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Clamping forces for collets
8.5

Machining generates forces (Fx, Fy and Fz). The force Fz generates the torque Mx, this torque may
cause the work piece to rotate in the collet.

The taper (a) transforms the axial force (Ft) into a radial force (Fn). The radial force generates the
friction which allows the transmission of the machining forces.

F F x
F = t
D
n (tanα + μ ) F × 2
z
1 F M =
y x 2
 2M  2
s  x  2 F z
F = + F


n μ  D  x
2  1 
F F = (tanα + μ )
t n 1

1
 2M  2 a, m
s  x  2 ½ F n
F = + F (tanα + μ ) m 2


t μ  D  x 1
2  1 
M
x
D
2
s = 1.2 ¸ 1.5 F D
t 1
F
safety factor x
F
y
μ = 0.05¸ 0.3
1
for work pieces in steel : ½ F
n
μ = 0.05¸ 0.3 with smooth bore
2
0.2¸ 0.4 with grooved bore
0.3 ¸ 0.6 with serrated bore

Amplification of the axial clamping force in
relation to the taper

10
= 0.3
μ
9 m = 0.3
1
μ
[-] 8 μ 1 = 0.2
m = 0.2
Amplification F n /F t 6 F t F = n (tanα + μ 1 )
= 0.1
7
μ m = 0.1
1
m = 0.05
= 0.05
1
5
4
3
2
1
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29
Angle of the taper [°]

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