An experimental investigation of temperatures and energy partition in grinding of cemented carbide with a brazed diamond wheel

Abstract

An experimental investigation is reported of the temperatures and energy partition in the grinding of cemented carbide with a vacuum brazed diamond wheel. During the experiments, the temperature distributions along the workpiece surface were measured using a sandwiched foil thermocouples and the energy partition to the workpiece estimated using a temperature matching method. The effects of the various grinding conditions, including wheel velocity, feed rate, and depth of cut, on the temperatures and the energy partition were investigated. The measured temperature responses were found to be in good relation with the analytical results of a moving heat source with a triangular distribution at the grinding zone. It was found that the grinding temperatures measured under different grinding conditions varied from 10°C to 100°C. The energy partition to the workpiece in dry grinding was found to be from 35% to 70%. Based on the energy partition values obtained from the experiments, the diamond tip temperature was calculated and found to be over the temperature necessary for the graphitization of diamond if the circular grain contact of radius is smaller than a critical value.

Appendices

Appendix 1

1.1 The quasi-steady-state temperature

Based on the moving heat source model with a triangular heat flux distribution or a uniform heat flux distribution, the quasi-steady-state temperature at a horizontal distance x from the center of the heat source and at depth z below the surface can be calculated as [4, 28]:

$$ {\theta_{{(x,z)}}} = \frac{{\varepsilon q}}{{\pi k}}{\int_{{ - 1}}^l e^{-{\frac{{{v_{{\rm w} }}(x - x\prime )}}{{2a}}}}}{K_0}\left\{ {\frac{{v{}_{{\rm w} }}}{{{2α}}}{{\left[ {{{(x - x\prime )}^2} + {Z^2}} \right]}^{{1/2}}}} \right\}f(x\prime ){\rm d} x\prime $$

q = F _t v _s/l _c b :

Total average heat flux at the grinding zone

ε :

Fraction of total energy conducted as heat to the workpiece (energy partition)

f(x′):

Distribution function for the heat flux

k :

Thermal conductivity of the workpiece

α = k/ρc :

Thermal diffusivity

v _w :

Workpiece velocity corresponding to the source velocity relative to the workpiece

K ₀ :

Modified Bessel function of the second kind of order zero

l _c :

Grinding zone length taken as equal to the geometric contact length (l _c = 2 l = (a _p d _s)^1/2)

b :

Width of cut

Appendix 2

$$ \varepsilon \frac{1}{{1 + \Omega {{\left( {\frac{{{v_{{\rm s} }}}}{{{v_w}}}} \right)}^{{1/2}}}}} $$

$$ \Omega = 0.94\frac{{(k\rho c)_{{\rm g} }^{{1/2}}}}{{(k\rho c)_{{\rm w} }^{{1/2}}}}Af(\zeta ) + \frac{{(k\rho c)_{{\rm f} }^{{1/2}}}}{{(k\rho c)_{{\rm w} }^{{1/2}}}}(1 - A) $$

$$ f(\zeta ) = \frac{2}{{{\pi^{{1/2}}}}}\frac{\zeta }{{1 - \exp {\zeta^2}erfc\,(\zeta )}} $$

$$ \zeta = {({\gamma^{{2}}}\pi {\alpha_{\text{g}}}{l_{\text{c}}}/{2}{{\text{A}}_0}{v_{\text{s}}})^{{{1}/{2}}}} $$

(kpc)_g :

Grain thermal contact coefficient

(kpc)_w :

Workpiece thermal contact coefficient

(kpc)_f :

Fluid thermal contact coefficient

α _g :

Thermal diffusivity of grain

γ :

Geometric grain shape parameter

A = C _a A ₀ :

Overall wear flat area

C _a :

Active grit density

A ₀ = πr ² :

Single grain–workpiece contact area

r :

Radius of circular grain contact