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Micro-grinding Temperature Prediction Considering the Effects of Crystallographic Orientation and the Strain Induced by Phase Transformation

  • Man Zhao
  • Xia JiEmail author
  • Steven Y. Liang
Regular Paper
  • 59 Downloads

Abstract

This paper proposes a physical-based model to predict the temperature in the micro-grinding of maraging steel 3J33b with the consideration of material microstructure and process parameters. In micro-grinding, the effects of crystallography on the grinding machinability become significant, since the depth of cut is of the same order as the grain size. In this research, the Taylor factor model for multi-phase materials is proposed to quantify the crystallographic orientation (CO) with respect to the cutting direction by examining the number and type of activated slip systems. Then, the flow stress model is developed, in which both the athermal stress resulted from the COs and the strain induced by the phase transformation are taken into account. On the basis of the flow stress model, the grinding forces are predicted followed by the calculation of the grinding heat. In the investigation, the triangular heat flux distribution and the reported energy partition model are applied in the calculation of workpiece temperature. Furthermore, the temperature model is validated by conducting an orthogonal-designed experiment, with the predictions of the maximum temperature in good agreement with the experimental data. Moreover, the predictive data is compared with the predictions resulted from the two other previously reported models. The results indicate that the proposed temperature model with considering the effect of CO and the phase transformation improved the prediction accuracy of the micro-grinding temperature.

Keywords

Micro-grinding Taylor factor Flow stress Crystallographic orientation Temperature Phase transformation 

List of Symbols

A,B,C,m,n

Johnson–Cook parameters

Asks

Parameters of wheel topography

ap

The depth of cut

b1

Burger vector

cpw

The workpiece specific heat

D

Grit diameter

E

Workpiece elasticity modulus

ech

Limiting chip energy

fγ0

The initial phase fraction of austenite

fα0

The initial phase fraction of ferrite

\(f_{\alpha 0}^{\prime }\)

The initial phase fraction of martensite

fγ

The phase transformation fraction of austenite

fα

The phase transformation fraction of ferrite

\(f_{\alpha }^{\prime }\)

The phase transformation fraction of martensite

fi

The ODF of crystalline with the orientation of j

HV

Vickers hardness

HB

Brignell hardness

\(h,k,l, u,v,w\)

Prime integers

\(I,I^{\prime }\)

Constant integers

\(K_{w}\), \(K_{t}\)

Workpiece and wheel elasticity

\(k_{g} ,k_{w}\)

Thermal conductivity of grit and workpiece

\(K_{{\alpha^{ } }} , K_{{\alpha^{\prime } }} ,K_{\gamma }\)

Plasticity index of the phase transformation

lc

The total contact length of the primary heat source

\(M^{F} ,M^{B}\)

Taylor factor of single FCC and BCC crystal

M

Taylor factor of multi-phase material

\(m\)

The number of activated slip system

\(q_{t}\)

Total grinding heat

\(q_{ch}\)

Heat flux to chips

\(q_{w}\)

Grinding heat to workpiece

Pe

Peclet number

\(R_{w}\)

Energy partition

r

The cutting edge radius

\(t_{cr}\)

The minimum undeformed chip thickness

\(T_{0} ,T_{m} ,T_{w}\)

Workpiece, ambient and melting temperature

t

Undeformed chip thickness

T(X, Z)

The temperature field of \(M \left( {{\text{X}}, {\text{Z}}} \right)\)

V

Surface speed

\(V_{w}\)

Workpiece speed or federate

w

Cutting width

\(\alpha_{w}\)

Thermal diffusivity

\(\alpha_{1}\)

Material constant

\(\gamma_{1, } \gamma_{2}\)

Correction angles

\(\dot{\dot{\varepsilon }}_{0}\)

Material constant

\(\varepsilon^{cp}\)

Plastic strain

\(\dot{\dot{\varepsilon }}\)

Plastic strain rate

\(\varepsilon^{tp}\)

Strain induced by phase transformation

v

Poisson’s ratio

\(\rho_{1}\)

Density of dislocation

\(\rho_{w}\)

Material density

\(\sigma\)

Total flow stress

\(\tau_{s}\)

Shear strength in tangential direction

\(\varphi\)

Contact angle

\(\psi\)

The cone angle of grit

\(\varphi_{1} ,\varphi_{2} ,{\emptyset }\)

Euler angles

Notes

Acknowledgements

The authors would like to acknowledge the Precision Machining Research Center (PMRC) in the Georgia Tech Manufacturing Institute (GTMI) at the Georgia Institute of Technology.

Funding

The funding was provided by National Natural Science Foundation of China (Grant No. 51705073).

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Copyright information

© Korean Society for Precision Engineering 2019

Authors and Affiliations

  1. 1.School of Mechanical EngineeringDonghua UniversityShanghaiChina
  2. 2.Woodruf School of Mechanical EngineeringGeorgia Institute of TechnologyAtlantaUSA

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