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We study the self-similar problem concerning the motion of a spherical piston in a medium with “dry” friction. The piston moves with constant velocity in a nonideal medium.

On the Dynamics of Scree Slopes It is shown that the following dynamical phenomena occur on a scree slope: Collapse because of lack of stability, rapid slides of debris material, slow sliding of large blocks, jumping and rolling of large stones, and particle-separation due to a sieving effect. The mechanisms of these phenomena are investigated in detail; it is shown that the stability and the slow sliding of blocks can be explained by soil mechanics methods, the debris slides by the law of dry friction, the rolling of stones by the laws or rolling of spheres, and the sieving effect by a theory analogous to that encountered in the filtration of suspensions through porous media.

The nonlinear vibratory motions of a three-axle semitrailer truck were investigated via the use of a digital computer. The nonlinear equations of motion are presented and a method of numerical integration is discussed. The analysis allows any shape of suspension force-deflection curve (including wheel hop, suspension stops, and dry friction damping) and a similar liberality of shock absorber force-velocity characteristics. An experimental vibration study, performed on a model truck, is described and the results compare favorably with the calculated results of the numerical integration.

The problem of the brachystochrone with dry friction is governed by an autonomous set of highly non-linear ordinary differential equations, which contain a small parameter μ (the coefficient of friction). Using perturbation technique an approximate solution is constructed.

The mathematical model of a hydraulic copying system, utilizing a fourway, critical centered spool valve and a symmetrical volume power cylinder under the action of dynamic cutting forces is developed. The model takes into account the following features: (a) dynamic behavior of the control valve and the action of the flow forces, (b) dry-friction between the copying system and its mountings, (c) dynamic behavior of the stylus, (d) time domain model of the kinematic input due to the template configuration, and (e) dynamic input that accounts for the cutting force fluctuations and its interaction with the velocity response of the system. A dynamic accuracy criterion which includes static, kinematic, and transient errors is formulated. The dynamic accuracy criterion is a function of the specified manufacturing tolerance of the produced workpiece and can be directly evaluated from the system analysis. Analog computer simulations are carried out to study the effects of various influencing parameters on the dynamic accuracy of copying systems. Plots are developed to be used as a guide for the design and operation of hydraulic copying systems. The dynamic accuracy is calculated for commercial copying systems using the methods developed and found that the results are in close agreement with the data supplied by the manufacturers.

The relationship was measured between the normal contact force and the force required to overcome friction between food samples and a surface simulating a typical texture test cell. Peas produced frictional behavior that combined the characteristics of dry friction and fluid flow. Friction coefficients for selected foods ranged from 0.04 to 0.52. Friction force was linearly related to the normal contact force and non-linearly to the area of contact between the sample and the surface, and the speed of the sample relative to the surface. This verifies the fact that, with empirical texture test devices, these test variables must be held constant. The estimated friction forces represented a significant amount of the total force required to operate a wire extrusion cell and a back extrusion cell. It was concluded that standardization of the test cell would be easier to achieve if the contact area between the sample and the cell surfaces was minimized and if low friction materials were used to construct the cells.

This is a theoretical paper concerned with the rise in the surface temperatures caused by frictional heating at sliding contacts. By taking into account in the theoretical model, the growth of junctions between contacting asperities due to the action of the friction force, a large improvement in the correlation with experimental surface temperature measurements at dry friction contacts has been obtained. These results are felt to support the use of the usual flash temperature technique for predicting the surface temperatures in lubricated or low friction conditions. Presented as an American Society of Lubrication Engineers paper at the Lubrication Conference held in Minneapolis, Minnesota, October 18–20, 1966.

The relation between the changes in surface appearance and wear of a specimen was observed. The specimen was pin-shaped having a cone tip of 90°C. It was slid on a hardened bearing steel disk at a sliding speed of 16.7cm/sec. under a load of 0.5-2kg in a dry condition. Appearances of the surface were examined by measuring contact resistance and by optical method.The results obtained were as follows:1) Specimen of 6:4 brass containing lead: The metal adhered to the disk was little in amount and the wear of the specimen was relatively small in the earlier stage. However, severe wear was initiated when the disk was covered with the transferred metal.2) Specimen of pure iron: The wear of the specimen linearly increased with sliding distance, and no remarkable changes were observed on the sliding surface during the friction up to 1, 000m.3) Specimen of 7:3 brass: The wear process corresponded well with appearances of the sliding surface. For instance, the wear decreased when an oxide was formed on the surface, but it again increased after the break-down of the oxide film.4) Specimen of 4% Sn-Cu alloy: Low contact resistance and low coefficient of friction were observed in the earlier stage, and severe wear abruptly occurred after sliding for some distance. However, the wear was retarded when high contact resistance and high friction, which indicated the formation of the oxide, were observed. No break-down of oxide film was observed for this alloy.

The nonlinear damping characteristicD(v) of a self-sustained system is replaced by two piece-wise linear characteristics. The integral curves calculated with their help bound the integral curve corresponding to the nonlinear damping characteristic. The method may be used for the determination of motion and velocity time history, integral curves, limit cycles and amplitude succession. The stability and period of limit cycles may also be determined. The method is used for studying oscillations due to dry friction.

Surface temperatures were measured by dynamic thermocouple technique. In dry friction the temperatures were in reasonable agreement with theory as proposed by Jaegar. When lubricants are used the behavior was very much a function of the lubricant. With some lubricants the temperatures can be obtained by extending the dry friction theory and assuming that the temperature rise observed is essentially due to the metal contact. When reaction films are involved, Rehbinder effect with the consequent reduction in plastic strength appears to be a possibility.

The time dependence of dry friction as a function of stress and strain in the contacting surfaces is analysed and an equation describing friction as a function of material properties and time is derived. Friction was measured for pairs of materials ranging from steel to plastics and the influence of periods of rest on the friction force was followed. It is shown that the experimental values can be predicted theoretically if certain rheological properties of the materials are taken into account.

Although, as has already been reported, the resonance of synchronous backward precession can occur when the bearing pedestals deflect, this resonance can also appear when the pedestals have no flexibility and there is a loose fit of ball bearing in pedestal. Since there are errors in machining the outer ring of ball bearing as well as the inner surface of bearing box where neither are made exact circle, the degree of flt is not equal in all directions and the shaft has an unequal flexibility. Consequently the critical speeds of synchronous backward precession do occur. Similarly these critical speeds appear in the shaft supported by single-row radial ball bearings, because such a shaft has non-symmetrical, non-linear characteristics and unequal flexibility. Because the phenomenon of shaft whipping induced by dry friction takes place, it is undesirable to equip a gard ring to check an increase of deflection of the shaft at the critical speeds of synchronous backward precession.

The wear resistance of 20–6000-μ-thick vacuum-deposited chromium coatings under dry friction and sand blasting conditions can be varied by varying the deposition conditions, especially the substrate temperature and deposition rate. The wear resistance of coatings deposited on substrates at ts < 300° C approaches that of electrodeposited coatings. It was shown that wear-resistant properties of the coatings studied are related to their structure, microhardness and other physicomechanical properties.

In the present paper, a numerical method to treat the problem of stationnary rolling with slip and spin is proposed which is valid for any distribution of the contact area in areas of adhesion and areas of slip. The method is tested with the experimental evidence obtained by Johnson , and by Haines and Ollerton , and it is found that the total force transmitted by the bodies is very close to the experimental results, while there is a reasonable agreement as to the local traction distribution. As it is described here, the method applies only to the case in which both bodies have the same elastic constants, but by a small modification it can probably be shown that it gives a good approximation in the case of unequal elastic constants.

Lubricated and unlubricated tests were conducted in the NASA spinning friction apparatus with SAE 52100 steel specimens with ball-race conformities of infinity (a ball on a flat), 60, 55, and 51-percent. For a constant conformity under lubricated conditions, the coefficient of spinning friction decreased from approximately 0.5 to 0.05 with increasing load and stress. At a constant stress, the coefficient of spinning friction increased with decreasing conformity (increasing percent conformity). Under unlubricated conditions, the coefficient of spinning friction remained relatively constant regardless of load, stress, or conformity, having values within a scatter band of 2.5 to 6.0. For a constant stress under both lubricated and unlubricated conditions, the greater the conformity (the smaller the percent conformity), the higher the torque.

A study was made of surface roughness effects on dry friction between two metals, assuming that the asperities are cones of slopes which depend on the surface roughness. Theoretical expressions were derived for ploughing, adhesion and total friction coefficients of cones, spheres and aquare pyramids ploughing along the soft metal surface. A comparison of calculated values based on this theory with experimental data shows good agreement. Moreover, theoretical discussion was made of surface roughness effects on dry friction on the basis of the analysis of mechanism of abrasive friction. The theoretical estimation of the coefficient of friction between two metal surfaces can be carried out using the relations between the surface roughness and the slope of the asperities, and the coefficient of friction due to the adhesion at the interface. The experiments also showed that the maximum displacement between two metal surfaces in contact before gross sliding occurs, increases with an increase of the surface roughness.

The dominant importance of hysteresis in lubricated friction of rubber was first outlined by Tabor and has been extensively confirmed since. A number of workers have also shown that dry friction is correlated with hysteresis, but the mechanistic connection is still unclear. Rubber hardness has been less definitely correlated with friction. This may result in part from the choice of surface on which to test the rubber compositions studied. We have previously shown the importance of the test surface and recommended use of wavy glass to simulate actual slippery roads in lieu of a representative road surface. Carr reported our finding that the relative influence of rubber hardness depends on the texture of the hard surface on which it slides. Using the wavy glass and a slippery road surface, we have now studied a very wide range of compositions, both gum and filled, derived from commonly used tire rubbers, as well as others included to extend the range of properties studied. These results fully confirm the importance of hysteresis and more clearly define that of hardness. These two properties together almost completely determine wet friction on slippery roads. Most of the variance not accounted for is attributable to measurement error.

Friction is the force resisting relative motion between surfaces in contact. The coefficient of friction is the ratio of the frictional force to the normal load. Consequently the measurement of friction involves measurement of a normal load, movement of a surface, and measurement of a tangential force. The first part of this review paper deals with the basic principles of the friction process. The second part is concerned with experimental methods of measuring the friction.

SUMMARY The changes of vibration comfort and stability of vehicles as effected by the value of frictional force generated in laminated springs are discussed and the probability of departure of the tyres from the ground is described. A partly automated analogue computer simulation being equivalent to a great number of highway experiments was applied in the study. The computer model was excited by several stochastic roadprofile - analogue signals generated by filters from the wide-band random signal of a digital noise generator.

In the preceding paper the author obtained experimentally the values of coefficient of dry friction for five metallic materials under high pressures and they decrease generally with the increase of contact-pressure. In this paper the author obtains the same tendency for copper. Furthermore, the values under low pressures are measured to compare with them under high pressures. Then factors to have an effect on the values under low pressures are researched and recognized that roughness of contact surface and hardness are essentialy effective to them. On the relation between the values and roughness, taking the values as ordinate and roughness as abscissa, the graph for each combination of six materials becomes a smooth curve respectively and the values suddenly increase with increase of roughness where be about 10-3mm. And the values decrease with increase of hardness number for every combination of materials and roughness.

IN the application of motors for specific duty cycles, driving an arbitrary time varying load, affected by nonlinear damping and dry friction, the time response is often quite difficult to determine analytically. In this paper a method is presented that yields a quick graphical answer which avoids all the difficulties that appear in the analytical treatment of the problem.

Wear and friction properties of austenitic manganese (Hadfield) steel were studied with two different sliding velocities under combined rolling, sliding and impact conditions using an Amsler wear test machine. Under dry friction, both wear rates and friction coefficients were higher at the lower slip velocity; with lubrication there was no measurable wear rate and the friction coefficient was lower at the lower slip velocity. Dry sliding produced considerably more work hardening of the surface than that obtained under lubricated conditions. The. depth of work hardening under dry sliding was more at the lower slip velocity. Dry sliding produced magnetic iron oxide wear products, and the surface was considerably roughened. Lubricated sliding produced no damage to the surface and probably improved the finish.

In order to improve the accuracy of an hydraulic copying system, the hydraulic stiffness must be increased and dry friction decreased. Both hydraulic stiffness and dry friction have important influences on the stability of the system, and so have several mechanical parameters. As a pure mathematical study of the influence of the non-linear dry friction is rather difficult, the behaviour of the system will be simulated on an analogue computer. This simulation will provide useful data about the stability criterion and the optimalization of the system.

The problem of damping out structural vibrations by the use of dry (Coulomb) friction, already discussed in relation to beam-like structures in a previous paper (1)†, is here considered in relation to the torsional vibrations of shafts.

1. A study was made of the effect of pressure on the friction, wear, and surface microhardness of some transition metals of Groups V, VI, and VIII sliding under dry friction conditions in a vacuum. 2. The existence is demonstrated of certain “threshold” pressures at which the frictional force and wear sharply increase. The microhardness of sliding surfaces at first rises and then falls. 3. The increase in frictional force is attributable to the fact that, with rise in pressure, the type of linkage between the atoms in the sliding surfaces in contact changes. The wear becomes more intense when the zone with a critical dislocation density moves away from the surface with rise in pressure.

The effect of liquid lubricants on antifriction properties of self-lubricating iron-base composite materials was studied. Crude oil products of the petrolatum type were found to have higher load-carrying capacities and permissible working temperatures than highly refined products. Test results are reported relating to the effect of active lubricant additives on the running-in and wear-resistance characteristics of the materials studied and to the rate of wear of these materials under dry friction conditions. The anti-friction characteristics and fatigue strength of iron-base composite materials in vacuum and in gas atmospheres were studied.

Self-excited vibrations caused by dry friction, which is generally expressed as a function of relative sliding velocities between two solid bodies, are analysed theoretically and observed experimentally. The characteristics of these vibrations are divided into two groups by the type of friction. One is experienced in the case of pure dry friction, where the amplitudes of steady vibration increase with the increase of sliding velocities and the frequencies are nearly equal to the natural frequency of the system. Another occurs in the case of boundary lubrication, where the amplitudes vary slowly with sliding velocities and the frequencies increase with the increase of sliding velocities. In the case of boundary lubrication, self-excited vibrations occur by hard excitation, even if the frictional force increases with the increase of relative velocities. Experimental results obtained from the case of dry friction show good coincidence with the theoretical results.

A method is described for the calculation of the flash temperatures in radial fluid seals during dry friction of the rotating shaft on the stationary seal. For a particular case of practical interest, diagrams are given for the hand computation of the flash temperatures. It was found that previous models can introduce considerable error in this calculation.

High vacuum effects on dry friction coefficient, lubricated friction coefficient and load carrying capacity of lubricants

"Silver" type microcracks in polymethyl methacrylate are self-removed on aging. Dry friction can assist in their accelerated removal; by intensifying relaxation processes and causing flow in the surface layer of the polymer, it is able to restore both the polymer structure in the zones of "silver" type microcracks and also to age obvious microcracks. The restored polymer quality is stable. Dry friction raises the resistance of polymethyl methacrylate to splitting in failure.

Dry friction of a series of crystalline polymers (polypropylene, nylon, PTFE) against steel over a wide range of sliding velocities (4.4–4.4×10−4 cm/sec) and loads (P=7.5–360 kg) with almost complete mutual overlap of the friction surfaces is studied. It is shown that friction of polymer materials against steel may be accompanied by melting of the crystalline polymer (at high velocities) or cold flow (at low velocities) in the surface layers associated with an orientation effect and the appearance of anisotropy.

Expressions are given to determine the torque capacity of a clutch and the rate at which heat is dissipated by dry friction during a single clutch engagement, together with equations to enable calculation of the rubbing-path temperatures as well as temperatures at various depths inside the contacting bodies during the slipping period. It is shown how the maximum friction surface temperature varies with the thickness of the pressure plate and for design purposes a rapid method of calculating temperatures is given when the slipping time is known. Some curves showing the agreement between temperatures determined theoretically and measured experimentally inside a clutch facing during continuous slipping are given. The temperatures attained after regular repeated clutch engagements are considered when cooling is by convection alone and a method of calculation is outlined, when in addition to convection losses radiation losses need to be taken into account. A formula is given to enable the area of the rubbing path to be calculated if the temperature is not to exceed a specified value. In an appendix the temperatures are calculated when the torque linearly decreases with slipping speed and a comparison is made with the case when the torques are assumed to be constant.

Disturbances in the torques and motions in angular contact instrument ball bearing pairs are described and analyzed. Among others, a motion of the ball retainer, analogous to dry friction whirl, is attributed to frictional coupling between balls and retainer, and an interaction between bearings, resulting in several low frequency perturbations, is explained in terms of ball errors. Experimental confirmation is obtained. Contributed to the American Society of Lubrication Engineers by the author. Manuscript received July 15, 1964.

The effect of loading rate on polymer wear in metal-polymer friction pairs is considered. Investigations show that at low loading rates the wear resistance of the polymer specimens increases, evidently owing to orientation of the elements of the molecular structure in the surface layer. This finding applies both to dry friction and friction with lubricants.

Careful measurements have been made of the wear of rubbing steel surfaces as a function of load, distance of travel, and hardness under controlled conditions which eliminated the effect of all factors except adhesion. At normal pressures averaged over the apparent contact area which are less than one third the hardness of the softer material the amount of wear was found to depend linearly on the distance of travel and on the load but was independent of the apparent area of contact. At average pressures greater than one third of the hardness, the depth of wear varied linearly with the distance of travel, was independent of the apparent area of contact for a given average normal stress, but increased many fold for small increases in stress. These findings rationalize the familiar observations on the running‐in of machine surfaces. The results are discussed in the light of the current adhesion theory of dry friction.

A study was made of the room-temperature dry friction and wear of alloys of the systems ZrB2-ZrN and HfB2- HfN in air. It was found that all the materials investigated possess high wear resistance. The lowest values of coefficient of friction (0.3–0.4) and increased wear resistance at a sliding speed of 1 m/sec are exhibited by composites based on hafnium diboride and those containing 40–70 mole % zirconium nitride.