Engineering Metrology

Transcription

1 Albaha University Faculty of Engineering Mechanical Engineering Department Engineering Metrology Lecture 04: Angular Measurements Ossama Abouelatta Mechanical Engineering Department Faculty of Engineering Albaha University Aims This lecture aims: to identify angular measurement. to describe angle gauges, Vernier bevel protractors, spirit level and autocollimator and its uses. to describe Sine bar and Sine center and its uses. Mechanical Engineering Department Lecture (4): Angular Measurements (2)

2 Outlines Introduction Units of Angular Measurement Angle Gauges Angle Gauge Sets Vernier Bevel Protractors Spirit Level Autocollimator Angular measurement by triangulation methods Sine bar Sine center Mechanical Engineering Department Lecture (4): Angular Measurements (3) Introduction Such work, is the necessary basis of the linear measurement carried out by the engineer. since almost invariably this takes the form of comparing the size of a workpiece or other part with the known size of an end gauge, i.e. comparative measurement. To carry out such measurements successfully, that is, to the order of accuracy required, often calls for ingenuity in the use of relatively simple equipment. It always requires the application of certain simple principles, together with patience, a systematic approach to a measurement problem, and the use of techniques only acquired by practice. These points are perhaps best illustrated by the apparently simple task of establishing the size of a plain gap gauge. There can be no substitute for experience in carrying out such a measurement. Mechanical Engineering Department Lecture (4): Angular Measurements (4)

3 Units of Angular Measurement The NATURAL unit of angular measurement is the circle. In the sexagesimal system the circle is divided into 360 degrees ( ); each degree is subdivided into 60 minutes (') and each minute into 60 seconds (''). An alternative unit of measurement is the radian, the angle subtended by an arc of length equal to the radius as shown in the figure. Mechanical Engineering Department Lecture (4): Angular Measurements (5) Units of Angular Measurement The radian is of greater significance than the degree in higher mathematics, and is of some convenience in Metrology when dealing with very small angles where the values of the sine and tangent of the angle are very nearly the same as the value of the angle in radians. From the above definitions: Mechanical Engineering Department Lecture (4): Angular Measurements (6)

4 Angle Gauges Angle Gauges are available as thin series gauges 50 mm x 9 mm or to NPL Specification MOY/SCMI/18 combination angle gauges. Both styles are made from high quality steel and hardened to 800 Hv (64 Rc) Minimum. Each gauge is lapped with a superior, highly reflective, wringable finish. Flatness of each lapped face is 0.2 µm or less and the faces are square to the ground sides within 2 µm. Angle is controlled to ±2 seconds of arc. All gauges, sets and individuals, can be supplied with a calibration certificate with a measurement uncertainty of ± 1 second of arc. The 27, 16 and 15 piece in addition to the gauges listed here also contain a plain parallel piece and a precision edged prism for light gap tests. Gauges are also available as individuals. The contents of 27 piece 16 piece and 15 piece sets have been calculated so that it is possible to wring together gauges to form 32,400 different angles from to in 10 second increments. Mechanical Engineering Department Lecture (4): Angular Measurements (7) Angle Gauge Sets Set A 1 No. each 1, 3, 9, 27 & 41 Degrees 1 No. each 1, 3, 9 & 27 Minutes 1 No. each 6, 18 & 30 Seconds 1 No. Precision square block Set B 1 No. each 1, 3, 5, 15, 30 & 45 Degrees 1 No. each 1, 3, 5, 20 & 30 Minutes 1 No. each 6, 12 & 30 Seconds 1 No. Precision square block Mechanical Engineering Department Lecture (4): Angular Measurements (8)

5 Angle Gauge: Example 1 Set A Show how the blocks can be built up to give an angle of 14 24' 18''. Set A 1 No. each 1, 3, 9, 27 & 41 Degrees 1 No. each 1, 3, 9 & 27 Minutes 1 No. each 6, 18 & 30 Seconds 1 No. Precision square block Solution: = ' 18'' Mechanical Engineering Department Lecture (4): Angular Measurements (9) Angle Gauge: Example 1 Set A Show how the blocks can be built up to give an angle of 14 24' 18''. Set A 1 No. each 1, 3, 9, 27 & 41 Degrees 1 No. each 1, 3, 9 & 27 Minutes 1 No. each 6, 18 & 30 Seconds 1 No. Precision square block Solution (Best): = ' 18'' Mechanical Engineering Department Lecture (4): Angular Measurements (10)

6 Angle Gauge: Example 2 Set B Show how the blocks can be built up to give an angle of 24 10' 18''. Set A 1 No. each 1, 3, 9, 27 & 41 Degrees 1 No. each 1, 3, 9 & 27 Minutes 1 No. each 6, 18 & 30 Seconds 1 No. Precision square block Solution: = ' 18'' Mechanical Engineering Department Lecture (4): Angular Measurements (11) Vernier Bevel Protractors Mechanical Engineering Department Lecture (4): Angular Measurements (12)

7 Vernier bevel protractor As well as linear measurement, vernier scales can equally well be used to determine angular measurement. The vernier bevel protractor again uses the principle of two scales, one moving and one fixed. Universal bevel protractor Mechanical Engineering Department Lecture (4): Angular Measurements (13) Vernier bevel protractor The fixed scale is graduated in degrees, every 10 degrees being numbered 0, 10, 20, 30, etc. The moving or vernier scale is divided into 12 equal parts which occupy the same space as 23 degrees on the fixed scale. This is 5 minutes less than two divisions on the fixed scale. Vernier protractor scale Self-Training Mechanical Engineering Department Lecture (4): Angular Measurements (14)

8 Examples Mechanical Engineering Department Lecture (4): Angular Measurements (15) Spirit Level This figure shows a section through the vial of a spirit level; the chain dotted outline represents the frame in which the vial is mounted. The sensitiveness of the level depends primarily upon the radius R to which the inside of the vial is made. Spirit levels are frequently used to detect a small change of height h over length l of the level base, or of a platform upon which the level rests. The value of h for a one division displacement of the bubble is directly proportional to the value of l. Mechanical Engineering Department Lecture (4): Angular Measurements (16)

9 Spirit Level Suppose a level is required to register an angular change of 20 sec of arc per division, for a displacement of the bubble relative to a scale divided into 2.5 mm divisions. Since the angular displacement is very small, where S is the linear change measured by the scale, and for the required conditions, and when has this value, S = 2.5 mm. Mechanical Engineering Department Lecture (4): Angular Measurements (17) Autocollimator This is the most important of the items of equipment for the measurement of small angular displacements and, since it operates on a fairly simple optical principle, an outline of the optical features of the instrument warrants study. This figure shows a simple convex lens having a focal plane represented by AB. Suppose a point source of light is placed at the focal centre of the plane, position S. The lens will collect this light and distribute it as a parallel beam as indicated by the outward-going arrows. If this beam strikes a reflecting surface exactly parallel to the focal plane AB, the light will return along the same path and be refocused at the point S. Optical principle of autocollimator Mechanical Engineering Department Lecture (4): Angular Measurements (18)

10 Autocollimator However, if the reflecting surface (as represented by CD) makes an angle with the focal plane, the reflected rays will make an angle 2 with respect to the incident rays, as shown by the arrows returning towards the lens. Since the beam remains parallel on its return path, not all of it will re-enter the lens, but that portion which does return through the lens will be focused at a point in the focal plane represented by T. The apparent shift (h) of the light, when re-focused by the lens, is directly proportional to the magnitude of the angle and so a linear displacement can be used to measure the small angular displacement which has been its cause. Optical principle of autocollimator Mechanical Engineering Department Lecture (4): Angular Measurements (19) Autocollimator The elementary system described, while displaying the principle of an autocollimator, could not be arranged to provide a practical instrument and the figure shows, in outline, the more conventional arrangement. Optical system of autocollimator Mechanical Engineering Department Lecture (4): Angular Measurements (20)

11 Autocollimator Mechanical Engineering Department Lecture (4): Angular Measurements (21) Angular measurement by triangulation methods The shown figure illustrates a simple scheme by which a rule can be used to set out an angle ( ) to moderate accuracy. The arrangement is based upon the fact that for any particular angle, the sides of a right angled triangle will have precise ratios, these ratios being available in trigonometrical tables. From the diagram, sin = 1/2.56, or cosecant = 2 56 and since cosec 23 = , = 23 very nearly. Obviously, as the angle approaches 90, the accuracy of the method will be low, because, for any small error in linear measurement there will be a large error in angle. Mechanical Engineering Department Lecture (4): Angular Measurements (22)

12 Sine bar This figure shows a common form of sine-bar. Essentially the equipment has two cylindrical 'feet' of exactly equal diameters positioned at centre distance (l) of exactly 125 mm (5 inches) or 25.4 mm (10 inches). The upper face of the sine-bar must be exactly parallel with the plane passing through the axes of both cylinders. Very small departures from these ideal conditions occur in most sine-bars which limits the accuracy to which angles may be set. Mechanical Engineering Department Lecture (4): Angular Measurements (23) Slip and block gauges Mechanical Engineering Department Lecture (4): Angular Measurements (24)

13 Sine Centers For larger work, the sine-bar principle can be extended by making equipment in the form of a sine-table, or of sine-centers. Mechanical Engineering Department Lecture (4): Angular Measurements (25)