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95 CHAPTER 6. SIMULATION ANALYSIS METHODS INTRODUCTION To evaluate vehicle dynamics based on a combination of various ditch design parameters, vehicle encroachment conditions, vehicle types, and driver inputs, an extensive simulation effort was needed. This evaluation was done using CarSim, which is a commercial multi-rigid body vehicle dynamics software. Reasons for selecting CarSim over some of the other codes are presented in this chapter. A feature that was incorporated into the vehicle dynamics simulations was the modeling of the vehicle bodyâs contact interaction with the local terrain. This feature was developed separately by TTI researchers for internal use. However, details of the contact formulation have been included in this chapter. Because of the large number of simulations to be performed, a special computer code, called the wrapper program, was needed to generate input files, run simulations in a batch mode, and to post-process the results from the simulation analyses. A detailed overview of this wrapper program, its inputs and outputs, and its algorithm are presented in this chapter. Many of the vehicles leaving the roadway start side slipping, resulting in soil-tripped rollovers. The researchers have employed a method of incorporating the soil tripping forces on a vehicleâs tires using a friction ellipse model for calculating tire forces. A discussion of CarSimâs default tire friction force model and the details of the friction-ellipse-based tire force model used by the researchers are also presented in this chapter. Various smaller-scale sensitivity studies were performed to evaluate the functionality of the friction ellipse model to incorporate the soil-furrowing forces. In this chapter, details of these studies are also presented. The researchers also performed a series of dynamic bump traversal and ditch traversal tests for validating some of the vehicle models. Details of the tests performed and vehicle models developed for use in this research are also presented in this chapter. SIMULATION TOOLS For many years, researchers have been using computer codes 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, to springs and dampers, to detailed finite element representations using many thousands of elements. Because of the large number of simulation cases to be performed in this research and the sufficient level of accuracy that needed to be achieved, the researchers had proposed using multi- rigid body vehicle dynamics code. At the time of submitting the proposal, the researchers evaluated various vehicle dynamics simulation codes for use in this study. Most of the newer vehicle dynamics codes can be used to build relatively sophisticated vehicle models with detailed suspensions, steering mechanisms, and braking systems. Various roadway or roadside terrain conditions can be readily modeled to study vehicle maneuvering, handling characteristics, ride
96 quality, and vehicle trajectory during roadside encroachments. However, these codes do not have the option of modeling the contact between a vehicleâs body and the terrain. Modeling the body-to-terrain contact is critical for evaluating the kinematics of vehicles entering roadside ditches. A customized version of a relatively older vehicle dynamics code, HVOSM, does have a simple body-to-terrain contact that was built into the program by TTI researchers (10, 56). However, this code is old and has not been updated or improved to incorporate changes in vehicle design features of the newer vehicle fleet. Even though the HVOSM code has not been updated, the availability of body-to-terrain contact feature and its importance to this research led the researchers to propose using it in this research over some of the other commercial codes such as CarSim, MSC-ADAMS, and so forth. During the course of this project, however, TTI researchers concluded that using a latest commercial vehicle dynamics simulation package such as CarSim was more advantageous to this research. In contrast to the HVOSM, CarSim vehicle models have an antilock braking system (ABS), which is now a standard feature in the current vehicle fleet and can have dramatic influence on vehicle control and kinematics once brakes are applied in a panic mode. CarSim also has a library of tire models that are more advanced compared to the HVOSM tire model. CarSim also has better suspension system models that account for suspension compliance effects that are missing in the HVOSM. Furthermore, a major advantage of using CarSim is the availability of a large number of predetermined vehicle parameters and properties for the current vehicle fleet. These properties can be used for building new vehicle models under this project without performing component and subcomponent level testing. Many of the vehicle parameters in the HVOSM were initially determined for the vehicle fleet at the time of its development. Although it is relatively straightforward to measure and change a vehicleâs geometric and inertial properties or basic properties, such as suspension spring and damper properties, not all parameters can be determined within the scope of this project. In the past, TTI researchers developed new vehicle models for the HVOSM, but the process of determining some of the vehicle properties relied on existing literature and research, which may not have been readily available for the current vehicle fleet. Thus, the ability to develop vehicle models using available and realistic subcomponent properties and datasets in CarSim was considered a major advantage for this project. During the course of this project, TTI separately funded internal work on developing a user-written subroutine to apply body-to-terrain contact forces in CarSim. The contact algorithm used was the same as what was previously used to account for body-to-terrain contact in TTIâs version of the HVOSM. Using this subroutine, contact forces can be applied to the vehicle during runtime in CarSim. This contact subroutine was completed while the initial work on this project was ongoing and was subsequently available to TTI researchers for use in this project. Due to the ability to incorporate a body-to-terrain contact, along with the other advantages of using CarSim, the researchers formally requested that the research panel allow its use as the vehicle dynamics simulation package instead of the HVOSM. This request was subsequently approved, and CarSim was the vehicle dynamics software used in this project.
97 VEHICLE BODY-TO-TERRAIN CONTACT In modeling a vehicle traversing roadside ditches, the vehicleâs body-to-terrain contact is important and can significantly affect the kinematics of the vehicle due to terrain forces applied to the vehicle. TTI researchers have developed a vehicle body-to-terrain contact algorithm for CarSim separate from this research. This contact algorithm uses the contact formulation previously used in TTIâs version of the HVOSM. 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 6.1), the contact algorithm calculates the penetration ðð â normal to the terrain. Using the penetration amount, vehicle velocity, and the penetrated point Pâs direction, 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: Figure 6.1. Body-to-terrain contact forces. Normal Force: Fn = K_total â n Tangential Force: Ff = K_total â U â T where, K_total = K_terrain â ðð â 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. 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 what were used in the HVOSM contact. The stiffness coefficient of the terrain (K_terrain) was set at 4,000 lb/inch,
98 which was based on a 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 the 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. Using the same contact algorithm and contact parameters, the researchers replicated the contact features that were previously only available in TTIâs version of the HVOSM. This version of the HVOSM was previously validated in various studies using full-scale crash testing with vehicles traversing sloped terrains and ditches (56, 9). WRAPPER PROGRAM A major task performed in this project was the coding of a wrapper program. This program was coded using Visual Basic programming language and 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 coded by TTI, it would 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): the Road input file, Event input file, Vehicle model, Run file, and 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 files contain the vehicleâs initial orientation, initial speed, initial yaw rate, driver steering and braking inputs as functions of time, and other such inputs. Vehicle Model: Contains vehicle properties and related inputs. Run File: Combines the Road, Event, and Vehicle model input files. A Run file threads together a particular terrain, vehicle type, driver input, and encroachment condition to formulate a specific simulation case, which gets submitted to the CarSim solver. Simfiles: These files have additional information, such as solver path, animation file path, results file path, and more, 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, Event files (which include information about vehicleâs encroachment speed, angle, and rate, driverâs steering, braking, and throttle information, etc.).
99 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 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 marked wet-soil terrain. 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, and the like. 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 TTIâs wrapper program and a generalized description of the tasks it performs. WRAPPER PROGRAM STRUCTURE AND OVERVIEW A high-level flowchart of TTIâs wrapper program is shown in Figure 6.2. 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, event inputs, and 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 Event inputs files only. It can also be run to generate all inputs, including final assembled input files for submission to CarSim solver, but stopped without performing the analyses. 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, and the like. 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 input generation module, as shown in Figure 6.3. 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 and 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 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
100 appropriate contact force needed to remove the penetration. The wrapper program submits the contact forces to the CarSim solver to be applied to the vehicle body points being tracked using the CarSim solver exchange variables. The wrapper program also evaluates the extent of the vehicleâs sideslip angle for each tire during a simulation run. Similar to the contact algorithm, the wrapper program exchanges information about the tire sideslip 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.
101 Figure 6.2. TTIâs CarSim wrapper program main flowchart.
102 Figure 6.3. Flowchart of the input generation module of TTIâs wrapper program.
103 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 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 input generation module is shown in Figure 6.3. There are four possible cases for inputs generation. Case 1: In this case, the user provides a table for all the Road and Event 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, Event, and Vehicle 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 program then assembles all Simfiles for each case, referencing appropriate Road, Event, 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 Event files and a table containing a list of all the files generated. The program then assembles all Simfiles for each case, referencing appropriate Road, Event, and Vehicle 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 Simfiles for each case. The Road files are generated by separate subroutine in TTIâs wrapper program. The flowchart of this subroutine is shown in Figure 6.4a. 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, and so forth. 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 6.4b. 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 used in generating the Event files are also read at this point. 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.
104 Figure 6.4. Flowcharts of the subroutines for generating CarSim (a) terrain/road inputs, and (b) event inputs (steering, braking, encroachment speeds, angles, rates, etc.). After generating the Road and Event files, the program generates/assembles a master Simfile that contains links to all the Road, Event, and Vehicle input files, along with other information needed for the analysis, such as start time, stop time, integration time step, and so forth. 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 that, if requested, proceeds with the CarSim analyses as described earlier. The flowchart of TTIâs contact module is also shown in Figure 6.5. 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)
105 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 6.5. Flowchart of TTIâs code for applying body-to-terrain contact with CarSim. 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, which prevents the
106 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 100 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 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, which 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 a specified value (set at 20 degrees). 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, a need existed 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 6.1 shows the types of outputs recorded. Additionally, terrain and driver input are also logged. See Appendix C for more details.
107 Table 6.1. 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 âERROR.â 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 interest to this research, the researchers used a separate program (available with CarSim) to extract more relevant output parameters. These included the vehicle CGâs path, velocity, acceleration, slip angle, roll, pitch, yaw, tire forces, tire sideslip angles, and others as a function of time. Table 6.2 shows the list of output parameters extracted for each simulation. The researchers also 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 (Appendix B). The usersâ guide also describes some of the key criteria used by the wrapper program in running the simulation analyses. This guide had been useful in communicating simulation results between researchers generating simulation results and those using the results for further analysis.
108 Table 6.2. 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 Sideslip 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) SOIL-FURROWING FORCES The default CarSim tire model determines lateral force on each tire using the vertical load and the sideslip 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 6.6). 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.
109 Note: Lateral force is plotted as function of slip angle for different vertical tire loads. Figure 6.6. Properties of tires in CarSim. 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 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.), the vehicleâs mass distribution and CG, the vehicleâs sideslip angle, the vehicleâs lateral speed, the duration of side slipping, and the distance the vehicle has side slipped. Many previous research studies have effectively used an increased lateral coefficient to model lateral tire forces due to soil-furrowing (13, 9, 16). 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 wherein different vehicles were made to side slip 90 degrees on soil at different speeds (58). 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 (59). 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
110 tests. However, both terrains differed significantly from each other, and no general method for determining the length and friction coefficient of adjacent surface patches existed. 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 that, in addition to taking into account the sideslip angle, increases the lateral friction coefficient as a function of the distance a vehicle has side slipped. This modification would have been an enhancement over the friction ellipse model, which only takes into account the sideslip 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. No straightforward process to determine how these results could be extrapolated for use with different vehicle types and for sideslip angles of other than 90 degrees was found. Thus, even though the researchers spent some time exploring how the abovementioned studies could be applied to 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, Âµsoil, is determined using the formulation shown in Figure 6.7. Figure 6.7. 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.
111 SENSITIVITY STUDIES Prior to performing simulations of the entire simulation matrix, it was important to evaluate the sensitivity of some of the parameters. These parameters included the maximum lateral friction coefficient to incorporate forces due to soil-furrowing (Âµsoil), the perception- reaction time for some of the driver inputs, and the encroachment yaw rate of the vehicle for non-tracking encroachments. The researchers evaluated the sensitivity of these parameters using a roadside V-ditch that had the profile shown in Figure 6.8. This profile was selected based on results of a survey conducted under this project to determine the most commonly used roadside ditch configurations. Figure 6.8. Roadside ditch profile used for sensitivity analysis. For a meaningful comparison of simulation results, the same terrain profile was used for all simulations while varying other parameters. Simulations were performed with encroachment speeds of 45 mph, 55 mph, and 65 mph. Encroachment angles of 10 degrees, 20 degrees, and 30 degrees were used. Simulations were performed based on the Manual for Assessing Safety Hardware (MASH) pickup truck (2270P) and small passenger car (1100C) vehicles. Driver inputs were selected from among the following five types: 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. 2. Spinout. 3. Marginal. 4. Overturn. Shoulder 6 ft, 4% slp Foreslope 16 ft, 1V:6H Backslope 16 ft, 1V:3H
112 If the vehicle rolled or pitched more than 65 degrees, it was categorized as an overturn. If it had higher than a 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. Maximum Lateral Friction Coefficient In 2004, Bligh et al. conducted research under NCHRP Project 17-11 (13). The objective of this research was to develop relationships between recovery-area distance and roadway and roadside features, vehicle factors, encroachment parameters, and traffic conditions for the full range of highway functional classes and design speeds that can subsequently be used to establish clear-zone guidelines. Under this study, the researchers determined the appropriate value for the maximum lateral friction coefficient using a large number of encroachment simulations with different sets of friction coefficient values. Each encroachment was weighted according to the probability of occurrence in the real world. The percentage of encroachments resulting in a rollover in the vehicle dynamics analysis for different friction values was compared to the percentage of rollovers determined from the crash databases. Using this approach, the researchers of the NCHRP Project 17-11 determined that the maximum lateral friction coefficient value of 1.2 was most appropriate. It is important to note that NCHRP Project 17-11 used the HVOSM and older vehicle models. Since the use of a higher lateral friction coefficient is only a surrogate means of incorporating soil-furrowing forces, it was important to evaluate the sensitivity of this friction coefficient value to the change in the vehicle dynamics code (from the older HVOSM to the newer and actively maintained CarSim) and the use of more recent vehicle models and modeling techniques. The sensitivity to the lateral coefficient was therefore evaluated using 1.2 as the base value and using small variations of this value. Simulations were performed with maximum lateral coefficients of 1.0, 1.2, and 1.4. Results of the analyses are summarized in Figure 6.9. The outcome of each simulation was categorized as described previously and then grouped according to the encroachment speed and angle because most of the overturns and marginal outcomes occur in the 65-mph and 30-degree encroachment group. Grouping simulation outcomes in this manner allowed an easy way to evaluate the sensitivity of the friction parameter. Results of the simulations with lateral friction coefficient of 1.0, 1.2, and 1.4 were very similar. Thus, the researchers initially selected the value of 1.2 for further analyses under this research. However, when the researchers performed simulations for the larger simulation matrix at a later stage in the project, it was determined that the value of 1.2 led to no rollovers on relatively flat terrains, which contradicted the crash data; thus, the researchers re-evaluated the friction ellipse model and the maximum lateral friction coefficient value. Details of this re-evaluation are presented in a later section of this report. Perception-Reaction Time Previous research 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 (39). 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 since it makes the driver input very similar to the âno inputâ category for most encroachment speeds and angles.
113 Simulations were performed with the âpanic steer, no brakeâ and âpanic steer and brakeâ driver inputs only. These inputs are the only driver inputs that require inclusion of PRT. Results of the analyses are summarized in Figure 6.10. It can be seen that the results are not very sensitive to PRT, and both PRT values result in very similar outcomes. The researchers therefore selected a PRT of 1 second, as in previous research. 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. Most previous studies used a yaw rate of 15 degrees/second. The researchers selected this as the base value and performed simulations with yaw rates of 10, 15, and 20 degrees/second. Simulations were performed for non-tracking encroachments only. Results of the analyses are summarized in Figure 6.11. Although 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 previous research. Figure 6.9. Results of the sensitivity analyses for determining maximum lateral friction coefficient.
114 Figure 6.10. Results of the sensitivity analyses for determining perception-reaction time. Figure 6.11. Results of the sensitivity analyses for determining encroachment yaw rate. EVALUATION OF FRICTION MODEL AND LATERAL COEFFICIENT As mentioned above, previous studies have used the friction ellipse model to apply soil- furrowing forces to vehicles. In NCHRP Project 17-11, the researchers determined an appropriate value of 1.2 for the lateral friction coefficient. Using this value, the researchers obtained a similar percentage of rollovers on flat terrains, as can be inferred to some extent from the crash data analysis. For this reason, in the current study, the researchers opted to use the same value for the lateral coefficient of friction. However, the researchers noted that since NCHRP Project 11-17 used the HVOSM and older vehicle models, it was important to evaluate the
115 sensitivity of the lateral friction coefficient value to the change in vehicle dynamics code (from older the HVOSM to newer and actively maintained CarSim) and the use of more recent vehicle models and modeling techniques. For this purpose, the researchers performed a small-scale sensitivity analysis in which the lateral friction coefficient was varied between 1.0, 1.2, and 1.4. While some variation in results was expected, the researchers wanted to ensure that the results were not dramatically different for small variations in the friction coefficient value. The results of the small-scale sensitivity analysis did not show much sensitivity to the lateral friction value. The researchers thus selected the previously used maximum lateral friction coefficient value of 2.0 and performed simulations using the simulation matrix developed for this project (the simulation matrix will be presented in the next chapter). When the results of the larger simulation matrix were evaluated, it was determined that there were no rollovers on relatively flat slopes (1V:10H and 1V:6H). This result was not expected based on some of the crash data and led the researchers to believe that the effectiveness of friction ellipse model and the choice of 1.2 as the maximum lateral friction coefficient needed to be investigated in more detail. Thus, the researchers performed a detailed evaluation of the friction ellipse model and appropriate lateral friction coefficient value. Details of the evaluation are presented next. The evaluation of the lateral friction coefficient and the friction ellipse model was geared toward answering the following questions: Does the friction ellipse model exhibit different behavior compared to the CarSimâs default tire-terrain friction model? Can the lateral tire forces due to side slipping be adequately adjusted using the friction ellipse model and variation in the lateral friction coefficient? What is the appropriate value of the 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 that include terrain friction forces, the vehicleâs encroachment angle, interaction of the vehicleâs body with the terrain, the slope of the terrain being traversed, and others. 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 available estimates of the probability of rollover on a flat terrain, which are based on crash data, can be used to select an appropriate value of the lateral friction coefficient that results in a similar probability of rollovers in the simulations. The simulation matrix was thus comprised of a flat terrain, and simulations were performed with the MASH small passenger car and pickup truck vehicles. Simulations were performed with six initial speeds of 25 mph, 35 mph, 45 mph, 55 mph, 65 mph, and 75 mph. The encroachment angle became irrelevant since a flat terrain was used. A total of four driver inputs were used. The âno steer or brakeâ input was not used since it also became irrelevant on a flat terrain. The four inputs included the following: 1. Tracking, panic return-to-road steer after perception/reaction time of 1 s.
116 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 simulation runs needed to be performed for each vehicle type, as numbered in Figure 6.12. The simulation study was further divided into 12 cases (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 grassy surface. When using the friction ellipse model, the longitudinal friction coefficient was 0.5, and the lateral friction coefficient was determined by the friction ellipse, with a minor radius of 0.5 (coefficient at no sideslipping condition) and major radius varying between 1.2, 2.0, 2.1, 2.2, and 2.8 (coefficient at 90-degree side slipping) (see Figure 6.12 for the simulation matrix used). Run Number Speed (mph) 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 6.12. Simulation matrix for evaluation of the friction ellipse model and determination of the lateral friction coefficient. For each of the cases in Figure 6.12, 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 to select an appropriate lateral friction coefficient. Key findings of the simulation study are presented next. Additionally, some of the related outcomes from each of the simulations are presented in Appendix C.
117 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 with a relatively less aggressive driver input, the differences between the two friction models are not that significant. This result 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 outcome is shown in Figure 6.13, 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. 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 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 sideslip angle. Due to the differences in the mass of the small car and the pickup truck, the lateral tire forces, which are functions of vehicle mass, band around different lateral force values. This outcome 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 6.14 for a vehicle starting with non-tracking conditions, with initial yaw rate of 15 deg/s, initial speed of 35 mph, 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 prominentâas expected. Based on these observations, it can thus 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.
118 Figure 6.13. Lateral tire forces for small car and pickup truck with 25-mph initial speed, tracking initial conditions, and panic return-to-road steer after 1 second P/R time. Figure 6.14. 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. 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 used in the friction ellipse model. Results of the simulations show that lateral tire forces can be adequately controlled by varying the maximum lateral friction coefficient. An example is
119 shown in Figure 6.15. 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 mph, and a constant steer angle and full ABS brakes applied throughout the simulation. As the lateral friction coefficient is increased, the lateral tire force increases for both vehicles and is significantly different for different values of the lateral friction coefficient. With friction coefficient of 1.2 and 2.0, the small car and the pickup do not roll over, even though the maximum roll angle increases for both vehicles with the increase in the friction coefficient (maximum roll angles can be seen in Appendix C for Run 15). With friction coefficient of 2.8, both vehicles roll over. Figure 6.15. 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. Results of the simulations thus demonstrate that the maximum later friction coefficient value can be used to adjust the maximum lateral tire force during side slipping, which in turn acts as a surrogate for soil-furrowing forces. Selection of Appropriate Lateral Friction Coefficient Based on the crash data, it is difficult to determine the probability of rollover on a flat surface when a vehicle leaves the roadway simply because many unintentional roadside encroachments do not result in a crash, and thus do not get reported. Even among the encroachments that result in a crash, many do not get reported. This fact is also supported by field studies of damaged roadside features. Although 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% (39, 60).
120 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 6.16. Figure 6.16a shows the overall percentages and Figure 6.16b shows the actual numbers of rollovers observed in the simulations. (a) Rollover Percentages (b) Number of Rollovers Figure 6.16. Percentages and numbers of rollovers for different values of maximum lateral coefficient of friction. While no rollovers occur for a lateral friction coefficient of 1.2, three (13%) pickup truck rollovers occur with a friction coefficient of 2.0. With a lateral friction coefficient of 2.1, there is one (4%) rollover for the small car, but the number of pickup rollovers increases to 7 (29%). At a lateral friction coefficient of 2.2, even higher numbers of rollovers are observed (38% for pickups and 17% for small cars). Results of the simulation indicate that a small increase in the lateral friction coefficient beyond 2.0 results in a significant increase in the number of rollovers, which is unrealistic when compared to the estimates of rollovers on flat terrains. With the 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 coefficient of friction in the friction ellipse model. 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
121 VEHICLE MODELING AND VALIDATION The researchers developed a model for a 5,000-lb (2270 kg) pickup truck using mostly predefined vehicle properties and datasets available in CarSim. Some of the geometric and kinematic properties were added to the model after measuring them from the test vehicles used by TTI or from other published data. Prior to embarking on the detailed simulation analysis with four different classes of vehicles (as selected in the final simulation matrix presented in the next chapter), the researchers wanted to perform a basic level of validation with at least one of the vehicle models built using CarSimâs predefined property datasets. Ideally, the researchers would have liked to perform basic validation for all vehicle models used in the research. However, due to a limitation of resources, validation was performed for the pickup truck model only. Other vehicle models were developed using the same basic approach used for developing the pickup truck model. It was expected that while there may be some differences between the simulation model and the specific make/model of a test vehicle, the simulation models would accurately represent the general class of the vehicles being considered. The validation process was carried out by performing a series of speed bump and ditch traversal tests. A 5,000-lb (2270 kg) Dodge RAM pickup truck was used for all of the testing. This vehicle was previously used by TTI in another full-scale crash test. The previous test did not result in any significant damage to the vehicle except some superficial damage to the front bumper. The vehicle and its key suspension components were intact and fully functional. Using this vehicle resulted in savings of vehicle cost for this project without compromising the accuracy of the data obtained from the new tests. The researchers also performed vehicle dynamics simulations of these tests using the pickup truck model developed in CarSim. After performing the speed bump and ditch traversal tests, the results were compared to simulation results for some of the key parameters, such as suspension compression, vehicle patch, and vehicle roll, pitch, and yaw angles. Details of the tests, vehicle model, and model validation are presented next. Field Testing for Vehicle Model Validation Two types of testsâspeed bump tests and V-ditch traversal testsâwere performed to compare test results with the simulation results for validation purposes. A total of six speed bump tests and two ditch traversal tests were performed. Speed Bump Tests The speed bump tests were live driver tests in which the test vehicle was driven over the bump(s) at various speeds. The first three tests were performed with the vehicle passing over a single speed bump. The remaining three tests were performed with the vehicle passing over two staggered speed bumps. The objective of the speed bump tests was to record the jounce and rebound of the vehicleâs suspension as it passed over the bumps at different speeds. In all tests, the vertical travel of all four wheel centers were recorded as a function of time. Test results were compared to simulation results during the validation phase. Locations of the speed bumps with respect to the vehicle are shown in Figure 6.17. The speed bumps were 4 inches tall and were fabricated from a 6-inch radius, Schedule 80 pipe (see Figure 6.17). The bumps were anchored to the ground to prevent sliding or other movement during the tests. The initial impact speed measured at the time of first contact with the speed bumps for each of the tests is presented in Table 6.3.
122 Ditch Traversal Tests Although the speed bump tests were designed to help researchers calibrate suspension properties of the vehicle model, the ditch traversal tests were considered more pertinent for this research because they allowed validation of the overall kinematic performance of the model. A 30-ft wide symmetric V-ditch with 5.5H:1V slopes was used in the testing, as shown in Figure 6.18. The test vehicle used in the ditch tests was the same vehicle previously used in the speed bump tests. The vehicle was towed into the ditch using a tow-truck and a cable reverse tow and guidance system. The tow and guidance system detached from the test vehicle just prior to entering the ditch. The vehicle was freewheeling and unrestrained once it entered the ditch. Two tests were performed at test speeds shown in Table 6.4. In both tests, the vehicle entered the ditch at an angle of 25 degrees. Figure 6.17. Speed bump test setup.
123 Table 6.3. Vehicleâs initial speed during speed bump tests. Single Speed Bump Test 1 11.5 mph Test 2 21.7 mph Test 3 30.8 mph Staggered Speed Bumps Test 4 11.9 mph Test 5 21.1 mph Test 6 29.3 mph Figure 6.18. Ditch traversal test setup. Table 6.4. Vehicleâs initial speed on entering the ditch. Test 1 41.6 mph Test 2 49.9 mph An onboard gyrometer system measured the roll, pitch, and yaw angles near the CG of the vehicle as it traversed through the ditch. Just prior to running each test, the ditch was lightly sprayed with water without significantly affecting the surface properties. This caused the vehicle to leave light tire marks in the ditch, which were enough to visually see the path of the vehicle. Immediately after the test, a total station theodolite device was used to record the path of the vehicle inside the ditch. The path of the vehicle and the roll, pitch, and yaw angles were used later on to compare to simulation results and validate the vehicle model. Vehicle Modeling The researchers developed a CarSim model of the MASH 5,000-lb (2270 kg) pickup truck using most of the available component and subcomponent property data sets available in CarSim, which included suspension spring and damper properties, a steering system, an ABS
124 braking system, aerodynamic loads, tire properties, suspension compliance coefficients, suspension auxiliary roll moments, and suspension bump stop properties. The overall geometric and mass properties for the vehicle model were obtained by measuring them from the test vehicle used in the speed bump and ditch traversal testing. The measured properties of the test vehicle are shown in Figure 6.19. The vehicleâs mass moments of inertia were not available for the Dodge RAM pickup truck used in the modeling and testing. The inertial properties of a Dodge RAM could also not be found in any of the published literature. Determining these properties requires specialized tests that were outside the scope of this project. In the past, the National Crash Analysis Center (NCAC) determined the roll, pitch, and yaw moments of inertia for a Chevy Silverado vehicle. The Chevy Silverado vehicle used by NCAC is also an acceptable MASH vehicle. In the absence of data for the Dodge RAM, the researchers used the inertial properties of the Chevy Silverado vehicle determined by NCAC (shown in Table 6.5). Since both Dodge RAM and Chevy Silverado belong to the same general class of vehicles, it is expected that the inertial properties of these vehicles will be similar. However, this assumption should be kept in mind when comparing simulation and test results for a specific test vehicle and its respective simulation vehicle. Table 6.5. Vehicle modelâs mass moments of inertia. Pitch 6155 kg-m2 Yaw 6453 kg-m2 Roll 1051 kg-m2 To model the contact between the vehicleâs body and the terrain, researchers selected several points underneath the vehicle body for input into the model. CarSim tracks these points during runtime and the user-written contact subroutine determines if any of these points have penetrated the terrain. If penetration is detected, contact forces are applied to the vehicle, as described earlier. For the pickup truck model, the researchers selected eight points near the bottom of the vehicle, as shown in Figure 6.20. The points were selected to be areas on the underside of the vehicle that were mostly likely to come in contact with the terrain and would offer significant resistance if the vehicle contacted the ground. Thus, these points were not necessarily on the outer shell of the vehicleâs body, which in some cases can easily deform without significantly affecting the overall kinematics of the vehicle.
125 Figure 6.19. Geometric and mass properties of the test vehicle.
126 Note: The table shows coordinates of these points with respect the modelâs origin. Figure 6.20. Location of tracked points (diamond-shaped) on pickup truckâs body. Terrain Modeling The terrain for both types of tests was modeled in CarSim. For the speed bump tests, the terrain incorporated the speed bumps used in the testing. The terrain for the staggered double speed bumps is shown in Figure 6.21. Similarly. the terrain for the V-ditch testing was also modeled, as shown in Figure 6.22. Figure 6.21. CarSim terrain incorporating two staggered speed bumps. Figure 6.22. CarSim terrain for V-ditch testing.
127 Model Validation Once the model of the vehicle and the terrain were completed, the researchers performed CarSim simulations matching the test conditions and compared simulation results to test results. The details of this model validation are presented next. The same vehicle model was used for all simulations (six speed bump and two ditch traversals) without changing any of the vehicle model properties for an individual case. Speed Bump Traversal Initially, three simulations were performed with the vehicle passing over a single speed bump. Then, three additional simulations were performed with the vehicle passing over the two speed bumps that were staggered as in the testing. The initial speed of the vehicle in each simulation case was matched to the respective test speed. Figure 6.23 shows the vehicle as it passes over the first speed bump in the simulation. In the speed bump simulations, the jounce and rebound of the wheel centers for all four wheels were calculated and compared to the test data. Since suspension system is a critical component of a multi-rigid body vehicle dynamics simulation involving slope traversal, the main objective of the speed bump tests and simulations was to validate the modelâs suspension response with reasonable accuracy. Figure 6.23. Typical CarSim speed bump traversal simulation. Comparisons of the simulation and test suspension responses (i.e., wheel center jounce and rebound) are shown in Figure 6.24 through Figure 6.29 for different test speeds and speed bump combinations. In the legend for these figures, F and R refer to front and rear suspension, and D and P refer to driver and passenger sides of the vehicle, respectively. The vertical travel of the wheel centers has been plotted as a function of time as the vehicle traverses the speed bump(s). Initial time (i.e., time = 0 seconds) in these plots represents the first contact of a tire with a speed bump. A good overall correlation was obtained between simulation and test results. The jounce and rebound response of the wheel centers was reasonably close in the test and simulations for most cases. In some cases, the simulation results indicated a slightly higher jounce (approximately 1.5 inches, or 38 mm). This difference can be partially attributed to the fact that some of the energy in an actual vehicle is dissipated in deflection of other vehicle parts/body (for example, elastic deformation of suspension mounts, torsional deflection of the vehicle body, etc.). However, the multi-rigid body vehicle dynamics model assumes mostly rigid behavior of the body and most of its linkages, joints, and other parts. Thus, slightly higher energy is likely
128 dissipated through the suspension spring and damper components in the simulation, which can result in slightly greater compression. Nevertheless, the differences in the test and simulation are not that significant. The jounce data of the rear suspension in Figure 6.25 indicates a possible malfunction in a suspension component (leaf spring or damper) of the rear driver side wheel, resulting in a higher jounce compared to the rear passenger-side wheel. Since the vehicle in this test drove over a single speed bump in a symmetric manner, it was expected that the test jounce and rebound would match for rear driver and passenger sides. Test videos showed no significant yaw in the vehicle after the front wheels passed over the speed bump. This result implies that the rear wheels passed over the speed bump in a symmetric manner, and therefore the compression of the suspension for each side should have been approximately the same. The researchers visually inspected the suspension leaf spring and damper of the rear driver side for any signs of damage. However, no visual damage could be identified. The damper also did not show any obvious signs of malfunction when the vehicle was rocked manually. A detailed examination including spring and damper property testing would have been needed to determine the reasons for the differences; however, such evaluation was not considered necessary or significantly beneficial to this research since a good correlation was achieved later on for the ditch traversal tests, which are more relevant for evaluating the vehicle modelâs validation for use in this research. In summary, the overall suspension jounce and rebound response of the model closely matched the test results. In some cases, though, there were differences of up to 1.5 inches in the jounce. Given that the suspension of a typical multi-rigid body vehicle dynamics model is overly simplified with simple springs and dampers, and without accounting for elastic or plastic deformation of the suspension components, linkages and joints or the flexibility in other parts of the vehicle, the differences observed in the simulation and test data were considered acceptable.
129 Figure 6.24. Speed bump traversal comparison for single speed bump with vehicle speed of 11.5 mph. Figure 6.25. Speed bump traversal comparison for single speed bump with vehicle speed of 21.7 mph.
130 Figure 6.26. Speed bump traversal comparison for single speed bump with vehicle speed of 30.8 mph. Note: Rear driver side camera failed to start in test, and data could not be obtained for that wheel center. Figure 6.27. Speed bump traversal comparison for two speed bumps with vehicle speed of 11.9 mph.
131 Figure 6.28. Speed bump traversal comparison for two speed bumps with vehicle speed of 21.1 mph. Figure 6.29. Speed bump traversal comparison for two speed bumps with vehicle speed of 29.3 mph.
132 Ditch Traversal Although the speed bump tests were used to validate the response of individual suspension components, a more relevant validation of the overall ability of the model to accurately predict vehicle kinematics while traversing ditches (as related to use in this project), relied on the ability to match the ditch traversal test data. The two ditch traversal tests were simulated with the vehicle entering the 5.5H:1V ditch at test speeds of 41.6 mph (66.9 km/h) and 49.9 mph (80.3 km/h) at an angle of 25 degrees. Figure 6.30 shows the vehicle passing through the ditch in one of the simulations. Traces of the vehicle are shown in the figure so that different states of the vehicle can be seen as it traverses the ditch. Figure 6.30. CarSim simulation of MASH pickup traversing 5.5H:1V V-ditch. The path of the vehicle through the ditch was calculated from the simulation analysis. Also calculated were the roll, pitch, and yaw angles as a function of time. Figure 6.31 and Figure 6.32 show the comparison of the vehicleâs path in the test to the simulation for the 41.6 mph (66.9 km/h) and 49.9 mph (80.3 km/h) tests, respectively. Figure 6.33 and Figure 6.34 show the comparison of the vehicleâs roll, pitch, and yaw angles plotted as a function of time for the 41.6 mph (66.9 km/h) and 49.9 mph (80.3 km/h) tests, respectively. It can be seen from these figures that a good correlation was achieved between the test and simulation results. The path of the vehicle model reasonably matched the path of the test vehicle for both speeds. Similarly, the roll, pitch, and yaw angles of the CarSim vehicle model were reasonably matched with the angles measured in the tests for both speeds. Although there are some noticeable differences, they are expected due to the simplification of the vehicle dynamics modeling methodology, which relies on lumped masses that are connected via springs and damper formulations rather than more sophisticated material properties. However, for a given class of vehicle, the behavior of the CarSim model is reasonably similar to the actual vehicle.
133 Figure 6.31. Vehicle path comparison at 41.6 mph. Figure 6.32. Vehicle path comparison at 49.9 mph.
134 Figure 6.33. Vehicle roll, pitch, and yaw comparison at 41.6 mph. Figure 6.34. Vehicle roll, pitch, and yaw comparison at 49.9 mph. In matching the overall kinematics of the vehicle traversing though the ditch, the researchers reasonably validated the pickup truck model for further use in this research. It should be noted that several other forms of validations can be performed to gain further confidence in
135 the use of CarSim models. Among such validations are the validation of driver input, side slipping, rollover, and the like. These validations require additional specialized testing and subsequent simulation analysis that were outside the current project scope and resources. As mentioned before, the researchers would have liked to perform basic validation described above for all vehicle models used in the research. However, due to limited resources, validation was performed for the pickup truck model only. Other vehicle models were developed using the same basic approach used for developing the pickup truck model. It was accepted that though there might be some differences between the simulation model and the specific make/model of a vehicle, the simulation models accurately represented the general class of the vehicles being considered. Vehicle Models In addition to the pickup truck model, the researchers developed vehicle models for three additional vehicles for use in the project. These included a 2006 Kia Rio (small passenger car), a 2002 Ford Explorer (midsize sports utility vehicle), and a 2006 Ford Taurus (large sedan). The dimensions and geometric properties for these models were measured from actual vehicles. However, the vehicle moments of inertia values were used from the Expert AutoStats software database (61). The Expert AutoStats software database is commonly used in accident reconstruction problems. This database provides the roll, pitch, and yaw moments of inertia for vehicles. The moments of inertia values are approximate and are based on analytical calculations. Due to limited resources, testing to determine actual moments of inertia could not be performed. However, it was accepted that for a give class of vehicle, the approximate analytical moments of inertia values were adequate for use in this project. SUMMARY AND CONCLUSIONS To understand and evaluate the effects of different ditch configurations, vehicle types, encroachment conditions, and diver inputs, the researchers selected the multi-rigid body vehicle dynamics code CarSim. Advantages of using CarSim instead of some of the other simulation tools and methods, was discussed in detail in this chapter. The researchers also incorporated a vehicle body-to-terrain contact in CarSim as a user-written subroutine. The algorithm of this contact is the same as previously used in TTIâs version of the HVOSM. The researchers also coded a wrapper program that can generate a large number of input files, automate running simulation cases in CarSim, and post-process the results. In addition to these features, the researchers developed a module for applying soil-furrowing forces to the vehicleâs tires using the friction ellipse model. This module was incorporated into the wrapper program for applying the forces during each simulationâs runtime. The researchers performed sensitivity studies to select appropriate values for PRT, vehicle yaw rate for non-tracking encroachments, and the maximum lateral friction coefficient for determining tire forces when a vehicle is side slipping on soil. The researchers developed a CarSim model of a MASH pickup truck and then performed various tests to perform a basic validation of the vehicle model. A series of dynamic bump traversal and ditch traversal tests were performed using a MASH pickup truck. In these tests, the response of the suspension and the overall vehicle kinematics were recorded. Simulations with the CarSim pickup truck model were performed with test terrain and initial conditions. A good
136 correlation was obtained between the test and simulation results, thus validating the vehicle model for further use in the project. It was noted that not all models used in this research can be validated in a similar manner due to budgetary constraints. However, the overall approach of developing the CarSim model was validated through this exercise of developing the pickup truck model. The researchers then developed vehicle models for a small passenger car, a midsize sports utility vehicle, and a large sedan. All of these models and codes were then used in performing the simulations analysis for the encroachment cases listed in the simulation matrix, which is presented in the next chapter.