Dynamic absorbers reduce vibration

Machine tool vibration often causes problems when machining, reducing part quality. Chatter, a self-excited vibration, can lead to poor surface finish and cutting tool chipping or breakage.

Vibration problems can sometimes be solved by selecting the spindle speed in a stable region using a stability lobe diagram. Users can also solve vibration problems by shortening or lengthening the cutting tool, changing the number of flutes or changing the orientation of the cut. A better solution would be to measure the tool’s frequency response function (FRF) and then choose stable conditions prior to NC programming. This works particularly well in shops where setup repeatability is very good. 

Figure 1. A frequency response function without a dynamic absorber.

When operating some machine tools, such as those in transfer lines where the machine performs the same task at the same speed for long periods of time, it may be more desirable to reduce problematic vibration by making a structural change to the machine to modify the FRF. This can be done with a dynamic absorber so the apparent stiffness at the tip of the cutting tool at the excitation frequency is very high.

A dynamic absorber is a mass, spring and damper assembly added to an existing structure. The motion of the added assembly produces a force that counteracts the excitation force. The dynamic absorber vibrates, but the motion of the base structure is greatly reduced. 

Figure 1 shows an FRF of a vibrating system. The vertical axis shows the amplitude of the vibration resulting from an externally applied force, such as a cutting force or an unbalanced tool. The horizontal axis shows the frequency of the exciting force. The FRF shows there is a particular frequency range of excitation where the amplitude of vibration is large—a resonance. If an FRF like this were measured at the tip of a cutting tool, and the rotation frequency was close to the resonance, the resulting vibration could be quite large.

Figure 2 (see below) shows the same vibrating system, but with a dynamic absorber added. At the frequency of the original resonance, the vibration amplitude has been reduced by a factor of more than 10. However, this reduction comes at a price, and that is the creation of two resonances: one above and one below the original resonance. As long as the operating speed stays in the low spot between the peaks, there’s less vibration. If the speed changes, it is possible to get into trouble with either of the two resonances.

We are left with the decision about spring and mass selection for the dynamic absorber and where to place them. Selecting the damping, however, is more difficult. Usually, the spring and damper come together, such as in a polymer pad. We choose the dimensions of the pad to get the desired stiffness and accept whatever damping it provides. In precision systems, it is possible to add damping using an actuated system, but this is generally not feasible for machine tools. For sizing the added spring and mass, there are three design rules:

1. The natural frequency of the added spring (kadd) and mass (madd), if taken separately, should match the frequency for the desired minimum (ωmin) on the FRF,

2. The dynamic absorber should be placed at a location where the problem mode is active. Each resonance in a machine tool is associated with a characteristic vibration pattern, or mode shape. The absorber must be attached at a location where the mode shape shows a large vibration. 

3. The added mass should be a substantial fraction of the apparent mass at the attachment point. In addition, it should be close to the mass obtained from an FRF measured at the attachment point.

Figure 2. An FRF with a dynamic absorber.

For a cutting tool, the ideal location for a dynamic absorber is near the tool tip, but that is rarely possible. However, it is often possible to find a location away from the cutting zone where the vibration frequency causing trouble at the tool tip is also causing motion, such as at the tail end of the spindle. It is a useful and nonintuitive fact that adding an absorber at another active spot also reduces vibration at the tool tip. By analogy, holding one leg of a vibrating tuning fork also stops the vibration of the other leg. 

The added mass can be a block of metal or a ring, for example, mounted on rubber pads or metal flexures, and glued, strapped or press fit onto the base structure. Dynamic absorbers are widely found in automobiles, airplanes and skyscrapers. They can also be used effectively in machine tools to solve vibration problems. CTE

About the Author: Dr. Scott Smith is a professor and chair of the Department of Mechanical Engineering at the William States Lee College of Engineering, University of North Carolina at Charlotte, specializing in machine tool structural dynamics. Contact him via e-mail at kssmith@uncc.edu.