-slip angle, vehicle lateral speed, duration of side-slipping, and the distance the vehicle has side slipped. Many previous research studies have effectively used increased lateral coefficient to model lateral tire forces due to soil furrowing (11, 13, 16, 39). In most of these studies, a friction ellipse model has been used to determine the lateral friction coefficient as a function of the tireâs lateral slip angle. At no lateral slip, the default terrain friction coefficient is used, which forms the minor radius of the ellipse. As the tireâs lateral slip increases, a higher lateral friction coefficient is used such that at a 90-degree slip, the major radius of the ellipse is used, which is the maximum lateral friction coefficient for the terrain. The researchers initially investigated incorporating a different model for determining the lateral friction coefficient that takes into account the length and duration of side-slipping in addition to the side-slip angle. In 1998, Cooperrider et al. performed a series of crash tests where different vehicles were made to side-slip 90 degrees on soil at different speeds (40). Results of the testing were later used by Grimes et al. to develop simulation models that varied lateral friction of the terrain based on the distance a vehicle had side slipped. Grimes et al. modeled the soil terrain as adjacent surface patches, each having a different friction coefficient (39). The length of the adjacent surfaces and their respective friction coefficients were varied to calibrate the terrain for a particular test. Terrains were built in this manner for two of the crash tests. However, both terrains differed significantly from each other and there was no general method for determining the length and friction coefficient of adjacent surface patches. The researchers looked into formulating a generalized method using the crash test data and modeling technique used by Grimes et al. While the number of crash tests conducted by Cooperrider et al. was very limited, the researchers wanted to evaluate if the data could be used to formulate a generalized method, which, in addition to taking into account the side-slip angle, increases the lateral friction coefficient as a function of the distance a vehicle has side slipped. This would have been an enhancement over the friction ellipse model, which only takes into account the side-slip angle to determine the surrogate lateral terrain friction. However, due to very limited test data and the complexity of the soil-trip rollover phenomenon, a generalized method that incorporates the extent of later sliding could not be formulated. Results of the crash tests conducted by Cooperrider et al. were dependent on the vehicleâs initial velocity, vehicle and the soil types used, and were only valid for the 90-degree lateral sliding. It was not straight- forward to determine how these results could be extrapolated for use with different vehicle types and for side-slip angles of other than 90 degrees. Thus even though the researchers spent some time exploring how the above mentioned studies could be applied for this project, a generalized and robust method could not be developed. The researchers then resorted to using the friction ellipse model for determining the effective lateral friction coefficient for incorporating the tire forces due to soil furrowing.
62 Guidelines for Traversability of Roadside Slopes The friction ellipse method was coded into the wrapper program, which interacts with CarSim during run time to determine if the vehicle is traversing a terrain that is marked as soil, and if so, calculates and applies lateral forces to the tire using the friction ellipse method. The effective lateral friction coefficient, Âµsoil, is determined using the formulation shown in Figure 5.11. The researchers coded the ability to incorporate soil furrowing forces only when the vehicle is traversing a terrain marked by the user as soil. This implies that when the vehicle is on a paved road or shoulder, the default CarSim friction formulation is used, which is more appro- priate for the non-soil terrains. 5.6 Sensitivity Studies Prior to performing simulations of the entire simulation matrix, it was important to evaluate the sensitivity of some of the parameters. These included the maximum lateral friction coef- ficient to incorporate forces due to soil furrowing (Âµsoil), the PRT for some of the driver inputs, and the encroachment yaw rate of the vehicle for non-tracking encroachments. In this section, the evaluation of the sensitivity to perception-reaction time and the yaw rate for non-tracking encroachment is presented. An evaluation of the maximum lateral friction coefficient is pre- sented in the next section. A small sensitivity study was performed using the roadside V-ditch profile shown in Figure 5.12. For a meaningful comparison of simulation results, the same terrain profile was used for all the simulations but other parameters varied. Simulations were performed with encroachment Figure 5.11. Friction ellipse model for modeling tire forces due to soil furrowing. Shoulder 6 ft, 4% slope Foreslope 16 ft, 1V:6H Backslope 16 ft, 1V:3H Figure 5.12. Roadside ditch profile used for sensitivity analysis.
Simulation Analysis 63 speeds of 45, 55, and 65. Encroachment angles of 10, 20, and 30 degrees were used. Simulations were performed with the MASH pickup truck (P2270) and small passenger car (1100C) vehicles. Following five driver input types were used in the sensitivity study: 1. No input (tracking); 2. Panic steer, no brake (tracking); 3. Panic steer and full brake (tracking); 4. Constant steer, no brake (non-tracking); and 5. Constant steer and full brake (non-tracking). The rate for panic steer was determined based on NHTSAâs Fishhook maneuver guidelines. The recommended steering rate of 720 degrees/s was used to develop a maximum steer of 360 degrees after passage of the perception-reaction time. A PRT of 0.5 s delay was used in the simulations, except when sensitivity to perception-reaction time was being evaluated. A yaw rate of 15 degrees/s was used for non-tracking encroachments, except when sensitivity to yaw rate was being evaluated. Once a simulation was performed, its outcome was categorized into one of the following four categories: 1. Stable, 2. Spinout, 3. Marginal, or 4. Overturn. If the vehicle rolled or pitched more than the 65 degrees, it was categorized as an overturn. If it had a higher than 55-degree roll or pitch, but did not overturn, it was categorized as marginal. If the vehicle had zero or negative forward velocity while it still had some lateral velocity, it was categorized as a spinout. All other simulations were categorized as stable. Results of the sensitivity study are presented next. 5.6.1 Perception-Reaction Time Previous research used 1 s as the appropriate PRT, which is the time delay used after leaving the edge of the travel lane and before applying any steering or braking input (10). The researchers evaluated the sensitivity to the PRT values of 1 and 0.5 s. A value greater than 1 s was not considered as it makes the driver input very similar to the âno inputâ category for most encroachment speeds and angles. Simulations were performed with the âpanic steer, no brakeâ and âpanic steer and brakeâ driver inputs only. These were the only driver inputs that required the inclusion of the PRT. Results of the analyses are summarized in Figure 5.13. The results are not very sensitive to the PRT and both PRT values result in very similar outcomes. The researchers therefore selected the PRT of 1 s as in previous research. 5.6.2 Encroachment Yaw Rate Analysis of the crash data can be used to determine if a vehicle was tracking or non-tracking at the time of the encroachment. However, the yaw rate with which the vehicle encroached cannot be determined. Previous studies have used a yaw rate of 15 degrees/s (10). The researchers selected this as the base value and performed simulations with yaw rates of 10, 15, and 20 degrees/s to evaluate the sensitivity of this parameter. Simulations were performed for non-tracking encroachments only. Results of the analyses are summarized in Figure 5.14. While there are some changes between the different yaw rates, the overall results are not significantly different. The researchers therefore selected the yaw rate of 15 degrees/s to model non-tracking encroachments, as in previous research.
64 Guidelines for Traversability of Roadside Slopes Figure 5.13. Results of the sensitivity analyses for determining PRT. Figure 5.14. Results of the sensitivity analyses for determining encroachment yaw rate.
Simulation Analysis 65 5.7 Evaluation of Friction Model and Lateral Coefficient As mentioned previously, the researchers used the friction ellipse model to apply soil furrow- ing forces to the vehicleâs tires. A key parameter for this model is the lateral friction coefficient, which controls the lateral force applied to the vehicle as it side-slips on the soil terrain. The researchers evaluated the sensitivity of the lateral friction coefficient by performing a small-scale simulation study. This evaluation was geared toward answering the following questions: 1. Does the friction ellipse model exhibit different behavior compared to CarSimâs default tire-terrain friction model? 2. Can the surrogate lateral tire forces due to soil furrowing be adequately adjusted using the friction ellipse model and variation in the lateral friction coefficient? 3. What is the appropriate value of the maximum lateral friction coefficient that should be used with the friction ellipse model to act as a surrogate for applying higher lateral forces due to soil furrowing? For evaluating the friction ellipse model and the lateral friction coefficient value, the researchers performed the simulations on a flat terrain. Rollovers usually occur due to a number of contributing reasons, which include terrain friction forces, vehicle encroachment angle, interaction of the vehicleâs body with the terrain, and the slope of the terrain being traversed. Because the main focus of this evaluation was the forces applied by the friction ellipse model, the researchers decided to eliminate all other factors that can contribute to a rollover by selecting a flat terrain. Furthermore, some estimates of the probability of rollover on a flat terrain, which are based on crash data, could be used to select an appropriate value of the maximum lateral friction coefficient that results in a similar probability of rollovers in the simulations. The simulations were thus performed on a flat terrain with the MASH small passenger car and pickup truck vehicles. Simulations were performed with six initial speeds of 25, 35, . . . , 75 mph. The encroachment angle became irrelevant because a flat terrain was used. A total of four driver inputs were used. The âno steer or brakeâ input wasnât used as it also became irrelevant on a flat terrain. The four inputs included were: 1. Tracking, panic return-to-road steer after a PRT of 1 s; 2. Tracking, panic return-to-road steer and ABS brakes after a PRT of 1 s; 3. Non-tracking, constant steer angle and full ABS brakes, with initial yaw rate of 15 degrees/s; and 4. Non-tracking, constant steer angle, with initial yaw rate of 15 degrees/s. For the parameters defined above, a total of 24 simulations needed to be performed for each vehicle type, as numbered in Figure 5.15. The simulation study was further divided into 12 cases (1a, 1b, 2a, 2b, . . . , 6a, 6b) based on the vehicle type and the maximum lateral friction coefficient used in the friction ellipse model. When using the CarSim friction model, the longitudinal and lateral friction coefficients were 0.5, which is a typical value for a dry grassy surface. When using the friction ellipse model, the longitudinal friction coefficient was 0.5. The lateral friction coefficient was determined by the friction ellipse with minor radius of 0.5 (coefficient at no side-slipping condition) and major radius, whose value was changed for the different cases between 1.2, 2.0, 2.1, 2.2, and 2.8 (i.e., the maximum lateral friction coefficient at 90 degree side-slipping, see Figure 5.15 for the simulation matrix used).
66 Guidelines for Traversability of Roadside Slopes For each of the cases in Figure 5.15, all 24 simulation runs were performed to compare the results. In examining the results of the simulations, the researchers evaluated the variations in lateral tire forces resulting from the tire-to-terrain contact when different friction models or coefficients were used. The researchers also evaluated the influence of the friction coefficient values on the number of rollovers for selecting an appropriate lateral friction coefficient. Key findings of the simulation study are presented next. 5.7.1 Effectiveness of the Friction Ellipse Model The researchers compared the lateral tire forces applied to the vehicle during the simulation as a result of the tireâs interaction with the terrain. Lateral tire forces for simulations performed with CarSimâs default friction model were compared to the simulations performed with the friction ellipse model. At a low speed and a relatively less aggressive driver input, the differences between the two friction models are not that significant. This is expected because at lower speeds, the vehicle cannot undergo significant lateral sliding, which is when the CarSim friction model and the friction ellipse model are expected to be different. An example of this is shown in Figure 5.16, which compares lateral tire forces on the front left tire that has the largest lateral friction force. Forces are shown for both small car and pickup truck vehicles for the different maximum lateral friction coefficients (MuY). In this case, the simulation starts with a tracking vehicle that has an initial speed of 25 mph. Panic return-to-road steer is applied after a PRT of 1 s. The results of the CarSim friction model and the friction ellipse model are very similar, even though the force from the CarSim friction model is slightly less than that from the friction ellipse model, which uses a higher lateral coefficient whose value depends on the side-slip angle. Because of the differences in the mass of the small car and the pickup truck, the lateral tire forces, which are a function of vehicle mass, band around each vehicle type. This is also as expected. Run Number Speed (mph) Driver Input* Simulation Cases for Different Vehicle Types and Friction Coefficients Case Number Vehicle Type Lateral Friction Coefficient Case 1a Pickup Truck 0.5** Case 1b Small Car 0.5 ** Case 2a Pickup Truck 1.2 Case 2b Small Car 1.2 Case 3a Pickup Truck 2.0 Case 3b Small Car 2.0 Case 4a Pickup Truck 2.8 Case 4b Small Car 2.8 Case 5a Pickup Truck 2.2 Case 5b Small Car 2.2 Case 6a Pickup Truck 2.1 Case 6b Small Car 2.1 *Driver inputs were numbered as follows: 1. tracking, panic return-to-road steer after a PRT of 1 s 2. tracking, panic return-to-road steer and ABS brakes after a PRT of 1 s 3. non-tracking, constant steer angle and full ABS brakes, with initial yaw rate of 15 degrees/s 4. non-tracking, contact steer angle, with initial yaw rate of 15 degrees/s **CarSimâs default friction model was used in these cases. All other cases used the friction ellipse model. 1 25 1 2 2 3 3 4 4 5 35 1 6 2 7 3 8 4 9 45 1 10 2 11 3 12 4 13 55 1 14 2 15 3 16 4 17 65 1 18 2 19 3 20 4 21 75 1 22 2 23 3 24 4 Figure 5.15. Simulation matrix for the evaluation of the friction ellipse model and determination of the lateral friction coefficient.
Simulation Analysis 67 When the speed is increased, or if the driver input is more aggressive, the differences between the CarSim friction model and friction ellipse model become more prominent. An example is shown in Figure 5.17 for a vehicle starting with non-tracking conditions, initial yaw rate of 15 degrees/s, initial speed of 35 mph, constant steer angle, and full ABS brakes applied through- out the simulation. In this case, the differences in lateral forces applied by the CarSim friction model and the friction ellipse model are more prominent as expected. These lateral forces increase with the increase in the MuY as expected. Based on these observations, it can be concluded that the friction ellipse model does exhibit different behavior compared to the CarSimâs default tire-terrain friction model, and the results are as expected. Another objective of the evaluation of the friction ellipse model was to determine if the lateral tire forces due to side-slipping can be adequately adjusted by varying the MuY used in the friction ellipse model. Results of the simulations show that lateral tire forces can be adequately controlled by varying MuY. An example of this is shown in Figure 5.18. Lateral tire forces are shown for the small car and the pickup truck. The vehicle starts with non-tracking conditions, with initial yaw rate of 15 degrees/s, initial speed of 55 mph, constant steer angle, and full ABS brakes applied throughout the simulation. As the maximum lateral friction coefficient increased, the lateral tire force increased for both vehicles and was significantly different for different values of MuY. With friction coefficients of 1.2 and 2.0, the small car and the pickup truck do not roll over, even though the maximum roll angle increased for both vehicles with an increase in the friction coefficient. With a friction coefficient of 2.8, both vehicles rolled over. Figure 5.16. Lateral tire forces for small car and pickup truck with 25 mph initial speed, tracking initial conditions, and panic return-to-road steer after a PRT of 1 s.
68 Guidelines for Traversability of Roadside Slopes Figure 5.17. Lateral tire forces for small car and pickup truck with 35 mph initial speed, non-tracking initial conditions, constant steer angle, and full ABS brakes. Figure 5.18. Lateral tire forces for small car and pickup truck with 55 mph initial speed, non-tracking initial conditions, constant steer angle, and full ABS brakes.
Simulation Analysis 69 Results of the simulations demonstrate that the maximum lateral friction coefficient value can be used to adjust the maximum lateral tire force during side-slipping, which implies that it can successfully act as a surrogate for soil furrowing forces. 5.7.2 Selection of Appropriate Lateral Friction Coefficient Using the crash data, it is difficult to determine the probability of rollover on a flat surface when a vehicle leaves the roadway. This is simply because many unintentional roadside encroach- ments do not result in a crash, and thus donât get reported. Even among the encroachments that result in a crash, many donât get reported. This is also supported by field studies of damaged roadside features. While a deterministic rollover probability cannot be found, many researchers have used crash data to speculate this probability. The research community agrees on this prob- ability being significant, but there are disagreements about its magnitude. A low-end estimate is around 10 percent (40, 41). Simulations performed with the maximum lateral friction coefficient of 1.2 did not result in any rollover on a flat terrain. Thus there was a need to determine an appropriate value of the lateral friction coefficient that results in close to 10 percent rollovers on a flat terrain. For this purpose, the researchers compared the number of rollovers for different values of maximum lateral friction coefficient. The results are shown in Figure 5.19. Figure 5.19a shows the overall percentages and Figure 5.19b shows the actual numbers of rollovers observed in the simulations. While no rollovers occur for a maximum lateral friction coefficient of 1.2, three (13 percent) pickup truck rollovers occur with a friction coefficient of 2.0. With maximum lateral friction coefficient of 2.1, there is one (4 percent) rollover with the small car, but the number of pickup truck rollovers increases to 7 (29 percent). At maximum lateral friction coefficient of 2.2, even higher numbers of rollovers are observed (38 percent for the pickup truck and 17 percent for the small car). (a) (b) 0 13 29 38 0 0 4 17 0 20 40 60 80 100 1.2 2 2.1 2.2 Ro llo ve r P er ce nt ag e Maximum Lateral Friction Coefficient Pickup Small Car 0 3 7 9 0 0 1 4 0 6 12 18 24 1.2 2 2.1 2.2 N um be r o f R ol lo ve rs Maximum Lateral Friction Coefficient Pickup Small Car Figure 5.19. Rollover (a) percentage and (b) number for maximum lateral friction coefficient values.
70 Guidelines for Traversability of Roadside Slopes Results of the simulation indicate that a small increase in the maximum lateral friction coefficient beyond 2.0 results in significant increase in the number of rollovers, which is unrealistic when compared to the estimates of rollovers on flat terrains. With the maximum lateral friction coefficient of 2.0, the percentage of rollovers is more acceptable. Based on the results of this detailed evaluation, 2.0 was selected as the appropriate value for the maximum lateral friction coefficient in the friction ellipse model (as presented in Figure 5.11). 5.8 Simulation Matrix The roadside slope design variables and their values that were evaluated using simulation analyses are presented in the simulation matrix in Figure 5.20. Also presented are the encroach- ment conditions and the vehicle types used. The simulation matrix comprises five roadside slopes ranging from relatively flat 1V:10H to very steep slope of 1V:2H. The width of the slope can influence the outcome of an encroachment as it determines the duration and the distance a vehicle traverses on the slope. Furthermore, change in the terrainâs slope at the end of the foreslope affects the kinematics of the encroach- ing vehicle. For this reason, four foreslope widths were selected as shown in Figure 5.20. These were 8, 16, 32, and an âinfiniteâ width. The âinfiniteâ foreslope width was selected to model encroachments in which the vehicle did not interact with the flat bottom of the slope. In the simulation analyses, one of the desired stopping conditions for the simulations was if the vehicle reached 100 ft beyond the edge of the shoulder without encountering a rollover. In such cases, the vehicle was considered to have traversed the slope without an adverse effect. The âinfiniteâ foreslope width in the simulations was modeled with a 105 ft width, which was slightly greater than the desired 100-ft stopping condition described above. In the simulation models, the area after the slope was modeled as a flat terrain. Three different shoulder widths were selected to evaluate the influence of the shoulder. Two of these were paved shoulders and one was a relatively wide 8-ft shoulder that was half paved and half turf. All shoulders had a constant 4 percent downward slope. Encroachment simulations were set up such that the vehicleâs encroaching corner enters the shoulder at the simulation start time. Simulations were performed with the four vehicle types listed in the simulation matrix. Six encroachment speeds and angles were selected as shown in Figure 5.20. These ranged from Variables Example Conditions Roadside Geometry â¢ Slope: 1V:10H, 1V:6H, 1V:4H, 1V:3H, and 1V:2H â¢ Slope width: 8, 16, 32 ft, and âinfiniteâ Shoulder Type and Width â¢ 4% cross slope â¢ Paved (width: 2 and 6 ft) â¢ Paved+turf [width: 8 ft (4ft paved and 4ft turf)] Vehicle Type â¢ Small passenger car (MASH 1100C, Kia Rio) â¢ Pickup truck (MASH 2270P, Dodge Ram) â¢ Midsize Sedan (2001 Ford Taurus) â¢ Midsize SUV (2002 Ford Explorer) Encroachment Speed 25, 35, 45, 55, 65, 75 mph Encroachment Angle 5, 10, 15, 20, 25, and 30 degrees Tracking/Non-tracking â¢ Tracking â¢ Non-tracking with yaw rate of 15 degrees/s Driver Control Input â¢ No input â¢ Panic return-to-road steer â¢ Combined return-to-road steer and full ABS braking Figure 5.20. Simulation matrix.
Simulation Analysis 71 slower speeds and angles of 25 mph and 5 degrees to higher speeds and angles of 75 mph and 30 degrees, respectively. The simulation matrix included both tracking and non-tracking vehicle encroachments. The tracking and non-tracking encroachments, along with the different driver control inputs, lead to the five driver input combinations listed in Figure 5.21. Driver Input 1 was essentially a driver who was asleep or impaired who did not apply any driver input. Driver Inputs 2 and 3 were tracking encroachments in which the driver reacted after a PRT of 1 s. The rate for panic steer was determined based on NHTSAâs Fishhook maneuver guidelines, which has a recommended steering rate of 720 degrees/s. This rate was used to develop a maximum steer of 360 degrees after passage of perception-reaction time. Inputs 4 and 5 were non-tracking encroachments. In this case the driver was assumed to have already reacted to some event on the roadway and had applied the steering and/or braking inputs prior to encroaching. Combinations of all the variables listed in the simulation matrix resulted in a total of 43,200 unique cases that were simulated in this project. 5.9 Simulation Results After performing the simulations, the researchers analyzed the results to evaluate general trends indicated by the simulation data. The combined and unweighted results of these simulations are presented in Figures 5.22 through 5.27. Prior to using these results for devel- oping the traversability guidelines, the researchers deemed it important to analyze the results and verify that general trends from the results were logical. The results presented in Figures 5.22 through 5.27 are unweighted. In these figures, every simulation case carries the same weight and the individual results have not been weighted according to the probability of occurrence in the real world. So for example, an encroachment with an SUV at 75 mph speed and 30-degree angle carries the same weight as an encroachment at 45 mph speed and 15-degree angle, even though the latter is expected to be more likely to occur in the real world. These results were later on weighted according to the probability of occurrence before developing the traversability guide- lines, and this process will be described in Chapter 7. Even in the unweighted form, simulation results and trends presented in Figures 5.22 through 5.27, provide meaningful insights and serve as an overall sanity check on the simulation results. The researchers plotted the influence of various parameters on the outcome of the encroachments. Encroachment outcomes were divided into following five categories. â¢ Returns. The vehicle returns to the roadway. â¢ Overturns. The vehicle rolls over or pitches over. Driver Input Details 1 No input (tracking) 2 Panic steer, no brake (tracking) After a PRT of 1 s delay on leaving the edge of travel lane, a 360-degree steer toward roadway is applied at the rate of 720 degree/s. 3 Panic steer and full ABS brake (tracking) After a PRT of 1 s delay on leaving the edge of travel lane, a 360-degree steer toward roadway is applied at the rate of 720 degree/s. 4 Constant Steer, no brake (non-tracking) Vehicle encroaches with yaw rate of 15 degree/s (yawing toward roadway), with a constant steer angle of 360 degrees. 5 Constant steer and full ABS brake (non-tracking) Vehicle encroaches with yaw rate of 15 degree/s (yawing toward roadway), with a constant steer angle of 360 degrees. And ABS brakes fully applied. Figure 5.21. Driver inputs for encroachment simulations.
72 Guidelines for Traversability of Roadside Slopes â¢ Marginal Rolls. The vehicle does not roll over, but has a roll angle of greater than 55 degrees. â¢ Spinouts. The vehicle yaws and spins out such that it has a negative forward velocity. â¢ Others. These included cases where the vehicle does not return to roadway, but it also does not undergo any of the other negative outcomes. In these encroachments, the vehicle is able to traverse the slope and reach the bottom safely. Even though the researchers marked overturns to include rollovers and pitch-overs, no pitch-overs resulted in the simulations. Thus overturn essentially refers to rollovers in the results presented here. Parameters whose influence was evaluated were roadside slope, shoulder width, slope width, encroachment speed, encroachment angle, and vehicle type. Two types of charts were created for each of these parameters to highlight their influence. In the first chart, percentages of returns, overturns, and marginal rolls were compared for different parameters. Influence of Slope on Simulation Outcomes (%) All 1V:2H 1V:3H 1V:4H 1V:6H 1V:10H Returns 30.11 20.67 26.62 29.59 34.72 38.95 Overturns 14.38 27.96 16.28 11.93 8.65 7.08 Marginal Rolls 0.41 0.98 0.38 0.27 0.20 0.22 Spinouts 16.16 11.57 16.84 17.81 17.74 16.82 Others 38.94 38.81 39.87 40.39 38.69 36.93 Total Simulations 43200 8640 8640 8640 8640 8640 Figure 5.22. Influence of roadside slope.
Simulation Analysis 73 To highlight the key trends in rollovers, the others category was not plotted. Similarly, spinouts were not plotted in the first plot. Most vehicles that roll over, spin out at some point prior to the rollover event. In other words, spinouts may turn into rollovers for more aggressive slope or encroachments conditions. Thus spinouts were evaluated separately in combination with the rollovers. This was done in the second chart shown in the figures for each of the parameters. The influence of roadside slope is shown in Figure 5.22. The percentage of returns increases with decreasing slope, as can be seen from the top plot. Similarly, percentage of overturns increases with the increase in the roadside slope. A significant jump in rollovers can be seen when slope is increased from 1V:3H to 1V:2H. Rollover percentages are more or less the same for the flatter 1V:6H and 1V:10H slopes. In the bottom plot, it can be seen that the sum of spinouts, overturns, and marginal rolls increases with the increase in the slope. However, as the slope increases, a significantly greater portion of the spinouts turn into overturns. The influence of shoulder width and type is shown in Figure 5.23. The 2- and 6-ft shoulders were modeled as paved. The 8-ft shoulder was modeled as half paved and half turf. These unweighted plots show very little influence of the shoulder on the overall results. Slightly higher overturns and spinouts were observed for the 2-ft shoulder. This is likely due to the fact that with the smaller shoulder, the vehicle stays longer on the sloped terrain compared to the wider shoulders, which can lead to greater instabilities. For the same reason, the percentage of returns is slightly less for the 2-ft shoulder. Because some of the steering and braking inputs are applied after a PRT of 1 second, with the smaller 2-ft shoulder, the vehicle travels much farther on the slope in the first second and thus it is more difficult for the vehicle to recover and return to the roadway in subsequent steering and braking. The influence of the slope width is shown in Figure 5.24. The terrain was modeled as flat after the width of the roadside slope. It can be seen from the top chart that the percentage of overturns increases when going from 8- to 16-ft wide slope. The rollover percentages remain more or less the same for 16- and 32-ft wide slopes. With the infinite slope, there is a significant reduction in the number of rollovers. A close evaluation of the simulation results revealed that the inter action of the vehicle with the slopeâs flat bottom resulted in a destabilizing effect on the vehicle in most cases. The vehicle was typically side-slipping and yawing out on the slope when it suddenly interacted with the flat bottom, which then helped trip the vehicle to cause a rollover. For the 8-ft wide slope, the vehicle did not traverse on the slope long enough to have significant side-slipping and yawing. Thus the number of rollovers for the 8-ft wide slope was less than the 16-ft wide slope. For the 16- and 32-ft wide slopes, the rollover percent- ages were very close. And because there was no interaction with the slope bottom for the infinite slope, the percentage of overturns was significantly reduced as there was no abrupt destabilization of the vehicle. It can also be seen from Figure 5.24 that the number of returns reduced as the width of the slope increased. This is because the wider the slope, the more difficult it was for the vehicles to recover and drive back up the slope to reach the roadway. The influence of the encroachment speed is shown in Figure 5.25. As the encroachment speed increases, the percentages of returns decrease, while the percentages of overturns increase. It can also be seen that the percentages of overturns and spinouts have a significant jump from 35 to 45 mph. The overturns also jump significantly from 45 to 55 mi/h. However, the increase in overturns and spinouts diminishes when speed is increased further. This is expected because initially the increase in speed had significant influence in causing rollovers, but as more and more marginal encroachments converted to rollovers because of the increase in speed, the effects of further speed increase tapered off.
74 Guidelines for Traversability of Roadside Slopes Influence of Shoulder Width/Type on Simulation Outcomes (%) 2-ft. 6-ft. 8-ft. Returns 27.28 31.30 31.75 Overturns 15.47 13.88 13.81 Marginal Rolls 0.42 0.36 0.45 Spinouts 17.50 15.49 15.48 Others 39.33 38.97 38.51 Total Simulations 14400 14400 14400 Figure 5.23. Influence of shoulder width.
Simulation Analysis 75 Influence of Slope Width on Simulation Outcomes (%) 8-ft 16-ft 32-ft Infinite Returns 35.10 31.27 29.15 24.93 Overturns 12.36 17.96 17.34 9.86 Marginal Rolls 0.30 0.45 0.54 0.35 Spinouts 14.26 14.12 16.69 19.56 Others 37.98 36.19 36.28 45.31 Total Simulations 10800 10800 10800 10800 Figure 5.24. Influence of slope width.
76 Guidelines for Traversability of Roadside Slopes Influence of Encroachment Speed on Simulation Outcomes (%) 25 mi/h 35 mi/h 45 mi/h 55 mi/h 65 mi/h 75 mi/h Returns 41.42 40.89 33.93 26.65 20.33 17.44 Overturns 0.88 3.65 10.94 21.69 24.74 24.39 Marginal Rolls 0.01 0.11 0.61 0.43 0.53 0.76 Spinouts 2.54 8.81 23.61 22.19 20.79 19.00 Others 55.15 46.54 30.90 29.03 33.61 38.40 Total Simulations 7200 7200 7200 7200 7200 7200 Figure 5.25. Influence of encroachment speed.
Simulation Analysis 77 Influence of Encroachment Angle on Simulation Outcomes (%) 5 deg. 10 deg. 15 deg. 20 deg. 25 deg. 30 deg. Returns 67.08 45.65 27.99 18.31 12.32 9.32 Overturns 3.68 10.96 18.14 20.53 17.65 15.33 Marginal Rolls 0.01 0.18 0.36 0.51 0.64 0.75 Spinouts 4.82 13.47 19.76 21.79 20.67 16.43 Others 24.40 29.74 33.75 38.86 48.72 58.17 Total Simulations 7200 7200 7200 7200 7200 7200 Figure 5.26. Influence of encroachment angle. The influence of the encroachment angle is shown in Figure 5.26. As the angle increases, the percentages of returns decrease. The percentages of overturns and spinouts initially increase with increasing angle, but decline after 20 degrees. As the encroachment angle increases beyond 20 degrees, vehicles are quicker to travel to the bottom of the slope than to traverse the slope, which results in a reduction in overturns. The influence of vehicle type, in unweighted form, is shown in Figure 5.27. Pickup trucks have a higher percentage of overturns compared to small cars and midsize sedans. But SUVs have more than twice the number of overturns than pickup trucks. In the bottom plot the combined percentages of spinouts and overturns are roughly the same for the different vehicle types. However, due to inherent vehicle design characteristics, more of the pickup truck and SUV spinouts result in a rollover compared to the small car and midsized sedan.
78 Guidelines for Traversability of Roadside Slopes In conclusion, the results of the simulations showed trends that are intuitive with some interesting insights that have been described. For developing the slope traversability guidelines, these results were weighted according to their probabilities of occurrence in the real world. This is described in Chapter 7. Influence of Vehicle Type on Simulation Outcomes (%) Pickup Truck Small Car Midsize Sedan (Ford Taurus) SUV (Ford Explorer) Returns 28.50 31.41 31.85 28.68 Overturns 13.75 5.62 8.12 30.03 Marginal Rolls 0.36 0.37 0.28 0.62 Spinouts 18.06 25.15 18.14 3.27 Others 39.33 37.45 41.59 37.37 Total Simulations 10800 10800 10800 10800 Figure 5.27. Influence of vehicle type.