Angular measurements

CHAPTER Angular Measurement

Presentation Prepared by Prof. Naman M. Dave Assistant Prof. (Mechanical Dept.) Gandhinagar Institute of Technology

Please refer this file just as reference material. More concentration should on class room work and text book methodology.

Introduction • The angle is defined as the opening between two

lines which meet at a point. • Circle is divided into 360 parts, each part is called a

degree ( º). • Each degree is divided in 60 minutes ( ') and each

minute into 60 Seconds ( “) • Unit of angle derived from theoretical

considerations is the radian, defined as the angle subtended at the centre of a circle by an are length equal to radius of circle.

The general formula for converting from degrees to radians is to simply multiply the number of degree by Π /180°. The general formula for converting from radians to degrees to simply multiply the number of degree by 180°/(Π)

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The general formula for converting from degrees to radians is to simply multiply the number of degree by Π /180°. The general formula for converting from radians to degrees to simply multiply the number of degree by 180°/(Π)

Angle Measurement Instrument

Line Standard Angular Measuring Devices • Protractors • Universal Bevel Protractors Face Standard Angular Measuring Devices • Sine bar • Sine Center Measurement of Inclines • Spirit Level • Clinometer Angle Comparators • Autocollimators

Vernier Bevel protractor • The simplest instrument for measuring the angle

between two faces of component. • Main scale on the protractor is divided into

degrees from 0 to 90 each way.

Vernier Bevel protractor

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http://www.craftsmanspace.com/knowledge/vernier-bevel-protractor.html

Measuring Acute Angles

Measuring Obtuse Angles

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http://its.foxvalleytech.com/MachShop1/Inspection/AngleMeas.htm http://www.mytoolstore.com/starrett/359.html


• These are marked 0-60 minutes of arc, so that each division equals 1/12 of 60, that is 5 minutes of arc.

• These 12 divisions occupy the same space as 23 degrees on the main scale. Therefore, each division of the Vernier is equal to

• As shown in the main scale is graduated in degrees of arc.

• The Vernier scale has 12 Divisions each side of the centre zero.

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Basic Manufacturing Processes By KAPOOR

Optical bevel protractor • A circle divided at 1.0 minutes intervals throughout the

circle is fitted inside the body. • Small microscope is fitted through which the circle

graduations can be viewed. • Adjustable blade is clamped to a rotating member which

carries its microscope.

Combination Set

Combination Set

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http://www.craftsmanspace.com/knowledge/combination-square-set.html

Combination Set

Sine bars • A precision angle measuring instrument

used along with slip gauges

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The holes drilled in the body of the sine bar to make it lighter and to facilitate handling, are known as relief holes.

Sine bars

Sine bars

The sine bars inherently become increasingly impractical and inaccurate as the angle exceeds 45° because of following reasons : — The sine bar is physically clumsy to hold in position. — The body of the sine bar obstructs the gauge block stack, even if relieved. — Slight errors of the sine bar cause large angular errors. — Long gauge stacks are not nearly as accurate as shorter gauge blocks. — A difference in deformation occurs at the point of roller contact to the support surface and to the gauge blocks, because at higher angles, the weight load is shifted more toward the fulcrum roller. — The size of gauges, instruments or parts that a sine bar can inspect is limited, since it is not designed to support large or heavy objects.

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The sine bars inherently become increasingly impractical and inaccurate as the angle�exceeds 45° because of following reasons :�— The sine bar is physically clumsy to hold in position.�— The body of the sine bar obstructs the gauge block stack, even if relieved.�— Slight errors of the sine bar cause large angular errors.�— Long gauge stacks are not nearly as accurate as shorter gauge blocks.�— A difference in deformation occurs at the point of roller contact to the support surface�and to the gauge blocks, because at higher angles, the weight load is shifted more�toward the fulcrum roller.�— The size of gauges, instruments or parts that a sine bar can inspect is limited, since�it is not designed to support large angular or heavy objects.

Sine bars

• Height over the rollers can be measured by a vernier height gauge; using a dial test gauge mounted on the anvil of height gauge to ensure constant measuring pressure.

• This is achieved by adjusting the height gauge until the dial gauge shows the same zero reading each time

Sine bars

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The sine bars inherently become increasingly impractical and inaccurate as the angle�exceeds 45° because of following reasons :�— The sine bar is physically clumsy to hold in position.�— The body of the sine bar obstructs the gauge block stack, even if relieved.�— Slight errors of the sine bar cause large angular errors.�— Long gauge stacks are not nearly as accurate as shorter gauge blocks.�— A difference in deformation occurs at the point of roller contact to the support surface�and to the gauge blocks, because at higher angles, the weight load is shifted more�toward the fulcrum roller.�— The size of gauges, instruments or parts that a sine bar can inspect is limited, since�it is not designed to support large or heavy objects.

Fiducial dial indicator

Sine bars • Advantages of sine bar 1. It is precise and accurate angle measuring device. 2. It is simple in design and construction. 3. It is easily available • Disadvantages 1. It is fairly reliable at angles less than 15 but become

increasingly inaccurate as the angle increases. It is impractical to use sine bar for angle above 45 .

2. It is difficult to handle and position the slip gauges. 3. The sine bar is physically clumsy to hold in position. 4. The application is limited for a fixed center distance

between two rollers. 5. Slight errors of the sine bar cause larger angular errors.

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Limitations of Sine Bars. The establishment of angle by the sine principle is�essentially a length measuring process. Thus the accuracy, in practice, is limited by measure-�ment of centre distance of two precision rollers. The geometrical condition involved in�measuring the exact, effective centre distance existing between two rollers of the sine bar to a�certainty of fraction of a um is an infinitely complex problem. This fundamental limitation�alone precludes the use of the sine bar as a primary standard of angle.�Devices operating on the sine principle are fairly reliable at angles less than 15°, but�become increasingly inaccurate as the angle increases.�Sine bars inherently become increasingly impractical and inaccurate as the angle�exceeds 45°.�The sine bars inherently become increasingly impractical and inaccurate as the angle�exceeds 45° because of following reasons :�— The sine bar is physically clumsy to hold in position.�— The body of the sine bar obstructs the gauge block stack, even if relieved.�— Slight errors of the sine bar cause large angular errors.�— Long gauge stacks are not nearly as accurate as shorter gauge blocks.�— A difference in deformation occurs at the point of roller contact to the support surface�and to the gauge blocks, because at higher angles, the weight load is shifted more�toward the fulcrum roller.�— The size of gauges, instruments or parts that a sine bar can inspect is limited, since�it is not designed to support large or heavy objects.�8.6.3. Precautions in use of sine bars. (i) The sine bar should not be used for angle�greater than 60° because any possible error in construction is accentuated at this limit. (Also�refer Prob. 8.2).�(ii) A compound angle should not be formed by mis-aligning of workpiece with the sine�bar. This can be avoided by attaching the sine bar and work against an angle plate.�(iii) Accuracy of sine bar should be ensured.�(iv) As far as possible longer sine bar should be used since many errors are reduced by�using longer sine bars.

Sine Centre • Sine center is basically a sine bar with block holding centers which

can be adjusted and rigidly clamped in any position. used for the testing of conical work, centered at each end as shown.

• Extremely useful since the alignment accuracy of the centers ensures that the correct line of measurement is made along the workpiece.

• The centers can also be adjusted depending on the length of the conical work piece, to be hold between centers.

Sine Centre

Angle Gauge

• Angle gauges are made of hardened steel and seasoned carefully to ensure permanence of angular accuracy, and the measuring faces are lapped and polished to a high degree of accuracy and flatness like slip gauges.

Angle Gauge • Like linear gauge blocks, angle gauge blocks can also be

wrung together to build up a desired angle. • In addition, they can also be subtracted to form a smaller angle

as a difference of two larger angles as shown in Figure. • The plus and minus ends of each block are marked.

Angle Gauge

Spirit Level

low viscosity fluids the vial is graduated in linear units

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Spirit Level Spirit level is one of the most commonly used instruments for inspecting the horizontal position of surfaces and for evaluating the direction and magnitude of minor deviation from that nominal condition. It essentially consists of a close glass tube of accurate form. It is called as the vial. It is filled almost entirely with a liquid, leaving a small space for the formation of an air or gas bubble. Generally, low viscosity fluids, such as ether, alcohol or benzol, are preferred for filling the vial. The liquid due to its greater specific weight tends to fill the lower portion of the closed space. Upper side of the vial is graduated in linear units. Inclination of a surface can be known from the deviation of the bubble from its position when the spirit level is kept in a horizontal plane. Temperature variations in the ambient condition cause both liquid and vial to expand or contract. Therefore, selection of proper liquid and material for the spirit level is very important for accurate result. To reduce the effect of heat transfer in handling spirit levels are made of a relatively stable casting and are equipped with thermally insulated handles. Figure 6.5 shows a schematic diagram of a spirit level. Figure 6.5 : Spirit Level Sensitivity of the vial used in spirit level is commonly expressed in the following two ways. Each graduation line representing a specific slope is defined by a tangent relationship, e.g. 0.01 cm per meter. An angular value is assigned to the vial length covered by the distance of two adjacent graduation lines, i.e. the distance moved by the bubble from the zero will correspond the angle directly.

Clinometers

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The tangent of θ is defined as the opposite side divided by the adjacent side. Mathematically, tanθ*d = H

Clinometers

Clinometers The clinometers is a special case of the application of the spirit level. It is an instrument used for measuring angle relative to the horizontal plane.

• A circular scale is provided on the housing. A circular scale is used to measure the angle of inclination of the rotary member relative to the base.

• The scale may cover the whole circle or only part of it.

• The base of the instrument is placed on the surface and rotary member is adjusted till zero reading of the bubble is obtained as shown in Fig.

• The angle of rotation is then noted on the circular scale against an index.

• It consists of a spirit level mounted on a rotary member carried in a housing.

• One face of the housing forms the base of the instrument.

Clinometers

Clinometers • Micrometer clinometers is shown in Fig. In this type, one end of spirit level is attached at end of the barrel of a micrometer

• The other end of the spirit level is hinged on the base. The base is placed on the surface whose inclination is to be measured.

• The micrometer is adjusted till the level is horizontal. This type of clinometers is suitable for measuring small angles.

• The most commonly used clinometers is of the Hilger and Walts type in which circular, scale is totally enclosed and is divided from 0 to 360 at l0' interval. For observation of 10‘-subdivision optical micrometer is provided..

Clinometers

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Precision Microptic Clinometer.�The special features of precision microptic clinometer are direct reading over the range�0°—360°, optical reading system ; totally enclosed glass circles and easy-to-read scales ; main�scale and micrometer scale visible simultaneously in the eyepiece external scale for rapid�coarse setting, slow motion screw for fine setting, eyepiece rotatable to most convenient viewing�position, and hardened ground steel base.�Precision Microptic Clinometer utilises bubble unit with a prismatic coincidence reader�which presents both ends of the bubble as adjacent images in a split field of view. As the vial�is levelled, the two half-images move into coincidence, making it very easy to see when the�bubble is exactly centered, without reference to any graduations To determine the inclination of the clinometer, the bubble unit is levelled and the scales�read. On looking through the reader eyepiece, three apertures can be seen. The upper aperture�contains two pairs of double lines and two single lines. To set the micrometer, the knob is�turned until the single line is brought exactly central between the double lines. The scales can�then be read, the required angle being the sum of the readings of the main scale and the�micrometer scale. http://what-when-how.com/metrology/clinometers-metrology/

Clinometers

Protractor Bevel protractor Vernier bevel protractor Optical bevel protractor Combination set…. Sine bar Sine centre Angle gauge Spirit level Clinometers

CHAPTER Angular Measurement

Chapter

Linear Measurement

Angular Measurement

Angular measurements

Engineering

Transcript of Angular measurements