Linear and angular measurements

Department of Mechanical Engineering
JSS Academy of Technical Education, Bangalore-560060
MECHANICAL MEASUREMENTS AND METROLOGY
(Course Code:18ME36B)

MECHANICAL MEASUREMENTS AND METROLOGY
CHAPTER 2: Linear and Angular Measurements

TEXT BOOKS
• Mechanical Measurements, Beckwith Marangoni and Lienhard, Pearson Education, 6th Ed., 2006.
• Instrumentation, Measurement and Analysis, B C Nakra, K K Chaudhry, 4th Edition, McGraw Hill.
• Engineering Metrology, R.K. Jain, Khanna Publishers, Delhi, 2009
REFERENCE BOOKS:
• Engineering Metrology and Measurements, N.V.Raghavendra and L.Krishnamurthy, Oxford
University Press..
Further Reference:
 National Programme on Technology Enhanced Learning (NPTEL)
http://nptel.ac.in/courses/112104121/1

• Understand the basic principles of design of linear measuring instruments.
• Explain the use of slip gauges, and their manufacture and calibration.
Outcomes

Module 1
Linear and angular measurements: Slip gauges-Indian standards on slip gauges,
Adjustable slip gauges, Wringing of slip gauges, Problems on building of slip gauges
(M87, M112), Measurement of angle-sine bar, Sine centre, Angle gauges, Optical
instruments for angular measurements. Autocollimator-Applications for measuring
straightness and squareness.

Introduction
Measuring instruments are designed either for;
• Line measurements (e.g., steel rule or Vernier caliper)
• End measurements (e.g., screw gauge).
• Calipers and dividers are basically dimension transfer instruments.
Quality of measurement depends on;
• Accuracy of the instruments.
• Application of simple principles to be followed during measurements.

Introduction
Today’s engineer have a choice of a wide range of instruments;
• Mechanically operated instruments
• Digital electronics instruments.
One has to consider only
• Nature of application
• Cost of measurement to decide which instrument is the best for an application.

Introduction
DESIGN OF LINEAR MEASUREMENT INSTRUMENTS
• To meet the modern industry demands to manufacture of components and
products to a high degree of dimensional accuracy and surface quality.
Linear measurement instruments have to be designed to meet;
• Stringent demands of accuracy and precision.
• The instruments should be simple to operate
• Low priced (economic sense for the user).
• Proper attachments need to be provided to make the instrument versatile.

Introduction
LINEAR MEASUREMENT INSTRUMENTS
SURFACE PLATE
Cast Iron Surface Plates
Granite Surface Plates
Glass Surface Plates

Introduction
V-BLOCKS
V-block V-block with a stirrup clamp Magnetic V-block

Introduction
GRADUATED SCALES

Introduction
Types of steel rules
Narrow tempered steel rule
Flexible fillet rule
Short rule with holder Angle rule Steel measuring tape

Introduction
Depth gauge

Introduction
Combination Set

Introduction
Square Head
Combination square as a height gauge

Introduction
Protractor Head
Use of a protractor head for angle measurement Use of a centre head for the measurement of diameter

Introduction
Callipers
(a) Outside calliper (b) Inside calliper
(c) Divider (d) Hermaphrodite calliper

Introduction
Vernier Calliper

Introduction
Dial Calliper

Introduction
Electronic Digital Calliper

Introduction
Vernier Depth Gauge Vernier height gauge

Introduction
MICROMETER INSTRUMENTS

Introduction
MICROMETER INSTRUMENTS: Types
(a) Disk type (b) Screw thread type (c) Dial type (d) Blade type

Introduction
Depth Micrometer

Introduction
Floating Carriage Micrometer

SLIP GAUGES
• The origin of gauge blocks: 18th century Sweden, where ‘gauge sticks’ were
known to have been used in machine shops.
• The modern-day slip gauges or gauge blocks: Pioneering work by C.E.
Johansson [Carl Edvard Johansson (1864–1943)], a Swedish armoury
inspector.
• Gauge blocks are also known as Johansson gauges

• He devised a set of slip gauges manufactured with very high degree of accuracy
and surface finish.
• He proposed the method of ‘wringing’ slip gauges.
• He emphasized that the resulting slip gauges, to be of universal value, must be
calibrated to the international standard.
• Johansson was granted a patent for his invention in the year 1901.
• He formed the Swedish company CE Johansson AB in the year 1917.
Johansson gauges

SLIP GAUGES / Gauge Blocks
• One of his customers was Henry Ford.
• The development of ‘GO’ and ‘NO-GO’ gauges also took place during this time.
Johansson gauges
Functional features of a slip gauge

Johansson gauges
• Made of hardened alloy steel having a 30 mm × 10
mm cross section.
• Steel is the preferred (economical).
• Height of a slip gauge is engraved on one of the
rectangular faces, also features a symbol to indicate
the two measured planes.

Johansson gauges
• The length between the measuring surfaces, flatness,
and surface conditions of measuring faces are the
most important requirements of slip gauges.

Johansson gauges
Gauge Block Shapes, Grades, and Sizes
Slip gauges are available in three basic shapes:
1. Rectangular
2. Square with a central hole
3. Square without a central hole.

Johansson gauges
• Grade defines the type of application for which a slip gauge is suited, such as
inspection, reference, or calibration.
• Slip gauges are designated into five grades;
1. Grade 2
2. Grade 1
3. Grade 0
4. Grade 00
5. Calibration grade.

Johansson gauges
1. Grade2: Workshop-grade slip gauge. Uses includes setting up machine tools etc.
2. Grade1: Tool room applications. Setting up sine bars, dial indicators, calibration of
Vernier, micrometer instruments.
3. Grade0: Inspection-grade slip gauge. Limited people will have access.
4. Grade00: Kept in the standards room. Used for inspection/calibration of high precision.
5. Calibration grade: Special grade, actual sizes of slip gauges stated on a special chart
supplied with the set.

Johansson gauges
• JIS B 7506-1997 (Japan)
• DIN 861-1980 (Germany)
• ASME (USA)
• BS 4311: Part 1:1993 (UK)
• The standards assign grades such as A, AA, AAA, and B.
• Grade B: Conform to the workshop-grade.
• Grades AA and AAA: Calibration and reference grades.
Other grading standards are followed for slip gauges.

Johansson gauges
• Slip gauges are available in standard sets in both metric and inch units.
• In metric units, sets of 31, 48, 56, and 103 pieces are available.

Johansson gauges
• To reduce wear on slip gauges a pair of protector gauge blocks are used.
• They are wrung to the ends of slip gauge combinations.
• The protector gauge blocks are made of tungsten carbide or similar wear
resisting material, protect the slip gauges from wear.
Protector gauge blocks

Wringing of Slip Gauges
Wringing is the phenomenon of adhesion of two flat and smooth surfaces when
they are brought into close contact with each other.
Technique of wringing slip gauges (a) Step 1 (b) Step 2 (c) Step 3 (d) Step 4

Wringing of Slip Gauges
The following are the preferred steps in the wringing of slip gauges:
• Clean slip gauge surfaces with a fine hairbrush and a dry cloth.
• Overlap gauging surfaces by about one-fourth of their length, as shown in Fig.(a).
• Slide one block perpendicularly across the other by applying moderate pressure.
The two blocks should now form the shape as shown in Fig.(b).
• Gently rotate one of the blocks until it is in line with the other block, as in Fig. (c)
and (d).
Wringing phenomenon

Johansson gauges
Problems on building of slip gauges (M87, M112)
Slip Gauge Set
Normal set
(M45)
Range (mm) Step (mm) Pieces
1.001-1.009 0.001 9
1.01 -1.09 0.01 9
1.1-1.9 0.1 9
1-9 1 9
10-90 10 9

Johansson gauges
Slip Gauge Set
Special set
(M87)
1.001 - 1.009 0.001 9
1.01 - 1.49 0.01 49
0.5 - 9.5 0.5 19
10 - 90 10 9
1.005 - 1

Johansson gauges
Slip Gauge Set
Set
M112
1.001 - 1.009 0.001 9
1.01 - 1.49 0.01 49
0.5 - 24.5 0.5 49
25 - 100 25 4
1.005 - 1

Johansson gauges
Slip Gauge Set
Set
E28
Range Pieces
0.01 – 0.209 in 9
0.21 – 0.029 in 9
0.01 – 0.09 in 9
0.02005 1

Johansson gauges
1. Build 58.975 mm using M 112 set of gauges.
• Always start with the last decimal place.
• Minimum no. of slip gauges should be selected.
• Here it is 0.005 mm, for this 1.005 mm slip gauge is selected.
Solution.

Johansson gauges
1. Build 58.975 mm using M 112 set of gauges.
• Min no. of slip gauges should be selected.
• We cannot select 1.07, as 56.900 would be left out and
the next gauge would be 1.4 mm
Thus, we have 50.000 + 6.500 + 1.47 + 1.005 = 58.975 mm
Solution.

Johansson gauges
2. List the slip gauges to be wrung together to produce an overall dimension of
92.357 mm using two protection slip gauges of 2.500 mm size. Show the slip
gauges combination.

Johansson gauges
Solution.
Thus, we have 75.000 + 10.000 + 1.350 + 1.007+2.500+2.500 = 92.357 mm

Measurement of Angle
• Sine bar
• Sine centre
• Angle gauges
• Optical instruments for angular measurements

Measurement of angle
Sine bar
• Used to measure angles, based on the sine principle.
• Upper surface forms the hypotenuse of a right angled triangle.
• When one of the roller, is resting on a flat surface, the bar can be set at any
desired angle by simply raising the second roller.

Sine bar
Sine bar Sine rule
h = is the height difference between the two rollers.
L= is the distance between the centres of the rollers.
Therefore, h = L Sin (θ )

Sine bar
Measuring Unknown Angles with Sine Bar
• The work is clamped to the sine bar
• The top surface is set to the angle, using
slip gauges, as shown in Fig.
• A dial gauge is brought in contact with the
top surface of the work part at one end
and set to zero.
• The dial indicator is moved to the other
end of the work part in a straight line.

Sine bar
• A zero on the dial indicator indicates that
the work surface is perfectly horizontal /
the set angle is the right.
• If the dial indicator shows any deviations,
adjustments in the height of slip gauges
is necessary to ensure that the work
surface is horizontal.

Sine bar
• The actual angle is calculated using,
total height of the slip gauges.

Requirements of a Sine bar
• Axes of the roller must be parallel and the center distance L must be known.
• Top surface of the bar must have a high degree of flatness.
• The roller must be of identical diameters.

Limitations of the Sine bar
• Sine bar is reliable for angle less than 15° and 45 °
• For building the slip gauges, there is no scientific approach available, it is to be
built on the trial and error basis and time-consuming.
• Any unknown projections present in the component will cause to induce errors in
the angle measured.

• A sine centre provides a means of measuring
angles of conical workpieces as shown in fig.
• One of the rollers is pivoted. The sine bar to be
set to an angle by lifting the other roller.
• Slip gauges are wrung and placed on it, to set
the sine bar at the required angle.
Sine centre

• The sine centre is used for measuring
angles up to 60°.
• The procedure for measuring angles is
very similar to the sine bar
Sine centre

• Angle gauges work on a principle similar to slip gauges.
• Slip gauges: Linear dimensions.
• Angle gauges: For required angle.
• Standard set of angle blocks, can be wrung together in a suitable combination to
build an angle.
ANGLE GAUGES

• Angle blocks have a special feature that is impossible in slip gauges—the former can
be subtracted as well as added.
ANGLE GAUGES

Example
If a 5° angle block is used along with a 30°
angle block, as shown in Fig. (a), the resulting
angle is 35°.
If the 5° angle block is reversed and combined
with the 30° angle block, as shown in Fig. (b).
ANGLE GAUGES
• The gauges are about 75 mm long and 15 mm wide.
• The two surfaces, generates the angles, accurate up to - 2".

Angle gauge block setsANGLE GAUGES
Smallest increment by
which any angle can be
produced
Number of individual blocks
contained in the set
Detailed listing of the blocks composing
the set
1° 6 Six blocks of 1°, 3°, 5°, 15°, 30°, and 45°
1′ 11
Six blocks of 1°, 3°, 5°, 15°, 30°, and 45°
Five blocks of 1', 3', 5', 20', and 30′
1″ 16
Six blocks of 1°, 3°, 5°, 15°, 30°, and 45°
Five blocks of 1', 3', 5', 20', and 30'
Five blocks of 1", 3", 5", 20", and 30"

ANGLE GAUGES
Combination of angle gauges for 42°35'20''
• Each angle gauge is engraved with the
symbol ‘<’, indicates the direction of the
included angle.
• Whenever an angle gauge is required to
be subtracted, the gauge should be wrung
such that the symbol < is in the other
direction (<).

ANGLE GAUGES
Uses
• Angle gauges are used for measurement and calibration purposes in tool
rooms.
• Used for measuring the angle of a die insert.
• Inspecting compound angles of tools and dies.
• Used in machine shops for setting up a machine.

OPTICAL INSTRUMENTS FOR ANGULAR MEASUREMENT
• Magnification enables easy and accurate measurement of object.
• A monochromatic light source ensures a high degree of accuracy.
• The third principle is one of alignment.
• The fourth, is the principle of interferometry.
• These principles have driven the development of a large number of measuring
instruments and comparators.

Autocollimator
A special form of telescope, used to measure small angles with a high degree of
resolution.
Applications
• Precision alignment
• Verification of angle standards
• Detection of angular movement.

Autocollimator
• It projects a beam of collimated light onto a reflector, which is deflected by a
small angle about the vertical plane.
• The light reflected is magnified and focused on to an eyepiece or a photo
detector.
• The deflection between the beam and the reflected beam is a measure of the
angular tilt of the reflector.

Autocollimator
Principle of autocollimation

Autocollimator
• If rotation of the plane reflector by an angle θ results in the displacement of the
image by an amount d, then, X = 2θf, where f = focal length of the objective lens

Autocollimator

Autocollimator
• The instrument is so sensitive that air currents between the optical path and the
target mirror can cause fluctuations in the readings.
• An autocollimator is housed inside a sheet-metal or a PVC plastic casing to
ensure that air currents do not hamper measurement accuracy.

Autocollimator
Autocollimators may be classified into three types:
1. Visual or conventional autocollimator
2. Digital autocollimator
3. Laser autocollimator

Autocollimator Applications
Autocollimators are used for:
• Measurement of straightness and flatness of machine parts and accessories
such as guideways, machine tables, surface plates.
• Assessment of parallelism of machine slide movement with respect to
guideways.
• Angle gauges can also be calibrated using an autocollimator.

Linear and angular measurements

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