Prediction of Temperature Distribution in Orthogonal Machining Based on the Mechanics of the Cutting Process Using a Constitutive Model
Journal of Manufacturing and Materials Processing
This paper presents an original method of predicting temperature distribution in orthogonal machining based on a constitutive model of various materials and the mechanics of their cutting process. Currently, temperature distribution is commonly investigated using arduous experiments, computationally inefficient numerical analyses, and complex analytical models. In the method proposed herein, the average temperatures at the primary shear zone (PSZ) and the secondary shear zone (SSZ) were
... (SSZ) were determined for various materials, based on a constitutive model and a chip-formation model using measurements of cutting force and chip thickness. The temperatures were determined when differences between predicted shear stresses using the Johnson-Cook constitutive model (J-C model) and those using a chip-formation model were minimal. J-C model constants from split Hopkinson pressure bar (SHPB) tests were adopted from the literature. Cutting conditions, experimental cutting force, and chip thickness were used to predict the shear stresses. The temperature predictions were compared to documented results in the literature for AISI 1045 steel and Al 6082-T6 aluminum in multiple tests in an effort to validate this methodology. Good agreement was observed for the tests with each material. Thanks to the reliable and easily measurable cutting forces and chip thicknesses, and the simple forms of the employed models, the presented methodology has less experimental complexity, less mathematical complexity, and high computational efficiency. Keywords: temperature at the primary shear zone; temperature at the secondary shear zone; Johnson-Cook constitutive model; chip formation model Experimental approaches using tool-work thermocouples, embedded thermocouples, radiation pyrometers, metallographic techniques, and a method using fine powders with a constant melting point were reported for measuring the temperatures of tools and workpieces. The tool-work-thermocouple technique was applied in milling and turning experiments with various metallic materials    . In this method, the contact area between the tool and the workpiece forms a hot junction, while the remote sections of the tool and the workpiece form a cold junction, and the average temperature at the SSZ is measured experimentally. The embedded-thermocouple technique was utilized to measure the temperature distribution of cutting tools. The thermocouple is inserted into a machined hole inside the cutting tool with varying depths [4, 5] . Radiation techniques were applied using an infrared (IR) pyrometer or an IR camera to measure the surface temperatures of the workpieces and the cutting tools, based on their emitted thermal energy     . The metallographic technique was utilized to investigate temperature by correlating the temperature with changes in microstructure and hardness due to elevated temperatures  . The fine-powder method was also used to find the temperature distribution within tools by observing the boundary line formed by melted powder scattered on the tool's surface  . The experimental approaches are arduous and difficult to implement in machining tests due to the complex contact phenomena and the restricted accessibility, especially in high-speed machining. Numerical approaches were developed based on finite-element (FE) simulations for modeling orthogonal machining processes. Dawson et al. predicted the shear plane temperature using a FE solution for the heat-transfer problem with an assumption of a moving band heat source . Kim et al. developed a thermo-viscoplastic cutting model using a finite-element method (FEM) to analyze the mechanics of the steady-state orthogonal cutting process. The temperature distribution was analyzed in this model by removing spurious oscillations which occurred in the solution . Moriwaki et al. developed a rigid-plastic FE model in orthogonal cutting, and the temperature distributions in workpieces and tools were analyzed based on the stress, strain, and material flow in the workpiece . Lei et al. developed a thermomechanical plane-strain FE model for the orthogonal cutting process with continuous chip formation . Levy et al. applied a two-dimensional finite-difference approach to determine the transient temperature variation in chips and cutting tools in orthogonal cutting . Chan et al. developed a thermal analysis using the boundary element method for the metal cutting process . Umbrello et al. developed a FE model to predict temperature when steady-state conditions were reached. The heat transfer coefficient between tools and workpieces in steady-state conditions was determined using a pure thermal simulation. The determined coefficient was then used in a thermomechanical simulation for temperature prediction . Kim et al. and Yang et al. developed similar FE models to investigate the temperature field in laser-assisted machining [19,20]. Özel et al. developed a FE model to investigate the influence of cutting-tool edge roundness on the temperature field at tool-chip and tool-work interfaces . Attia et al. developed a FE model to investigate the influence of tool coatings on the temperature field . Although numerical approaches using FEM made considerable progress in predicting temperature distribution in machining, the high computational cost and the large number of input parameters, including contact conditions, and material properties of cutting tools and workpieces, which must be obtained from extensive experimental work and material property tests, cause inconvenience and difficulty in the temperature prediction. Chip morphology, cutting force, temperature distribution, and residual stress obtained from experiments are needed for comparison with the simulation results for calibration and validation. Analytical approaches were developed to predict temperature distribution in machining. Boothroyd developed an analytical model for temperature prediction using Wiener's energy partition analysis [23, 24] . The following assumptions were made in this model: (1) independent workpiece thermal properties; (2) uniform heat sources on the tool rake face; (3) a constant fraction of total heat transferred into the tool; and (4) negligible heat transfer in the chip flow direction. Radulescu et al. developed an analytical model to calculate transient cutting temperature using cutting forces as inputs.