6 tangential and normal directions, respectively. The elemental axial depth of cut (𝑑𝑍)
can be calculated as 𝑑𝑍 tan 𝜂
, where
η is the helix angle. However, the cutting forces can be measured only in feed, transverse and axial direction during experiment. So, the Cartesian coordinate can be converted
into global coordinate such as (
𝑑𝐹
𝑥
(𝜃)
𝑑𝐹
𝑦
(𝜃)
𝑑𝐹
𝑧
(𝜃)
) = (
𝑐𝑜𝑠𝜃
𝑠𝑖𝑛𝜃 0
−𝑠𝑖𝑛𝜃 𝑐𝑜𝑠𝜃 0 0
0 1
) (
𝑑𝐹
𝑡
(𝜃)
𝑑𝐹
𝑛
(𝜃)
𝑑𝐹
𝑎
(𝜃)
) (5)
Further, in micro end milling process multi tooth engagement occurs due to helical shape of the tool [10]. Therefore, by considering the assumptions proposed by Srinivasa and Shunmugam [10] and by integrating equation 5 within the limit of entry
and exit angle of the flute, the total forces acting on the tool can be expressed as
𝐹
𝑥
(𝜃) tan 𝜂
∑
∫
[𝐾
𝑡𝑐
ℎ(𝜃) cos 𝜃 + cos 𝜃 + 𝐾
𝑛𝑐
ℎ(𝜃) sin 𝜃 +
𝜃
𝑒𝑛𝑡𝑟𝑦
𝜃
𝑒𝑥𝑖𝑡
𝑖=𝑁−1
𝑖=0
sin 𝜃] (a)
𝐹
𝑦
(𝜃) tan 𝜂
∑
∫
[−𝐾
𝑡𝑐
ℎ(𝜃) sin 𝜃 − sin 𝜃 + 𝐾
𝑛𝑐
ℎ(𝜃) cos 𝜃 +
𝜃
𝑒𝑛𝑡𝑟𝑦
𝜃
𝑒𝑥𝑖𝑡
𝑖=𝑁−1
𝑖=0
cos 𝜃] (b)
𝐹
𝑧
(𝜃) = tan 𝜂
∑
∫
[−𝐾
𝑎𝑐
ℎ(𝜃) − 𝐾
𝑎𝑒
]
𝜃
𝑒𝑛𝑡𝑟𝑦
𝜃
𝑒𝑥𝑖𝑡
𝑖=𝑁−1
𝑖=0
(c)
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