Spatial Dynamics of Multibody Tracked Vehicles Part II: Contact Forces and Simulation Results

In this part of the paper, three dimensional computational capabilities, that includes significant details, are developed for the nonlinear dynamic analysis of large scale spatial tracked vehicles. Three dimensional nonlinear contact force models that describe the interaction between the track links and the vehicle components such as the rollers, sprockets, and idlers as well as the interaction between the track links and the ground are developed and used to define the generalized contact forces associated with the vehicle generalized coordinates. Tangential friction and contact forces are developed in order to maintain the stability of the track motion and avoid the slippage of the track or its rotation as a rigid body. Body and surface coordinate systems are introduced in order to define the spatial contact conditions. The nonlinear equations of motion of the tracked vehicle are solved using the velocity transformation procedure developed in the first part of this paper. This procedure is used in order to obtain a minimum set of differential equations, and avoid the use of the iterative Newton-Raphson algorithm. A computer simulation of a tracked vehicle that consists of one hundred and six bodies and has one hundred and sixteen degrees of freedom is presented in order to demonstrate the use of the formulations presented in this study.     

Spatial Dynamics of Multibody Tracked Vehicles Part I: Spatial Equations of Motion

In this paper, the nonlinear dynamic equations of motion of the three dimensional multibody tracked vehicle systems are developed, taking into consideration the degrees of freedom of the track chains. To avoid the solution of a system of differential and algebraic equations, the recursive kinematic equations of the vehicle are expressed in terms of the independent joint coordinates. In order to take advantage of sparse matrix algorithms, the independent differential equations of the three dimensional tracked vehicles are obtained using the velocity transformation method. The Newton-Euler equations of the vehicle components are defined and used to obtain a sparse matrix structure for the system dynamic equations which are represented in terms of a set of redundant coordinates and the joint forces. The acceleration solution obtained by solving this system of equations is used to define the independent joint accelerations. The use of the recursive equations eliminates the need of using the iterative Newton-Raphson algorithm currently used in the augmented multibody formulations. The numerical difficulties that result from the use of such augmented formulations in the dynamic simulations of complex tracked vehicles are demonstrated. In this investigation, the tracked vehicle system is assumed to consist of three kinematically decoupled subsystems. The first subsystem consists of the chassis, the rollers, the sprockets, and the idlers, while the second and third subsystems consist of the tracks which are modeled as closed kinematic chains that consist of rigid links connected by revolute joints. The singular configurations of the closed kinematic chains of the tracks are also avoided by using a penalty function approach that defines the constraint forces at selected secondary joints of the tracks. The kinematic relationships of the rollers, idlers, and sprockets are expressed in terms of the coordinates of the chassis and the independent joint degrees of freedom, while the kinematic equations of the track links of a track chain are expressed in terms of the coordinates of a selected base link on the chain as well as the independent joint degrees of freedom. Singularities of the transformations of the base bodies are avoided by using Euler parameters. The nonlinear three dimensional contact forces that describe the interaction between the vehicle components as well as the results of the numerical simulations are presented in the second part of this paper.     

Identifying optimal data aggregation interval sizes for link and corridor travel time estimation and forecasting

With the recent increase in the deployment of ITS technologies in urban areas throughout the world, traffic management centers have the ability to obtain and archive large amounts of data on the traffic system. These data can be used to estimate current conditions and predict future conditions on the roadway network. A general solution methodology for identifying the optimal aggregation interval sizes for four scenarios is proposed in this article: (1) link travel time estimation, (2) corridor/route travel time estimation, (3) link travel time forecasting, and (4) corridor/route travel time forecasting. The methodology explicitly considers traffic dynamics and frequency of observations. A formulation based on mean square error (MSE) is developed for each of the scenarios and interpreted from a traffic flow perspective. The methodology for estimating the optimal aggregation size is based on (1) the tradeoff between the estimated mean square error of prediction and the variance of the predictor, (2) the differences between estimation and forecasting, and (3) the direct consideration of the correlation between link travel time for corridor/route estimation and forecasting. The proposed methods are demonstrated using travel time data from Houston, Texas, that were collected as part of the automatic vehicle identification (AVI) system of the Houston Transtar system. It was found that the optimal aggregation size is a function of the application and traffic condition.

Port privatization under Cournot vs. Bertrand competition: a third-market approach

By incorporating port competition into a third-market model consisting of two exporting firms and one importing country, we demonstrate the endogenous choice of port structures (i.e. privatization or public ownership) under either Bertrand or Cournot competition. In contrast to previous studies on port competition, we analyze the port strategy in view of all trading countries (i.e. importing country and exporting countries). We find that regardless of transport cost, the port ownership strategy alters according to exporting firm’s competition mode. Under Bertrand competition, the choice of port ownership structure depends on the degree of imperfect substitutability. However, under Cournot competition, all trading countries choose same ownership structures of each port. By comparing equilibrium of each competition mode, we show that welfare of exporting country under Cournot competition is higher than under Bertrand competition if goods are sufficiently substitutes. In contrast, importing country prefers Bertrand competition to Cournot competition when the competitive pressure is sufficiently high.     

Solution of an unstable inverse problem: wave source evaluation from observation of velocity distribution

This paper illustrates how to estimate a wave source generating a wave system, including local waves, with the assumption of linear dispersive waves of two dimensions. The estimation of wave source is realized by using an inverse problem. Unfortunately, the inverse problem is ill-posed in the sense of stability, since the wave source information included in local waves diminishes as the distance from the wave source increases. In the area of applied mathematics, there are well-developed methods to tackle ill-posed problems, which are called regularizations. In this paper, three different regularizations which are well known in applied mathematics are introduced and investigated to learn whether they are applicable to the present problem of the estimation of wave source. From the numerical experiments, it is shown that the estimation is realized by the regularizations introduced in this study, so that they can be applied to the determination of a wave source generating a wave system including local waves. Received: June 6, 2000 / Accepted: February 7, 2001     

Occupant injury risk analysis at NASS/CDS database

Injury information for vehicle occupants from the body regions of the head, thorax, abdomen, and upper and lower extremities, due to the restraints and interior parts of the vehicle, were extracted from the 2009 ~ 2012 NASS/CDS database. For those cases with high occurrence frequency, a detailed and comprehensive data analysis was performed to find the relationship between the accident, occupant, vehicle, and injury data. A numerical frontal impact sled model with the Hybrid III dummy and the GHBMC human body model was constructed to simulate and identify those injury risks according to NASS/CDS. Among the 5,734 injuries to the aforementioned body regions from frontal crashes are, listed by frequency of occurrence, the lower extremity (27.8 %), upper extremity (21.3 %), thorax (15.1 %), face (10.9 %), spine (8.7 %), head (7.3 %), and abdomen (6.9 %). The main injury sources to the head were the windshield, side structure, and steering wheel. For the thorax and abdomen they were the seat belt and steering wheel. For the lower extremity it was the instrument panel. The main injury patterns for the head were the concussion and the contusion. For the thorax they were vessel laceration and lung contusion. For the abdomen they were laceration and contusion of the organs. For the lower extremity they were bone fracture and ligament rupture. The steering wheel and seat positions were main factors affecting head and thorax injury risks. From the sled impact simulation, high injury risks of the head and thorax were assessed respectively at conditions of steering column tilt down and rear most seat position, which correlated well with the findings from the NASS/CDS data analysis.     

Durability prediction for automobile aluminum front subframe using nonlinear models in virtual test simulations

This research work presents fatigue life evaluation techniques for an automotive vehicle aluminum front subframe using virtual test simulation technology with nonlinear suspension components model. The technology was used for improving the accuracy of the polynomial model used in conventional analysis. The proposed nonlinear suspension components models were developed using direct approach. The effects of the nonlinear elements on the prediction of the fatigue life were also analyzed. Actual aluminum front subframe was tested using half-car road test simulator to verify the accuracy of the models. It was found that the proposed nonlinear models yield more accurate results than conventional polynomial models. The proposed virtual test simulation technology with nonlinear suspension components model can be used to predict fatigue life for vehicle chassis structures more accurately.     

The Evaluation of the 2nd Ocean Plan in Korea: Focused on the Implementing Power of the Plan

There seem to be two types of ocean planning system in the world. First, the federal or united government suggests a basic framework of the plan which is followed by states, countries or areas as shown in the European Union, the United States, Canada, Australia, and so on. Second, a powerful central government prepares a basic ocean plan that guides the following sector plans of the relevant ministries. These cases are shown in Japan, Korea, and China. In Korea, the 2nd Ocean and Fishery Development Plan (OK21, 2011–2020) was made as a comprehensive ocean plan reflecting recent natural and social changes including global warming. The OK21 is declarative in its nature, and so evaluated by its sector plans, which have some specific implementing means such as budgets and manpower, organization, and so on, by the relevant laws. The 2nd OK21 is supported by 21 legally binding sector plans, 14 more than in the 1st plan, thus guaranteeing more effective implementation than in the 1st plan. In addition, most of sector plans are planned to be carried out through the well-coordinated system among the related ministries, thus showing a high degree of implementing efficiency of the plan. Every marine area in the plan, including marine environment, is being supported by more sector plans than before, indicating the equitable development of marine areas in the future. In sum, the 2nd OK21 is expected to show more implementing power due to the well-organized sector plans than in the 1st plan.