Vibration instability in rolling mills: Modeling and experimental results

Models for the occurrence of the vibrational instability during rolling known as third octave chatter are presented and discussed. An analysis of rolling mill chatter was performed for the purpose of identifying characteristics of the vibrations and to determine any dependency on the rolling schedule. In particular, a stability criterion for the critical rolling speed is used to predict the maximum rolling speed without chatter instability on schedules from a 5 stand tandem mill rolling thin steel product. The results correlate well with measurements of critical speed occurring on the mill using a vibration monitor: This research provides significant insights into the chatter phenomena and has been used to investigate control methods for suppression of the instability.

A new relaxation method for roll forming problems

Finite element analysis (FEA) of nonlinear problems in solid mechanics is a time consuming process, but it can deal rigorously with the problems of both geometric, contact and material nonlinearity that occur in roll forming. The simulation time limits the application of nonlinear FEA to these problems in industrial practice, so that most applications of nonlinear FEA are in theoretical studies and engineering consulting or troubleshooting. Instead, quick methods based on a global assumption of the deformed shape have been used by the roll-forming industry. These approaches are of limited accuracy. This paper proposes a new form-finding method - a relaxation method to solve the nonlinear problem of predicting the deformed shape due to plastic deformation in roll forming. This method involves applying a small perturbation to each discrete node in order to update the local displacement field, while minimizing plastic work. This is iteratively applied to update the positions of all nodes. As the method assumes a local displacement field, the strain and stress components at each node are calculated explicitly. Continued perturbation of nodes leads to optimisation of the displacement field. Another important feature of this paper is a new approach to consideration of strain history. For a stable and continuous process such as rolling and roll forming, the strain history of a point is represented spatially by the states at a row of nodes leading in the direction of rolling to the current one. Therefore the increment of the strain components and the work-increment of a point can be found without moving the object forward. Using this method we can find the solution for rolling or roll forming in just one step. This method is expected to be faster than commercial finite element packages by eliminating repeated solution of large sets of simultaneous equations and the need to update boundary conditions that represent the rolls.

Three-dimensional simulation of the rolling of a saturated fibro-porous media

This paper describes recent advances made in computational modelling of the sugar cane liquid extraction process. The saturated fibro-porous material is rolled between circumferentially grooved rolls, which enhance frictional grip and provide a low-resistance path for liquid flow during the extraction process. Previously reported two-dimensional (2D) computational models, account for the large deformation of the porous material by solving the fully coupled governing fibre stress and fluid-flow equations using finite element techniques. While the 2D simulations provide much insight into the overarching cause-effect relationships, predictions of mechanical quantities such as roll separating force and particularly torque as a function of roll speed and degree of compression are not satisfactory for industrial use. It is considered that the unsatisfactory response in roll torque prediction may be due to the stress levels that exist between the groove tips and roots which have been largely neglected in the geometrically simplified 2D model. This paper gives results for both two- and three-dimensional finite element models and highlights their strengths and weaknesses in predicting key milling parameters. (c) 2005 Elsevier B.V. All rights reserved.

Review of Contact and Dynamic Phenomena in Cold Roll Forming

This review reflects the state of the art in study of contact and dynamic phenomena occurring in cold roll forming. The importance of taking these phenomena into account is determined by significant machine time and tooling costs spent on worn out forming rolls replacement and equipment adjustment in cold roll forming. Predictive modelling of the tool wear caused by contact and dynamic phenomena can reduce the production losses in this technological process.

Prediction of impact forces in a vibratory ball mill using an inverse technique

To understand the dynamic mechanisms of the mechanical milling process in a vibratory mill, it is necessary to determine the characteristics of the impact forces associated with the collision events. However, it is difficult to directly measure the impact force in an operating mill. This paper describes an inverse technique for the prediction of impact forces from acceleration measurements on a vibratory ball mill. The characteristics of the vibratory mill have been investigated by the modal testing technique, and its system modes have been identified. In the modelling of the system vibration response to the impact forces, two modal equations have been used to describe the modal responses. The superposition of the modal responses gives rise to the total response of the system. A method based on an optimisation approach has been developed to predict the impact forces by minimising the difference between the measured acceleration of the vibratory ball mill and the predicted acceleration from the solution of the modal equations. The predicted and measured impact forces are in good agreement. Copyright (C) 1996 Elsevier Science Ltd.

On the dynamics of mechanical milling in a vibratory mill

The dynamics of mechanical milling in a vibratory mill have been studied by means of mechanical vibration, shock measurements, computer simulation and microstructural evolution measurements. Two distinct modes of ball motion during milling, periodic and chaotic vibration, were observed. Mill operation in the regime of periodic vibration, in which each collision provides a constant energy input to milled powders, enabled a quantitative description of the effect of process parameters on system dynamics. An investigation of the effect of process parameters on microstructural development in an austenitic stainless steel showed that the impact force associated with collision events is an important process parameter for characterizing microstructural evolution. (C) 1997 Elsevier Science S.A.

The influence of calcium on granular sludge in a full-scale UASB treating paper mill wastewater

Calcium precipitation can have a number of effects on the performance of high-rate anaerobic performance including cementing of the sludge bed, limiting diffusion, and diluting the active biomass. The aim of this study was to observe the influence of precipitation in a stable full-scale system fed with high-calcium paper factory wastewater. Granules were examined from an upflow anaerobic sludge blanket reactor (volume 1,805 m(3)) at a recycled paper mill with a loading rate of 5.7-6.6 kgCOD.m(-3).d(-1) and influent calcium concentration of 400-700 gCa(.)m(-3). The granules were relatively small (1 mm), with a 200-400 mum core of calcium precipitate as observed with energy dispersive X-ray spectroscopy. Compared to other granules, Methanomicrobiales not Methanobacteriales were the dominant hydrogen or formate utilisers, and putative acidogens were filamentous. The strength of the paper mill fed granules was very high when compared to granules from other full-scale reactors, and a partial linear correlation between granule strength and calcium concentration was identified.

Comparison of DEM and experiment for a scale model SAG mill

Predictions of flow patterns in a 600-mm scale model SAG mill made using four classes of discrete element method (DEM) models are compared to experimental photographs. The accuracy of the various models is assessed using quantitative data on shoulder, toe and vortex center positions taken from ensembles of both experimental and simulation results. These detailed comparisons reveal the strengths and weaknesses of the various models for simulating mills and allow the effect of different modelling assumptions to be quantitatively evaluated. In particular, very close agreement is demonstrated between the full 3D model (including the end wall effects) and the experiments. It is also demonstrated that the traditional two-dimensional circular particle DEM model under-predicts the shoulder, toe and vortex center positions and the power draw by around 10 degrees. The effect of particle shape and the dimensionality of the model are also assessed, with particle shape predominantly affecting the shoulder position while the dimensionality of the model affects mainly the toe position. Crown Copyright (C) 2003 Published by Elsevier Science B.V. All rights reserved.

Anatomy of a hemiramphid pharyngeal mill with reference to arrhamphus sclerolepis krefftii (steindachner) (teleostei: hemiramphidae)

The structure and function of the pharyngeal jaw apparatus (PJA) and postpharyngeal alimentary tract of Arrhamphus sclerolepis krefftii, an herbivorous hemiramphid, were investigated by dissection, light and scanning electron microscopy, and X-ray analysis of live specimens. A simple model of PJA operation is proposed, consisting of an adductive power stroke of the third pharyngobranchial that draws it posteriorly while the fifth ceratobranchial is adducted, and a return stroke in which the third pharyngobranchial bone is drawn anteriorly during abduction of the fifth ceratobranchial. Teeth in the posteromedial region of the PJA are eroded into an occlusion zone where the teeth of the third pharyngobranchial are spatulate incisiform and face posteriorly in opposition to the rostrally oriented spatulate incisiform teeth in the wear zone of the fifth ceratobranchial. The shape of the teeth and their pedestals (bone of attachment) is consistent with the model and with the forces likely to operate on the elements of the PJA during mastication. The role of pharyngeal tooth replacement in maintaining the occlusal surfaces in the PJA during growth is described. The postpharyngeal alimentary tract of A. sclerolepis krefftii comprises a stomachless cylinder that attenuates gradually as it passes straight to the anus, interrupted only by a rectal valve. The ratio of gut length to standard length is about 0.5. Despite superficial similarities to the cichlid PJA (Stiassny and Jensen [1987] Bull Mus Comp Zool 151: 269-319), the hemiramphid PJA differs in the fusion of the third pharyngobranchial bones, teeth in the second pharyngobranchials and the fifth ceratobranchial face anteriorly, the presence of a slide-like diarthroses between the heads of the fourth epibranchials and the third pharyngobranchial, the occlusion zone of constantly wearing teeth, and the unusual form of the muscularis craniopharyngobranchialis. The functional relationship between these structures is explained and the consequence for the fish of a complex PJA and a simple gut is discussed. (C) 2002 Wiley-Liss, Inc.

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.