VIDYA JYOTHI INSTITUTE OF TECHNOLOGY
DEPARTMENT OFMECHANICAL ENGINEERING
TOPIC: LIMITS AND FITS
ABDUL KHADEER SK,Asst.Prof.
Limit and Fits
1 Terms of Sizes
Hole: designates all internal features of a part, including parts which are not cylindrical as shown
in Fig1(a).
Shaft: designates all external features of a part, including parts which are not cylindrical as
shown in Fig 1(b) and (c).
(a)hole
(b)shaft
(c)shaft
Figure 1 Hole and Shaft
Basic Size/Nominal Size (D, d): The theoretical dimension from which the hole/shaft limits are
derived. It is given during the process of design. As shown in Fig. 2, the basic size of shaft is 50,
i.e., d  50 . The basic size is the same for both members of a fit, i.e., D  d . For example，
D  d  50
Figure 2 A Shaft
Limits of Size: The applicable maximum and minimum sizes.
• Maximum limit of size (Dmax, dmax): the greater of the two limits of size. As shown in
Fig. 2, the maximum limit of size for the shaft is 49.975 , i.e., dmax  49.975 .
• Minimum limit of size (Dmin, dmin): the smaller of the two limits of size. As shown in
Fig.2-2, the minimum limit of size for the shaft is 49.950 , i.e., d min  49.950 .
Actual Size (Da, da): A measure size obtained from a finished part as shown in Fig. 3. For
example, Da  49.972 .
Fig. 3 Actual Size
Any actual size shall not exceed the maximum limit of size or the minimum limit of size, i.e.,
Dmin  Da  Dmax , d min  d a  d max , otherwise, the component is unqualified.
Maximum Material Condition (MMC) and Maximum Material Size (MMS): the maximum
material condition is a feature where contains the maximum amount of material within the stated
limits of size. Maximum material size (DM, dM) is the limits of size in this state, i.e., the
minimum hole size Dmin and the maximum shaft size dmax (shown in Fig. 4). For another
example, as shown in Fig.2, the maximum material size for the shaft is 49.975 , i.e.,
d M  d max  49.975 .
Least Material Condition (LMC) and Least Material Size (LMS): the least material condition
is a feature where contains the least amount of material within the stated limits of size. Least
material size (DL, dL) is the limits of size in this state, i.e., the maximum hole size Dmax and the
minimum shaft size dmin (shown in Fig. 4). For another example, as shown in Fig. -2, the
mniimum material size for the shaft is 49.950 , i.e., d L  d min  49.950 .
Figure 4 The Maximum Material Condition and the Least Material Condition
2.2 Terms of Deviations and Tolerances
Deviation of Size: the algebraic difference between the limits of size and the basic size.
 The Upper Deviation (ES, es): the algebraic difference between the maximum size and the
basic size.
 The Lower Deviation (EI, ei): the algebraic difference between the minimum size and the
basic size.
Hole :
ES  Dmax  D
EI  Dmin  D
(1)
Shaft : es  d max  d
ei  d min  d
Tolerance (TD, Td): The total permissible deviation of a size. It is also equal to the difference
between the limits of size. The value of tolerance is always positive.
Hole : TD  Dmax  Dmin  ES  EI
Shaft : Td  d max  d min  es  ei
(2)
Example1: A hole 5000.025 is known. Calculate these sizes D, Dmax, Dmin, DL, DM, ES, EI, and
TD.
Solution:
D=  50mm
Dmax=  50.025mm
Dmin=  50mm
DL= Dmax =  50.025mm
DM = Dmin =  50mm
ES=+0.025mm
EI=0
TD= Dmax -Dmin =ES- EI=0.025mm
Size Tolerance Zones: is the tolerance range of the size as shown in Fig. 5. In the tolerance zone
diagram, an area bounded by the two lines represents the upper and lower deviation. The
tolerance zone consists of “the size of the tolerance zone” and “the position of the tolerance
zone”, the former is determined by the standard tolerance, and the later is determined by the
basic deviation.
Zero Line: In the tolerance zone diagram, the datum line used to determine the deviation of size
is called zero line as shown in Fig. 5. Generally the zero line is used to represent the basic size. It
is defined that the value of deviation above the zero line is positive, while the value of deviation
below the zero line is negative.
Fig. 5 shows a size tolerance zone where the basic size is  50, the upper deviation is +0.008,
the lower deviation is -0.008, the tolerance is 0.016.
Figure 5 Size Tolerance Zone
Basic Deviation: It is the upper or lower deviation used to determine the relative position
between the tolerance zone and zero line. Generally, the deviation nearer to the zero line is
treated as the basic deviation.
Example2:
As shown in Fig. 6, the deviation of hole and shaft is Hole: 5000.025 and Shaft: 5000..025
050 . Give
the graphical representation of hole and shaft.
Figure 6 An Example of Size Tolerance Zone
2.3 Terms of Fit
Since even the simplest machine involves the fitting together of several parts for the purpose of
design and production, it is necessary to know how the various parts fit together. A fit between
two parts to be assembled can be defined as the difference between their sizes before assembly.
Or in other words, FIT is the general term to signify the range of tightness or looseness resulting
from the application of a specific combination of allowances and tolerances in the design of the
mating parts.
Allowance: It is the dimensional difference between the maximum mating limits of mating parts,
intentionally provided to obtain the desired degree or class of fit. If the allowance is positive, it
will result in the minimum clearance between the mating parts, and of the allowance is negative,
it will result in the maximum interference.
Clearance (X): in a fit, it is the difference between the sizes of the hole and the shaft, before
assembly. Minimum clearance is a clearance fit and is the difference between the minimum size
of the hole and the maximum size of the shaft. Maximum clearance is the difference between the
maximum size of the hole and the minimum size of the shaft.
Interference (Y): in a fit, it is the difference between the sizes of the hole and the shaft, before
assembly. The minimum interference is the arithmetical difference between the maximum size of
the hole and the minimum size of the shaft before assembly. The maximum interference is the
arithmetical difference between the minimum size of the hole and the maximum size of the shaft
before assembly.
Fit:the relationship between the hole tolerance zone and shaft tolerance zone with the
same basic size. Fits are of three general types: clearance, interference, and transition, depending
on the actual limits of the hole or shaft. Fig. 7 illustrates the three types of fits.
Figure 7 Three Types of Fits
Clearance Fits (shown in Fig. 8): the difference between the hole and shaft sizes before
assembly is positive. Clearance fits have limits of size prescribed such that a clearance always
results when the mating parts are assembled. Clearance fits are intended for the accurate
assembly of parts and bearings. The parts can be assembled by hand because the hole is always
larger than the shaft. Some application examples are shown in Fig. -9.
X max  Dmax  d min  ES  ei
(-3)
X min  Dmin  d max  EI  es
Figure 8 Clearance Fit
(a)
(b)
Figure 9 Application Examples of Clearance Fit
Transition Fits (shown in Fig. 10): this fit may provide either clearance or interference,
depending on the actual value of the tolerance of individual parts. Transition fits are a
compromise between the clearance and interference fits. They are used for applications where
accurate location is important, but either a small amount of clearance or interference is
permissible. Some application examples are shown in Fig. -11.
Ymax  Dmin  d max  EI  es
(-4)
X max  Dmax  d min  ES  ei
Figure 10 Transition Fit
(a)
Figure
-11 Application Examples of Transition Fit
Interference Fits (shown in Fig.12): the arithmetic difference between the hole and shaft sizes
before assembly is negative. Interference fits have a limit of size prescribed that an interference
always results when mating parts are assembled. The hole is always smaller than the shaft.
Interference fits are for the permanent assemblies of parts which require rigidity and alignment,
such as dowel pins and bearings in casting. Some application examples are shown in Fig. 13.
Ymin  Dmax  d min  ES  ei
Ymax  Dmin  d max  EI  es
(-5)
Figure 12 Interference Fit
(a)
(b)
Figure 13 Application Examples of Interference Fit
Fit Tolerance: allow change amount of the clearance or interference and can be calculated as
Clearance fit: Tf = |Xmax - Xmin|
Interference fit: Tf = |Ymin - Ymax|
Transition Fit: Tf = |Xma x - Ymax|
(6)