If you are working in vibration isolation with rubber pads and similar materials, you will find AYO-IV to be a versatile instrument. It allows you to estimate the natural frequency of your system as well as the static and dynamic spring constants and the amount of damping you can expect. By manipulating the location and number of weights, AYO-IV can be used to simulate the vibration isolation environment and determine the range of expected natural frequencies, spring constants, and damping. Figure 1 shows the results of a typical AYO-IV run.
Static spring constant (units lb./in) of a rubber pad can be defined as:
(Static Modulus) * Area / Height
Similarly, dynamic spring constant of a rubber pad is:
(Dynamic Modulus) * Area / Height
We use the parameters for “hard rubber B” as measured by AYO-IV and displayed in Figure 1. Let’s say we have a 6000 lb. machine to be isolated by three rubber pads. Let’s assume that we place these pads such that each pad carries roughly 1/3 of the weight; thus, each pad carries 2000 lbs. Let’s say we are going to use round pads that are 1 inch thick with a diameter of 4 inches. Area = 12.566 in2.
Static Spring Constant = 1387.6 lb./in2 * 12.566 in2 / 1 in. = 17,437 lb./in
Static Deflection = 2000 / 17437 = 0.115 in.
Interestingly, this is the same static deflection that was observed in the AYO-IV test shown in Figure 1.
The natural frequency of the spring-mass system is given by:
Where “fn” is cycles/sec. K is (lb/in), g is the acceleration of gravity 386in/sec. sq and W is the weight in lb.
In this case, we use the Dynamic Spring Constant Kd = 2665*12.566/1 => 33,488 lb/in.
The calculated natural frequency is: 12.795 cycles/sec. We can reduce the natural frequency by increasing the height and/or reducing the area of our pads.
Controlling the natural frequency is not the only means of vibration isolation; the other is damping. Damping is the dissipation of energy. In the case of elastomeric materials, energy is dissipated by internal friction by a mechanism known as “hysteretic damping”. Yerzley Hysteresis, among the results, is a measure of this property.