Viscous damping has been widely used as the energy dissipation mechanism of choice in abating resonant vibration in structures. Such damping is commonly provided either by the flow of high viscosity fluid thru large openings (gaps) in ‘laminar flow viscous damping units’ (dashpots) or the flow of low-viscosity fluid thru small openings (orifices) in ‘turbulent flow viscous dampers’. The latter type is commonly used in the making of shock absorbers in automobile suspensions. ‘Turbulent flow viscous dampers’ are uni-directional with a rather complex mechanical design and require periodic maintenance, but ‘laminar flow viscous damping units’ are multi-directional with a simple mechanical design and are maintenance free. Alternatively, viscous damping can be provided by the motion of conductive solid material through a magnetic field in ‘magnetic dampers’ also known as ‘eddy current dampers’. The kinetic energy of a mechanical system being dampened by a magnetic damper is transferred to the conductor and dissipated as heat.
Laminar Flow Viscous Dampers (Dashpots)
‘Laminar flow viscous dampers’ (dashpots) are multi-directional damping units made up of a plunger (piston) and a container (cylinder) partially filled with a highly viscous liquid. The vibratory motion of the plunger thru the viscous liquid shears the fluid, dissipating the vibration energy into heat. There is ample clearance between the plunger and the container and no seals are used in their making; as such, they have no metal to metal and/or metal to rubber (seal) contact resulting in no stiction (static friction) or other undesirable nonlinearities associated with solid to solid contacts.
DEICON uses computational fluid dynamics (CFD) tools to design viscous dampers. The cut-out image shown in Figure 1 (a) depicts the velocity field distribution predicted by the CFD analysis of a ‘laminar flow viscous damper’. Figure 1(b) shows a snapshot of the same information at the cross-section encircled in Figure 1 (a). Clear from Figure 1, the large velocity gradient induced by the motion of the plunger in conjunction with the high viscosity of fluid create the desired damping force.
The CFD software tool allows the designer to select the proper geometry for the plunger and housing as well as the right fluid so the desired damping coefficient is realized.
DEICON custom designs and fabricates ‘laminar flow viscous dampers’, dashpots, for a variety of structural damping applications.
Following the design of viscous dampers, they are prototyped and their damping effectiveness verified, experimentally. This is done by subjecting the dampers to harmonic motion and measuring their force and displacement. The area enclosed by harmonic loading and unloading paths of a dashpot, called the hysteresis loop, is a measure of the damping effect, and corresponds to the dissipated energy per cycle. The two traces in Figure 2 depict the measured (blue trace) and the identified (red trace) force vs. displacement of the viscous damper. The area of the hysteresis loop is used to determine the equivalent viscous damping coefficient of a dashpot. The tilt of the hysteresis loop is used to evaluate the stiffness coefficient (the elastic attribute of the dashpot).
Modeling
Viscoelastic attributes of a realistic damper can be described by a combination of springs and ideal viscous dampers. Kelvin-Voight model (A spring and a viscous damper in parallel) is commonly used to characterize dashpots at a single frequency. The damping coefficient and stiffness used in the Kelvin-Voight model are identified, experimentally, at various frequencies. The viscoelastic dashpot model is extended to all frequencies by fitting a generalized three-parameter (also known as generalized Maxwell) viscoelastic model to the experimentally evaluated damping coefficient and stiffness at various frequencies. Figure 3 shows the experimentally evaluated damping and stiffness coefficients of a dashpot at various frequencies (the blue marks) as well as a five-term generalized three-parameter viscoelastic model fitted to that (the experimentally evaluated) data.
The Impact of Temperature Variation
Viscosity-Temperature Coefficient (VTC) is used to characterize the variation of viscosity of a fluid with temperature. VTC is a measure of the change of fluid viscosity over the temperature range 38ºC to 99ºC; VTC = 1 – (viscosity @ 99ºC / viscosity @ 38ºC). Thus, the lower the VTC, the less the viscosity variation over the temperature range.
With the low VTC of around 0.6 the viscosity of silicone-based damping fluid used in DEICON’s dashpots is by far less temperature dependent than that of mineral, synthetic, and petroleum-based oil. Nevertheless, there is some temperature dependency on the rheological properties of silicone fluid. Figure 4 shows the dependency of silicone fluid viscosity on temperature over the temperature range of 0-50 deg C. Although not excessive, but the fluid experiences about +/- 50% variation in viscosity around its nominal value.
Magnetic Dampers (Eddy Current Dampers)
Magnetic damping (also known as eddy current damping) is generated when there is a relative movement between magnets and conducting material. When either magnets move relative to a conductor or a conductor passes thru a magnetic field, the electromotive force (emf) will be generated inside the conductive material.
The eddy currents running through the internal resistance of the conductor will be dissipated into heat. The dissipation of eddy currents results in removal of energy from the system, resulting in damping.
The emf in turn induces eddy current in the conductor. As the result, a second magnetic field will be generated inside the conductive material by the eddy current. This magnetic field produces a magnetic force that opposes the force that is generated by the original magnetic field (created by the magnets). The opposing force which is proportional to the relative velocity of the conductor and the magnets, acts as a viscous damping force; this qualifies magnetic dampers (eddy current dampers) as viscous dampers. Demonstration of magnetic damping is commonly conducted by dropping a magnet down a copper tube. In addition to structural vibration abatement, magnetic dampers are used in braking applications (e.g., in roller coasters, elevators, race cars) as well as automobile suspension. The advantages of magnetic dampers include, but not limited to, being liquid-free, temperature independent, non-contact and thus nearly maintenance-free.
Applications
Viscous dampers may be used as a stand-alone damping unit to dampen a single or multiple resonances of underdamped structures such as piping systems, buildings (to reduce interstory drift), and floor systems or in conjunction with spring elements in vibration isolation applications and realization of tuned mass dampers. Figure 5 shows a stand-alone viscous damper built into a structure and a viscous dampers as an element of a tuned mass damper.
The blue traces in Figure 6 depict the magnitude and phase of the frequency response function of an underdamped structure. They clearly show two resonant modes at 6 and 12 Hz. The red traces on the same figure present the same frequency response function after two dashpots were installed to the structure. Comparison of the blue and red traces in Figure 6 shows the effectiveness of the viscous dampers in dampening both resonant modes.
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