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Modified iterative approach for predicting machined surface topography in ball-end milling operation

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Abstract

Machined surface topography prediction is an important and useful tool for optimizing cutting parameters. However, accurate prediction of machined surface topography in ball-end milling operation has been extremely challenging, due to the complexity in tool-workpiece interaction induced by the trochoidal motion of cutting edge and computing burden. In this present research, a modified iterative approach was proposed to solve the intersections between the cutting-edge sweeping surface and the discrete Z-vector model of workpiece, which were used to predict the machined surface topography in ball-end milling operation. Firstly, the accurate model of cutting-edge sweeping surface was established utilizing homogeneous coordinate transformation, in which the tool runout was considered. Secondly, the cutting-edge sweeping surface was dispersed into a series of patches in accordance with equal parameter interval, and the in-cut patch was extracted by using the minimum and maximum axial immersion angle of the cutting edge. Thirdly, the intersection between each in-cut patch and discrete Z-vector was solved using the Newton’s method, which was used to update the endpoint of the corresponding discrete Z-vector. Finally, ball-end milling experiments of AISI P20 steel were carried out to validate the proposed approach as well as investigate the effect of cutting parameters on the machined surface topography and roughness. The predicted machined surface topography and roughness were in good agreement with the measured results. Moreover, the proposed approach needs less computing time than the traditional iterative approaches at the same predicting accuracy. This research also provides guidance for optimizing cutting parameters to control surface quality in ball-end milling operation.

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Abbreviations

O T -X T Y T Z T :

Cutting tool coordinate system

O S -X S Y S Z S :

Machine tool spindle coordinate system

O L -X L Y L Z L :

Cutting location point coordinate system

O-XYZ :

Workpiece coordinate system

x p T, y p T , z p T :

Coordinates of the selected point P on cutting-edge point in the cutting tool coordinate system OT-XTYTZT

R 0 :

Tool radius

κ :

Axial position angle

φ :

Lag angle

β 0 :

Nominal helix angle

ϕ j :

Radial position angle of cutting edge

j :

Index of cutting edge

N :

Number of cutting teeth

T T→S :

Transformation matrix between OT-XTYTZT and OS-XSYSZS

ρ :

Eccentricity of milling cutter

α :

Phase angle of cutting edge measured in O-XYZ

ω :

Angular speed of spindle

t :

Machining time

α 0 :

Initial phase angle of cutting tool

λ :

Initial phase angle of cutting edge

β, γ :

Tilt and yaw angles of cutting tool

T S→L :

Transformation matrix between OS-XSYSZS and OL-XLYLZL

T L→W :

Transformation matrix between OL-XLYLZL and O-XYZ

i :

Index of the tool path

a e :

Radial depth of cut

f :

Feed per tool rotation

H :

Height of cubic workpiece blank

a p :

Axial depth of cut

Q a,b :

Grid point on the XY plane

s a,b :

Grid points of workpiece surface

a, b :

Index of grid points

h a,b :

Length of discrete Z-vector

k :

Unit vector of Z-axis

F r,s :

Patch of the cutting-edge sweeping surface

r, s :

Index of vertex of patch of cutting-edge sweeping surface

Δκ, Δα :

Size of patch of cutting-edge sweeping surface

κ min, κ max :

Minimum and maximum axial immersion angle of the cutting edge

L a,b :

Discrete Z-vectors of workpiece

x a,b, y a,b :

Coordinates of the grid point Qa,b in XY plane

P L :

Intersection between vertical reference line and cutting-sweeping surface

κ L, α L :

Parameters of the intersection point PL

k :

Step of iterative calculation

Sa :

Average roughness

St :

Area peak-to-valley height

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Availability of data and material

The authors declare that the data and material used or analyzed in the present study can be obtained from the corresponding author at reasonable request.

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Custom code.

Funding

This work was supported by the National Natural Science Foundation of China (Grant No. 51975333), the National New Material Production and Application Demonstration Platform Construction Program (Grant No. 2020-370104-34-03-043952), 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

    Renwei Wang, Song Zhang, Renjie Ge, Xiaona Luan & Qing Zhang

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

    Renwei Wang, Song Zhang, Renjie Ge, Xiaona Luan & Qing Zhang

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

    Jiachang Wang & Shaolei Lu

Authors
  1. Renwei Wang
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  2. Song Zhang
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  3. Renjie Ge
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  5. Qing Zhang
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Contributions

Renwei Wang provided the methodology, wrote the program code, investigated the experiments, and wrote the original manuscript. Song Zhang also provided the methodology, reviewed the manuscript, and provided the funding. Renjie Ge investigated the experiments and reviewed the manuscript. Xiaona Luan provided the methodology and reviewed the manuscripts. Qing Zhang wrote the program code and investigated the experiments. Jiachang Wang reviewed the manuscript. Shaolei Lu reviewed the manuscript. All authors have read and agreed to the published version of the manuscript.

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Correspondence to Song Zhang.

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Wang, R., Zhang, S., Ge, R. et al. Modified iterative approach for predicting machined surface topography in ball-end milling operation. Int J Adv Manuf Technol 115, 1783–1794 (2021). https://doi.org/10.1007/s00170-021-07245-6

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  • DOI: https://doi.org/10.1007/s00170-021-07245-6

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