Prediction of Cutting Forces in Micro Milling of p-20 Steel by TiAln coated wc tool: An Analytical Approach

Modified Undeformed Chip Thickness (UCT) Algorithm

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Modified Undeformed Chip Thickness (UCT) Algorithm
The undeformed chip thickness model fora conventional end mill cutter can be expressed as [7]
ℎ(𝜃) = sin) (1) where,
ℎ(𝜃) is the instantaneous undeformed chip thickness (mm, 𝑓
𝑡
is feed per tooth
(mm/tooth) and
𝜃 is the rotational angle of the tool (degree. However, the effect of tool run outcomes into picture which creates unbalance of the undeformed chip thickness for different teeth of the milling cutter.
Fig.2. Tool center and tool flute trajectory of the micro mill cutter due to tool run out As shown in figure 2, values of undeformed chip thickness generated by two teeth are not same for same positional angle. Due to lower feed value and tool diameter as compared to macro end milling, run out effect cannot be neglected. The undeformed chip thickness model by considering tool run out can be expressed as [9]
𝐴𝐴
′
= ℎ(𝜃 ) = 𝑟 + 𝐿 sin (𝑤𝑡 −
2𝜋𝑖
𝑁
− 𝛿 + 𝜆) − (𝑟
2
− 𝐿
2
𝑐𝑜𝑠
2
(𝑤𝑡 −
2𝜋𝑖
𝑁
− 𝛿 +
𝜆))
0.5
(2) where, r is radius of cutter (mm, L is the distance between the center of the tool for two consecutive passes (mm, w is the angular velocity of the cutter (radian/second), δ is the lag angle due to helical flute (degree, N is the number of flute and i = 0, 1, 2, …,
(N-1).

5 Further, size effect has a dominating effect during chip formation in micro cutting. When undeformed chip thickness is below a critical value (minimum chip thickness) proper chip formation is not possible, only some part of the workpiece plastically deformed and rest elastically recovered after passing of the tool [8]. Therefore, effect of minimum chip thickness and elastic recovery should be added to make the undeformed chip thickness algorithm more reliable and realistic, which can be expressed as
ℎ(𝜃)
𝑎𝑐𝑡𝑢𝑎𝑙
= (1 − 𝐸)ℎ(𝜃) , when ℎ(𝜃) ≤ ℎ
𝑚𝑖𝑛
(a)
ℎ(𝜃)
𝑎𝑐𝑡𝑢𝑎𝑙
= ℎ(𝜃) , when ℎ(𝜃) > ℎ
𝑚𝑖𝑛
(b) where, E is the elastic recovery rate and
ℎ
𝑚𝑖𝑛
is the minimum undeformed chip thickness which can be considered from the literature [8] and [13], respectively.

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