Contact of surfaces and contact characteristics of offset surfaces

Based on differential geometry, the contact problems of two surfaces are discussed in this paper. The relationship between the contact status of two surfaces and that of offset surfaces are also analyzed. For a 5-axis NC machining, some research such as optimization of cutter location and calculation of the geometrical cusp height are important. The research results indicate that the relative normal curvature is an important geometrical invariant for describing the contact state of two surfaces. For point contact two surfaces, the calculation equation for the second order remained error is given. For line contact two surfaces, the condition of the second order line contact is that the principal directions and curvatures of the two surfaces are the same along the contact curve. If two surfaces keep the second order line contact, their two offset surfaces will also keep the second order line contact, and their third order remained errors are also uniform with that of the two offset surfaces.     

Contact of surfaces and contact characteristics of offset surfaces

Based on differential geometry, the contact problems of two surfaces are discussed in this paper. The relationship between the contact status of two surfaces and that of offset surfaces are also analyzed. For a 5-axis NC machining, some research such as optimization of cutter location and calculation of the geometrical cusp height are important. The research results indicate that the relative normal curvature is an important geometrical invariant for describing the contact state of two surfaces. For point contact two surfaces, the calculation equation for the second order remained error is given. For line contact two surfaces, the condition of the second order line contact is that the principal directions and curvatures of the two surfaces are the same along the contact curve. If two surfaces keep the second order line contact, their two offset surfaces will also keep the second order line contact, and their third order remained errors are also uniform with that of the two offset surfaces. __________ Translated from Journal of Dalian University of Technology, 2007, 47(1): 39–44 [译自: 大连理工大学学报]     

Interactive adjustment of surfaces

The dilation or contraction of either a sub-region or the whole of an arbitrary, smooth, single v?alued surface-patch defined in an $\text{X,Y}$ plane by Monge's equation, $\text{Z = F(X,Y)}$, is achieved by superposition of influence surfaces without loss of smoothness.The arbitrary surface is first transformed into a surface defined above the projection of its boundaries into a unit square in the $\text{x,y}$ plane. The unit-square is next partitioned by an orthogonal rectangular grid and then, by a series of further transformations, approximately into a circle of unit radius.Within the circle of unit radius a second, influence surface is next postulated and its $\text{z}$ values superimposed on the transformed arbitrary surface at corresponding nodes of the partitioning grid. This influence surface is defined as the shape assumed by a thin flexible elastic plate bounded by the circle and subjected to an eccentric, normal point-displacement at any desired grid-node. Displacements at other nodes are calculable by Michell's two-term closed solution for encastré boundaries or approximately by Föppl's or Clebsch's series solutions for semi-restrained boundaries.If an arbitrary surface is displayed as a net of profile-curves on a computer graphics terminal, the locations and amounts of desired displacements to effect shape-changes can be estimated. Influence surfaces “centred” at such nodes can then be specified and superimposed in the unit circle. Inverse transformation from unit circle to the original arbitrary surface then yields a modified surface for redisplay and reassessment.If a surface having a set of arbitrary $\text{Z}$ values at particular grid-nodes is required, a set of influence surfaces, each appropriate to unit-displacement at each node of the set may be scaled and superimposed to yield a smooth corrective surface or to generate a surface, ab initio.In all cases the influence of corrective surfaces may be limited to sub-regions within the global boundaries of arbitrary surfaces.     

Friction between metal surfaces

The conditions which exist at successfully run-in engineering surfaces are reviewed and mechanisms of friction are discussed with some emphasis on those most likely to be applicable under these conditions. Some important gaps in fundamental knowledge are indicated.     

Machining of slot surfaces

The shaping of external and internal slot surfaces is considered. Corresponding machining methods are outlined, as well as methods of monitoring the basic slot parameters.     

Wear of wheel-rail surfaces

The interactions between the tribological stress parameters and the measurable wear quantities during rolling with slip are examined with the help of experimental results already published and the results of some new investigations by the authors of this paper.It is from these that the following model for wear behaviour is derived.

• 1.(1) The wear quantities (wear volume and mass loss due to wear) are first of all proportional to the frictional work.
• 2.(2) The factor of proportionality between frictional work and wear volume depends on (a) the structure of the tribological system (material pairing and environment) and (b) the temperature of the contacting surfaces. This temperature is a function of the stress collective, the influence of which may be approximated as the relation of frictional power to contact area, the surface temperature thus governing the transitions between mild and severe wear.

     

Electron microscopy of surfaces

Electron beam techniques used to study clean surfaces and surface processes on a microscopic scale are reviewed. Recent experimental examples and possible future developments are discussed. Special emphasis is given to (i) transmission diffraction and microscopy techniques, including atomic imaging; (ii) Auger microscopy on bulk and thin film samples; (iii) secondary electron microscopy, especially low energy secondaries for work-function imaging and photoelectron imaging; and (iv) reflection electron microscopy and diffraction.     

Material surfaces for electron-optical equipment

Electron-beam inspection systems for VLSICs and electron-beam pattern generation require exact positioning of the electron beam on the specimen. In this connection the question arises as to what properties the walls and diaphragms in the ambience of the path of the electron beam are required to have with respect to material, surface layers and cleanness in order to exclude their collecting electric charges that will undesirably influence the electron beam. Experimental investigations of this problem by means of electron-shadow projection show that the conductivity of a material should not be the sole criterion for its choice, but that its behavior under exposure to backscattered electrons and secondary electron emission must also be taken into account. Graphite of poor conductivity was found to be particularly favorable. Electroplated surfaces are often less favorable than untreated surfaces. Magnetic materials always exhibit minor defects. For cleaning, a carefully controlled ultrasonic technique using conventional cleaning agents is necessary and sufficient.     

点采样曲面的曲率估计

本文提出一种直接在点采样曲面上计算曲面的高斯曲率、平均曲率及主曲率等局部微分性质的方法。首先，为了去除测量产生的噪声和误差，引入高斯核函数为每个采样点加权；接着计算每个采样点的最近邻域点集；然后用双三次B样条曲面最小二乘拟合邻域点集，构造局部参数曲面来逼近原始曲面，以局部参数曲面的曲率估计点采样曲面的曲率；最后给出曲率估计的应用。实验结果表明，该方法能有效地反映曲面的基本特征。     

Wear mechanisms of boundary-lubricated surfaces

Examination of steel specimens tested under boundary lubrication conditions indicates the existence of three distinct processes which lead to wear particle formation: deformation and fracture of original machining marks; deformation and fracture of edges of plowing tracks; delamination. Deformation and fracture of original machining marks and the raised edges of the plowing furrows generate wear particles which are 1–15 μm in the largest dimension. The process of delamination, however, generates particles that are 100 μm wide. The formation of these large wear particles coincides with a high rate of wear and scuffing failure.     

Cylindrical milling of ruled surfaces

In this work a methodological scheme for a reduction of both the try-out and lead-time of complex dies is presented. The finite element simulation of the system press/tool behaviour along the stamping process results in criteria for the best design of high-cost dies/punches. Modifications of the main geometry, components and functional parameters are so recommended. Die deflection during the pressing process is in this work investigated. With the proposed methodology die manufacturers are able to avoid errors coming from die deformation due to their asymmetrical shape. At the same time, time of manual adjustment and polishing is reduced in a 30%. Examples are deeply explained as well as experimental evidences.     

Measurement of coated abrasive surfaces

The measurement and characterisation of coated abrasive surfaces are reported. Four different techniques were used with the emphasis on simplicity, sensitivity and, most important, repeatability. As a process control technique stylus measurement with simple statistical analysis was found to satisfy most of the necessary requirements for “shop floor” use.