Bell

Integrating Vehicle System Dynamics Simulation into the Product Development Process Ragnar Ledesma and Edward Eshelman ArvinMeritor Commercial Vehicle Systems

ABSTRACT The use of ADAMS as a virtual prototyping tool and its integration into the product development process is described in this paper. By way of examples derived from our experience at ArvinMeritor Commercial Vehicle Systems, we describe how ADAMS evolved from a tool used for troubleshooting field problems to a virtual prototyping tool for vehicle system dynamics that is fully integrated into the new product development process. We discuss some of the key factors in the successful deployment of this technology as an integral part of the development cycle. The first part of this paper reviews some of the cases where ADAMS was used in trouble-shooting field problems: 1) A-train double trailer roll and lateral stability; 2) interaction of suspension and drive train and dynamics; 3) front axle brake chatter; 4) transmission case acoustics; 5) city bus ride comfort; 6) steering system vibration; and 7) impact loads on trailer suspensions. The second part of this paper deals with the integration of vehicle system dynamics into the product development process. We describe some examples of this integration process which include, among others: 1) virtual K&C tests for front, rear, and trailer suspensions; 2) design of alignment parameters for front steer axle; 3) specification of shock absorber rates; and 4) determination of loading block cycles for subsystem-level and component-level fatigue tests. Finally, we deal with some open issues on model versus test correlation. INTRODUCTION Vehicle system dynamics plays a central role in the design and analysis of commercial vehicle systems. The often conflicting requirements of ride comfort, vehicle handling, and component durability require that vehicle engineers take a systems approach in arriving at an optimum design of a vehicle [1,2]. Such an approach allows the engineer to efficiently assess the impact of the suspension design on the performance of the total vehicle in terms of ride comfort, vehicle handling, noise and vibration, and durability loads on every component. Another benefit is that vehicle system dynamics can be performed throughout the product development process, starting from the conceptual design stage where specific design decisions still have to be made, to the final design stage where component dimensions are optimized. Several factors have contributed to a greater need for vehicle system dynamic analysis today than in the past. From the engineering design perspective, we now have more design

alternatives from various types of suspension systems. From the customers’ perspective, we have seen an increase in demand for reducing noise and vibration in the medium-duty and heavy-duty vehicles. From the business perspective, we have heard the mandate for lower product development costs and faster time to market, as well as the push for lower warranty costs. These demands point to the need for more vehicle system dynamic analysis up-front for predicting vehicle handling characteristics, predicting component durability and reliability, reduction of NVH problems, and consideration of the best design among all possible design alternatives. Some of the design considerations that can be addressed with the use of vehicle system dynamics are listed in Table 1.

Design Area Function

Design Consideration • vehicle roll stability • vehicle lateral and directional stability • cornering and braking response • shimmy stability • tire wear • steering effort • stopping distance • minimum turn radius • packaging and mechanical lock-up • sprung-to-unsprung mass ratio • load transfer • dive, lift, squat NVH • ride comfort • sprung mass isolation • engine isolation • frame compliance • powertrain/suspension interaction • steering system vibration • brake noise • natural frequencies and damping ratios Durability • component and joint forces • tire forces and moments • component flexibility • material selection: toughness and ductility • bump stop/rebound stop selection • bushing and shock damper selection Table 1: Some considerations in the design of suspensions

KEY FACTORS FOR SUCCESSFUL USE OF VEHICLE SYSTEM DYNAMICS TECHNOLOGY So far, we have discussed the need for a systems approach in several vehicle system performance issues and the benefits of using vehicle system dynamics in addressing these issues effectively. In this section, we will attempt to outline the processes involved in this approach, as well as the prerequisites of being able to apply this approach early in the design cycle. Every application may have its own set of procedures, but some general procedures are common to all system dynamic analyses. Some of the basic procedures involved in tackling vehicle system performance issues with the system dynamics approach include the following: • • • • • • • • •

define the engineering problem and the objective of the analysis define the physical system define the idealized system build the mathematical model perform the appropriate analysis validate the model and verify the results update the model if necessary perform design sensitivity studies and design of experiments optimize the design

The first three items require the suspension design engineer to have a good understanding (through experience) of the product’s function in order to define the objective of the inquiry and to define the boundaries of the vehicle subsystems that are important to the phenomenon under investigation. Building the mathematical model and performing the appropriate analysis, either through commercial codes or through in-house programs, require that the engineering analyst should have solid analytical skills and an expertise in using the computer program. Validating the model and verifying the results, usually through field tests, requires some expertise in experimental methods, signal processing and test data analysis. The last two items on the list which pertain to design optimization requires that the designer should have some insight as to what design parameters can have a significant impact on the performance of the system. The varied skills required to successfully complete a vehicle system analysis and design can be fulfilled through a team approach where each team member, each being highly skilled in a specific area, can contribute to the process. Besides personnel skills, other resources are necessary to be successful in applying the system dynamics approach in a medium-duty and heavy-duty vehicle production environment. First, the team must have access to computer hardware with adequate capabilities. Second, software such as industrystandard commercial codes or programming software, appropriate for solving the problem at hand, should be

available. Third, in a production environment, core models for each application should have been developed. These models should be easy to maintain and to modify in order to accommodate changes in design configurations. Fourth, a database that can support the core models is crucial if the model is to be successfully used in tight product development schedules. The database should be continuously maintained and updated because products and practices evolve over time. Finally, there should be adequate resources for field-testing, model correlation, and model updating to ensure that predictions obtained from the simulation models are valid, especially for new products or new designs. A key factor in the successful deployment of vehicle system dynamics technology into the product development cycle is getting management approval. Investments in computer hardware, software, and specialized personnel involve significant capital expenditures. At ArvinMeritor, getting management to commit to this investment was achieved in stages. The initial stage involved setting up several pilot studies to demonstrate the potential of this technology. These studies naturally came about in addressing field problems that involved vehicle system dynamics. Having proved the potential of the technology through successful resolution of field problems, it became obvious to management that the product design process should be revised in order to include vehicle system dynamics early in the product design cycle. In the next section, we describe some of the cases where vehicle system dynamics was successfully used in resolving some field problems. We then describe some examples of how virtual prototyping is being used for integrating vehicle system dynamics into the new product development cycle. A summary description of the models used in these cases, including the components considered in the system, model outputs, and other model features are summarized in Table 2.

EXAMPLES OF USE OF VEHICLE SYSTEM DYNAMICS IN TROUBLE-SHOOTING FIELD PROBLEMS At ArvinMeritor, vehicle system dynamic simulation is conducted through the use of the industry-standard multibody dynamics code ADAMS along with the commercial finite element code ANSYS, while test data analysis and model updating are performed through in-house codes developed in the Matlab environment. The finite element code is used in modeling component flexibility and in estimating the modal properties of the vehicle components. In the following paragraphs, we describe seven applications that demonstrate the use of vehicle system dynamics in trouble-shooting system-level performance issues. Trailer Roll Stability. This example demonstrates the use of dynamic system simulation in comparing the effect of two types of trailer suspensions on the roll stability of an A-train

Figure 1: Model of an A-train double for roll and lateral stability

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double-trailer truck combination. The first type of trailer suspension considered is the conventional trailing arm air suspension, and the second type of trailer suspension considered is the proposed ArvinMeritor parallelogram suspension for single trailer axles. Two versions of the ADAMS model of the A-train double shown in Figure 1 have been developed. One version has the conventional trailing arm suspension on the trailer axles, and the other version has the proposed parallelogram suspension on the trailer axles. The truck combination consists of a tractor with tandem drive axles, a semi-trailer with a single trailer axle, and a full-trailer with a converter dolly. The full trailer and the converter dolly have single axles as well. The tractor, which is identical to both models, has a positive understeer gradient to ensure static stability of the multiple train system. Inputs to the model include sprung mass and unsprung mass inertia properties, component geometry and material properties, beam element representation of axle shafts and torque tubes, air suspension force-displacement curves, shock absorber force-velocity curves, bushing rates, and tire properties. The comparison was conducted by simulating a lane change maneuver at highway speeds and with the trailers fully laden. The axle roll angles and lateral accelerations of the center of gravity of the full trailer for both types of trailer suspensions are shown in Figure 2. This figure shows that the proposed parallelogram suspension is more stable in roll than the conventional trailing arm suspension. Furthermore, the resulting lateral acceleration at the trailer’s center of gravity is less when the proposed single axle parallelogram suspension is used for the trailer axles. Computer animation of the lane change simulation also shows that besides being more stable in roll, the A-train double with the parallelogram trailer suspension also has a better tracking capability than the A-train double with a conventional trailing arm suspension.

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Figure 2: Roll and lateral dynamic performance for two candidate designs of trailer suspensions

Interaction of Drive Train and Suspension. In this example, vehicle system dynamics is used in predicting the U-joint angles in the drive train during acceleration and deceleration, and to determine the resulting torsional excitation on the drive train due to the magnitude of the U-joint angles. High U-joint angles during normal operation can lead to excessive torsional vibration in the drive train, and this may result in premature fatigue failures in the drive train components. The industry has seen an increase in this mode of failure since the advent of the trailing arm type of air suspension, which gives the truck operator the ability to arbitrarily set the ride height of the drive axles. Figure 3 shows an ADAMS model of an integrated drive train, tandem drive axle, and a trailing arm type air suspension. This model can predict the load transfer between the front axle and the tandem rear axles during acceleration and braking, and simultaneously compute the articulation of the drive axles, which result from the deflection of the rear suspension during the load transfer. The model can be easily modified to include more detailed information such as the effect of U-joint angles on the dynamic bearing force fluctuation or gear teeth force fluctuation. Data used as input to the model are the geometric and material properties for each of the drive train and suspension components, including mass, stiffness, damping ratios, gear ratios, and attachment point locations. The output of the model contains a wealth of information besides U-joint angles and drive train vibration. These include reaction forces at each of the joints, vehicle performance such as speed and acceleration, and internal torque and angular motion of each component in the drive train. The analysis is performed in the time domain, although the results can be easily converted into the frequency domain in the post-processing stage. Useful performance trends include natural frequencies of the drive train and suspension system as a function of the gear setting, change in U-joint angle as a function of drive torque, magnitude of drive train

torsional excitation as a function of U-joint angle and driveline speed, resonance between the axle carrier pitch mode and the drive train torsional vibration mode. As an example of the model’s output, Figure 4 shows the vehicle speed, U-joint angle variation, and transmission input shaft torque during vehicle acceleration and gear shifting. This figure shows that at a certain speed and gear setting, the excitation from the Ujoint angle will resonate with the drive train’s second torsional mode of vibration.

Figure 3: Drive train and suspension interaction model drive train and suspension interaction: WOT acceleration

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coupling occurs when the difference between the generalized stiffness of radial and tangential modes get below a threshold, the value of which depends on the coefficient of friction and contact properties between the brake shoe and the brake drum. The generalized stiffness of the radial mode depends on the brake pressure, which is a time-varying state variable, while the generalized stiffness of the tangential mode depends on the wrap-up stiffness of the leaf springs and on the torsional stiffness of the axle. When mode coupling occurs, a point on the brake shoe lining follows an elliptical path such that the amount of frictional energy entering into the suspension, axle, and brake assembly is positive, thus giving rise to the limit cycle phenomenon [3]. Figure 5 shows the finite element representation of the axle-suspension-brake assembly. The finite element model is embedded into an ADAMS model which includes the moving parts of the brake system as well as a state equation for the brake pressure. Inputs to the model include geometric and material properties for each of the components, as well as friction and contact properties at the brake shoe and brake drum interface. Figure 6 shows an example output of the nonlinear, time-domain, simulation of the brake chatter phenomenon. This figure shows the time history plots of the normal contact force and the friction contact force between the leading shoe and the brake drum. Brake chatter is more likely to occur as the friction coefficient at the brake shoe/drum interface is increased. Measured data used for model validation and model updating include brake pressure levels at which chatter occurs and the frequency spectrum of the axle vibration during brake chatter. Design recommendations that were derived from the dynamic system simulations include the addition of damping sources at various locations, the use of a soft layer underneath the brake lining to reduce the contact stiffness, and separating the radial and tangential modes farther through the introduction of auxiliary devices such as torque rods.

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Figure 4: Vehicle speed, U-joint angle, and transmission input torque during WOT acceleration

Brake Chatter. Brake chatter is an example of the dynamic interaction between the suspension system and the brake system. It is characterized by self-sustained oscillations induced by friction between the brake shoes and the brake drum. Brake chatter occurs when the brake shoe radial motion mode coalesces with the tangential mode (or rocking mode) of suspension/brake assembly due to leaf spring wrap-up. Mode

Figure 5: Front axle, brake, and suspension assembly

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Figure 6: Brake chatter: contact force at the brake shoe/brake drum interface

Transmission Case Acoustics. In this example, vehicle system dynamics is combined with other technologies to reduce the noise generated by meshing gears and radiated through the transmission case (transmission housing). The process of designing a new transmission case that will reduce the level of radiated noise involves several computer codes that use different technologies. These include the following in sequential order: 1) Load Distribution Program; 2) ADAMS; 3) Matlab; 4) ANSYS; and 5) Comet Acoustics. The Load Distribution Program, developed at The Ohio State University, is a computer code that will predict the static transmission error in the meshing gears and stresses in the gear teeth for a given gear design (teeth profile, pressure angle, number of teeth, diametric pitch, etc.) and a given load torque. The static transmission error predicted by the LDP program is used as input to the ADAMS model of the gear-shaft-bearing system shown in Figure 7. The ADAMS model will then predict the dynamic transmission error and the fluctuating reaction forces at the bearings, which transmit the loads from the transmission shafts to the transmission housing. The Matlab program is next used in obtaining the frequency spectrum of the bearing loads from the time-domain outputs from ADAMS. The ANSYS finite element program is then used in predicting the frequency response of the transmission case to the dynamic bearing loads. Within the frequency range of interest, the surface velocity profiles of the transmission case are obtained from the finite element analysis (see Figure 8). These are subsequently used by Comet Acoustics to predict the sound pressure level of the noise radiated through the transmission case (see Figure 9). The entire procedure is repeated for every new design of the transmission case. The ADAMS model of the gear-shaft-bearing system captures the dynamic interaction between the bearing compliance, gear tooth compliance, and shaft torsion and beaming modes.

Bearing compliance is characterized by a nonlinear relation between the bearing forces and the relative displacement between the bearing cup and cone [4]. Gear tooth compliance is described by a time-varying stiffness of the pair of gear teeth in contact (a function of the rotation angle). Shaft torsion and bending are modeled by short beam elements with circular cross-sections. The ADAMS model is driven by motion inputs which are the time-varying static transmission error at each of the gear pairs. The static transmission error, in turn, depends on the applied load and angular velocity. Inputs to the gearshaft-bearing model include component geometric and material properties, dynamic properties such as gear mesh stiffness and damping, and roller bearing properties such as taper angle, dimensions of roller elements, and dimensions of cup and cone. Besides dynamic bearing forces, model outputs include estimates of system natural frequencies and internal forces in each component. An example of the frequency spectrum of the dynamic bearing load obtained from this model is shown in Figure 10.

Figure 7: Gear-shaft-bearing model of 9-speed twin-shaft transmission in 5th gear configuration

Figure 8: Transmission case surface velocity profile from ANSYS frequency response analysis

rates and shock absorber rates for each of the three axles, location of engine and transmission mounts, and structural characteristics of the chassis, as well as the introduction of active or semi-active suspensions [5,6]. Figure 12 is a comparison of ride quality performance between the optimal passive shock damper and a semi-active shock damper at the drive axle. The plots in this figure are the power spectral density of the vertical acceleration measured at a selected passenger seat. It was shown in these modeling exercises that system-level design optimization can be accomplished with the use of vehicle system dynamic simulation.

Figure 9: Sound pressure level predicted by Comet Acoustics transmission gear−shaft−bearing axial radial

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City Bus Ride Comfort. This example demonstrates the usefulness of vehicle system dynamics as a tool in evaluating the performance of the total vehicle system when evaluating different suspension design alternatives. A typical ride comfort study for an on-highway heavy-duty vehicle is a passenger bus subjected to vertical excitation due to pavement joints in the highway, while the bus is cruising at highway speeds. The system performance metric in this case is the root mean square (RMS) values of the vertical and fore-aft components of acceleration measured at the driver’s seat and at a selected passenger’s seat. Figure 11 shows an ADAMS model of a passenger bus. The model includes the suspension system, engine and transmission mounts, and a finite element model of the bus chassis and frame. For this particular model, the compliance of the bus chassis and frame can adversely affect ride quality. Design considerations for improving ride comfort include the optimization of the following: suspension

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Figure 12: Frequency content of vertical acceleration at a selected passenger seat Steering System Vibration. Examples of steering system vibration include axle tramp, shimmy, and wobble. In the axle tramp and shimmy modes of vibration, the two wheels oscillate in phase, while in the wobble mode of vibration, the two wheels oscillate out of phase. The wobble type of steering

Figure 13: Front axle and suspension model for steering system vibration axle tramp: 4" bump at 25 MPH 0.04

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system vibration occurs at a higher frequency (greater than 15 Hz) and is usually damped out by tire damping, hence, it is not a common problem in medium and heavy-duty trucks. Axle tramp is a severe, transient steering system oscillation that results from the unbalanced gyroscopic moment of a turning wheel that is produced when one wheel hits a bump and causes the front axle to roll. Axle tramp usually occurs when one wheel lifts off the ground, so that there will be insufficient aligning moment at the tire-ground interface to resist the gyroscopic moment of the turning wheel. Hence, the axle tramp mode of steering system vibration is tightly coupled with the design of the front suspension system, and the most effective countermeasure against axle tramp is to design a suspension system that prevents the tire from lifting off the ground. Wheel shimmy is a self-excited, sustained steering system vibration which can result in loss of vehicle stability if the amplitude of vibrations are not controlled [7]. Similar to axle tramp, wheel shimmy is tightly coupled to the axle roll mode, hence the design of the front suspension can also affect the propensity of occurrence of shimmy. The crucial parameters which govern the occurrence of shimmy include cornering stiffness, tire relaxation length, tire wall stiffness, tire-ground friction properties, wheel caster, and suspension stiffness. Other factors which can also have significant effects on axle tramp and shimmy include steering system alignment parameters such as caster angle, kingpin inclination angle, wheel offset or scrub radius, and location of drag link and steering arm ball joints. Damping of axle tramp and shimmy vibration primarily come from internal damping in the tires and from internal friction in the kingpin bushings. In addition, external damping may be introduced in the form of tie rod dampers which are attached between the tie rod and the axle beam. Therefore, it appears that the most effective way of evaluating the design of the steering system with respect to steering system vibration is through the integrated vehicle system dynamics approach. With such an approach, the effect of each design parameter, or the combination of several design parameters, on the steering system performance can be effectively quantified through design of experiment (DOE) methods. Figure 13 shows an ADAMS model used in the study of steering system vibration in a heavy-duty truck. In this model, the tire properties play a crucial role in predicting the occurrence of steering system vibrations. The axle tramp performance of two candidate designs of the steering system are compared in the time history plots of Figure 14. This figure shows that the modified design performs better than the original design with respect to axle tramp vibrations. The same model can be used, without modifications, to study shimmy vibration under several scenarios such as shimmy due to random road roughness or shimmy as a result of lane change steering maneuvers.

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Impact Loads on Trailer Suspensions. This example shows how vehicle system dynamics simulation can be used to determine the proper loads and boundary conditions for the finite element analysis of a component. In this particular example, the slider frame of the trailer suspension shown in Figure 15 is subjected to impact loading with the trailer frame. This happens when the truck operator forgets to lock the slider to the frame (a common occurrence in the field) and applies the brake, causing impact between the slider and the trailer frame. The impact forces can result in localized buckling (higher buckling mode) in the slider frame. Design engineers typically want to be able to predict the buckling mode so that they can reinforce the structure at the appropriate locations. Using ADAMS, the dynamic simulation of this impact event can provide the magnitudes of the impact load, as well as the distribution of reaction loads at the attachment points of the slider frame. This information is critical in determining the

proper boundary conditions in a subsequent buckling analysis, which is typically performed using a finite element code such as ANSYS. An example of a localized buckling mode that was determined by using the above approach is shown in Figure 16. This buckling mode (higher than the fundamental buckling mode) matched the buckling mode observed in a field test with respect to the mode shape and also with respect to the buckling load.

dynamics has been integrated into the product development process. Virtual K&C Tests. Virtual K&C (kinematics and compliance) tests of front axles, rear axles, and trailer axles are now performed early in the design cycle. The process has been standardized through the use of user-friendly programs such as ADAMS/Car and ADAMS/Pre. Design engineers who are not simulation/analysis experts can routinely perform these tests to determine the geometric properties (roll center, roll steer coefficient, toe change, camber angle change, etc.) and compliance properties (wheel rate, lateral force compliance, aligning torque compliance, etc.) of candidate designs of suspension systems. Figure 17 shows a model of a hybrid airleaf suspension set up for a virtual K&C test.

Figure 15: Tandem trailer axle and suspension

Figure 17: K&C test of a hybrid air-leaf suspension

Figure 16: Localized buckling mode of slider frame

INTEGRATING VEHICLE SYSTEM DYNAMICS INTO THE PRODUCT DEVELOPMENT PROCESS Having proved out the advantages of using vehicle system dynamics in the resolution of field problems, the management team at ArvinMeritor has decided to invest in resources that will allow vehicle system dynamics to be an integral part of the product development cycle. In the following paragraphs, we briefly describe some areas in which vehicle system

Design of Front Axle Alignment Parameters. Vehicle dynamic simulation is now routinely performed to design the front axle alignment parameters. The design variables typically include caster angle, kingpin inclination angle, wheel offset, track width, maximum turning angle, tie rod ball joint location, and steering arm ball joint location. The objective performance metrics that are considered in finding an optimum design include the following: Ackermann error (tire wear), steering system vibration (tramp and shimmy), steering effort, durability of front axle components, and vehicle handling performance. Vehicle operations that are typically considered in determining the objective performance metrics include: dry park steer (parking lot steering), steady-state cornering, combined braking and cornering, step steer, on-center handling, bump steer (one-side bump), constant-µ braking, split-µ braking and driving straight on a rough road. Figure 18 shows a typical plot of steering effort (performance metric) as a function of kingpin inclination angle during a dry park steer maneuver. Figure 19 shows a typical plot of wheel steer angle (steering vibration amplitude) as a function of kingpin

inclination angle and wheel offset during straight-line driving on a rough road. 4

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step steer maneuver, and lateral acceleration or yaw rate peakto-steady state ratio (frequency response). For ride comfort, a typical performance metric is the RMS acceleration or the absorbed power at the driver seat track during straight-line driving on a computer-generated, random road profile. Figure 20 shows a typical plot of RMS vertical acceleration as a function of the front shock scale (linear scaling factor for the nonlinear force-velocity curve) and the rear shock scale of a 4x4 off-road vehicle.

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Specification of Shock Absorber Rates. Vehicle dynamics simulation is performed early in the design cycle to optimize the shock absorber rates with respect to vehicle handling performance and ride comfort. The shock absorber forcevelocity curve, which is usually characterized as a piecewiselinear curve, is a parametric function of 6 design variables, namely: 1) first slope in compression zone, 2) second slope in compression zone, 3) transition velocity (blow-off valve activates) in compression zone, 4) first slope in rebound zone, 5) second slope in rebound zone, and 6) transition velocity in rebound zone. Typical vehicle handling performance metrics for shock absorber specification include response time, peak lateral acceleration, peak yaw rate, and settling time during a

Durability Loads Prediction. This last example illustrates an important contribution of vehicle system dynamics to the product design process. This is the prediction of dynamic loads acting on the suspension components during transient events. These dynamic forces can be used as input to subsequent finite element stress analysis of the suspension system components, and they can also be used as the basis for the loading block cycle for subsystem-level or componentlevel fatigue qualification tests [8]. Typical suspension components such as the axle housing for a tandem drive axle shown in Figure 21 have several attachment point locations. A finite element stress analysis of this component will require the analyst to provide all the force components at every attachment point. Measuring all of these force components on a test vehicle is very costly and impractical. Furthermore, the finite element analysis procedures require that the applied forces and inertia forces in the component are in dynamic equilibrium at all times. If this requirement is not satisfied, spurious stresses due to the unbalanced forces are obtained from the finite element analysis. Due to errors in the measurement process, the measured forces will not satisfy this requirement. A better alternative to testing a vehicle in the field in order to obtain dynamic loads on the suspension components is to create a virtual proving ground and perform vehicle system dynamics. This process will yield dynamic

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loads at all attachment points that are required for subsequent finite element analysis. Furthermore, the dynamic loads produced by vehicle system dynamics will automatically satisfy dynamic equilibrium for every component in the suspension system. A validated durability tire model is critical to the success of this approach. In addition, the analytical model should be verified and updated by comparing the natural frequencies predicted by the model with those of the test vehicle. The plot in Figure 22 shows a comparison of the simulation results with the vehicle test for a tractor-trailer going over a 4” chuckhole at 10 mph. For random road profiles, the loads predicted by the vehicle system dynamics model can be validated by comparing the histograms of the forces measured in the field test and their counterparts in the simulation. Appropriate load factors can then be applied to the predicted loads such that the resulting design load corresponds to a desired level of loading as observed in the field. For example, the mean plus three-sigma criterion is a common level of loading used in checking against yield failure. Figure 23 illustrates the results of using the time history of a force component in estimating the design load for a suspension component. The time history of the suspension forces predicted by vehicle system dynamics can also be used in predicting the fatigue life of the suspension components, either through a strain-based, linear elastic fracture mechanics approach, or through a statistics-based approach for reliability analysis [9].

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OPEN ISSUES IN MODEL CORRELATION

Figure 21: Tandem drive axle housing model for stress analysis

We conclude this paper with a discussion on some open issues on model correlation. A simulation model is only useful to the extent of one’s confidence in the accuracy of the results of the simulation. We propose two measures to quantify how good the ADAMS model correlates with actual hardware. The first measure is the correlation function. If we have two signals, say, x(t) and y(t), the correlation function is defined as R(τ) = E[x(t)*y(t+τ)], where E[•] denotes the expectation value. The correlation function is a measure of the linearity between two signals. It also identifies the time lag between the two signals, i.e., the absolute value of R(τ) is maximum when τ is equal to the time lag. The correlation function can be scaled such that |R(τ)| ≤ 1. A value near ±1 for the correlation function implies

a strong linear relationship while a value near zero implies either a non-linear relationship or no correlation between the two signals. A second measure of correlation is the coherence function, γ(f), normally used in modal testing and analysis. The coherence function is a measure of the linearity between the two signals in the frequency domain. It identifies the frequencies at which the signals have a strong linear relationship, γ(f) = 1, and the frequencies at which the signals do not have a linear relationship γ(f) ≅ 0. Both measures are useful tools in identifying elements in the model that need tuning or updating. We propose the following guidelines for model tuning or updating. First, correlation should initially be conducted at the subsystem level where the inputs to the test article and to the model are exactly the same. For example, spindle loads on the front axle can be measured by using a 6-d.o.f. force transducer on each of the front wheels, and these are then used as force inputs to the front suspension test rig. Other measured quantities such as axle accelerations or suspension deflections can then be compared to obtain correlation metrics. After the subsystems have been correlated, only then should a fullvehicle correlation be attempted, if necessary. The first step in full-vehicle correlation is to make sure that the axle loads are equal to those of the test vehicle. The next step is to duplicate the natural frequencies and damping ratios of the test vehicle. This will involve modal testing and analysis of the test vehicle. The final step is to compare the response of the model and the test vehicle to steering inputs and road excitations. One difficulty with full-vehicle correlation is that the speed of the test vehicle can not be precisely controlled by the driver, hence there will always be some differences in the instantaneous speeds between the model and the test vehicle. For example, in comparing the ride performance of a vehicle going over a durability course, differences in instantaneous speeds will cause a change in frequency and phasing in the excitation at the tire contact patches. One way to alleviate this problem is to correlate events that involve only single, welldefined obstacles such as a pothole or a single bump.

CONCLUSION Several examples have been presented to illustrate the effectiveness of using ADAMS as a virtual prototyping tool for up-front simulation/analysis that is an integral part of the product development process. Through integrated vehicle system modeling and vehicle system dynamic simulation, a thorough performance analysis can be conducted early in the design cycle, resulting in a superior design of a suspension, steering, brake, or drive train system. At ArvinMeritor, the advantages of the approach are fully recognized and simulation models have been developed and are being utilized towards the attainment of this goal.

REFERENCES 1. Seminar Notes, “The Mechanics of Heavy-Duty Trucks and Truck Combinations,” University of Michigan Transportation Research Institute, 1996. 2. T. Gillespie, “Fundamentals of Vehicle Dynamics,” SAE Publications, 1994. 3. R. Ledesma, “Modeling Friction-Induced Dynamic Instabilities Using Flexible Multibody Dynamics with ADAMS”, 1996 International ADAMS Users Conference Proceedings. 4. L. Houpert, “A Uniform Analytical Approach for Ball and Roller Bearings Calculations,” ASME Journal of Tribology, Vol. 119, pp. 851-858, 1997. 5. D. C. Karnopp, “Active Damping in Road Vehicle Suspension Systems,” Vehicle System Dynamics, Vol. 12, pp. 291-312, 1983. 6. D. C. Karnopp, “Design Principles for Vibration Control Systems Using Semi-Active Dampers,” ASME Journal of Dynamic Systems, Measurement, and Control, Vol. 112, pp. 448-455, 1990. 7. H. B. Pacejka, “The Wheel Shimmy Phenomenon,” Ph.D. Dissertation, Delft University of Technology, 1966. 8. R. Somnay and S. Shih, “Product Development Support with Integrated Simulation Modeling,” SAE Technical Paper 1999-01-2812, 1999. 9. K. Chang, X. Yu, and K. Choi, “Probabilistic Structural Durability Prediction,” Proceedings of the Sixth AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization, 1996.

Purpose Trailer Roll and Lateral Stability

Suspension and Drive Train Interaction Brake Chatter: Front Axle SCam Brakes Transmission Gear-ShaftBearing Ride Comfort: Bus w/ Frame Flexibility Steering System Vibration

Impact Loads on Trailer Suspension Virtual K&C Test Vehicle Handling Performance Front Axle Alignment Parameters Ride Comfort: 4x4, 6x6, 8x8 Independent Suspension Durability Loads Prediction

Dynamic System Model Description • components include: tractor with tandem drive axles, semi-trailer, converter dolly, full trailer, air springs, trailing arms, torque rods, trailer axles, shock absorbers, tires • outputs include: roll angles, yaw rates, lateral acceleration, tracking • other features: driver steering model, lane change and obstacle avoidance maneuvers • components include: engine, clutch, 10-speed transmission, driveline and U-joints, tandem drive axle with axle shafts and differential, trailing arm suspension • outputs include: U-joint angle vs. ride height (steady state response), frame lift during high torque acceleration (transient response), bearing loads, driveline torques, vehicle speed and acceleration • components include: front axle, leaf spring suspension, brake spider, brake shoes, drum, S-cam, air chamber bracket, push rod, slack adjuster, rollers • outputs include: leaf spring and brake spider motion, brake shoe motion, brake shoe/brake drum contact force, brake pressure variation • components include: spur gears, helical gears, tapered roller bearings, shafts • outputs include: dynamic transmission error, dynamic bearing forces, internal forces, natural frequencies • other features: nonlinear bearing reaction forces for statically indeterminate systems • components include: bus frame, engine and transmission inertia, engine mounts, off-frame masses, solid axles, air springs, shock absorbers, bushings, control rods, tires • outputs include: RMS acceleration at several seat locations • other features: pavement joints, random road profiles, choice of passive, active, or semi-active dampers • components include: medium-duty straight truck, steering gear, pitman arm, drag link, steering arm, tie rod arm, tie rod, leaf spring suspension, tire model for handling • outputs include: wheel steer angles, Ackerman error, camber angles, axle tramp or shimmy vibrations • other features: driver steering model • components include: tractor with tandem drive axles, semi-trailer frame, air springs, trailing arms, torque rods, tandem trailer suspension and axles, braking system, shock absorbers, tires • outputs include: impact force, joint reaction forces, impact acceleration and velocity • standard features of ADAMS/Car and ADAMS/Pre suspension test rig (half-vehicle tests) • other features: templates developed for Specialty Axles and Suspensions • standard features of ADAMS/Car and ADAMS/Pre full vehicle analysis • other features: templates developed for Specialty Axles and Suspensions • • • •

components include: front suspension, axle beam, knuckles, tie rod arms, steering arms, tie rod, drag link outputs include: steering gear torque, wheel steer angle, aligning torque, Ackermann error other features: tire model for dry park steer components include: sprung mass with frame torsion, payload, carriers, prop shafts, control arms, knuckles, coil springs, shock absorbers, bump stops, rebound stops, durability tire model • outputs include: absorbed power at driver seat and passenger seat • other features: driver steering model, random road profiles, choice of passive, active, or semi-active dampers • components include: heavy duty truck with tandem drive axles, leaf spring suspension for drive axles, shock absorbers, control rods, bushings, elastomer pads, durability tire model • outputs include: component dynamic loads on axle housing and control rods • other features: staged events such as staggered bumps and chatter bumps, interleaf friction in the leaf springs Table 2: Summary of model features