Dae-Sung Bae

A compliant track link model for high‐speed, high‐mobility tracked vehicles

Several modelling methods have recently been developed for the dynamic analysis of low-speed tracked vehicles. These methods were used to demonstrate the significant effect of the force of the interaction between the track links and vehicle components, even when low speeds are considered. It is the objective of this investigation to develop compliant track link models and investigate the use of these models in the dynamic analysis of high-speed, high-mobility tracked vehicles. There are two major difficulties encountered in developing the compliant track models discussed in this paper. The first is due to the fact that the integration step size must be kept small in order to maintain the numerical stability of the solution. This solution includes high oscillatory signals resulting from the impulsive contact forces and the use of stiff compliant elements to represent the joints between the track links. The characteristics of the compliant elements used in this investigation to describe the track joints are measured experimentally. A numerical integration method having a relatively large stability region is employed in order to maintain the solution accuracy, and a variable step size integration algorithm is used in order to improve the efficiency. The second difficulty encountered in this investigation is due to the large number of the system equations of motion of the three-dimensional multibody tracked vehicle model. The dimensionality problem is solved by decoupling the equations of motion of the chassis subsystem and the track subsystems. Recursive methods are used to obtain a minimum set of equations for the chassis subsystem. Several simulations scenarios including an accelerated motion, high-speed motion, braking, and turning motion of the high-mobility vehicle are tested in order to demonstrate the effectiveness and validity of the methods proposed in this investigation. Copyright

A Generalized Recursive Formulation for Constrained Mechanical System Dynamics

ABSTRACT Recursive formulas have been effective in solving the equations of motion for large scale constrained mechanical systems. However, derivation of the formulas has been limited to individual terms in the equations of motion, such as velocity, acceleration, and generalized forces. The recursive formulas are generalized in this paper. The velocity transformation method is employed to transform the equations of motion from Cartesian to the joint spaces. Computational structure of the equations of motion in the joint space is carefully examined to classify all necessary computational operations into several categories. The generalized recursive formula for each category is then developed and applied whenever such a category of computation is encountered. Since the velocity transformation method yields the equations of motion in a compact form and computational efficiency is achieved by generalized recursive formulas, the proposed method is not only easy to implement but is also efficient. A library of ...

An explicit integration method for realtime simulation of multibody vehicle models

Abstract High performance computers have been used for realtime simulation of multibody vehicle dynamics models consisting of many bodies and joints, a powertrain model, antiroll bars, and tires. This research proposes an efficient implementation algorithm for explicit numerical integration methods so that relatively low cost computers can be used for the realtime simulation of the multibody vehicle dynamics models. Newton chord method is employed to solve the equations of motion and constraints. The equations of motion and constraints are formulated such that the Jacobian matrix for Newton chord method is needed to be computed only once for a dynamic analysis. Numerical experiments showed that the Jacobian matrix generated at the initial time could have been utilized for the Newton chord iterations throughout simulations under various driving conditions. Convergence analysis of Newton chord method with the proposed Jacobian updating method is carried out. The proposed algorithm yielded almost exact solutions for a prototype vehicle multibody model in realtime on a 400 MHz PC compatible.

Development of a Multi-body Dynamics Simulation Tool for Tracked Vehicles

In this paper, the nonlinear dynamic modeling methods for the virtual design of tracked vehicle are investigated by using multibody dynamic simulation techniques. The results include high oscillatory signals resulting from the impulsive contact forces and the use of stiff compliant elements to represent the joints between the track links. Each track link is modeled as a body, which has six degrees of freedom, and two compliant bushing elements is used to connect track links. The efficient contact search kinematics and algorithms in the context of the compliance contact model are developed to detect the interactions between track links, rollers, sprockets, and ground for the sake of speedy and robust solutions. In order to validate the developed nonlinear multibody dynamic model against the experimental measurements, several empirical techniques are suggested and applied to the physical proving ground tests of the high mobility tracked vehicle. In this empirical validations, positions, velocities, accelerations and forces of the chassis and the track sub-systems are correlated accordingly.

An Implementation Method for Constrained Flexible Multibody Dynamics Using a Virtual Body and Joint

A convenient implementation method for constrained flexiblemultibody dynamics is presented by introducing a virtual rigid body andjoint. The general purpose program for rigid and flexible multibodydynamics consists of three major parts of a set of inertia modules, aset of force modules, and a set of joint modules. Whenever a new forceor joint module is added to the general purpose program, the modules forthe rigid body dynamics are not reusable for the flexible body dynamics.Consequently, the corresponding modules for the flexible body dynamicsmust be formulated and programmed again. Since the flexible bodydynamics handles more degrees of freedom than the rigid body dynamicsdoes, implementation of the module is generally complicated and prone tocoding mistakes. In order to overcome these difficulties, a virtualrigid body is introduced at every joint and force reference frames. Newkinematic admissibility conditions are imposed on two-body referenceframes of virtual and original bodies by introducing a virtual flexiblebody joint. There are some computational overheads due to the additionalbodies and joints. However, since computation time is mainly dependenton the frequency of flexible body dynamics, the computational overheadof the presented method is not a critical problem, while implementationconvenience is dramatically improved.

Recursive formulas for design sensitivity analysis of mechanical systems

Design sensitivity analysis of a mechanical system is an essential tool for design optimization and trade-off studies. This paper presents a design sensitivity analysis method, using direct differentiation and generalized recursive formulas. The equations of motion are first generated in the Cartesian coordinate system and then transformed into the relative coordinate system by using a velocity transformation. The design-sensitivity equations are derived by directly differentiating the equations of motion. The equations of motion and of design sensitivity are discritized by using the backward difference formula (BDF) in time domain. The resulting equations constitute an overdetermined differential algebraic system (ODAS) and are treated as ordinary differential equations (ODEs) on manifolds. The computational structure of the resulting equations is examined to classify all necessary computations into several categories. The generalized recursive formula for each category is then developed and applied whenever such a category of computation is encountered in the equations of motion and of design sensitivity. Since the velocity transformation yields the equations in a compact form and computational efficiency is achieved by the generalized recursive formulas, the proposed method is not only easy to implement but also efficient. A practical example of a vehicle consisting of many joints, bushings, and tires is given to show the efficiency of the proposed method.

A Decoupling Solution Method for Implicit Numerical Integration of Constrained Mechanical Systems

Abstract A decoupling solution method is presented for implicit numerical integration of constrained multibody systems. Compared to implicit numerical integration methods, explicit numerical integration methods usually spend less computation time per iteration, since the equations of motion and an explicit integration formula coupled with the constraint manifolds are solved separately. However, the integration step size can be excessively small for highly nonlinear or stiff problems, due to the small stability region of the explicit method. In contrast, implicit numerical integration methods do not have the problem of excessive small step size. Implicit integration methods, however, generally require one to solve a large system equations simultaneously. The solution method proposed in this paper eliminates the problem of large system equations, while maintaining the advantage of the implicit method. Furthermore, the proposed method provides a well-conditioned iteration matrix for the implicit method, whic...

Configuration design sensitivity analysis of dynamics for constrained mechanical systems

A continuum-based configuration design sensitivity analysis method is developed for dynamics of multibody systems. The configuration design variables of multibody systems define the shape and orientation changes. The equations of motion are directly differentiated to obtain the governing equations for the design sensitivity. The governing equation of the design sensitivity is formulated as an overdetermined differential algebraic equation and treated as ordinary differential equations on manifolds. The material derivative of a domain functional is performed to obtain the sensitivity due to shape and orientation changes. The configuration design sensitivities of a fly-ball governor system and a spatial four bar mechanism are obtained using the proposed method and are validated against these obtained from the finite difference method.

Configuration design sensitivity analysis of kinematic responses of mechanical systems

A continuum-based configuration design sensitivity analysis method is presented for kinematically driven mechanical systems. Configuration design variable for mechanical systems are defined. The 3-1-3 Euler angle is used as the orientation design variable. The reassembly process for a mechanical system after a configuration design change is eliminated by imposing kinematic admissibility conditions of the velocity field. The direct differentiation method is used to derive design sensitivity equations. Numerical examples are presented to demonstrate the validity and effectiveness of the proposed method.

Use of Joint Geometric Conditions in Formulating Cartesian Constraint Equations

Basic constraint equations derived from orthogonality conditions between a pair of body-fixed vectors and a body-fixed vector or a vector between two bodies are reformulated by using geometric conditions built into each joint. Arithmetic numbers of operations required to compute derivatives of the constraint equations are drastically reduced. A mixed constraint formulation of relative and Cartesian coordinates is developed to further simplify derivatives of the constraints. Advantages and disadvantages of the new formulation are discussed. The kinematic analysis of a Macpherson strut suspension system is carried out to illustrate the use and efficiency of the new formulation.