Janusz Frączek

Molecular dynamics simulation of simple polymer chain formation using divide and conquer algorithm based on the augmented Lagrangian method

This paper presents an efficient multibody methodology for the simulation of molecular dynamics of simple polymer chains. The algorithm is formulated in terms of absolute coordinates. The augmented Lagrangian method is incorporated into the divide and conquer framework giving new parallel, logarithmic order algorithm suitable for the simulation of general multibody system topologies. The approach is robust in case of potential rank deficiencies of the Jacobian matrices that embrace the group of systems involving redundant constraints, and which may repeatedly enter singular configurations. Series of nanosecond-long molecular dynamics simulations of simplified polymer chain models are performed to demonstrate the correctness of the methodology and investigate the structure formation of the system subjected to non-bonded (Lennard–Jones) and bonded (torsional) interactions. Conformational changes and dynamic properties of the polymer chains are studied under gradual cooling of the system. The simulation results show that some of the homopolymers collapse into well-formed helices. The fraction of the succeeded runs, in which defect-free helices are found, is a function of initial conditions, chain length, and cooling rate. The employed computational multibody approach appeared to be useful in molecular dynamics simulations implying potential for future research and further development in this field.

Application of General Multibody Methods to Robotics

In this chapter robotic applications of general multibody system (MBS) simulation methods, based on absolute coordinates formalism, are presented. Three typical problems, often encountered in robotics, are discussed: kinematic analysis with singular configuration detection, simulation of parallel robot dynamics investigated jointly with the robot control systems properties, and finally, simulation of a robot with flexibility effects taken into account. In case of singular configuration detection simplest types of singular configurations are analyzed – turning point and bifurcation point. The second case of MBS application is an example of parallel robot dynamic analysis when model based control is taken into account. The last part of the chapter is devoted to the analysis of complex, flexible power transmission mechanism carried out with general MBS formalism.

Optimal Design of Multibody Systems Using the Adjoint Method

Optimal design of multibody systems (MBS) is of primary importance to engineers and researchers working in various fields, e.g.: in robotics or in machine design. The goal of this paper is a development and implementation of systematic methods for finding design sensitivities of multibody system dynamics with respect to design parameters in the process of optimization of such systems. The optimal design process may be formulated as finding a set of unknown parameters such that the objective function is minimized under the assumption that design variables may be subjected to a variety of differential and/or algebraic constraints. The solutions of such complex optimal problems are inevitably connected with evaluation of a gradient of the objective function. Herein, a multibody system is described by redundant set of absolute coordinates. The equations of motion for MBS are formulated as a system of differential-algebraic equations (DAEs) that has to be discretized and solved numerically forward in time. The design sensitivity analysis is addressed by using the adjoint method that requires determination and numerical solution of adjoint equations backwards in time. Optimal design of sample planar multibody systems are presented in the paper. The properties of the adjoint method are also investigated in terms of efficiency, accuracy, and problem size.

Physical experiment and computer simulation of the speed-up manoeuvre using the absolute nodal coordinate formulation:

This paper presents an experimental validation of the absolute nodal coordinate formulation spatial element with the speed-up manoeuvre. A long, thin steel beam with a circular cross-section is analysed. The beam is fixed at the middle with the clamp that itself is attached to the brushless motor housing. The drive is controlled by a dedicated speed controller and the final speed is set by adjusting the PWM signal level. The position of specific points at the beam and the drive is measured by attached markers with a high-speed camera that records the picture with 2400 frames per second. The position of the rotor is then used as input for further multibody dynamic analysis. The top rotational speed of the rotor is far larger than the critical speed for the linear floating frame of reference model. The beam is modelled with a continuum-based, standard, curved, two-node absolute nodal coordinate formulation beam element. As Poisson locking often occurs in thin absolute nodal coordinate formulation beams, selective reduced integration is employed to alleviate the locking influence. The air drag is modelled with a simple model of idealised air flow around the cylinder. A comparison of the experimental and the computer simulation reveals a good agreement between the results.

Multibody Modelling of a Tracked Robot’s Actuation System

A simulation model of a mobile robot is presented in the chapter. The robot is equipped with four track systems, wrapped around four movable and independently driven track holders. Driving torques are transmitted to the track systems and track holders via speed reducers. The study is focused on friction effects in gearing, and especially on the self-locking properties. A simplified mathematical model of friction in speed reducers is presented. The model is based on the Coulomb friction law and exploits the analogy between reducers and wedge mechanisms. This friction model is implemented in a general purpose simulation software in which the entire tracked mobile robot is modelled. A multibody model of the complete robot is briefly described. Simulation results obtained for different friction levels, varying from friction absence to friction beyond the self-locking limit, are compared and discussed. The robot motors are also modelled and requirements for electric power in various operating conditions are estimated.

Aircraft Subsystems Modelling Using Different MBS Formalisms

The paper presents three case studies of dynamic analysis of aircraft during landing manoeuvre using two basic formalisms encountered in rigid and flexible multibody system (MBS) modelling. In the first case a formulation in natural coordinates has been used to analyze the dynamics of a medium size aircraft. Equations of motion have been formulated and solved using velocity transformation method. The aircraft has been modelled as consisting of rigid bodies connected by universal joints with springs. Aerodynamic forces have been taken into account by applying the Vortex Lattice Method (VLM) to the calculations performed. The effect of ground proximity on the results (ground effect) has been analyzed. In the second case, a dynamic analysis of a glider during the landing manoeuvre has been carried out from the point of view of stress recovery by means of various methods. Body positions and orientations have been written in absolute coordinates with floating frame approach for flexible bodies. Finite element method (FEM) and component mode synthesis has been used to model the flexibility of the bodies. A comparison of stress results obtained for different computation methods has been carried out. In the third analysis a MBS model of the Su-22 military airplane main landing gear has been presented. The absolute coordinates and the differential algebraic equations (DAE) formulations were used in all calculations. The whole landing gear model includes individual models of hydraulic actuators, shock absorber, flexible tire and contacts between some landing gear parts. Several types of simulations like landing gear extension and selected ground manoeuvres were performed. On that basis values of the forces which will allow to assess fatigue and durability of landing gear in future experiments were obtained. The received results were compared to the experimental measurements which were carried out on a real military airplane. The key issues of that comparison and general remarks were formulated. In the final part of the paper general conclusions regarding application of various computation MBS methods to dynamical analyses of aircrafts have been presented.