H.R. Le

A robust model for rolling of thin strip and foil

A new analysis for cold rolling of thin strip and foil is developed. This model follows the approach of Fleck et al. [8], but relaxes their assumption of a central flat neutral zone. Instead of following their inverse method to obtain the pressure distribution in this neutral zone, an explicit equation for the contact pressure variation is obtained from the sticking condition in this region. This significantly simplifies the solution method, leading to a much more robust algorithm. Moreover the method treats the cases either where the roll retains its circular arc or where there is very significant roll deformation in the same way, greatly simplifying the method of obtaining solutions. This will facilitate the incorporation of other effects such as the friction models currently being developed. Results are in line with the theory of Fleck et al. [8]. The effect of entry and exit tensions on the non-dimensional load and forward slip is investigated. It is found that the effect of equal entry and exit tensions is equivalent to reducing the yield stress of the strip by this tension stress.

Analysis of surface roughness of cold-rolled aluminium foil

This paper describes a detailed analysis of the surface finish of aluminium foil which has been cold-rolled under industrial conditions in the mixed lubrication regime. The foil was rolled with freshly ground rolls at a constant speed for the first pass and at a wide range of speeds for the second pass. Samples were collected after the second pass. For comparison, samples were also collected after rolling with worn rolls. Surface replicas of the rolls were taken with surface replicating tape. The surface roughness of the strip samples and roll surface replicas was measured with a three-dimensional non-contact interferometric profilometer. The spectrum of the surface roughness was analysed by the fast Fourier transform method to identify the way in which different wavelengths of roughness behave. Theory suggests that longer wavelengths of roughness should be crushed more easily. This was confirmed by results. A new image analysis technique has been developed to identify and quantify the area of the micro-pits. To differentiate between these pits and grind marks transferred from the rolls, the height information was first filtered in the rolling direction using a digital filter. The low-frequency component of the surface roughness, which represents the contribution from the roll marks, was subtracted off to leave the pits. Results showed a significant decrease in pit area during the pass schedule, while there was a significant increase in pit area with increasing rolling speed during a single pass.

Measurements of friction in strip drawing under thin film lubrication

Abstract Strip drawing is used to investigate the friction behaviour under thin film lubrication in metal forming with plastic deformation. Friction coefficients are measured under a wide range of tribological conditions. The surface roughness is measured on an interferometric profilometer. The results show that the friction coefficient decreases with increasing oil film thickness h w , as estimated using a formula appropriate for smooth tool and workpiece. Measurements of the surface topography show that change in friction is associated with a change in contact ratio between the tool and strip. The effect of strip reduction, strip roughness and die roughness on the friction coefficient is also investigated.

Modeling of Micro-Pit Evolution in Rolling or Strip-Drawing

The micro-plasto-hydrodynamic lubrication (MPHL) model of pit evolution is extended to account for the variation of sliding speed and strain rate in rolling and drawing processes. Results show that all of the following factors are important: pit angle, lubricant viscosity and pressure viscosity coefficient, material yield stress and sliding speed. Theoretical predictions for the change in pit area during the deformation process are well correlated by a non-dimensional group of these parameters. The model agrees reasonably with the measured change in pit volume and area from drawing experiments on cold rolled stainless steel strip containing both artificial and stochastic roughness.

A semi-empirical friction model for cold metal rolling

A semi-empirical model of friction is developed for cold metal rolling in the mixed lubrication regime. An asperity flattening model is used to investigate the evolution of the contact area and hydrodynamic pressure between the roll and strip surfaces. An appropriate coefficient of friction for the contact areas between roll and strip surfaces is determined empirically using tests on a strip drawing rig. The asperity flattening model is combined with the empirical data for friction on the contact areas to predict the effect of speed on friction in rolling. Predicted values of friction coefficient are in reasonable agreement with published measurements. Presented as a Society of Tribologists and Lubrication Engineers Paper at the ASME/STLE Tribology Conference in Seattle, Washington, October 1–4, 2000

Rolling of Thin Strip and Foil: Application of a Tribological Model for “Mixed” Lubrication

A mechanical model of cold rolling of foil is coupled with a sophisticated tribological model. The tribological model treats the mixed lubrication regime of practical interest, in which there is real contact between the roll and strip as well as pressurized oil between the surfaces. The variation of oil film thickness and contact ratio in the bite is found by considering flattening of asperities on the foil and the build-up of hydrodynamic pressure through the bite. The boundary friction coefficient for the contact areas is taken from strip drawing tests under similar tribological conditions. Theoretical results confirm from strip drawing tests under similar tribological conditions. Theoretical results confirm that roll load and forward slip decrease with increasing rolling speed due to the decrease in contact ratio and friction. The predictions of the model are verified using mill trials under industrial conditions. For both thin strip and foil, the load predicted by the model has reasonable agreement with the measurements. For rolling of foil, forward slip is overestimated. This is greatly improved if a variation of friction through the bite is considered.

Evolution of Surface Pits on Stainless Steel Strip in Cold Rolling and Strip Drawing

Theoretical models are presented for describing the evolution of pits in the inlet and work zone during cold rolling and strip drawing of shot-blast stainless steel under ‘mixed’ lubrication. Results shows that the rough shot-blast surface is flattened rapidly in a short inlet zone, thereby entrapping the lubricant in surface pits. The subsequent evolution of these surface pits in the work zone can be explained by micro-plasto-hydrodynamiclubrication (MPHL) models described previously. A development of these models is presented which takes into account the effects of the oil film entrained in the inlet, an oil film penetrating from adjacent pits and the finite depth of the pits. The role of an inlet oil film and penetrating MPHL oil film is to limit the potential reduction of pit size. Lubrication regime maps are constructed which describe the evolution of the surface pits for a range of pit geometries. Results explain the experimental observation that some pits survive even after a multi-pass schedule. Predictions of the pit area show good agreement with measurements on samples obtained in strip drawing or rolled under industrial conditions. @DOI: 10.1115/1.1504088#

Measurements of Surface Roughness in Cold Metal Rolling in the Mixed Lubrication Regime

This paper describes measurements of the change in surface roughness of aluminium strip due to cold rolling. Rolling is in the mixed lubrication regime, where there is both asperity contact and hydrodynamic action. The strip is in the as-received condition before rolling, with a continuous spectrum of roughness wavelengths. The spectra of roughness for both the initial and rolled surfaces are used to extract amplitudes for long and short wavelength components, with an arbitrary division at a wavelength of 14 μm between these components. It is found that the short wavelength components persist more than the long wavelength components, and that flattening of the strip increases with reduction in strip thickness. The qualitative effect of wavelength on flattening is similar to that observed with unlubricated rolling (Sutcliffe, 1999), and is in line with theoretical models of mixed lubrication. The effect of reduction is not predicted by existing theories, but is in agreement with measured variations of friction with reduction. Presented as a Society of Tribologists and Lubrication Engineers Paper at the STLE/ASME Tribology Conference in Orlando, Florida, October 11–13, 1999

A Two-Wavelength Model of Surface Flattening in Cold Metal Rolling with Mixed Lubrication

A new model of surface flattening is developed for cold metal rolling in the mixed regime. Longitudinal surface roughness is modeled by two separate wavelengths. The new model follows the asperity crushing analysis of Sutcliffe (1999) for unlubricated rolling but additionally includes a hydrodynamic model to account for the effect of the lubricant. The effect of various parameters including speed, reduction in strip thickness, roughness wavelength and lubricant properties is examined. The results show similar behavior to previous models of mixed lubrication, with a speed parameter As having the most influence, and confirm the results for unlubricated rolling that the short wavelength components of the surface roughness persist more than the long wavelength components. The predicted changes in roughness are in good agreement with experiments. Presented as a Society of Tribologists and Lubrication Engineers Paper at the STLE/ASME Tribology Conference in Orlando, Florida, October 11–13, 1999

Characterisation of tribological behaviour of silicon and ceramic coatings under repeated sliding at micro-scale

Because of large surface-to-volume ratios and low restoring forces, surface stiction and friction can dominate the performance of Micro-Electro-Mechanical Systems (MEMS) currently being developed. To achieve the functionality and reliability of these devices, tribologists strive to understand the mechanisms of adhesion, friction and wear over a broad range of length scales. This paper presents the design and commission of a simple tribological test rig for the characterisation of MEMS materials from micro-scale to meso-scale. The effects of normal load, environment and various coatings on the friction and wear are explored using this rig.