Method of determination of truncation parameters from measured surface profile

The probability density function of the roughness height of a sliding surface is not always Gaussian like that of a truncated surface caused by running-in or mild wear. Therefore, it is important for obtaining contact pressure or frictional characteristics to estimate the truncation level of the non-Gaussian distribution function. This paper presents a method of determination of the two truncation parameters in the truncation model presented by King et al. [Proceedings of the 4th Leeds–Lyon Symposium on Tribology, MEP, London, 1978, p. 333]. The two truncation parameters p and β can be determined by plotting the values of skewness S_k and kurtosis K obtained from a measured profile of surface roughness on the S_k–K diagram calculated with the truncation model for various given values of parameters p and β. The height distributions reproduced by the truncation model with the truncation parameters p and β identified by the present method is in good agreement with the original ones of the measured surfaces.     

Measurement and compensation of error motions of a diamond turning machine

This paper describes the measurement and compensation of error motions of a diamond turning machine for nanofabrication of large sinusoidal metrology grids. The diamond turning machine has a T-base design, which consists of a spindle with its rotation axis along the Z-direction and a cross-slide with its movement direction along the X-direction. A fast-tool-servo (FTS) unit is mounted on the X-slide to generate sinusoidal microstructures on a flat workpiece surface mounted on the spindle. The error motions of the X-slide and the spindle, which introduce Z-directional profile errors (out-of-flatness) on the grid surface, are measured and compensated. The out-of-straightness of the X-slide is measured to be approximately 60 nm over a travel of 80 mm by using the reversal method. It is also confirmed that the out-of-straightness of the X-slide has a 10-nm periodic component with a period of 11 mm corresponding to the diameter of the needles used in the roller bearing of the X-slide. The angular motion of the spindle is measured to be approximately 0.3″ by using an autocollimator, which can cause a 73-nm out-of-flatness over a workpiece 100 mm in diameter. The axial motion of the spindle is measured to be approximately 5 nm, which is the smallest error motion. The out-of-flatness of the workpiece is reduced from 0.27 to 0.12 μm through compensating for the error motions by utilizing the FTS unit based on the measurement results of error motions.     

Surface profile measurement of a sinusoidal grid using an atomic force microscope on a diamond turning machine

This paper describes the surface profile measurement of a XY-grid workpiece with sinusoidal microstructures using an atomic force microscope (AFM) on a diamond turning machine. The sinusoidal micro-structures, which are fabricated on an aluminum plate by fast tool servo-assisted diamond turning, are a superposition of periodic sine-waves along the X- and Y-directions (wavelength (XY): 150 μm, amplitude (Z): 0.25 μm). A linear encoder with a resolution of 0.5 nm is integrated into the AFM-head for accurate measurement of the Z-directional profile height in the presence of noise associated with the diamond turning machine. The spindle and the X-slide of the machine are employed to spirally scan the AFM-head over the sinusoidal grid workpiece. Experiments fabricating and measuring the sinusoidal grid workpiece are carried out after accurate alignment of the AFM cantilever tip with the spindle centerline.     

Precision surface finish of the mold steel PDS5 using an innovative ball burnishing tool embedded with a load cell

A load-cell-embedded burnishing tool has been newly developed and integrated with a machining center, to improve the surface roughness of the PDS5 plastic injection mold steel. Either the rolling-contact type or the sliding-contact type was possible for the developed ball burnishing tool. The characteristic curves of burnishing force vs. surface roughness for the PDS5 plastic injection mold steel using the developed burnishing tool for both the rolling-contact type and the sliding-contact type, have been investigated and constructed, based on the test results. The optimal plane surface burnishing force for the PDS5 plastic injection mold steel was about 420 N for the rolling-contact type and about 470 N for the sliding-contact type, based on the results of experiments. A force compensation strategy that results in the constant optimal normal force for burnishing an inclined surface or a curved surface, has also been proposed to improve the surface roughness of the test objects in this study. The surface roughness of a fine milled inclined surface of 60 degrees can be improved from R_a 3.0 μm on average to R_a 0.08 μm (R_max 0.79 μm) on average using force compensation, whereas the surface roughness was R_a 0.35 μm (R_max 4.56 μm) on average with no force compensation.     

Comparison between precision roughness master specimens and their electroformed replicas

Two random profile precision roughness calibration specimens with R_a = 0.028 and 0.043 μm are compared with their electroformed replicas. Measurements of surface texture and roughness parameter values show very good agreement. Fluctuations in the R_a values across the replicas track those across the masters to within 1.8 nm. However, the form errors of the replicas, approximately 0.6 μm over a 3.2 × 2.6 mm² area, are much bigger than those of the masters, and their hardness (HV = 243) is not as good as the master specimens' (HV = 852).     

Theoretical method for estimation of mean pressure on contact area between rolling tools and workpiece in cross wedge rolling processes

The paper gives a new method no determine the mean unit contact pressures on a material—tool contact surface in cross wedge rolling processes (CWR). The dependencies worked out on the basis of the energy and the upper bound methods permits rolling forces to be determined which are comparable to experimentally measured ones. The analysis provides equations which relate the mean contact pressure q_m to the basic process parameters, namely the forming angle α, the spreading angle β, the relative reduction of a portion δ and the shear friction factors m and m_k.     

Predictive Modeling of Surface Roughness in Grinding of Ceramics

The surface roughness represents the quality of ground surface since irregularities on the surface may form nucleation for cracks or corrosion and thus degrade the mechanical properties of the component. The surface generation mechanism in grinding of ceramic materials could behave as a mixture of plastic flow and brittle fracture, while the extent of the mixture hinges upon certain process parameters and material properties. The resulting surface profile can be distinctively different from these two mechanisms. In this article, a physics-based model is proposed to predict the surface roughness in grinding of ceramic materials considering the combined effect of brittle and ductile material removal. The random distribution of cutting edges is first described by a Rayleigh probability function. Afterwards, surface profile generated by brittle mode grinding is characterized via indentation mechanics approach. Last, the surface roughness is modeled through a probabilistic analysis of ductile and brittle generated surface profile. The model expresses the surface finish as a function of the wheel microstructure, the process conditions, and the material properties. The predictions are compared with experimental results from grinding of silicon carbide and silicon nitride workpieces (SiC and Si₃N₄, respectively) using a diamond wheel.     

An elastic–plastic stress analysis steel-reinforced thermoplastic composite cantilever beam

In the present study an analytical elastic–plastic stress analysis is carried out for a low-density homogeneous polyethylene thermoplastic cantilever beam reinforced by steel fibers. The beam is loaded by a constant single force at its free end. The expansion of the region and the residual stress component of σ_x are determined for 0°, 30°, 45°, 60° and 90° orientation angles. Yielding begins for 0° and 90° orientation angles at the upper and lower surfaces of the beam at the same distances from the free end. However, it starts first at the upper surface for 30° and 45° orientation angles. The elastic–plastic analysis is carried out for both the plastic region which spreads only at the upper surface and the plastic region which spreads at the upper and lower surfaces together. The residual stress components of σ_x and τ_xy are also determined. The intensity of the residual stress component is maximum at the upper and lower surfaces of the beam, but the residual stress component of τ_xy is maximum on or around the x-axis. The beam can be strengthened by using the residual stresses. The distance between the plastically collapsed point and the free end is calculated for the same load in the beam for 0°, 30°, 45°, 60° and 90° orientation angles.     

High-resolution large-strain measurement of plastically deformed specimen by Fourier phase correlation

The Fourier phase correlation method is applied to position circular marks one by one printed on the specimen before and after deformation in order to measure the large plastic strain. This method is extremely sensitive to the differences between the profile of a mark and noise. Therefore, it detects marks easily even under non-uniform illumination without any processing such as flattening illumination, noise exclusion and boundary enhancement in image transformation into binary codes. In addition, a new method of moving reference images (MRI) to position the observed marks in the sub-pixel range is proposed. The MRI technique introduces the theoretical resolution 1/n (n: number of divisions of one pixel). The MRI method enables the positions of the deformed marks to be determined with a resolution of ±0.1 pixel (standard deviation σ_p is 0.042 pixel). Strain of the tensile specimen can be measured within an error of ±0.0015 (standard deviation σ_ε=0.00055).     

Tool life monitoring during the diamond turning of electroless Ni–P

Diamond tools become severely worn when machining Ni–P plating materials. Tool life monitoring is therefore essential to avoid the deterioration of workpiece quality. In this paper, in order to better detect tool life while the tools are in use, detailed investigations of the cutting force and acoustic emission (AE) measured during diamond turning process have been made. The results of this tool-life testing show that the cutting force and AE supply valuable information on tool failure; the dynamic component of the thrust force fluctuates chaotically when the tool dulls. This phenomenon can be detected using the 1/f^β power spectrum with a spectral exponent of β > 1. On the other hand, the AE amplitude a tends to rise just when chipping occurs on the cutting edge. This feature can be detected by the amplitude distribution spectrum, in which the AE event rate follows the power law a^−m with a scaling exponent of m < 2. Therefore, we can conclude that a spectral exponent of β > 1 and a scaling exponent of m < 2 can be used as the criteria to gauge tool life, because it was observed at the end of the tool life that tool corner had become worn out and that chipping had occurred on the cutting edge.     

A universal slip-line model with non-unique solutions for machining with curled chip formation and a restricted contact tool

A universal slip-line model and the corresponding hodograph for two-dimensional machining which can account for chip curl and chip back-flow when machining with a restricted contact tool are presented in this paper. Six major slip-line models previously developed for machining are briefly reviewed. It is shown that all the six models are special cases of the universal slip-line model presented in this paper. Dewhurst and Collins's matrix technique for numerically solving slip-line problems is employed in the mathematical modeling of the universal slip-line field. A key equation is given to determine the shape of the initial slip-line. A non-unique solution for machining processes when using restricted contact tools is obtained. The influence of four major input parameters, i.e. (a) hydrostatic pressure (P_A) at a point on the intersection line of the shear plane and the work surface to be machined; (b) ratio of the frictional shear stress on the tool rake face to the material shear yield stress (τ/k); (c) ratio of the undeformed chip thickness to the length of the tool land (t₁/h); and (d) tool primary rake angle (γ₁), upon five major output parameters, i.e. (a) four slip-line field angles (θ, η₁, η₂, ψ); (b) non-dimensionalized cutting forces (F_c/kt₁w and F_t/kt₁w); (c) chip thickness (t₂); (d) chip up-curl radius (R_u); and (e) chip back-flow angle (η_b), is theoretically established. The issue of the “built-up-edge” produced under certain conditions in machining processes is also studied. It is hoped that the research work of this paper will help in the understanding of the nature and the basic characteristics of machining processes.     

Picosecond mid-IR laser induced surface damage on Gallium Phosphate (GaP) and Calcium Fluoride(CaF<Subscript>2</Subscript>)

Picosecond mid-IR USPL induced surface damage on a Gallium Phosphate (GaP) and Calcium Fluoride (CaF₂) is reported. A semiconductor GaP and a dielectric material CaF₂, that are transparent over3–10μm, were exposed to one picosecond mid-IR light (4.7μm) to investigate laser-induced surface morphological changes on the target The initiation of damage along the polishing scratch line of GaP and the random location of damage digs on the CaF₂ suggests that the mid-IR picosecond laser-induced damage on targets started from intrinsic surface defects. Multiple pulse irradiations produced periodic corrugated surface structures (ripples) perpendicular to the polarization of light on both GaP and CaF₂. In terms of the orientation and the spacing between ripples, observed ripples have common features with previously reported ripples.     

Estimation of length and surface of anisotropic capillaries

Surface density (S_V) and length density (L_V) of myocardial capillaries have hitherto been estimated from their profile boundary length (B_A) and their numerical density (Q_A) on transverse sections by the simplifying assumptions of the Krogh model (perfectly anisotropic, straight, unbranched capillaries with constant cross-sectional area). As the capillaries actually are partially anisotropic, curved, branching cylinders with variable cross-sectional area, a geometrical bias arises from the model-reality discrepancies. We have applied and compared two methods to overcome these inconsistencies: (1) estimation of L_V and S_V by a more realistic model (the Dimroth-Watson distribution); (2) estimation of L_V and S_V from isotropic uniform random (IUR) sections. Twelve male Wistar rats were fixed by retrograde vascular perfusion. One pair of longitudinal and transverse sections, and six IUR sections per animal were selected at random from the left ventricular papillary muscles. Ultrathin sections were silver-impregnated and studied by light microscopic morphometry. Nearly identical estimates of L_V and S_V were found by both methods. The model-based estimation provides biologically meaningful anisotropy constants, but it presupposes knowledge of the anisotropy axis. The IUR method provides no measure of anisotropy, but it can be applied in tissues where the anisotropy axis is not known. Both methods are equally efficient and practically unbiased in S_V estimation, but the model-based estimation is far more efficient in L_V estimation.     

Super-precision cylindrical machining

A study has been made of the theory and techniques of turning precise circular components. The possibility of such high accuracy cylindrical machining was analysed according to the principle of making a precise circle. In the study, a form of chucking-type preciison cylindrical machining was developed by combining an insensitive vibration cutting mechanism - using a main spindle system which features an air bearing - with superposition superfinishing. In the first process, the work is chucked on the main spindle and machined using a continuously and systematically pulsating cutting force. In the second process, the work is finished by a newly developed superposition superfinishing device which features equivalent grades of ultrasonic vibration stone. Key points of the techniques are a torsional vibration mode tool for producing accurate, high amplitude vibration of the cutting point, and a contrivance for making accurate movements of the superposition superfinishing device. Machined roundness of 0.1–0.2 μm and surface roughness of 0.03–0.09 μm R_max were obtained with plain carbon steels, stainless steels and hardened steels (H_RC 41, 53, 60). It is considered that turning to roundness ≈ 0, cylindricity ≈ 0 and surface roughness ≈ 0 can be realized by means of this new machining process and its lathe.     

Frictional properties of some additives for sliding guide way lubricants in a sliding speed range between 0.002 and 1.5 m/s with a thrust collar friction tester

Frictional properties of some additives used in sliding guide way lubricants were studied for a pair of mild steels under sliding speeds ranging from 0.002 to 1.5 m/s with a thrust collar type friction tester. As the sliding speed was decreased, the coefficient of friction first decreased, then after reaching the minimum value, it increased. The minimum friction coefficient μ_min and the transition sliding speed V_min showing μ_min depended upon the additive. That is, μ_min for the oil containing sulfurized lard was lower than those for the other oils tested and its V_min was as low as 0.005–0.1 m/s compared with the transition speeds of 0.2–0.5 m/s for the other oils tested. Observations of the surface profile and surface analyses of the test specimen after the tests indicated that the unique phenomena for sulfurized lard were due to the formation of a boundary film containing a long carbon chain with a chemical bond between the sulfur and carbon.     

Investigating the change in wear behaviour of a tool steel after surface melting and gaseous alloying

In this study it is shown that surface melting in the presence of a reactive gas can be used as a method of changing the tribological properties of a hot forging die steel. A H13 tool steel surface was melted in the presence of a gaseous shield of pure argon, nitrogen, carbon dioxide and a mixture of 80% carbon dioxide–20% argon. Microhardness profile measurements and metallographic examination was used to study the changes in wear behaviour after surface modification. The results indicate a significant increase in surface hardness after the melting and gaseous alloying process with the most wear resistant surfaces produced under a shield of CO₂ and CO₂–Ar gases. This was attributed to the formation of a fine dendritic microstructure consisting of chromium–vanadium carbides. The presence of these hard phases in the surface reduce the degree of plastic deformation and wear by adhesive mechanisms.     

A surface motor-driven planar motion stage integrated with an XYθZ surface encoder for precision positioning

This paper describes a surface motor-driven XY planar motion stage equipped with a newly developed XYθ_Z surface encoder for sub-micron positioning. The surface motor consists of four linear motors placed on the same surface, two pairs in the XY-axes. The magnetic array and the stator winding of the linear motor are mounted on the platen (the moving element) and the stage base, respectively. The platen can be moved in the X-direction by the X-linear motors, and in the Y-direction by the Y-linear motors. It can also be rotated about the Z-axis if the X- or Y-linear motors generate a moment about the Z-axis. The surface encoder consists of two two-dimensional angle sensors and an angle grid with two-dimensional sinusoidal waves on its surface. The angle grid is mounted on the platen of the stage which is levitated by air-bearings. The angle sensors and the air-bearing pads are fixed on the stage base so that the motion of the platen is not affected by the electronic cables and air hoses. The XY-positions and θ_Z rotation of the platen can be obtained from the angle sensor outputs with resolutions of approximately 20 nm and 0.2′′, respectively. The surface encoder is placed inside the stage so that the stage system is very compact in size. Experimental results indicate that precision positioning can be carried out independently in X, Y and θ_Z with resolutions of 200 nm and 1′′, respectively.     

The surface chemistry of alkyl and arylphosphate vapor phase lubricants on Fe foil

The surface chemistry of tributylphosphate (TBP) and tricresylphosphate (TCP) on a polycrystalline Fe surface was studied using temperature programmed reaction spectroscopy and Auger electron spectroscopy to illustrate some of the initial steps in the reaction mechanisms of alkyl and arylphosphate vapor phase lubricants. During heating, TBP [(C₄H₉O)₃P=O] adsorbed on the Fe surface decomposes via C–O bond scission to give butyl surface intermediates [C₄H₉–] that react via β-hydride elimination to desorb as 1-butene [CH₃CH₂CH=CH₂] and H₂ without appreciable carbon deposition onto the surface. The thermal decomposition of 1-iodobutane [I-C₄H₉] on Fe was observed to proceed via the same β-hydride elimination mechanism. In contrast to tributylphosphate, meta-tricresylphosphate (m-TCP) [(CH₃–C₆H₄O)₃P=O] decomposes on Fe via P–O bond scission to produce methylphenoxy intermediates [CH₃–C₆H₄O–]. During heating to 800 K, methylphenoxy intermediates either desorb as m-cresol [CH₃–C₆H₄–OH] via hydrogenation or decompose further to generate tolyl intermediates [CH₃–C₆H₄–]. Some of the tolyl intermediates desorb as toluene [CH₃–C₆H₅] via hydrogenation but the majority decompose resulting in H₂ and CO desorption and carbon deposition onto the Fe surface. The P–O bond scission mechanism of m-TCP was verified by showing that the temperature programmed reaction spectra of m-cresol yield products that are almost identical to those of m-TCP. These results provide insight into the origin of the differences in the performance of alkyl and arylphosphates as vapor phase lubricants. The alkylphosphates decompose via alkyl intermediates that readily undergo β-hydride elimination and desorb into the gas phase as olefins, thus removing carbon from the surface. In contrast, the arylphosphates generate aryloxy intermediates by P–O bond scission and aryl intermediates by further C–O bond scission. Neither of these intermediates can undergo β-hydride elimination and thus they decompose to deposit carbon onto the Fe surface. The higher efficiency for carbon deposition may be the primary reason for the superior performance of the arylphosphates over alkylphosphates as vapor phase lubricants.     

Study of surface roughness effects in elastohydrodynamic lubrication of rolling line contacts using a deterministic model

A sinusoidal surface roughness model is adopted for the analysis of the effects of roughness amplitude and wavelength on pressure profile, film shape, minimum film thickness and coefficient of friction in a steady state EHL line contact. The influence coefficients used for the evaluation of surface displacements are calculated by utilizing a numerical method based on Fast Fourier Transform. Significant reduction is observed in the minimum film thickness due to surface roughness. Such reduction is quantified by roughness correction factor, C_R, and a relationship between C_R and non-dimensional surface roughness amplitude A is derived as: C_R=1−0.7823A^0.8213. This equation may prove to be of interest from designer's viewpoint. The friction coefficient is found to increase appreciably with increasing amplitude and decreasing wavelength of surface roughness.