Towards an Energetic Modeling of Rotorcraft Using Bond-Graphs

Presented at the AHS 69th Annual Forum, Phoenix, Arizona,May 21 –23, 2013. Copyright © 2013 by the AmericanHelicopter Society International, Inc. All rights reserved.The paper presents an energetic method of helicopters dynamics analysis to study the air resonance (AR)phenomena. First, a brief state of art of AR phenomena is presented and a simple energetic explanation is given.Then part of the state of art is devoted to the Bond Graph (BG) and Multi-Bond Graphs (MBG) modeling methodshowing several advantages of the tool and few examples of MBG researches applications. This work proposes amacroscopic energetic description of a helicopter through the Word Bond Graph representation. The MBG is thenused for Rotor/fuselage structure modeling in order to study the AR phenomena instability. The MBG model resultsare presented and show the potential of the MBG method to predict such a complex phenomenon.International audienceThe paper presents an energetic method of helicopters dynamics analysis to study the air resonance (AR)phenomena. First, a brief state of art of AR phenomena is presented and a simple energetic explanation is given.Then part of the state of art is devoted to the Bond Graph (BG) and Multi-Bond Graphs (MBG) modeling methodshowing several advantages of the tool and few examples of MBG researches applications. This work proposes amacroscopic energetic description of a helicopter through the Word Bond Graph representation. The MBG is thenused for Rotor/fuselage structure modeling in order to study the AR phenomena instability. The MBG model resultsare presented and show the potential of the MBG method to predict such a complex phenomenon

Modelling & analysis of hybrid dynamic systems using a bond graph approach

Hybrid models are those containing continuous and discontinuous behaviour. In constructing dynamic systems models, it is frequently desirable to abstract rapidly changing, highly nonlinear behaviour to a discontinuity. Bond graphs lend themselves to systems modelling by being multi-disciplinary and reflecting the physics of the system. One advantage is that they can produce a mathematical model in a form that simulates quickly and efficiently. Hybrid bond graphs are a logical development which could further improve speed and efficiency. A range of hybrid bond graph forms have been proposed which are suitable for either simulation or further analysis, but not both. None have reached common usage. A Hybrid bond graph method is proposed here which is suitable for simulation as well as providing engineering insight through analysis. This new method features a distinction between structural and parametric switching. The controlled junction is used for the former, and gives rise to dynamic causality. A controlled element is developed for the latter. Dynamic causality is unconstrained so as to aid insight, and a new notation is proposed. The junction structure matrix for the hybrid bond graph features Boolean terms to reflect the controlled junctions in the graph structure. This hybrid JSM is used to generate a mixed-Boolean state equation. When storage elements are in dynamic causality, the resulting system equation is implicit. The focus of this thesis is the exploitation of the model. The implicit form enables application of matrix-rank criteria from control theory, and control properties can be seen in the structure and causal assignment. An impulsive mode may occur when storage elements are in dynamic causality, but otherwise there are no energy losses associated with commutation because this method dictates the way discontinuities are abstracted. The main contribution is therefore a Hybrid Bond Graph which reflects the physics of commutating systems and offers engineering insight through the choice of controlled elements and dynamic causality. It generates a unique, implicit, mixed-Boolean system equation, describing all modes of operation. This form is suitable for both simulation and analysis

Dynamic Model of a Non-Linear Pneumatic Pressure Modulating Valve Using Bond Graphs

This research develops a mathematical model of the dynamic pressure response to a variable travel input of a pneumatic pressure modulating valve intended for use in a vehicle air brake system. Generically, the valve is a multi-domain system consisting of a mechanical portion and a pneumatic portion. Included in the mechanical portion of the model are compliance of the springs, inertia of the components, and resistance of the sliding components. The pneumatic portion of the model includes capacitance due to the compressibility of the gas, flow resistance through connected plumbing, and flow resistance through the valve control orifices. The development of the mathematical model is accomplished using bond graphs and is complicated by the existence of several sources of non-linearities in the valve being modeled. The non-linearities are the results of mixed modes of operation, fluid dynamics of the gas, use of non-linear springs, and Coulomb friction. First, a bond graph is presented that accurately represents a linear version of the valve. Next the linear state derivative equations are derived. Next, the non-linearities are individually introduced by replacing those linear assumptions with actual, analytically derived non-linear equations and parameters are measured for inclusion in the model. Finally, the model is used to simulate the dynamic response of the valve using a simulation software package.The simulated results are compared to experimental results and found to have good correlation. The model is suitable for use with simulation based design, or as a replacement for an actual valve in a Hardware In the Loop simulator of a vehicle braking syste

Dynamic Model of a Non-Linear Pneumatic Pressure Modulating Valve Using Bond Graphs

This research develops a mathematical model of the dynamic pressure response to a variable travel input of a pneumatic pressure modulating valve intended for use in a vehicle air brake system. Generically, the valve is a multi-domain system consisting of a mechanical portion and a pneumatic portion. Included in the mechanical portion of the model are compliance of the springs, inertia of the components, and resistance of the sliding components. The pneumatic portion of the model includes capacitance due to the compressibility of the gas, flow resistance through connected plumbing, and flow resistance through the valve control orifices. The development of the mathematical model is accomplished using bond graphs and is complicated by the existence of several sources of non-linearities in the valve being modeled. The non-linearities are the results of mixed modes of operation, fluid dynamics of the gas, use of non-linear springs, and Coulomb friction. First, a bond graph is presented that accurately represents a linear version of the valve. Next the linear state derivative equations are derived. Next, the non-linearities are individually introduced by replacing those linear assumptions with actual, analytically derived non-linear equations and parameters are measured for inclusion in the model. Finally, the model is used to simulate the dynamic response of the valve using a simulation software package.The simulated results are compared to experimental results and found to have good correlation. The model is suitable for use with simulation based design, or as a replacement for an actual valve in a Hardware In the Loop simulator of a vehicle braking syste

A New Framework for the Simulation of Equation-Based Models with Variable Structure

Many modern models contain changes that affect the structure of their underlying equation system, e.g. the breaking of mechanical devices or the switching of ideal diodes. The modeling and simulation of such systems in current equation-based languages frequently poses serious difficulties. In order to improve the handling of variable-structure systems, a new modeling language has been designed for research purposes. It is called Sol and it caters to the special demands of variable-structure systems while still representing a general modeling language. This language is processed by a new translation scheme that handles the differential-algebraic equations in a highly dynamic fashion. In this way, almost arbitrary structural changes can be processed. In order to minimize the computational effort, each change is processed as locally as possible, preserving the existing computational structure as much as possible. Given this methodology, truly object-oriented modeling and simulation of variable-structure systems is made possible. The corresponding process of modeling and simulation is illustrated by two examples from different domains

Sizing of an Electric Power Steering system on dynamic and energetic criteria

International audienceThis paper presents the methodology to size a mechatronic system on dynamic and energetic criteria. The methodology is based on the establishment of the inverse model from the bond graph representation of the system by using the bicausality concept. By means of an automotive example, we illustrate the methodology and we present a solution to extend it to more complex problem

Topology Considerations in Hybrid Electric Vehicle Powertrain Architecture Design.

Optimal system architecture (topology or configuration) design has been a challenging design problem because of its combinatorial nature. Parametric optimization studies make design decisions assuming a given architecture but there has been no general methodology that addresses design decisions on the system architecture itself. Hybrid Electric Vehicle (HEV) powertrains allow various architecture alternatives created by connecting the engine, motor/generators and the output shaft in different ways through planetary gear systems. Addition of clutches to HEV powertrains allows changing the connection arrangement (configuration) among the powertrain components during the vehicle operation. Architectures with this capability are referred to as multi-mode architectures while architectures with fixed configurations are referred to as single-mode architectures. HEV architecture optimization requires designing the powertrain’s configuration and its sizing simultaneously. Additionally, evaluation of an HEV architecture design depends on a power management (control) strategy that distributes the power demand to the engine and motor/generators. Including this control problem increases the complexity of the HEV architecture design problem. This dissertation focuses on a general methodology to make design decisions on HEV powertrain architecture and component sizes. The representation of the architecture design problem is critical to solving this problem. A new general representation capable of describing all architecture alternatives is introduced. Using the representation, all feasible configurations are generated where these feasible configurations are used to create single- and multi-mode HEV architectures. Single-mode and multi-mode architecture design problems considering fuel economy, vehicle performance and architecture complexity are formulated separately and solution strategies are developed. The high complexity of the resulting optimization problem does not allow us to claim true optimality rigorously; therefore, the terms ``promising" or ``near-optimal" are more accurate in characterizing our results. The results show that different architectures must be designed for different applications. The case studies designing architectures for some available vehicles from the market find the architectures already implemented in these vehicles under some design constraints. Alternative architectures that improve these designs under different design constraints are also demonstrated. Architectures for a new application that is not available in the market are also designed.PHDMechanical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/111412/1/bayrak_1.pd

Modeling and Simulation in Engineering

This book provides an open platform to establish and share knowledge developed by scholars, scientists, and engineers from all over the world, about various applications of the modeling and simulation in the design process of products, in various engineering fields. The book consists of 12 chapters arranged in two sections (3D Modeling and Virtual Prototyping), reflecting the multidimensionality of applications related to modeling and simulation. Some of the most recent modeling and simulation techniques, as well as some of the most accurate and sophisticated software in treating complex systems, are applied. All the original contributions in this book are jointed by the basic principle of a successful modeling and simulation process: as complex as necessary, and as simple as possible. The idea is to manipulate the simplifying assumptions in a way that reduces the complexity of the model (in order to make a real-time simulation), but without altering the precision of the results