1. Limits ,Tolerance
and Fits
Must be reflected on production drawing

2. Introduction
The manufacture of interchangeable parts require precision.
Precision is the degree of accuracy to ensure the functioning of a part as intended.
However, experience shows that it is impossible to make parts economically to
the exact dimensions. This may be due to,
(i) Inaccuracies of machines and tools,
(ii) Inaccuracies in setting the work to the tool, and
(iii) Error in measurement, etc.
The workman, therefore, has to be given some allowable margin so that he can
produce part, the dimensions of which will lie between two acceptable
limits, a maximum and a minimum.
The system in which a variation is accepted is called the limit
system

3. Following are some of the terms used in the limit system :
Tolerance
The permissible variation of a size is called tolerance.
It is the difference between the maximum and minimum permissible limits of the given size.
Two types
 Unilateral tolerance, Bilateral tolerance eg. 1.005 ± 0.002 in
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.
Allowance
It is the dimensional difference between the maximum material limits of the mating parts.
Or The minimum stated clearance or the maximum stated interference for mating parts.
 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.
Limit System

4. Basic size
It is determined solely from design calculations.
Design Size
It is that size, from which the limits of size are derived by the application of
tolerances.
Actual Size
It is the size obtained after manufacture

5. Tolerance in relation to Method of Manufacturing
and Cost
• Great care and judgment must be exercised in deciding the tolerances which may
be applied on various dimensions of a component because:
I. If tolerances are to be minimum, that is, if the accuracy requirements are
severe, the cost of production increases.
II. In fact, the actual specified tolerances dictate the method of manufacture.
Hence, maximum possible tolerances must be recommended wherever
possible.

7. Fundamental of Tolerance
• Tolerance is denoted by two symbols, a letter symbol and a number symbol,
called the grade.
E.g. 30 e8 , 50 H6
• The symbols used (Fig. 15.3) for the fundamental deviations for the shaft and
hole are as follows :
Hole Shaft
Upper deviation ES es
Lower deviation EI ei
Fundamental Deviation

8. • Figure below shows the graphical illustration of tolerance sizes or
fundamental deviations for letter symbols
A to ZC for holes and from a to zc for shafts.

13. • For each letter symbol from a to zc for shafts and A to ZC for holes; the magnitude and
size of one of the two deviations may be obtained from Table 15.2 or 15.3 and the other
deviation is calculated from the following relationship :
Shafts, ei = es – IT
Holes, EI = ES – IT
where IT is fundamental tolerance of grade obtained from Table 15.1.
Reading Assignment: Table 15.4
Examples

14. Calculating Value of tolerance
• Thus, the fundamental tolerance values for different grades (IT) may be obtained
either from Table 15.1 or calculated from the relations given in Table 15.1A.
• Standard tolerance unit, i = 0.45 × 3 D + 0.001 D where i is in microns and D is the
geometrical mean of the limiting values of the basic steps, in millimetres.
• This relation is valid for grades 5 to 16

16. Fits
• The relation between two mating parts is known as a fit. Depending upon the actual
limits of the hole or shaft sizes, fits may be classified as clearance fit, transition fit and
interference fit.
Clearance Fit
It is a fit that gives a clearance between the two mating parts.
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.

17. Transition Fit
This fit may result in either an interference or a clearance, depending upon the actual values
of the tolerance of individual parts.

18. Interference Fit
If the difference between the hole and shaft sizes is negative before assembly; an interference
fit is obtained.
Minimum Interference
It is the magnitude of the difference (negative) between the maximum size of the hole and the
minimum size of the shaft in an interference fit before assembly.
Maximum Interference
It is the magnitude of the difference between the minimum size of the hole and the maximum
size of the shaft in an interference or a transition fit before assembly.

20. Hole and Shaft bases system
In working out limit dimensions for the three classes of fits; two systems are in use, viz.,
the hole basis system and shaft basis system.
Hole bases 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 size of the shaft. In this system, the lower
deviation of the hole is zero. The letter symbol for this situation is ‘H’.
The hole basis system is preferred in most cases, since standard tools like drills,
reamers, broaches, etc., are used for making a hole.
Shaft bases system
In this system, the size 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’.

26. Method of Placing Limit Dimensions(Tolerance Individual Dimensions)
• There are three methods used in industries for placing limit dimensions or
tolerancing individual dimensions.
Method 1
In this method, the tolerance dimension is given by its basic value, followed by a symbol,
comprising of both a letter and a numeral.
φ 25H7, 10H10, 40C11, 10h9 , Φ φ 40h11
Method 2
In this method, the basic size and the tolerance values are indicated above the dimension
line; the tolerance values being in a size smaller than that of the basic size and the lower
deviation value being indicated in line with the basic size.

27. Method 3
In this method, the maximum and minimum sizes are directly indicated above the dimension
line
When assembled parts are dimensioned, the fit is
indicated by the basic size common to both the
components, followed by the hole tolerance symbol
first and then by the shaft tolerance symbol (e.g., φ
25 H7/h6, etc., in Fig. 15.9).

28. Assignment - 5
1. Suggest suitable fits and their letter and tolerance grades for the components shown on the fig.
A – Shaft rotating in the Bush
B - Bush fixed in the House
C – Bush is secured on to the Gear
D – Base Plate of the Gear unite is secured on to the casting by cylindrical Pin
E – Gear with the Bush rotating on to the Pin
F – Pin is secured on to the base Plate
G – Bush with Plate

29. Tolerances of form and Position
• Tolerances of size are not always sufficient to provide the required control of
form.
Fig. Error of form
Form Variation
• It is a variation of the actual condition of a form feature (surface, line) from
geometrically ideal form.
Position Variation
• It is a variation of the actual position of the form feature from the geometrically ideal
position, with reference to another form (datum) feature.

30. Geometrical tolerance is defined as the maximum permissible overall variation of
form or position of a feature.
Geometrical tolerances are used,
(i) to specify the required accuracy in controlling the form of a feature,
(ii) to ensure correct functional positioning of the feature,
(iii) to ensure the interchangeability of components, and
(iv) to facilitate the assembly of mating components.
Tolerance Zone
It is an imaginary area or volume within which the controlled feature of the
manufactured component must be completely contained
Geometrical tolerance

31. Definitions
Datum
It is a theoretically exact geometric reference (such as axes, planes, straight lines, etc.)
to which the tolerance features are related
Datum features
 The datum feature is the feature to which tolerance of orientation, position and run-out
are related.

33. Standard followed by Industries

36. Surface Roughness
• It is not possible to achieve in practice, a geometrically ideal surface of component and
hence, production drawings of components must also contain information about the
permissible surface conditions.
• The properties and performance of machine components are affected by the degree of
roughness of the various surfaces.
• The higher the smoothness of the surface, the better is the fatigue strength and
corrosion resistance.
• Friction between mating parts is also reduced due to better surface finish.

37. Surface Roughness
The geometrical characteristics of a surface include,
1. Macro-deviations,
2. Surface waviness, and
3. Micro-irregularities.
The surface roughness is evaluated by the height, Rt and mean roughness index Ra of
the micro-irregularities.
Terms
Actual Profile
Reference Profile, Rf
Datum Profile, Df
Mean Profile, Mf
Peak-to-Valley Height, Rf
Mean Roughness Index, Ra

38. Surface Roughness Number
The surface roughness number represents the average departure of the surface from perfection over a
prescribed sampling length, usually selected as 0.8 mm and is expressed in microns.

39. Machining Symbols
This article deals with the symbols and other additional indications of surface
texture, to be indicated on production drawings.
a) This symbol may be used where it is necessary to indicate that the surface is machined,
without indicating the grade of roughness or the process to be used.
b) If the removal of material is not permitted, a circle is added to the basic symbol, as
shown in Fig. 16.2b. It also help to indicate that a surface is to be left in the state,
resulting from a preceding manufacturing process
c) If the removal of material by machining is required
d) When special surface characteristics have to be indicated

40. Indication of Surface Roughness
• The value or values, defining the principal criterion of roughness, are added to the
symbol as shown in Fig
a) May be obtained by any production method.
b) Must be obtained by removal of material by machining.
c) Must be obtained without removal of material.
Indication of Special Surface Roughness Characteristics

41. The principal criterion of surface roughness, Ra may be indicated by the corresponding
roughness grade number, as shown in Table 16.2.

43. Indication of Surface Roughness Symbols on Drawing

44. 1. By means of neat sketch and explanatory notes, interpret the meaning of the geometric tolerances shown in
the fig.
Assignment - 5

45. 2. Explain the meaning of the geometric tolerance indicated in microns for the machine tool component
shown below.