Model reduction techniques in flexible multibody dynamics with application to engine cranktrain simulation

The development of a multibody model of a motorbike engine cranktrain is presented in this work, with an emphasis on flexible component model reduction. A modelling methodology based upon the adoption of non-ideal joints at interface locations, and the inclusion of component flexibility, is developed: both are necessary tasks if one wants to capture dynamic effects which arise in lightweight, high-speed applications. With regard to the first topic, both a ball bearing model and a journal bearing model are implemented, in order to properly capture the dynamic effects of the main connections in the system: angular contact ball bearings are modelled according to a five-DOF nonlinear scheme in order to grasp the crankshaft main bearings behaviour, while an impedance-based hydrodynamic bearing model is implemented providing an enhanced operation prediction at the conrod big end locations. Concerning the second matter, flexible models of the crankshaft and the connecting rod are produced. The well-established Craig-Bampton reduction technique is adopted as a general framework to obtain reduced model representations which are suitable for the subsequent multibody analyses. A particular component mode selection procedure is implemented, based on the concept of Effective Interface Mass, allowing an assessment of the accuracy of the reduced models prior to the nonlinear simulation phase. In addition, a procedure to alleviate the effects of modal truncation, based on the Modal Truncation Augmentation approach, is developed. In order to assess the performances of the proposed modal reduction schemes, numerical tests are performed onto the crankshaft and the conrod models in both frequency and modal domains. A multibody model of the cranktrain is eventually assembled and simulated using a commercial software. Numerical results are presented, demonstrating the effectiveness of the implemented flexible model reduction techniques. The advantages over the conventional frequency-based truncation approach are discussed.

New model of Christian missions to popish, Mahometan, & pagan nations explained, in four letters to a friend.

Mode of access: Internet.

A liberation model for comminution based on probability theory

Mineral processing plants use two main processes; these are comminution and separation. The objective of the comminution process is to break complex particles consisting of numerous minerals into smaller simpler particles where individual particles consist primarily of only one mineral. The process in which the mineral composition distribution in particles changes due to breakage is called 'liberation'. The purpose of separation is to separate particles consisting of valuable mineral from those containing nonvaluable mineral. The energy required to break particles to fine sizes is expensive, and therefore the mineral processing engineer must design the circuit so that the breakage of liberated particles is reduced in favour of breaking composite particles. In order to effectively optimize a circuit through simulation it is necessary to predict how the mineral composition distributions change due to comminution. Such a model is called a 'liberation model for comminution'. It was generally considered that such a model should incorporate information about the ore, such as the texture. However, the relationship between the feed and product particles can be estimated using a probability method, with the probability being defined as the probability that a feed particle of a particular composition and size will form a particular product particle of a particular size and composition. The model is based on maximizing the entropy of the probability subject to mass constraints and composition constraint. Not only does this methodology allow a liberation model to be developed for binary particles, but also for particles consisting of many minerals. Results from applying the model to real plant ore are presented. A laboratory ball mill was used to break particles. The results from this experiment were used to estimate the kernel which represents the relationship between parent and progeny particles. A second feed, consisting primarily of heavy particles subsampled from the main ore was then ground through the same mill. The results from the first experiment were used to predict the product of the second experiment. The agreement between the predicted results and the actual results are very good. It is therefore recommended that more extensive validation is needed to fully evaluate the substance of the method. (C) 2003 Elsevier Ltd. All rights reserved.

Using DEM to model ore breakage within a pilot scale SAG mill

The best accepted method for design of autogenous and semi-autogenous (AG/SAG) mills is to carry out pilot scale test work using a 1.8 m diameter by 0.6 m long pilot scale test mill. The load in such a mill typically contains 250,000-450,000 particles larger than 6 mm, allowing correct representation of more than 90% of the charge in Discrete Element Method (DEM) simulations. Most AG/SAG mills use discharge grate slots which are 15 mm or more in width. The mass in each size fraction usually decreases rapidly below grate size. This scale of DEM model is now within the possible range of standard workstations running an efficient DEM code. This paper describes various ways of extracting collision data front the DEM model and translating it into breakage estimates. Account is taken of the different breakage mechanisms (impact and abrasion) and of the specific impact histories of the particles in order to assess the breakage rates for various size fractions in the mills. At some future time, the integration of smoothed particle hydrodynamics with DEM will allow for the inclusion of slurry within the pilot mill simulation. (C) 2004 Elsevier Ltd. All rights reserved.

Scaling limits of a model for selection at two scales

The dynamics of a population undergoing selection is a central topic in evolutionary biology. This question is particularly intriguing in the case where selective forces act in opposing directions at two population scales. For example, a fast-replicating virus strain outcompetes slower-replicating strains at the within-host scale. However, if the fast-replicating strain causes host morbidity and is less frequently transmitted, it can be outcompeted by slower-replicating strains at the between-host scale. Here we consider a stochastic ball-and-urn process which models this type of phenomenon. We prove the weak convergence of this process under two natural scalings. The first scaling leads to a deterministic nonlinear integro-partial differential equation on the interval $[0,1]$ with dependence on a single parameter, $\lambda$. We show that the fixed points of this differential equation are Beta distributions and that their stability depends on $\lambda$ and the behavior of the initial data around $1$. The second scaling leads to a measure-valued Fleming-Viot process, an infinite dimensional stochastic process that is frequently associated with a population genetics.

An approximate method for the solution of an influence function foil rolling model

Fleck and Johnson (Int. J. Mech. Sci. 29 (1987) 507) and Fleck et al. (Proc. Inst. Mech. Eng. 206 (1992) 119) have developed foil rolling models which allow for large deformations in the roll profile, including the possibility that the rolls flatten completely. However, these models require computationally expensive iterative solution techniques. A new approach to the approximate solution of the Fleck et al. (1992) Influence Function Model has been developed using both analytic and approximation techniques. The numerical difficulties arising from solving an integral equation in the flattened region have been reduced by applying an Inverse Hilbert Transform to get an analytic expression for the pressure. The method described in this paper is applicable to cases where there is or there is not a flat region.