Control Engineering

Why will a machine tool chatter at one speed, but not others?
July 9, 2007

Tool chatter is a serious problem for machine-tool builders as it limits the maximum processing speed for machine-cutting applications. In the past, machinists have attempted to avoid it through trial and error. There are also attempts to counteract it through mechanical feedback mechanisms. Most promising is the mechatronic approach in which computer simulations are used to first predict the machine’s dynamical behavior, then modify it to achieve a stable cutting regime.

Tool chatter is similar to slip-stick movement which occurs when you combine mechanical resonance with non-linear resistance to movement. Perhaps the best known instance of slip-stick movement, and one of the easiest to describe, is bowing a violin.

In the violin example, the mechanical resonance occurs as a transverse standing displacement wave in the violin string. The non-linear resistance is from friction.

Simple friction is highly non-linear with respect to speed. As one object slides over another, the friction force is largely independent of the sliding speed, but as the sliding speed approaches zero, the friction force rapidly rises to a high value. The coefficient of static friction between two cast iron parts, for example, is 1.1. For every Newton of force pressing the surfaces together, it takes 1.1 N to get them to slide. The coefficient of sliding friction, however, is only 0.15. Once the surfaces start to slide, it is relatively easy to keep them sliding.

The slip-stick motion couples a large pulse of energy into a transverse wave on the violin string. The driving force has the form of a sawtooth wave, which contains a fundamental and all harmonics. Since standing waves in the string resonate with all these harmonics as well, coupling is quite efficient and relatively little effort is needed to produce a loud sound. The lowest-frequency standing wave, of course, determines the sawtooth’s fundamental frequency as well.

Regenerative chatter grows when peaks left by vibration in one pass line up with troughs being created by the next pass.

Regenerative chatter dies away when peaks left by one pass line up with peaks being cut by the next.

Tool chatter works in a similar way. The nonlinear resistance arises from the way the cutting tool digs into the material being removed. This topic is still intensively being researched, but clearly the instantaneous cutting force must relate to the depth of cut, the cutting-tool angle and, perhaps, the tool speed through the material.

The resonance comes from flexing of the cutting-tool shank and the tool post, which act as a tuning fork. For the sake of argument we can think of this whole stack of components as the tool post. It will have one dominant and several less important vibration modes, each with its own resonant frequency and harmonics.

As the tool post vibrates, all three cutting-force variables (cut depth, cutting-edge speed, and cutting-edge angle) vary with the motion. The cutting force, therefore, will vary in an oscillatory manner, as will the depth of cut. This is called non-regenerative tool chatter and will occur to some extent whenever machine tools are used. The vibration’s amplitude depends largely on both the average tool speed and cut depth.

Regenerative chatter occurs when:

1) The cutting conditions are such that non-regenerative chatter has sufficient amplitude to leave the cut surface with undulations of significant depth; and

2) The time between cutting passes is an odd integer number of vibration half periods.

The first condition causes the surface height for the next cutting pass to vary. The second causes that force to vary out of phase with the tool-post vibration. The result is a time varying amount of material to be removed and thus a time varying cutting force that feeds energy into the tool-post vibration.

Changing the tool speed just enough to make the time between passes an even integer number of vibration half periods causes the peaks of the second pass to line up with the peaks of the first pass. The material removed at each pass, therefore, remains constant with time, so the cutting force remains constant and no energy feeds into the vibration, which tends to die away.

Mathematically, if the time between passes is P, and the vibration frequency is f, then the first condition is:

P = 0.5 (2n + 1) / f

where n is any integer.

The second condition is

P = n/f

For a two-flute drill, it’s twice the rotation period. Tool chatter grows in amplitude whenever the first condition is satisfied. How high it will get depends on what mechanisms there are to suck energy out of the vibration.

The chatter will die away whenever the second is satisfied. For any rotation speeds in between, there will be some chatter at reduced amplitude.

Since the rotation period is usually much, much larger than the vibration period, the integer is very high. The resonances appear so close together that it takes only a small change in rotation speed to move from resonance to anti-resonance and back again.

Posted by on July 9, 2007 | Comments (0)