Heat transfer model of semi-transparent ceramics undergoing laser-assisted machining

doi:10.1016/j.ijheatmasstransfer.2004.10.035

International Journal of Heat and Mass Transfer

Volume 48, Issue 10, May 2005, Pages 1999-2012

https://doi.org/10.1016/j.ijheatmasstransfer.2004.10.035 Get rights and content

Abstract

A three-dimensional, unsteady heat transfer model has been developed for predicting the temperature field in partially-stabilized zirconia (PSZ) undergoing laser-assisted machining. The semi-transparent PSZ is treated as optically thick within a spectral band from approximately 0.5 to 8 μm. After comparing the diffusion approximation and the discrete ordinates method for predicting internal radiative transfer, suitability of the diffusion approximation is established from a comparison of model predictions with surface temperature measurements. The temperature predictions are in good agreement with measured values during machining. Parametric calculations reveal that laser power and feedrate have the greatest effect on machining temperatures.

Introduction

Laser-assisted machining (LAM) provides a means of increasing the material removal rate, improving dimensional control, and reducing surface flaws when shaping difficult-to-machine materials such as structural ceramics. A laser is used to locally heat the workpiece above a threshold temperature, reducing its yield strength below the fracture strength and enabling quasi-plastic material removal by a cutting tool, rather than brittle fracture. To characterize the process and to enhance understanding of related fundamentals, several experimental and theoretical studies have been performed. In particular, for opaque materials (silicon nitride and mullite) a transient three-dimensional thermal model of the process has been developed and experimentally validated [1], parametric effects have been considered [2], and the efficacy of the process for ceramics has been experimentally demonstrated [3], [4], [5]. However, unlike previous work, this study focuses on LAM of partially-stabilized zirconia (PSZ), which is semi-transparent [6] and hence able to volumetrically absorb, scatter, and emit radiation. Partially-stabilized zirconia is widely used as a structural ceramic, and its thermal conductivity is almost an order of magnitude smaller than that of silicon nitride.

This paper describes a transient, three-dimensional, heat transfer model of a semi-transparent PSZ workpiece undergoing LAM. Use of the diffusion approximation to determine internal radiative transfer is assessed by comparing predictions with those based on the more rigorous discrete ordinates method (DOM). The sensitivity to uncertainties in model parameters is determined, and predictions based on the complete model are compared with measured surface temperatures. A parametric study is performed to demonstrate the effect of the most influential operating parameters (laser power, feedrate, and depth-of-cut) on the workpiece temperature distribution.

The workpiece geometry and machining conditions for laser-assisted turning of a cylindrical workpiece, at some intermediate stage of machining, are shown in Fig. 1. Relative to the incident laser radiation and the cutting tool, motion of the workpiece is characterized by rotation and translation in the circumferential and axial directions, respectively. The boundary between machined and unmachined portions of the workpiece is represented by a helical chamfer, whose shape is defined by the cutting tool geometry and feedrate, and on which the small r–z plane at ϕ = 0 corresponds to the location of material removal. The location of material removal relative to the laser center is designated by the parameters ϕ_ℓ and L_ℓ, where L_ℓ extends to the farthest edge of the chamfer. To facilitate a numerical solution of the temperature field, the material removal plane is approximated as a rectangle of depth d and width L_f, which corresponds to a cutting tool of zero lead angle (Ω_ℓ = 0) and radius (r_t = 0). The necessity of reaching a threshold temperature at the depth-of-cut for successful LAM requires a preheat phase during which the workpiece rotates with laser heating, but without machining or axial translation. During preheating the cylindrical workpiece does not have the helical chamfer or machined portion shown in Fig. 1, and the free end of the workpiece is located at the chamfer (z_fe = z_ch).

Section snippets

Experimental methods

Numerical simulation of the LAM process was coordinated with experiments conducted using a 1.5 kW (continuous wave) CO₂ laser, whose beam delivery is integrated with a CNC lathe [7], thereby synchronizing axial translation of the optics with that of the cutting tool. A radiation pyrometer [8] is mounted beneath the workpiece and moves with the laser beam and cutting tool in the axial (z) direction, thereby measuring the surface temperature at a fixed distance from the cutting zone and the

Mathematical model

Since zirconia ceramics are semi-transparent between wavelengths of 0.5 and 8.0 μm and opaque above 8 μm [6], internal heat transfer by radiation, as well as by diffusion and advection, must be included in the model. Advection is due to workpiece rotation and axial translation (V_z) in an Eulerian reference frame. Two different treatments of internal radiation are described.

Diffusion approximation

The diffusion approximation to radiative transfer in an optically thick medium is based on Rosseland’s simplification of the radiative transfer equation [17], for which the radiative flux, $q_{r}^{″} = - k_{r} \nabla T$ is proportional to a radiation conductivity that is a function of temperature cubed. Since the effect of radiation is embodied in the effective thermal conductivity, k_eff, only the energy equation must be solved. The approximation applies to an optically thick medium for which the product of the

Sensitivity/uncertainty

The sensitivity of model predictions to parameter uncertainties was determined by varying a single parameter in each of several simulations for the nominal conditions (Table 1). The absorptivity to laser radiation, α_ℓ, jet impingement heat transfer coefficient, h, specific heat, c_p, effective thermal conductivity, k_eff, and total emissivity, ε, were varied according to the uncertainties given in Table 2.

Uncertainties in the jet impingement heat transfer coefficient relate to its magnitude and

Conclusions

A transient, three-dimensional heat transfer model is developed, and temperature predictions based on an optically thick assumption (diffusion approximation) for internal radiative transfer are compared with those based on a discrete ordinates method of solution (DOM). Measured surface temperatures are found to lie within the sensitivity limits of both predictions. During the machining phase it is found that the diffusion approximation and the DOM solution overpredict and underpredict measured

Acknowledgement

Support of this work by the National Science Foundation under grant nos. 9802047-CTS and 0115172-DMI and the School of Mechanical Engineering at Purdue University through the Laura Winkelman and Ingersoll-Rand fellowships is gratefully acknowledged.

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Heat transfer model of semi-transparent ceramics undergoing laser-assisted machining

Abstract

Introduction

Section snippets

Experimental methods

Mathematical model

Diffusion approximation

Sensitivity/uncertainty

Conclusions

Acknowledgement

Int. J. Heat Mass Transfer

Int. J. Heat Mass Transfer

Experimental investigation of thermo-mechanical characteristics in laser assisted machining of silicon nitride ceramics

ASME J. Manufact. Sci. Eng.

Laser-assisted machining of reaction sintered mullite ceramics

ASME J. Manufact. Sci. Eng.

Experimental evaluation of the laser assisted machining of silicon nitride ceramics

ASME J. Manufact. Sci. Eng.

Thermal radiation properties of ceramic materials

Heat Transfer—Japanese Res.

Surface temperature measurement of semi-transparent ceramics by long-wavelength pyrometry

ASME J. Heat Transfer

Transparent titania–yttria–zirconia ceramics

J. Mater. Sci. Lett.

Recrystallization textures during laser-assisted machining of zirconia ceramics

Mater. Sci. Forum

Densification of zirconia—conventional methods

Key Eng. Mater.

Surface microstructure changes on laser treatment of MGO-partially-stabilized zirconia

J. Am. Ceram. Soc.

Radiative transfer and interactions with conduction and convection