Dimensional Measurement

Dimensional measurement using lasers is illustrated by measurement of wire diameter. When a fine wire is inserted in the highly collimated beam of a laser, the light is diffracted by the wire to form a distinct line of spots perpendicular to the length of the wire. The spots appear at angles 9 with respect to the direction of the laser beam. 9 is given by... 

There are basically two possible approaches for real-time SPC. The first, done on-line, involves the rapid dimensional measurement of a part or a non-dimensional bulk... 

The first question is what kind of information the chemical control can and should provide. Must it be a qualitative and/or quantitative analysis, is it based on a one- or two-dimensional measurement and should the latter consist of an analog and/or digital display The meaning of all this can be well illustrated by the example of the differential titration (see Fig. 5.1) of equivalent amounts of a strong acid (cf., Fig. 2.17, AA) and a weak acid (cf., Fig. 2.18, BA, pK, = 4). 

There are two-dimensional NOE experiments (see below, Section 2.3), but first we shall consider the one-dimensional measurements, which are of two types. To make these clear we shall use molecules 1 and 3. 

Perimeter is the measure around a polygon. Perimeter is an addition concept it is a linear, one-dimensional measurement. 

Decision levels and detection limits are relatively easy to define and evaluate for simple" (zero dimensional) measurements. The transition to higher dimensions and multiple components introduces a number of complications and added assumptions related to the number and identity of components, shapes and parameters of calibration functions and spectra, and distributional consequences of non-linear estimation. 

Densities of cured resins were obtained by accurately weicfiing rectangular solids which were precisicxi-machined from expended tensile specimens. Approximate dimensions of the specimens were lcmxlcmxO.32 cm accurate dimensional measurements were obtained using a micremeter. 

Figure 5. Eigenvector Projection (Principal Vector Plot). A plane is least squares fitted to all the data. This plane constitutes a two-dimensional window into the multi—dimensional measurement space. The projections of the object points down to the plane are visualized in this plot.

Area is a two-dimensional measure. You re counting up how many squares — all the same size — fit into some flat region. You use area measures for floors in buildings and spaces in parking lots, as well as when you want to find out how much room there is in a backyard. 

Volume is a three-dimensional measure and tells you how many cubes of a particular size fit into an object. Volume measures tell you about the inside of a refrigerator or the size of a cardboard carton. 

To determine the volume change of a given material following immersion, 1" by ln pieces of the subject materials were individually placed in beakers which contained the halogenated ethanes and the particular PCB of this study. At 1, 4, and 24h following immersion, the material was removed from its solvent and dimensional measurements obtained within 1 min. following removal. 

It is perhaps less easy to excuse the lack of a chapter on non-destructive testing. The reason is a mixture of the fact that the major NDT techniques are, in the main only applied to a few particular rubber products and the realisation that to properly describe all methods would require a book, not a chapter. It is, however, worth remembering that it is not only ultrasonics, radiography, holography and so on which are non-destructive. A number of the more traditional rubber tests, for example electrical properties, many dynamic tests, hardness and dimensional measures leave you with the product intact. There are text books which deal with NDT techniques generally and. a comprehensive review of NDT of polymers by Gross in Handbook of Polymer Testing3. 

The most common dimensional measurements relate to the size of test pieces because this information is required for virtually all physical test methods. There is also sometimes need to measure dimensions of components of the apparatus, such as the thickness of spacers in compression set tests. Other aspects of dimensional measurement that are relevant to rubber testing include extensometry, surface roughness, dimensional stability and dispersion. 

On-line inspection is a form of testing and in this context dimensional measurements are those most often made. Apart from gauges, micrometers and so on, there are various optical, electrical, nuclear and other methods which may have advantages in production circumstances. Descriptions of the use of such techniques can be found in the literature and in manufacturers data sheets. Some fairly recent examples relating to rubber and plastics products are given in references 12 - 16. However, the various techniques will not be reviewed here. 

These references are of course by no means exhaustive, many more particular cases of dimensional measurement will have been described and a number of methods of interest will be mentioned in later chapters in conjunction with particular physical tests. 

The various direct methods of estimating dispersion are essentially dimensional measurements on more or less a microscopic scale and this is just one example of the value of microscopy for fault diagnosis in rubber products. Dispersion measurements are normally made on cured rubber although it is possible to prepare test pieces from some uncured materials. 

Figure 6.4. Scatter diagram of the results of two groups of subjects (open and filled spheres) in a three-dimensional measurement space. The groups differ in location. The difference between the groups can be fully described only by considering all three variables simultaneously.

Figure 6.7. Scatter diagram of two groups of subjects (crosses (treatment) and circles (control)) in a two-dimensional measurement space. In (a), the difference between the groups is the largest source of variation in the data and the first PC will describe the difference. In (b), the difference between the groups does not constitute the largest source of variation in the data and PCA will therefore not detect the difference. By projecting the data onto the dotted line, it can be seen that the two groups are completely...

This basic approach to the special interpretation shows that there are correlations which cannot be studied satisfactorily using two-dimensional sections. However, they also show that there are very efficient methods to extrapolate three-dimensional realities from two-dimensional measurements. 

A company sent a set of gage blocks to NBS at regular intervals to be calibrated. NBS dutifully calibrated the blocks and provided a calibration certificate and data report. The company kept their current NBS calibration certificate on file to prove to their auditors that they were traceable to NBS for dimensional measurements. The problem was that each time the blocks returned to NBS, our people found the seal unbroken. The gage blocks had never been used, yet the company satisfied the auditors that they were traceable to NBS as required. 

Croarkin MC, Varner RN (1982) Measurement assurance for dimensional measurements on integrated circuit photomasks. NBS Technical Note 1164... 

Dimensional measurements taken when the material is hot will be much larger than when the material is at room temperature and 50% relative humidity. This means that parts that may be in specification if measured during machining may be too small when reinspected later. Experience is needed to know how much extra must be allowed so that on cooling the dimensions will be correct. 

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