Geometric models of non-standard serrated end mills
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ORIGINAL ARTICLE
Geometric models of non-standard serrated end mills Pritam Bari 1 & Mohit Law 1 & Pankaj Wahi 2 Received: 6 December 2019 / Accepted: 14 September 2020 # Springer-Verlag London Ltd., part of Springer Nature 2020
Abstract Serrated end mills reduce process forces and improve chatter-free material removal rates. Improvements in cutting performance are governed mainly by the serration profile on these cutters. The geometric models of serration profiles are necessary to guide the design of improved cutters. Since these geometric models are usually not available a priori, this paper presents two methods to reconstruct geometric models from scanned measurements of eight different serrated cutter types available commercially. One representation is parametric-based, and another is NURBS-based. Reconstructed serration profiles are classified as the standard sinusoidal, circular, and trapezoidal profile types; and the non-standard semi-circular, circular-elliptical, semi-elliptical, inclined semi-circular; and the inclined circular types. For all eight profiles, the variation in local radius and irregular chip thickness distribution that are a characteristic of serrated cutters are captured by both approaches to approximate the geometry. Force models with the proposed geometric models as inputs are used to predict forces and those forces were experimentally validated. Validated forces confirm that the proposed geometric models are indeed correct. Comparing the cutting performance of all eight serrated cutters suggests that the circular and non-standard serrated end mills can preferentially reduce cutting forces as compared to the standard sinusoidal and/or trapezoidal profiles. However, in terms of the ratios of maximum to minimum peak resultant cutting force, we find that the standard sinusoidal profiled cutter outperforms the other four-fluted cutters, whereas the nonstandard inclined circular profiled cutter retains its advantages over other three-fluted cutters. Keywords Serrations . Tool geometry . NURBS . Milling . Cutting force
Nomenclature ap Axial depth of cut A Amplitude of the serration profile c Total number of input cloud data points in the optimization problem C(u) NURBS curve having parameter u Cb Coordinates of the bth output NURBS point d Total number of output NURBS points in the optimization problem dFrta, i(z, t) Differential cutting forces in the rta frame for the ith flute at the height z at time t
dFxyz, i(z, t)
D e E f fi, l(z, t) ft Fxyz (t) gi(z, t)
* Mohit Law [email protected]
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1
Machine Tool Dynamics Laboratory, Department of Mechanical Engineering, Indian Institute of Technology Kanpur, Uttar Pradesh 208016, India
i
2
Department of Mechanical Engineering, Indian Institute of Technology Kanpur, Uttar Pradesh 208016, India
Ia
Transformed differential forces in the xyz frame for the ith flute at the height z at time t Shank diameter of the serrated cutter Index for knot values for NURBS Objective function Feed rate per minute Feed per revolutio
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