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Chapter 3: Basic of Applied Mechanical Measurement

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Chapter 3: Basic of Applied Mechanical Measurement CHAPTER 3: BASIC OF APPLIED MECHANICAL MEASUREMENT 3.1. Introduction Basic quantities for measurement in mechanical field are measurement for length, mass, time, temperature and angle. These quantities can be obtained using certain measurement devices. Several measurement devices can measure some of the quantities, while the remains need to use specific measurement devices. Classification of mechanical measurement and its measurement devices that will be discussed are as follows: No Mechanical quantities Measurement devices 1 Linear dimension • ruler • caliper • micrometer caliper • vernier caliper • dial gauge 2 Mass • mechanical balance • spring balance 3 Force • spring coil • proving coil • strain gauge • load cell 4 Torque • brake • dynamometer • strain gauge • transducer Temperature, pressure and other quantities will be discussed later. 3.2. Linear Dimension Measurement 3.2.1 Micrometer A micrometer is a widely used device in mechanical engineering for precisely measuring thickness of blocks, outer and inner diameters of shafts and depths of slots. Appearing frequently in metrology, the study of measurement, micrometers have several advantages over other types of measuring instruments like the Vernier caliper - they are easy to use and their readouts are consistent. There are three types of micrometers based on their application: • External micrometer • Internal micrometer • Depth micrometer 41 An external micrometer is typically used to measure wires, spheres, shafts and blocks. An internal micrometer is used to measure the opening of holes, and a depth micrometer typically measures depths of slots and steps. The precision of a micrometer is achieved by a using a fine pitch screw mechanism. Figure 1: External, internal, and depth micrometers 3.2.1.1 Reading an Inch-system Micrometer. The spindle of an inch-system micrometer has 40 threads per inch, so that one turn moves the spindle axially 0.025 inch (1 ÷ 40 = 0.025), equal to the distance between two graduations on the frame. The 25 graduations on the thimble allow the 0.025 inch to be further divided, so that turning the thimble through one division moves the spindle axially 0.001 inch (0.025 ÷ 25 = 0.001). To read a micrometer, count the number of whole divisions that are visible on the scale of the frame, multiply this number by 25 (the number of thousandths of an inch that each division represents) and add to the product the number of that division on the thimble which coincides with the axial zero line on the frame. Figure 2: Inch Micrometer The result will be the diameter expressed in thousandths of an inch. As the numbers 1, 2, 3, etc., opposite every fourth sub-division on the frame, indicate hundreds of thousandths, the reading can easily be taken mentally. Suppose the thimble were screwed out so that graduation 2, and three additional sub-divisions, were visible (as shown in Fig. 2), and that graduation 10 on the thimble coincided with the axial line on the frame. The reading then would be 0.200 +0.075 +0.010, or 0.285 inch. 42 3.2.1.2 Reading a Metric Micrometer. The spindle of an ordinary metric micrometer has 2 threads per millimeter, and thus one complete revolution moves the spindle through a distance of 0.5 millimeter. The longitudinal line on the frame is graduated with 1 millimeter divisions and 0.5 millimeter subdivisions. The thimble has 50 graduations, each being 0.01 millimeter (one-hundredth of a millimeter). To read a metric micrometer, note the number of millimeter divisions visible on the scale of the sleeve, and add the total to the Figure 3: Metric Micrometer particular division on the thimble which coincides with the axial line on the sleeve. Suppose that the thimble were screwed out so that graduation 5, and one additional 0.5 subdivision were visible (as shown in Fig. 3), and that graduation 28 on the thimble coincided with the axial line on the sleeve. The reading then would be 5.00 +0.5 +0.28 = 5.78 mm. Some micrometers are provided with a vernier scale on the sleeve in addition to the regular graduations to permit measurements within 0.002 millimeter to be made. Micrometers of this type are read as follows: First determine the number of whole millimeters (if any) and the number of hundredths of a millimeter, as with an ordinary micrometer, and then find a line on the sleeve vernier scale which exactly coincides with one on the thimble. The number of this coinciding vernier line represents the number of two-thousandths of a millimeter to be added to the reading already obtained. Thus, for example, a measurement of 2.958 millimeters would be obtained by reading 2.5 millimeters on the sleeve, adding 0.45 millimeter read from the thimble, and then adding 0.008 millimeter as determined by the vernier. Note: 0.01 millimeter = 0.000393 inch, and 0.002 millimeter = 0.000078 inch (78 millionths). Therefore, metric micrometers provide smaller measuring increments than comparable inch unit micrometers—the smallest graduation of an ordinary inch reading micrometer is 0.001 inch; the vernier type has graduations down to 0.0001 inch. When using either a metric or inch micrometer, without a vernier, smaller readings than those graduated may of course be obtained by visual interpolation between graduations. Vernier Micrometer By adding a vernier to the micrometer, it is possible to read accurately to one ten- thousandth of an inch. The vernier markings are on the sleeve of the micrometer and are parallel to the thimble markings. There are 10 divisions on the vernier that occupy the same space as 9 divisions on the thimble. Since a thimble space is one thousandth of an inch, a vernier space is 1/10 of 9/1000 inch, or 9/10000 inch. It is 1/10000 inch less than a thimble space. Thus, as in the preceding explanation of verniers, it is possible to read the nearest ten-thousandth of an inch by reading the vernier digit whose marking coincides with a thimble marking. 43 In figure 6-6 (A), the last major division showing fully on the sleeve index is 3. The third minor division is the last mark clearly showing (0.075). The thimble division nearest and below the index is the 8 (0.008). The vernier marking that matches a thimble marking is the fourth (0.0004). Adding them all together, we have, The reading is 0.3834 inch. With practice these readings can be made directly from the micrometer, without writing the partial readings. Figure 6-6.–Vernier micrometer settings. Practice problems: 1. Read the micrometer settings in figure 6-6. Answers: 1. (A) See the foregoing example. (B) 0.1539 (C) 0.2507 (D) 0.2500 (E) 0.4690 (F) 0.0552 44 3.2.2 Vernier scale A vernier scale lets one read more precisely from an evenly divided straight or circular measurement scale. It is fitted with a sliding secondary scale that is used to indicate where the measurement lies when it is in-between two of the marks on the main scale. It was invented in its modern form in 1631 by the French mathematician Pierre Vernier (1580- 1637). In some languages, this device is called a nonius, which is the latin name of the Portuguese astronomer and mathematician Pedro Nunes (1492-1578) who invented the principle. Figure 4: A set of vernier calipers. When a measurement is taken by mechanical means using one of the above mentioned instruments, the measure is read off a finely marked data scale ( the "fixed" scale, in the diagram). The measure taken will usually be between two of the smallest gradations on this scale. The indicating scale ("vernier" in the diagram) is used to provide an even finer additional level of precision without resorting to estimation. An enlarged view of the calipers in Figure 5 shows they have an accuracy of 0.02 mm. The reading is 3.58 mm. The 3 mm is read off from the upper (fixed) data scale. The 0.58 mm is obtained from the lower (sliding) indicating Figure 5: Large view of vernier caliper scale at the point of closest alignment between the two scales. The superimposed red markings show where the readings are taken 3.2.2.1 Construction The indicating scale is constructed so that when its zero point is coincident with the start of the data scale, its gradations are at a slightly smaller spacing than those on the data scale and so do not coincide with any on the data scale. N gradations of the indicating scale would cover N-1 gradations of the data scale (where N is the number of divisions the maker wishes to show at the finer level). 45 3.2.2.2 Use When a length is measured the zero point on the indicating scale is the actual point of measurement, however this is likely to be between two data scale points. The indicator scale measurement which corresponds to the best-aligned pair of indicator & data gradations yields the value of the finer additional precision digit. Examples On instruments using decimal measure, as shown in the Figure 6, the indicating scale would have 10 gradations covering the same length as 9 on the data scale. Note that the vernier's 10th gradation is omitted. On an instrument providing angular measure, the data scale could be in half-degrees with an indicator scale providing 30 1-minute gradations (spanning 29 of the half-degree gradations). Figure 6: Measurement process 46 3.2.3 Caliper A caliper is a device used in the metalworking field of mechanical engineering, to measure the distance between two symmetrically opposing sides.
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