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Surface topography model with considering corner radius and diameter of ball-nose end miller

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Abstract

Surface topography, as one of the significant roles in surface integrity, has a great impact on the performances and service life of the machined parts. This research focuses on the surface topography model for the ball-nose end miller in machining of AISI P20 steel. First, the model is developed to predict the surface topography and surface roughness in ball-nose end milling process. Secondly, the accuracy of the developed surface topography model was verified by a series of milling experiments. Thirdly, the effects of corner radius and diameter of ball-nose end miller on surface roughness is analyzed, it is observed that the ratio of feed per tooth (fz) to radial depth of cutting (ae) for obtaining minimum surface roughness is related to the ratio of diameter (D) to corner radius (r) of ball-nose end miller. Finally, in terms of the minimum surface roughness, a mathematical model is established with consideration of corner radius and diameter of ball-nose end miller. This research indicates that proper selection of cutting parameters (fz and ae) with consideration of diameter and radius corner of ball-nose end miller is a novel avenue for acquiring desired surface roughness.

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Abbreviations

f z :

Feed per tooth (mm/tooth)

a e :

Radial depth of cutting (mm)

v c :

Cutting speed (m/min)

a p :

Axial depth of cutting (mm)

r :

Corner radius of ball-nose end miller (mm)

R :

Radius of ball-nose end miller (mm)

D :

Diameter of ball-nose end miller (mm)

S a :

Three-dimensional arithmetic average deviation (μm)

C :

Ratio of feed per tooth to radial depth of cutting

T1, T2 :

Coordinate transformation matrixes

P :

Arbitrary point on the cutting edge

x, y, z :

Coordinate of point P in workpiece coordinate system

u, v, w :

Coordinate of point P in cutting tool coordinate system

x0, y0, z0 :

Initial position of point P

β1, β2 :

Rotation angles of tool coordinate system around the X-axis and Z-axis of workpiece coordinate system, respectively

OT-UVW :

Tool coordinate system

OW-XYZ :

Workpiece coordinate system

γ :

Helix angle of cutter

α :

Angle between the OTP and W-axis

ψ :

Lag angle of point P

R(α):

Radius of point P

H :

Matrix consists of the points coordinates in workpiece model

m :

Number of the mesh along the feed direction in workpiece model

n :

Number of the mesh along the step-over direction in workpiece model

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Funding

This work was supported by the National Natural Science Foundation of China (Grants No. 51975333 and No. 51575321) and Taishan Scholar Project of Shandong Province (No. ts201712002).

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Authors and Affiliations

  1. Key Laboratory of High Efficiency and Clean Mechanical Manufacture of MOE, School of Mechanical Engineering, Shandong University, Jinan, 250061, People’s Republic of China

    Jing Zhang, Song Zhang & Dongdong Jiang

  2. Key National Demonstration Center for Experimental Mechanical Engineering Education, Shandong University, Jinan, 250061, People’s Republic of China

    Jing Zhang, Song Zhang & Dongdong Jiang

  3. Qingdao Hisense Mould Co., Ltd, Qingdao, 266071, People’s Republic of China

    Jiachang Wang & Shaolei Lu

Authors
  1. Jing Zhang
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  2. Song Zhang
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  5. Shaolei Lu
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Correspondence to Song Zhang.

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Zhang, J., Zhang, S., Jiang, D. et al. Surface topography model with considering corner radius and diameter of ball-nose end miller. Int J Adv Manuf Technol 106, 3975–3984 (2020). https://doi.org/10.1007/s00170-019-04897-3

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