VISCOUS DAMPERS

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 forcing a low-viscosity fluid thru small openings (orifices) in ‘turbulent flow viscous dampers’ or shearing a high viscosity fluid between moving surfaces in ‘laminar flow viscous damping units’ (dashpots). The former type is commonly used in the making of shock absorbers in automobile suspensions. ‘Turbulent flow viscous dampers’ (shock absorber type dampers) are uni-directional with a rather elaborate mechanical design but ‘laminar flow viscous damping units’ (dashpots) are multi-directional with a simple mechanical design and are maintenance free.

In addition, viscous damping can be implemented by a) shearing special polymers in viscoelastic dampers or b) moving a conductive material through a magnetic field in devices known as magnetic or eddy current dampers.

Fluid Viscous Dampers

Fluid viscous damping is an energy dissipation mechanism in which the damping force is a function of velocity of an object moving through a viscous fluid. Equation (1) presents the relationship between the damping force and velocity of the damper

f=c*v^a (1)

where c represents the damping coefficient, primarily determined by the damper’s design, while $v$ denotes the velocity of the damper. The exponent a can vary from 0.15 to 1.85 depending on the geometry of the piston head and the orifices. For seismic mitigation applications, the exponent is set closer to the lower end of this range. For a linear viscous damper in which damping force is proportional to velocity, the exponent a=1.

Turbulent Flow (Shock Absorber Type) Viscous Damping Devices

Turbulent flow viscous dampers are similar in make-up to shock absorbers in an automobile suspension system, albeit they could be larger in size and stroke, operate with much higher forces, and be made with higher precision. Low viscosity silicone is commonly used as the fluid in these viscous damping devices. This fluid is inert, non-flammable, non-toxic, and stable.

Schematic of a shock absorber type viscous damper

The damping action is achieved by the reciprocating motion of the piston forcing the damping fluid thru: a) the annular clearance between the piston and the cylinder wall, b) small orifices built internally within the piston, c) an external by-pass channel, or a combination of these paths— each creating significant pressure drops that results in energy dissipation.

Shock absorber type viscous dampers are one-dimensional energy dissipating devices and can only provide damping along their axis of motion (cylinder axis). These dampers require some maintenance, mainly in terms of their seals leaking after so many cycles of oscillation.

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.

Figure 1 The velocity field (a) and velocity distribution in a cross-section of a ‘laminar flow viscous damper’

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 these, 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).

Figure 2 The measured (blue trace) and identified (red trace) force vs. displacement of a dashpot

Modeling

Viscous dampers are not just viscous but viscoelastic devices modeled best by a series combination of pure viscous dampers and springs, known as Maxwell model.

The derivation of the mathematical model of linear fluid dampers, including its viscoelastic behavior, shows that the viscoelastic attributes of a such dampers can be described by a frequency-dependent parallel combination of springs and ideal viscous dampers known as Kelvin-Voight model, commonly used to characterize fluid dampers at various frequencies.

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.

Figure 3 Typical frequency-dependent stiffness and damping coefficients of a dashpot

The Impact of Temperature Variation

As temperature increases in liquids, molecules gain more kinetic energy, reducing the intermolecular forces that resist flow. This makes the liquid less viscous.

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.

Figure 4 The ratio of the viscosity of silicone fluid over its viscosity at 25 deg C

Magnetic Dampers (Eddy Current Dampers)

Magnet moving within a conductor

Magnetic damping (eddy current damping) is generated when there is a relative movement between magnets and a conducting material (normally Aluminum or Copper). When either a magnet move relative to a conductor or a conductor passes thru a magnetic field, the electromotive force (emf) will be generated inside the conductive material. This in turn induces a localized electric current (known as eddy current) within the conductor. This eddy current creates a second magnetic field that opposes the field of the original moving magnet, thus creating an opposing (damping) force proportional to the relative velocity of the magnet and conductor.

The opposing (damping) force, being proportional to the relative velocity between 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 can be employed in various configurations, including: (a) as standalone devices to mitigate one or more resonant modes in underdamped structures such as piping systems, buildings (to reduce inter-story drift), and bridges; (b) in combination with spring elements for shock isolation applications; and (c) as the dissipative components in the implementation of tuned mass dampers.

The images below show a stand-alone viscous damper built into a structure and two viscous dampers as the dissipative element of a tuned mass damper.

Stand alone viscous damper built into structure Viscous damper used as component inside of tuned mass damper

The frequency responses of Figure 5 and transient time responses of Figure 6 illustrate the dynamic behavior of a highly underdamped structure, both before and after viscous damping is added.

Figure 5 Frequency response functions of a structure without (blue traces) and with (red traces) viscous damping

Figure 6 Transient responses of a structure without (blue trace) and with (red trace) viscous damping

Social

Contact