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Vibration Isolation and the Yerzley Oscillograph

Impact energy absorption and hysteresis are important parameters that predict vibration isolation characteristics of rubber compounds. The rubber used in vibration isolators should have an optimum amount of fillers (carbon black) to maximize energy absorption. The work by Dr. Sujit K. Datta of IRM Corp. of India shows that there is an optimum level of carbon black filler beyond which energy absorption characteristics are degraded. As illustrated below, at 75 Parts per Hundred parts of Rubber (PHR) energy absorption is maximized; whereas, the hysteresis plot flattens out after 75 PHR.

These results were obtained by using an Advanced Yerzley Oscillograph.

hysteresis impactimpact energy image

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Using Yerzley Oscillograph in Vibration Isolation

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.

Typical AYO-IV Analysis Results
Figure 1: Typical AYO-IV Analysis Results

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:

vibration_equation

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.

Dyn_Parameters_Compression_Test_Results
Figure 2: Dynamic Parameters Compression Test Results
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Testing Rubber Sheet Material

SheetRubberWe can’t always press a proper test specimen. In order to test rubber sheet material with AYO-IV, you can use a layered approach. Get a 3/4″ hole punch. As seen in the image, punch out enough round plugs so the total thickness is close to 1/2 inch. The idea is to put enough round plugs on top of each other to reach a height of approximately 1/2 inch. During AYO-IV setup, enter the actual height. In this case, the area is the same as a standard specimen: 3/4 inch. Thus, the area is the same as the standard specimen. Please note that this approach is not approved by ASTM D945; however, it is useful for comparing different sheet materials.
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Advanced Yerzley Oscillograph – System Calibration Procedure

System Calibration Procedure

Yerzley Oscillograph is an efficient means of obtaining the mechanical properties of rubber and similar materials. The calculations for dynamic properties rely on the “moment of inertia – I” of “the beam”. The component of the oscillograph, called “the beam” does not have a simple geometry; so it is not easy to determine it’s “I” value purely from geometry. Furthermore, there are many components attached to this beam that affect the actual moment of inertia. The ASTM Standard D945-06 on page 9, in paragraph 13.10 mentions that 0.100 slug-ft.sq is an approximate value that has historical acceptance.

It is possible to determine the moment of inertia of the beam together with all it’s attached components experimentally. The method is based on the paper by Dr. F.L.Yerzley, published in the proceedings of the ASTM in volume 39, 1939.