A taper is defined as uniform
decrease or increase in diameter of the work piece along its length. A taper
has four elements. Sometimes taper is denoted as taper per inch or taper per
foot or taper per meter.
(a) Diameter of larger end (LD)
(b) Diameter of smaller end (SD)
(c) Length of taper portion (L)
(d) Included angle between the
sides (Î¸)
Common Methods of
Expressing Taper on Blue Print
Taper In Ratio  If it is written 1:5 then it means that taper is 1
mm in 5 mm length, or the number of taper may be given.
Taper Per Inch  The difference between both diameters in a fixed
length of one inch is called taper per inch. It can be calculated by the
formula:
Taper per inch = Larger dia Smaller dia /.Length of taper
Taper per foot  In the fixed length of one foot, difference in
both the diameters is called Taper per foot. It can be calculated by the
formula: 
Taper per foot = [(Larger dia Smaller dia) x 12] / Length of
taper
Given

To find

Rule


Taper/foot

Taper/inch

divide taper per ft / 12


LD, SD, L in inch

Taper/ft

(LDSD) x 12
L


LD, L in inch

SD
in inches

LD – (Taper/ft/12 x L)


SD, L in inches

LD
in inches and taper / ft

SD + (Taper/ft/12 x L)


Taper /ft
and two diameters in inches

distance between given diameters in inches

(LDSD) x 12
Taper/ft


Taper / ft

amount of taper in a certain length
given in inches

Taper per foot
x L
12


Taper Angle  Angle made by taper representing lines with axis line
is called taper angle or included angle. It can be calculated by the formula:
Tan Î¸ = Larger Dia  Smaller Dia
Length of taper
For example the D = 80 mm and d =
70 mm and L = 100 mm
Now Tan Î¸ = Dd
L
But this
is full angle
and we want
to know the
angle for, which compound rest be set. So the formula
will be: 
Tan Î¸ =Dd = 8070 = 0.05
2L 2 x
100
From the log table we find the
value of Tan0.05 corresponds to an angle 2° 50'. So the included angle will be
2.5 x 2 = 5° 40”
Taper angle can also be
calculated by another formula
LDSD x 200
L 7
LD is diameter at large end. SD
is diameter at small end. L is length of the taper.
200 is a constant.
7
Standard Tapers
The tapered surfaces have been
standardized to have a uniform standard and to facilitate the use of different
tools. The tapers are strictly defined and universal for all engineering
plants. Tapered surfaces manufactured to a standard dimensions are called
Standard Tapers.
Types of Standard Tapers
Morse Taper. Morse tapers are
most commonly used in the machine tools and tool manufacturing industries.
These are used in taper shank drills, reamers, sockets and machine spindles.
Morse tapers are available in seven numbers 0, 1, 2, 3, 4, 5 and 6. Each number
corresponds to a definite size of taper and has definite amount of taper.
Number 0 is the smallest and number 6 is the largest. There is one disadvantage
of Morse taper and that is that all the numbers have different angles of taper.
But in most of cases it is approximately 3/5”per foot or 1:20.
Reed Taper  Reed taper has a taper of 5/8” per foot.
Steep Taper  Steep taper has a taper of 3 ½” per foot. As the name
indicates it is very steep.
Brown and Sharp Taper  This taper is used for taper shanks on
small end mills and reamers. It is approximately half inch per foot for all
sizes except for the taper number 10, where the taper is 0.5161 inch per foot
or ½” or 124. Brown and sharp taper sockets are used for many arbores, collets
and machine tool spindles, especially for milling machines and grinding machines.
RAF Taper  This type of taper has a taper of ¼” per foot or 1:48.
For taper pins where taper is not mentioned this taper is taken into
consideration.
Jarno Taper  This taper was originally proposed by Oscar J. Beale.
This taper is based on such simple formula that no calculations are needed when
the number of taper is known. The taper per foot for all Jarno Taper sizes is
6” per foot on the diameter. The diameter at the larger end is as many eighth s
and the diameter of the smaller end is as many tenths and the length as many
half inches as are indicated by the number of taper. For example a number 7
Jarno Taper is 7/8 inch at the larger end and 7/10 or 0.7 inch at the smaller
end and 7/2 (3 1/2inch) long. The Jarno Taper is used on various machine tools
especially profiling machines and die sinking machines.
Taper Pin Standard  This taper is used in taper pins, which are
used to connect the two separate parts so that a unit is formed. It is
generally 1/4 inch per foot.
Metric Taper  This standard taper is used in metric system and
available in sizes like Morse Taper, which are represented as 4, 6, 80, 100,
120, 160 and 200 numbers. The number of metric taper indicates the size of the
larger diameter of the taper hole. All metric tapers have same angles of taper.
This is of considerable advantage both in practical applications and in their
manufacture. Its ratio is 1:20 and the full angle is 2° 51' 51".
Indian Standard Taper  Indian standard institute recommended the
number I.S. 34581966. According to it, taper is in metric system but it has
numbers 4, 6,100 and 200. The ratios are different for different types of
works.
Very nice and easy to find formula. Highly appreciated. Thanks.
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