Limits and Fits, Limit System, Hole Basis System and Shaft Basis System, Important Terms Used in Limit System, Deviation, Allowance, Fits, Classification of Fits, Clearance Fit, Interference Fit, Transition Fit
Limit System:
Every day products we come across operate at certain
performance levels. This is made possible when the products are made with
certain degree of precision. The degree of precision needed differs greatly
when the performance levels are different. Tolerancing [permissible variation
of size] allows the designer to control dimensions and to imply a certain
precision. Tolerancing controls the maximum and minimum size of parts. The
range of allowed variation in size is the tolerance, which in turn affects the
tooling/method of manufacture to produce it. Higher tolerances can use less
precision methods. Tolerancing allows the designer to have a means of
controlling the sizes of features, which in turn influences the part performance
and the tooling required. Parts with high tolerances are greatly cheaper, hence
a designer normally selects maximum value of tolerance that can allow a part to
perform as desired. The system, in which a variation in dimension is accepted,
is called a limit system and be allowable deviations / variations are
tolerances. The actual size lies between the two limits of a dimension. The
relationships between the mating parts are called fits.
Limits:
The two extreme permissible sizes between which the actual
size is contained, are called limits. The maximum size is called the upper
limit and the minimum size is called the lower limit. The limits are fixed with
reference to the basic size of that dimension.
Important terms used in limit system
Nominal Size:
It is the size of a part specified in the drawing as a
matter of convenience.
Basic Size:
It is the size of a part to which all limits of variation
[i.e. tolerances] are applied to arrive at final dimensioning of the mating
parts. The nominal or basic size of a part is often the same.
Actual Size:
It is the actual measured dimension ofthe part. The
difference between the basic size and the actual size should not exceed a
certain limit, otherwise it will interfere with the interchangeability of the
mating parts.
Tolerance Zone:
It is the zone between the maximum and minimum limit size,
as shown in Fig.
Zero Line:
It is a straight line corresponding to the basic size. The
deviations are measured from this line. The positive and negative deviations
are shown above and below the zero line respectively.
Upper Deviation:
It is the algebraic difference between the maximum size and
the basic size. The upper deviation of a hole is represented by a symbol ES
[Ecart Superior] and of a shaft, it is represented by es.
Lower Deviation:
It is the algebraic difference between the minimum size and
the basic size. The lower deviation of a hole is represented by a symbol EI
[Ecart Inferior] and of a shaft, it is represented by ei.
Actual Deviation:
It is the algebraic difference between an actual size and
the corresponding basic size.
Mean Deviation:
It is the arithmetical mean between the upper and lower
deviations.
Deviation:
It is the algebraic difference between size (actual, maximum
etc.,] and the corresponding basic size. The algebraic difference between upper
limit of the size and the corresponding basic size is called the upper
deviation and the difference between the lower limit of the size and the
corresponding basic size is called the lower deviation.
The upper limit may be
greater or lesser than the basic size and similarly, the lower limit may be
greater or lesser than the basic size. When the upper limit is greater than the
basic size, the upper deviation is positive and when the lower limit is greater
than the basic size, the lower deviation is positive. When the upper limit is
less than the basic size, the upper deviation is negative and if the lower
limit is smaller than the basic size, the lower deviation is negative.
Indication of limits and tolerances for hole and shaft.
Component Size:
Fundamental deviation is the deviation [upper/ lower]
whichever is closer to the basic size for both hole and shaft. It is indicated
by capital letter for hole and by lower case letter for shaft.
Maximum Material Condition/Limit [MMC]:
It is the
condition in which a feature of size contains maximum amount of metal/material
within the standard limits of size. For example, a shaft having a diameter
29.98 mm only be at MMC if it is manufactured at 29.98 mm.
Similarly, a part with a hole of diameter 30.00 mm would be
at MMC if the hole is drilled at 30.00 mm diameter.
The upper limit of a shaft
and lower limit of a hole correspond to MMC. Clearance fits are usually
dimensioned on the basis of MMC and if parts are produced at MMC, the clearance
obtained will be minimum. This type of dimensioning has an advantage when the
workman aims at the principal dimensions, but by error produces an oversize
hole or an undersize shaft, the parts might still be acceptable, provided the
dimensions do not exceed the tolerance limits specified by the drawings.
Least Material Condition/Limit [LMC]:
The condition in which a feature of a size contains least
amount of material, within the stated, limits of size. For instance a shaft
having a diameter of 30.022 will only be at the least material condition, if it
is manufactured at 30.022 mm. Similarly a part with a hole of diameter would be
at the LMC, if the hole is drilled at 30.021 mm diameter.
The lower limit of a
shaft and upper limit of a hole correspond to LMC. The interference fits are
usually dimensioned on the basis of LMC to ensure minimum interference of the
mating parts.
Allowance:
It is the dimensional difference between the MMC of mating
parts, intentionally provided to obtain the desired class of fit. If the
allowance is positive, it will result in clearance between mating parts and if
the allowance is negative it will result in max interference. The table
illustrates the differences between tolerance and allowance.
Clearance fits are usually dimensioned on the basis of MMC
and the clearance obtained will be minimum. Interference fits are usually
dimensioned on the basis of LMC to ensure minimum interference between the
mating parts.
Fits:
A machine is built by assembling all its constituting parts.
During assembling sometimes a part maybe required to be fitted into another
part. In such cases, and during the working of the machine, they may or may not
be intended to have a relative motion between them. If there should be a
relative motion between the two parts, they must be fitted loose, or tight
otherwise. The fitting of one part into the other, either loose or tight
depends on the relationship existing between their mating surfaces which in
turn depends on the dimensional differences between the parts. The relationship
existing between the mating surfaces of the parts because of the differences in
their dimensions is called fit.
Shaft and Hole Terminology:
In mechanical engineering practice, generally a rod of
circular cross section and a circular hole are termed as shaft and hole respectively.
In the system of fits and tolerances, for the sake of simplicity even the non
circular sections and also the space containing or contained by the two
parallel faces of any part such as, the thickness of a key and the width of a
keyway or a slot, are also referred as ‘shaft’ and ‘hole’ respectively.
Classification of Fits:
A fit is established when one part is inserted into the
other. The type of fit obtained between the two parts is governed by the
dimensional deviations assigned for the basic size of the shaft and the hole. A
given basic size, the deviations assigned and the performance are
interdependent. The performance is the ultimate objective, the deviations
assigned for a basic size must satisfy the performance intended. The performance
itself is of varied type like, a shaft fitting tightly into a hole, or capable
of just rotation, or sliding loosely in it. So, for a given basic size, we can
have different performances. Therefore to obtain different performances we need
to fix different deviations for the basic size of the shaft and the hole. Each
set of deviations for the given basic size results in a particular type of
performance.
For example, for the shaft to rotate in a hole, obviously
its dimensions should be less than the hole. Alternately, when a shaft is to be held
rigidly in a hole, its sizes should be greater than that of the hole so that when the shaft is driven into
the hole, the outer surface of the shaft interferes with the inner surface of
the hole.
ClearanceFfit:
When a positive clearance exists between the hole and the
shaft. It is obtained by selecting the maximum and minimum limits of the shaft
and the hole. So that the clearance due to the difference between the
dimensions of the smallest possible hole and the largest possible shaft is
always positive. There are different classes in this type of fit depending on
the clearance and the specific operating conditions of the given mating parts.
They vary with the shaft speed, shaft bearing load, lubricating oil grade, temperature
and the length of the mating surfaces.
The clearance between the smallest
possible hole and the largest possible shaft = ø 29.95 - ø 29.90 = 0.05 mm. The
conventional representation of a clearance fit, where the tolerance zone of the
hole lies above that of the shaft.
Interference Fit:
When a negative clearance exist between the sizes of the
hole and the shaft. It is obtained by selecting the maximum and minimum limits
of the shaft and the hole so that there is an interference of the surfaces and
the clearance due to the difference between the dimensions of the largest
possible hole and the smallest possible shaft is always negative. Interference
fits are obtained by several methods, for instance, a shaft may be driven into
the hole with a considerable force, or heating the part having the hole in
order to increase the diameter of the hole, or by cooling the shaft and thus
decreasing its diameter.
The difference between the dimensions of the largest
possible hole and the smallest possible shafts = ø 30.25 - ø 30.30 = -0.05 mm.
The conventional representation of an interference fit where the tolerance zone
of the hole lies entirely below that of the shaft.
Transition Fit:
When the dimensions of the hole and the shaft are such that
there exists a positive clearance or a negative clearance when the shaft is
fitted into the hole. It is obtained by selecting the maximum and minimum
limits for the shaft and the hole such that there exists a positive clearance
when the smallest possible shaft is fitted into the largest possible hole, or a
negative clearance when the largest possible shaft is forced into the smallest
possible hole.
The fitting of the smallest possible shaft of 30.55 mm in the
largest possible hole of 30.60 mm allowing a positive clearance ø 30.60 - ø
30.55 = 0.05 mm. The fitting of the largest possible shaft of 30.65 mm in the
smallest possible hole of 30.50 mm gives an interference fit of ø 30.50 - ø
30.65 = - 0.15 mm. The conventional representation of transition fits in which
the tolerance zones of the hole and the shaft overlap.
System of Fits:
To obtain the various types of fits, the amount of maximum
and minimum clearances, either positive or negative. That must exist between
the mating parts are chosen, and then the aggregate tolerance which is equal to
the difference between the maximum and minimum clearances is apportioned
between them. While apportioning the aggregate tolerance between the two mating
parts, from the point of View of production economy one of the mating parts is
regarded as being constant in size by fixing its limit dimensions and by
varying the limit dimensions of the other, various types of fits are obtained.
In one of the system, the hole limit dimensions are considered constant and
various types of fits are obtained by suitably varying the limit dimensions of
the shaft. While in the other, the shaft limit dimensions are constant and
various types of fits are obtained by suitably varying the hole limit
dimensions.The former is called “hole basis system” since the hole limit
dimensions are regarded constant, while the latter is called “shaft basis
system” since the shaft limit dimensions are considered constant.
Classification in system of fits:
•Hole basis system,
•Shaft basis system.
Hole Basis System:
The difference types of fits are obtained by associating
shafts of varying limit dimensions with a single hole whose lower deviation is
zero. When the lower deviation of the hole is zero, the minimum limit of the
hole will be equal to its basic size, which is taken as the base for computing
all the other limit dimensions. The limit dimensions on the hole and the shaft
are computed by selecting suitable clearances and tolerances on the shaft and
the hole.
Fig. A shows the tolerance zone for the hole having its lower
limit equal to the basic size. The zero line is drawn through the lower limit
since the lower deviation is zero. Both the limit dimensions of the shaft lie
below the zero line for the clearance fit as shown in Fig B. While they are
above the zero line for the interference fit as shown in Fig C.
Shaft Basis System:
In this system, the different types of fits are obtained by
associating holes of varying limit dimensions with a single shaft, whose upper
deviation is zero. When the upper deviation of the shaft zero, the maximum
limit of the shaft will be equal to its basic size, which is taken as the base
for computing all other limit dimensions. The limit dimensions on the hole and
the shaft are computed by selecting suitable clearances and tolerances on the
shaft and the hole.
Fig. A shows the tolerance zone for the shaft having its
maximum limit equal to the basic size. The zero line is drawn through the
maximum limit since its upper deviation is zero. Both the limit dimensions of
the hole lie above the zero line for the clearance fit as shown in fig B while
they are below the zero line for the interference fit as shown in fig C.
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