Asperity Slope Research Articles

圧延加工における表面粗さの変動特性

This paper deals with the statistical analysis of the characteristics of plastic deformation to make clear the relationship between the rolling conditions and the surface roughness on the dull-finished cold rolling steel strip. The rolling experiments are carried out under a 33-factorial design of the rolling conditions which are the gap of the work rolls, the number of the rolling passes and the speed of the back-up roll. Using the cluster analysis jointly with the multiple regression analysis and the stationary stochastic process analysis, the followings become clear. The surface roughness and the mean slope of asperities are influenced by the rolling conditions in the order, the gap of the work rolls, the number of the rolling passes, the speed of the back-up roll. In the case of the same rolling condition, it can be generally considered that the valley of surface height deforms more than the peak of it. Also, the non-dimensional plasticity index is proposed to estimate the probability of plastic deformation of surface roughness under the rolling process.

Relative contact pressure - Dependence on surface roughness and Vickers microhardness

An explicit expression for the contact hardness and the relative contact pressure is developed. This expression is simple and clearly shows the dependence of the contact hardness and the relative contact pressure upon the Vickers microhardness correlation coefficients and the surface roughness parameters. Parametric studies of the contact conductance are performed, and it is shown that theoretical predictions and experimental data are in good agreement. Nomenclature = mean contact radius, m = apparent contact area, m2 = constant for Vickers microhardness correlation ah = dimensionless conductance, C = - = Vickers indentation diagonal, m = conductance, W/mZ.K = bulk hardness, MPa = contact microhardness, MPa = Vickers microhardness, MPa = thermal conductivity, W/m.K = harmonic mean thermal conductivity, W/m.K = mean absolute asperity slope = constants in Eqs. (20) and (21) mks

Friction stress and normal stress in bulk metal-forming processes

When analysing pressure distributions in bulk metal-forming processes, it is conventional to adopt either Amonton's friction law, τ = μ p , or the law of constant friction stress. Neither of these two laws however, is applicable universally. In this paper a general friction model including both laws is presented. Using a slip-line analysis of the plastic deformation of surface asperities, the influence on friction stress of normal pressure, friction factor and surface roughness (defined by asperity slope) is expressed analytically. Examples of applications of the friction model when analysing bulk metal-forming processes are given: the tool/workpiece interface pressure and friction stress distributions are estimated for simple upsetting, forward bar extrusion and plate rolling. The calculated pressure distibutions show good accordance with those measured experimentally.

The effect of surface parameters on friction

The effects of several surface parameters on friction were investigated. The results indicate that of the surface parameters that affect friction the following two parameters should be considered simultaneously: the asperity height and the wavelength. The average slope of asperities was found to be the single parameter that correlated best with the coefficient of friction. The autocorrelation coefficient was only suitable for purposes of comparison between various sets of bearings.

Rolling Bearing Life Modifying Factors for Film Thickness, Surface Roughness, and Friction

This paper facilitates practical calculation of rolling contact fatigue life, allowing for material, lubrication, and surface topography effects. Modifying factors for the predicted fatigue life are given for: material matrix strength; material defect severity; EHD film thickness/surface roughness ratio Λ; surface asperity slope σθ and boundary lubricated traction coefficient μa. Readily evaluated formulas are provided for the above factors. Calculated results show predicted life versus Λ with σθ and μa as parameters. Comparison with experimental data shows that the model covers most documented test results of life versus Λ. Scanty experimental data covering σθ and traction effects on life are compatible with the model predictions.

表面凹凸の離散測定におけるサンプリング間隔の一決定法

In this paper, the sampling intervals have been studied for measuring discretely the surface asperities in order to process with a digital computer. These intervals were decided by using the autocorrelation function of asperity heights so that the deviations of the simulated profile interpolated linearly between sampled data from the continuous profile were less than the limit value. The standard deviation of the above-mentioned deviations was selected to be 1% of that of asperity heights for the optimum sampling intervals. The sampling intervals in this research were investigated for ground surfaces and lapped ones. For the two- or the three-dimensional analysis of surface asperities, the sampling intervals should have mutually a strong correlation. A validity of these intervals was verified by the form of profiles chained with the sampled data and the standard deviation of asperity slopes.

Surface Topography Changes in Polymer-Metal Sliding - I

The adhesive wear of polymers, sliding against smooth metal surfaces, is influenced by the manner in which the surface topography of sliding surfaces is modified. The variation in the surface topographical parameters with sliding between a ground steel disc and a poly(methyl methacrylate) pin was, therefore, investigated for both the unsteady state and steady state wear conditions. The surface profiles of the unrubbed and rubbed metal disc were recorded, using a profilometer, both along and perpendicular to the direction of sliding. From the profile ordinate data read at 10 μm intervals, the surface roughness parameters, namely, the rms and c.l.a. roughness, asperity radius of curvature, asperity density, and average asperity slope were calculated using a computer program. Three point analysis was used to define a peak and compute the asperity slope and radius of curvature. The distributions of surface parameters were determined using a Weibull distribution approach. The analysis showed that the surface parameters have a large initial variation followed by more or less stable conditions, which explains the transition of unsteady state wear to steady state wear. The changes on the disc surface perpendicular to the sliding direction are minimal. The rms roughness and the average asperity slope were found to have a linear relationship.

Prediction of Traction and Microgeometry Effects on Rolling Contact Fatigue Life

A refined mathematical model for the prediction of rolling contact fatigue is presented. It analyzes the effect of frictional traction in the contact surface, and of surface asperity slope, on the failure hazard functions applicable to surface and subsurface originated spalls. Major effects of traction on life arise from three sources: (a) increased surface distress micropitting; (b) increased microscopic shear stresses beneath surface furrows; (c) greatly increased macroscopic shear stresses in the zone relatively free from shear-stress which exists, in the absence of traction, between the asperity stress region and the Hertzian shear stress region. The major effect of steeper asperity slopes is to increase surface distress micropitting. A strong effect of traction on the angular orientation of the Hertz stress field is used to correlate experimentally observed changes in the Martin angle of orientation of deformation bands. The correlation permits calculation of the variation in the effective traction coefficient as a function of film thickness/roughness ratio. The traction coefficients obtained are then used as input to numerical life prediction. Satisfactory agreement is obtained between theory and experiment in predicting the life of seven groups of fatigue tested ball bearings with different surface roughness, run at different film thickness/roughness ratios.

Real area of contact and friction stress — The role of trapped lubricant

A theory is developed which shows the influence of the normal pressure, asperity slope, friction factor and pressure-sensitive lubricant bulk modulus on the real area of contact and the friction stress between a rough specimen and a smooth tool surface. Theory as well as experiments show that the normal pressure and bulk modulus have great influence on the real area of contact, whereas the asperity slope and friction factor are of minor importance.

Real area of contact and friction stress at high pressure sliding contact

An experimental investigation of the plastic deformation of the surface asperities of a soft rough specimen surface in sliding contact with a hard smooth tool surface is described. The experimental equipment allows independent variation of the normal pressure and sliding length. The normal pressure was varied from 0.5 to 2.5 times the yield stress of the specimen material and the sliding length was varied from 0 to 20 mm. Experiments with soap-coated phosphated specimen surfaces showed that the real area of contact and the friction stress were related to normal pressure and sliding length as expected from theoretical considerations. Measurements of the change of the asperity slopes were also in agreement with theory. Experiments with dry friction showed a steadily increasing contact area with increasing sliding length; this explains the fact that the coefficient of friction can rise to a very high value, increasing with decreasing normal pressure. On the basis of the experimental results a new slip-line field was developed taking the slope of the asperities into consideration.

Influence of surface roughness and work-hardened layers on the contact between a rough and a flat surface

The validity of a theory which was derived considering the distribution of the surface slopes of conical asperities and the variation of the flow pressure of each contact due to the work-hardened layer of the softer surface was checked by comparing the theoretical and experimental results. The number, the real area and the distribution of the radii of contact points produced by impressing hard and rough surfaces into soft and flat surfaces with work-hardened layers were measured. The distribution of the surface slopes of contact asperities and the variation of the flow pressure with increasing penetration of the hard asperities were also obtained experimentally.

Effects of distribution of surface slopes and flow pressures of contact asperities on contact between solid surfaces

An analysis of the mechanism of contact between two solids was carried out considering the distribution of the surface slopes of conical asperities and the variation of the flow pressure of each contact asperity due to work-hardening and the work-hardened layer of the softer surface. From the analysis, where the distributions of the surface heights and the surface slopes are Gaussian the number of contact points decreases and their mean radius increases with increasing ranges of the distribution of the surface slopes for a given value of the mean surface slope. The number of contact points, the total real area, the separation and the radius of the contact points are influenced by the variation of the flow pressure of each contact asperity due to work-hardening of the contact asperities or the work-hardened layer of the softer surface. The validity of the theory was checked by comparing the theoretical and experimental results of the number, the separation and the distribution of the radii of contact points.

The theory of partial elastohydrodynamic contacts

The concept of partial elastohydrodynamic (EHD) Hertzian contacts is defined between solids with real (rough) surfaces, using the film thickness/r.m.s. roughness ratio h/ σ as parameter. The influence of the partial EHD condition is described on EHD film thickness, normal load sharing between asperities and EHD film, frictional traction, mild and severe wear, surface fatigue and spalling fatigue. Kinematic effects of the traction vs. sliding rate relationship characteristic of partial EHD are identified in rolling bearings. Rough surfaces are treated as two-dimensional random processes, using height, slope, curvature and level-crossing statistics derived, for Gaussian height distributions, with the aid of statistics of the height and its first two derivatives. Scanning electron microscope observations of surfaces are used to visualize asperity geometry, lay and defect population. Normal load and traction force sharing between EHD film and asperities is analyzed for plastic and elastic asperities. Indentation hardness and h/ σ are parameters of plastic load sharing. Elastic load sharing depends on elastic modulus, h/ σ, and asperity slope and may depend weakly on the spectral distribution of asperity amplitudes. Traction force sharing depends on similar parameters and on the EHD traction/ sliding rate function. Stresses in elastic asperities and the size of asperity contact areas are expressed in terms of roughness height, its derivatives and h/ σ. Roughness parameters influencing wear, smearing (galling), and surface fatigue are identified from the asperity contact stresses obtained.

An Analysis of the Deformation of Contacting Rough Surfaces : 4th Report. Formulae for Practical Use on Deformation of Plane Joints Making the Directions of Surface Asperities Parallel to Each Other

Contact of rough surfaces can be replaced by that between a rough surface and a rigid flat one, so that the methods of the 3rd report can be reapplied here. In this report, the factors of surface asperities (for example, slope and height of surface asperities in contact) were synthesized, and formulae for practical use on the elastic and the plastic deformation of rough surfaces in contact when the directions of surface asperities were parallel to each other were suggested. This report revealed that the variance of slope of surface asperities of surface asperities in contact is σθ12+ σθ22, where σθ12, σθ22 are variances of slope of projections respectively. As a result, the relations between the elastic and the plastic deformations δE, δS yielded by the existence of surface asperities and the normal load are as follows. δ^-E=ae{(P^-+P^-0) } where, δ^-E=δE/σ, δ^-S=δS/σ, σ: standard deviation of surface asperity in contact, P^-=P/Apm, A: nominal contact area, pm : plastic flow pressure, ae, as, P^-0 : constants. These constants were given in this research.

Effect of Weak Surface Autocorrelation on the Size Effect in Electrical Conduction

Correlation between points on a conductor surface may be important in explaining the relatively large specularity parameters attributed to measurements in single-crystal samples. An expression for the size effect in the electrical conductivity is obtained that takes into account the effect of weak surface autocorrelation. The expression shows that, as expected, the correlation increases the electrical conductivity. It also shows that even an angle-dependent specularity parameter may not be an adequate description in the sense of the Fuchs model. Numerical estimates are given for the size effects due to surface roughness and autocorrelation. These are explained in terms of the competing effects of flux conservation and surface asperity slopes.

Estimation of the number and the mean area of real contact points on the basis of surface profiles

A statistical analysis is made of the geometrical nature of contacting surfaces and mathematical expressions are deduced for the number and the mean area of the real contact points. The expressions are derived, first in generally applicable forms, and numerical examples are given for the case where Gaussian distribution is assumed for the height and the slope of asperities.

On the Mechanism of Contact between Solid Surfaces : 2nd Report, The Real Area of Contact, the Separation and the Penetrating Depth

Assuming that the asperities on normally distributed surface are cones of the same slope that depends on the surface roughness, it is deduced theoretically by the slip-line theory that the real area of contact in the case of contact between a soft conical asperity and a hard flat surface or between a hard conical asperity and a soft flat surface depends on the slopes of the conical asperities, the coefficient of friction at the interface of contact asperities, and the flow pressure. If the real area of contact is corresponding to the geometrical area obtained immediately from the bearing-area curve, the relation between the real area of contact and the separation or the penetrating depth is also obtained theoretically. A comparison of calculated values based on this theory with experimental data shows good agreement.

On the Mechanism of Contact between Solid Surfaces : 1st Report, The Initial Separation and the Distributions of Slopes of Asperities and of the Profile Curve

On the Mechanism of Contact between Solid Surfaces : 1st Report, The Initial Separation and the Distributions of Slopes of Asperities and of the Profile Curve