Multibody Technique Research Articles

Terramechanics Models for Tracked Vehicle Terrain Interaction Analysis A Review

Efficient manoeuvrability of off-road tracked vehicles such as military tanks and rovers is essential in ensuring the success of military/extra-terrestrial operations. To achieve this, in-depth research on vehicle-terrain interaction is crucial. This manuscript deals with reviewing the ways to study terramechanics viz. theoretical, empirical, and field tests, and proposing the merits and demerits of each method. Under the theoretical approach, empirical, numerical, and semi-empirical methods are discussed. Under the empirical approach, the method based onthe vehicle cone index for tracked and wheeled vehicles is discussed. Under the numerical approach, advantages and disadvantages of Finite Element Method (FEM) and Discrete Element Method (DEM) are discussed. Semi-empirical method, based upon a combination of the best features of numerical and empirical approaches discusses terrain response to normal repetitive loads and shear repetitive loads for tracked as well as wheeled vehicles. Pressure sinkage relationship for terrains at various loading conditions and shear stress displacement relationship for different terrains obtained through penetration and shear tests are discussed to determine the vehicle’s mobility parameters under a semi-empirical approach. Further, the Super element model, multi-body simulation model, and ride and cornering vibration model are discussed under computer simulation models. A detailed review of various models customized towards tracked vehicle-terrain interaction discussed in this manuscript helps the authors set up a laboratory for terramechanics at DIAT. Preliminary analysis along with conceptual design of the experimental setup is also discussed. In a nutshell, this paper attempts to summarize the research that has been carried out in the field of tracked vehicle-terrain inter action comprising of VCI, MMP, FEM, DEM, Super element model, Multibody technique, and Semi-empirical methods helping the authors to establish a laboratory of terramechanics for their M. Tech. program on Armament and Combat Vehicles at DIAT Pune.

Numerical and Machine-Aided Experimental Models for Simulating the 3D Compliance of a Toothbrush

One of the most discussed topics in toothbrush design is identifying the contact force exerted by the bristles on the teeth. Each bristle must generate a contact force to ensure tooth cleaning without damaging it. Numerical simulation is a very powerful tool for understanding the influence of design parameters (bristle shape and materials). This paper proposes a flexible multibody model to efficiently simulate the 3D compliance of a toothbrush. Each bristle is modeled using a discrete, flexible approach. The contact between the bristles and the target surface is established using the penalty contact method. An experimental test bench with a Universal Robot and a flat, transparent surface is set up. Validation is provided by comparing the reaction forces of the toothbrush with the reaction forces acquired by the load cells mounted on the end effector of the Robot. The results demonstrate the accuracy of estimating normal and tangential forces in various operating situations. The discrete flexible multibody technique has also demonstrated its viability in evaluating the displacement of the bristles when the toothbrush’s base body is put through a specified motion, even when it is exposed to a sudden change in direction. As a result, the model can be effectively utilized to assess how well various brush classes remove dental plaque. Therefore, the suggested model could provide guidance for holistic modeling and advancements in toothbrush design to boost their effectiveness for thorough cleaning.

Head, chest and femur injury in teenage pedestrian–SUV crash; mass influence on the speeds

This work studies the teenage pedestrian–sport utility vehicle (SUV) crash; injury to the vital parts of the body, such as the head and chest, and to the femur is evaluated. More advanced injury criteria are applied, as provided in the rules. The multibody technique is applied by making use of SimWise software and of the teenager anthropomorphic model, the use of which is now consolidated. Head injury criterion (HIC) is used for the head, thoracic trauma index (TTI) criterion for the thorax in the case of side impact and 3 ms criterion in the case of frontal impact, while the force criterion is used for the femur. Both the TTI and femur load evaluation require non-substantial modifications of the dummy, by insertion of sensors for the measurement of the acceleration of the 4th rib and the 12th vertebra and two very thin plates at the knees for the correct individuation of the contact point with the vehicle bumper. Particular attention is paid to the front shape of the vehicle, concluding that the SUV examined in this paper is less dangerous than the sedan studied in a previous work, since its frontal dimensions (bonnet angle, bumper height and bonnet height) are more advantageous. However the teenage pedestrian in a lateral position is less prone to injuries in the head and chest, with respect to the frontal position; the pedestrian’s position has little influence on femur damage. Furthermore, the braking of the vehicle reduces the possibility of crash fatality. In conclusion, a theoretical approach is shown, to highlight the influence of the vehicle mass on the pedestrian speed after the impact.

The dynamic behavior induced by different wind turbine gearbox suspension methods assessed by means of the flexible multibody technique

The continuous demand for increase in power output for new wind parks under strict cost constraints, the greater wind resource at elevation and the desire for fewer machines per Mega-Watt to reduce operations resulted in a demand for bigger turbines. The drive train is an important component in realizing reliable and robust wind turbines.This paper investigates a geared wind turbine. In this type a gearbox is used to convert the low rotor speed to the required high generator speed. In the market several solutions are available to constrain the gearbox in the nacelle. The used configuration significantly determines the gearbox response to rotor loads and the transmission of gearbox vibrations to the turbine. This paper investigates the effectiveness of three configurations: the three point mounting, the double bearing configuration and the hydraulic damper system. The flexible multibody modeling technique can be used to accurately characterize gearbox dynamics. The goal of this work is to use an experimentally validated multibody model of a wind turbine drive train as a starting point to characterize the ability of the three configurations to minimize the introduction of non-torque loads in the gearbox and the ability to isolate the high speed shaft initiated gearbox vibrations from the rest of the turbine.A case study with parameter variation was performed on the existing three point mounted NREL GRC drive train. Furthermore some modifications were done to simulate a two bearing configuration and a hydraulic suspension system. We performed a parametric study to visualize the trends governing suspension influences.This paper shows that the two bearing configuration and the hydraulic system generally have lower rear planet carrier bearing response amplitudes than the three point mounting configuration. In addition, the hydraulic system was able to remove an important resonance.The paper concludes with a sensitivity analysis to link the trends above to their driving parameters.

Crash response optimisation of helicopter seat and subfloor

This paper describes the integrated analysis of energy absorbing stages of seat and subfloor in helicopters during a crash landing, and their influence on the occupant's response. Their optimisation, when performed considering both the stages and their mutual interaction, leads to significant reductions of the occupant's injury levels. The study is based on validated numerical models of an anthropomorphic test device, seat and subfloor developed in a multi-body technique. Beyond the optimisations, a series of response surfaces were generated that show the max lumbar spine load, seat stroke and subfloor deflection as functions of mechanical parameters of the seat and subfloor, pointing out the design regions. Different impact speeds were considered. The results suggest that the mechanical properties of the solutions currently adopted for helicopter energy absorption could be easily re-tuned to further improve occupant's protection during a crash landing.

Modeling the Flexural Dynamic Behavior of Axially Moving Continua by Using the Finite Element Method

Mechanical systems including conveyor belts, band saw blades, and power transmission belts are influenced by the lateral motion of the moving structure. This phenomenon was studied in the literature both using the theory of the continuous linear and nonlinear systems and following the multibody technique. The subject is studied by using the finite element method (FEM) validated with reference to the analytical models described in the literature. The contributions of the Coriolis forces, the negative stiffness linked to the transport speed, and the bending stiffness due to the transverse moment of inertia are discussed. The dynamic behavior of a prototypical belt transmission layout with two fixed pulleys and an automatic tensioner is then analyzed. The results show the effect of the transport speed on the reduction of the flexural natural frequencies of the mode shapes strictly related to the lateral motion of the belt span and evidence the design strategy that needs to be followed for a correct operation of the whole system.

Motorcycle Modeling with SimMechanics

A new motorcycle multi-body modeling technique with SimMechanics was presented which can be used in vehicle handling and stability analysis. The established model included tyre nonlinear characters and vehicle frame compliance. Combining with motorcycle driver model, established in Simulink, a typical vehicle handling test was implemented. With Simulink Virtual Reality, the animation of the motorcycle test was realized.

Multibody modelling of varying complexity for modal behaviour analysis of wind turbine gearboxes

In the currently booming market of wind turbines, a clear focus is put on the design of reliable and cost-effective subsystems, such as the gearbox. A requirement for reliable gearbox design calculations is sufficient insight in the dynamics of the entire wind turbine drive train. Since traditional wind turbine design codes reduce the drive train to just a few degrees of freedom, considerable research effort is spent in advanced modelling and simulation techniques to gain more insights in the dynamics at hand. This work focusses on the gearbox modal behaviour assessment by means of three more complex modelling techniques of varying complexity: the purely torsional-, rigid six degree of freedom with discrete flexibility and flexible multibody technique. Both simulation and experimental results are discussed. Typical mode categories for traditional wind turbine gearboxes are defined. Moreover the challenge of the definition of an accurate approach to condense finite element models for representing the flexible components in the flexible multibody models is overcome. Furthermore the interaction between the structural modes of the planet carrier and planetary ring flexibility with the overall gearbox modes is investigated, resulting in the definition of two new mode categories: the planet carrier modes and planetary ring modes.

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.

Endgame Problem Part 1: V-Infinity-Leveraging Technique and the Leveraging Graph

Renewed interest by ESA and NASA in missions to Europa, Ganymede, Enceladus, and Titan poses the question of how to best solve the endgame problem. Endgames typically aim at an inexpensive insertion maneuver into the science orbit and can be designed using either V ∞ -leveraging maneuvers or the multibody dynamics. Although historically linked to insertion maneuvers, the endgame problem is symmetric and equally applies to departure. In this two-part series, we analyze and draw connections between the two apparently separate approaches, providing insight into the dynamics of the multibody gravity-assist problem. In this paper we derive new formulas for the V ∞ -leveraging maneuver and build the leveraging graph to be used as a reference guide for designing endgame tours. We prove that the cost of a V ∞ -leveraging-maneuver sequence decreases when using high-altitude flybys (as done in the multibody technique). Finally, we find a simple quadrature formula to compute the minimum ΔV transfer between moons using V ∞ -leveraging maneuvers, which is the main result of the paper, and a method to estimate transfer times. The leveraging graphs and associated formulas are derived in canonical units and therefore apply to any celestial system with a smaller body in a circular orbit around a primary. Specifically, we demonstrate the new method to provide rapid calculations of the theoretical boundary values for ΔV requirements and estimated transfer times for moon tours in the Saturn and Jupiter systems using the V ∞ -leveraging-maneuver model.

Endgame Problem Part 2: Multibody Technique and the Tisserand-Poincare Graph

This two-part series studies the anatomy of the endgame problem, the last part of the spacecraft trajectory before the orbit-insertion maneuver into the science orbit. The endgame provides large savings in the capture A v, and therefore it is an important element in the design of ESA and NASA missions to the moons of Jupiter and Saturn. The endgame problem has been approached in different ways with different results: the ν ∞ -leveraging-maneuver approach leads to high-Δ ν, short-time-of-flight transfers, and the multibody technique leads to low-Δν, long-time-of-flight transfers. This paper series investigates the link between the two approaches, giving a new insight to the complex dynamics of the multibody gravity-assist problem. In this paper we focus on the multibody approach using a new graphical tool, the Tisserand-Poincare graph. The Tisserand-Poincare graph shows that ballistic endgames are energetically possible and it explains why they require resonant orbits patched with high-altitude flybys, whereas in the ν ∞ -leveraging-maneuver approach, flybys alone are not effective without impulsive maneuvers in between them. We then use the Tisserand-Poincare graph to design quasi-ballistic transfers. Unlike previous methods, the Tisserand-Poincare graph provides a valuable energy-based target point for the design of the endgame and begin-game and a simple way to patch them. Finally, we present two transfers. The first transfer is between low-altitude orbits at Europa and Ganymede using almost half the Δν of the Hohmann transfer; the second transfer is a 300-day quasi-ballistic transfer between halo orbits of the Jupiter-Ganymede and Jupiter-Europa. With approximately 50 m/s the transfer can be reduced by two months.

Linear vibration analysis of rotating wind-turbine blade

In the wind-turbine design, linear vibration analysis of the wind-turbine blade should be performed to get vibratory characteristics and to avoid structural resonance. EOM (equations of motion) for the blade are derived and vibratory characteristics of a rotating blade are observed and discussed in this work. Linear vibration analysis requires the linearized EOM with DOF (degree of freedom). For the system with large DOF, the derivation and linearization of EOM are very tedious and difficult. Constrained multi-body technique is employed to derive EOM’s to alleviate this burden. It is well known that natural frequencies and corresponding modes vary as rotating velocity changes. At the operating condition with relatively high rotating velocity, almost all commercial programs cannot predict the blade frequencies accurately. Numerical problems were solved to verify the accuracy of the proposed method. Through the numerical problems, this work shows that the proposed method is useful to predict the vibratory behavior of the rotating blade. Furthermore, a numerical problem was solved to check the numerical accuracy of commercial program results within operating region.

Inverse dynamics of a toggle mechanism

The inverse dynamics problem aimed at determining the driving forces that produce a specific motion is presented. It is necessary to know the velocities and accelerations to be able to estimate the inertia forces which provide the basis to calculate the required actuating forces. A constrained multibody technique is employed to calculate the position, velocity and acceleration of the toggle mechanism. For the multibody dynamic analysis, Hamilton's principle and Lagrange multiplier method are applied to formulate the equations of motion. By using geometric relationships the differential-algebraic equations can be reduced to pure differential equations form and Runge-Kutta numerical method is used to perform numerical simulations. The results of kinematic and dynamic analysis are presented and compared for the four-point type and the five-point toggle mechanisms.

Use of mode orthogonalization and modal damping in flexible multibody dynamics

In nonlinear multibody000namics simulations a model superposition for flexible bodies is often of advantage. For combined sets of modes such as constraint modes, fixed-interface eigenmodes, attachment modes, etc. it is of interest to use mode orthogonalization. This procedure gives information about the frequency content of a flexible body model discretization. Of special interest in this study is that some orthogonalized modes may be detected as rigid body modes which cannot be used in conjunction with the multibody technique of using a co-rotating and co-translating reference frame. The orthogonalization procedure thus can be used for both rigid body mode annd high frequency mode rejection. The orthogonalization procedure makes it possible to introduce modal damping in a convenient way.