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55 CHAPTER 5. SIMULATION ANALYSIS 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 discussion on 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 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 final selection of such code-model 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 due to the fact the 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. It is the source of all disturbance forces that are applied to the vehicle under 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 of the vehicle in order to accurately capture the motion of the vehicle during the slope traversal. Driver's reaction is one of the most significant factors that can affect the likelihood of vehicle rollover during a
56 slope traversal. The code selected for the simulation must have the capability to define driver's reaction in terms of steering angle, braking force, and acceleration, if needed. 5.2.2 Terrain Modeling Geometry of the terrain. 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. Ability of the selected simulation package to model this contact is useful in evaluating the effect of sudden change 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 dynamics codes (e.g. Carsim, ADAMS, HVOSM, HVE, etc.) 2. Non-linear finite element analysis codes (e.g. LS-DYNA, ANSYS, NASTRAN, etc.) Bases on the issues described above and the considerations discussed next, the researchers used multi-rigid body vehicle dynamics code instead of a finite element code. And among the multi-rigid body vehicle dynamics codes, the researchers used Carsim. A detailed discussion of reasons for this selection is presented next. 5.2.4 Multi-rigid Body Vehicle Dynamics Codes vs. Finite Element 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 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 3-5 seconds may require several days of computations. In contrast, a similar simulation performed using a multi- rigid body vehicle dynamics code typically completes in less than 3-5 seconds. This is because the large number of degrees of freedom involved in finite element codes like LS-DYNA requires large computation time to simulate a vehicle encroachment event. In a multi-rigid-body vehicle dynamics code however, the model has much smaller number of degrees of freedom and thus vehicle handling and encroachment event can be simulated with minimum computation time.
57 Due to the significantly larger degrees of freedom in the model, the finite element 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 element 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 (presented later in this chapter) was expected to be very large in order to incorporate the many variables associated with evaluating vehicleâs traversability on slopes. Use of a finite element code (such as LS-DYNA or others) was therefore impractical due to the time needed to complete each simulation, or 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 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 and an 820C Geo Metro car on a 1V:6H foreslope (36). As shown in Figure 5.1, 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 sec to simulate each event in Carsim. An 8-core processor, on the other hand, required 2-hrs (i.e. 16 hrs. 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 multi-rigid-body dynamics code like Carsim was considered to be most suitable. (a) (b) Figure 5.1. Comparisons Carsim and LS-DYNA in simulating vehicle encroachment events on slope (a) pickup truck encroachment, (b) passenger car encroachment. 184.108.40.206 Vehicle Model Development The development of a vehicle model for a finite element code such as LS-DYNA requires significant resources. There are very limited number of vehicle finite element models available in the public domain. Under funding from FHWA, National Crash Analysis Center (NCAC) had 0 2 4 6 8 10 12 14 16 -30 -20 -10 0 10 20 30 40 50 60 Lateral Offset (ft) Bu m 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) Bu m 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
58 developed public domain finite element models of a 5000-lb pickup truck and a 2425-lb small passenger car. In the past, NCAC had also developed several vehicle models, however the overall number of vehicle models in the public domain remain limited. More importantly, these vehicle models were usually developed with focus on use in impact analyses, thus their validations are limited to recommend their use for slope traversals. Proper modeling and validation of steering and suspension linkages, joints, and springs and dampers properties is needed for these models. 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 and multi-rigid body vehicle dynamics codes have limitations in modeling soil tripped rollover that results from the digging of the tires into the soil as the vehicle slides laterally. So 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 tire 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, 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 sub- routines 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 affects 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 impact scenario in mind where the vehicle impacts an object almost immediately at the start of the simulation. Thus the available public domain finite
59 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 antilock braking system (ABS). Without a well-defined braking model, use of finite element codes such as LS- DYNA would have been 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 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 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 (37). 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 antilock braking system (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 pre-determined 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 contract 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 (37). The algorithm tracks several user-defined points on the body of the vehicle and
60 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. Figure 5.2. Body to terrain contact forces. For a penetrated point P on the vehicleâs body (see Figure 5.2), the contact algorithm calculates the penetration 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 ï n Tangential Force: Ff = K_total ï U ï T Where, K_total = K_terrain ï ï [1 + Mu ï 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 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-second/inch. And the coefficient of friction for vehicle body to terrain interface (U) was set at 0.25. While these values were used in previous studies using TTIâs version of HVOSM, they were not recommended as default since 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.
61 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 (38, 39). 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 performing large number of simulations, availability of new vehicle design features such as ABS braking and advanced suspension properties, the ability to apply reliable steering and braking inputs, and 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, the 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 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 relative risk of rollover, as shown in Table 3.7. The crash data analysis showed that 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, 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 relative risk of a 4-door sedan is less than a pickup or an SUV, due to 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 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. After the selecting the vehicle makes and models, the research team proceeded with developing vehicle dynamics models of these vehicles. A problem faced by the research team was the availability 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 the Table 3.8 also showed that the second highest number of rollovers of a 4-door sedan were for 2001 Ford Taurus. This vehicle was available to the researchers for taking the measurements. The researchers compared some of the main vehicle
62 properties of a 2001 Ford Taurus and a 2004 Honda Accord published in the literature (34). 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 suspensions types are the same and most vehicle properties are very closely matched for the two vehicles. Due to the similarities of the 2001 Ford Taurus with the 2004 Honda Accord, and the availability of the former for taking measurements, the 2001 Ford Taurus was used to develop a Carsim model of a mid-size 4-door sedan. 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 & Back Independent Front & Back - Figure 5.3. Comparison of vehicle properties between 2001 Ford Taurus and 2004 Honda Accord. TTI has previously developed a Carsim model for the 2270P pickup truck model under NCHRP Project 16-05 (21). This is a model for a 5000-lb Dodge RAM pickup truck that meets MASH design criteria for 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 MASH 1000C vehicle criteria and is commonly used in the roadside safety hardware testing. The Ford Explorer and Ford Taurus models were also developed using the same process. An evaluation of the âpre-setâ vehicle models included with CarSim software was performed to select a base model which closely resemble the 2006 Kia Rio. This evaluation was based on factors including vehicle mass, weight distribution, dimensions (wheelbase, wheel center height, and vehicle length), center of gravity (CG) location, and various engine specifications. Researchers determined that Carsimâs Class-B car model (shown in Figure 5.4) was the closest to Kia Rio passenger car and was thus selected as the base model for making further changes.
63 Figure 5.4. Carsimâs Class-B vehicle model was used as base model to making changes. The 2006 Kia Rio vehicle that the researchers used for development of 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 of the Kio 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 coordinates of seven âhard pointsâ underneath the vehicle. Hard points are relatively stiff structural locations underneath 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 centerline and front axle of the vehicle. Kia Rio Points Description X Y Z DriverÂ SideÂ BottomÂ ofÂ FrontÂ BumperÂ 838.20Â 508Â 262.5Â PassengerÂ SideÂ BottomÂ ofÂ FrontÂ BumperÂ 838.20Â â508Â 262.5Â DriverÂ SideÂ MiddleÂ ofÂ VehicleÂ â1480Â 682.5Â 200Â PassengerÂ SideÂ MiddleÂ ofÂ VehicleÂ â1480Â â682.5Â 200Â DriverÂ SideÂ BottomÂ ofÂ RearÂ BumperÂ â3252.45Â 619Â 400Â PassengerÂ SideÂ BottomÂ ofÂ RearÂ BumperÂ â3252.45Â â619Â 400Â Coordinate System Figure 5.5. Locations of hard points underneath Kia Rio (in millimeters). As mentioned previously, the researchers developed Carsim 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 pre-assembled Carsim vehicle models and then incorporating geometric and inertial properties that were determined from existing literature or by measuring from the actual vehicles. The âhard pointsâ for vehicle body to terrain contact were also measured for each vehicle type.
64 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. 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 components of a Carsim input (for each simulation case). These are the Road input file, Event input file, vehicle model, Run file, and a Simfile. A brief description of each one is presented below. Road File: Contains all geometric information about the terrain and associated terrain friction coefficients. Event File: Events or Procedures are inputs that âdriveâ the vehicle on the terrain. These contain vehicleâs initial orientation, initial speed, initial yaw rate, driver steering and braking inputs as functions of time, and others such inputs. Vehicle Model: Contains vehicle properties and related inputs needed to define the vehicle model. Run File: Combines the Road, Event, and vehicle model input files. This gets submitted to the Carsim solver. Simfiles: These files have additional information such as solver path, animation file path, results file path, etc. 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, events files (which include information about vehicle's encroachment speed, angle, and rate, driver's steering, braking, and throttle information, etc.). 3. Runs Carsim in loop to perform analysis for all simulation cases. In doing so, the wrapper program checks for vehicle body-to-terrain penetration using TTI's 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.
65 5. Manages each simulation run time and terminates simulation based on various termination criteria, such as if the vehicle returns to the road, travels too far, overturns, etc. 6. Generates output logs for all simulation cases, recording key simulation outcomes for further use in data analysis of the simulation outcomes. 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 wants 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 inputs, events inputs, and generate final input files 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 road input files only, and/or generate events inputs files only. It can also be run to generate all inputs, including final assembled input files for submission to Carsim solver, but quit without performing the analyses. And similarly, 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 effects of different parameters, such as terrain friction, driver perception- reaction times, etc. Additionally, this flexibility allows researchers to make small changes to road, events, 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 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 program
66 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.
Figure 5.6. TTIâs Carsim Wrapper Program main flowchart.
Figure 5.7. Flowchart of the inputs generation module of TTIâs wrapper program.
69 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 determines the types of inputs the user is providing (in Carsims 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 (PARSFILES) 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, events, and vehicle files for final submission to the Carsim solver. Case 2: In this case, the user provides a table of all the Events files and the wrapper program generates the road files and a table containing a list of all the road files generated. The program then assembles all simulations files (simfiles) for each case, referencing appropriate road, events, and vehicle 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, events, and vehicle files for final submission to the Carsim solver. Case 4: In this case, the wrapper program generates all Roads and Events files. It then assembles all simulations files (simfiles) for each case. The Road files are generated by separate subroutine in the 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, backslopes, etc. 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 Events 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 information on different driver inputs to be used in generating the Events files are also read at this point. The subroutine then calculates the total number of Events files needed based on the number of parameters read. It then generates these Events files in a format needed by the Carsim solver.
70 Figure 5.8. Flowcharts of the subroutines for generating Carsim (a) terrain/road inputs, and (b) events inputs (steering, braking, encroachment speeds, angles, rates, etc.). After generating the Roads and Events files, the program generates/assembles a master simulation file (simfile) which contains links to all the Roads, Events, and vehicle input files, along with other information needed for the analysis such as start time, stop time, integration time step, etc. 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 also shown Figure 5.9. While performing a simulation, the wrapper program interfaces with the Carsim solver to get coordinates of all 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 (a) (b)
71 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. Figure 5.9. Flowchart of TTIâs code for applying body-to-terrain contact with Carsim.
72 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 mi/h). 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 travelled for more than 10 seconds 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 a 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 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 runâs 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 3 for more details.
73 Table 5.1. Simulation outcomes logged in the aggregate simulation results table. 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 following values. â Time Exceeded â Returns â Stops â Gone Far â Overturns Description A brief description of the outcome High Roll Flag for high roll (> 55 deg.). It has value of 1 or 0 (1 = high roll) Max Roll Maximum vehicle roll during simulation (deg.) High Pitch Flag for high pitch (> 55 deg.). It has value of 1 or 0 (1 = high pitch) Max Pitch Maximum vehicle pitch during simulation (deg.) Sideslip Flag for side slipped vehicle (> 20 deg.). It has value of 1 or 0 (1 = vehicle sideslips) Max. Slip Maximum sideslip angle during simulation (deg.) Spinout Flag for vehicle spinout. It has value of 1 or 0 (1 = vehicle spins out) Max Lat. Vel (km/h) Max. lateral vehicle velocity during simulation (km/h) Max Lat. Travel (m) Max. distance vehicle travels laterally from edge of roadway (m) Xcg at sim. Stop (m) X-coord. of vehicleâs sprung mass CG when simulation stops (m) Ycg at sim. Stop (m) Y-coord. of vehicleâs sprung mass CG when simulation stops (m) As mentioned previously, Carsim generates outputs for a large number of parameters for each individual simulation. Since 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 usersâ guide for TTIâs wrapper program that provides lists of these inputs and outputs, along with a description of the reported parameters and their units (presented in Appendix 3). The usersâ guide also describes some of the key criteria used by the wrapper program in running the simulation analyses. This guide was useful in communicating simulation results between researchers generating simulation results and those using the results for further analysis.
74 Table 5.2. Simulation output data saved for each simulation case. Label Description Time Simulation time (seconds) XCG_SM X-coord. of vehicleâs sprung mass CG in global coords. (m) YCG_SM Y-coord. of vehicleâs sprung mass CG in global coords. (m) ZCG_SM Z-coord. of vehicleâs sprung mass CG in global coords. (m) VxBf_SM X-comp. velocity for vehicleâs sprung mass CG in body-fixed coord. sys. (km/h) VyBf_SM Y-comp. velocity for vehicleâs sprung mass CG in body-fixed coord. sys. (km/h) VzBf_SM Z-comp. velocity for vehicleâs sprung mass CG in body-fixed coord. sys. (km/h) AxBf_SM X-comp. accel. for vehicleâs sprung mass CG in body-fixed coord. sys. (g) AyBf_SM Y-comp. accel. for vehicleâs sprung mass CG in body-fixed coord. sys. (g) AzBf_SM Z-comp. accel. for vehicleâs sprung mass CG in body-fixed coord. sys. (g) Pitch Vehicleâs Euler pitch (deg.) Roll_E Vehicleâs Euler roll (deg.) Yaw Vehicleâs Euler yaw (deg.) YawLocal Vehicleâs Euler yaw offset to zero at start of simulation (deg.) Beta Side-slip angle of vehicle based on Vx and Vy (deg.) Alpha_L1 Tire L1 lateral slip (L/R is Left/Right, 1/2 is front/rare axle) (deg.) Alpha_L2 Tire L2 lateral slip (deg.) Alpha_R1 Tire R1 lateral slip (deg.) Alpha_R2 Tire R2 lateral slip (deg.) 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) 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 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.
75 Figure 5.10. Properties of tires in Carsim. Lateral force is plotted as function of slip angle for different vertical tire loads. 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 sideslip on soil, the furrowing forces build up gradually. The amount of lateral force applied on the vehicle due 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.), vehicleâs mass distribution and CG, vehicleâs side slip angle, vehicleâs 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, 41). 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 (41). 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
76 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 the modeling technique used by Grimes et al. While the number of crash tests performed 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 Cooperrider et al.âs crash test data 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 straightforward 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. 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, ïsoil, is determined using the formulation shown in Figure 5.11. Figure 5.11. Friction ellipse model for modeling tire forces due to soil furrowing. 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 appropriate for the non-soil terrains.
77 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 coefficient to incorporate forces due to soil furrowing (ïsoil), the perception-reaction time 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. Evaluation of the maximum lateral friction coefficient is presented in the next section. A small sensitivity study was performed using the roadside V-ditch profile shown in Figure 5.12. For a meaning full comparison of simulation results, same terrain profile was used for all simulations while varying other parameters. Simulations were performed with encroachments speeds of 45 mi/h, 55 mi/h, and 65 mi/h. Encroachments angles of 10 degrees, 20 degrees, and 30 degrees were used. Simulations were performed with MASH pickup truck (P2270) and small passenger car (1100C) vehicles. Figure 5.12. Roadside ditch profile used for sensitivity analysis. 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) 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/second was used to develop a maximum steer of 360 degrees after passage of perception-reaction time. A 0.5 second perception-reaction time delay was used in the simulations, except when sensitivity to perception-reaction time was being evaluated. A yaw rate of 15 degrees/second 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 Shoulder 6 ft, 4% slope Foreslope 16 ft, 1V:6H Backslope 16 ft, 1V:3H
78 2. Spinout 3. Marginal 4. Overturn If the vehicle rolled or pitched more than the 65 degrees, it was categorized as an overturn. If it had 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 has used 1.0 seconds as the appropriate perception-reaction time (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 1.0 and 0.5 seconds. A value greater than 1 second 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 are the only driver inputs that require inclusion of PRT. Results of the analyses are summarized in Figure 5.13. It can be see that the results are not very sensitive to PRT and both PRT values result in very similar outcomes. The researchers therefore selected PRT of 1 second as in the 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/second (10). The researchers selected this as the base value and performed simulations with yaw rates of 10, 15, and 20 degrees/second 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 different yaw rates, the overall results are not significantly different. The researchers therefore selected the yaw rate of 15 degrees/second to model non-tracking encroachments, as in the previous research.
79 Figure 5.13. Results of the sensitivity analyses for determining perception-reaction time. Figure 5.14. Results of the sensitivity analyses for determining encroachment yaw rate. 5.7 EVALUATION OF FRICTION MODEL AND LATERAL COEFFICIENT As mentioned previously, the researchers used the friction ellipse model to apply soil furrowing forces to the vehicleâs tires. A key parameter for this model is the lateral friction
80 coefficient, which controls the lateral force applied to the vehicle as it side slops 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, vehicleâs encroachment angle, interaction of the vehicleâs body with the terrain, and the slope of the terrain being traversed, etc. Since 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 (6) initial speeds of 25 mi/h, 35 mi/h, â¦, 75 mi/h. Encroachment angle became irrelevant since a flat terrain was used. A total of four (4) 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: 1. tracking, panic return to road steer after perception/reaction time of 1 s 2. tracking, panic return to road steer and ABS brakes after P/R time of 1 s 3. non-tracking, constant steer angle and full ABS brakes, with initial yaw rate of 15 deg/s 4. non-tracking, constant steer angle, with initial yaw rate of 15 deg/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 âCasesâ (1a, 1b, 2a, 2b, â¦, 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,
81 2.1, 2.2, and 2.8 (i.e. the maximum lateral friction coefficient at 90-deg side-slipping) (see Figure 5.15 for the simulation matrix used). Run Number Speed (mi/h) Driver Input* Simulation Cases for Different Vehicle Types and Friction Coefficients Case Number Vehicle Type Lateral Friction Coeff. Case 1a Pickup 0.5** Case 1b Small Car 0.5 ** Case 2a Pickup 1.2 Case 2b Small Car 1.2 Case 3a Pickup 2.0 Case 3b Small Car 2.0 Case 4a Pickup 2.8 Case 4b Small Car 2.8 Case 5a Pickup 2.2 Case 5b Small Car 2.2 Case 6a Pickup 2.1 Case 6b Small Car 2.1 *Driver inputs were numbered as follows: 1. tracking, panic return to road steer after perception/reaction time of 1 s 2. tracking, panic return to road steer and ABS brakes after P/R time of 1 s 3. non-tracking, constant steer angle and full ABS brakes, with initial yaw rate of 15 deg/s 4. non-tracking, contact steer angle, with initial yaw rate of 15 deg/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 evaluation of the friction ellipse model and determination of the lateral friction coefficient. 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 and the friction ellipse models 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
82 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 mi/h. Panic return-to-road steer is applied after 1 second of P/R time. The results of the Carsim friction model and that of the friction ellipse are very similar, even though the force from the Carsim model is slightly less than the friction ellipse model, which uses a higher lateral coefficient whose value depends on the side slip angle. Due to 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. When the speed is increased, or if the driver input is more aggressive, the differences between the Carsim and friction ellipse model become more prominent. An example is shown in Figure 5.17 for vehicle starting with non-tracking conditions, with initial yaw rate of 15 deg/s, initial speed of 35 mi/h, and a constant steer angle and full ABS brakes applied throughout the simulation. In this case, the differences in lateral forces applied by the Carsim and the friction ellipse models are more prominent as expected. These lateral forces increase with the increase in the MuY (maximum lateral friction coefficient) 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. Figure 5.16. Lateral tire forces for small car and pickup truck with 25 mi/h initial speed, tracking initial conditions, and panic return-to-road steer after 1 second P/R time.
83 Figure 5.17. Lateral tire forces for small car and pickup truck with 35 mi/h 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 mi/h initial speed, non-tracking initial conditions, constant steer angle, and full ABS brakes. 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 maximum lateral friction coefficient (MuY) used in the friction ellipse model. Results of the simulations show that
84 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 (left) and the pickup truck (right). The vehicle starts with non-tracking conditions, with initial yaw rate of 15 deg/s, initial speed of 55 mi/h, and a constant steer angle and full ABS brakes applied throughout the simulation. As the maximum lateral friction coefficient is increased, the lateral tire force increases for both vehicles and is significantly different for different values of MuY. With friction coefficient of 1.2 and 2.0, the small car and the pickup do not rollover, even though the maximum roll angle increases for both vehicles with the increase in the friction coefficient. With friction coefficient of 2.8, both vehicles roll over. Results of the simulations demonstrate that the maximum later 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 encroachments 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 probability being significant, but there are disagreements about its magnitude. A low-end estimate is around 10%. (40, 43). 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% 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.
85 (a) Rollover Percentages (b) Number of Rollovers Figure 5.19. Percentages and numbers of rollovers for different values of maximum lateral coefficient of friction. While no rollovers occur for a maximum lateral friction coefficient of 1.2, three (13%) pickup truck rollovers occur with a friction coefficient of 2.0. With maximum lateral friction coefficient of 2.1, there is one (4%) rollover with the small car, but the number of pickup rollovers increases to 7 (29%). At maximum lateral friction coefficient of 2.2, even higher numbers of rollovers are observed (38% for pickup and 17% for small car). Results of the simulation indicate that 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 (presented previously 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 encroachment conditions and the vehicle types used. The simulation matrix was prepared by incorporating feedback of the research panel received during the Panel Meeting and the quarterly progress reporting and review process. The simulation matrix comprises of 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. 0 13 29 38 0 0 4 17 0 20 40 60 80 100 1.2 2 2.1 2.2 Ro llo ve rÂ P er ce nt ag e MaximumÂ LateralÂ FrictionÂ Coefficient Pickup SmallÂ Car 0 3 7 9 0 0 1 4 0 6 12 18 24 1.2 2 2.1 2.2 N um be rÂ o fÂ R ol lo ve rs MaximumÂ LateralÂ FrictionÂ Coefficient Pickup SmallÂ Car
86 Furthermore, change in the terrainâs slope at the end of the foreslope affects the kinematics of the encroaching vehicle. For this reason, four foreslope widths were selected as shown in Figure 5.20. These were 8 ft, 16 ft, 32 ft 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. Variables Example Conditions Roadside Geometry ï· Slope: 1V:10H, 1V:6H, 1V:4H, 1V:3H, and 1V:2H ï· Slope width: 8 ft, 16 ft, 32 ft, and âinfiniteâ Shoulder Type and Width ï· 4% cross slope ï· Paved (width: 2 and 6 ft) ï· Paved+turf (width: 8 ft (4ft paved and 4ft turf)) Vehicle Type ï· Small passenger car (MASH 1100C, Kia Rio) ï· Pickup truck (MASH 2270P, Dodge Ram) ï· Midsize Sedan (2001 Ford Taurus) ï· 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 ï· Tracking ï· Non-tracking with yaw rate of 15 deg/sec Driver Control Input ï· No input ï· Panic return-to-road Steering ï· Combined return-to-road steer & full ABS braking Figure 5.20. Simulation matrix. 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% 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 slower speeds and angles of 25 mi/h and 5 degrees to higher speeds and angles of 75 mi/h 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 that is asleep or impaired who does not apply any driver input. Inputs 2 and 3 were tracking encroachments in which the driver reacts after a perception reaction time of 1 second.
87 The rate for panic steer was determined based on NHTSAâs Fishhook maneuver guidelines, which has a recommended steering rate of 720 degrees/second. 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. Driver Input Details 1 No input (tracking) 2 Panic steer, no brake (tracking) After 1.0 sec PRT delay on leaving the edge of travel lane, a 360-deg steer towards roadway is applied at the rate of 720 deg/s. 3 Panic steer and full ABS brake (tracking) After 1.0 sec PRT delay on leaving the edge of travel lane, a 360-deg steer towards roadway is applied at the rate of 720 deg/s. 4 Constant Steer, no brake (non-tracking) Vehicle encroaches with yaw rate of 15 deg/s (yawing towards roadway), with a constant steer angle of 360 deg. 5 Constant steer and full ABS brake (non-tracking) Vehicle encroaches with yaw rate of 15 deg/s (yawing towards roadway), with a constant steer angle of 360 deg. And ABS brakes fully applied. Figure 5.21. Driver inputs for the encroachment simulations. 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 Figure 5.22 through Figure 5.27. Prior to using these results for developing the traversability guidelines, the researchers deemed it important to analyze the results and verify that general trends from the results were logical. It should be noted that the results presented in Figure 5.22 through Figure 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 encroachment speed and 30-degree angle carries the same weight as an encroachment at 45 mph and 15 degrees, 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 guidelines, and this process will be described in Chapter 7. Even in the unweighted form, simulation results and trends presented in Figure 5.22 through Figure 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. ï· Returns: Vehicle returns to the roadway
88 ï· Overturns: Vehicle rolls over or pitches over ï· Marginal Rolls: Vehicle does not rollover, but has roll angle of greater than 55 degrees ï· Spinouts: Vehicle yaws and spins out such that it has negative forward velocity ï· 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 herein. 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. To highlight the key trends in rollovers, 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-ft 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. Since some of the steering and braking inputs are applied after a perception-reaction time 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-ft wide to 16-ft wide slope. The rollover percentages remain more or less the same for 16-ft 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 interaction of the vehicle with the slopeâs flat bottom results in a destabilizing effect on the vehicle in most cases. The vehicle is typically side-slipping and yawing out on the slope when it suddenly interacts with the flat bottom, which then helps trip the vehicle to cause a
89 rollover. For the 8-ft wide slope, the vehicle does not traverse on the slope long enough to have significant side-slipping and yawing. Thus we see that the number of rollovers for the 8-ft wide slope is less than the 16-ft wide slope. For the 16-ft and 32-ft wide slopes, the rollover percentages are very close. And since there is no interaction with the slope bottom for the infinite slope, the percentage of Overturns is significantly reduced as there is no abrupt destabilization of the vehicle. It can also be seen from Figure 5.24 that the number of returns reduces as the width of the slope increases. This is because wider the slope, more difficult it is 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 mi/h to 45 mi/h. The Overturns also jump significantly from 45 mi/h 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 has significant influence in causing rollovers, but as more and more marginal encroachments convert to rollovers due to the speed increase, the effects of further speed increase taper off. The influence of 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 reduction in Overturns. The influence of vehicle type, in unweighted form, is shown in Figure 5.27. Pickup trucks have higher percentage of Overturns compare to small cars and mid-size sedans. But SUVs have more than twice the number of Overturns than Pickup Trucks. It is interesting to note in the bottom plot that 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 Mid-Size Sedan. In conclusion, the results of the simulations showed trends that are intuitive with some interesting insights that are described above. 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.
90 Influence of Slope on Simulation Outcomes (percentages) 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.
91 Influence of Shoulder Width/Type on Simulation Outcomes (percentages) 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.
92 Influence of Slope Width on Simulation Outcomes (percentages) 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.
93 Influence of Encroachment Speed on Simulation Outcomes (percentages) 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 Simulation s 7200 7200 7200 7200 7200 7200 Figure 5.25. Influence of encroachment speed.
94 Influence of Encroachment Angle on Simulation Outcomes (percentages) 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.
95 Influence of Vehicle Type on Simulation Outcomes (percentages) Pickup Small Car Mid-Size 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.