Jujiro Kagami

Mechanisms of elastic contact and friction between rough surfaces

Abstract The mechanisms of elastic contact and friction between two rough surfaces were analysed, assuming that the surface asperities were spherical, at least near their summits, and that they contacted elastically. It was found that the real contact area and the number of contact spots are approximately proportional to the load, whereas the mean area of contact spots and the mean pressure at the contact areas are almost independent of load. The frictional force F is almost equal to sA r , where s is the shearing strength at the contact area and A r is the real contact area. The experimental results using Pyrex glass specimens agreed within experimental limits with the theoretical results.

Contact between a sphere and rough plates

Abstract The contact between a smooth sphere and a rough plate is theoretically analysed for a mixed asperity contact theory in which asperities with displacements below and above a critical value are deformed elastically and plastically respectively. Contact asperities that are all deformed elastically or plastically independently are also analysed. There are some differences between the analytical results that are obtained for mixed, elastic and plastic contacts. Analytical results were confirmed by experimental investigations in which a smooth steel sphere was pressed against rough steel and copper plates under various loads. To observe indentations a rough plate was coated with a lamp black film after it had been coated with an evaporated carbon film in vacuo . The compliances between a smooth steel sphere and rough steel and copper plates were also measured under various loads with differential transformers. Theoretical and experimental results are in general agreement.

Surface density of asperities and real distribution of asperity heights on rubbed surfaces

Abstract Methods for obtaining the surface density of asperities and the real distribution of asperity heights, which differs from the distribution appearing on the surface profile curve, are considered for isotropic and anisotropic surfaces. For isotropic surfaces the asperities are assumed to be spherical at least near their peaks, and the surface density of asperities and the real distribution of asperity heights are obtained from the number of asperity peaks within a defined traverse length of the profile curve. For anisotropic surfaces the asperities are assumed to be ellipsoidal at least near their peaks. A method is derived by which the ellipsoidal asperities are replaced by equivalent spherical asperities. Comparison of theoretical and experimental results using Pyrex glass specimens showed that for worn surfaces the experimental and theoretical results agreed.

Micro-displacement characteristics under tangential force

In this paper, firstly the obtained analytical results are briefly summarised. Next some experimental results are shown developed using finished ceramic surfaces of ZrO{2} and Al{2}O{3} together with SiC. And comparison of obtained experimental results with theoretical analyses and approximate equations introduced in the preceding works was made. The main conclusions are as follows. (1) Little difference can be seen in appearance between the experimental and calculated displacement behaviours, although frictional force of SiC is higher compared with those of other two ceramics and the slope of the curve after macro-slip of SiC is greater than those of the others. (2) Experimental values of tangential stiffness r{g} at the start of increasing the tangential force lie between calculated values by the two contact models. (3) Experimental values of tangential displacement δ{cmax} at the start of macro-slip are larger than those calculated by the two contact models and this is more evident for ZrO{2}.

Measurement of surface profiles by the focusing method

Abstract To measure the surface profile of an object in a relatively high roughness range, a first attempt is made to develop an optical profilometer, the principle of which is based on the focusing method; a laser beam is focused onto the surface of the object by a lens driven through a magnetic system by differential electrical output fed back from two photo-sensors. In particular, the effects on the surface measurement of irregularly reflected beams and local slopes of the surface irregularities are investigated and steps to remove these effects are taken. To test the reliability of the developed profilometer, profile measurements are performed for various rough surfaces.

Analysis of the mechanism of steady wear by the fatigue theory as a stochastic process

Abstract The mechanism of mild and steady wear was analysed assuming that the peaks of the asperities covering a surface are spherical and in elastic contact. The effects of sliding velocity, load and mechanical and physical properties of the specimen on wear were determined. The critical sliding velocity ν c at which the wear rate becomes minimum was obtained. From the analytical results it was found that in the lower and higher ranges of sliding velocity the wear rate V l is greater and becomes minimum at ν c . In the lower ranges of the load W , V l is proportional to W , but in the higher ranges V l is abruptly increased. The ratio of the number of elastic contacts to total contacts was analysed to check the assumption of elastic contact.

Contact width and compliance between cylinders and rough plates

Abstract The contact mechanism between a cylinder and a rough plate is theoretically analysed for mixed, elastic and plastic contacts of asperities. The analysis leads to the result that the contact pressure, the contact width and the compliance between the cylinder and plate differ considerably from those calculated from the Hertz equation and the Lundberg equation when the surface roughness in contact is greater and the normal load is lower. It is also found that the difference between the calculated contact width and the compliance based on mixed asperity contacts and those based on elastic or plastic asperity contacts is small. To confirm the analysed results, the contact width between the cylinder and the rough steel or rough copper plate was measured by means of evaporated carbon and lamp black film coatings on the rough surfaces. The compliance between the surfaces was also measured using differential transformers. Little difference was found between the analysed results and the experimental results.

Influences of bearing pitch diameter, roller length and roller diameter on the frictional torque of a needle roller thrust bearing

In this study, the frictional toque of a needle roller thrust bearing was investigated theoretically and experimentally. In order to evaluate the torque, the roller motion of the bearing was clarified under the condition that the energy loss generated at the contact between the rollers and raceways become minimum. Secondly, by using these results, the relative sliding between the rollers, and raceways and the frictional torque of needle roller thrust bearing were obtained. Following the theoretical studies, experimental investigations were carried out with a wide range of thrust loads and rotational speeds. Various types of bearings having different numbers of rollers, different pitch diameters, different roller length and different roller diameters were prepared. The results obtained in this work are summarized as follows: o (1) The frictional torque of a needle roller thrust bearing is nearly proportional to the thrust load and roller length. (2) The torque is almost independent of the rotational speed, number of rollers, bearing pitch diameter and roller diameter. (3) Experimental results agree with the theory.

Frictional torque of cylindrical roller thrust bearing in grease lubrication

In general, greases are widely used as the lubricants of the majority of rolling bearings, but their fluidity or lubrication characteristics are complicated. Therefore, it is not clear how the lubricant flow in bearings is or what the lubrication mechanism is. Also, the effects of grease lubrication on the operating performance of rolling bearings are not clear. In this study, the frictional torque of grease-lubricated cylindrical roller thrust bearings was investigated over a wider range of thrust loads and rotational speeds. For comparison, the same tests were also performed with three types of cylindrical roller thrust bearings, single-row, double-row and triple-row. The frictional torque obtained can be summarized as follows. o (1) The frictional torque is proportional to the square root of the thrust load in a lower load range. (2) The torque is proportional to the thrust load in the higher load range. (3) The torque is very similar in the lower load range regardless of the type of bearing; single-row, double-row or triple-row. However, in the higher load range, the value is nearly inversely proportional to the number of rows.

Experimental investigations to confirm the theoretical analysis of steady wear

Abstract Experimental investigations were carried out with Pyrex glass and copper to check the analytical results of a steady wear mechanism treated as a stochastic process. The wear rates were minimized for both specimens at a critical sliding velocity determined by analysis. The critical sliding velocities obtained experimentally agree with the calculated values. An inflection point is observed on a cumulative wear curve for copper in the transition period between the initial and steady wear.