Showing papers on "Contact area published in 1970"

The Contact of Two Nominally Flat Rough Surfaces

Abstract: Most models of surface contact consider the surface roughness to be on one of the contacting surfaces only. The authors give a general theory of contact between two rough plane surfaces. They show that the important results of the previous models are unaffected: in particular, the load and the area of contact remain almost proportional, independently of the detailed mechanical and geometrical properties of the asperities. Further, a single-rough-surface model can always be found which will predict the same laws as a given two-rough-surface model, although the required model may be unrealistic. It does not seem possible to deduce the asperity shape or deformation mode from the load-compliance curve.

Contact between a gas bubble and a solid surface and froth flotation

Abstract: The process of formation of the contact silica surface/air when pressing a liquid meniscus on to the solid/liquid interface is investigated. The kinetics of expansion of the contact area and the final states characterized by contact angles in both directions (by spreading and withdrawing of the contact) are examined. Preliminary data about the effect of surfactants on the velocity of expansion of the contact and on the contact angle and its hysteresis are presented. The new methods applied in the investigations are described. The results are compared with flotation experiment data.

Establishment of contact parameters from surface profiles

Abstract: The problem of obtaining sufficient information from the profile of a rough surface, in order to predict the variation of the true contact area between it and a smooth surface as a function of load, is discussed. The effects of load and orientation on surface profiles were examined experimentally for anisotropic and several isotropic surfaces, all with randomly distributed surface heights, and the observations were analysed by computer. The results for the isotropic surfaces agree well with theory, while those for the anisotropic surface are consistent with proposed simple surface models. The variation of the number of contact spots per unit area with load was also measured directly. If an assumption is made concerning the original height distribution, the predictions for the number of contacts per unit area agree well with the experimental observations, while the discrepancy between theoretical predictions and experimental observations for the number of contacts per unit length is less than 4%.

Real Area of Contact between a Rough Surface and a Softer Optically Flat Surface

Abstract: The mean number of contact spots per unit area and their mean radius were measured and hence the real area of contact deduced for a rough-to-flat interface under normal loading. The contact pressure was varied from zero to half the micro-hardness of the softer material. The resulting experimental evidence did not endorse the predictions from the recent theory of Tzukizoe and Hisakado, which incorrectly assumes that the real contact area is given by the applied pressure P divided by the micro-hardness M of the softer material. It was found that this area equalled K(P/M)n, where the coefficient K and index n depend upon the applied pressure range. A maximum number of contact points was encountered at a dimensionless loading (P/M) approximately equal to 7·5 × 10-3.

Estimation Of The Tangential Stresses In The Stator/Rotor Contact Of Travelling Wave Ultrasonic MotorsUsing Visco-elastic Foundation Models

Abstract: A new stator/rotor contact model of travelling wave ultrasonic motors is developed, in which the stick/slip behavior within the contact area is taken into account. The distributions of displacement and velocity and normal and tangential interface forces between rotor and stator are calculated. The results allow to estimate motor performance like e.g. the torque-speed curves as a function of the motor's parameters. Furthermore, the influence of main material and geometrical parameters and different operating conditions are investigated. The mathematical model developed in this paper can be used as a design tool for optimizing motor performance with the flexibility for a wide variety of geometries and materials.

A Practical Method for Determining Contact Stresses in Elastically Loaded Line Contacts

Abstract: Forecasting life of a cylindrical rolling element under cyclic elastic loading and with misalignment requires determining the exact shape of the mutual contact as well as its area. The classical Hertzian equations for predicting half width of the contact area and resulting mean and maximum stresses are only sufficient to determine the stress levels for symmetrically loaded, uncrowned cylinders under static and dry surface conditions. However, the theory fails in predicting stress distributions for crowned cylinders, symmetrically or asymmetrically loaded and does not describe end of contact phenomena. Toward this end a method has been developed for recording the contact area or “footprint”, created by the symmetrical or asymmetrical static loading of a partially crowned, cylindrical steel roller on an unlubricated flat steel plate. Analysis of the “foot print” yields the load and stress distributions over the contact area and may be employed as a practical tool in experimental investigations and product d...

Minimal insertion force connector

Abstract: An electrical connector of the type receiving a male component lead is characterized by imposition of extremely small or no insertion forces on the male lead in order to make electrical connection. An elastically deformable contact strip forms at least one side of a cavity, and means are provided for deforming the contact strip in a lengthwise direction. When the contact strip is in its relaxed state, the male lead can be inserted freely in the cavity alongside the strip without significant insertion force. The contact strip has a curved portion with a contact area facing the inserted male lead, and a compressible portion connected at one end to the curved contact portion and being substantially fixed with respect to the cavity at the other end. As the contact strip is deformed lengthwise, the contact area tends to expand across the cavity to exert a contact force against the male lead, and the compressible portion shrinks in its lengthwise dimension, thereby wiping the contact area along the male lead for reliable film-removing electrical contact. The contact strip, in some examples, is formed with a portion having a second contact area which resiliently touches the opposite side of the male lead from that contacted by the first contact area. Use of the foregoing connector involves first, inserting the male lead while the contact strip is in its relaxed state, permitting free insertion, second, deforming the contact strip in a lengthwise direction to being about a film wiping contact between the male lead and contact area, and third, holding the contact strip in its deformed configuration for as long as electrical contact is desired to be maintained. Sockets, for example to receive integrated circuit modules with linear arrays of male leads, employ connectors of the type described in multiple configuration, with cavity means positioned for receiving the male leads, a plurality of contact strips deformable lengthwise to yield the firm wiping contact described above, movable means for simultaneously deforming a plurality of the contact strips, and fastener means, such as screws, for holding the contact strips in deformed configuration.

Some Calculations to Assess the Effect of Spin on the Tractive Capacity of Rolling Contact Drives

Abstract: The tractive capacity of rolling with superimposed spinning motion in elastohydrodynamic lubrication is analysed on the basis of a simplification, that the contact area can be divided into strips in the direction of rolling and that the total traction carried by the contact can be obtained from the sum of these strips.For the contact conditions considered here, the slide (or creep) occurs in the rolling direction. It is shown that the traction versus slide relationship for this situation can be constructed from the basic traction data of the lubricant provided by a two-disc machine.The results can be used to assess the performance of a rolling contact drive design. The analysis also highlights the essential ***rheological properties of a good transmission fluid.

Model for Strength of Brittle Materials Built up of Particles Joined at Points of Contact

Abstract: Theoretical analysis of the strength of materials consisting of particles joined along contact areas small in relation to particle size resulted in the model where p denotes strength, D particle size, γ surface energy, d linear extent of the contact area, E modulus of elasticity for the particles, and θ porosity. The first factor has the same form as the Griffith model except that particle size is substituted for crack size; it shows that strength increases inversely with the square root of particle size. The model can be used as a guide in the design of materials such as mortars with low cement content, sand-lime bricks, soil stabilizers, and sintered products. The strengths of mortars made from finely ground quartz and cement and cured at high temperatures were 4 to 40 times higher than those of normal mortars with the same cement/water ratio.

Semiconductor with bonded electrical contact

Abstract: A method is disclosed for batch forming extended beam leads to the pads or contact areas of a solid state device (e.g., monolithic integrated circuit hybrid integrated circuit, discrete device) whereby external connections to the device may be made. The process involves depositing a metal or a plurality of metals over the device in a predetermined manner with the metal adhering to the device contact area but only weakly, if at all, adhering to the remainder of the surface. The device is separated by backside scribing which leaves the beams extending from the contact area of each device.

Analysis of the Elastic Contact of a Hollow Ball with a Flat Plate.

Abstract: : The objective of this program was to conduct a preliminary analytical investigation of the stress field in a hollow sphere in the vicinity of the contact area. The sphere is subjected to a normal load applied through a flat plate. The elastic contact shape and extent were developed for a load of 1000 lb. applied to a one-inch diameter hollow ball with a 0.08 inch thick wall. (Author)

Variable temperature cooling apparatus

Abstract: Variable temperature cooling apparatus in which a cooling element and an element to be cooled are provided with interfitting thermally conducting members arranged so that relative movement between the elements varies the area of contact between the members and hence the rate of heat transfer therethrough. Means for accomplishing the relative movement may be incorporated in or independent of the contact area varying arrangement.

Influence of electric fields on friction electrification between metals and borosilicate glass

Abstract: In a cylindrical geometry, electric fields were applied through the entire contact area between the sliding metal and the glass surface. The maximum electric charges developed on the metal were measured and plotted against the applied voltage producing the field. The metals were high-purity nickel and gold. The borosilicate glass was Pyrex, brand 7740. The experiments with nickel, which has a work function greater than that of the glass, were performed in 10 −7 mm Hg vacuum. The experiments with gold, with a work function smaller than that of glass, were carried out in air at atmospheric pressure. The results show that: 1. 1) There is both asymmetry and a reversed slope portion in the charge vs. voltage plot. 2. 2) For a certain range of reversing fields, the electric charge developed on the nickel is always negative and the charge on gold is always positive.

Experimental determination of adhesion and slip areas in rolling contact

Abstract: An experimental technique has been developed to allow the rapid determination of adhesion and slip areas in steady-state rolling contact.The technique consists in rolling solid black-rubber toroids on a ground-glass plate under carefully controlled conditions. It enables the division of the contact area into slip and adhesion areas to be observed and photographed whilst rolling is taking place.A loading frame was devised to enable rolling with longitudinal shearing traction, rolling with transverse creep, and rolling with spin to be investigated either separately or in combinations.The results of the experiments have been compared with existing theories, and some conclusions as to the accuracy of the theories have been made.

Torque required for changing intersecting angle between warp and weft yarns in shear deformation of woven fabrics

Abstract: Previously, the shear deformation theory which covers general shear deformation composed with biaxial tensile and shearing in finite deformation, has been developed by the authors.In this theory, the moment for rotating the intersecting angle between warp and weft yarns was characterized by five constants by following linear approximation formula.As we have no theoretical knowlege about these constants at this stage, it is important to obtain these constants by experimental method.In this paper, a method for obtaining these constants from yarn measurement is studied. Two yarns are crossovered with each other, and compressible force Fc is applied at the cross-over point, and the torque Tr required for changing the intersecting angle φ is measured as a function of φ and Fc.Several kinds of samples are measured and it has been confirmed that the linear approximation formula is sufficient for practical calculations using the shear deformation theory.In above formula, C1, C2 and Tr0 are the constants related to the yarn property which is concerned with some frictional effect on contact area of these yarns accompanied by the change of φ. C1 represents the pure frictional effect, but Tr0 and C2 have more complicated characteristics. The effect of mechanical entanglement of fibres in the contact area may be represented by Tr0 and C2.On the other hand, C3 and C4 characterize the elastic behaviour. It was found that C2 takes very small value compared with the others and was negligible, and also found that the values of C3 and C4 measured from this direct method must be corrected for practical use.Since these constants are obtained experimentally by this method as a yarn property, the mechanical behaviour of fabrics in general shear deformation state can be calculated theoretically.

Improvements in and relating to Contact Bodies

Abstract: 1,175,911. Drying air. C. G. MUNTERS. 18 Jan., 1967 [26 Jan., 1966], No. 2705/67. Headings B1L and B1R. [Also in Division F4] A contact body comprises corrugated layers 14, 16 compacted to form flow channels for two media, the layers being joined together adjacent one or more edges of the body by beads 38, 40 of thermoplastic or curable adhesive applied to the ridges of the corrugations, and the layers merely abutting one another over the major portion of the contact area. The contact body may be used for drying air using an aqueous solution of calcium or lithium chloride. As shown, the layers are made of foam rubber, foamed polystyrene or asbestos paper impregnated with a curable or thermoplastic resin such as phenol resin or melamine, and are joined at their upper, lower and optionally at their vertical edges. The beads 38, 40 may be applied to one or both corrugations at a contact point. A continuous strengthening bead 42 of plastics, resin or the same adhesive as beads 38, 40 may be applied along one or both sides of at least one edge of each layer. Alternatively adhesive strips may be used. The contact body is employed with counter- or cross-flows. In the latter case, the body is inclined towards an air intake or alternatively, the corrugations of adjacent layers are at different angles to the horizontal.

An apparatus for determining the actual footprint area of tires

Abstract: AN APPARATUS FOR MEASURING THE ACTUAL CONTACT AREA OF TIRES REGARDLESS OF THEIR TREAD DESIGN IS DESCRIBED. THE PROCEDURE IS BOTH RAPID AND ACCURATE. THE METHOD UTILIZES A BANK OF LIGHTS, AN OPAL GLASS PLATE, A SIMPLE LIGHT FOCUSING SYSTEM, AND A SILICON SOLAR CELL WHICH LINEARLY TRANSFORMS THE INCIDENT LIGHT TO AN ELECTRICAL CURRENT. THE REDUCTION IN CURRENT IS THE MEASURE OF THE TRUE CONTACT AREA OF THE TIRE. /AUTHOR/

Static charge generated by pressure-sensitive tapes

Abstract: Two solid surfaces will usually make true contact over a very small fraction of their apparent area. As described by W. R. Harper (1), this can be increased by rubbing but the resultant static charge generation is then modified by thermal gradients and, sometimes, by transfer of material. Pressure-sensitive tapes offer an opportunity to study basic contact-separation charge production without interference from other mechanisms, because the actual contact area is nearly 100%. The theoretical field strength and edge effects over a charged strip of finite width are derived. They predict no noticeable edge effects for a 1 inch wide strip. Charge patterns developed by special powders indicate a corona discharge between two insulating surfaces, and a spark discharge when one surface is a conductor. A neutralizing electrode arrangement has come closest to overcoming the problem of air breakdown. Results are higher and more consistent, but apparently still limited by the small gap breakdown strength of air.

Complete 3-D Elasticity Solutions In TheHalf-space For Constant And LinearlyVarying Pressure Loads

Abstract: The 3-D elasticity solutions for the infinite half-space under point loading conditions form the basis of many currently used algorithms for contact stress analysis. Using standard techniques, the point solution, i.e. Green's functions, can be integrated over various contact areas and various loading profiles. For a rectangular contact area, the subsurface solutions for constant and linearly varying pressure loads had been unavailable because of the difficulty in obtaining the closed form integrals. This paper presents the complete solutions to the integrals for constant and linearly varying loads in both the normal and tangential directions.

Analysis Of Fretting Fatigue Failure

Abstract: The failure of a shaft after a relatively short service life has been analyzed. Based mainly on the fractographic investigation the failure was attributed to fretting fatigue. The fretting was caused by the contact of an inner ring of a roller bearing on the shaft. Material properties and in-service loads showed no significant deviations that could have led to the failure. A new design has been put in service to prevent future failure due to fretting fatigue. A numerical analysis by the finite element method was performed to compare the new to the old design with respect to fretting. The local load situation in the contact area was modeled and the mechanical parameters most important for fretting fatigue were identified. For this purpose the zone of contact was specially treated using gap-friction elements in the finite element models. The possibilities and limitations of a commercial finite element software for the analysis of a contact problem are shown. General rules for the improvement of shrink fit designs are derived. According to the numerical analysis the improved design will be safe with respect to fretting fatigue in the contact area.

Physics of the Slipping Wheel. III. Slip under Camber and Other Forces in Pneumatic Tires

Abstract: An elementary theory is proposed for the origin of the camber force arising when the plane of a traveling wheel is inclined to the vertical and for its interaction with the lateral slip force when the wheel is at an angle to its traveling direction. The theory considers the path of the periphery of the wheel through the ground contact to be deflected from that taken if the wheel were undeformed, and the resulting tangential stress is summed over the contact area. The results are consistent with experiment for small camber angles.

Boundary Element Tools For The Finite Body Unilateral Contact Problem

Abstract: A numerical solution of the three dimensional frictionless contact problem and its data parallel implementation on the Connection Machine system CM-2 is presented. The numerical solution is obtained by means of boundary element discretization of a variational inequality and related extremum principle; the associated Green's function is approximated by means of standard direct boundary element procedure. Important new results for the three dimensional finite body contact problem are reported. The results clearly illustrate the distinct ability of the method to capture the influence of the body shape and loading on the contact area and the pressure acting in it.

Computer Modelling Of Layered Conformal Contact

Abstract: This work is concerned with a finite element investigation of conformal contact between cylindrical and spherical layered components to study the effects of material properties and load on the contact. The study stems from the analysis of the contact between the piston barrel and cylinder block and the piston ball and slipper seat of an axial piston pump but could apply equally well to any components with conformal cylindrical or spherical contact such as actuators or hip joints. The purpose of the research is to develop procedures to aid in the selection of lining, sleeve and seat materials which might be chosen for a particular property (eg. chemical resistance, low friction) and then fixed in or onto a standard, and generally less expensive, bulk material. The nonlinear nature of the problem means that simple material substitution can lead to significant changes in the size of the contact area with a corresponding variation in the contact pressure.