Chatter in milling is predominantly regenerative. Each tooth cuts a surface left wavy by the tooth before it, the chip thickness varies with the phase between the two waves, and under unfavourable conditions the variation feeds a growing vibration. The mechanism was identified in the 1950s and 1960s (Tobias and Fishwick, 1958; Tlusty and Polacek, 1963), and the stability boundary for milling was put in a compact analytical form by Altintas and Budak (1995). Two consequences matter for detection. In a stable cut the vibration consists of the tooth passing frequency, the spindle rotation frequency and their harmonics. When chatter develops, a new component appears close to a natural frequency of the most flexible part of the system, and this frequency is in general not a harmonic of the spindle speed (Altintas and Weck, 2004).

Detection therefore amounts to finding energy at frequencies that are not synchronous with the spindle. One exception should be kept in mind. At low radial immersion a second kind of instability occurs in which the vibration repeats every second tooth period, and its spectral lines fall midway between the tooth passing harmonics (Altintas et al., 2008). A detector that only looks for a single peak near a natural frequency may miss it.

Force, acceleration, sound and motor current have all been used as the sensed quantity. Delio et al. (1992) argued that a microphone compares well with other sensors for chatter detection and built a control scheme on its signal. Kuljanic et al. (2008) compared several sensors in milling and concluded that combining signals makes detection more robust than relying on one. The survey of machining monitoring by Teti et al. (2010) places these efforts in context. An indicator based on sampling the signal once per spindle revolution, so that synchronous vibration appears constant and chatter appears as scatter, was proposed by Schmitz (2003). The procedure below draws on all of these.

The sensor and sampling rate cannot be chosen until the builder knows roughly where chatter will appear. For the tools the machine normally carries, the dominant flexible modes of the tool, holder and spindle assembly should be located. The proper method is an impact test with an instrumented hammer (Ewins, 2000; Schmitz and Smith, 2009). Where no hammer is available, a workable substitute is to record the response of the stationary tool to a light tap with the sensor that will later be used, and read the ringing frequencies from its spectrum. Slender end mills in long holders have low first modes, while short, stiff tools ring considerably higher. The band to be monitored should cover the modes of every tool in regular use, with a margin on both sides.

Table 1 compares the candidate sensors. For a low cost system the realistic choices are a micro-electromechanical accelerometer and a microphone. The accelerometer is preferred here because it is insensitive to shop noise and can be fixed permanently, but its datasheet must be checked against the band found in Step 1: many inexpensive devices have a usable bandwidth too narrow for stiff tools, and their noise floor is higher than that of piezoelectric sensors. The sensor should be mounted rigidly, by a stud or a thin layer of hard adhesive, on the spindle housing as near the front bearing as access allows, with its sensitive axis in the plane of the cut. Two axes are better than one, since the direction of the chatter mode is not known in advance.

The sampling theorem requires a rate of more than twice the highest frequency present (Shannon, 1949). In practice the rate should be at least two and a half times the top of the monitored band, and content above half the sampling rate must be removed before sampling, or it will fold back and appear as false peaks. Digital accelerometers usually include a filter for this purpose; an analogue sensor needs one added. A single-board computer or a microcontroller with a fast serial bus is adequate to read the sensor, provided samples are taken at even intervals by a hardware timer and not by a software loop. The spindle speed must also be known for each record. A once-per-revolution pulse from an optical or inductive pickup is the most dependable source and costs little.

Before any indicator is defined the system should record what normal looks like: the spindle running in air across its speed range, and a set of cuts known to be stable, taken at light depths with the usual tools and materials. These records show the spindle and tooth passing harmonics, any resonance of the sensor mounting, and electrical interference. They also give the distribution of the indicator in the absence of chatter, which Step 6 requires.

The signal is processed in short blocks, each long enough to resolve neighbouring harmonics and short enough to respond within a fraction of a second. Each block is multiplied by a window to limit leakage (Harris, 1978) and transformed to a spectrum. Averaging a few overlapping blocks in the manner of Welch (1967) steadies the estimate. Lines within a narrow tolerance of every multiple of the spindle frequency are then set aside, which removes the tooth passing harmonics and runout together. The indicator proposed is the ratio of the energy remaining in the monitored band to the total energy in that band. It is dimensionless, lies between zero and one, and is only weakly affected by the depth of cut in a stable cut, so that one threshold can serve many operations. The once-per-revolution scatter of Schmitz (2003) can be computed alongside it as a check.

The threshold is placed above the range of the indicator seen in the baseline cuts. It should then be confirmed against cuts taken deliberately into chatter on a sacrificial workpiece, by increasing the axial depth in small increments at a fixed speed until the sound and the surface marks leave no doubt. A persistence rule, requiring the indicator to exceed the threshold for several consecutive blocks, guards against alarms from entry and exit transients and from chips striking the housing.

The simplest output is a lamp or sounder at the operator station, together with a display of the dominant non-synchronous frequency. That frequency is useful in itself. The established rule for escaping chatter by a speed change is to choose a spindle speed at which the tooth passing frequency equals the chatter frequency, or that frequency divided by a whole number, which places the cut in a pocket of higher stability (Delio et al., 1992; Schmitz and Smith, 2009). A low cost system should display the suggested speeds and leave the change to the operator. Writing to the machine control is a separate project with safety implications of its own.

Every alarm should be stored with its time, spindle speed, indicator value and spectrum. Reviewing the log against scrap and tool breakage records shows whether the threshold is set sensibly, and over time it maps the speeds at which each tool is troublesome. The sensor mounting should be inspected periodically, and the baseline repeated after a spindle repair or any change to the mounting.