A surface roughness parameter in Hertz contact

The influence of surface roughness on the accuracy with which the Hertz theory of elastic contact predicts the contact pressure and contact area between a sphere and a plane is examined theoretically and experimentally. Statistical theories of surface contact suggest that the influence of surface roughness is governed primarily by a single non-dimensional parameter α defined by $\text{α }\text{σR}\text{a}{}_0{}^2$ where σ is the combined roughness of the two surfaces, R is the radius of the sphere and a₀ is the contact radius for smooth surfaces given by the Hertz theory. Experimental measurements of contact area correlate well with this parameter. Provided that the value of α is less than about 0.05, errors in the application of the Hertz theory due to roughness of the surfaces are not likely to exceed about 7%.     

Effects of surface roughness and surface films on contact resistance

An analysis of the electrical contact resistance between two metals with a tarnish film was carried out assuming the asperities to be represented by randomly distributed cones with base angles which vary with the surface roughness, and assuming that the radius of the broken area of the film at the interface of each contact asperity is constant beyond a critical depth of penetration of an asperity.The validity of the proposed theory was confirmed by experimental data of the electrical contact resistance between a silver cone and a silver flat on which carbon films were deposited, and between a silver flat with an Ag₂S tarnish and a palladium flat without tarnish. Comparison of theoretical and experimental data shows that the critical depth of penetration U_e of an asperity varies mainly with the surface roughness, the thickness of the tarnish film and the amount of plastic deformation of the contact asperities with films, i.e.$\text{U}{}_{\mathrm{e}}\text{σ}\text{= kR}{}^{\mathrm{j}}{}_{\max }$, where R_max and σ are the maximum height and the standard deviation (r.m.s. roughness) of the profile ordinates, and j and k are constants dependent on the type of finish, the thickness of the film and the difference in the hardness of the mating surfaces.     

Mechanisms of graphite fluoride [(CFx)n] lubrication

Friction, wear and wear life results were compared with optical microscope observations as a function of sliding distance for graphite fluoride rubbed films applied to three surface finishes — polished, sanded and sandblasted. The lubricating process consisted of the plastic flow of thin films of graphite fluoride between flat areas on the rider and on the metallic substrate. If the substrate was rough, flat areas were created during run-in, and the [(CF_x)_n] flowed across them. Wear life was enhanced by restricting radial (or transverse) flow of the graphite fluoride from the contact region by increasing surface roughness. Valleys in the roughened substrate surface served as a reservoir for graphite fluoride and as a deposit site for wear debris. Failure resulted from the gradual depletion of graphite fluoride from the contact region with the subsequent formation of powdery metallic debris that covered both rider and disk surfaces.     

The behavior of an elastic-perfectly plastic sinusoidal surface under contact loading

The goal of this paper is to provide the foundation for an analysis of contact between elastic-plastic solids, whose surface roughness is idealized with a Weierstrass profile. To this end, we conduct a parametric study of the plastic deformation and residual stress developed by the two-dimensional contact between a flat, rigid platen and an elastic-perfectly plastic solid with a sinusoidal surface. Our analysis shows that the general characteristics of the deformation can be characterized approximately by two parameters: α = a/λ, where a is the half-width of the contact and λ is the period of the surface waviness; ψ = E^*g/σ_Yλ, where E^* and σ_Y are the effective modulus and yield stress of the substrate, respectively, and g is the amplitude of the surface roughness. Depending on the values of these parameters, we identify eight general types of behavior for the asperity contacts: (a) elastic, elastic-plastic or fully plastic isolated Hertz type contacts; (b) elastic, or elastic-plastic non-Hertzian isolated contacts; and (c) elastic, elastic-plastic or fully plastic, interacting contacts. Relationships between contact pressure, contact size, effective indentation depth and residual stress are explored in detail in each regime of behavior. Implications on rough surface contacts are discussed.     

Nanoscopic surface texture formed by indentation and sliding of a smooth wedge tool

To achieve reliable replication of a flat tool surface through a metalforming process with nanometer-scale surface roughness, a wedge tool was indented and slid under a constant normal load. In a workpiece finished with abrasive paper, some of the initial valleys remain on the tested surface, though at the boundary contact area the surface roughness is as small as that of the tool. The final surface roughness of the workpiece was much reduced by starting with a smoother surface of the workpiece and by unlubricated short sliding. A nanoscopically smooth surface of 0.8 nm sRa was obtained with a gold-coated copper workpiece after unlubricated indentation and sliding. This suggests the beneficial effect of a soft surface film coated over a hard substrate, causing complete filling of the interfacial vacancies.     

Mathematical modeling of the thermal relaxation of nominally flat surfaces in contact using fractal geometry: Maxwell type medium

This work aims at studying the stress relaxation behavior of a nominally flat (rough) surface of a viscoelastic material in contact with a rigid half space. The effect of temperature will be included through the concept of activation energy using Arrhenius's equation. A synthesized Cantor-Borodich (C_B) profile is used to construct the rough surface. C_B profile has two scaling parameters, a and b, and different heights h_i for each generation of asperities. This simple model is applicable for fractal surfaces in which a single exponent (the fractal dimension) is enough to describe their quality.The surfaces in contact are viscoelastic, and they are assumed to behave according to the linear Maxwell model. An asymptotic power law is obtained, which relates the force and the bulk temperature acted on the punch to its approach. This model is valid only when the approach between the punch and the half space is in the range of the roughness size. The proposed model admits an analytical solution for the case when the deformation is linear thermo-viscoelastic. The obtained model shows a good agreement when compared with the experimental results obtained by Handzel-Powierza et al. [Handzel-Powierza Z, Klimczak T, Polijaniuk A. On the experimental verification of the Greenwood-Williamson model for the contact of rough surfaces. Wear 1992;154:115-24].     

The roughness effect on the frequency of frictional sound

Dry sliding of two bodies in contact generates a wide range of effects like friction, wear, heat and sound among others. The main interest of this study is in the frequency characteristics of the generated sound.In the past, frequency spectrum and sound pressure level with relation to surface topography (surface roughness in particular), have been studied mainly for concentrated contacts like stylus or hemispherical tip pin on a rough surface. Studies on flat–flat contacts were mainly focused on the topography of contacting surfaces and its relation to occurrence or non-occurrence of squeal (high pitch, high sound pressure level sound) in brake systems.The present study aims to clarify the effect of surface roughness on the frequency of non-squealing frictional sound generated in dry flat–flat sliding contact.Sound was generated by the dry contact in rubbing by hand of two rectangular cross-section stainless-steel plates having similar surface roughness. The roughness of the contacting surfaces varied in the range R_z=0.8–12.4 μm. The sound spectra had 5 peaks (P₁, P₂, P₃, P₄ and P₅) in order of increasing frequency and it was found that the peak frequency was shifted when the roughness of the rubbed surfaces changed. The first peak P₁ was most sensitive to change of surface roughness and it shifted from 3.0 to 4.5 kHz when the maximum surface roughness changed from R_z=10.9 to . When the surface was relatively rough, this peak was close to the first bending natural frequency of the plate at 2.377 kHz.     

Toroidal versus ball nose and flat bottom end mills

This paper compares the surface roughness along and across the feed directions produced by toroidal, ball nose, and flat bottom end mills. The study is conducted numerically and by cutting tests of aluminium. The results show that the toroidal cutter inherits the merits of the other two cutters; it produces small scallops across the feed direction, and low roughness along the feed direction.Nomenclature h scallop height - R _s radius of curvature of surface - inclination angle - 2a _c cross-feed - 2 subtended angle between the point of contact on the tool profile and the surface - R _a surface roughness - e offset distance of insert from tool axes for toroidal cutter - r _c cutter radius - r _i radius of insert for toroidal cutter - f _t feed per tooth - h _u undercut height - y, , intermediate variables     

Effect of wedge angle on surface roughness in finish turning: analytical and experimental study

Most of the theoretical models for surface roughness in finish turning assume that the work piece surface profile is formed by the rounded tip of the tool nose. The effect of the straight flank section in the tool nose region on the surface roughness is usually neglected. In this work, the straight flank section is taken into account in order to predict the arithmetic average roughness R _a and root-mean-square roughness R _q more accurately. The analytical models for R _a and R _q are developed as a function of three parameters, namely feed rate, nose radius, and wedge angle. These models were verified using digital simulation method. The surface roughness determined using the new three-parameter models were compared with the existing two-parameter models that consider only the feed rate and nose radius. Decreasing wedge angle was found to lower the surface roughness significantly. An experiment was conducted to test the validity of the three-parameter model at different feed rates in real machining operation. The experimental results agreed more closely with the proposed three-parameter models compared to the two-parameter models.     

A modified fractal microcontact model developed for asperity heights with variable morphology parameters

The cross-sections formed by the contact asperities of two rough surfaces at an interference are actually island-shaped, rather than having the commonly assumed circular or elliptic contour. These island-shaped contact area contours show fractal behavior with fractal dimension D_s of the two-dimensional profile. The three-dimensional surface fractal dimension for the topography of asperity heights is defined as D and the topothesy is defined as G. In Mandelbrot's study, the relationship between D and D_s was given as D = D_s + 1 if these two fractal dimensions are obtained before contact deformation. In the present study, D, G, and D_s are considered to be varying with the mean separation between two contact surfaces. The D–D_s relationships for the contacts at the elastic, elastoplastic, and fully plastic deformation regimes are derived and the inceptions of the elastoplastic and fully plastic deformation regimes are redefined using the equality of two expressions established in two different ways for the number of contact spots (N). A revised elastic–plastic contact model of a single fractal asperity is also proposed. The revised model shows that a fractal asperity behaves according to classical contact mechanics, but not those predicted by the MB model. The contact parameters, including the total force and the real contact area, were evaluated when the size distribution functions (n) for the three deformation regimes were available. The results indicate that both the D and D_s parameters in these deformation regimes increased with increasing mean separation.     

Characteristics of magnesium oxide single crystals polished with vibrational sliding in water

The finished surface of magnesium oxide single crystals polished with vibrational sliding in water was studied. The specimen was rubbed on a rotating disk of sintered magnesium oxide while being moved spirally and vibrated perpendicular to the sliding direction. Two distinct types of finished surface were observed: a rough surface with. R_max = 1–3 μm and a smooth surface with R_max = 0.01 μm. Surface characteristics were examined using optical microscopy, X-ray diffraction and ion microprobe mass analysis in order to understand the formation mechanisms of the finished surface. The rough surface was mainly formed by cleavage planes, caused by the brittle fracture which occurred irregularly around the surface. The hydration of the magnesium oxide played a dominant role in the formation of the smooth surface.The finishing of the surface on the {100} plane was markedly dependent on the mechanical contact conditions and the presence of water and independent of the main direction of sliding. A critical set of contact conditions for the formation of the smoothed surface was determined in terms of the contact load, the amplitude and frequency of vibrational sliding and the rotational speed of the disk. The volume removed was increased by vibrational sliding because of the increase in sliding distance and the equivalent increase in contact load caused by the moment of inertia of the apparatus.     

Prediction of surface roughness of turned surfaces using neural networks

In this study, the prediction of surface roughness heights R_a and R_t of turned surfaces was carried out using neural networks with seven inputs, namely, tool insert grade, workpiece material, tool nose radius, rake angle, depth of cut, spindle rate, and feed rate. Coated carbide, polycrystalline and single crystal diamond inserts were used to conduct 304 turning experiments on a lathe, and surface roughness heights of the turned surfaces were measured. A systematic approach to obtain an optimal network was employed to consider the effects of network architecture and activation functions on the prediction accuracy of the neural network for this application. The reliability of the optimized neural network was further explored by predicting the roughness of surfaces turned on another lathe, and the results proved that the network was equally effective in predicting the R_a and R_t values of the surfaces machined on this lathe as well.     

Investigation for optimal parametric combination for achieving better surface finish during turning of Al/SiC-MMC

This paper presents an experimental investigation of the influence of cutting conditions on surface finish during turning of Al/SiC-MMC. In this study, the Taguchi method, a powerful tool for experiment design,is used to optimise cutting parameters for effective turning of Al/SiC-MMC using a fixed rhombic tooling system. An orthogonal L₂₇(3¹³) array is used for 3³ factorial design and analysis of variance (ANOVA) is employed to investigate the influence of cutting speed, feed and depth of cut on the surface roughness height R _a and R _t respectively. The influence of the interaction of cutting speed/feed on the surface roughness height R _a and R _t and the effect of cutting speed on cutting speed/feed two factor cell total interaction for surface roughness height R _a and R _t are analysed through various graphical representations. Taking significant cutting parameters into consideration and using multiple linear-regression, mathematical models relating to surface roughness height R _a and R _t are established to investigate the influence of cutting parameters during turning of Al/SiC-MMC. Confirmation test results established the fact that the mathematical models are appropriate for effectively representing machining performance criteria, e.g. surface roughness heights during turning of Al/SiC-MMC.     

Influence of surface preparation on roughness parameters,friction and wear

The aim of the present research was to investigate influence of surface preparation on roughness parameters and correlation between roughness parameters and friction and wear. First the correlation between different surface preparation techniques and roughness parameters was investigated. For this purpose 100Cr6 steel plate samples were prepared in terms of different average surface roughness, using different grades of grinding, polishing, turning and milling. Different surface preparation techniques resulted in different R_a values from 0.02 to 7 μm. After this, correlation between surface roughness parameters and friction and wear was investigated. For this reason dry and lubricated pin-on-disc tests, using different contact conditions, were carried out, where Al₂O₃ ball was used as counter-body. It was observed that parameters R_ku, R_sk, R_pk and R_vk tend to have influence on coefficient of friction.     

Predicting surface roughness of hardened AISI 1040 based on cutting parameters using neural networks and multiple regression

In this study, models for predicting the surface roughness of AISI 1040 steel material using artificial neural networks (ANN) and multiple regression (MRM) are developed. The models are optimized using cutting parameters as input and corresponding surface roughness values as output. Cutting parameters considered in this study include cutting speed, feed rate, depth of cut, and nose radius. Surface roughness is characterized by the mean (R _a) and total (R _t) of the recorded roughness values at different locations on the surface. A total of 81 different experiments were performed, each with a different setting of the cutting parameters, and the corresponding R _a and R _t values for each case are measured. Input–output pairs obtained through these 81 experiments are used to train an ANN is achieved at the 200,00th epoch. Mean squared error of 0.002917120% achieved using the developed ANN outperforms error rates reported in earlier studies and can also be considered admissible for real-time deployment of the developed ANN algorithm for robust prediction of the surface roughness in industrial settings.     

Using specially designed high-stiffness burnishing tool to achieve high-quality surface finish

This paper is focused on the process of ball burnishing. The influence of tool stiffness on surface roughness parameters was considered theoretically, while experimental investigation was conducted to establish the influence of initial surface roughness (previous machining) on the effects of ball burnishing as the finishing process. Experimental investigations were conducted over a wide interval of most influential process parameters (burnishing forces, burnishing feed, and number of burnishing passes). The material used in the experiments was aluminum alloy EN AW-6082 (AlMgSi1) T651. Burnishing was performed using a specially designed tool of high stiffness. Statistical analysis of experimental data revealed strong correlation between roughness, R _a, and burnishing force, burnishing feed, and number of passes for the three surfaces, each with different roughness parameters. Particular combinations of process parameters yielded very low surface roughness, R _a, equivalent to polishing. It is worth noting that high surface quality can be achieved with relatively small burnishing forces, which differs from the investigations published so far. Contrary to conventional approaches, which are based on elastic tool systems, the authors propose the burnishing process to be conducted with high-stiffness tools. Further investigation shall be focused on optimization of burnishing process parameters in order to achieve surface finish equivalent to high polish.     

Modeling surface roughness for polishing process based on abrasive cutting and probability theory

The surface roughness is a variable used to describe the quality of polished surface. This article presents a surface roughness model based on abrasive cutting and probability theory, which considers the effects of abrasive grain shape, grit and distribution feature, pressure on surface roughness. The abrasive grain protrusion heights are thought to close to Gaussian distribution, and then the relationship between the indentation depth and the pressure based on Hertz contact theory is obtained. Surface roughness prediction model is established by calculating indentation depth of the abrasive grains on workpiece surface. The maximum surface profile height (R_y) is approximately equal to the maximum indentation depth of the abrasive grain. The arithmetic average surface roughness (R_a) is equal to the average indentation depth of the abrasive grain. The effects of process parameters such as pressure and grit on R_y and R_a were simulated and analyzed in detail.     

Modeling of surface roughness effect on dry contact friction in metal forming

Interfacial conditions such as friction and roughness substantially affect the process characteristics of metal forming. This study developed a dry friction model that accounted for the adhesion and interference effects of surface roughness. A sliding friction coefficient was suggested to provide fundamental information about the interfacial conditions of the contact surface. The proposed model was easily verified by published experiments and predicted values agreed with experimental results. Accordingly, friction coefficient ?? clearly increased as relative roughness R _m (=?roughness of tool $ R_a^T $ /roughness of workpiece $ R_a^M $ , measured as interference effect) increased. Simulations confirmed that the friction coefficient ?? decreased as dimensionless stress S _m (=?contact pressure p _m /tensile strength $ \sigma_u^0 $ ) increased at small strain hardening exponent n-values. Under the conditions of large n and small R _m values, the friction coefficient ?? initially decreased and then increased. It then slightly decreased as dimensionless stress S _m increased. However, this trend became less apparent as relative roughness R _m increased since friction coefficient ?? simply decreased.     

Effect of material microstructure and tool geometry on surface generation in single point diamond turning

There is a strong desire in industry to improve surface finish when performing ultra-precision, single point diamond turning (SPDT) to reduce the amount of post process polishing required to meet final product specifications. However there are well known factors in SPDT which limit achievable surface finish. This paper focuses on the role of material microstructure, including grain boundary density and the presence of inclusions, as well as tool design on surface roughness using the concept of size effect. Size effect can be described as an interplay between the material microstructure dimension and the relative size of the uncut chip thickness with respect to the cutting edge radius. Since one of the controllable parameters in size effect is grain size and dislocation density, controlled studies were performed on samples whose microstructure was refined by mechanical strain hardening through rolling and a friction stir process (FSP). The use of the ultra-fine grained workpiece prepared using an FSP was observed to reduce side flow as well as grain boundary and inclusion induced roughness. The role of tool geometry on material induced roughness was investigated using a tool with a rounded primary cutting edge and a flat secondary edge. The use of the flat secondary edge was observed to improve surface finish when machining a flat surface. This improvement was primarily attributed to a reduction in side flow and material microstructural effects. By combining these approaches an average surface roughness R_a value of 0.685 nm was achieved when SPDT a flat surface. Furthermore the custom tool has the potential to significantly improve the productivity of SPDT by allowing for a much higher feed rate while still achieving a high quality surface finish.     

Quantifying surface modification events from scanning force microscopy images

Scanning force microscopy (SFM) is widely used to monitor surfaces and surface modification processes. Some surface modification processes involve the addition (or removal) of discrete entities to (or from) a surface in circumstances where the absolute number of entities is related to some aspect of the process. A two-dimensional surface characterisation parameter – the surface area ratio (SAR) – was previously developed as a means of quantifying such modification and can be readily obtained from SFM images. Simulations have shown that the SAR parameter is superior for quantification purposes to conventional surface roughness parameters such as roughness average S_a, the area equivalent of R_a. Key features of SAR are as follows: its linear dependence with coverage; dependence of linearity slope on coverage mechanism; and its independence from the form, waviness or roughness of the underlying surface. A further advantage of this method is its simplicity given that the SAR parameter is readily obtained from SFM images. Simulations of adsorption onto flat surfaces have been validated using SFM images of polystyrene spheres adsorbed onto mica.