09 Jun Utilizing Low Shape Factor Elastomers
Viscoelastic polymers or elastomers are widely used in vibration control applications due to their inherently high level of damping. Elastomers can also effectively isolate low frequency vibrations by being formed in certain shapes. Shape factor is the term of art used to quantify the isolation performance of a given elastomer shape. The implication is that the lower the shape factor, the lower the potential resonance frequency. A low resonance frequency typically results in a wide bandwidth of vibration isolation. This is due to the isolation of vibration frequencies above the resonance frequency.
For most common shapes, shape factor is generally defined as:
Shape factor =Bulging surface area
The average loaded surface area is the average of the upper and lower surface areas supporting the load. The bulging surface area is the surface area free to bulge perpendicularly to the load.
The stability of an elastomer can become compromised below a certain shape factor as the material becomes increasingly tall and narrow. Some elastomer manufacturers recommend staying above a shape factor of 0.3 in order to prevent buckling – an issue that can cause the supported equipment to topple over.
When designing the ViscoRing™ elastomer utilized in the Carbide Base footers, a shape factor of 0.17 was planned. This was chosen in order to push the resonance frequency low enough so that the lowest audible frequencies could be effectively isolated.
An experiment was conducted to test the ability of the ViscoRing™ to vertically support a load and avoid buckling. The experiment consisted of gradually applying mass and measuring the vertical deformation of the material. Weights were applied on top of the Medium ViscoRing™ in 1.13 kg (2.5 lbs) increments in a room temperature environment. The vertical deformation distance was plotted in the form of the stress-strain curve shown. The y-axis represents the stress or amount of mass applied, and the x-axis represents the strain or vertical deformation caused by the application of mass.
The red curve shows the ViscoRing™ alone without a housing. It can be seen that shortly after the initial application of mass, the material began to buckle and deform considerably under the load. The material did a poor job of supporting even a small mass which was to be expected given its extremely low shape factor.
To improve the stability of the ViscoRing™, a housing was designed for it within the upper portion of the Carbide Base footer as shown in the simplified graphic. Ridges were added at spaced intervals around the perimeter of the ViscoRing™ to brace it and prevent buckling. The ridges were spaced apart so that surface area was free to bulge between the them thus preserving the benefits of the low shape factor.
As the ViscoRing™ bulged outward, a progressively larger percentage of the bulging surface area came into contact with the sloped ridges. This increasing shape factor with an increase in mass gave a more consistent resonance frequency across a broader range of load masses. Isolation performance of the Carbide Base footer became more constant across varying supporting masses.
The blue curve shows the same ViscoRing™ placed in the housing of the upper portion of the Carbide Base footer. A relatively linear increase in strain or vertical deformation with an application of stress or mass was observed. The material was not buckling as intended.
Elastomers are unable to be compressed into a smaller volume. Therefore, elastomers must be allowed to bulge outward in order to deform under a load. The selectively braced ViscoRing™ did not show a sudden increase in slope or stiffness as would have occurred if the material was prevented from further bulging. This is important, because a low stiffness or spring rate is necessary to achieve a low resonance frequency.
Beyond about 11 kg (25lbs), the stiffness of the material gradually began to increase. This is indicated by a steeper slope, as more of the bulging surface area contacted the ridges. The increased stiffness continued up until a vertical deformation of 7.6mm (0.3 in). This was the maximum distance that the housing was designed to translate in order to protect the ViscoRing™ from over-compression.
Improving Horizontal Isolation
Once successful in utilizing a low shape factor elastomer for vertical isolation, similar benefits for horizontal isolation were desired. Horizontally oriented low shape factor elastomers along with ball bearings were incorporated to further improve horizontal isolation performance.
Utilizing ball bearings to provide horizontal isolation is a well known concept. Many designs interpose ball bearings between curved bearing races. The curved bearing surfaces of other designs keep the bearings centered. They also allow for the transmission path of the vibration to be diverted as the upper and lower races translate horizontally relative to each other. This transmission-path evasion provides horizontal isolation.
The design devised for the lower portion of Carbide Base footers was different, as the bearings rolled on flat rather than curved races. The horizontally oriented elastomers acted as highly damped springs keeping the device centered in response to vibrations. In order to minimize deformation and rolling resistance, zirconium was chosen for the bearings and polished hardened spring steel for the bearing races. Horizontal isolation was achieved with a higher level of damping than previous designs.
Measuring Horizontal Isolation
To asses the improvement in horizontal isolation another experiment was conducted. The goal of the experiment was to quantify the improvement the addition of the ball bearings and horizontally oriented elastomers provided for horizontal isolation.
An electromagnetic vibration table was used to generate vibrations for the experiment. This tool was customized to allow for the independent or simultaneous generation of vibrations in the X, Y, and Z axes of movement. The table was digitally controlled via a touch screen and dials wired to Variable Frequency Drives (VFDs). These were used to precisely modulate the vibration amplitude and frequency of the table surface.
Four Carbide Base footers with Medium ViscoRings™ installed were placed on top of the vibration table. A weighted aluminum plate with a total mass of approximately 45 kg (100 lbs) was then bolted on top of the footers. Two Measurement Specialties ACH-01 accelerometer sensors were used to measure vibrations. The first sensor was attached with double sided tape to the forward edge of the vibration table. The second sensor was similarly attached to the forward edge of the aluminum plate. Each sensor was hooked up to its own calibrated vibration sensor amplifier which in turn fed its own benchtop multimeter. The VRMS readings from each multimeter were used to separately determine the acceleration being experienced by the table and the aluminum plate with 1 mVRMS = 1 m/s2 acceleration.
Graphing Horizontal Isolation
The forward and back (Y axis) vibration frequency was set in 10 Hz increments from 10 Hz to 300 Hz. The VRMS values of both sensors were plotted at each interval. The amplitude of the table was adjusted to ensure that the table was oscillating sinusoidally with an acceleration of approximately 4 m/s2.
Subtracting the output of the plate sensor by the output of the table sensor yielded the transmission of vibrations through the Carbide Base footers. Positive values indicated an amplification of vibrations through the device. This was expected at vibration frequencies around the resonance frequency of the device. Negative values indicated a reduction in vibrations generated by the table. In other words, an isolation of vibrations which was desired. The more negative the value, the greater the isolation.
The red line shows measurements taken with the Carbide Base footers missing the ball bearings and horizontally oriented elastomers. Only the ViscoRing™ elastomer was being utilized for horizontal isolation. The blue line shows measurements taken with the bearings and horizontal elastomers in place. The incorporation of ball bearings and horizontal elastomers substantially improved the horizontal isolation performance. The reduction in vibration amplitude was particularly pronounced around the resonance frequency indicating a higher level of damping.
Several design features were incorporated into the Carbide Base footers to reliably utilize low shape factor elastomers for the purposes of low frequency vibration isolation. Elastomers formed in shape factors that were previously considered too unstable were made sufficiently stable with a properly designed housing. The additional combination of bearings and horizontally oriented elastomers further improved horizontal isolation. These novel features were later incorporated into a pending patent.