Steady Rolling Research Articles

Simulation Analysis and Research of Tire Wear

The theory of tire wear computation is researched, and steady state transfer analysis and steady state rolling slippage are analyzed and deduced; the uniform wear rate of discrete node on the tire tread pattern is induced based on adhesive wear mechanism. Tire body model and tread pattern model are established by using Neo-Hooken constitutive model and linear elastic model, and the whole tire model is formed. Tire wear simulation analysis is preceded with combination of Abaqus Arbitary Lagrangian and Eulerian (ALE) method and the user subroutine programmed according to tire wear computation model. Tire wear of different mileage under free rolling state, tire wear under breaking condition and driving condition are compared, and slip angle, load and tire pressure’s impact on tire wear are analyzed.

Transfer Model of Transverse Asymmetry Characteristic in Standers during the Steady Hot Rolling Stage

During the hot rolling process, the perturbation of transverse asymmetry factor will generate strip steering, strip delivery wedge and other failure state. During the steady rolling stage, the constraint action of tension and so on can restrain strip steering. Transverse asymmetry characteristic mainly passes in the form of strip delivery wedge between the standers. Firstly this paper researches correlation of transverse asymmetry characteristic parameter toward single stander, establishes a function model to reflect transverse asymmetry result status, for instance strip delivery wedge, strip entry wedge, strip eccentric, gap wedge and other transverse asymmetry disturbance factor. Then the paper establishes transfer model of transverse asymmetry characteristic between standers, gets result status of strip delivery wedge between each ensuing standers under strip entry wedge, strip eccentric, gap wedge and other combination of disturbance. At last the paper takes working condition of actual aluminum hot rolling production line as an example, computes transfer coefficient of strip delivery wedge under several perturbation and discuss transfer discipline of transverse asymmetry characteristic between standers.

Analyses of Guiding Force for the Ring Rolling Mill

The guiding forces will affect the stability of the ring rolling process and the quality of the product directly. In this paper, the guiding forces and the sector gear forces are analyzed by building theoretical equations and numerical value simulations. The variation tendencies of the guiding forces and the sector gear forces changing with the ring’s outer diameter in both steady and unsteady ring rolling phases are found out base on the theoretical and simulation analyses.

FASTSIM2: a second-order accurate frictional rolling contact algorithm

In this paper we consider the frictional (tangential) steady rolling contact problem. We confine ourselves to the simplified theory, instead of using full elastostatic theory, in order to be able to compute results fast, as needed for on-line application in vehicle system dynamics simulation packages. The FASTSIM algorithm is the leading technology in this field and is employed in all dominant railway vehicle system dynamics packages (VSD) in the world. The main contribution of this paper is a new version FASTSIM2 of the FASTSIM algorithm, which is second-order accurate. This is relevant for VSD, because with the new algorithm 16 times less grid points are required for sufficiently accurate computations of the contact forces. The approach is based on new insights in the characteristics of the rolling contact problem when using the simplified theory, and on taking precise care of the contact conditions in the numerical integration scheme employed.

Lubricating film thickness measurements with bovine serum

Lubricant film thickness measurements were made for bovine serum solutions under steady state rolling and sliding. The effect of low (30MPa) and high contact pressures (200MPa) was examined. In the high pressure rolling tests BS initially formed films 5–50nm thick over the speed range. However, in subsequent speed sweeps, a relatively speed independent film of 40–50nm developed. In some cases thick (up to 100nm) films were formed at low speeds; this behaviour was considered representative of high-viscosity surface layers rather than of solid films. At the end of each test residual boundary films of 9–19nm were measured under static loading. These are attributed to the multilayer adsorption of protein molecules and will provide surface protection during stance or on initiation of gait. The results at low pressure showed that much thicker films (∼60–80nm) were formed over the same speed range. Again thicker films were formed at the lower speeds. There was significant scatter in the film thickness results, possibly due to the inherent nature of the fluid, which is an inhomogeneous biological solution. The film thickness/speed behaviour was not representative of a simple Newtonian fluid and this has considerable implications for the development of predictive film thickness models and new designs of artificial hip joints.

Euler's disk: examples used in engineering and applied mathematics teaching

Euler's disk is a toy described at http://www.eulersdisk.com. Aspects of its motion are modelled as an ideal disk rolling on a horizontal plane. In the final stages of Euler disk motions, the disk is nearly flat to the plane. Asymptotic approximations to the frequency of finite amplitude oscillations on steady (non-dissipative) rolling motions of the Euler disk are described. There are two different approximations which are appropriate in different limits. When the parameters are such that both apply, the formulae for the frequency agree: this appears to be new and simple. The material has been used in teaching; the teaching, and related, materials are available via the web [Keady, Math2200 Lecture Handouts, UWA]. References M. Batista. The nearly horizontally rolling of a thick disk on a rough plane. of a thick rigid disk Regular and Chaotic Dynamics 13 (4) (2008), 344--354. doi:10.1134/S1560354708040084 H. Caps, S. Dorbolo, S. Ponte, H. Croisier and N. Vandewalle. Rolling and slipping motion of Euler's disk. Physical Review E 69 (6) (2004), 056610. doi:10.1103/PhysRevE.69.056610 R. H. Cushman and J. J. Duistermaat. Nearly flat falling motions of the rolling disk. Regular and Chaotic Dynamics 11 (1) (2006) 31--60. doi:10.1070/RD2006v011n01ABEH000333 G. Keady. MATH2200 Lecture Handouts. The rolling of a disk on a horizontal plane. Part I, General; and Part II, Euler disk motions. http://school.maths.uwa.edu.au/ keady/papers.html H. K. Moffatt. Euler's disk and its finite-time singularity. Nature 404 (2000) 833. doi:10.1038/35009017 A. H. Nayfeh and D. T. Mook. Nonlinear Oscillations (Wiley: 1979). O. M. O'Reilly. The dynamics of rolling disks and sliding disks. Nonlinear Dynamics 10 (1996) 287--305. M. Srinivasan and A. Ruina. Rocking and rolling: a can that appears to rock might actually roll. Phys. Rev. E 78 (6) (2008) 066609. doi:10.1103/PhysRevE.78.066609 A. A. Stanislavsky and K. Weron. Nonlinear oscillations in the rolling motion of Euler's disk. Physica D 156 (2001) 247--259. doi:10.1016/S0167-2789(01)00281-0 J. L. Synge and B. A. Griffith. Principles of Mechanics. (McGraw-Hill, 3rd ed, 1959). W. T. Thomson. Introduction to Space Dynamics. (Dover: 1986 reprinting of Wiley 1963). R. Villanueva and M. Epstein. Vibrations of Euler's disk. Phys. Rev. E 71 (7) (2005) 066609. doi:10.1103/PhysRevE.71.066609 E. T. Whittaker. A treatise on the analytical dynamics of particles and rigid bodies. (CUP, 2nd ed, 1917).

On modeling a rolling wheel in the presence of plastic deformation as a three- or two-dimensional process

This paper compares predictions of deformation and horizontal (drag) force resulting from three- and two-dimensional numerical simulation of a torque-free (towed) wheel operating on ductile material. The finite-element code ABAQUS/Explicit is used to simulate a complete process beginning with wheel indentation and ending, if admissible, with steady rolling. The wheel is rigid, and the material is modeled as elastic/perfectly plastic with the von Mises yield condition, with focus on plastic rather than elastic effects. It is shown that two-dimensional analysis of a rolling wheel cannot readily be applied to a narrow wheel to predict wheel penetration, although horizontal forces from three- and two- dimensional simulations follow a similar trend. In particular, it is observed that steady-state penetration is constant over a range of applied vertical forces in the two-dimensional analysis, whereas steady-state penetration is an increasing function of vertical force for narrow wheels simulated in three dimensions. This illustrates potential errors in simplifying wheel rolling by utilizing two-dimensional analysis and the necessity of considering a fully three-dimensional process. In the paper, the latter is investigated in detail.

Statistical load characteristics in the primary lines of broad-strip rolling cells

The quality of the grooving and the rolling system may also be evaluated by means of v x . For reduction, bar, and pipe mills, the mean variation coefficients of the rolling force and torque and also the spindle torques are stable. However, the operation and state of the equipment in the primary line have not been evaluated using the variation coefficients of the maximum dynamic torque v d and the combined dynamic state v c . In the present work, we consider the three variation coefficients v st , v d , and v c in terms of their information content regarding the technological process and the operation of the equipment. This is particularly important in that continuous mills consist of a sequence of cells in which the strip is rolled as batches of a particular size. Obviously, the variation in these parameters in each cell will provide certain information. Data on the torque of the elastic forces in cells 5‐7 of the 1680 mill in the interval between the motor and the gear will now be subjected to statistical analysis. 1 For each strip within a batch of a single size, the mean (over the length) static torque M st in steady rolling conditions, the maximum torque of the elastic forces M d , and the dynamic coefficient K are calculated. In addition, for the same batch, the mean values of M st , M d , and K are calculated, as well as their mean square deviation and variation coefficients. As a result, we determine v st , v d , and v c . In rolling a single batch of strip, the speed and deformation are practically unchanged. Therefore, 1 Participants in this work include A. P. Danilchuk and V. V. Korennoi. sample M st has the smallest variation coefficient v st1 if the specified technological conditions (supply rate of the billet in the cell, absence of downtime, etc.) are observed. Analysis of v st for batches rolled in a different time period and comparison of the results permits the selection of the batch with the minimum coefficient v st.min , i.e., the batch rolled with the least spread in the technological parameters. The value of v st.min for cell i may be adopted as the comparison sample when evaluating the rolling technology for other batches of the same size. If the satisfaction of the technological conditions is best (or practically the best) in the first finishing cell 5, we may expect smaller v st in the other cells. If that is not the case, we must suspect that some technological perturbation has occurred. In this way, a table of minimum values v st.min may be formulated for the basic steels and slab (strip) sizes. The v st values obtained for subsequent measurements may be compared with the tabular values, for quantitative evaluation of the technological process in the specific cell. Comparison of the v st values for a continuous mill permits the identification of the cells where instability develops or of the range characterized by instability. The maximum dynamic load M d and dynamic coefficient K depend more significantly on the angular gaps in the drive line than on the technological parameters. Hence, v d and v c may be regarded as informative parameters related to the state of the drive line. By comparing their values in rolling strip of the same type in different operating periods, we may evaluate the state of the equipment in the cells. If we characterize the coefficients as large and small (subscripts L and S, respectively), we may write eight combinations of the three coefficients, in the general case. Analysis shows that, of these combinations, the following are seen in practice: small values of v st.S , v d.S , and v c.S , indicating stable (good) technology and a good engineering state of the drive line; small v st.S and large values of v d.L and v c.L , corresponding to good technology and a poor state of the line; large v st.L and small v d.S and v c.S , corresponding to poor technology and a good state of the line; and large values v st.L , v d.L ,

Effect of small harmonic oscillations during the steady rolling of a cylinder on a plane

If a wheel rolling over a rail transmits a tangential traction, frictional microslip occurs in part of the contact area, resulting in energy dissipation and localized wear. If the applied forces oscillate in time, the resulting wear will be non-uniform, resulting in ‘corrugations’ that can grow with progressive passes, depending on the dynamics of the overall system. In this paper, a linear perturbation method is used to obtain closed-form expressions for the receptance of a two-dimensional rolling contact subjected to small oscillations in normal force and rotational speed superposed on a mean value in the limit of large coefficient of friction. Corresponding expressions are also obtained for the amplitude and phase of the energy dissipation in the contact, which is expected to correlate with the local wear rate. The results are compared with a simpler Winkler model of the contact and with other models that have been used for the analysis of rail corrugation. Surprisingly good agreement is obtained with numerical results due to Gross-Thebing for the receptances due to oscillations in rotational speed.

Winkler partial slip solution for harmonic oscillations in steady rolling contact problems

A Winkler model (Kalker’s simplified theory) is adopted for solving analytically partial slip rolling contact problem in the first order perturbation form of small periodic oscillations of generally both normal and tangential load about a steady state. At present, only numerical investigations exist for this problem, with various approximations to deal with the transient effects (often, simply neglected), and particularly the effect of varying normal load and hence contact area, has not been investigated in detail, despite the problem of corrugation is essentially driven by the change of normal load. The linear perturbation analysis is used to obtain closed form expressions for the receptances of the tangential load. Also, similar expressions are obtained for the energy dissipation, which is correlated with the local wear.

ROLLING PROCESS SIMULATION USING A DEVELOPED EULERIAN FORMULATION

ABSTRACTIn this paper, an Eulerian formulation is developed from the more general ArbitraryLagrangian Eulerian (ALE) formulation and is used in rolling process simulation.Starting from the basic principles of continuum mechanics, a consistent ALEformulation is derived. An Eulerian formulation is then obtained by fixing the finiteelement mesh in space. A finite element program based on the Eulerian formulationhas been developed. The program is used to simulate a steady state rolling process.The roll pressure distribution is compared with published experimental results.Comparisons reveal the effectiveness of the developed formulation.

Complete Identification of E-Selectin Ligands on Neutrophils Reveals Distinct Functions of PSGL-1, ESL-1, and CD44

The selectins and their ligands are required for leukocyte extravasation during inflammation. Several glycoproteins have been suggested to bind to E-selectin in vitro, but the complete identification of its physiological ligands has remained elusive. Here, we showed that E-selectin ligand-1 (ESL-1), P-selectin glycoprotein ligand-1 (PSGL-1), and CD44 encompassed all endothelial-selectin ligand activity on neutrophils by using gene- and RNA-targeted loss of function. PSGL-1 played a major role in the initial leukocyte capture, whereas ESL-1 was critical for converting initial tethers into steady slow rolling. CD44 controlled rolling velocity and mediated E-selectin-dependent redistribution of PSGL-1 and L-selectin to a major pole on slowly rolling leukocytes through p38 signaling. These results suggest distinct and dynamic contributions of these three glycoproteins in selectin-mediated neutrophil adhesion and signaling.

Rotary aerodynamic derivatives in the asymptotic theory of a high-aspect-ratio wing

The linear problem of inviscid incompressible flow around a high-aspect-ratio wing at an angle of attack and in the presence of steady pitching and rolling rotation is considered. The main integral equation of the problem is reduced to a sequence of one-dimensional integral equations without use of the matched asymptotic expansions method. The first few terms of the series for the circulation distribution over the wing surface are calculated. For an elliptic high-aspect-ratio wing the corresponding aerodynamic forces are calculated. The derivatives of the aerodynamic coefficients of the wing with respect to the angle of attack and the angular velocities are determined. The asymptotic expressions obtained are compared with the results of numerical calculations of the corresponding derivatives using the discrete vortex method.

Existence of Solutions to the Linearized Spinning Wheel Problem

AbstractSpinning wheels, or rather steady rolling cylinder‐like deformable bodies occur in many mechanical (contact) problems, e.g. car‐ or aircraft‐tires, gears or grinding processes. In order to avoid transient calculation for such problems and in order to obtain a steady‐state formulation we make use of a model – advocated by Oden and Lin in [1] and further elaborated by Govindjee andMihalic in [2] – based on a spinning reference coordinate system. After developing the kinematics and deriving the weak formulation we will show the existence of a weak solution for the linearized spinning wheel problem by applying the Lax Milgram Lemma. The presented contribution will be concluded by some numerical examples. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

ESL-1 Is a Major Physiological Leukocyte Ligand for E-Selectin That Cooperates with PSGL-1 and CD44, and Together Mediate All Binding Activity to Endothelial Selectins In Vivo.

Endothelial selectins mediate leukocyte (WBC) rolling on activated endothelium. ESL-1 was isolated by affinity purification more than 10 years ago but whether it is a physiological ligand for E-selectin remains unclear. Recent studies suggest that PSGL-1 and CD44 are physiological E-selectin ligands on neutrophils (PMNs)(J. Exp. Med. 2005 201:1183). To analyze the contribution of ESL-1, PSGL-1 and CD44, we knocked down ESL-1 expression using lentiviral transfer of short hairpin (sh) RNA into wild-type (WT), PSGL-1- or/and CD44-deficient bone marrow lineage-negative (Lin-) cells. Sorted GFP+ cells from mice transplanted with Lin- cells transduced with the shESL-1 exhibited >90% reduction in total ESL-1 levels by Q-PCR and Western blot analyses, and complete absence of ESL-1 on the PMN surface. shESL-1 transduced Lin- cells engrafted recipients mice with the same efficiency as control vector. Downregulation of ESL-1 slightly affected (~33%) the binding of soluble E-selectin to PMNs, but did not alter WBC rolling numbers in TNF-α-stimulated cremasteric venules. Absence of ESL-1 or CD44, but not PSGL-1, resulted in significant increases in mean rolling velocities (4.7 ± 0.4 μm/s for WT; 8.3 ± 0.4 μm/s for shESL-1*; 7.2 ± 0.2 μm/s for CD44−/−* and 5.4 ± 0.4 μm/s for PSGL-1−/−; *p<0.001). Moreover, WBCs lacking ESL-1 exhibited a characteristic “skipping” rolling motion, suggesting that ESL-1 plays a critical role in stabilizing WBC rolling. Remarkably, ESL-1 downregulation in the absence of PSGL-1 led to dramatic reductions in WBC binding to soluble E-selectin (~99%), and rolling (~93%) on TNF-α-stimulated venules. To determine the contribution of these 3 glycoproteins in WBC recruitment, mice transplanted with WT, PSGL-1- and/or CD44-deficient Lin- cells that were transduced with the shESL-1 or control vectors, were injected i.p. with thioglycollate and the number of peritoneal GFP+ PMNs determined. Only the absence of all 3 glycoproteins compromised PMN recruitment to the levels observed in P- and E-selectin double-deficient mice (82% reduction compared to WT; p<0.001), suggesting that ESL-1, PSGL-1 and CD44 comprise all endothelial selectin ligand activity on PMNs in vivo. To assess the role of E-selectin ligands in WBC activation, we monitored in vivo L-selectin clustering on the surface of over 4,000 rolling WBCs using high-speed multichannel fluorescence videomicroscopy. The majority of wild-type rolling WBCs exhibited polarization of L-selectin 150 to 230 min after TNF-α. L-selectin clustering was greatly reduced in E-selectin−/− mice (58 ± 4% polarized cells in WT vs 23.5 ± 1% in E-selectin−/− mice; p<0.001). To determine which E-selectin ligand(s) mediated L-selectin clustering in vivo, we evaluated L-selectin distribution on rolling WBCs deficient in ESL-1, CD44 or PSGL-1. Absence of CD44, but not ESL-1 or PSGL-1, reduced L-selectin redistribution to levels found in E-selectin−/− mice (20 ± 2% polarized cells), indicating that CD44 is the signalling E-selectin ligand required for L-selectin clustering. In addition, E-selectin-mediated CD44 signalling was p38-dependent, as assessed in WT mice treated with the p38 inhibitor SB203580 (77% reduction; p<0.001). Our results indicate that ESL-1, PSGL-1 and CD44 comprise all selectin ligand binding activity on WBCs, and suggest specialized contributions for each ligand where PSGL-1 mediates the initial tethering, ESL-1 is critical for the conversion into steady slow rolling, and CD44 is required for E-selectin-mediated signals contributing to WBC activation.

Steady State Rolling Analysis of a Radial Tyre: Comparison with Experimental Results

This research paper is devoted to the description of a finite element model for the numerical study of a radial tyre under steady state rolling condition. The finite element model was developed using the commercial computer software ABAQUS. The simulation started with an axisymmetric model to analyse the tyre under inflation pressure load. Then a full three-dimensional model was generated for the modelling of the tyre under static vertical load. Having obtained the tyre configuration under contact load, a steady state rolling analysis was conducted using a mixed Lagrangian/Eulerian technique. In this stage, a constant ground velocity was assumed and the spinning velocity was changed to find the free rolling speed of the tyre. The computed loaded dimensions of the tyre in both static and dynamic situations were also compared with experimentally measured data for three commercial tyres available on the market. The comparison verified the validity and applicability of the proposed model. In addition, the distributions of pressure and frictional shear stress fields at the contact zone are presented and discussed.

Finite element analysis of steady rolling tyre with slip angle: effect of belt angle

The purpose of the present research was to study the effect of different belt angles on the steady state rolling behaviour of a steel belted radial tyre with slip angle. To achieve this goal, a finite element model has been developed using ABAQUS computer software. The simulation started with an axisymmetric model to analyse the tyre under inflation pressure. Then a full 3D model was generated to model the tyre under static vertical load. Having obtained the tyre configuration under contact load, a steady state rolling analysis was conducted using a mixed Lagrangian/Eulerian technique. The final stage of the modelling was the inclusion of the slip angle in the model. Each set of simulations was repeated for three belt angles and the effect of the belt angle variation on the tyre structural variables, including contact pressure and area, lateral force, interlayer shear stress and total strain energy was examined. In addition, the computed value of the number of revolutions per kilometre was compared with experimentally reported data which confirms the accuracy of the present model.

Computational modelling of thermoforming processes in the case of finite viscoelastic materials

In this paper we describe the computational simulation of the inflation phase of a thermoforming process under which a thin polymer sheet is deformed into a mould under the action of applied pressure. It is assumed that the sheet undergoes finite viscoelastic deformation which is treated using a hyperelastic model containing internal variables. The simplification is adopted that the sheet can be treated as a membrane and also that there is a total sticking contact condition when the sheet comes in contact with the mould. The computational model uses finite elements in space and incorporates mesh adaptivity based on a residual estimator in order to simulate the deformation accurately and efficiently. The internal variables satisfy an ordinary differential equation in time which is solved using a predictor–corrector scheme. The constitutive model is a generalisation of that of Le Tallec and Rahier [P. Le Tallec, C. Rahier, Numerical models of steady rolling for non-linear viscoelastic structures in finite deformations, Int. J. Numer. Methods Engrg. 37 (1994) 1159–1186]. In the simulation it is demonstrated how effectively the estimator works in controlling the meshes for some demanding mould shapes.

Numerical estimation of aircrafts' unsteady lateral-directional stability derivatives

A technique for predicting steady and oscillatory aerodynamic loads on general configuration has been developed. The prediction is based on the Doublet-Lattice Method, Slender Body Theory and Method of Images. The chord and span wise loading on lifting surfaces and longitudinal bodies (in horizontal and vertical plane) load distributions are determined. The configuration may be composed of an assemblage of lifting surfaces (with control surfaces) and bodies (with circular cross sections and a longitudinal variation of radius). Loadings predicted by this method are used to calculate (estimate) steady and unsteady (dynamic) lateral-directional stability derivatives. The short outline of the used methods is given in [1], [2], [3], [4] and [5]. Applying the described methodology software DERIV is developed. The obtained results from DERIV are compared to NASTRAN examples HA21B and HA21D from [4]. In the first example (HA21B), the jet transport wing (BAH wing) is steady rolling and lateral stability derivatives are determined. In the second example (HA21D), lateral-directional stability derivatives are calculated for forward- swept-wing (FSW) airplane in antisymmetric quasi-steady maneuvers. Acceptable agreement is achieved comparing the results from [4] and DERIV.

On the Dynamics of Rolling Tires in Contact with Rough Road Surfaces

AbstractFor the reduction of traffic noise significant progress has been achieved for the main engine of motor vehicles so far. Meanwhile the rolling noise of tires is the main source at speeds above 40 km/h for passenger cars and 60 km/h for trucks. So there is need for a simulation procedure of rolling tire dynamics and sound radiation [1].In a nonlinear steady state rolling analysis the deformation of the tire in contact with a plane road is computed. The next step is the eigenvalue analysis of the gyroscopic system yielding complex eigenvectors. The modal space of the tire system is excited by surface textures of the road in the contact region in a deterministic description. Modal superposition results in the dynamic response of the system in dependance of the excitation function. Additionally, the normal velocities of the tire surface are used as boundary conditions for the acoustic simulation of the sound pressure field. With these steps it is possible to determine and optimize the characteristics of tire structures with respect to lower noise levels for virtual prototyping. (© 2005 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)