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Isolating Vibration Using Urethane

VIBRATION ISOLATION WITH URETHANE
The dynamic properties of urethane in combination with its high load bearing capacity make it an excellent choice for a number of vibration isolation applications. In order to get started let's go over some definitions.

Natural Frequency:
It is usually expressed in Hertz (Hz) or cycles per second:

While the above is the formula for undamped natural frequency, the damped natural frequency in applications does not differ much from the undamped natural frequency.

Frequency Ratio:
The Forcing Frequency, ff (sometimes called disturbing or driving frequency), divided by the Natural Frequency, fn, is the ratio that indicates the effectiveness of a vibration isolator. The Forcing Frequency units are Hertz or cycles per second.

Damping:
This is the hysteresis (viscous) component of a polyurethane isolator. It is this hysteresis characteristic that converts mechanical energy into heat which is then dissipated. In free vibration a fair percentage of the input energy is dissipated in the form of heat during each cycle causing the vibration to die out.

The Damping Ratio, C/Ccr is used to indicate the amount of damping in a system. C/Ccr is affected by temperature and preload. Typically for most urethanes it can be varied from a low of .05 for highly resilient compounds to .15 for the low resilience urethanes.

Using the above information and the Transmissibility Curve shown below we can design urethane isolators.

Example:
A rotary compressor weighing 5000 lbs. is to be supported on four sandwich type mounts (urethane pad bonded between metal plates). The motor operates at 1800 rpm. At least 75% of the disturbing vibratory forces must be isolated; that is, the transmissibility is to be less than 25%.

First, assume a Damping Ratio of .1, we need a starting point to get into the ballpark and we can always come back and change it. Next, by examination of the Transmissibility Curve we see that to be at 25% Transmissibility with a C/Ccr of .1 the Frequency Ratio (ff /fn) should be 2.5 or higher.

Therefore the system natural frequency must be 12 Hz (or lower).
Now we know that each mount must deflect .068 inches under the total 65,000 lbs. or 1,250 lbs. per mount in order to have a natural frequency of 12 Hz.

Next we need to design an element with .068" deflection at 1250 lbs. In consideration of the long term static load plus the possible heat generation due to hysteresis let's use a free height of .75 inches of urethane. That means that the .068" deflection is a 9% deflection. GC 1085 is a good material choice for this type application. By making a few trial and error calculations at different pad cross sections and using the Stress-Strain Curves we arrive at a 2" x 2" urethane pad, with a Shape Factor of .67, and a compressive stress of 313 psi produces a deflection of 10% of 0.75 inches. A test should be performed to verify the calculated results.

NEXT: Coefficient of Friction



Transmissibility curves applicable to all elastomers.