This can be done in real time without the need for exhaustive cutting tests. In the implementation described here, the machine tool spindle and a non-contact magnetic force actuator are used to produce the time-varying impulse train. This impulse train has significant energy at the spindle speed and its harmonics. As the spindle speed is ramped up from zero to the maximum speed, those speeds that maximize the dynamic response of the tool are the speeds that minimize regenerative chatter. The device is suitable for integration with the machine-tool controller, and could potentially allow the optimal speeds for each tool to be downloaded and stored for later use in NC programming.

Regenerative Chatter

Regenerative chatter in machining is a self-excited vibration of the workpiece and/or tool that results in poor surface finish, increased rates of tool wear and potentially irreparable damage to the machine or the workpiece. In high-speed machining operations, it is often the dominant factor limiting the attainable rates of material removal. Regenerative chatter is caused by the force-feedback that occurs when a previously cut surface is re-cut in a subsequent machining operation (see Figure 1(a)). For example, on a lathe, the previously cut surface is re-cut during each spindle rotation; in milling each flute cuts a surface that was produced by the preceding flute. This phenomenon gives rise to the stability behavior illustrated schematically in Figure 1(b).

The most stable spindle speeds are those that produce the least phase shift between the current cutter oscillations and the wave left during the previous cut. To first order, these speeds, indicated by the dotted lines in Figure 1(b), are dependent only on the dynamics of the structural loop including the tool, the machine structure and the workpiece. For a rigid workpiece the most stable spindle speeds are independent of the material being cut. The correct identification of these stable speeds is critical for efficient use of new high-speed machining techniques, often leading to an order of magnitude higher metal removal rate than could be obtained under less optimal conditions [1,2,3,4,5].

Use in High-Speed Machining

Within the past decade, there has been a marked increase in the industrial use of so-called high-speed machining technology. This decade has seen the development of machining centers capable of spindle and slide speeds that are an order of magnitude higher than those available on conventional machining centers. For example, a number of different industrial suppliers have recently introduced reliable machining centers with slide speeds that exceed 40 meters per minute and spindles capable of delivering in excess of 20 kilowatts of power to the cutting zone at spindle speeds greater than 20 thousand revolutions per minute.

While these new machining centers offer the possibility of much higher material removal rates, markedly improved surface finish and increased workpiece quality, their use also requires much more technical expertise than conventional machining centers. Chatter is one of the most difficult phenomena to master in high-speed machining because solutions are most often counterintuitive; for example speeding up the spindle or increasing the overhang of the tool may actually diminish the tendency of the system to chatter.

This behavior must be made intuitive if high-speed machining centers are to be used to their full potential. As shown in figure 1 (b), correct choice of spindle speeds for a particular tool is critical because under some conditions a spindle speed change of only 10 % can result in an order of magnitude change in achievable material removal rates [1,2,3].

The purpose of the device described is to provide a simple, low-cost method for rapidly determining the most stable spindle speeds for a particular cutting tool/machine combination with no need for cutting tests. Note that the simplicity of the device is possible because it does not attempt to determine the stable depth/width of cut; this must be determined by the machinist through trial and error. However, because of its simplicity, it can remain on the machine tool and should be comparable to a tool-length sensor in terms of ease of use. For this reason it is extremely suitable for use in smaller job shops where tool configurations (such as overhang) and hence stable speeds are changed to suit each new job.

Theoretical Description

The functioning of this device relies on empirical, theoretical and numerical observations that to first order, the stable speeds for a particular machine-cutting tool configuration are independent of the material being cut. Thus, while changes in workpiece material will cause the stability chart shown in figure 1(b) to translate parallel to the depth/width-of-cut axis, they will not result in translation parallel to the spindle speed axis. Therefore, the most stable spindle speeds remain fixed as long as the dynamics of the machine-tool system is unchanged. This result is theoretically demonstrated in Appendix A using a well-established model for machine-tool chatter. Given this observation, a method to measure the most stable speeds was devised.

The method is based upon the second important observation that the best spindle speeds satisfy the following relationship [1,2,3,4,5].

Here, f is the resonant frequency of the most flexible mode of the tool in Hertz, N is the number of flutes for a milling operation and N = 1 for a turning operation. There are an infinite number of stable speeds that get lower and more densely packed as the integer index i is increased. The stable regions become tall and wider as i approaches 1, and for practical purposes the lowest attainable i values are the most useful stability regions. This has led to one popular definition of high-speed machining - operation at spindle speeds that are a significant fraction of f/N.

Equations (1) may be recognized as conditions of resonance for the tool given a harmonic excitation at Wi it is these resonance conditions that give the most favorable phase relationship

Figure 2: (a) Schematic of an impulsive driving force in the time and frequency domain; (b) measured response function of a machine-tool and endmill combination with dominant resonant frequency f, and the power spectra of the driving force for resonant and non-resonant conditions.

From Equations (1), it is apparent that if the tool tip were driven by a force with suitable harmonic content, sweeping the frequency of the forcing function would produce large responses of the tool at frequencies corresponding to the most stable spindle speeds. This situation is diagrammed in Figures 2(a) and 2(b). Figure 2(a) shows an impulsive driving force with frequency fd in the time and frequency domains. The force has large energy content at fd and its harmonics; for a perfect impulsive force the energy content at all harmonics is equal while for imperfect impulsive loading the harmonic content drops asymptotically to zero with increased frequency. If a machine-cutting tool system with the response function shown in Figure 2(b) is driven by the force shown in Figure 2(a), its response will be maximized for cases where fd satisfies the following relationship.

This situation is shown in figure 2(b) for the case where i is 2. If fd = WiN , Equations (1) and (2) are identical. This will be true if the spindle of the machine tool and a non-contact force actuator are used to produce an impulsive force at a frequency NW  and then W  is swept over spindle speeds in a predetermined range of interest. One suitable non-contact actuator is a permanent magnet positioned as shown in Figure 3(a) for turning and 3(b) for milling. As the magnet comes is close proximity with either the lathe tool (Figure 3(a)) or a flute of the milling cutter (Figure 3(b)) a large force is produced. This force is impulsive due to the very rapid, nonlinear, monotonic change in magnetic attractive force with distance. Thus, it is very suitable for the scheme outlined in Figure 2. As the spindle speed is varied, the structure of the milling machine or lathe will be excited most when the resonance conditions outlined in Figure 2 and given by equation (1) are met.

Reduction to Practice

A prototype device was built, simulated and tested and has produced encouraging results. A photograph and a diagram of the device are shown in Figure 4. It consisted of a magnet and a capacitance probe mounted on an aluminum block that was then bolted to a 3-axis piezoelectric dynamometer and mounted to the pallet of a horizontal, four axis high-speed milling center with a maximum spindle speed of 20 thousand rpm. A 12.5 mm diameter, round high-speed steel test rod was mounted in the spindle of the machining center with an unclamped length of 114.3 mm. Flat sections were ground on the ends of the rod to simulate the flutes of a milling tool. An impact hammer and the capacitance probe were used to measure the dynamic response of the rod. The measured Frequency Response Function (FRF) for displacement of the tip of the rod in response to an applied force at the tip of the rod is given in Figure 5. The peak frequency of the response

is approximately 905 Hz. The five most stable spindle speeds for this simulated milling tool were calculated and are displayed in Figure 5.

The rod was then positioned so that the flutes passed within 2 mm of the magnet when they were aligned vertically. The spindle was rotated at a constant speed of 500 rpm and the forces were measured using the dynamometer. A sample of the measured forces is shown in Figure 6. The first six harmonics are clearly visible in the power spectrum shown in Figure 6(b). However, only the first three harmonics are significantly above the noise floor associated with harmonics of 60 Hz.

Simulation Process

To gain some insight into the method, the FRF of the test rod was fit with a single degree-of-freedom simple harmonic oscillator model (mass 0.022 kg, damping ratio 0.0087 and a natural frequency of 5686 s^-1). The response of the system to a periodic, purely impulsive (delta function) load with an amplitude of 0.005 N-s (e.g. 5 N force for a millisecond) ramping frequency

Figure 8: Experimental results showing the RMS amplitude of the simulated endmill as a function of spindle speed.

(frequency). Figure 7 shows a plot of mean squared amplitude for this simulation assuming a twice per revolution impulsive load (N=2) for a spindle speed sweep of 5000 rpm to 15000 rpm in ten seconds. The maxima in the mean squared amplitudes indicate all of the stable speeds for the simulated endmill in this range. The locations of the peaks indicate four best speeds: (1) between 5000 and 6000 rpm; (2) between 6000 and 7000 rpm; (3) slightly greater than 9000 rpm and (4) slightly less than 14000 rpm. The first speed appears to have a double peak, likely due to the effect of initial conditions. However, in general the peaks in the rms amplitude of the response of the simulated tool correspond closely to the expected most stable cutting speeds.

Experimentation

Figure 8 shows the mean squared voltage from the capacitance probe as a function of spindle speed for the device depicted in Figure 4(a) for a sweep in spindle speeds from zero to fifteen thousand rpm in 80 seconds. Three peaks are evident: (1) between 6000 rpm and 7000 rpm; (2) between 10000 rpm and 11000 rpm; and (3) between 13000 rpm and 14000 rpm. The first and third peaks agrees very well with the expected values, while the middle one is somewhat higher than expected and the peak is not as immediately evident as the other two. While these results are encouraging, more work needs to be done in several areas to further reduce the device to practice. These areas are described below.

1. The forces must be made to better represent a pure periodic impulse train. This will increase the energy content in the driving force at the harmonics and make the peaks in the rms-amplitude curve more evident. In addition, this will allow identification of a larger number of stable speeds, and will enable more rapid determination of stable speeds without degrading performance. This could potentially be accomplished simply by optimizing the shape of the magnet and the distance to the tool.
2. A rapid scheme for calculating rms-amplitude and identifying the peaks must be developed. Custom electronics are the quickest and most desirable way to accomplish this task.
3. The device must be made robust in a machine-tool environment. To accomplish this a custom enclosure must be designed and tool-vibration-sensors lest sensitive to a dirty machine tool environment must be investigated. Perhaps a microphone or non-contact magnetic sensor is all that will be necessary to sense the peaks in the amplitude of the tool response.
4. The device must be designed to accommodate tools of various diameters. Probably the desirable diameter range is 3 mm diameter to 30 mm diameter and lengths of 40 mm to 150 mm.

These issues are challenging but not technically insurmountable. The results of the simulation and the prototype device have proven that the idea is sound.

Competing Technologies

A number of schemes for identifying, avoiding and controlling chatter have been developed [5, 6, 7, 8, 9, 10,11]. These different schemes can be roughly broken into two categories:

• devices that provide additional forces either through passive or active means to the machine and tool combination to reduce or eliminate chatter at a given set of cutting conditions;
• devices that take data during the machining process and attempt to make corrections in process parameters to guide the machine to stable cutting conditions.

The first type of device uses active or passive means to vary the shape of the stability curves. The second type of device operates during machining and actively corrects the machining conditions to avoid chatter. A notable system of the second type is the chatter recognition and control (CRAC) system developed and patented by Delio [11] which is currently being sold as a commercial package. This system uses a microphone to monitor the cutting conditions and is interfaced with the machine-tool controller so that it can adjust machining parameters in real-time to find chatter-free machining conditions. However, systems such as this are often very expensive and require a substantial amount of expertise to operate correctly. Typically, these systems are best suited for use by process engineers in sophisticated industrial shops, but are not particularly suited for use by a machinist in a small job shop who has no expertise in machine-tool dynamics.

The device presented here takes a different approach to the problem, providing information to the machinist about the dynamics of the machine-tool system so that intelligent decisions about machining conditions can be made. The device presented here could be used in conjunction with either of the two types of devices mentioned above. In addition, it can be manufactured at a small fraction of the cost of other more sophisticated systems.

Potential for Commercialization

As the market for high-speed machining grows the need for devices for stable speed determination will grow commensurately. Weiss spindles has estimated that after the current period of rapid development in high-speed machine components, the spindle speeds on a substantial portion of CNC machine tools will be approximately 25 thousand rpm, and they have focused most of their development on developing high-powered spindles in this speed range. A device such as this one would be extremely useful on machines of this type since many of the modes of common machine/tool combinations have frequencies such that large stable regions are attainable with spindle speeds of 10 thousand rpm or more (for example, a two flute tool with a modal frequency of 1500 Hz produces stable large speeds at 11250 rpm, 15000 rpm, 22500 rpm and 45000 rpm).

The aspects of this device that make it a competitive means of determining the most stable spindle speeds are:

(1)  speeds can be determined without the need for cutting tests;
(2)  the device can be produced relatively cheaply;
(3)  the device is small and if designed correctly can be used by those with minimal expertise in machine tool dynamics;
(4)  depending on the sensor used, the device can be made relatively robust to the machining environment;
(5)  the device might be used in conjunction with other chatter recognition and control as well as “tool-tuning” strategies;
(6)  the device does not rely on identifying a limited number of resonances for the machine tool combination – any resonant frequency will be identified as a stable speed;
(7)  the measurements are done on the rotating tool rather than in the static non-rotating configuration.

With regard to comment (2), we estimate that with dedicated electronics, the device could be produced for less than five hundred dollars and could probably be marketed as an integrated option on a CNC machining center at a cost of two-thousand five hundred dollars. With regard to comment (4) it is likely that a relatively low cost and robust sensor such as a microphone could be used in the device in place of the capacitance probe used in the prototype device.

The market for such a device could potentially be comparable to other simple devices like tool-length sensors, which are regularly sold on modern CNC machining centers.

References

[1] Tlusty, J., “High-speed machining”, 1993, Annals of the CIRP, 42 (2):733-738.
[2]  Tlusty, J. , Smith, S., and Winfough, “Techniques for the Use of Long Sender End Mills in High-speed Milling”, 1996, Annals of the CIRP, 45(1):393-396.
[3]  Davies, M. A., Dutterer, B., Pratt, J. R., and Schaut, A., submitted by Bryan, J., “On the dynamics high-speed milling with long slender endmills”, Annals of the CIRP, 47(1), 1998.
[4]  Davies, M. A. and Smith, S., “ High-speed machining”, McGraw- Hill 1999 Yearbook of Science and Technology, McGraw Hill, 1998.
[5]  Altintas, Y. and Budak, E., “Analytical Prediction of Stability Lobes in Milling” , 1995, Annals of the CIRP, 44(1):357-362.
[6]  United States Patent Number 3,967,515, Apparatus for Controlling Vibration and Chatter in a Machine-tool Utilizing an Updated Synthesis Circuit, C. L. Natchtigal, R. G. Klein, K. C Maddux, July 6, 1976.
[7]  United States Patent Number 5,170,103, Active Vibration Control Device, K. E. Rouch, S. Tewani, T. R. Massa, R. W. Stephenson, L. S. Stephens, December 8, 1992.
[8]  United States Patent Number 5,033,340, Apparatus and Method for Tool Vibration Damping, L. T. Siefring, July 23, 1991.
[9]  United States Patent Number 4,604,834, Method and Apparatus for Optimizing Grinding, R. A. Thompson, April 12, 1986.
[10]  United States Patent Number 3,938,626, Vibration Damping Assembly, D. A. Hopkins, February 17, 1976.
[11]  United States Patent Number 4,759,243, Method and Apparatus for Optimizing Single Point Machining Operations, R. A. July 26, 1988.
[12]  United States Patent Number 5,170,358, Method for Controlling Chatter in a Machine Tool, T. S. Delio, December 8, 1992.

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