y: Bend / deflection (mm)
W: Load (N)
ℓ: Overhang (mm)
E: Young's modulus (Gpa)
I: Second moment of area* =
π • D
3 • E • I
D: Rod diameter corresponding to an end mill (rod diameter when converting to
represent the end mill diameter D1, D =
(0.7 ~ 0.8) D1)
The diameter of the end mill affects rigidity. An end mill can be seen as a round rod, so there is a relationship shown in the formula between the diameter and the amount it will bend or deflect.
The amount an end mill will bend is an inverse proportion to the fourth power of the diameter (see formula above).
That is, as the diameter increases, an end mill is less likely to bend. For example, if a diameter doubles with the same tool overhang, the deflection will be one-sixteenth with the same cutting load (see image to the right). For example, the machined surface deflection when using a 4-flute carbide end mill is 25μm, if the diameter is doubled, the machined surface deflection will be 25μm × 1/16 = 1.5μm. This shows that high wall surface accuracy can be obtained.
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As the depth of cut of an end mill is increased, the cutting resistance increases, therefore making the end mill more prone to bending. Therefore, for larger depths of cut, a large diameter, highly rigid end mill should be used. Consequently, the amount of chips discharged per unit of time can be increased in proportion to a rise in diameter for both square and a ball nose end mills as shown in the graphs to the right, thereby increasing machining efficiency.
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The effect of diameter
The unit cost of a tool becomes higher as the diameter becomes larger due to increased material and manufacturing costs.
The table to the right shows the effects of different diameters.