Metrology and Measurements

Unit 3 – Tolerance Analysis

Contents
• Tolerancing
– Interchangeability, Selective assembly, Tolerance
representation, Terminology
• Limits and Fits
– Problems (using tables)
• Design of Limit gauges
– Problems
• Tolerance analysis in manufacturing
• Process capability
• Tolerance stackup
• Tolerance charting
Interchangeable Manufacture

Bottle caps Rims Tires

Examples for interchangeability

Interchangeability
• An interchangeable part is one which can be substituted for
similar part manufactured to the same drawing
• When one component assembles properly (and which
satisfies the functionality aspect of the assembly) with any
mating component, both chosen at random, then it is known
as interchangeability
• The parts manufactured under similar conditions by any
company or industry at any corner of the world can be
interchangeable
Advantages of Interchangeable Manufacture
• Replacement: One such part can freely replace
another, without any custom fitting (such as filling)
• Easy to Assembly: This interchangeability allows easy
assembly of new devices
• Repairing: Easier repair of existing devices
• Minimizing time and cost: Minimizing both the time
and skill required of the person doing the assembly
or repair
• Rapid Manufacturing: Machine tool enables the
components to be manufactured more rapidly
Selective Assembly
• Components are measured and sorted into groups by
dimension, prior to the assembly process in selective
assembly. This is done for both mating parts
• Often special cases of accuracy and uniformity arises which
might not be satisfied by certain of the fits given under a fully
interchangeable system
• For example, if a part at its low limit is assembled with the
mating part a high limit, the fit so obtained may not fully
satisfy the functional requirements of the assembly
• Also machine capabilities are sometimes not compatible with
the requirements of interchangeable assembly
Advantages of Selective Assembly
• There is a larger number of acceptable parts as original
tolerances are greater
• This in turn allows the manufacture of cheaper parts as less
will be consigned to the waste bin
• Selective Assembly assures better and more accurate
assembly of parts by insuring closer tolerances between the
mating parts
• Rise the quality and lower manufacturing costs by avoiding
tight tolerances
• Reduces the rejection rate (scrap rate)
Limitations of Selective Assembly
• During usage of the assembly if one component fails, first we
need manual of assembly and identify the group to which
failure component belongs to, and search the component in
spare parts
• By focusing on the fit between mating parts, rather than the
absolute size of each component so there will small deviation
in size of component
Tolerance

• Due to the inevitable inaccuracy of manufacturing methods,

a part cannot be made precisely to a given dimension, the
difference between maximum and minimum limits of size of a
part is the tolerance
• Tolerance is the total amount that a specific dimension is
permitted to vary
• There is no such thing as an "exact size". Tolerance is key to
interchangeable parts
• When two parts are to be assembled, the relation resulting
from the difference between their sizes before assembly is
called a fit
How to Decide Tolerance?
• Functional requirements of mating parts
• Cost of production
• Available manufacturing process
• Tolerance is chosen as large as possible without
compromising functional requirements
• Proper balance between cost and quality of parts
Definitions
Size
• It is a number expressed in a particular unit in the
measurement of length
Actual size (of a part)
• The measured size of the finished part after
machining
Basic size
• The theoretical size used as a starting point for the
application of tolerances
Definitions
Design size
• The ideal size for each component (shaft and hole) based
upon a selected fit
Limits of size
• The maximum and minimum sizes shown by the tolerance
dimension
Maximum limit of size
• It is the maximum size permitted for the part
Minimum limit of size
• It is the minimum size permitted for the part limit of size
Definitions
Maximum material limit
• It is the condition of a part when it contains the most amount
of material. The MMC of an external feature (such as a shaft) is
the upper limit. The MMC of an internal feature(such as a hole)
is the lower limit
Minimum material limit
• It is the condition of a part when it contains the least amount
of material possible. The LMC of an external feature is the
lower limit of the part. The LMC of an internal feature is the
upper limit of the part
Tolerance
• Tolerance is the difference between maximum limit of size and
minimum limit of size
Definitions
Zero line
• It represents the basic size
Upper deviation - ES (for hole) or es (for shaft)
• It is the algebraic difference between maximum limit of size
and its corresponding basic size
Lower deviation - EI (for hole) or ei (for shaft)
• It is the algebraic difference between minimum limit of size
and its corresponding basic size
Fundamental Deviation
• It is the deviation, either upper or lower deviation, which is
nearest to the zero line for either a hole or a shaft
Tolerance zone
• A region representing the difference between the upper and
the lower limits
 Definitions
Unilateral tolerance
In this method of presenting the limits, variation is allowed only on
one side of the zero line
Bilateral tolerance
• Here the limits variation is allowed on either sides of the zero line
Tolerance Grade
• It is degree of accuracy of manufacturing. It is designed by the
letter IT (International Tolerance) IT01, IT0, IT1, IT2 …
Tolerance Class
• This term is used for a combination of fundamental deviation and
tolerance grade
 Definitions
Allowance
• It is an intentional difference between the maximum material
limits of mating parts
Fits
• The relationship existing between two parts, shaft and hole,
which are to be assembled, with respect to the difference in their
sizes is called fit
Shaft
• It refers to any external feature of a part, including any non
cylindrical features as well
Hole
• The term used for any internal feature of a part including any non
cylindrical as well
Size
Tolerance

The Tolerance is 0.001” for the Hole as well as for the Shaft
Limits
Tolerance Types

Unilateral tolerance Bilateral tolerance

Material Limits
• Maximum material limit
• Minimum material limit
 The Effects of Tolerance
Minimum:
+0.01 1.38+0.01, 1.50-0.01
-0.01 A = 1.49-1.39= 0.1
Maximum:
1.38-0.01=1.37, 1.51
A=0.14

+0.01
-0.01

Calculate the maximum and minimum possible dimension of A

Fit
• Fit is the relationship that exists between two mating
parts, a hole and shaft with respect to their
dimensional difference
• A clearance fit results in a clearance between the
two mating parts under all tolerance conditions
• An interference fit results in an interference
between two mating parts under all tolerance
conditions
• A transition fit results in either a clearance or an
interference condition between two assembled parts
 CHAPTER ONE : Fits and Tolerances
Types of Fit

Transition fit

d
Clearance Fits

Slide Clearance Fits: gear box, lathe tailstock, drilling spindle

Running Clearance Fits: gear box bearing, shaft carrying pulleys
Grades: RC1 - No noticeable clearance, not for free run
• RC2 - small clearance, not for free run
• RC3 – Precision running fits with small clearance
• RC4 – Close running fits
• RC5, RC6 – Medium running fits with higher clearance
• RC 7 – Free running fits. For higher temperature applications
• RC8,RC9 – Loose running fits. Fits exposed to corrosion, contamination etc
Interference Fits

Longitudinal Press (Force Fit): Forcible pushing, surface may be stripped

Transverse Fit (Shrink Fit): Heating or cooling fit, high loading capacity
Grades: FN1 – Light drive fits, cast iron outer member
• FN2 – Medium drive fits, high grade cast iron
• FN3 – Heavy drive fits, heavy steel parts
• FN4, FN5 – Force fit with maximum interference
Transition Fits

Push Fit: gear box, bushing

Wringing Fit: reusable/repairable parts
Grades
LT1 , LT2 – Tight fits with small clearances or negligible interference, gears,
pulleys, bushing
LT3, LT4 – Fits with small clearances or negligible interference, clutches,
brakes discs
LT5, LT6 – Fixed fits with negligible clearance, fixed plugs, driven bushings
 Basic Shaft System of Fits
• Size of the shaft
remains the same and
the hole size is varied to
get the required fit
• Maximum shaft size is
taken as the basic size,
an allowance is
assigned, and
tolerances are applied
on both sides of and
away from this
allowance
 Basic Hole System of fits
• Hole remains the same and
shaft size is varied to get
the required fit
• Minimum hole is taken as
the basic size, an allowance
is assigned, and tolerances
are applied on both sides of
and away from this
allowance
Shaft and Hole Based Systems
Deviations

Or Zero deviation line

For remembrance
es: Error from zero line (Basic Size) to superior size of shaft
ei: Error from zero line (Basic Size) to inferior size of shaft
ES: Error from zero line (Basic Size) to superior size of hole
EI: Error from zero line (Basic Size) to inferior size of hole
Fundamental Deviation
Symbols for Tolerances, Deviations and Fits
• Tolerance value is a function of the basic size and is indicated by a
number called the grade (IT7 --> 7)
• Tolerance zone position is the position of the tolerance zone with
respect to the zero line, is indicated by a letter symbol, a capital letter for
holes and a small letter for shafts (A, B, C…H….X, Y, Z & a, b, c…h...x, y, z)
• The tolerance size thus defined by its basic value followed by a symbol
composed of a letter and a number. It is established by a combination of
the fundamental deviation indicated by a letter and the IT grade number.
In the dimension 50H8, the H8 specifies the tolerance zone.
Example for shaft: 45g7
• A fit is indicated by the basic size common to both components, followed
by symbol corresponding to each component, the hole being quoted first

Example: 45 H8 g7
Possibly 45 H8 – g7 Or 45 H8/g7
Symbols for Tolerances, Deviations and Fits

International Tolerance (IT) Grading System

Fundamental Deviations

Fundamental Deviations Letter For Hole and Shaft Basis

The value for the hole from "A" to "H" are positive (+), for the shaft from "a" to "h"
negative (-). The value of the hole from "J" to "K" either positive (+) or negative (-), for
shaft form "j" to "k" either positive (+) or negative (-)
Fundamental Deviations for Shafts
Fundamental Deviations for Shafts
Fundamental Deviations for Holes
Fundamental Deviations for Holes
Tolerance Grades
• Eighteen tolerance grades are available and
denoted as IT01, IT0 and IT1 to IT16
Size Specification Methods
Metric Preferred Hole Based System of Fits
Metric Preferred Shaft Based System of Fit
Tolerance Grades
Tolerance grade Intended for Applicable to components or machines
I T 01
IT0 Slip blocks, Reference gauges
IT1
Gauges
IT2
IT3 High quality gauges
IT4
IT5 Ball bearing
IT6 Grinding, Honing
IT7 Broaching
IT8 Fits Center lathe turning
IT9 Worn automatic lathe
I T 10 Milling
I T 11 Drilling, Rough turning
I T 12 Light press work
I T 13 Press work
I T 14 Not for fits Die casting
I T 15 Stamping
I T 16 Sand casting
International Tolerance Grade Selection
• Tolerance grade defines the range of dimensions that can vary
(allowable dimensional variation)
Product requirements and Manufacturing constraints are
considered while choosing a tolerance grade
Calculation of International Tolerance Grades
IT Grades IT01 to IT5 are the most accurate and used essentially for gauge. IT
Grades IT6 to IT 16 are less accurate and are used for non mating dimensions.
International Grade can be calculated as given below:

where T : International Tolerance grade in µm

D : Geometric mean dimension in millimetres in mm
ITG : IT Grade (a positive integer)

Also T : International Tolerance can be calculated as;

where "i“ is standard tolerance unit/factor

for IT5 to IT16: (µm)

Tolerance for other grades
here, D (mm) is the geometric mean of the lower
and upper diameters of a particular diameter step
(D1->D2) within which the chosen the diameter D lies.
Calculation of International Tolerance Grades

Standard diameter steps

INTERNATIONAL TOLERANCE GRADES

IT5 IT6 IT7 IT8 IT9 IT10 IT11 IT12 IT13 IT14 IT15 IT16

7i 10i 16i 25i 40i 64i 100i 160i 250i 400i 640i 1000i
Fundamental Deviation for Shafts
Example Problem
Determine the type of fit 55H7/f8
Example Problem
Limit Gauges
• Limit gauging is a method of checking dimensions in which a fixed gauge is
applied to the work in order to determine whether a given component lies
within its limits
• It does not have any scale and inspects only whether, the part is inside or
outside its tolerance zone
• The gauge neither measures a value of dimensions, nor shows the value of
error evolved in the component. It simply checks that part is correct or not
Limit Gauges
• Used for inspection purposes
– Provide quick means of checking specific dimension
• Easy to use and accurately finished to required
tolerance
– Generally finished to ten times the tolerance
designed to control

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 Types of Gauges
1. Hole Gauge is used to check the dimensions of the hole present
in the element
2. Shaft Gauge is used to check the dimensions of the shaft
3. Taper Gauge is used to check the dimensions of the tapers
4. Thread Gauge is used to check the threading of the element
5. Form Gauge is used to check the forms of the elements
Cylindrical Plug (Hole) Gauges
• Dimensions usually stamped on handle at each end
• "go" end longer than "no-go" for easy
identification
• Many made with carbide tips to increase gauge life

55
Plain Ring (Shaft) Gauges
• Used to check outside diameter of work pieces
• Ground and lapped internally to a desired size
• Size stamped on the side of gauge
• Outside diameter knurled and "no-go" end identified by annular
groove on knurled surface
• Precautions and procedures similar to those outlined for a plug gauge

56
Snap Gauges
• One of most common types of comparative measuring instruments
• Faster to use than micrometers
• Limited in their application
• Used to check diameters within certain limits by comparing part size
to preset dimension of snap gauge
• Have C-shaped frame with adjustable gauging anvils or rolls set to "go"
and "no-go" limits of the part

57
Taper Gauges
• Taper gauges are made in both the plug and ring styles and, in general,
follow the same standard construction as plug and ring gauges
• When checking a taper hole, the taper plug gauge is inserted into the
hole and a slight pressure is exerted against it
• If it does not rock in the hole, it indicates that the taper angle is correct.
The same procedure is followed in a ring gauge for testing tapered
spindle

58
Thread Plug/Ring Gauges
• Used for checking internal threads of the "go" and "no-go" variety
• Based on same principle as cylindrical plug gauges
• "go" end (longer end) should be turned in flush to bottom of hole
• "no-go" end should just start into hole and become snug before third
thread enters

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Thread Plug/Ring Gauges
Form and Pitch Gauges
Radius and Fillet Gauges
Feeler Gauge

• It is an accurately manufactured strip of metal

• Also used to measure piston ring gap, piston ring side clearance and
connecting rod side clearance
Plate and Wire Gauges
Design of Limit Gauges
(Material Condition)
Taylor’s Principle
• The “Go” gauge should always be so designed that it will cover the
maximum metal condition (MMC), whereas a “NOT-GO” gauge will cover
the minimum (least) metal condition (LMC) of a feature, whether external
or internal
• The “Go” gauge would be plug gauge having a minimum length equal to
the length of the hole or the length of the engagement of the associated
part, whichever is smaller
• The “Go” gauge should always be so designed that it will cover as many
dimensions as possible (size, roundness, location etc) in a single operation,
whereas the “NOT-GO” gauge will cover only one dimension
Gauge Tolerance
1. Unilateral system, the gauge tolerance zone lies entirely with in the
work tolerance zone
– Work tolerance zone available is only about 80%
– Ensures that every accepted component will be lies within the work
tolerance zone and mostly used in industries
2. Bilateral system, the gauge tolerance zones are bisected by the work
tolerance zone
– Components which are within working limits can be rejected and parts
which are outside the working limits can be accepted. But the percentage of
such components is less
Gauge Tolerance Specification
First Method
• Workshop gauge tolerances are inside the work tolerance, whereas the
inspection gauge tolerances fall outside the work tolerance
• Some of the components are rejected even if they are well within the
work tolerance limits
• Workshop and inspection gauges have to be manufactured separately
Gauge Tolerance Specification
Revised System of Gauges
• The tolerance zone on inspection gauges is reduced and the tolerance on
workshop are kept as initial system
• Inspection gauges are reduced due to the reduction of tolerance on these gauges
Gauge Tolerance Specification
British System
• Tolerance zone for the GO gauges is placed inside the work limits and that for the
NOT GO gauges is outside the work limits
• In accordance with Taylor’s principle and is widely accepted in industries
• Same tolerance limits are specified on workshop and inspection gauges
• Wear allowance (10%)should not be permitted beyond the MML of the work
Gauge Tolerance
Wear Allowance
• The measuring surfaces of gauges, although chrome platted, hardened
and lapped, wear out with the time they are in use
• Wear allowance is added to the nominal diameter of a plug gauge and
subtracted from that of a ring gauge
• Wear allowance is applied to the nominal gauge diameter before gauge
tolerance is applied
• The wear allowance must be kept as small as possible
• Wear allowance is usually taken as 5% of work tolerance
• This wear allowance is generally applied to only “GO-gauge”
Plug Gauge Design
Example Problem
Design a plug gauge for checking a bearing hole of size
considering unilateral system. Use gauge tolerance and wear
allowance as 10% and 5% of work tolerance respectively.
High limit of bearing = 30.02 mm
Low limit of bearing = 29.98 mm
Total work tolerance = 0.04 mm

Wear allowance = 5% of work tolerance = 0.002 mm

Nominal size of Go-plug-gauge = 29.98 + 0.002 = 29.982 mm
Process Capability
• Process Capability is the ability of an engineering process to
produce an output within specification limits
• The concept of process capability only holds meaning for
processes that are in a state of statistical control
• This means it cannot account for deviations which are not
expected, such as misaligned, damaged, or worn equipment
• The minimum tolerance that can be applied to components,
which can be produced by a machine with more than 99% of
acceptability is called as process capability of the machine
 80±0.1 680/1000 (Acceptability:68%)
 80±0.2 910/1000
 80±0.3 991/1000 (Acceptability:99%)
 80±0.4 993/1000
 80±0.6 1000/1000 (Acceptability:100%)
Process Capability Index
• The process capability index is a statistical measure of process
capability
• The concept of process capability only holds meaning for
processes that are in a state of statistical control
• This means it cannot account for deviations which are not
expected, such as misaligned, damaged, or worn equipment
• Process capability indices measure how much "natural
variation" a process experiences relative to its specification
limits, and allows different processes to be compared to how
well an organization controls them
• Higher index values indicate better performance
Process Capability Indices
• The process capability index,
Cp = (USL – LSL) / 6σ
• The upper side process capability index,
Cpu = (USL – ) / 3σ
• The lower side process capability index,
Cpl = ( – LSL) / 3σ
• The least process capability index,
Cpk = min((USL – ) / 3σ, ( – LSL) / 3σ)
USL – Upper specification limit (maximum size)
LSL – Lower specification Limit (minimum size)
USL-LSL = Tolerance
σ – Population standard deviation
– Control size/Mean/Size