Engineering Metrology : System of Limits and Fits

ENGINEERING METROLOGY
SYSTEM OF LIMITS AND FITS

Introduction
The need for limits and fits for machined work pieces was brought about mainly by
the inherent inaccuracy of manufacturing methods, coupled with the fact that
“exactness” of size was found to be unnecessary for most work pieces. In order that
function could be satisfied, it was found sufficient to manufacture a given work piece
so that its size lay within two permissible limits, i.e. a tolerance, this being the
variation in size acceptable in manufacture.
Similarly, where a specific fit condition is required between mating work pieces, it is
necessary to ascribe an allowance, either positive or negative, to the basic size to
achieve the required clearance or interference, i.e. a “deviation”.

Role of Metrology in Design for
Manufacturing
ManufacturingAspect
Key Functional Requirements
Fit between the mating parts
Tolerances, dimensions on mating
parts
Manufacturing Processes &
Sequences
Cost of Manufacturing
Tolerance
CostofMfg.

Evaluation for Limits and Fits
StepsinvolvedintheEvaluationofLimitsof
Tolerances
Selection of an Appropriate FIT
based on functional requirement
Selection of Type of Shaft and Hole
Selection of Tolerance Grade for shaft and
Hole
Evaluation of standard Tolerance
Evaluation of Limits of Tolerances

Introduction
Precision and Accuracy:
Precision refers to repeatability
Accuracy refers of result to the true value
Accuracy can be found by
Accuracy = √(Repeatability)2 + (Systematic error)2
where, systematic error =True value- mean of set of readings

Terms and Definitions
LIMITS:
These are two extreme permissible sizes of
dimension between which actual size of
dimension is contained.
Maximum limit of Size:
The greatest permissible size of a feature.
Minimum limit of Size:
The smallest permissible size of a feature.
Tolerance:
Permissible variation in size or dimension is
called tolerance. Amount by which a job is
Allowed to go away from accuracy without any
functional trouble.

FIT:
It is the relationship existing between two mating parts with respect to amount of play
or interference which is present when they are assembled together.
It is the degree of tightness or looseness between two mating parts to perform a
definite function
It is the relation between dimensions of two mating parts before their assembly.

Terms and DefinitionsTYPES OF FITS
Clearance Fit:
A fit that always provides a clearance between the hole and shaft when assembled,
i.e. the minimum size of the hole is either greater than or, in the extreme case, equal
to the maximum size of the shaft
Minimum Clearance:
In a clearance fit, the positive difference between the minimum limit of size of the
hole and the maximum limit of size of the shaft.
Maximum Clearance:
In a clearance or transition fit, the positive difference between the maximum limit of
size of the hole and the minimum limit of size of the shaft.

Interference (Press or Force )Fit:
A fit which everywhere provides an interferers between the hole and shaft when
assembled, i.e. the maximum size of the hole is either smaller than or, in the extreme
case, equal to the minimum size of the shaft.
Minimum interference:
In an interference fit, the negative difference, before assembly, between the
maximum limit of size of the hole and the minimum limit of size of the shaft.
Maximum interference:
In an interference or transition fit, the negative difference, before assembly, between
the minimum limit of size of the hole and the maximum limit of size of the shaft .

Transition Fit:
Fit which may provide either a clearance or an interference between the hole and
shaft when assembled, depending on the actual sizes of the hole and shaft, i.e. the
tolerance zones of the hole and the shaft overlap completely or in part.

General Terms used in limits & fits:
Shaft:
A term used, according to convention, to describe an external feature of a Workpiece,
including features which are not cylindrical
Hole :
A term used, according to convention, to describe an internal feature of a Workpiece,
including features which are not cylindrical
Basic Size:
It is the size with reference to which upper or lower limits of size are defined.
Actual size:
The size of a feature, obtained by measurement.
Zero Line:
It is a line along which represents the basic size and zero(or initial point) for
measurement of upper or lower deviations.

Deviation:
The algebraic difference between a size(actual size, limit of size, etc.) and the
corresponding basic size.
Upper Deviation:
The algebraic difference between the maximum limit of size (of either hole or shaft)
and the corresponding basic size, like ES, es.
Lower Deviation:
The algebraic difference between the minimum limit of size (of either hole or shaft)
and the corresponding basic size, like EI, ei.
Fundamental Deviation:
It is one of the two deviations which is chosen to define the position of the tolerance
zone.
Tolerance:
The algebraic difference between upper and lower deviations. It is an absolute value.

Maximum Material Condition (MMC):
The condition where a size feature contains the maximum amount of material within
the stated limits of size. I.e., largest shaft and smallest hole.
Least Material Condition (LMC):
The condition where a size feature contains the least amount of material within the
stated limits of size. I.e., smallest shaft and largest hole.
SIZE DIMENSION
MMC
LMC
ENVELOPE OF SIZE
(2.003)
(2.007)
ENVELOPE PRINCIPLE
Tolerance:
Difference between MMC and LMC
limits of a single dimension.
Allowance:
Difference between the MMC of
two mating parts.
(Minimum clearance and maximum
interference)

Systems of Fit:
A system of fits comprising shafts and holes belonging to a limit system.
There are two systems by which a fits can be accomplished –
Hole Basis System
A system of fits in which the required clearances or interferences are obtained by
associating shaft of various tolerance classes with hole of a single tolerance class.
• Hole size is kept constant and shaft is varied to give various types of fit.
• Basic size taken is low limit of hole
• High limit of hole & two limits (HL&LL) give the desired fit

Shaft Basis System
A system of fits in which the required clearances or interferences are obtained by
associating holes of various tolerance classes with shafts of a single tolerance class.
• Shaft size is kept constant & hole size is varied to give various fits.
• Basic size is taken as max limit size of shaft.
• LL of shaft and two limits (HL & LL) of hole give the desired fit.
• Method not preferred in large production

Standard Tolerance grades:
It is an indication of the level of precision. The standard tolerance grades are
designated by the letters IT followed by a number, e.g. IT7.
The IS0 system provides for a total of 20 standard tolerance grades of which grades
IT1 to IT18 are in general use and are given in the main body of the standard.
Grades IT0 and ITO1, which are not in general use, are given in Annex-A for
information purposes.
IT01 to IT4 - For production of gauges, plug gauges, measuring instruments
IT5 to IT 7 – For fits in precision engineering applications
IT8 to IT11 – For General Engineering
IT12 to IT14 – For Sheet metal working or press working
IT15 to IT16 – For processes like casting, general cutting work

Tolerance class:
The position of the tolerance zone with respect to the zero line, which is a function of
the basic size, is designated by (an) uppercase letter(s) for holes (A . . . ZCI or (al lower
case letter(s) for shafts (a . , . zc)
A tolerance class shall be designated by the letter(s) representing the fundamental
deviation.
For any basic size there are 28 different holes progressively oversize and undersize.
28 holes are ‐‐A,B,C,CD,D,E,EF,F,FG,G,H,J,JS,K,M,N,P,R,S,T,U,V,X,Y,Z,ZA,ZB,& ZC

Bases of limits and fits
Basic size steps:
For convenience, the standard tolerances and fundamental deviations are not
calculated individually for each separate basic size, but for steps of the basic size.
These steps are grouped into main steps and intermediate steps.
The values of the standard tolerances and fundamental deviations for each basic size
step are calculated from the geometrical mean (D) of the extreme sizes(D1 & D2) of
that step, as follows :
D =  D1x D2
For the first basic size step (less than or equal to 3 mm), the geometrical mean, D,
according to convention, is taken between the sizes 1 and 3 mm,
therefore D = 1.732 mm.

Standard tolerance grades
The IS0 system of limits and fits provides for 20 standard tolerance grades designated
IT01, IT0, IT1, , IT18 in the size range from 0 up to 500 mm (incl.), and 18 standard
tolerance grades in the size range from 500 mm up to 3 150 mm (incl.), designated IT1
to IT18.
Derivation of standard tolerances (IT) for basic sizes up to and including 500 mm
Standard tolerance grades IT01 to IT4
The values of standard tolerances in grades IT01, IT0 and IT1 are calculated from the
formulae given in table Below. It should be noted that no formulae are given for
dddddd grades IT2, IT3 and IT4. The values
for tolerances in these grades have
been approximately scaled in
geometrical progression between
the value for IT1 and IT5.

Derivation of standard tolerances (IT) for basic sizes up to and including 500 mm
The values for standard tolerances in grades IT5 to IT18 for basic sizes up to and
including 500 mm are determined as a function of the standard tolerance factor, i.
The standard tolerance factor, i, in micrometres, is calculated from the following
formula :
i = 0.45D + 0.001D
where, D (mm) is the geometric mean of the lower and upper diameters of a
particular diameter step within which the chosen the diameter D lies.
3

Derivation of standard tolerances (IT) for basic sizes from 500 mm up to and
including 3500 mm
The values for standard tolerances in grades IT1 to IT18 are determined as a function
of the standard tolerance factor, I.
The standard tolerance factor, I in micrometres, is calculated from the following
formula :
I = 0.004D + 2.1
where, D (mm) is the geometric mean of the lower and upper diameters of a
particular diameter step within which the chosen the diameter D lies.

Derivation of fundamental deviations
Fundamental deviations for shafts
The fundamental deviations for shafts are calculated from the formulae given in
Table 9.
The fundamental deviation given by the formulae in table 9 is, in principle, that
corresponding to the limits closest to the zero line, i.e. the upper deviation for shafts a
to h and the lower deviation for shafts k to zc.
Fundamental deviations for Hole
The fundamental deviations for holes are calculated from the formulae given in table 9
and, therefore, the limit corresponding to the fundamental deviation for a hole is
exactly symmetrical, in relation to the zero line, to the limit corresponding to the
fundamental deviation for a shaft with the same letter.

Example #1
Evaluate limits and fits for a pair of – Diameter 6 H7/g6
Solution: The size 6 mm lies in the diameter step of 3-6, therefore, D is given by
D = 3×6 = 4.24mm
The value of fundamental tolerance unit is given by –
i = 0.45D + 0.001D
i = 0.454.24 + 0.001x4.24
i = 0.7327μm
Limits of tolerance for hole H7
The standard tolerance is 16 i = 16x0.7327 = 11.72 = 12 μm
The fundamental deviation H hole is = 0
Limits of tolerance for g6 shaft
The standard tolerance is 10i =10x0.7327 = 7.327 = 8 μm
The fundamental deviation g shaft is = −2.5D0.34 = −2.5(4.24)0.34 = −4.085=(-)4μm
3
3

H7 Hole
g6 Shaft
12μm
4μm
8μm
6.000
BASIC SIZE
6.012
5.988
5.996
Disposition of tolerance zone around the zero line
Fit
Maximum clearance = Maximum size of hole - Minimum size of shaft
= 6.012 – 6.988 = 0.024 mm = 24 μm
Minimum clearance = Minimum size of hole - Maximum size of shaft
= 6.000 - 6.996 = 0.004 mm = 4 μm
The type of fit is Clearance.

Example #2
Calculate the limits of sizes for Dia. 20 P7/h6 and identify the fit.
Solution: The size 20 mm lies in the diameter step of 18-24, therefore, D is given by
D = 18×24 = 20.78mm
The value of fundamental tolerance unit is given by –
i = 0.45D + 0.001D
i = 0.4520.78 + 0.001x20.78
i = 1.258μm
Limits of tolerance for hole H7
The standard tolerance is 16 i = 16x1.258 = 20.128 = 21 μm
The fundamental deviation H hole is= IT7 + 0 to 5 = 10i+5 = 10x1.258+5=17.58= 18μm
Limits of tolerance for h6 shaft
The standard tolerance is 10i =10x1.258 = 12.58 = 13 μm
The fundamental deviation h shaft is = 0
3
3

H7 Hole
h6 Shaft18μm 13μm
21μm
20.000
BASIC SIZE
19.982 19.987
Disposition of tolerance zone around the zero line
Fit
Maximum clearance = Maximum size of hole - Minimum size of shaft
= 19.982 – 19.987 = - 0.005 mm = -5 μm
Minimum clearance = Minimum size of hole - Maximum size of shaft
= 19.961 – 20.000 = 0.039 mm = -39 μm
The fit is Interference. But it can become Transition if you choose some value of
FD for p shaft between IT7 + 1 to 5 μm
19.961

Applications
Shafts Grades Description of fit Application
a, b, c 11 Very large clearance Generally not used
d 8, 9, 10 Loose running Loose pulleys
e 7, 8, 9 Loose clearance Electric motor bearings, heavily
loaded bearing
f 6, 7, 8 Normal running Lubricated bearings (with oil or
grease), pumps and smaller
motors, gear boxes
g 5, 6 Precision running Lightly loaded shafts, sliding
spools, accurate bearings
h 5 to 11 Extreme clearance
(preferably for non running parts)
Sockets and spigots of joints
Clearance Fits (Hole Basis System):

Applications
Transition Fits (Hole Basis System):
js 5, 6, 7 Slight clearance to slight
interference
Very accurate location, couplings,
spigots, gears,
k 5, 6, 7 No clearance to little clearance Precision joints likely to be
subjected to vibrations
m 5, 6, 7 Slight interference (on average) Forced assembly is required
n 5, 6, 7 Slight interference and very little
clearance
Semi-permanent or tight fit
assemblies

Applications
Interference Fits (Hole Basis System):
p 6,7,8 True interference (light) Fixing bushes, standard press fit
r 5, 6, 7 Interference
(but can be dismantled)
Tight press fit. Keys in key ways
s 5, 6, 7 Semi permanent/
permanent fit
Valve seating, collars on shafts
t,u -------- High degree of
interference
Permanent assemblies

Engineering Metrology : System of Limits and Fits

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