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Cutting temperature analysis considering the improved Oxley’s predictive machining theory

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Abstract

This article deals with the identification of the temperature distributions in the chip, tool and workpiece based on orthogonal cutting data estimated analytically from the improved version of the Oxley’s machining theory, including the strain-hardening constant (n eq) and the Johnson–Cook (JC) flow stress equation. The improved Oxley’s machining theory and thermal model were separately considered to compute temperature distributions. The initial parameters (δ, C 0, ϕ) and temperature factors (η, ψ) of Oxley’s model were optimized to improve the computation efficiency and estimation accuracy. The thermal model considers the effects of the primary and secondary heat sources. The primary heat source was depicted as a uniformly acting oblique band. The secondary heat source was modeled by applying non-uniform distribution of the heat partition ratio. The estimated results were compared with the published results of an experimental investigation in machining of AISI 1045 steel. It was found that the results of the improved Oxley’s model were closer to the experimental values than the outcomes of its extended version. A detailed set of the temperature distributions was introduced and the estimated temperature values were in good agreement with the experimental results.

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Abbreviations

a :

Thermal diffusivity

A, B, C, m, n :

Constants of the JC model

B i,chip, B i,tool :

Heat partition ratios for chip and tool

C 0 :

Strain rate constant along AB

E j , E k :

Quadratic sum of relative errors

f :

Feed rate

F, N :

Frictional and normal forces at the tool/chip interface

F c, F f :

Cutting and feed forces

F c,E, F f,E :

Cutting and feed forces estimated from extended Oxley’s model

F ci , F c,ij ,:

Measured and estimated cutting forces

F c,I, F f,I :

Cutting and feed forces estimated from the improved Oxley’s model

F fi , F f,ij :

Measured and estimated feed forces

F s, F n :

Shear and normal forces at AB

k AB, k chip :

Shear flow stresses of AB and chip

K 0 :

Zero-order Bessel function

l AB, l p, l c :

Shear plane, sticking region and tool–chip contact lengths

l i :

Position of differential element dl i

n eq :

Strain-hardening constant

M :

Point for calculating temperature increase

q shear, q friction, q induced :

Shear, friction and induced heat source intensities

R :

Resultant force

R T :

Thermal number

R 1, R 2 :

Distance between heat source and point M

t c :

Chip thickness

t ci , t c,ij :

Measured and estimated chip thicknesses

t c,I, t c,E :

Chip thicknesses calculated from improved and extended Oxley’s models

S :

Specific heat

T, T m :

Instantaneous and melting temperatures of workpiece

T AB :

Average temperature of AB

T int, T M,int :

Average and maximum temperatures of tool/chip interface

T inti , T int,ij :

Measured and estimated average temperatures along the tool/chip interface

T M :

Temperature increase at point M

T r :

Room temperature

V, V c, V ch, V s :

Velocity of shear plane, cutting speed, chip and shear velocities

w :

Width of cut

x i , y i :

Positions of differential elements dx i and dy i

X, z :

Coordinates of point M used for temperature calculation

α, ϕ, φ :

Rake, shear and oblique angles

β a :

Global friction angle

β T :

Ratio of heat transferred into the workpiece

\( \gamma_{\text{AB}} , \) \( \gamma_{\text{int}} \) :

Shear strains of AB and the tool/chip interface

\( \dot{\gamma }_{\text{AB}} , \) \( \dot{\gamma }_{\text{int}} \) :

Shear strain rates of AB and the tool/chip interface

δ :

Strain rate constant of the tool/chip interface

ΔF c :

Relative difference between outcomes F c estimated from improved and extended Oxley’s models

ΔF f :

Relative difference between outcomes F f estimated from improved and extended Oxley’s models

Δt c :

Relative difference between outcomes t c estimated from improved and extended Oxley’s models

ΔT c :

Average temperature increase in the chip

ΔT M,c, ΔT M,t :

Maximum temperature increases in the chip and tool

ε, \( \dot{\varepsilon } \) :

Equivalent strain and strain rate

ε AB, \( \dot{\varepsilon }_{\text{AB}} \) :

Equivalent strain and strain rate at AB

ε E :

Absolute error between outcomes measured and estimated from the extended model

ε int, \( \dot{\varepsilon }_{\text{int}} \) :

Equivalent strain and strain rate at the tool/chip interface

ε I :

Absolute error between outcomes measured and estimated from the improved model

εT c :

Relative difference between average temperatures in the chip for tools with negative and positive rake angles

εT int,c :

Relative difference between the estimated maximum chip temperature and measured maximum tool/chip interface temperature

εT int,t :

Relative difference between the estimated maximum tool temperature and measured maximum tool/chip interface temperature

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

Reference strain rate

η, ψ :

Shear zone and tool/chip interface temperature factors

η k , ψ k :

Estimated values of temperature factors η and ψ

θ :

Angle between R and AB

λ c, λ t :

Thermal conductivities of chip and tool

μ, μ local :

Global and local friction coefficients

ξ :

Exponential constant

ρ :

Density

σ AB :

Flow stress at AB

σ N, \( \sigma^{\prime}_{\text{N}} \) :

Normal stresses of tool/chip interface and point B

τ int, τ st :

Shear stresses of tool/chip interface and sticking zone

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Authors and Affiliations

  1. Department of Industrial Product Design, Bilecik Şeyh Edebali University, 11210, Bilecik, Turkey

    Mehmet Aydın

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  1. Mehmet Aydın
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Correspondence to Mehmet Aydın.

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Technical Editor: Márcio Bacci da Silva.

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Aydın, M. Cutting temperature analysis considering the improved Oxley’s predictive machining theory. J Braz. Soc. Mech. Sci. Eng. 38, 2435–2448 (2016). https://doi.org/10.1007/s40430-016-0514-x

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