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Energy consumption modelling in milling of variable curved geometry

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Abstract

The accurate estimation of energy consumption is beneficial to manufacturing enterprises economically as well as to overcome global energy crisis. The present work concentrates on developing an energy consumption model in milling of variable curved geometries where magnitudes and directions of workpiece curvature vary along tool contact path of a component. The current work deals with estimation and analysis of energy consumption in peripheral milling of variable curved surfaces where cutting forces differ along tool contact path in the presence of workpiece curvature. The proposed hybrid model developed in MATLAB involves process mechanics, cutting forces and energy consumption and has modules for idle, auxiliary and cutting power. The proposed model is validated by the experimental work. The model is generic and versatile in nature and is useful for milling of straight, circular and curved surfaces. In addition to it, the influence of workpiece curvature on power consumption has been investigated to realize the variation of power consumption along the tool contact path. The developed model offers a basic platform to understand and characterize the energy consumption for general peripheral milling considering workpiece geometry. The comparison of predicted and measured results indicates that the model is capable to estimate the power consumption accurately. The proposed model will be used by the practitioners to find the optimum cutting conditions to reduce power consumption during the machining of curved geometries – a pragmatic condition but not much researched condition in machining.

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Abbreviations

\(P_{{{\text{idle}}}}\) :

Idle power [W]

\(\overline{P}_{{{\text{cutting}}}}\) :

Cutting power [W]

\(P_{{{\text{auxiliary}}}}\) :

Auxiliary power [W]

\(P_{{{\text{total}}}}\) :

Total power [W]

X t (u), Y t (u) :

Parametric curve of locus of tool centre

X wb (u), Y wb (u) :

Parametric curve of before cut workpiece trajectory

X wa (u), Y wa (u) :

Parametric curve of after cut workpiece trajectory

X′(u), Y′(u) :

Derivative of parametric w.r. parameter

d r :

Offset distance between before cut and after cut workpiece trajectory [mm]

r :

Milling cutter radius [mm]

f cc :

Feed per tooth along tool contact path [mm]

θ en :

Entry angle [radian]

θ ex :

Exit angle [radian]

R :

Radius of curvature [mm]

t c :

Uncut chip thickness

a e :

Radial immersion [mm]

a p :

Axial immersion [mm]

\(\alpha\) :

Helix angle [radian]

K t,  K r :

Cutting constants

\(dF_{i,j,f} (\varphi )\) :

Feed force acting on tooth j at angular rotation \(\varphi\)

\(dF_{i,j,n} (\varphi )\) :

Normal force acting on tooth j at angular rotation \(\varphi\)

\(P_{{{\text{cutting}}}}\) :

Instantaneous cutting power [W

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Funding

The authors thank and acknowledge the Science and Engineering Research Board (SERB), Department of Science and Technology (DST), Government of India for providing financial support to carry out this research work (Project No: SB/FTP/ETA-03/2013).

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Authors and Affiliations

  1. Mechanical Engineering Department, Birla Institute of Technology and Science, Pilani, Rajasthan, 333031, India

    Shrikant Shankarrao Pawar, Tufan Chandra Bera & Kuldip Singh Sangwan

Authors
  1. Shrikant Shankarrao Pawar
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  2. Tufan Chandra Bera
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  3. Kuldip Singh Sangwan
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Contributions

SSP: original draft writing, investigation, performing experimentation, validation, resources, software. TCB: conceptualization, investigation, methodology, formal analysis, reviewing, supervision. KSS: investigation, reviewing, supervision.

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Correspondence to Tufan Chandra Bera.

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Highlights

• Energy consumption model for milling of variable curved geometries is hybrid in nature.

• Cutting power consumption is expressed as a function of cutting and feed forces.

• Cutting power consumption is also a function of workpiece curvature in milling.

• Proposed model is more generic and applicable for straight, circular and variable curved geometries.

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Pawar, S.S., Bera, T.C. & Sangwan, K.S. Energy consumption modelling in milling of variable curved geometry. Int J Adv Manuf Technol 120, 1967–1987 (2022). https://doi.org/10.1007/s00170-022-08854-5

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