Abstract:
In milling operations, periodically sensed vibration signals synchronous with tool revolution enables a determination of whether the tool returns to approximately the same position each revolution. If so, stability is indicated by tightly grouped values of the periodically sensed vibration signal. If the tool does not return to the same position, spread in the value of the periodically sampled vibration signals is produced thereby indicating chatter conditions. Variance values may be calculated and displayed; histograms may be produced and displayed; corrective action, if needed, may be taken in response to the variance values and/or histogram. Nominal (or commanded) spindle speed, while not necessarily exactly synchronous with actual tool rotation, is entirely adequate to trigger samples and achieve clear indication of the presence or absence of chatter.

Description:
[0001]    This application claims the benefit of U.S. Provisional Patent Application No. 60/271,396 filed Feb. 26, 2001 and is an invention of the National Institute of Standards and Technology, Department of Commerce, United States Government. 
     
    
     
         [0002]    The invention relates to milling and other material removal operations and more particularly to method and device for alerting machine operators to chatter conditions.  
         BACKGROUND OF THE INVENTION  
         [0003]    Milling and other material removal processes are performed by engaging the cutting teeth of a tool with a workpiece. A complex dynamic process results which can produce undesirable self-excited vibrations usually called chatter between the tool and the workpiece. Parameters which effect vibratory motions include the spindle speed, tool geometry and sharpness, workpiece material, tool and workpiece stiffness and damping, and feed rate of the tool through the material. The cutting operation includes periodic impacts of cutting teeth with the workpiece, thereby setting up vibrations between the two. These vibrations cause a wavy undulating surface to be left by the cutting tool. Removal of the undulating surface produced by the preceding tooth with the current tooth produces a regeneration of waviness and is a primary source of instability in milling and other material removal operations. Regeneration of waviness leads to a variable chip thickness, and therefore, to a variable cutting force which can lead to increased vibrations of the tool. The resulting closed loop feedback in force variation provides the mechanism for the production of chatter. The ultimate result is poor quality of the machined surface, high force levels, and potential damage to the workpiece and/or machine.  
           [0004]    An important analytic tool that has been developed to aid in the selection of stable cutting parameters is the stability lobe diagram. These diagrams enable the user to select the appropriate combination of chip width, i.e. instantaneous depth of cut, and spindle speed by separating stable from unstable regions with the analytic “lobes.” Construction of stability lobe diagrams requires pre-process knowledge of the cutting operation, including the tool point frequency response function and specific cutting energy coefficients that depend on the workpiece material, tool geometry, and cutting parameters. Cutting energy coefficients are typically obtained through a series of costly machining tests for each material/tool combination and maintained in a database. The tool point frequency response function (FRF) is usually obtained by impact testing where an instrumented hammer is used to excite the tool and the resulting vibration recorded using an accelerometer or capacitance probe. The FRF differs for each tool/holder/spindle combination. Production of the FRF is time consuming and requires a trained technician to complete the measurement. As a result, the calculation of optimum milling conditions using stability lobe diagrams is often neglected due to inadequate engineering support, especially in moderately sized job shops. The current invention is a device and method with the ability of identifying approaching chatter conditions through an in-process technique that does not require pre-process activity by trained technicians or engineers.  
         SUMMARY OF THE INVENTION  
         [0005]    Briefly stated, the invention is a device and method for identifying chatter conditions utilizing a first signal, such as an audio, displacement, acceleration, or force signal, which is capable of identifying chatter in the material removal operation. A second signal is provided at periodic intervals of tool revolution enabling sampling of the first signal in synchronism with tool revolution. By synchronously sampling the vibrations produced in the cutting operation, the stability of the operation is sensed since stable operation produces vibratory motion synchronous with spindle rotation. Physically, the tool returns to approximately the same position in each revolution under steady state stable conditions. In contrast, tool motion during regenerative chatter is not synchronous with spindle rotation; instead, vibrations occur near the natural frequency corresponding to the most flexible system mode, due to the nature of self-excited vibrations. When unstable cuts are sensed, it is because the tool has not returned to the same position each revolution. Therefore, by accumulating data over a sample window, the stability of the operation can be sensed and analysis of the accumulated data can be used to provide a display of the stability of the operation for the machine operator. If chatter or approaching chatter conditions are sensed, the machine operator can take corrective measures. The ability to accumulate and analyze the data may also be incorporated into machine tool controllers by manufacturers of such tools.  
           [0006]    Implementation of the invention can be at any convenient sampling interval synchronous with tool revolution and is exampled herein as occurring once per revolution. Also, it has been found that data accumulated in synchronism with nominal or commanded spindle speed rather than using an independently generated sampling signal produces the ability to identify chatter. Therefore, as used herein, sampling in synchronism with tool rotation includes sampling in synchronism with nominal spindle rotation. 
       
    
    
     BRIEF DESCRIPTION OF THE DRAWING  
       [0007]    [0007]FIG. 1 is a block circuit diagram showing major system components of the invention.  
         [0008]    [0008]FIG. 2 shows elements used in the circuit diagram of FIG. 1 to sample vibration signals in synchronism with tool revolutions.  
         [0009]    [0009]FIG. 3A shows the cutting tool of FIG. 2 in juxtaposition with a workpiece for a 50% radial immersion milling operation.  
         [0010]    [0010]FIG. 3B is a schematic diagram of the milling operation of FIG. 3A.  
         [0011]    [0011]FIGS. 4 and 5 show vibratory motion of the cutting tool for stable and unstable milling operations.  
         [0012]    [0012]FIGS. 6 and 7 show charts of variance values and histograms for stable and unstable milling operations.  
         [0013]    [0013]FIG. 8 shows a chart of variance values using nominal spindle speed as the sampling parameter.  
         [0014]    [0014]FIG. 9 is a flowchart of operations performed on the vibration signals to produce variance values and histograms.  
         [0015]    [0015]FIG. 10 shows a sample display of variance values and histogram to visually indicate the presence or absence of chatter conditions. 
     
    
     DETAILED DESCRIPTION  
       [0016]    The above mentioned and other features and objects of the invention and the manner of obtaining them will become more apparent, and the invention itself will best be understood by reference to the following description of embodiments of the invention taken in conjunction with the accompanying drawing.  
         [0017]    [0017]FIG. 1 shows a sensing device  10  placed near the tool workpiece interface in order to sense vibrations produced at the interface. The sensed signal is sent over line  14  to a processor  11  where it is sampled in synchronism with a signal received by processor  11  over line  15  from device  12 . Device  12  produces a sampling signal in synchronism with spindle rotation, therefore in synchronism with tool revolutions. A display  13  may be provided to visually alert the machine operator to chatter conditions or approaching chatter conditions. Amplifiers and other such accessory components are not shown.  
         [0018]    [0018]FIG. 2 shows one setup for implementing the invention wherein a microphone  20  is the sensing device for capturing an audio signal indicative of vibrations between the tool and the workpiece. Other vibration sensors could be used, for example, sensors to sense variations in displacement, force, acceleration, etc. FIG. 2 shows a tool  24  held by tool holder  25  and driven by a spindle  26 . An emitter/detector  22  is positioned adjacent to the tool holder  25  in order to sense a reflective mark  27  passing under detector  22  once per revolution. The tool  24  may be, for example, an end mill although flutes are not shown on end surface  24 A in FIG. 2.  
         [0019]    [0019]FIG. 3A shows an end mill  24  with two flutes (teeth)  30  in juxtaposition with a workpiece  31 . As tool  24  is fed in direction  32 , teeth  30  contact workpiece  31  and begin to remove material. FIG. 3B is a schematic diagram of the milling operation shown in FIG. 3A with four teeth  30  schematically represented on end surface  24 A. FIGS. 3A and 3B show a 50% radial immersion operation, that is, the radial depth  33  of the cut is 50% of the diameter of the tool  24 .  
         [0020]    The x and y axes are the axes of end surface  24 A and are shown in FIG. 3B to illustrate the axes of vibratory motion set up in the interface between tool and workpiece. A sensing device such as microphone  20  is placed near the tool/workpiece interface to sense that vibratory motion. Signals from microphone  20  are sampled in synchronism with tool rotation so that an analysis in accord with the invention can be made of the vibratory motion produced at the interface. The invention is based on the observation that when vibratory motion is stable the tool  24  returns to approximately the same position each revolution. Although the tool is vibrating in both the x and y directions in FIG. 4, at the time of sampling (once per revolution) the x, y plot of sampled tool position  40  is tightly grouped thereby showing the return of the tool to approximately the same position each revolution.  
         [0021]    [0021]FIG. 5 shows a plot of x, y tool motion when regenerative chatter is present and tool motions are not synchronous with tool rotation; instead, they occur near the natural frequency corresponding to the most flexible system mode due to the nature of self-excited vibrations. FIG. 5 shows that the synchronously sampled points  41  (once-per-revolution) of tool position produce an elliptical shape vs. the much tighter, more linear shape shown in FIG. 4. The elliptical shape of sampled tool positions  41  is indicative of quasi-periodic motion and shows that the tool does not return to the same position each revolution when chatter is present.  
         [0022]    A histogram of the tightly spaced cluster of sampled signals produced for a stable cut such as shown in FIG. 4 can be produced and displayed so that a machine operator can visually observe the stability of the machining operation. Such a histogram is shown in FIG. 7, except for histograms  70 ,  71  and  72 . When chatter is present, instability in the cut, due to regenerative chatter, demonstrates asynchronous motion and produces a set of signals similar to those shown in FIG. 5. A histogram of those sampled signals will give a more distributed set of samples with a much larger variance as shown at  70 ,  71  and  72 . The histogram of those signals visually alerts the machine operator that instability is present and corrective action is needed. Similarly, as the displayed data tends to move from stable condition toward an unstable condition, a machine operator can visually observe increased variance and take corrective action prior to the time that chatter actually occurs to an extent that would damage the quality of the machining operation.  
         [0023]    As the histograms in FIG. 7 show, there is a dramatically different distribution for the synchronously sampled data, thereby making it possible to distinguish between stable and unstable cutting conditions using only a once-per-revolution sampled process signal with adequate signal-to-noise ratio and some performance metric. Such a metric can be used alone or in conjunction with displayed histograms to alert a machine operator of approaching chatter conditions. The selected metric described below is a calculated number showing the statistical variance in the synchronously sampled milling audio signal  20 . Variance was selected because it provides a measure of the spread in a sample distribution. The variance, σ 2 , of sample distributions consisting of N values of signal, x i , was calculated according to Equation 1 below, where x m  is the mean or arithmetic average of the samples.  
                 σ   2     =         ∑     i   =   1     N          (       x   i     -     x   m   2       )         N   -   1         ,       where                   x   m       =         ∑     i   =   1     N          x   i       N               (   1   )                               
 
         [0024]    Experimental verification of the invention was performed utilizing 50% radial immersion down-milling cutting tests with a 12.7 mm diameter, two flute, helical carbide end mill with a 44 mm overhang. The workpiece material was 6061-T6 aluminum. Twenty-five cutting tests were performed covering spindle speeds from 14000 rpm to 18000 rpm (1000 rpm steps) and axial depths from 2.03 mm to 5.08 mm (0.76 mm steps.) In all cases, a constant feed per tooth of 102 μm was maintained. The microphone and once-per-revolution sampling signals were obtained using the setup shown in FIG. 2. The microphone signal was analog low pass filtered at 7 kHz and both the microphone and once-per-revolution signals were collected using a sampling frequency of 50 kHz.  
         [0025]    The first analysis method applied to the audio milling signal was to use the once-per-revolution signal obtained using the infrared emitter/detector  22  to sample the data directly, then calculate the variance in the result. The variance value in mV 2  for each cutting test (i.e., each spindle speed/axial depth combination) is shown in FIG. 6. A dramatic increase in variance from 48 mV 2  to 709 mV 2  is seen for the transition from 2.79 mm to 3.56 mm axial depth at 15000 rpm. Larger depths of 4.32 mm and 5.08 mm also show increasing variance values. These large values indicate an increase in the spread of the data and identify unstable cutting conditions. The unstable cuts are denoted by large variance values, reference numerals  60 ,  61  and  62  in FIG. 6. All other spindle speed/axial depth combinations are stable, exhibiting small variance values. These results agree with independent evaluations of the process stability including surface finish measurements of the machined workpiece using a scanning white light interferometer and FFT-based analyses of the milling audio signal. (The comparison to FFT results necessitated the high sampling rates for data capture.) To further emphasize the dramatic difference in the distribution of the synchronously sampled data between stable and unstable cuts, a histogram chart shown in FIG. 7 was developed. FIG. 7 shows equally scaled histograms for each of the cutting tests. As described above, the stable cuts show tightly grouped distributions, while the three unstable cuts demonstrate a much wider spread in the data as shown by histograms  70 ,  71  and  72 .  
         [0026]    In condition-based monitoring applications, it is generally preferred to simplify the architecture of the sensors and required hardware as much as possible. Toward that end, analysis was made utilizing a sampling signal derived from the nominal spindle speed as opposed to actually sampling a once-per-revolution signal such as with the emitter/detector  22  shown in FIG. 2. Nominal spindle speed typically differs slightly from the actual spindle speed and therefore the sampling signals are not in exact synchronism with tool revolution. For the machine used in this study, a nominal or commanded spindle speed of 15,000 revolutions per minute (rpm) gave an actual spindle speed of 14,994.1 rpm. Analysis was made using linear interpolation when the number of samples per revolution was not an integer value. The resulting variance chart is shown in FIG. 8. It is seen that the variance values are somewhat higher than those shown in FIG. 6 due to the slightly asynchronous sampling involved when nominal speed is used, but the large relative increases in variance are still available to indicate the transition from stable to unstable cutting. Note that all variance values are relatively small except for the three unstable cuts, large variance values  80 ,  81  and  82 . When nominal speed is used, the required components include only a unidirectional microphone or other appropriate sensor, a single channel of data acquisition, simple data processing to calculate the variance based on the nominal spindle speed, and a real-time display to provide monitoring of the condition-based process. A histogram chart based on the same data which produced FIG. 8 would look similar to the histogram chart, FIG. 7, showing the easily ascertained presence or absence of chatter. When presentations of data are made easily ascertainable, obvious benefits accrue for the machine operator (locally or remotely located) and the machining process.  
         [0027]    The production of histograms and the calculation of statistical variance may be implemented by the processor  11  shown in FIG. 1. A vibration sensor  10 , such as microphone  20  in FIG. 2, is used to provide an indication of vibration activity to the processor  11  and that signal is monitored once per revolution. The emitter/detector  22  shown in FIG. 2 may be used to provide a sampling pulse. For example, the falling edge of each sampling pulse from a normally high once-per-revolution output of the emitter/detector  22  can be used as a trigger to sample the vibration sensor output. Any sensor capable of providing the once-per-revolution signal is acceptable. For example, most machine spindles have an encoder, i.e., an angular position sensor that typically has a once-per-revolution pulse. That encoder signal could be used and would be preferred provided that the machine controller provides access to it. Also, while an audio vibration sensor is shown in FIG. 2, any type of vibration sensor can be used.  
         [0028]    [0028]FIG. 9 provides for the analysis of the once-per-revolution sampled tool position data in order to analyze it in two complimentary fashions, one for the histogram and the other for variance. In FIG. 9, at step  90 , the number of samples N to be taken in an accumulation is established. At step  91  if a histogram is to be produced, groups of signal values from the vibration sensor are established. For example, a first group from 0.25 to 0.3 mV 2 ; a second from 0.3 to 0.35 mV 2 , etc. At step  92  the in-process monitoring of the once-per-revolution sampling signal for a state change is performed, and at step  93  if a state change is sensed, the signal value from the vibration sensor is added to the accumulated data as shown in step  94 . Thus, the number of occurrences of signal values falling in the first group, 0.25 to 0.3 mV 2  is recorded, the number of occurrences falling in the second group is recorded, etc. Once the number of samples to be taken in a first accumulation is reached, the display is updated as shown at step  95 , and the histogram is updated at step  96 . If the statistical variance is calculated, then the variance values are updated as shown at step  97 .  
         [0029]    The update rate for calculating the instantaneous variance values and histogram charts can be varied as desired. A logical way is to select: (1) the number of revolutions of data that will be used for each calculation (thus defining a moving window along the once-per-revolution sampled data vector), and (2) the number of revolutions between new calculations. For example, the moving window may include the most recent 20 samples for updating the histogram and may be updated every 10 revolutions. In any case, the computational requirements are minimal.  
         [0030]    [0030]FIG. 10 shows a sample visual display including both a histogram and a number “54” representing the variance value. By viewing such a display a machine operator can easily determine the status of the process health, and can also visually see any deterioration in the process since chatter conditions will cause the variance value to rise and cause the histogram to begin spreading. Rather than displaying the instantaneous value of the variance, it is also possible to plot a trend line showing the current and previous values of the calculated variance.  
         [0031]    From the above description, it is clear that the invention provides data which identifies chatter conditions and can be used to initiate corrective action by a machine operator. The invention, applied to a plurality of machine tools, can be used to activate displays at a remote location for observation of several machines. The invention can easily be added to existing machine tools for immediate benefit with or without an interface to the machine controller. The invention can be implemented into a machine tool by manufacturers.  
         [0032]    While the invention has been shown and described with reference to preferred embodiments thereof, it should be understood that changes in the form and details of the invention may be made therein without departing from the spirit and scope of the invention. For example, once per revolution sampling signals are exampled herein but any periodic interval in synchronism with tool rotation is acceptable. As noted above, words referring to sampling in synchronism with the material removal operation include sampling with some slight asynchronism such as sampling at nominal spindle speed; the essence of the invention is method and device for obtaining clear indications of the presence or absence of chatter so that corrective action can be taken.