Taper and Taper Turning

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 (θ)

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


To find
divide taper per ft / 12
LD, SD, L in inch

(LD-SD) x 12
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
(LD-SD) x 12
Taper / ft
amount of taper in a certain length given in inches
Taper per foot x L

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 θ = Larger Dia - Smaller Dia
                  Length of taper
For example the D = 80 mm and d = 70 mm and L = 100 mm
Now Tan θ = D-d
But  this  is  full  angle  and  we  want  to  know  the  angle  for,  which compound rest be set. So the formula will be: -
Tan θ =D-d          =             80-70     =             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
LD-SD 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.

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 1-24. 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. 3458-1966. 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.

1 comment:

  1. Very nice and easy to find formula. Highly appreciated. Thanks.