Dynamic model of overwind and crash beam arresting with descending head ropes having distributed mass and stiffness

A singular rail or wheel surface irregularity, such as a squat, insulation joint or wheel flat, can cause large wheel-rail impact force. Both the magnitude and frequency content of the impact force need to be correctly modelled because they are closely related to the formation, deterioration and detection of such irregularities. In this paper, we compare two types of commonly used wheel-track interaction models for wheel-rail impact problems, i.e., a beam and a continuum finite element model. We first reveal the differences between the impact forces predicted by the two models due to a typical rail squat using a time-frequency analysis. Subsequently, we identify the causes for the differences by evaluating the effects of different model assumptions, as well as different model parameters. Results show that the impact force consists of a forced vibration peak M1 followed by free vibration related oscillations with three dominant frequencies: f1 (340 Hz), f2 (890 Hz) and f3 (1120 Hz). Compared with the continuum model, the beam model with a Hertzian contact spring overestimates the M1 peak force. The discrepancy can be reduced by using a Winkler bedding contact model. For the track model, the beam model is comparable to the continuum model up to about 800 Hz, beyond which the track damping starts to deviate. As a result, above 500 Hz, the contact forces dominate at f2 for the beam while at f3 for the continuum model. Finally, we show that the continuum model is more accurate than the beam model by comparing to field observations. The effects of stress wave propagation on the differences are also discussed.

Clearly, the assumption that all bodies are perfectly rigid, hence the introduction of singular distributions in the modeling of collisions has the advantage of providing an attractive framework of impact dynamics. Note however that bodies that collide do possess a certain compliance, so that the collision duration is strictly positive (1) and local deformations occur near the point of impact. Actually global (vibrational) deformations are also created, and they may play a major role in the dynamics. They may even play a much more important role than the local deformations. Consequently, rigid body dynamics may be considered as a limit case only, which however does not preclude its practical as well as theoretical utility (the pros and cons of rigid and flexible body approaches are not the topic of this chapter). One may therefore choose to work with continuous-dynamics models of collision, such that the bodies deform during the impact, and the collision dynamics are treated as continuous time dynamic phenomena (restricted to local deformations in most of the studies). Historically, it has very often been difficult to certain scientists to accept the idea of perfect rigidity [979]. For instance Leibniz himself [509] [510] (and Bernoulli after him [77]) refused this idea because rigidity yields violation of the “law of continuity” in nature. A strong scientific debate motivated by the London Royal Society in 1668 also concerned the concept of “hardness” (which is to be understood as rigidity in this context): is a hard body able to rebound? Or is it necessary that the bodies possess some “springiness”? Wallis and Mariotte concluded that springs are necessary, while Huygens, Wren and Malebranche thought that hardness is sufficient [979]. We know now the difference between a model of nature and nature itself. We also have many more mathematical tools at our disposal to accept perfect rigidity and to study accurately the relationship between compliant and rigid models (2). Moreover the very short collision durations allow one to safely work with two timescales in many practical cases. And it is possible to lump the deformations effects in one single coefficient while keeping the attractiveness of rigid body models, see section 4.2 and subsection 4.2.10.KeywordsContact ForceInteraction ForceExternal ActionCompliant ModelUnilateral ConstraintThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Two types of dynamic models will be used in plume analysis for the space station Freedom: finite-element and large-displacement rigid body. The rigid-body model will be used for two purposes: (1) to assist in predicting likely plume loads, and (2) to test the hypothesis that incremental dynamic feathering during approach can bring extra plume load relief over the current baseline option. The plume impingement aspect of the rigid model and the use of the rigid model in simulation and in partnership with structural dynamic analysis are discussed. >

Matching of head ropes and drum grooves in multi-rope friction winding systems is essential for effective load sharing between the winding ropes. Analytical methods were developed in the 1960s to evaluate rope load disparity when rope groove depths are mismatched. Although this historical analysis ignored flexibility in rope groove lining materials, it is widely accepted that rope groove flexibility has the effect of reducing the disparity in load sharing. This paper recounts the original 1960s work in which rope load disparity was analyzed to provide rope groove depth tolerances of rigid grooves and provides a new rope groove depth tolerance for flexible grooves. Both rigid and flexible groove analyses show the importance of an adequate distance between the conveyance at its uppermost normal position in the shaft and the head ropes’ tangent point on the hoist drum. They also show that ground-mounted hoists are more tolerant to groove depth mismatch. Maintenance methods, including the collar-to-collar test, are revisited to reflect this latest analysis.

The transverse deformation of the beam will lead to the longitudinal shortening deformation, and this transverse-longitudinal deformation coupling will bring the dynamic stiffening effect term on the generalized rigidity of the beam model. For the rotating beam structure, the centrifugal force will cause axial tension, with coupling axial and transverse deformation of the beam and bring additional geometric stiffness, which is more obvious for the thick short beam. The central rigid body-Timoshenko beam model with a large-range-motion center was investigated. Firstly, the dynamic model with centrifugal forces was established by means of the Timoshenko beam theory and the Hamilton principle. Secondly, the unconstrained mode concept was introduced, and the unconstrained mode shape functions and natural frequencies were solved with the Frobenius method. Finally, numerical simulations were carried out to explore the difference of generalized stiffness between the unconstrained mode and the constrained mode at different constant speeds, and the effects of centrifugal forces on the model under unconstrained mode condition were discussed.

In this work, an energy and momentum conserving method is developed for doing coupled flexible and rigid body dynamics. The main focus is on the bilateral connection of flexible finite elements to rigid bodies. The coupling of rigid bodies at joints is also introduced. Existing conserving algorithms for individual (un‐coupled) rigid and flexible bodies are exploited and modified for the coupled system. By using the appropriate rigid body rotational update and generalized force definitions, the resulting rigid–flexible and rigid–rigid systems are unconditionally stable and conserve linear and angular momentum. The conservation and stability properties are demonstrated in numerical simulation. Published in 2001 by John Wiley & Sons, Ltd.

Movement modeling and control of a ‘bonnet tool’ polishing machine, based on a strategy of static highest-stiffness, are presented. The aim is to achieve polishing controllability as the bonnet tool executes a precessive motion trajectory. Taking an aspheric optical surface, e.g. lens or mirror, as the workpiece, the precessive polishing tool trajectory is designed as if the moving parts were rigid bodies connected by ideal articulations. Then by establishing the Jacobian stiffness matrix of the bonnet tool machine, the static stiffness of the machine is derived taking into account tool loading along its path. To minimize deformation, the control algorithm that achieves a maximum static stiffness strategy is superposed on the rigid body system tool trajectory model. This combined bonnet tool trajectory is produced by numerical simulation. Finally suitability of the rigid body movement model, compensated for desired static, but not inertial, load deflection, is assessed by simulating the trajectory of the tool’s rotational axis to determine how much angular deviation it sustains from the local surface normal. It was found that this bonnet polishing tool compensation method, based on a greatest static stiffness strategy, will produce satisfactory results.

This chapter addresses the numerical modeling of freestanding rigid blocks by means of a semi-discrete approach. The pure rocking motion of single rigid bodies can be easily studied with the differential equation of motion, which can be solved by numerical integration or by linearization. However, when we deal with sliding and jumping motion of rigid bodies, the mathematical formulation becomes quite complex. In order to overcome this complexity, a Semi-Discrete Model (SMD) is proposed for the study of rocking motion of rigid bodies, in which the rigid body is considered as a mass element supported by springs and dashpots, in the spirit of deformable contacts between rigid blocks. The SMD can detect separation and sliding of the body; however, initial base contacts do not change, keeping a relative continuity between the body and its base. Extensive numerical simulations have been carried out in order to validate the proposed approach.

We propose a framework for the full two-way coupling of rigid and deformable bodies, which is achieved with both a unified time integration scheme as well as individual two-way coupled algorithms at each point of that scheme. As our algorithm is two-way coupled in every fashion, we do not require ad hoc methods for dealing with stability issues or interleaving parts of the simulation. We maintain the ability to treat the key desirable aspects of rigid bodies (e.g. contact, collision, stacking, and friction) and deformable bodies (e.g. arbitrary constitutive models, thin shells, and self-collisions). In addition, our simulation framework supports more advanced features such as proportional derivative controlled articulation between rigid bodies. This not only allows for the robust simulation of a number of new phenomena, but also directly lends itself to the design of deformable creatures with proportional derivative controlled articulated rigid skeletons that interact in a life-like way with their environment.

Adopt the literature review method, apply the computer numerical simulation technology, and combine the research method and characteristics of the physical exercise technology. It discusses the application methods, process, specific steps and function of the computer numerical simulation technique from the establishment of the sport technique simulation model, steps, data input, and data pre-processing of the computer numerical simulation, computer numerical simulation calculation, modification of the movement technique proposal, application of the new action design and computer numerical simulation in the movement technique training, etc. In the physical exercise teaching and exercise training practice, it generally uses the camera to shoot the athletes’ skilled movement, and then analyzes it. However, this method only can simply replay the skilled movement of the athletes, while its quantization and comparative analysis on the kinematics, dynamics, and biology of the movement technique cannot achieve satisfactory result. The rapid development of the modern computer technology lays scientific foundation for the comparison, superposition, dynamics test and calculation of the movement technique image. Especially, the computer numerical simulation technique enables the coach to predict the result of the movement technique in the design phase of the movement technique and then proceed with the optimal design of the movement technique. No matter for the improvement of the movement technique or the reconstruction of the movement technique, it is feasible to greatly shorten the research period, and improve the feasibility and actual application value of the movement technique design proposal. Establishment of the Digital Simulation Model of the Human Motion The system simulation is a powerful tool for using the computer to analyze and design various complex systems. Its application and influence have been widely applied in many science researches, engineering domain and non-engineering domain. In the movement technique research, as the research is involved in the features of the human motion, the human body is generally simplified into a multiple rigid system mode according to the purpose of the movement technique, rules and features of the human to finish the movement technique. The skeleton, muscle, tendon, and other movement system tissue of the human body is processed into the acting force and torque among each rigid by, and then the kinematics and dynamics equation for studying the human motion is established. When the independent generalized coordinate is adopted to study the skilled movement, its mathematical model is an ordinary differential equation[1]. If the dependent generalized coordinate is adopted, the differential algebra equation will be achieved. These equations generally belong to higher-order and highly-coupled non-linear equation. Apart from simplifying and achieving the analysis results under tiny minority of the situations, the arithmetic solution can be achieved through the computer in general. International Conference on Advances in Mechanical Engineering and Industrial Informatics (AMEII 2015) © 2015. The authors Published by Atlantis Press 144 Methods and Procedure of the Computer Numerical Simulation 2.1 Methods of computer numerical simulation The methods for simulating the human movement through the computer include: input the original parameter, calculate, achieve the description result of the skilled movement, form the principle of the movement technique, etc. This process is named as numerical simulation. During the calculation, it is possible to face positive and reverse problems. For instance, get the mechanical conditions (e.g. muscle moment force, drag torque, human hypogene transmission and angular momentum transmission, exogenous process, etc.) that form the skilled movement when the movement status (e.g. space and time feature of the movement of each link) of each link of the human body is known. During the computing progress of the computer numerical simulation, it is necessary to increase the mechanics additional constraint conditions, so as to get the optimal combination of each input amount, and finish the optimal design of the movement technique. Under the condition of establishing accurate parameters of the numerical simulation model, the calculation result can accurately reflect the actual movement status, which has strong prediction and practical guidance effect for the results obtained by the research on the movement technique. Picture 1 working process diagram of the computer numerical simulation It puts forward the optimal movement technique proposal toward the throwing technique of Wilkinson. As this research is established on the basis of the scientific theory, it an provide scientific guidance for optimizing the movement technique of the athletes, which has great significance in improving the movement technique level[2]. 2.2 Procedure of the computer numerical simulation The procedure of the computer numerical simulation gets involved in different aspects. For instance, according to the researched movement technique subject, target and task, establish continuous movement digitalization model of the multiple rigid body system, establish the Multi rigid body model Calculation result Basic parameter

The concept that the lithosphere behaves as a perfectly rigid body during plate tectonism is challenged as a fundamental rule in the theory of new global tectonics. Experimental studies in rock mechanics indicate that confining pressure, temperature, solutions, the size of masses, and strain rate produce plates of little fundamental strength which can be subjected to plastic deformation by conventional geologic processes. A plastic plate tectonics model is geologically more realistic than the rigid body concept. The rigid model is believed to place some confining and perhaps unnecessary restrictions on the theory of global tectonics. The plastic plate model allows new possibilities concerning the fit of continental masses, as well as new interpretations related to the change in shape of such plates as they are transported across the surface of the Earth.

Molecularsimulations have the potential to advance the understandingof how the structure of organic materials can be engineered throughthe choice of chemical components but are limited by computationalcosts. The computational costs can be significantly lowered throughthe use of modeling approximations that capture the relevant featuresof a system, while lowering algorithmic complexity or by decreasingthe degrees of freedom that must be integrated. Such methods includecoarse-graining techniques, approximating long-range electrostaticswith short-range potentials, and the use of rigid bodies to replaceflexible bonded constraints between atoms. To understand whether andto what degree these techniques can be leveraged to enhance the understandingof planar organic molecules, we investigate the morphologies predictedby molecular dynamic simulations using simplified molecular modelsof perylene and perylothiophene. Approximately, 10 000 wall-clockhours of graphics processing unit-accelerated simulations are performedusing both rigid and flexible models to test their efficiency andpredictive capability with the two chemistries. We characterize the1191 resulting morphologies using simulated X-ray diffraction andcluster analysis to distinguish structural transitions, summarizedby four phase diagrams. We find that the morphologies generated bythe rigid model of perylene and perylothiophene match with those generatedby the flexible model. We find that ordered, hexagonally packed columnarphases are thermodynamically favored over a wide range of densitiesand temperatures for both molecules, in qualitative agreement withexperiments. Furthermore, we find the rigid model to be more computationallyefficient for both molecules, providing more samples per second andshorter times to equilibrium. Owing to the structural accuracy andimproved computational efficiency of modeling polyaromatic groupsas rigid bodies, we recommend this modeling choice for enhancing thesampling in polyaromatic molecular simulations.

The dynamic responses of two-dimensional granular material subjected to the oblique impact and side impact of a spherical projectile are investigated experimentally and also numerically by using discrete element method. The granular material is modeled by the 329 nylon spheres arranged regularly and two-dimensionally in a rectangular container. The numerical simulations are carried out at the impact velocities less than 10 m/s. The numerical simulations are compared with the results of measurements using high-speed video camera. It is ascertained that the motion of each particle can be well simulated by discrete element method. The dynamic response of the particulate aggregation is elucidated by probing the distribution of velocity vectors of individual particle and normal direction component of contact forces between particles in detail. The effect of wave propagation on the shattering behavior of granular materials is manifested. It is found that the dynamic arching in granular material is formed just under impact point.

The validity of a rigid body model of a cricket ball-bat impact

Modeling of a deformable manikin neck for multibody dynamic simulation