Tony L. Schmitz

Predicting High-Speed Machining Dynamics by Substructure Analysis

Abstract The practical implementation of high-speed machining (HSM) requires accurate knowledge of the machine dynamics. We apply receptance coupling substructure analysis to the prediction of the tool point dynamic response, combining frequency response measurements of individual components through appropriate connections to determine assembly dynamics using simple vector manipulations. This paper shows that the dynamic response before and after system changes may be predicted, thus dramatically reducing the number of required experimental measurements. The application of this technique to the tuning of tool dynamics for improved stability by overhung length variation is demonstrated.

Tool Point Frequency Response Prediction for High-Speed Machining by RCSA

The implementation of high-speed machining for the manufacture of discrete parts requires accurate knowledge of the system dynamics. We describe the application of receptance coupling substructure analysis (RCSA) to the analytic prediction of the tool point dynamic response by combining frequency response measurements of individual components through appropriate connections. Experimental verification of the receptance coupling method for various tool geometries (e.g., diameter and length) and holders (HSK 63A collet and shrink fit) is given. Several experimental results are presented to demonstrate the practical applicability of the proposed method for chatter stability prediction in milling. @DOI: 10.1115/1.1392994#

Three-Component Receptance Coupling Substructure Analysis for Tool Point Dynamics Prediction

In this paper we present the second generation receptance coupling substructure analysis (RCSA) method, which is used to predict the tool point response for high-speed machining applications. This method divides the spindle-holder-tool assembly into three substructures: the spindle-holder base; the extended holder; and the tool. The tool and extended holder receptances are modeled, while the spindle-holder base subassembly receptances are measured using a “standard” test holder and finite difference calculations. To predict the tool point dynamics, RCSA is used to couple the three substructures. Experimental validation is provided.

Improving High-Speed Machining Material Removal Rates by Rapid Dynamic Analysis

Abstract Stability prediction and chatter avoidance in high-speed machining requires knowledge of the tool point dynamics. In this paper, three advances toward the rapid identification of the tool point frequency response and corresponding stable cutting parameters are described: 1) stable speeds determination using non-contact periodic impulsive excitation of the tool point (produced by spindle rotation and a stationary magnet) in conjunction with once-per-revolution sampling, 2) Receptance Coupling Substructure Analysis for the analytic prediction of the tool point response, and 3) once-per-revolution sampling of the audio signal during cutting to determine stability behavior.

The difficulty of measuring low friction : Uncertainty analysis for friction coefficient measurements

The experimental evaluation of friction coefficient is a common laboratory procedure; however, the corresponding measurement uncertainty is not widely discussed. This manuscript examines the experimental uncertainty associated with friction measurements by following the guidelines prescribed in international standards. The uncertainty contributors identified in this analysis include load cell calibration, load cell voltage measurement, and instrument geometry. A series of 20 tests, carried out under nominally identical conditions, was performed using a reciprocating pin-on-disk tribometer. A comparison between the experimental standard deviation and uncertainty analysis results is provided.

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.

Effects of Radial Immersion and Cutting Direction on Chatter Instability in End-Milling

Low radial immersion end-milling involves intermittent cutting. If the tool is flexible, its motion in both the x- and y-directions affects the chip load and cutting forces, leading to chatter instability under certain conditions. Interrupted cutting complicates stability analysis by imposing sharp periodic variations in the dynamic model. Stability predictions for the 2-DOF model differ significantly from prior 1-DOF models of interrupted cutting. In this paper stability boundaries of the 2-DOF milling process are determined by three techniques and compared: (1) a frequency-domain technique developed by Altintas and Budak (1995); (2) a method based on time finite element analysis; and (3) the statistical variance of periodic 1/tooth samples in a time-marching simulation. Each method has advantages in different situations. The frequency-domain technique is fastest, and is accurate except at very low radial immersions. The temporal FEA method is significantly more efficient than time-marching simulation, and provides accurate stability predictions at small radial immersions. The variance estimate is a robust and versatile measure of stability for experimental tests as well as simulation. Experimental up-milling and down-milling tests, in a simple model with varying cutting directions, agree well with theory.Copyright

Wear-Rate Uncertainty Analysis

Wear due to relative motion between component surfaces is one of the primary modes of failure for many engineered systems. Unfortunately, it is difficult to accurately predict component life due to wear as reported wear rates generally exhibit large scatter. This paper analyzes a reciprocating tribometer in an attempt to understand the instrument-related sources of the scatter in measured wear rates. To accomplish this, an uncertainty analysis is completed for wear-rate testing of a commercially available virgin polytetrafluoroethylene pin on 347 stainless steel counterface. It is found that, for the conditions selected in this study, the variance in the experimental data can be traced primarily to the experimental apparatus and procedure. Namely, the principal uncertainty sources were found to be associated with the sample mass measurement and volume determination.

Chatter recognition by a statistical evaluation of the synchronously sampled audio signal

Milling is a complex dynamic process that includes periodic impacts of the cutting teeth with the workpiece, corresponding vibrations of the cutter and workpiece that define the machined surface, and overcutting of the surface left by previous teeth by the current tooth. The removal of the undulating surface produced by the preceding tooth with the current tooth is referred to as regeneration of waviness and is a primary source of instability in milling [1]. Regeneration of waviness leads to a variable chip thickness and, therefore, variable cutting force which causes, in turn, vibrations of the tool and workpiece. This closed-loop feedback of force and vibration provides the mechanism for self-excited vibration, or chatter. Depending on the selected chip width (for a particular dynamic system, cutter geometry, and workpiece material), the subsequent vibrations of the cutter can diminish for stable cutting, or increase to some bounded limit for chatter. A schematic representation of a 50% radial immersion down-milling operation is shown in Fig. 1. Because the variable cutting force can become large and the machined surface quality is poor, it is desirable to avoid unstable milling conditions. An important analytic tool that has been developed to aid in the selection of stable cutting parameters is the stability lobe diagram [2–6]. These diagrams allow the user to select appropriate combinations of the control parameters, chip width and spindle speed, by separating stable from unstable regions with the analytic ‘lobes’; see Fig. 2. The construction of these diagrams requires pre-process knowledge including the tool point frequency response function, expected radial immersion, and specific cutting energy coefficients that depend on the workpiece material, tool geometry, and cut parameters. In many instances, the calculation of optimum milling conditions using stability lobes diagrams for each tool/holder/spindle/machine/material combination on the shop floor is not possible due

Examination of surface location error due to phasing of cutter vibrations

The purpose of this research is to investigate the relative importance of spindle speed, system dynamics, and cutting conditions on the accuracy of surface location in computer numerical-control (CNC) finish machining operations. The relationship between the spindle speed, the most flexible modes of the machine/cutting tool system and the final part dimensions is rather complex. The underlying theory, based on the situation of forced vibrations, is outlined. It is shown that the critical factor is the ratio of the tooth passing frequency to the system most flexible mode and corresponding natural frequency. Simple analytical calculations are carried out to illustrate the overcut/undercut surface error phenomenon. A simple simulation for end milling operations is also described which calculates the force on the cutter, the resulting cutter deflection, and the final error of surface. A comparison between the simulated and experimental results is presented. From experimental data, it shown that a change in surface location (and part dimension) of up to 50 μm is seen for a set of given conditions (i.e., cutter, material, chip load) simply by changing spindle speeds. Furthermore, it is seen that certain spindle speeds produce surfaces with no error introduced by the machining process.