PDT 1103 METROLOGY CHAPTER 7 Angle measurement OVERVIEW

PDT 110/3 METROLOGY CHAPTER 7 Angle measurement

OVERVIEW • From division of the circle, all of angular measurement is derived and provable. • Angle deal with direction–not space. • Angle is a relationship between two lines. • We can measure this relationship if we extend the lines until they intersect. • The intersection is called the vertex, and the lines are sides.

Overview

Overview • Right angle - one-fourth of circle or one quadrant. • Acute angle - an angle measures less than 90º. • Obtuse angle - an angle measure more than 90º.

Overview

Angle Measurement • The instrument for angle measurement are equivalent to those for linear measurements and range from simple scaled instrument to highly sophisticated types using interferometry.

Angle Measurement • Interferometry is a family of techniques in which waves, usually electromagnetic, are superimposed in order to extract information about the waves.

Equivalent Instruments The angular measurement instruments closely approximate their linear measurement equivalents.

Protractor • For measuring angles, the simple protractor is equivalent to the rule for measuring length. • Like a steel rule, the simple protractor has limited use. • But mechanical additions to the rule resulted in the versatile combination square (e. g: vernier caliper & height gage). • We make similar modifications on the simple protractor, we get universal bevel protractor.

Universal bevel protractor

Universal bevel protractor • The heart of this instrument is a dial (graduated in degrees). • Grouped into four 90º quadrants. • The degrees are numbered to read either way: from zero to 90, the back to a zero, which is opposite the zero you started at. • The vernier scale is divided into 24 spaces, 12 on each side of zero, numbered 60 -0 -60. • The difference between one vernier division and two dial division is 1/12 degree or 5 minutes. • When angle is an exact degree, the zero graduations of the vernier and the two 60 -minute graduations line up with dial division.

Universal bevel protractor The degree scales

Degree are read directly, but minutes are read with vernier scale Care must be used to read the minutes from the correct pair of linedup graduation.

Application of vernier protractor • We can determine the angle or degrees in any arc with the universal bevel protractor. • When protractor is set at 90, (figure B), all four angles are as read. • If you turn the blade counterclockwise (figure A) which happens in two position as shown. • If you turn the blade clockwise(figure C), the angle read will be formed only in two places, which are always from the blade to the base rotating clockwise.

When reading from 90º, these are positions where the angle and its supplement are found. When reading from 90º, there is little danger of confusing the angle and its supplement.

Errors when using bevel protractor

The level • One of the most useful measurement instruments is the level. • These ‘bubble instrument’ are widely use in engineering metrology. • For precision measurement: – Precision levels – Clinometers – Theodolites • Use in the shop (less precision measurement): –Bench level –Mechanic’s level

Precision level Bench level Clinometer Mechanic’s level Theodolite

Spirit level • To keep the level from freezing, the tubes were filled with ‘spirit of wine’ which led to the term spirit. • The precision of a level depends in the curvature of the glass tube. • Cheap levels have a bent tube, but precision level have straight tube that are internally ground to the desired result. • The larger the radius of the tube, the greater the sensitivity(the same for a level and are designated by the discrimination of the instrument).

Spirit level

Spirit level

Spirit level

Thermal error • Temperature affects levels-shrinking the bubble inside the tube. • Like other high-implication instruments, a high sensitivity level is calibrated at the standard temperature ( 20 ºC or 68 ºF). • When the level is warmed, the liquid expands, reducing the length of the bubble making the reading smaller than true value. • Sensitivity also depends on the viscosity of the fluid in the vial. • Level filled with low viscosity liquids have high vapor pressure which can result in some erratic readings when the vial is heated.

Reading level The centered position is marked by long graduations-or sometimes a dot at each end. The readings are the number of divisions that the bubble moves.

Level adjustment

Disadvantage of level There are four principal disadvantage of levels: 1. General ignorance about their proper use and application. 2. The time required to settle down. 3. Their single sensitivity characteristic. 4. They do not produce any output that can be used as loading for a measurement system.

Clinometer • The block level is restricted to relatively small angles. • This restriction is removed in the clinometer. • It is a level mounted in a frame so that the frame may be turned at any desired angle to the horizontal reference.

Clinometer A few of many types of clinometers

Trigonometric functions • The trigonometric functions, formed by the sides of triangles. • For elementary angle computation, we simply use the natural functions: –Sine –Cosine –Tangent

Sine bar • The sine bar, a steel bar that has a cylinder near each end, forms a hypotenuse. • The instrument is designed with a distance between the cylinder that make computation easy. • When one of the cylinders is resting on a surface, you can set the bar at any desired angle by simply raising the second cylinder. • You obtain the desired angle when the height difference between the cylinder id equal to the sine angle multiplied by the distance between the centers of the cylinders.

The sine bar is a hypotenuse of triangle frozen in steel with a length selected to minimize computations.

Comparison measurement using sine bar • We use gage blocks for measurement of angles with high amplification instrumentation and measure by comparison. • The sine bar is used to construct an angle equal to angle that we need to measure, but the constructed angle is in opposite direction of the actual angle. • Part is supported by sine bar. • The deviation can be detected by measuring the parallelism between the part feature and the reference surface (using dial indicator).

Sine blocks, sine plates and sine tables • Sine blocks are wide sine bar (a sine instrument wide enough to stand unsupported). • Sine plates are wider sine blocks. (a sine instrument rest on an integral base). • Sine tables are still wider. (a sine instrument is an integral part of another device, such as machine tool).

Sine Tables

Mechanical angle measurement • Another method of angle measurement, called mechanical indexing and its related tools. –The dividing head, indexing head or index head • Were developed specifically for machining rather than measurement. • This devices were originally developed to divide circles into equal division. • Because the circle is the standard for angles, any division of a circle is angle measurement, whether we measure it in numbers of division or degrees or minutes.

Mechanical angle measurement • There are three principal classes of index head. –Dial index head –Plain index head –Universal

Dial index head • It consist of horizontal spindle mounted on the base that rests on a reference surface. • On one end of the spindle is a plate for clamping part. • The other end is a wheel for turning the spindle. • The plate which also an index plate, contains holes with a plunger that engages the stationary housing. • The typical plate has 24 holes, which provides 360º rotation in 15º increment.

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