Keith A. Young

Simultaneous Stability and Surface Location Error Predictions in Milling

Optimizing the milling process requires a priori knowledge of many process variables. However the ability to include both milling stability and accuracy information is limited because current methods do not provide simultaneous milling stability and accuracy predictions. The method described within this paper, called Temporal Finite Element Analysis (TFEA), provides an approach for simultaneous prediction of milling stability and surface location error. This paper details the application of this approach to a multiple mode system in two orthogonal directions. The TFEA method forms an approximate analytical solution by dividing the time in the cut into a finite number of elements. The approximate solution is then matched with the exact solution for free vibration to obtain a discrete linear map. The formulated dynamic map is then used to determine stability, steady-state surface location error, and to reconstruct the time series for a stable cutting process. Solution convergence is evaluated by simply increasing the number of elements and through comparisons with numerical integration. Analytical predictions are compared to several different milling experiments. An interesting period two behavior, which was originally believed to be a flip bifurcation, was observed during experiment. However, evidence is presented to show this behavior can be attributed to runout in the cutter teeth.

Theory of Torsional Chatter in Twist Drills: Model, Stability Analysis and Composition to Test

The mechanism of torsional chatter in drilling differs qualitatively and quantitatively from other types of chatter. In this paper we show that torsional chatter can be explained by the torsional-axial coupling inherent in a twisted beam; the beam untwists and extends in response to an increase in cutting torque. Based on a model of this mechanism, predictions of stability boundaries and chatter frequencies are derived by frequency domain analysis, and confirmed by numerical simulation and experimental tests. The effect of the torsional-axial coupling is opposite that of traditional cutting in that an increase in cutting forces leads to axial extension and greater chip load. Because of this sign difference, the limiting depth of cut is governed by the positive real part of the frequency response function, which explains the unexpected fact that torsional chatter occurs below the natural frequency of the tool.

Analysis of Tool Oscillation and Hole Roundness Error in a Quasi-Static Model of Reaming

A quasi-static model of reaming is developed to explain oscillation of the tool during cutting and the resulting roundness errors in reamed holes. A tool with N evenly-spaced teeth often produces holes with N+1 or N-1 lobes. These profiles correspond respectively, to forward or backward whirl of the tool at N cycles/rev. Other whirl harmonics (2N cycles/rev, e.g.) are occasionally seen as well. The quasi-static model is motivated by the observations that relatively large oscillations occur at frequencies well below the natural frequency of the tool, and that in this regime the wavelength of the hole profile is largely independent of both cutting speed and tool natural frequency. In the quasi-static approach, inertial and viscous damping forces are neglected, but the system remains dynamic because regenerative (time-delayed) cutting and rubbing forces are included. The model leads to an eigenvalue problem with forward and backward whirl solutions that closely resemble the tool behavior seen in practice.

An empirical approach for delayed oscillator stability and parametric identification

This paper investigates a semi-empirical approach for determining the stability of systems that can be modelled by ordinary differential equations with a time delay. This type of model is relevant to biological oscillators, machining processes, feedback control systems and models for wave propagation and reflection, where the motion of the waves themselves is considered to be outside the system model. A primary aim is to investigate the extension of empirical Floquet theory to experimental or numerical data obtained from time-delayed oscillators. More specifically, the reconstructed time series from a numerical example and an experimental milling system are examined to obtain a finite number of characteristic multipliers from the reduced order dynamics. A secondary goal of this work is to demonstrate a benefit of empirical characteristic multiplier estimation by performing system identification on a delayed oscillator. The principal results from this study are the accurate estimation of delayed oscillator characteristic multipliers and the utilization the empirical results for parametric identification of model parameters. Combining these results with previous research on an experimental milling system provides a particularly relevant result—the first approach for identifying all model parameters for stability prediction directly from the cutting process vibration history.

Machining Accuracy Due to Tool or Workpiece Vibrations

This paper presents a newly developed method for predicting dimensional errors caused by vibrations of either the cutting tool or workpiece. In previous literature, this phenomenon has been described as the “surface location error” from process dynamics. Analytical predictions are compared to several milling experiments: 1) a flexible workpiece and rigid tool; and 2) a rigid workpiece and flexible tool. Tool or workpiece vibrations were measured with non-contact sensors during the cutting process. In addition, dimensional errors were directly measured on machined parts. The results from experimental cutting tests show good agreement with theoretical predictions.© 2003 ASME

Peripheral milling of thin titanium plates: modelling, analysis, and process planning

This paper presents research conducted to model and analyse the peripheral milling of thin titanium plates. Impact tests are performed and the vibration characteristics of a thin titanium plate modelled empirically. The force process is described by a mechanistic model and experimental data are used to determine the model parameters. The particle swarm optimization technique is used to determine the parameters of the plate vibration and force process models, which are combined to create a complete model of the thin titanium plate peripheral milling operation. The models are validated experimentally and excellent agreement is shown between the simulation and experimental results. A process planning scheme for peripheral milling of thin titanium plates is developed and applied. In this scheme integer numbers of widths-of-cut and depths-of-cut are used and the optimal helix angle and feed are computed for each combination of width-of-cut and depth-of-cut. The process planning test case revealed that the optimal material removal rate decreases as the width-of-cut decreases, the optimal helix angle is independent of the width-of-cut, and the optimal feed increases as the width-of-cut decreases. The test case also revealed that the optimal material removal rate is independent of depth-of-cut, the optimal helix angle increases as the depth-of-cut decreases, and the optimal feed increases as the depth-of-cut decreases.