Most machine tools are lightly damped [Tobias 1965]. Typically, the damping ratio is approximately 0.05 to 0.15. Damping in a machine tool derives mainly from sliding joints and bearings. Significant damping also arises from screwed and bolted joints. The reason that damping arises from joints is because dissipation of vibration energy requires irreversible strains to take place on a continual basis. Irreversible strains or friction, as it is more commonly known, occurs through plastic and viscous shear mechanisms and not through elastic deflections from which the vibration energy is recovered. Frictional dissipation occurs mainly in joints and only in a minor way by deflections within the body of a casting. It is for this reason that the main structural elements provide only a minor contribution to the total damping of a machine. In order to introduce damping into a structure, it is necessary to engineer the distribution of mass, structural stiffness, friction, and movement within the design.
15.1.5 Large Mass Bases
One approach to design of a machine base is to make it truly massive. An example is the use of a solid granite base described later in this chapter. This makes the machine base very rigid and minimizes distortion of the base when subjected to a rocking motion. Most machines exhibit rocking behavior in the frequency range 20 to 35 Hz as described by Tobias [1965]. The rocking motion has to be minimized by careful attention to the foundation and mounting on the foundation. From a vibration viewpoint, a massive base reduces the rocking frequency to a low value. This has the advantage that it tends to isolate the rocking vibration from the higher frequency modes of the machine. A massive and rigid base, therefore, inhibits vibration of the whole machine assembly rather than contributing toward it.
15.1.6 Tuned Mass Dampers
A particular vibration can be substantially reduced by addition of a spring-mounted mass tuned to have the same resonant frequency as the unwanted vibration. The additional mass required can be less than one fifth the size of the mass requiring to be damped [Den Hartog 1956]. For example, if the rocking frequency of the base is of particular concern, a mass suspended on springs within the base and tuned to the appropriate frequency will greatly reduce the amplitude of vibration for a relatively low cost. This principle was employed in a 508-m-high tower in Taipei to eliminate sway of the building. A large steel ball weighing approximately 600 tonnes was suspended internally at the top of the tower. It has also been used very successfully for damping of long wheel spindles for grinding of landing gear, and for eliminating resonances when plunge roll dressing of wide vitrified cubic boron nitride (CBN) wheels.