Dynamic Friction Models for Road/Tire Longitudinal Interaction

Summary In this paper we derive a new dynamic friction force model for the longitudinal road/tire interaction for wheeled ground vehicles. The model is based on a dynamic friction model developed previously for contact-point friction problems, called the LuGre model. By assuming a contact patch between the tire and the ground we develop a partial differential equation for the distribution of the friction force along the patch. An ordinary differential equation (the lumped model) for the friction force is developed, based on the patch boundary conditions and the normal force distribution along the contact patch. This lumped model is derived to approximate closely the distributed friction model. Contrary to common static friction/slip maps, it is shown that this new dynamic friction model is able to capture accurately the transient behaviour of the friction force observed during transitions between braking and acceleration. A velocity-dependent, steady-state expression of the friction force versus the slip coefficient is also developed that allows easy tuning of the model parameters by comparison with steady-state experimental data. Experimental results validate the accuracy of the new tire friction model in predicting the friction force during transient vehicle motion. It is expected that this new model will be very helpful for tire friction modeling as well as for anti-lock braking (ABS) and traction control design.     

On the role played by turbulence closures in hull shape optimization at model and full scale

 The practical use of automated computational fluid dynamics (CFD)-based design tools in the ship-building industry requires powerful flow solvers which are able to take into account realistic geometries as well as complex physical phenomena, such as turbulence. A shape optimization tool is developed in this framework. A derivative-free optimizer, yielding both flexibility and robustness, is preferred to the classical gradient-based method, which is more difficult to implement and is still limited to only moderately complex problems. The flow solver included in the design procedure solves the incompressible Reynolds-averaged Navier–Stokes equations on unstructured grids using a finite-volume formulation involving several near-wall low-Reynolds-number turbulence models. The design tool is used to optimize the stern of a modern hull shape at model and full scale, with different purposes being considered. More precisely, the drag reduction and the homogenization of the flow in the wake are expected by controlling the longitudinal vortex generated. Our interest is particularly focused on the influence of turbulence modeling in the design process. The effects of a two-equation model based on the eddy-viscosity assumption and a second-order closure relying on the Reynolds stress transport equations are compared. Received: September 24, 2002 / Accepted: April 14, 2003 RID="*" Acknowledgment. The authors thank the scientific committee of CINES (project dmn2050) for the attribution of CPU time.     

Rainflow fatigue analysis for loads with multimodal power spectral densities

This paper provides theoretical formulas to calculate conservative estimates of the rainflow fatigue damage from the spectral parameters for spectra composed of the combination of one or several narrow-band low-frequency loads and a higher frequency one, such as are often encountered with moored marine structures. With respect to the semi-empirical formulas that have been proposed by other authors, those presented here are theoretically constructed from the mathematical definition of rainflow and from the statistical properties of Gaussian processes.     

Protist entrapment in newly formed sea ice in the Coastal Arctic Ocean

Protist abundance and taxonomic composition were determined in four development stages of newly formed sea ice (new ice, nilas, young ice and thin first-year ice) and in the underlying surface waters of the Canadian Beaufort Sea from 30 September to 19 November 2003. Pico- and nanoalgae were counted by flow cytometry whereas photosynthetic and heterotrophic protists ≥ 4 µm were identified and counted by inverted microscopy. Protists were always present in sea ice and surface water samples throughout the study period. The most abundant protists in sea ice and surface waters were cells < 4 µm. They were less abundant in sea ice (418–3051 × 10³ cells L^− 1) than in surface waters (1393–5373 × 10³ cells L^− 1). In contrast, larger protists (≥ 4 µm) were more abundant in sea ice (59–821 × 10³ cells L^− 1) than in surface waters (22–256 × 10³ cells L^− 1). These results suggest a selective incorporation of larger cells into sea ice. The ≥ 4 µm protist assemblage was composed of a total number of 73 taxa, including 12 centric diatom species, 7 pennate diatoms, 11 dinoflagellates and 16 flagellates. The taxonomic composition in the early stage of ice formation (i.e., new ice) was very similar to that observed in surface waters and was composed of a mixed population of nanoflagellates (Prasinophyceae and Prymnesiophyceae), diatoms (mainly Chaetoceros species) and dinoflagellates. In older stages of sea ice (i.e., young ice and thin first-year ice), the taxonomic composition became markedly different from that of the surface waters. These older ice samples contained relatively fewer Prasinophyceae and more unidentified nanoflagellates than the younger ice. Diatom resting spores and dinoflagellate cysts were generally more abundant in sea ice than in surface waters. However, further studies are needed to determine the importance of this winter survival strategy in Arctic sea ice. This study clearly shows the selective incorporation of large cells (≥ 4 µm) in newly formed sea ice and the change in the taxonomic composition of protists between sea ice and surface waters as the fall season progresses.     

Variability of snow and ice thermal, physical and optical properties pertinent to sea ice algae biomass during spring

Changes in the thermal, physical and optical properties of the snow–sea ice system and feedbacks between various temporal and spatial scales affect accumulation of microalgae at the sea ice bottom and are the focus of this research. During the spring transition period, May 4 to June 9, 2002, we closely monitored atmospheric conditions and properties of the snow–sea ice system, including thermal, physical and optical properties of the snow cover (e.g., temperature, grain size, light attenuation), ice thickness and salinity, and biomass of bottom ice algae. Results show that snowdrift size averaged 31.2 by 10.6 m with a depth range of 2 to 45 cm. Snowpacks also varied in age, distinguished by coincident peaks of snow salinity and grain size and a lower PAR extinction coefficient. Spatial variability of the snowpack was superimposed by temporal variability associated with seasonal snow–ice melt and wind redistribution of snow. Maximum biomass of ice algae was observed under intermediate snow covers. Under thin snow covers, algae biomass declined steadily coincident with seasonal warming and desalination of the ice cover. Under thick snow covers, algae biomass was negatively correlated with snow depth. These results suggest that thin snow covers were associated with a thermal effect causing sloughing of algae, whereas under deep snow, algae were still light limited and thermally insulated from the warming atmosphere. Our results highlight the importance of snow cover history on the sea ice system operating below. Furthermore, in the context of current climate change scenarios, shifts in snow depth would result in decreases of ice algae biomass.     

Assessment of a semi-Hertzian method for determination of wheel-rail contact patch

Wheel-rail contact calculations are essential for simulating railway vehicle dynamic behavior. Currently, these simulations usually use the Hertz contact theory to calculate normal forces and Kalker's 'FASTSIM' program to evaluate tangential stresses. Since 1996, new methods called semi-Hertzian have appeared: 5, 7 (STRIPES). These methods attempt to estimate the non-elliptical contact patches with a discrete extension of the Hertz theory. As a continuation of 2, a validation of the STRIPES method for normal problem computing on three test cases is proposed in this article. The test cases do not fulfill the hypothesis required for the Hertz theory. Then, the Kalker's FASTSIM algorithm is adapted to STRIPES patch calculus to perform tangential forces computation. This adaptation is assessed using Kalker's CONTACT algorithm.     

Locating rapid transit lines

This paper describes the main criteria used to design rapid transit alignments. It also shows how Operational Research tools can assist the design process.     

Influence of the Mackenzie River plume on the sinking export of particulate material on the shelf

We examined the influence of the Mackenzie River plume on sinking fluxes of particulate organic and inorganic material on the Mackenzie Shelf, Canadian Arctic. Short-term particle interceptor traps were deployed under the halocline at 3 stations across the shelf during fall 2002 and at 3 stations along the shelf edge during summer 2004. During the two sampling periods, the horizontal patterns in sinking fluxes of particulate organic carbon (POC) and chlorophyll a (chl a) paralleled those in chl a biomass within the plume. Highest sinking fluxes of particulate organic material occurred at stations strongly influenced by the river plume (maximum POC sinking fluxes at 25 m of 98 mg C m^− 2 d^− 1 and 197 mg C m^− 2 d^− 1 in 2002 and 2004, respectively). The biogeochemical composition of the sinking material varied seasonally with phytoplankton and fecal pellets contributing considerably to the sinking flux in summer, while amorphous detritus dominated in the fall. Also, the sinking phytoplankton assemblage showed a seasonal succession from a dominance of diatoms in summer to flagellates and dinoflagellates in the fall. The presence of the freshwater diatom Eunotia sp. in the sinking assemblage directly underneath the river plume indicates the contribution of a phytoplankton community carried by the plume to the sinking export of organic material. Yet, increasing chl a and BioSi sinking fluxes with depth indicated an export of phytoplankton from the water column below the river plume during summer and fall. Grazing activity, mostly by copepods, and to a lesser extent by appendicularians, appeared to occur in a well-defined stratum underneath the river plume, particularly during summer. These results show that the Mackenzie River influences the magnitude and composition of the sinking material on the shelf in summer and fall, but does not constitute the only source of material sinking to depth at stations influenced by the river plume.