Alexander Reid

QUARTER CAR MODEL STRESS ANALYSIS FOR TERRAIN/ROAD PROFILE RATINGS

The US Army currently uses the root mean square of elevation (RMSE) and power spectral density (PSD) to characterise road/terrain roughness for ground vehicle durability assessment. This paper describes research aimed toward improving these measures. One potential method is running a relatively simple, yet vehicle class specific model over a given terrain and using predicted vehicle response(s) to characterise the terrain. A precedent for this concept is the International Roughness Index (IRI), used in the highway industry. The IRI consists of a simple tyre model and quarter car vehicle model run at a specified speed to estimate suspension velocity over a road profile. Another method of estimating road roughness is fatigue analysis. In this study, a generic specimen was subjected to the quarter car suspension forces. The stresses developed were used to make a fatigue life cycle prediction. This paper presents the key concepts and results from this analysis.

Characterizing 2D road profiles using ARIMA modeling techniques

The principal excitation to a vehicles chassis system is the road profile. Simulating a vehicle traversing long roads is impractical and a method to produce short roads with given characteristics must be developed. There are many methods currently available to characterize roads when they are assumed to be homogeneous. This work develops a method of characterizing non-stationary road profile data using ARIMA (Autoregressive Integrated Moving Average) modeling techniques. The first step is to consider the road to be a realization of an underlying stochastic process. Previous work has demonstrated that an ARIMA model can be fit to non-stationary road profile data and the remaining residual process is uncorrelated. This work continues the examination of the residual process of such an ARIMA model. Statistical techniques are developed and used to examine the distribution of the residual process and the preliminary results are demonstrated. The use of the ARIMA model parameters and residual distributions in classifying road profiles is also discussed. By classifying various road profiles according to given model parameters, any synthetic road realized from a given class of model parameters will represent all roads in that set, resulting in a timely and efficient simulation of a vehicle traversing any given type of road.

All-Season Virtual Test Site for a Real-Time Vehicle Simulator

Abstract : A virtual, all-season test site for use in real-time vehicle simulators and mobility models was constructed of an Army firing range in Northern Vermont. The virtual terrain will mimic the terrain of our Virtual Data Acquisition and Test Site (VDATS) at Ethan Allen Firing Range (EAFR). The objective is to realistically simulate on- and off-road vehicle performance in all weather conditions for training and vehicle design for the US Army. To this end, several spatial datasets were needed to accurately map the terrain and estimate the state-of-the- ground and terrain strength at different times of the year. The terrain strength is characterized by terramechanics properties used in algorithms to calculate the forces at the vehicle-terrain interface. The performance of the real vehicles will be compared to the simulated vehicle performance of operator-in-the-loop and unmanned vehicles for validation of the simulations. Real vehicles are instrumented and perform maneuvers at the test site to develop and validate mathematic models describing vehicle behavior in all-season conditions, including snow, ice, frozen and thawing ground.

High-Frequency Terrain Content and Surface Interactions for Off-Road Simulations

Standard visual database modeling practices in driving simulation reduce geometric complexity of terrain surfaces by using texture maps to simulate high frequency detail. Typically the vehicle dynamics model queries a correlated database that contains the polygons from the high level of detail of the visual database. However the vehicle dynamics database does not contain any of the high frequency information included in the texture maps. To overcome this issue and enhance both the visual and vehicle dynamics databases, a mathematical model of the high frequency content of the ground surface is developed using a set of Non-Uniform Rational B-Splines (NURBS) patches. The patches are combined in the terrain query by superimposing them over the low-frequency polygonal terrain, reintroducing the missing content. The patches are also used to generate Bump Map textures for the image generator so that the visual representation matches the terrain query. An imagery-based approach to generating the mathematical surfaces and Bump Maps from the database’s decal textures is also presented. Future research will include full implementation in a driving simulator. This research was supported by an SBIR Phase I Contract (No. W56HZV-04-C-0101) in conjunction with the U.S. Army TARDEC. BACKGROUND

A Physics-Based Vehicle/Terrain Interaction Model for Soft Soil Off- Road Vehicle Simulations

In the context of off-road vehicle simulations, deformable terrain models mostly fall into three categories: simple visualization of an assumed terrain deformation, use of empirical relationships for the deformation, or finite/discrete element approaches for the terrain. A real-time vehicle dynamics simulation with a physics-based tire model (brush, beam-based or Finite Element models) requires a terrain model that accurately reflects the deformation and response of the soil to all possible inputs of the tire in order to correctly simulate the response of the vehicle. The real-time requirement makes complex finite/discrete element approaches unfeasible, and the use of a ring or beam -based tire model excludes purely empirical terrain models. We present the development of a three-dimensional vehicle/terrain interaction model which is comprised of a tire and deformable terrain model to be used with a real-time vehicle dynamics simulator. The governing equations of both models are physics-based, rather than utilizing popular terramechanics models that are empirical. The tire draws on a lumped-mass model based on a radial spring-damper-mass distribution. The terrain model utilizes Boussinesq and Cerruti soil mechanics equations to determine the pressure distribution and deformation of a volume of soil as a function of normal and tangent forces applied at the soil surface by the tire. The soil volume that describes the terrain is discretized as a set of vertical columns of soil, and the deformation of each is modeled using visco-elasto-plastic compressibility relationships that relate subsoil pressures to a change in bulk density of the soil, which in turn produces soil displacements. Different loading combinations applied by a tire passing over a column of soil will be reflected in the state of each volume of soil contained in the column, rather than treating the column of soil as homogeneous in the vertical direction and only associating one set of parameters with the entire column, e.g. a Bekker type model. Furthermore, the time-dependent elastic and plastic response of the soil to repetitive compression/rebound tire loads is also taken into account. Horizontal soil force/displacement produced by tractive and turning forces will also be incorporated into the model. Both the vertical and horizontal force/displacement relationships allow the calculation of total energy and power required to deform the terrain. These physics-based models will be integrated into a real-time vehicle dynamics simulator and is anticipated to lead to a realistic vehicle dynamic response when driving on off-road, deformable terrain conditions, especially when repeated loading occurs or non-homogeneous soil conditions are present. Additionally, the changes in soil states can be used to directly compute the energy and power required to deform the terrain. In order to retain the ability to run real-time simulations, a GPU-accelerated approach is considered to leverage the inherently parallel nature of performing multiple independent terrain geometry queries and soil-mechanics calculations. Numerical experiments include a single soil volume node under a known load and a simplified tire model applying normal forces on the surface of the terrain. Results are given for the vertical plastic soil deformation, and for the power and energy required to perform the deformations.

Review of current developments in terrain characterization and modeling

As computational power builds to meet the needs of ground vehicle designers, the focus has begun to shift from laboratory testing of prototype parts and subsystems to computational simulations of the vehicle. In the automotive and defense industries, large strides have been made in simulating full vehicle responses, such as durability. These simulations are most meaningful when excited by proper mathematical models that accurately characterize the terrain. It is important to understand the roughness indices that are used to judge the terrain profiles. The state-of-the-art in terrain characterization and modeling is reviewed in this work for models including Power Spectral Density (PSD), Markov Chains, Autoregressive Integrated Moving Average (ARIMA), Parametric Road Spectrum (PRS), Shifted Spatial Range Spectrum (SSR), Direct Spectrum Estimation (DSE) and Transformed Direct Spectrum Estimation (TrDSE). The applicability, limitations, and benefits of these models are assessed based on their effectiveness in capturing the stochastic nature of the terrain being characterized. A discussion of terrain characterization usage to advance reliability testing concludes this work as an example of the applicability of this technology.

A planar quasi-static constraint mode tyre model

The fast-paced, iterative, vehicle design environment demands efficiency when simulating suspension loads. Towards that end, a computationally efficient, linear, planar, quasi-static tyre model is developed in this work that accurately predicts a tyres lower frequency, reasonably large amplitude, nonlinear stiffness relationship. The axisymmetric, circumferentially isotropic, stiffness equation is discretised into segments, then parameterised by a single stiffness parameter and two shape parameters. The tyres deformed shape is independent of the overall tyre stiffness and the forces acting on the tyre. Constraint modes capture enveloping and bridging properties and a recursive method yields the set of active constraints at the tyre–road interface. The nonlinear stiffness of a tyre is captured by enforcing unidirectional geometric boundary conditions. The model parameters are identified semi-empirically; simulated cleat test loads match experiments within 7% including nonlinear stiffness when simulating a flat plate test and a discontinuous stiffness when simulating a cleat test.

Further Analysis of Potential Road/Terrain Characterization Rating Metrics

The U.S. Army uses the root mean square and power spectral density of elevation to characterize road/terrain (off-road) roughness for durability. This paper describes research aimed toward improving these metrics. The focus is on taking previously developed metrics and applying them to mathematically generated terrains to determine how each metric discerns the relative roughness of the terrains from a vehicle durability perspective. Multiple terrains for each roughness level were evaluated to determine the variability for each terrain rating metric. One method currently under consideration is running a relatively simple, yet vehicle class specific, model over a given terrain and using predicted vehicle response(s) to classify or characterize the terrain.

Analysis of Potential Road/Terrain Characterization Rating Metrics

The U.S. Army uses the root mean square and power spectral density of elevation to characterize road/terrain (off-road) roughness for durability. This paper describes research aimed toward improving these metrics. The focus is on taking previously developed metrics and applying them to mathematically generated terrains to determine how each metric discerns the relative roughness of the terrains from a vehicle durability perspective. Multiple terrains for each roughness level were evaluated to determine the variability for each terrain rating metric. One method currently under consideration is running a relatively simple, yet vehicle class specific, model over a given terrain and using predicted vehicle response(s) to classify or characterize the terrain.

Capturing Planar Tire Properties Using Static Constraint Modes

The interaction between the tire and road has long been of interest for vehicle dynamic simulation. A planar tire model is developed to capture the tire circumferential displacements and calculate the spindle force according to the tire shape. The tire is discretized into segments and Hamilton’s principle is used to derive the model mathematical expression. It is shown that the static constraint modes are functions of two non-dimensional parameters; a third parameter defines the overall stiffness. These parameters are experimentally identified for a specific tire. The bridging and enveloping properties are examined circumferentially. The prediction accuracy of spindle force with respect to tire-road interference is evaluated by comparing the simulation and experimental response for a quasi-static cleat test. The simulation result of spindle force agrees with the experimental data and the process can be implemented as a morphological pre-filter of road profiles for more efficient vehicle modeling and simulation.Copyright