Numerical Simulations of Vibration Assisted Machining

A two-dimensional (2-D) finite element model (FEM) has been developed to perform numerical simulations of vibration assisted machining (VAM). The model is based on an updated Lagrangian formulation, with adaptive remeshing. The model is capable of simulating the amplitude and frequency independently of the tool in the cutting (x) and thrust (y) force directions over a wide range of values. The resultant vibrations include linear, circular, and elliptical paths. Results of the finite element analysis include: chip formation, work piece deformation, cutting and thrust forces, pressures, temperatures, stress, strain, and strain rate. Materials modeled include: aluminum, steel and silicon carbide. These materials represent a comprehensive array of material properties and demonstrate the general utility of the modeling method. Other variables in the model include: cutting edge radius, rake angle, clearance angle, feed, cutting speed, depth of cut, length of cut, work piece dimensions, friction coefficient, and ambient conditions. The simulation results allow for a detailed study of the materials behavior in response to the VAM process variables. The work reported in this paper includes nano to micro meter feeds and depth of cut. VAM results are compared to base line simulations without vibrating conditions. The results reported are for diamond cutting tool material, i.e. single point diamond turning (SPDT) operation. The VAM results show a significant reduction in cutting (Fc) and thrust (Ft) forces as the degree of vibration (amplitude) and frequency are increased. Other parameters determined directly from the simulation results of interest include: Force ration (Fc/Ft), maximum temperatures and maximum pressures in the work piece. The results and analyses for the VAM process demonstrate the model’s general utility over a wide range of process conditions (work piece materials), machining parameters (speeds, feeds and depth of cut) and VAM variables (amplitude and frequency of vibration). Comparisons to experimental results are included. Future work will attempt to reduce the scale of the vibration, to nanometers, and provide enhancements to the tool wear model to directly incorporate the effect of VAM to improve the machining process. This latter work will concentrate on further reductions in tool forces and temperatures, and research on the beneficial results of cutting fluids to the machining process in general the VAM process in particular. It is expected that improved tool designs will directly result from this work. INTRODUCTION Vibration assisted machining (VAM) has proved beneficial at machining metals and ceramics, with special applications being applied to steels and SiC [1-3]. This paper presents complementary work on numerical simulations of the VAM process using a commercial FEM software package AdvantEdge, from Third Wave Systems Inc. One of the authors (Patten) worked with TWS on the development and implementation of the VAM module, which is now incorporated into their commercial software product. The software has been tested and evaluated for a limited set up materials and process conditions. The work reported on in this paper concerns diamond turning of steels, as practiced by Overcash [2]. Of particular interest is the evaluation of the forces (cutting and thrust) and resultant temperatures. It is often assumed that the primary benefit of the VAM process to do reduce tool wear, when cutting (particularly diamond machining) difficult to machine materials (such as steels and ceramics). Reduced tool wear is assumed to result from decreased machining forces and/or decreased temperatures during machining. Tool wear is not explicated considered in this paper, nor is the application of a cutting fluid or coolant addressed. These conditions will be explored further in future work. EXPERIMENTS-SIMULATIONS A 2-D Lagrangian Finite Element Model (FEM), utilizing adaptive remeshing is utilized [5] for the simulations. Process parameters of interest include, which are explicated simulated include: feed, speed, amplitude and frequency of vibration. The work reported in this paper is for machining steel with single crystal diamond tooling. The work piece material is a 12L14 Steel [2] and the diamond tool used is a zero degree rake angle of varying cutting edge radius (0.002 to 0.001 mm). A constant frequency of vibration of 10,000 Hz is utilized in all of the results reported on herein [2], however the simulation model is capable of a wide range of vibration frequencies. The feed, or uncut chip thickness, used for these simulations is 20 micrometers (μm, or 0.020 mm) and the amplitude of vibration ranges include: 0, 2, 4 and 8 micrometers (0, 0.002, 0.004, and 0.008 mm respectively). Three different cutting speeds are reported on in this paper, these are: 1 m/s, 0.5 m/s and 0.25 m/s. The simulated conditions are summarized in Table 1. Only circular vibrations are considered in this paper, i.e. the x and y vibrations are identical (amplitude and frequency); however the software can simulate linear and elliptical vibrations as well. For reference, at the intermediate cutting speed, 0.5 m/s, the tool and work piece partially separate (lose contact) at the highest vibration amplitude (8 μm, in accordance with [1]). TABLE 1. Simulated Process Variables Amplitude (μm) 0 2 4 8 Speeds (m/s) 1.0 and 0.5 1.0 and 0.5 1.0 and 0.5 1, 0.5 and 0.25 Thermal on/off On/off On/off On/off On/off RESULTS The VAM simulation results are included for the effects of vibration amplitude and cutting speed on the resultant cutting forces and temperatures (tool and work piece). Cutting Forces The force values reflect the time varying periodic nature of the forced vibrations of the VAM process. These characteristic force signals are similar to the actual VAM processes as shown by Brehl and Dow [1]. The periodic nature of the time varying cutting force values are shown in figure 1, for the case of a 4 μm amplitude at a cutting speed of 1.0 m/s, these conditions are just below the threshold where the tool and work piece separate during the VAM machining process; i.e. there is no actual separation of the tool and work piece due to the VAM action. FIGURE 1. Cutting Forces (not filtered) The average of the maximum or peak force values, at steady state, as a function of vibration amplitude are shown in figure 2. These values were determined by averaging the peak forces, as seen in the force plots (such as figure 1), to establish a force for comparison with thermal conditions not included, i.e. no thermal effect. The observed effects are due to the mechanical oscillations alone and do not include a thermal component, this is useful for separating out the influence of the mechanical induced vibrations from any resultant thermal effects due to the relative change in apparent cutting velocity (due to the vibration oscillations being superimposed on the cutting velocity). Avgerage of the Peak Cutting Force thermal model off and cutting speed 1m/s