Flexible multibody dynamics and intelligent control of a hydraulically driven hybrid redundant robot machine

The assembly and maintenance of the International Thermonuclear Experimental Reactor (ITER) vacuum vessel (VV) is highly challenging since the tasks performed by the robot involve welding, material handling, and machine cutting from inside the VV. The VV is made of stainless steel, which has poor machinability and tends to work harden very rapidly, and all the machining operations need to be carried out from inside of the ITER VV. A general industrial robot cannot be used due to its poor stiffness in the heavy duty machining process, and this will cause many problems, such as poor surface quality, tool damage, low accuracy. Therefore, one of the most suitable options should be a light weight mobile robot which is able to move around inside of the VV and perform different machining tasks by replacing different cutting tools. Reducing the mass of the robot manipulators offers many advantages: reduced material costs, reduced power consumption, the possibility of using smaller actuators, and a higher payload-to-robot weight ratio. Offsetting these advantages, the lighter weight robot is more flexible, which makes it more difficult to control. To achieve good machining surface quality, the tracking of the end effector must be accurate, and an accurate model for a more flexible robot must be constructed. This thesis studies the dynamics and control of a 10 degree-of-freedom (DOF) redundant hybrid robot (4-DOF serial mechanism and 6-DOF 6-UPS hexapod parallel mechanisms) hydraulically driven with flexible rods under the influence of machining forces. Firstly, the flexibility of the bodies is described using the floating frame of reference method (FFRF). A finite element model (FEM) provided the Craig-Bampton (CB) modes needed for the FFRF. A dynamic model of the system of six closed loop mechanisms was assembled using the constrained Lagrange equations and the Lagrange multiplier method. Subsequently, the reaction forces between the parallel and serial parts were used to study the dynamics of the serial robot. A PID control based on position predictions was implemented independently to control the hydraulic cylinders of the robot. Secondly, in machining, to achieve greater end effector trajectory tracking accuracy for surface quality, a robust control of the actuators for the flexible link has to be deduced. This thesis investigates the intelligent control of a hydraulically driven parallel robot part based on the dynamic model and two schemes of intelligent control for a hydraulically driven parallel mechanism based on the dynamic model: (1) a fuzzy-PID self-tuning controller composed of the conventional PID control and with fuzzy logic, and (2) adaptive neuro-fuzzy inference system-PID (ANFIS-PID) self-tuning of the gains of the PID controller, which are implemented independently to control each hydraulic cylinder of the parallel mechanism based on rod length predictions. The serial component of the hybrid robot can be analyzed using the equilibrium of reaction forces at the universal joint connections of the hexa-element. To achieve precise positional control of the end effector for maximum precision machining, the hydraulic cylinder should be controlled to hold the hexa-element. Thirdly, a finite element approach of multibody systems using the Special Euclidean group SE(3) framework is presented for a parallel mechanism with flexible piston rods under the influence of machining forces. The flexibility of the bodies is described using the nonlinear interpolation method with an exponential map. The equations of motion take the form of a differential algebraic equation on a Lie group, which is solved using a Lie group time integration scheme. The method relies on the local description of motions, so that it provides a singularity-free formulation, and no parameterization of the nodal variables needs to be introduced. The flexible slider constraint is formulated using a Lie group and used for modeling a flexible rod sliding inside a cylinder. The dynamic model of the system of six closed loop mechanisms was assembled using Hamilton’s principle and the Lagrange multiplier method. A linearized hydraulic control system based on rod length predictions was implemented independently to control the hydraulic cylinders. Consequently, the results of the simulations demonstrating the behavior of the robot machine are presented for each case study. In conclusion, this thesis studies the dynamic analysis of a special hybrid (serialparallel) robot for the above-mentioned special task involving the ITER and investigates different control algorithms that can significantly improve machining performance. These analyses and results provide valuable insight into the design and control of the parallel robot with flexible rods.

Studies of rotor dynamics using a multibody simulation approach

The non-idealities in a rotor-bearing system may cause undesirable subcritical superharmonic resonances that occur when the rotating speed of the rotor is a fraction of the natural frequency of the system. These resonances arise partly from the non-idealities of the bearings. This study introduces a novel simulation approach that can be used to study the superharmonic vibrations of rotor-bearing systems. The superharmonic vibrations of complex rotor-bearing systems can be studied in an accurate manner by combining a detailed rotor and bearing model in a multibody simulation approach. The research looks at the theoretical background of multibody formulations that can be used in the dynamic analysis of flexible rotors. The multibody formulations currently in use are suitable for linear deformation analysis only. However, nonlinear formulation may arise in high-speed rotor dynamics applications due to the cenrrifugal stiffening effect. For this reason, finite element formulations that can describe nonlinear deformation are also introduced in this work. The description of the elastic forces in the absolute nodal coordinate formulation is studied and improved. A ball bearing model that includes localized and distributed defects is developed in this study. This bearing model could be used in rotor dynamics or multibody code as an interface elements between the rotor and the supporting structure. The model includes descriptions of the nonlinear Hertzian contact deformation and the elastohydrodynamic fluid film. The simulation approaches and models developed here are applied in the analysis of two example rotor-bearing systems. The first example is an electric motor supported by two ball bearings and the second is a roller test rig that consists of the tube roll of a paper machine supported by a hard-bearing-type balanceing machine. The simulation results are compared to the results available in literature as well as to those obtained by measuring the existing structure. In both practical examples, the comparison shows that the simulation model is capable of predicting the realistic responses of a rotor system. The simulation approaches developed in this work can be used in the analysis of the superharmonic vibrations of general rotor-bearing systems.

Simulation model for the study of overhead rail current collector systems dynamics, focused on the design of a new conductor rail

Overhead rigid conductor arrangements for current collection for railway traction have some advantages compared to other, more conventional, energy supply systems. They are simple, robust and easily maintained, not to mention their flexibility as to the required height for installation, which makes them particularly suitable for use in subway infrastructures. Nevertheless, due to the increasing speeds of new vehicles running on modern subway lines, a more efficient design is required for this kind of system. In this paper, the authors present a dynamic analysis of overhead conductor rail systems focused on the design of a new conductor profile with a dynamic behaviour superior to that of the system currently in use. This means that either an increase in running speed can be attained, which at present does not exceed 110 km/h, or an increase in the distance between the rigid catenary supports with the ensuing saving in installation costs. This study has been carried out using simulation techniques. The ANSYS programme has been used for the finite element modelling and the SIMPACK programme for the elastic multibody systems analysis.

Dynamic Response Optimization of Vehicles through Efficient Multibody Formulations and Automatic Differentiation Techniques

El diseño y desarrollo de sistemas de suspensión para vehículos se basa cada día más en el diseño por ordenador y en herramientas de análisis por ordenador, las cuales permiten anticipar problemas y resolverlos por adelantado. El comportamiento y las características dinámicas se calculan con precisión, bajo coste, y recursos y tiempos de cálculo reducidos. Sin embargo, existe una componente iterativa en el proceso, que requiere la definición manual de diseños a través de técnicas “prueba y error”. Esta Tesis da un paso hacia el desarrollo de un entorno de simulación eficiente capaz de simular, analizar y evaluar diseños de suspensiones vehiculares, y de mejorarlos hacia la solución optima mediante la modificación de los parámetros de diseño. La modelización mediante sistemas multicuerpo se utiliza aquí para desarrollar un modelo de autocar con 18 grados de libertad, de manera detallada y eficiente. La geometría y demás características de la suspensión se ajustan a las del vehículo real, así como los demás parámetros del modelo. Para simular la dinámica vehicular, se utiliza una formulación multicuerpo moderna y eficiente basada en las ecuaciones de Maggi, a la que se ha incorporado un visor 3D. Así, se consigue simular maniobras vehiculares en tiempos inferiores al tiempo real. Una vez que la dinámica está disponible, los análisis de sensibilidad son cruciales para una optimización robusta y eficiente. Para ello, se presenta una técnica matemática que permite derivar las variables dinámicas dentro de la formulación, de forma algorítmica, general, con la precisión de la maquina, y razonablemente eficiente: la diferenciación automática. Este método propaga las derivadas con respecto a las variables de diseño a través del código informático y con poca intervención del usuario. En contraste con otros enfoques en la bibliografía, generalmente particulares y limitados, se realiza una comparación de librerías, se desarrolla una formulación híbrida directa-automática para el cálculo de sensibilidades, y se presentan varios ejemplos reales. Finalmente, se lleva a cabo la optimización de la respuesta dinámica del vehículo citado. Se analizan cuatro tipos distintos de optimización: identificación de parámetros, optimización de la maniobrabilidad, optimización del confort y optimización multi-objetivo, todos ellos aplicados al diseño del autocar. Además de resultados analíticos y gráficos, se incluyen algunas consideraciones acerca de la eficiencia. En resumen, se mejora el comportamiento dinámico de vehículos por medio de modelos multicuerpo y de técnicas de diferenciación automática y optimización avanzadas, posibilitando un ajuste automático, preciso y eficiente de los parámetros de diseño. ABSTRACT Each day, the design and development of vehicle suspension systems relies more on computer-aided design and computer-aided engineering tools, which allow anticipating the problems and solving them ahead of time. Dynamic behavior and characteristics are thus simulated accurately and inexpensively with moderate computational times and resources. There is, however, an iterative component in the process, which involves the manual definition of designs in a trialand-error manner. This Thesis takes a step towards the development of an efficient simulation framework capable of simulating, analyzing and evaluating vehicle suspension designs, and automatically improving them by varying the design parameters towards the optimal solution. The multibody systems approach is hereby used to model a three-dimensional 18-degrees-of-freedom coach in a comprehensive yet efficient way. The suspension geometry and characteristics resemble the ones from the real vehicle, as do the rest of vehicle parameters. In order to simulate vehicle dynamics, an efficient, state-of-the-art multibody formulation based on Maggi’s equations is employed, and a three-dimensional graphics viewer is developed. As a result, vehicle maneuvers can be simulated faster than real-time. Once the dynamics are ready, a sensitivity analysis is crucial for a robust optimization. To that end, a mathematical technique is introduced, which allows differentiating the dynamic variables within the multibody formulation in a general, algorithmic, accurate to machine precision, and reasonably efficient way: automatic differentiation. This method propagates the derivatives with respect to the design parameters throughout the computer code, with little user interaction. In contrast with other attempts in the literature, mostly not generalpurpose, a benchmarking of libraries is carried out, a hybrid direct-automatic differentiation approach for the computation of sensitivities is developed, and several real-life examples are analyzed. Finally, a design optimization process of the aforementioned vehicle is carried out. Four different types of dynamic response optimization are presented: parameter identification, handling optimization, ride comfort optimization and multi-objective optimization; all of which are applied to the design of the coach example. Together with analytical and visual proof of the results, efficiency considerations are made. In summary, the dynamic behavior of vehicles is improved by using the multibody systems approach, along with advanced differentiation and optimization techniques, enabling an automatic, accurate and efficient tuning of design parameters.

Multibody System Mechanics: Modelling, Stability, Control, and Robustness by V. A. Konoplev and A. Cheremensky

BOOK REVIEWS Multibody System Mechanics: Modelling, Stability, Control, and Ro- bustness, by V. A. Konoplev and A. Cheremensky, Mathematics and its Appli- cations Vol. 1, Union of Bulgarian Mathematicians, Sofia, 2001, XXII + 288 pp., $ 65.00, ISBN 954-8880-09-01

Integrating structural and input design of a 2-DOF high-speed parallel manipulator: A flexible model-based approach

This paper discusses the integrated design of parallel manipulators, which exhibit varying dynamics. This characteristic affects the machine stability and performance. The design methodology consists of four main steps: (i) the system modeling using flexible multibody technique, (ii) the synthesis of reduced-order models suitable for control design, (iii) the systematic flexible model-based input signal design, and (iv) the evaluation of some possible machine designs. The novelty in this methodology is to take structural flexibilities into consideration during the input signal design; therefore, enhancing the standard design process which mainly considers rigid bodies dynamics. The potential of the proposed strategy is exploited for the design evaluation of a two degree-of-freedom high-speed parallel manipulator. The results are experimentally validated. (C) 2010 Elsevier Ltd. All rights reserved.

A FEM procedure based on positions and unconstrained vectors applied to non-linear dynamic of 3D frames

This study presents an alternative three-dimensional geometric non-linear frame formulation based on generalized unconstrained vector and positions to solve structures and mechanisms subjected to dynamic loading. The formulation is classified as total Lagrangian with exact kinematics description. The resulting element presents warping and non-constant transverse strain modes, which guarantees locking-free behavior for the adopted three-dimensional constitutive relation, Saint-Venant-Kirchhoff, for instance. The application of generalized vectors is an alternative to the use of finite rotations and rigid triad`s formulae. Spherical and revolute joints are considered and selected dynamic and static examples are presented to demonstrate the accuracy and generality of the proposed technique. (C) 2010 Elsevier B.V. All rights reserved.

A hybrid-mixed finite element formulation for the geometrically exact analysis of three-dimensional framed structures

This paper addresses the development of a hybrid-mixed finite element formulation for the quasi-static geometrically exact analysis of three-dimensional framed structures with linear elastic behavior. The formulation is based on a modified principle of stationary total complementary energy, involving, as independent variables, the generalized vectors of stress-resultants and displacements and, in addition, a set of Lagrange multipliers defined on the element boundaries. The finite element discretization scheme adopted within the framework of the proposed formulation leads to numerical solutions that strongly satisfy the equilibrium differential equations in the elements, as well as the equilibrium boundary conditions. This formulation consists, therefore, in a true equilibrium formulation for large displacements and rotations in space. Furthermore, this formulation is objective, as it ensures invariance of the strain measures under superposed rigid body rotations, and is not affected by the so-called shear-locking phenomenon. Also, the proposed formulation produces numerical solutions which are independent of the path of deformation. To validate and assess the accuracy of the proposed formulation, some benchmark problems are analyzed and their solutions compared with those obtained using the standard two-node displacement/ rotation-based formulation.

Hybrid and multi-field variational principles for geometrically exact three-dimensional beams

This paper addresses the development of several alternative novel hybrid/multi-field variational formulations of the geometrically exact three-dimensional elastostatic beam boundary-value problem. In the framework of the complementary energy-based formulations, a Legendre transformation is used to introduce the complementary energy density in the variational statements as a function of stresses only. The corresponding variational principles are shown to feature stationarity within the framework of the boundary-value problem. Both weak and linearized weak forms of the principles are presented. The main features of the principles are highlighted, giving special emphasis to their relationships from both theoretical and computational standpoints. (C) 2010 Elsevier Ltd. All rights reserved.

Environmental and track perturbations on multiple pantograph interaction with catenaries in high-speed trains

The top velocity of high-speed trains is generally limited by the ability to supply the proper amount of energy through the pantograph-catenary interface. The deterioration of this interaction can lead to the loss of contact, which interrupts the energy supply and originates arcing between the pantograph and the catenary, or to excessive contact forces that promote wear between the contacting elements. Another important issue is assessing on how the front pantograph influences the dynamic performance of the rear one in trainsets with two pantographs. In this work, the track and environmental conditions influence on the pantograph-catenary is addressed, with particular emphasis in the multiple pantograph operations. These studies are performed for high speed trains running at 300 km/h with relation to the separation between pantographs. Such studies contribute to identify the service conditions and the external factors influencing the contact quality on the overhead system. (C) 2013 Elsevier Ltd. All rights reserved.

Influence of the hip joint modeling approaches on the kinematics of human gait

The influence of the hip joint formulation on the kinematic response of the model of human gait is investigated throughout this work. To accomplish this goal, the fundamental issues of the modeling process of a planar hip joint under the framework of multibody systems are revisited. In particular, the formulations for the ideal, dry, and lubricated revolute joints are described and utilized for the interaction of femur head inside acetabulum or the hip bone. In this process, the main kinematic and dynamic aspects of hip joints are analyzed. In a simple manner, the forces that are generated during human gait, for both dry and lubricated hip joint models, are computed in terms of the system’s state variables and subsequently introduced into the dynamics equations of motion of the multibody system as external generalized forces. Moreover, a human multibody model is considered, which incorporates the different approaches for the hip articulation, namely ideal joint, dry, and lubricated models. Finally, several computational simulations based on different approaches are performed, and the main results presented and compared to identify differences among the methodologies and procedures adopted in this work. The input conditions to the models correspond to the experimental data capture from an adult male during normal gait. In general, the obtained results in terms of positions do not differ significantly when the different hip joint models are considered. In sharp contrast, the velocity and acceleration plotted vary significantly. The effect of the hip joint modeling approach is clearly measurable and visible in terms of peaks and oscillations of the velocities and accelerations. In general, with the dry hip model, intra-joint force peaks can be observed, which can be associated with the multiple impacts between the femur head and the cup. In turn, when the lubricant is present, the system’s response tends to be smoother due to the damping effects of the synovial fluid.

Global and local coordinates

This chapter described the global and local coordinate systems utilized in the formulation of spatial multibody systems. Global coordinate system is considered in the present work to denote the inertia frame. Additionally, body-fixed coordinate systems, also called local coordinate systems, are utilized to describe local properties of points that belong to a particular body. Furthermore, the process of transforming local coordinates into global coordinates is characterized by considering a transformation matrix. In the present work, Cartesian coordinates are utilized to locate the center of mass of each rigid body, as well as the location of any point that belongs to a body.

Euler angles, Bryant angles and Euler parameters

This chapter deals with the different approaches for describing the rotational coordinates in spatial multibody systems. In this process, Euler angles and Bryant angles are briefly characterized. Particular emphasis is given to Euler parameters, which are utilized to describe the rotational coordinates in the present work. In addition, for all the types of coordinates considered in this chapter, a characterization of the transformation matrix is fully described.

Angular velocity and acceleration

In this chapter, a complete characterization of the angular velocity and angular acceleration for rigid bodies in spatial multibody systems are presented. For both cases, local and global formulations are described taking into account the advantages of using Euler parameters. In this process, the transformation between global and local components of the angular velocity and time derivative of the Euler parameters are analyzed and discussed in this chapter.

Vector of coordinates, velocities and accelerations

This chapter describes the how the vector of coordinates are defined in the formulation of spatial multibody systems. For this purpose, the translational motion is described in terms of Cartesian coordinates, while rotational motion is specified using the technique of Euler parameters. This approach avoids the computational difficulties associated with the singularities in the case of using Euler angles or Bryant angles. Moreover, the formulation of the velocities vector and accelerations vector is presented and analyzed here. These two sets of vectors are defined in terms of translational and rotational coordinates.