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An effective and automatic approach for parameters optimization of complex end milling process based on virtual machining

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Abstract

The demand for optimization of manufacturing processes rises as a reflection of the highly competitive market environment that requires shorter lead time and lower production costs. Although some approaches to milling process optimization have been developed based on analytical model using average cutting parameters, they are not available for complex workpieces when cutting parameters are time-varying and instantaneous cutting conditions need to be considered. In order to automate the optimization process and avoid costly machining tests, in this paper, an effective approach for parameters optimization of complex end milling process based on virtual machining is proposed. A computer-aided design (CAD)/computer-aided manufacturing (CAM) application is integrated for actual tool path generation and feedrate scheduling based on material removal rate. Then, a machining simulator based on octree and instantaneous force model is developed to evaluate feasibility of the given numerical control (NC) program, and the correctness of this simulator is verified by machining tests. The optimization process is controlled by the efficient global optimization method to find global optimal solution with fewer simulations and less computation time. During each iteration of the optimization process, NC programs are generated and evaluated automatically by the CAD/CAM application and the simulator, respectively. The effectiveness and efficiency of the proposed approach are proved by comparing the generated optimal solution (has reduced machining time and production cost) with the recommended cutting parameters from machining experts when machining an impeller.

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Abbreviations

\( a_{p} \) :

Axial depth of cut (mm)

\( a_{r} \) :

Radial depth of cut (mm)

\( C_{production} \) :

Production cost

\( C_{s} ,C_{m} ,C_{c} ,C_{t} \) :

Set-up time cost, actual machining cost, tool changing time cost and tool wear cost

\( C_{T} ,C_{x} ,C_{y} ,C_{z} \) :

Coefficients of the tool life model

\( ds \) :

Contact length of the segment cutting edge

\( dF_{t} ,dF_{r} ,dF_{a} \) :

The differential tangential, radial and axial cutting forces

\( dF_{x} ,dF_{y} ,dF_{z} \) :

The differential x, y and z cutting force

\( dz \) :

Height of the axial element of the sliced cutter

\( f_{z} \) :

Feed per tooth (mm/tooth)

\( F\left( {x,y,z} \right) \) :

Implicit function

\( h_{cy} ,h_{uc} ,h_{ct} ,h_{lc} \) :

The different section heights of the automatically programmed tool (APT) cutter

\( h_{j} \left( {\varphi ,z} \right) \) :

Uncut chip thickness of the segment cutting edge

\( H \) :

Total machining depth in one process (mm)

\( j \) :

Flute number

\( k_{l} ,k_{t} \) :

The labor and tool cost factors

\( K_{tc} ,K_{rc} ,K_{ac} \) :

The tangential, radial and axial shear force coefficients

\( K_{te} ,K_{re} ,K_{ae} \) :

The tangential, radial and axial edge force coefficients

\( n \) :

Spindle speed (rpm)

\( N_{p} \) :

Milling pass number

\( t_{s} ,t_{m} ,t_{c} \) :

The set-up time, machining time and tool-change time

\( T \) :

Tool life

\( V \) :

Cutting speed (m/min)

\( VB_{ \hbox{max} } \) :

Maximum allowable tool wear

\( {\mathbf{x}} \) :

The design variable vector

\( \hat{y} \) :

The kriging model

\( \kappa \) :

Axial immersion angle

\( \varphi \) :

Radial immersion angle

\( \varphi_{st} ,\varphi_{ex} \) :

Radial entry and exit angles

\( \alpha ,\beta ,f,R,r,h,D \) :

Parameters to define the geometry of an APT cutter

\( \mu \left( {\mathbf{x}} \right),\varepsilon \left( {\mathbf{x}} \right) \) :

The regression and Gaussian process of the kriging model

\( \mu ,\sigma ,\theta ,p \) :

Parameters for kriging model

\( {\varvec{\Omega}} \) :

Design space

\( \Delta_{tol} \) :

Convergence tolerance

\( {\text{corr}}\left[ { \cdot , \cdot } \right] \) :

The correlation function

\( \Phi \left( \cdot \right),\phi \left( \cdot \right) \) :

Standard normal distribution and density function

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Acknowledgements

This work was supported by the National Science and Technology Major Project China Under Grant No. 2017ZX04016001.

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Authors and Affiliations

  1. National Engineering Research Center of Die and Mold CAD, Shanghai Jiao Tong University, 1954 Hua Shan Road, Shanghai, 200030, China

    Hengyuan Ma, Wei Liu, Xionghui Zhou, Qiang Niu & Chuipin Kong

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  1. Hengyuan Ma
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  2. Wei Liu
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Correspondence to Wei Liu or Xionghui Zhou.

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Ma, H., Liu, W., Zhou, X. et al. An effective and automatic approach for parameters optimization of complex end milling process based on virtual machining. J Intell Manuf 31, 967–984 (2020). https://doi.org/10.1007/s10845-019-01489-6

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