# Vibration Damping

### What is damping? Damping is the energy dissipation properties of a material or system under cyclic stress. Active damping and passive damping:

Active damping:
Active damping refers to energy dissipation from the system by external means, such as controlled actuator, etc.
Passive damping:
Passive damping refers to energy dissipation within the structure by add-on damping devices such as isolator, by structural joints and supports, or by structural member's internal damping.

Material damping and system damping:
Material damping:
Energy dissipation in a volume of macro-continuous media.
System damping:
Energy dissipation in the total structure. in addition to damping due to materials, it also includes energy dissipation effects of joints, fasteners, and interfaces.

Damping Measurement:

There are many methods for measuring the damping of a vibtation system. Logarithmic decrement method and bandwidth meathod are introduced here.

Logarithmic decrement method is used to measure damping in time domain. In this method, the free vibration displacement amplitude history of a system to an impulse is measured and recorded. A typical free decay curve is shown as below.Logarithmic decrement is the natural logarithmic value of the ratio of two adjacent peak values of displacement in free decay vibration.

To estimate damping ratio from frequency domain, we may use half-power bandwidth method. In this method, FRF amplitude of the system is obtained first.Corresponding to each natural frequency, there is a peak in FRF amplitude. 3 dB down from the peak there are two point corresponding to half power point, as shown in the figure below. The more the damping, the more the frequency range between this two point. Half-power bandwidth BD is defined as the ratio of the frequency range between the two half power points to the natural frequency at this mode.

Damping in Machine Tools:

Damping in machine tools basically is derived from two sources--material damping and interfacial slip damping. Material damping is the damping inherent in the materials of which the machine is constructed. The magnitude of material damping is small comparing to the total damping in machine tools. A typical damping ratio value for material damping in machine tools is 0.003. It accounts for approximately 10% of the total damping.

The interfacial damping results from the contacting surfaces at bolted joints and sliding joints. This type of damping accounts for approximately 90% of the total damping. Among the two types of joints, sliding joints contribute most of the damping. Welded joints usually provide very small damping which may be negleted when considering damping in joints.