Unit III Introduction Angular measurement is an important element in measuring. It involves the measurement of angles of tapers and similar surfaces. In angular measurements, two types of angle measuring devices are used. They are Angle gauges corresponding to slip gauges. Divided scale corresponding to line standard. The most common instrument is sine bar. The main difference between linear and angular measurement is the no absolute standard is required for angular measurement. Sine bar Sine bar are always used along with slip gauges as a device for the measurement of angles very precisely. They are used to: Measure angle very accurately. Locate the work piece to given angle with very high precision. Sine bars are made from high carbon, high chromium, and corrosion resistant steel. These materials are highly hardened, ground and stabilised. In sine bar, two cylinders of equal diameter are attached at the ends with its axes mutually parallel to each other. Two cylinders are also equal distance from the upper surface of the sine bar. Mostly the distance between the axes of two cylinders is 100mm, 200mm or 300mm. The working surfaces of the rollers are finished to 0.2μm Ra value. The cylindrical holes are provided to reduce the weight of the sine bar and alsoto facilitate handling. Working principle of sine bar The working of sine bar is based on trigonometry principle. To measure the angle of the specimen, one roller of the sine bar is placed on the surface plate and another one roller is placed over the surface of slip gauges. Now, ‘h’ be the height of the slip gauges and ‘L’ be the distance between roller canters, then the angle is calculated as sin h L 1 sin h L 1
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Unit III
Introduction
Angular measurement is an important element in measuring. It involves the measurement
of angles of tapers and similar surfaces. In angular measurements, two types of angle measuring
devices are used. They are
Angle gauges corresponding to slip gauges.
Divided scale corresponding to line standard.
The most common instrument is sine bar. The main difference between linear and angular
measurement is the no absolute standard is required for angular measurement.
Sine bar
Sine bar are always used along with slip gauges as a device for the measurement of angles
very precisely. They are used to:
Measure angle very accurately.
Locate the work piece to given angle with very high precision.
Sine bars are made from high carbon, high chromium, and corrosion resistant steel.
These materials are highly hardened, ground and stabilised.
In sine bar, two cylinders of equal diameter are attached at the ends with its axes mutually
parallel to each other.
Two cylinders are also equal distance from the upper surface of the sine bar.
Mostly the distance between the axes of two cylinders is 100mm, 200mm or 300mm.
The working surfaces of the rollers are finished to 0.2µm Ra value.
The cylindrical holes are provided to reduce the weight of the sine bar and alsoto facilitate
handling.
Working principle of sine bar
The working of sine bar is based on trigonometry principle. To measure the angle of the
specimen, one roller of the sine bar is placed on the surface plate and another one roller is placed
over the surface of slip gauges. Now, ‘h’ be the height of the slip gauges and ‘L’ be the distance
between roller canters, then the angle is calculated as
sinh
L
1sinh
L
1
Principle of Sine bar
Accuracy requirements of sine bar:
The accuracy of sine bar depends on the following constructional features:
The rollers must have equal diameter and equal cylinder.
The rollers should be placed parallel to each other and also to upper face.
The accurate center to center of rollers must be known.
The top surface of the bar must be flat with high degree of accuracy.
Use of sine bar
Sine bar are used for
I. Locating any work to a given angle.
II. To check unknown angle.
III. Measurement of unknown angles for heavier components
IV. Measurement of unknown angles of heavier components with more accurate
readings.
I. Locating any work to a given angle
To set at a given angle, first ‘h’ of the slip gauge is calculated by the formula
sin =h/L.
After calculating the height ‘h’ ,the required height ‘h’ is made by suitable slip gauge
combinations.
After this, one of the roller is placed on the surface plate and other on is placed on the top
of the slip gauges combination.
II. To check unknown angle :
2
Before checking the unknown angle of the specimen, the angle of the given specimen is
found approximately by bevel protector.
Then the sine bar is set at angle of and clamped on the angle plate.
Now the work piece is placed on the sine bar and the dial indicator is set at one end of the
work and it’s moved across the work piece and deviations are noted.
Slip gauge is adjusted so that the dial indicator reads zero throughout the work piece.
III. Measurement of unknown angles for heavier components :
For heavy components, the sine bar is mounted on the work piece at inverted position (i.e.
the rollers are placed in such a way that the rollers should face upward).
The heights of the rollers are measured on the vernier height gauge.
The dial test indicator is mounted on the vernier height gauges to ensure constant
measuring pressure.
Now, the sine angle is calculated as the difference between two vernier height gauge
readings divided by center distance of sine bar rollers.
1 2sinh h
L
Limitations of sine bars
Sine bars are fairly reliable for angles less than 15 0.
It is physically difficult to hold in position.
Slight errors in sine bar cause larger angular error.
The size of parts to be inspected by sine bar is limited.
Sources of error in sine bar
The different sources of errors are listed below:
Error in distance between roller centers.
Error in slip gauge combination. 3
Error in equality of size of rollers and cylindricity.
Error in flatness of the upper surface of sine bar
Error in parallelism of roller axes with each other.
Bevel protractors
Bevel protractors are nothing but angular measuring instruments.
Types of bevel protractors:
The different types of bevel protractors used are:
1) Vernier bevel protractor
2) Universal protractor
3) Optical protractor
Vernier bevel protractor:
Working principle:
A vernier bevel protractor is attached with acute angle attachment.
The body is designed its back is flat and no projections beyond its back. The base plate is
attached to the main body and an adjustable blade is attached to the circular plate
containing vernier scale.
The main scale is graduated in degrees from 0° to 90° in both the directions. The
adjustable can be made to rotate freely about the center of the main scale and it can be
locked at any position.
For measuring acute angle, a special attachment is provided. The base plate is made fiat
for measuring angles and can be moved throughout its length. The ends of the blade are
beveled at angles of 45°and 60°.
The main scale is graduated as one main scale division is 1° and vernier is graduated into
12 divisions on each side of zero. Therefore the least count is calculated as
Least count = One main scale division/No. of on vernier scale
=10/12
4
=1/12*60
=5 minutes
Thus, the bevel protractor can be used to measure to an accuracy of 5 minutes.
Optical bevel Protractor
Stock
The working edge of the stock is about 90 mm in length and 7 mm thick. It is very
essential that the working edge of the stock be perfectly straight.
Blade
It can be moved along the turret throughout its length and can also be reversed. It is
about 150 or 300 mm long, 3 mm wide and 2 mm thick and ends bevelled at angles of 45° and
60° within the accuracy of 2 minutes of arc. It can be clamped in any position.
The values are obtained by means of an optical magnifying system. This optical
magnifying system is attached with the bevel protractor itself separate arrangement is provided
for adjusting the focus of the system for the normal variation of eyesight. The main and vernier
scale are arranged always in focus of the optical system.
Applications of bevel protractor
The bevel protractor can be used in the following applications.
1. For checking a ‘V’ block:
Checking ‘V’ block
2. For checking acute angle
5
Measuring acute angle
Auto- collimator:
An autocollimator is an optical instrument for non-contact measurement of angles.
It’s used for the measurement of small angular differences, changes or deflection, plane
surface inspection etc.
For small angular measurements, autocollimator provides a very sensitive and accurate
approach.
An auto-collimator is essentially an infinity telescope and a collimator combined into one
instrument.
Basic principle:
Principle of Auto-collimator
If a light source is placed in the flows of a collimating lens, it is projected as a parallel
beam of light.
If this beam is made to strike a plane reflector, kept normal to the optical axis, it is
reflected back along its own path and is brought to the same focus.
If the reflector is tilted through a small angle ‘’. Then the parallel beam is deflected twice
the angle and is brought to focus in the same plane as the light source.
The distance of focus from the object is given by
Note:
The position of the final image does not depend upon the distance of reflector from the
lens. i.e. distance x is independent of the position of reflection from the lens.
But if the reflector is moved too much back then reflected rays would completely miss the