A Machining Program Employing a Slip Line Field Modelling Technique Over Other Constitutive Models

A Machining Program Employing a Slip Line Field Modelling Technique Over Other Constitutive Models

Hridayjit Kalita (Birla Institute of Technology, Ranchi, India) and Kaushik Kumar (Birla Institute of Technology, Ranchi, India)
DOI: 10.4018/IJMMME.2020040102
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Machining involves complex plastic material flow at the chip separation site which makes it difficult to predict forces and other machining outputs to higher accuracy. Modelling is a common technique which facilitates incorporation of analytical and experimentally derived equations to visualize the process and analyses the mechanism. It saves time and machining factors can be optimized without any trial and error method. In this paper, the significance of slip line field model over other constitutive laws in defining the complex regions in machining are thoroughly reviewed and a slip line field model is chosen which incorporates build up edge (BUE) of a larger size than the other previously defined slip line models for machining. The modified model also incorporate a region of shear zone instead of a shear line, takes into account the chip curl effect and conform to the velocity discontinuity and stress equilibrium. The slip line fields are generated using MATLAB and employing Dewhurst-Collin's matrix technique.
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1. Introduction

Nomenclature (with reference to Modified slip line model):

  • IJMMME.2020040102.m01: Angular range of the slip line ‘GD’.

  • IJMMME.2020040102.m02: Angular range of the slip line ‘BD’.

  • IJMMME.2020040102.m03: Angular range of the slip line ‘AB’.

  • IJMMME.2020040102.m04: Angular range of the slip line ‘CD’.

  • PA: Hydrostatic pressure at ‘A’.

  • PA1: Hydrostatic pressure at ‘A1’.

  • IJMMME.2020040102.m05: frictional shear stress along the rake angle.

  • k: Maximum shear flow stress.

  • IJMMME.2020040102.m06: Velocity discontinuity along ‘ABC’.

  • IJMMME.2020040102.m07: Velocity discontinuity along CE.

  • a1, a2: Overstressing angles at ‘A’ and ‘A1’.

  • IJMMME.2020040102.m08: Initial base slip line (velocity discontinuity along ‘BD’)

  • IJMMME.2020040102.m09: Angle turned by the slip line during curving.

  • IJMMME.2020040102.m10: X Mikhlin coordinates.

  • IJMMME.2020040102.m11: Y Mikhlin coordinates.

  • x: X cartesian coordinates.

  • y: Y cartesian coordinates.

  • V: Cutting velocity.

  • IJMMME.2020040102.m12: rake angle.

  • IJMMME.2020040102.m13: Angular velocity of the chip.

  • Vg:: Velocity of the chip at point ‘G’.

  • IJMMME.2020040102.m14: Forces in X direction along the Mikhlin X coordinates.

  • IJMMME.2020040102.m15: Forces in Y direction along the Mikhlin Y coordinates.

  • Fc: Cutting force in machining.

  • Ft: Thrust force in machining.

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