Timothy J. Burns

Stability Prediction for Low Radial Immersion Milling

Traditional regenerative stability theory predicts a set of optimally stable spindle speeds at integer fractions of the natural frequency of the most flexible mode of the system. The assumptions of this theory become invalid for highly interrupted machining, where the ratio of time spent cutting to not cutting (denoted p) is small. This paper proposes a new stability theory for interrupted machining that predicts a doubling in the number of optimally stable speeds as the value of p becomes small. The results of the theory are supported by numerical simulation and experiment. It is anticipated that the theory will be relevant for choosing optimal machining parameters in high-speed peripheral milling operations where the radial depth of cut is only a small fraction of the tool diameter.

The Stability of Low Radial Immersion Milling

Abstract Traditional regenerative stability theory predicts a set of spindle speeds with locally optimum stability at integer fractions of the natural frequency of the most flexible mode of the system. The assumptions of this theory become invalid for highly interrupted machining, where the ratio of time spent cutting to not cutting (denoted ρ) is small. This paper proposes a new stability theory for interrupted machining that predicts a doubling in the number of optimally stable speeds as the value of ρ becomes small. The predictions are verified against experiment and numerical simulation.

On repeated adiabatic shear band formation during high-speed machining ☆

Abstract We compare the repeated adiabatic shear band formation that takes place at sufficiently large cutting speeds in a number of materials during high-speed machining operations with the more well-known formation of a single shear band that often takes place at sufficiently large strain rates in dynamic torsion tests on these materials. We show that there are several major differences in the physics of the two deformation processes. In particular, the shear stress in machining over the tool-material contact length is not even approximately homogeneous. Additionally, in high-speed machining, the material flow can become convection-dominated, so that the tool can “outrun” the thermal front generated in the workpiece material by the high-strain-rate cutting process. We demonstrate by means of a one-dimensional continuum model that these differences can lead to repeated oscillations in the plastic flow of the workpiece material during high-speed machining, leading to the repeated formation of adiabatic shear bands.

On the Dynamics of Chip Formation in Machining Hard Metals

Abstract The results of orthogonal cutting tests on electroplated nickel-phosphorus (15% phosphorus) and AISI 52100 bearing steel are presented and compared. For both materials, chips become segmented at relatively low cutting speeds (0.3 m/s to 2 m/s) due to the onset of an oscillation in the material flow that is manifested in the repetitive formation of localised shear bands. The average spacing between the shear bands increases monotonically with cutting speed and asymptotically approaches a limiting value that is determined by the cutting conditions and the properties of the material being cut. The similarity in the behaviour of the two materials (which have significantly different microstructure) and the regularity of the shear band pattern observed in the chips provides strong evidence for a continuum mechanics model of the process. A simplified one-dimensional thermo-mechanical model of a continuous, homogeneous material being sheared by an impinging rigid wedge is developed to explain the observed behaviour. Numerical simulations of this model show that at low wedge speeds, material deformation reaches a thermo-mechanical equilibrium, in which material flow is homogenous and the stress, strain-rate and temperature fields reach a steady state behaviour that is constant in time (when viewed from a tool-fixed reference frame). As the wedge speed is increased, the stress, strain-rate and temperature fields become oscillatory, and the material flow becomes inhomogenous. As the speed of the wedge is increased further, the material shows repetitive shear localisation, with the distance between shear zones increasing montonically to some limiting value, as was observed in experiments.

Calibrated Thermal Microscopy of the Tool–Chip Interface in Machining

This paper presents the results of calibrated, microscopic measurement of the temperature fields at the tool–chip interface during the steady‐state, orthogonal machining of AISI 1045 steel. The measurement system consists of an infrared imaging microscope with a 0.5 mm square target area, and a spatial resolution of less than 5 µm. The system is based on an InSb 128 × 128 focal plane array with an all‐reflective microscope objective. The microscope is calibrated using a standard blackbody source from NIST. The emissivity of the machined material is determined from the infrared reflectivity measurements. Thermal images of steady state machining are measured on a diamond‐turning class lathe for a range of machining parameters. The measurements are analyzed by two methods: 1) energy flux calculations made directly from the thermal images using a control–volume approach; and 2) a simplified finite‐difference simulation. The standard uncertainty of the temperature measurements is ± 52°C at 800°C.

Thermomechanical oscillations in material flow during high-speed machining

This paper presents a nonlinear dynamics approach for predicting the transition from continuous to shear–localized chip formation in machining. Experiments and a simplified one–dimensional model of the flow both show that, as cutting speed is increased, a transition takes place from continuous to shear–localized chip formation in the flowfield of the material being cut. Initially, the process appears to be somewhat disordered. With further increases in cutting speed, the average spacing between shear bands increases monotonically, and the spacing becomes more regular and asymptotically approaches a limiting value that is determined by the cutting conditions and the properties of the workpiece material.

Tool Length-Dependent Stability Surfaces

Abstract This article describes the development of three-dimensional stability surfaces, or maps, that combine the traditional dependence of allowable (chatter-free) chip width on spindle speed with the inherent dependence on tool overhang length, due to the corresponding changes in the system dynamics with overhang. The tool point frequency response, which is required as input to existing stability lobe calculations, is determined analytically using Receptance Coupling Substructure Analysis (RCSA). In this method, a model of the tool, which includes overhang length as a variable, is coupled to an experimental measurement of the holder/spindle substructure through empirical connection parameters. The assembly frequency response at the tool point can then be predicted for variations in tool overhang length. Using the graphs developed in this study, the technique of tool tuning, described previously in the literature, can then be carried out to select a tool overhang length for maximized material removal rate. Experimental results for both frequency response predictions and milling stability are presented.

COMPARISON OF ANALYTICAL AND NUMERICAL SIMULATIONS FOR VARIABLE SPINDLE SPEED TURNING

The turning process with varying spindle speed is investigated. The well-known single degree of freedom turning model is presented and the governing delay-differential equation with time varying delay is analyzed. Three different numerical techniques are used to solve the governing equation: (1) direct Euler simulation with linear interpolation of the delayed term, (2) Taylor expansion of the time delay variation combined with Euler integration and (3) semi-discretization method. The results of the three method are compared. Stability charts are constructed, and some improvements in the process stability is shown, especially for low spindle speed domains.Copyright

Does a shear band result from a thermal explosion

Abstract Based on results of computer simulations using the numerical method of lines, a simplified one-dimensional reaction—diffusion type of model, with an Arrhenius-type model for the plastic flow surface, is presented for the localization of thermoelastic—plastic shear in ductile solids into an adiabatic shear band at high strain rate. This model is shown to share a number of similarities with a model of thermal reaction in a rigid solid explosive. Using small strain-rate-sensitivity asymptotics, which is analogous to high activation-energy asymptotics in the mathematical theory of combustion, it is shown there is an analogue in the mathematical theory of plasticity of the ignition problem in chemical combustion. This raises the interesting question: Does an adiabatic shear band result from a thermal explosion?

DYNAMIC PROPERTIES FOR MODELING AND SIMULATION OF MACHINING: EFFECT OF PEARLITE TO AUSTENITE PHASE TRANSITION ON FLOW STRESS IN AISI 1075 STEEL

The Pulse-Heated Kolsky Bar Laboratory at the National Institute of Standards and Technology (NIST) has been developed for the measurement of dynamic properties of metals. With this system, a small sample can be pre-heated from room temperature to several hundred degrees C in less than a second, prior to rapid loading in compression at strain rates up to the order of 104 per second. A major focus of this research program has been on investigating the influence of the heating rate and time at temperature on the flow stress of carbon steels, for application to the modeling and simulation of high-speed machining operations. The unique pulse heating capability of the NIST Kolsky bar system enables flow stress measurements to be obtained under conditions that differ significantly from those in which the test specimens have been pre-heated to a high temperature more slowly, because there is less time for thermally activated microstructural processes such as dislocation annealing, grain growth, and solid state phase transformations to take place. New experimental results are presented on AISI 1075 pearlitic steel samples that were pulse-heated up to and beyond the austenite formation temperature of the material (723 °C). The data show that the flow stress decreased by about 50 % due to a phase transformation in the microstructure of the material from the stronger pearlitic phase to the weaker austenitic phase. As a result, the constitutive response behavior of the material cannot be modeled by a fixed-parameter constitutive model, like the Johnson-Cook flow stress model that is widely used in computer simulations of high-speed machining processes.