Ch-2: System of limits, fits, tolerance and gauging
1. MECHANICAL MEASUREMENT & METROLOGY
CH-2: SYSTEM OF LIMITS, FITS, TOLERANCE AND GAUGING
PROF. SURAJ A. SHUKLA
• Every production process involves a combination of three elements viz, men, machines, and materials. Each
of these elements has some natural variations as well as unnatural variations.
• For example, suppose a drilling operation is to be performed on castings. The first source of variation is the
• If operations are done on mass production by a number of workers on different machines, the second source
of variation is the machine. The third source of variation, man, is the most variable of them all.
• Thus we conclude that:
1. It is not possible to make any part perfectly to a given dimension, due to the variability of elements of the
2. Even by chance, the part is made exactly to a given dimension, it is impossible to measure it accurately
enough to prove it.
3. If attempts are made to achieve perfect size the cost of production will increase.
• In mass production, where large numbers of parts are to be made by different operators on different machines, it
is impossible to make all parts exactly alike and to exact dimensions. It is obvious that some permissible variation
in dimension to be allowed for variability.
• Therefore, the ranges of permissible difference in dimension have been standardized under name limits. The
limits of the size of a dimension of parts are two extreme sizes either maximum or minimum, between which the
actual size of the dimension may lie.
• The largest permissible dimension is known as the upper limit or upper tolerance limit, while the lowest
permissible dimension is called the lower limit or lower tolerance limit.
• The permissible variation of size or dimension is called tolerance. It is the difference between the maximum and
minimum permissible limits of the given size.
• The difference between the upper limit and the lower limit of a dimension represents the margin for variation in
workmanship and is called a tolerance zone.
• Tolerance is denoted by two symbols –a number symbol called the grade and a letter symbol (a capital letter
being used for holes and small letters for shafts).
4. TERMINOLOGY FOR LIMITS AND FITS
Basic or Nominal Size: It is the standard size of part with reference to which the limits of variation of size are
determined. The basic size is the same for the hole and its shaft. It is designed to size obtained by calculations for
Actual Size: It is the dimension as measured on a manufactured part.
Zero Line or Datum Line: It is a straight line drawn horizontally to represent the basic size. In the graphical
representation of limits and fits, all the deviations are shown with respect to zero lines. The positive deviations
are shown above the zero line and negative deviation below the zero lines.
Deviation: It is an algebraic difference between size and corresponding basic size.
Upper Deviation: It is an algebraic difference between the upper (maximum) limit of size and corresponding
basic size. It is a positive quantity when the maximum limit of size is greater than the basic size and a negative
quantity when the upper limit of size is less than the basic size. It is denoted by ’ES’ for a hole and ‘es’ for a
Lower Deviation: It is an algebraic difference between the lower limit of size and the corresponding basic size.
It is a positive quantity when the maximum limit of size is greater than the basic size and a negative quantity
when the lower limit of size is less than the basic size. It is denoted by ‘EI’ for a hole and ‘ei’ for a shaft.
5. TERMINOLOGY FOR LIMITS AND FITS
The relationship of deviation with tolerance (IT) is given by,
it = es – ei (upper deviation – lower deviation)
IT = ES – EI
Fundamental Deviation: It is that one of the two deviations (either upper or lower) which is nearest to the zero
lines for either hole or shaft. It fixes the position of the ‘Tolerance Zone’ in relation to the zero lines.
Basic Shaft: It is the shaft whose upper deviation is zero. Thus the upper limit of the basic shaft is the same as
the basic size. It is denoted by letter ‘h’.
Basic Hole: It is the hole whose lower deviation is zero. Thus the lower limit is the same as the basic size. It is
denoted by the letter ‘H’.
Tolerance Zone: It is the zone bounded by two limits of the size of a part in the graphical representation of
tolerance. It is defined by its magnitude and by its position in relation to the zero lines.
Tolerance Grade: It is an indication of the degree of accuracy of manufacture and it is designed by the letters
‘IT’ followed by a number, where ‘IT’ stands for “International Tolerance grade”. Tolerance grades are IT0, IT1,
IT2, up to IT16, the larger the number larger will be the tolerance.
6. TERMINOLOGY FOR LIMITS AND FITS
Standard Tolerance Unit: A unit that is a function of basic size and which is common to the formula defining
the different grades of tolerance. It is denoted by the letter ’i’ and expressed in terms of microns. It serves as a
basis for determining the standard tolerance of the system.
• It may be defined as a degree of tightness or looseness between two mating parts to perform a definite function
when they are assembled together. Accordingly, a fit may result either in a movable joint or a fixed joint.
Types of fits:
• On the basis of positive, zero and negative values of clearance, there are three basic types of fits.
• In this type of fit, shaft is always smaller than the hole i.e., the largest permissible shaft diameter is smaller than
the diameter of the smallest hole. So that the shaft can rotate or slide through with a different degree of freedom
according to the purpose of the mating part.
• For example, a shaft running in a bearing, spindle of a lathe, tailstock of a lathe, etc.
Types of fits:
Minimum clearance: It is the difference between the minimum size of the hole and the maximum size of the shaft
in a clearance fit.
Maximum clearance: It is the difference between the maximum size of the hole and the minimum size of the shaft
in a clearance or transition fit.
• It lies mid-way between clearance and interference fit. In this type of size limits of mating parts are so selected
that either clearance or interference may occur depending upon the actual size of the parts. For example, change
gears, slip bushings, etc.
Types of fits:
• In this type of fit, the minimum permissible diameter of the shaft is larger than the maximum allowable diameter
of the hole. Thus the shaft and the hole members are intended to be attached permanently and used as a solid
• For example, steel tires on railway car wheels, bearing in the gear of a lathe headstock, etc.
• It is the dimensional difference between the maximum material limit of mating parts, intentionally provided to
obtain the desired class of fit.
• If the allowance is positive, it will result in minimum clearance between the mating parts and if the allowance is
negative, it will result in maximum interference.
10. SYSTEMS OF OBTAINING DIFFERENT TYPES OF FIT
• There are two systems of fit for obtaining clearance, interference or transition fit.
Hole Base System:
• In this system, the size of the shaft is obtained by subtracting the allowance from the basic size of the hole. This
gives the design the size of the shaft. Tolerances are then applied to each part separately.
• In this system, the lower deviation of the hole is zero. The hole basis system is preferred in most cases, since
standard tools like drills, reamers, broaches, etc., are used for making holes.
11. SYSTEMS OF OBTAINING DIFFERENT TYPES OF FIT
Shaft Base System:
• In this system, the side of the hole is obtained by adding the allowance to the basic size of the shaft. This gives
the design size for the hole. Tolerances are then applied to each part.
• In this system, the upper deviation of the shaft is zero. The letter symbol for this situation is ‘h’. The shaft base
system is preferred by industries using semi-finished shafting as row materials, e.g. textile industries, etc.
• The hole basis system is most commonly used because it is more convenient to make correct holes of fixed size
than to make correct shafts of fixed size.
12. SURFACE ROUGHNESS AND ITS MEASUREMENT
• There are many ways of expressing the surface roughness numerically, but the following two methods are
commonly used :
1. Centreline average method (briefly known as CLA method), and
2. Root mean square method (briefly known as the RMS method).
• The centerline average method is defined as the average value of the ordinates between the surface and the mean
line, measured on both sides of it.
• According to Indian standards, the surface finish is measured in terms of ‘CLA’ value and it is denoted by Ra.
CLA value or Ra = (h1 + h2 + h3 + ….) / n
13. SURFACE ROUGHNESS AND ITS MEASUREMENT
• h1, h2, h3are coordinates measured on both sides and n are the no. of ordinates.
• The root means the square method is defined as the square root of the arithmetic mean of the squares of the
R. M. S value = ℎ1
2 + ℎ2
2 + ℎ3
2 + … / n
14. SURFACE ROUGHNESS AND ITS MEASUREMENT
• The following table shows the surface roughness expected from manufacturing processes.
Roughness Values (Ra) Roughness grade number Roughness grade symbol
16. MATERIAL CONDITION
Maximum material condition (MMC):
• The maximum material condition in which a feature of size contains the maximum amount of material within the
stated limits of size. For example, a shaft having a diameter of 29.98-0.015
0.005 material condition, if it is
manufactured at 29.98 mm.
• Similarly, the part with a hole of 300.00
0.025 the diameter would be at maximum material condition if the hole is
drilled at 30.00 mm diameter. Clearance fits are usually dimensioned on the basis of MMC and if the parts are
produced at MMC, the clearance obtained will be minimum.
17. MATERIAL CONDITION
Maximum material condition (MMC):
• This type of dimensioning has other advantages. When the workman aims at the principal dimensions, but by
error, produced an oversized hole or an undersized shaft, the parts might still be acceptable; provided the
dimensions do not exceed to tolerance limits, specified on the drawings.
Least material condition (LMC):
• The least material condition in which a feature of size, contains the least amount of material, within the stated
limits of size.
• For example, a shaft having a diameter of 300.02
0.035 will only be at the least material condition, if it is
manufactured at 30.022 mm.
18. GEOMETRICAL TOLERANCES
• In certain circumstances, tolerances of size, which was discussed in the previous point are not sufficient to
provide the required control of form or not sufficient to ensure the acceptance of component.
• For example, in figure (a) the shaft has the same diameter in all possible positions but is not circular.
• Similarly, in figure (b) the rib has the same thickness throughout but it is not flat. Also in figure (c), the
component i.e. circular shaft is circular in all cross-section but it is not straight.
• All the above parts are unacceptable if they were checked only for dimensional variation, thus here another
tolerance comes into picture which controls the shape or form of component i.e. geometrical tolerance.
• Thus the geometrical tolerances are defined as the maximum permissible overall variation of form or position of
19. GEOMETRICAL TOLERANCES
• The geometrical tolerances are used :
1. To specify the required accuracy in controlling the form of component.
2. To ensure the correct function position of components.
3. To ensure the interchangeability of components.
4. To facilitate the assembly of the mating of components.
20. GEOMETRICAL TOLERANCES
Terms used in Geometrical tolerances:
Datum: It is theoretically exact geometric reference such as axes, planes, straight lines, etc. to which the
tolerance features are related.
Datum features: A datum feature is a feature of a part, such as an edge, surface or a hole, which forms the basis
for a datum or is used to establish its location.
Datum triangle: The datum is indicated by a leader line, terminating in a filled or an open triangle.
Datum letter: To identify a datum for reference purposes, a capital letter is enclosed in a frame, connected to the
21. GEOMETRICAL TOLERANCES
Terms used in Geometrical tolerances:
Datum system: Datum system is a group of two or more separated datums, used a combined reference for
tolerance features. In this case, the sequence of datums referred to has considerable influence on the result.
22. GEOMETRICAL TOLERANCES
Indications of Geometric tolerances on a drawing:
• To eliminate the need to descriptive notes, geometrical tolerances are indicated on drawings by symbols,
tolerances and datums, all contained in components of a rectangular frame.
• The following table shows the symbols representing the characteristics of tolerance.
23. GEOMETRICAL TOLERANCES
Indications of Geometric tolerances on a drawing:
Advantages of using geometrical tolerances:
1. Geometric tolerances convey very briefly and precisely, the complete geometrical requirements on engineering
2. The use of symbols and boxes eliminates the need for lengthy descriptive notes and corresponding dimensions,
because of which the drawings are much clearer to read.
3. The symbols used are internationally recommended.
4. One type of geometrical tolerance can control another form. For instance, sureness can correct flatness and
24. LIMIT GAUGING
• In mass production, where a large number of similar components are manufactured on an interchangeable basis,
measuring the dimensions of each part will be a time-consuming and expensive exercise.
• Therefore, in mass production, gauges can be used to check for the compliance of the limits of the part with the
permissive tolerance limits, instead of measuring the actual dimensions.
• The term ‘limit gauging’ signifies the use of gauges for checking the limits of the components.
• Gauging plays an important role in the control of dimensions and interchangeable manufacture.
• Limit gauges ensure that the components lie within the permissible limits, but they do not determine the actual
size or dimensions.
• The gauges required to check the dimensions of the components correspond to two sizes conforming to the
maximum and minimum limits of the components.
• They are called GO gauges and NO GO (or NOT GO) gauges, which correspond, respectively, to the MML and
LML of the component.
• MML is the lower limit of a hole and higher limit of the shaft and LML corresponds to the higher limit of a hole
and lower limit of the shaft.
25. LIMIT GAUGING
• The GO gauge manufactured to the maximum limit will assemble with the mating (opposed) part, whereas the
NOT GO gauge corresponding to the low limit will not.
• The main intention in the design of gauges is simplicity, which helps in making continuous and accurate
26. LIMIT GAUGING
Classification of Gauges:
According to their type:
1. Standard gauges (An exact copy mating part)
2. Limit gauges (Made to the limits of dimensions)
According to the form of the tested surfaces:
1. Plug gauges for checking holes
2. Snap and ring gauges for checking shafts
According to their purposes:
1. Workshop gauges for checking dimensions after manufacture
2. Inspection gauges for checking parts before final acceptance
3. Purchase inspection gauges for checking parts of other factories
4. Reference of Master gauges for checking dimensions of gauges
According to their design:
1. Single-ended gauges
2. Double-ended gauges
3. Progressive gauges
27. LIMIT GAUGING
• Taylor’s principle has generally been applied to the principle of the limit gauging and extensively used in the
design of limit gauges.
• Prior to 1905, simple GO gauges were used. The components were carefully manufactured to fit the gauges.
Since NOT GO gauges were not used, these components were without tolerance on their dimensions.
• The theory proposed by Taylor, which is extensively used in the design of limit gauges, not only defines the
function but also defines the form of most limit gauges.
• Taylor’s principle states that the GO gauge is designed to check maximum metal conditions, that is, LLH (Lower
Limit of Hole) and (Higher Limit of Shaft) HLS.
• It should also simultaneously check as many related dimensions, such as roundness, size, and location, as
• The basic or nominal size of the GO side of the gauge conforms to the LLH or HLS since it is designed to check
maximum metal conditions.
• The NOT GO gauge is designed to check minimum metal conditions, that is, HLH (Higher Limit of Hole) and
LLS (Lower Limit of Shaft).
28. LIMIT GAUGING
• It should check only one dimension at a time. Thus, a separate NOT GO gauge is required for each individual
• The basic or nominal size of the NOT GO gauge corresponds to HLH or LLS, as it is designed to check
minimum metal conditions.
• During the inspection, the GO side of the gauge should enter the hole or just pass over the shaft under the weight
of the gauge without using undue force. The NOT GO side should not enter or pass.
29. LIMIT GAUGING
Material for gauges:
• The material used to manufacture gauges should satisfy the following requirements:
1. The material used in the manufacture of gauges should be hard and wear-resistant for prolonged life.
2. It should be capable of maintaining dimensional stability and form.
3. It should be corrosion resistant.
4. It should be easily machinable, in order to obtain the required degree of accuracy and surface finish.
5. It should have a low coefficient of expansion, in order to avoid temperature effect.
High Carbon steel:
• It is the most suitable and inexpensive material used for manufacturing gauges.
• It can be heat treated suitably to provide stability and high hardness.
• It can easily be machined to a high degree of accuracy.
30. LIMIT GAUGING
Material for gauges:
• Mild steel gauges are the most suitable for larger gauges.
• They are suitably heat-treated by carburizing to the required depth and then case hardened on their working
surfaces to allow for final grinding and finishing.
• After hardening, internal stresses are relieved to improve stability.
• Chromium-plated gauges are very popular and extensively used for gauging.
• Chromium plating makes the surface of the gauge very hard, and resistant to abrasion and corrosion.
• It is also very useful in reclaiming worn-out gauges. For gauging aluminum or other materials having an abrasive
action, chromium-plated gauges are extensively used.
31. LIMIT GAUGING
Material for gauges:
• Glass gauges are not very popular although they have good wear and corrosion resistance properties.
• The problem with these gauges is that they either get damaged or are easily broken if dropped.
• They are not affected by changes in temperature and have a very low coefficient of thermal expansion.
• Although Invar, which contains 36% of nickel, has a low coefficient of expansion, it is not suitable over a long
• Elinvar has 42% of nickel, is more stable than Invar, and also has a low coefficient of expansion.
32. GAUGE TOLERANCE
• Gauges, like any other component, cannot be manufactured to their exact size or dimensions.
• In order to accommodate these dimensional variations, which arise due to the limitations of the manufacturing process,
the skill of the operator, etc., some tolerance must be allowed in the manufacture of gauges.
• Thus, the tolerance that is allowed in the manufacture of gauges is termed gauge maker’s tolerance or simply gauge
• The normal practice is to take gauge tolerance as 10% of the work tolerance.
• During the inspection, the NOT GO side should not enter or pass.
• The NOT GO gauge engages fully with the work and therefore does not undergo any wear. Hence, there is no need to
provide an allowance for wear in case of NOT GO gauges.
• The GO side of the gauge should enter the hole or just pass over the shaft under the weight of the gauge without using
• During the inspection, the measuring surfaces of the gauge constantly rub against the mating surfaces of the workpiece.
Therefore, the GO gauges suffer wear on the measuring surfaces and thus lose their initial dimension. Hence, wear
allowance is provided for GO gauges to extend their service life.
• The wear allowance provided for the GO gauge is added in a direction opposite to wear. This allowance is added in for
a plug gauge while subtracted for a ring or gap gauge.
• A wear allowance of 10% of gauge tolerance is widely accepted in industries.
33. NEED OF COMPARATORS
• In mass production identical component parts are produced on a very large scale. To achieve interchangeability
these parts should be produced to a dose dimensional tolerances.
• As a result, inspection is often more concerned with the dimensional variation from the standard or basic
dimension of the part. To this extent, inspection becomes a process of comparing manufactured parts to the
master part envisaged by the designer.
• The use of vernier caliper, micrometer, etc. will not be feasible because of the skill involved and the time required
to measure the dimension.
• The use of a comparator requires little or no skill for the operator to eliminate the human element for taking
measurement and gives quick and highly consistent results.
34. BASIC PRINCIPLE AND OPERATION OF COMPARATORS
The basic principle of operation of a comparator is:
• The comparator is first adjusted to zero on its dial or recording device with a gauge block in position. The gauge
block is of dimension which the workpiece should have. The workpiece to be checked is then placed in position
and the comparator gives the difference in dimension in relation to the gauge block.
• The dimension of the workpiece may be less than, equal to or greater than the standard dimension. If the
dimension is less or greater than the standard, the difference will be shown on the dial or the recording device of
• Thus, a comparator does not give the dimension of a workpiece, but only gives the difference between the
standard and the actual dimension of the workpiece. In comparators, this difference is shown as magnified on the
dial or the recording device.
• For example, if a comparator has a magnification of 1000, and if the difference between the standard and the
actual dimensions of a. workpiece is 0.02 mm, it will result in a pointer movement of 20 mm on the dial or
recording device of the comparator.
35. ESSENTIAL CHARACTERISTICS OF A GOOD COMPARATOR
1. Robust design and construction: The design and construction of the comparator should be robust so that it can
withstand the effects of ordinary uses without affecting its measuring accuracy.
2. Linear characteristics of scale: Recording or measuring scale should be linear and uniform (straight-line
characteristic) and its indications should be clear.
3. High magnification: The magnification of the comparator should be such that the smallest deviation in the size
of a component can be easily detected.
4. Quick in results: The indicating system should be such that the readings are obtained in the least possible time.
5. Versatility: Instruments should be designed that can be used for a wide range of measurements.
6. Minimum wear of contact point: The measuring plunger should have hardened steel contact or diamond to
minimize wear effects.
7. Further, the contact pressure should be low and uniform.
36. USES OF COMPARATOR
The various ways in which comparators can be used:
1. Laboratory Standards: Comparators are used as laboratory standards from which working or inspection
gauges are set and co-related.
2. Working Gauges: They are also used as working gauges to prevent work spoilage and to maintain required
tolerance at all important stages of the manufacturer.
3. Final Inspection Gauges: Comparators may be used as final inspection gauges where selective assembly, of
production parts, is necessary.
4. Receiving Inspection Gauges: AE receiving inspection gauges comparators are used for checking parts
received from outside sources.
5. For checking newly purchased gauges: The use of comparators enables the checking of the parts (components
in mass production at a very fast rate.)
37. CLASSIFICATION OF COMPARATOR
A wide variety of comparators are commercially available at present. They are classified according to the method
used for amplifying and recording the variations measured into the following types.
1. Dial indicators
2. Read type comparators
3. Sigma comparators
4. Johansson mikrokator
Mechanical optical comparators:
1. Optical lever
2. Zeiss optimeter
3. Zeiss ultra optimeter
4. Zeiss optotest comparators
39. MECHANICAL COMPARATORS
• Principle of working: A mechanical comparator employes mechanical means for magnifying the small movement
of the measuring stylus, brought about due to the difference between the standard and the actual dimension being
• In these comparators, the magnification of the small stylus movement is obtained by means of levers, gear trains,
rack, and pinion or a combination. The usual magnification obtained by these comparators ranges from about 250
to 1000, mechanical comparators are of the following types:
1. Dial indicator (Dial gauge)
2. Johansson Mikrokator
3. Read type mechanical comparator
4. Sigma comparator
40. MECHANICAL COMPARATORS
Dial Indicator (Dial Gauge):
• The simplest type of mechanical comparator is a dial indicator. It consists of a base with a rigid column rising
from its rear.
• An arm is mounted on this column and it carries a dial gauge at its outer end. The arm can be adjusted vertically
up and down along the e column.
• An anvil or a worktable is mounted on the base, which provides a reference on which workpieces are placed
during measuring operation.
• Such a simple comparator is ideal for the checking of components with a tolerance of say ± 0.05 millimeters.
• In its operation, the indicator is set to zero by the use of slip gauges representing the basic size of the part. The
part to be checked is then placed below the measuring plunger of the indicator.
41. MECHANICAL COMPARATORS
Dial Indicator (Dial Gauge):
• The linear movement of the plunger is magnified by means of a gear and pinion train into a sizable rotation of the
pointer. The variation in the dimension of the part from the basic size is indicated on the dial.
• Dial indicator is generally used for inspection of small precision machined parts. The dial indicator with various
attachments may be used for a large number of works; with V-block attachment it can be used for checking out of
roundness of a cylindrical part.
42. MECHANICAL COMPARATORS
• This instrument was first devised by m/s C.F. Johansson and hence the name. It uses a twisted strip to convert
small linear movement of a plunger into a large circular movement of a pointer.
• It is, therefore, also called as twisted strip comparator. It uses the simplest method for obtaining the mechanical
magnification designed by H. Abramson which is known as 'Abramson, movement'. A twisted thin metal strip
carries at the center of its length a very light pointer made of thin glass.
• One end of the strip is fixed to the adjustable cantilever strip and the other end is anchored to the spring elbow,
one arm of which is carried on measuring plunger. The spring elbow acts as a bell crank lever. The construction
of such a comparator is shown in the figure below.
43. MECHANICAL COMPARATORS
• A slight upward movement of the plunger will make the bell crank lever to rotate. Due to this, a tension will be
applied to the twisted strip in the direction of the arrow. This causes the strip to untwist resulting in the movement
of the point.
• The spring will ensure that the plunger returns when the contact pressure between the bottom tip of the plunger
and the workpiece is not there, that is when the workpiece is removed from underneath the plunger. The length of
the cantilever can be varied to adjust the magnification.
• In order to prevent excessive stress on the central portion, the strip is perforated along the centerline by
preformation as shown in the figure above.
• The magnification of the instrument is approximately equal to the ratio of the rate of change of pointer movement
to rate of change in length of the strip, i.e. dQ / dL. It can be shown that the magnification of the instrument
(dQ / dL) α (L / w2n)
where, Q = twist of mid-point of a strip with respect to the end
L = length of twisted strip measured along its neutral axis
w = width of the twisted strip
n = number of turns
44. MECHANICAL COMPARATORS
Reed type mechanical comparator:
• In reed type mechanical comparator, the gauging head is usually a sensitive, high quality, dial indicator. The dial
indicator is mounted on a base supported by a sturdy column.
• Figure below shows a read type mechanical comparator the reed mechanism is a frictionless device for
magnifying small motions of the spindle.
• It consists of a fixed block. Which is rigidly fastened to the gauge head case, and floating block B, which carries
the gauging spindle and is connected horizontally to the fixed block by reed C.
• A vertical reed is attached to each block with upper ends joined together. These vertical reeds are indicated by D.
Beyond this joint extends a pointer.
45. MECHANICAL COMPARATORS
Reed type mechanical comparator:
• Linear motion of the spindle moves the free block vertically causing the vertical reed on the floating block to
slide past the vertical reed on the fixed block.
• However, as the vertical reeds are joined at the upper end, instead of slipping, the movement causes both reeds to
swing through an arc.
• The scale may be calibrated by means of a gauge block to indicate any deviation from an initial setting. The
mechanical amplification is usually less than 100 but it is multiplied by the optical lens system. It is available in
amplification ranging from 500 to 1000.
46. MECHANICAL COMPARATORS
• This is a mechanical comparator providing magnification in the range of 300 to 5000. It consists of a plunger
mounted on two flat steel strings (slit diaphragms). this provides a frictionless linear movement for the plunger.
• The plunger carries a knife-edge, which bears upon the face of the mounting block of a cross-strip hinge. The
cross strip hinge is formed by pieces of flat steel springs arranged at right angles and is a very efficient pivot for
smaller angular movements.
• The moving block carries a light metal ¥forked arms. A thin phosphor bronze ribbon is fastened to the ends of the
forked arms and wrapped around a small drum, mounted on a spindle carrying the pointer.
47. MECHANICAL COMPARATORS
• Any vertical displacement of the measuring plunger and hence that of the knife-edge makes the moving block of
the cross strip liver to pivot. This causes the rotation of the Y-arms.
• The metallic band attached to the arms makes the driving drum and hence the pointer to rotate. The ratio of the
effective length (L) of the arm and the distance (a) of the knife edge from the pivot gives the first stage
magnification and the ratio of the pointer length (l) and radius (r) of the driving drum gives second stage
magnification of the instrument.
• The total magnification of the instrument is thus. The magnification of instrument can be varied by changing the
distance (a) of Knife-edge of tightening or slackening of then adjusting screws: The range of instruments
available provides magnifications of x 300 to X 5000, the most sensitive models allowing scale estimation of the
order of 0.0001 mm to be made.
48. MECHANICAL COMPARATORS
Some important features (advantages) of the sigma comparator are:
• Safety: As the knife-edge moves away from the moving member of the hinge and is followed by it, therefore, if
the too robust movement of the plunger is made due to shock load that will not be transmitted through the
• Dead beat Readings: By mounting nonferrous disc on the pointer spindle and making it move in the field of a
permanent magnet, dead beat reading can be obtained.
• Parallax: The error due to Parallax is avoided by having a reflective strip on the scale.
• Constant pressures. The constant measuring pressure over the range of the instrument is obtained by the use of a
magnet plunger on the frame.
• Fine adjustments are possible.
• Due to the motion of the parts, there is wear in the moving parts.
• It is not sensible as an optical comparator due to friction of the moving parts.
49. MECHANICAL COMPARATORS
Advantages & disadvantages of mechanical comparators:
• Cheaper. Mechanical comparators are less costly as compared to other amplifying devices.
• No need for an external agency. These instruments do not require any external agency such as electricity or air
and as such the variations in outside supply do not affect the accuracy.
• Linear Scale. Usually, the-mechanical comparators have a linear scale.
• Robust and compact: These instruments are robust and compact in design and easy to handle.
• Portable: For ordinary workshop conditions, these instruments are very suitable and being portable can be issued
from the stores.
50. MECHANICAL COMPARATORS
Advantages & disadvantages of mechanical comparators:
• Less accuracy (a) Due to more moving parts, the friction is more which reduces the accuracy (b) Any slackness in
moving parts also reduces the accuracy considerably.
• Sensitive to vibrations: The mechanisms in mechanical comparators have more inertia and this may cause them to
be sensitive to vibrations.
• Faults magnified: Any wear backlash dimensional faults in the mechanical devices used will also be magnified.
• Limited range: The range of the instrument is limited as the pointer moves over a fixed scale.
• Parallax error: Error due to Parallax are more likely with these instruments as the pointer moves over a fixed
51. OPTICAL COMPARATORS
• In these comparators, use is made of fundamental optical law and instead of a printer, the edge of the shadow is
projected on to a curved graduated scale to indicate the comparison measurement. The optical principle adopted
is that of, optical lever, which is shown in the figure below. If a ray of light OA strikes a mirror, it is reflected as
ray AB such that,
∠𝑂𝐴𝑁 = ∠𝑁𝐴𝐵
• Now, if the mirror is titled through an angle α reflected ray of light has moved through an angle 2 α. In optical
comparators, the mirror is tilted by the measuring plunger movement and the movement of the reflected light is
recorded as an image on a screen.
52. OPTICAL COMPARATORS
Mechanical Optical comparators:
• In mechanical optical comparators, a small displacement of the measuring plunger is amplified first by a
mechanical system consisting of pivoted levers.
• The amplified mechanical movement is further amplified by a single optical system involving the projection of
• As shown in fig.9.6 the mechanical system causes a plane reflector to tilt about an axis and the image of an index
is projected on a scale on the inner surface of a ground glass screen. Magnification: As shown in fig.2.29.
53. OPTICAL COMPARATORS
Mechanical Optical comparators:
1. Mechanical amplification = L2 / L1 (by lever principle)
2. Now, if the movement of the plunger causes the mirror to tilt by angle α, then the image, will be tilted by 2α.
3. Therefore optical amplification = 2 × (L4 / L3)
4. Thus, overall magnification of this system = 2 × (L2 / L1) × (L4 / L3)
54. OPTICAL COMPARATORS
Zeiss Ultra Optimeter:
• The optical system of Zeiss ultra optimeter involves light and thus double reflection gives a higher degree of
magnification. Figure below shows the optical system of this type of comparator.
• The light rays from the lamps fall on the green filter. The green filter filters all and green light pass to a
condenser, which projects are on to a movable mirror M1.
• It is then reflected another fixed mirror M2 and then back again to the first movable mirror. The objective lens
brings the reflected beam from the first mirror to a focus at a transparent graticule containing a precise scale
which is viewed by an eye-piece.
55. OPTICAL COMPARATORS
Zeiss Ultra Optimeter:
• Magnification: If the distance from the plunger centerline to the first mirror pivot is x and the plunger moves a
height then angler movement of the mirror δθ = (h / x), if f be the focal lens, then the movement of scale is 2f δθ
i.e. 2f × (h / x).
Therefore, magnification = (2fh / xh) = (2f / x).
Overall magnification = (2f / x) × Eyepiece magnification
• High accuracy: These comparators have very few moving parts and hence gives higher accuracy.
• No parallax error: The scare can be made past a datum line and thus have a high range and no parallax error.
• High magnification: Hence suitable for precision measurements.
• An optical lever is weightless.
• Illuminated scale: since scare is illuminated, it enables readings to be taken irrespective of room lighting
56. OPTICAL COMPARATORS
Zeiss Ultra Optimeter:
• As the magnification is high, heat from the lamp, transformers, etc. may cause the setting the drift.
• It depends on the external electrical power supply.
• Apparatus is usually bulky and expensive.
• When a scale is projected on a screen, the instrument is to be used in the darkroom.
• The instrument is inconvenient for continuous use because the scale is to be viewed through the eyepiece.
57. ELECTRICAL COMPARATORS
• These comparators depend on their operation on an A.C. Whetstone bridge circuit incorporating a galvanometer
in these comparators, the movement of the measuring contact is converted into an electrical signal. This electrical
signal is recorded by an instrument that can be calibrated in terms of plunger movement.
• The principle of an electrical comparator is shown in figure below. An armature supported on thin steel strips is
suspended between two coils A and B. when the distance of the armature surface from the two coils is equal, the
whetstone bridge is balanced and no current flows through its galvanometer. Sight movement of the measuring
plunger unbalances the bridge resulting in the flow of current through the galvanometer.
• The scale of the galvanometer is calibrated to give the movements of the plunger. Electrical comparators have
minimum moving parts and therefore give a high degree of reliability. Magnification of the order of X 30,000 are
possible with these comparators.
58. PNEUMATIC COMPARATORS
• The use of air as a means of magnification in metrology was originally developed by the Solex company in
France for the calibration of carburetor jets. The technique was subsequently developed for other types of
• In pneumatic comparators, the deviation of the dimension being measured from the standard is shown by a
variation in either (a) air pressure or (b) the velocity of airflow.
• The technique offers the advantage of enabling high magnification to be obtained (30,000: 1) or more; coupled
with good stability and reliability.
• Such a high order of magnification is possible because no physical contact is made either with the setting gauge
or the part being measured, and the internal dimensions may be readily measured not only with respect to
tolerance boundaries but also with respect to geometric form.
• Further, a single or a number of dimensions can be inspected simultaneously a wide variety of measuring heads
may be used to suit a particular type of work.
• The two most serious disadvantages are the limited range available and the low speed of response compared with
the electrical magnification system.
• The response of the comparator working on airflow is quicker than those working on air pressure. But the
comparators working on air pressure are more versatile.
59. PNEUMATIC COMPARATORS
Solex Pneumatic Gauges:
• This instrument was commercially introduced by Solex Air Gauges Ltd. It is generally designed for internal
measurement, but with suitable measuring head, it can be used for external gauging also.
• It uses a water manometer for the indication of backpressure. It consists of a vertical metal cylinder filled with
water up to a certain level and a dip tube immersed into it up to a depth corresponding to the air pressure
required. A calibrated manometer tube is connected between the cylinder and control artifice as shown in the
• If the pressure of the air supplied is higher than the desired pressure, some air will bubble out from the bottom of
the dip tube and air moving to the control volume will be at the desired constant pressure.
• The constant pressure air then passes through the control orifice and escape from the measuring jets when there is
no restriction to the escape of air, the level of water in the manometer tube will coincide with that in the cylinder.
60. PNEUMATIC COMPARATORS
Solex Pneumatic Gauges:
• But, if there is a restriction to the escape of air through the jets, back pressure will be induced in the circuit and
the level of water in the manometer tube will fall. The restriction to the escape of air depends upon the variations
in the dimensions to be measured.
• Thus the variation in the dimension to be measured is converted into corresponding pressure variations, which
can be read from the calibrated scale provided with the manometer.
• To find concentricity (roundness of any job at any section). The workpiece may be revolved around measuring
• If no change in reading is there, then it is a perfectly round hole. Similarly, the diameter can be noted down at
several places along the length of bore and thus tapering of a hole is determined.
• This method is, therefore, best suited for measuring roundness and taperness of cylinder bases and gun barrel