THE BASICS OF VIBRATION ISOLATION USING ELASTOMERIC MATERIALS
Isolation mounts reduce the transmission of energy from one body to another by providing a resilient connection between them. Selecting an improper mount for an application, however, can actually make the problem worse. The incorrect mount may reduce the high frequency vibration, but resonant conditions at lower frequencies can actually amplify the induced vibration. During an impact, the mount deflects and returns some of the energy by rebounding. Preventing this energy return can extend product life and prevent performance problems such as skipping in a CD drive and read/write errors on a hard disk drive. Adding damping to a resilient mount greatly improves its response. Damping reduces the amplitude of resonant vibration by converting a portion of the energy into low-grade heat. Damping also dissipates shock energy during an impact. This reduces the amount of deflection required to absorb the shock, providing protection in smaller spaces. This property is especially significant when designing shock protection for portable electronics, which become increasingly "miniaturized" with each new model. A highly damped material can provide the required impact protection in a smaller envelope than would be required for an undamped material. Natural Frequency
All mounting systems have a natural frequency (fn)—the frequency at which the system will oscillate if it is displaced from its static position and released. For example, consider a weight suspended from a rubber band, similar to the single degree of system model in Figure 1. If the mass is pulled down from its resting state, stretching the rubber band, and then released, the mass will move up and down at a certain frequency. This is the natural frequency. The natural frequency, fn, is dependent upon the stiffness of the spring, K, and the mass of the load that it is supporting (M), and can be determined by the following equations:
where K is the stiffness in newtons per meter (N/m) and M is the mass in kilograms (Kg), or
where K is the stiffness in pound per inch (lb/in) and W is the weight of the mass in pounds. The natural frequency may also be determined using the static deflection that the mass induces on the spring in the equation
where G is the acceleration due to gravity (9.8 m/s2 or 32.2 ft/s2) and d is the static displacement in meters or inches. DampingControlling the natural frequency provides one means to control vibration. Damping provides another. Damping is the dissipation of energy, usually by releasing it in the form of low-grade heat. For example, dry friction, the most common damping mechanism, is the reason an object sliding on a surface will slow down and stop. Some mechanical devices use viscous damping as a means of energy dissipation. In these systems, fluid losses caused by a liquid being forced through a small opening provide the necessary energy loss. The shock absorbers on an automobile are an example of viscous dampers. Mathematical models for viscous damping are well established and provide a means for analysis. Viscous damping capability is characterized by the damping ratio, C/Cc or z. Most elastomeric engineering materials for vibration isolation use a mechanism known as hysteretic damping to dissipate energy. When these materials are deformed, internal friction causes high energy losses to occur. The loss factor is used to quantify the level of hysteretic damping of a material. The loss factor (h ) is the ratio of energy dissipated from the system to the energy stored in the system for every oscillation. It is often useful to relate the loss factor to the damping ratio so viscous damping models can be used for analysis. At resonance, loss factor is
A loss factor of 0.1 is generally considered a minimum value for significant damping. Compared to this value, most commonly used materials, such as steel, aluminum and most rubbers, do not have a high level of damping. Other specialized materials can have very high damping. Here are some materials and their approximate loss factor.
The performance of an isolation system is determined by the transmissibility of the system—the ratio of the energy going into the system to the energy coming from the system. This can be expressed in terms of acceleration, force or vibration amplitude. Transmissibility (T) is equal to
Where: T = Transmissibility Aout = Energy out of system (transmitted force) Ain = Energy into system (Disturbing force) z = Damping ratio fd = Driving frequency fn = Natural frequency
Figure 2 shows two typical transmissibility curves, one for a highly damped material (z » 0.5), another for a material with much lower damping (z » 0.05). At very low frequencies (fd/fn << 1), the input vibration virtually equals output (the transmissibility is equal to 1), and input displacement essentially equals that of output. If the driving frequency equals the natural frequency (fd/fn = 1), the system operates at resonance. If damping is ignored in the equation for transmissibility that was given earlier, a system that is operating at resonance will have a transmissibility approaching infinity. As damping increases, the transmissibility at resonance decreases. Figure 3 shows the relationship between peak natural frequency at resonance and loss factor. Of course, all real world systems have some level of inherent damping, but this demonstrates the important role that damping can play in vibration isolation. When a vibration isolation mount with very little damping is used at or near resonance, the energy amplification can create many problems, ranging from a simple increase in noise levels to catastrophic damage to mechanical equipment.
Figure 3 shows the relationship between peak natural frequency at resonance and loss factor. Of course, all real world systems have some level of inherent damping, but this demonstrates the important role that damping can play in vibration isolation. When a vibration isolation mount with very little damping is used at or near resonance, the energy amplification can create many problems, ranging from a simple increase in noise levels to catastrophic damage to mechanical equipment. When the frequency ratio equals the square root of two (fd/fn = As frequency continues to increase above the crossover frequency, the level of isolation, or the isolation efficiency, increases. Figure 4 shows this relationship. Designers must know the isolation efficiency of the mounting system when transferred energy must be below a specified level, in devices such as CD-ROM or hard disk drives.
There are many material options for producing resilient elastomeric mounts. Thermoplastic materials (ones that can be melted and formed), such as many vinyl and rubber elastomers, can be injection-molded into cost efficient and detailed parts. Thermosets (materials that react in the mold and cannot be remelted) offer another option, and must be molded through other methods, commonly compression or transfer molding. Due to longer cycle times, thermoset piece prices often exceed that of thermoplastics, but the materials can also offer chemical and strength properties that can not be met by thermoplastics. Damping and stiffness can also vary greatly with different materials. The following section outlines several key points to be considered when designing isolation systems. Design GuideHere are guidelines that will assist in the design of axially loaded isolation mounts and pads from sheet materials.
Proper performance depends on proper loading. Referring to the natural frequency equation,  , if the mass of the load is very small for the stiffness of the selected mount, the natural frequency of the system will be high, reducing the isolation performance. An overloaded mount, can compress completely, or bottom out, increasing the effective stiffness of the
mount. This also increases the natural frequency. Overloading an elastomeric
mount can also cause internal stresses that can reduce the useful life of the
mount. Generally, a 5% static compression of the mount is appropriate for most
materials, although static compressions of up to 15% may provide adequate
isolation and part life. For homogeneous elastomers with a durometer
(hardness) of around 50-60 shore A, ideal loading is generally around 50
pounds per square inch (psi), although loading of anywhere from 10 - 100 psi
may still be effective. Softer elastomers should be loaded less than stiffer
elastomers.
Solid elastomers act as incompressible solids, and therefore must have room to bulge in order to deflect. Therefore, the shape factor, or bulge factor, should be optimized to achieve the expected stiffness. Shape factor (S) is defined as: 
Figure 6 shows some examples. Example A shows a block in series with a disk (they are stacked on top of each other). Example B shows two disks in series (they are next to each other). These two disks are also in series with the block. To determine to overall stiffness, use the equations below to combine the stiffnesses of the individual shapes. Shapes in series: Assume the blocks in Figure 6 have a stiffness of 20 lb/in and the disks have a stiffness of 10 lb/in. The total stiffness of Example A would be
The total stiffness of Example B would be Stiffness of disks in parallel, Stiffness of block and disks in series,
English units:  Metric units:  Remember, vibration isolation in the system will occur above E-A-R Specialty Composites offers a wide range of standard molded grommets, bushings and other isolators molded from ISODAMP C-1000 Series vinyl thermoplastic, ISOLOSS® HD urethane, and VersaDamp® TPE. These have been designed with the appropriate geometry and load specifications in mind, and have been used in many kinds of products. Please consult E-A-R's "Designing with Isolators" booklet for more information, including a worksheet to determine the natural frequency when using the molded parts. E-A-R also manufactures several other propriety materials that can be used to solve various vibration and shock isolation problems. These include ISOLOSS VL Low Modulus Urethane Elastomer ISOLOSS LS High Density Urethane Foams CONFOR® Ergonomic Urethane Foams AcknowledgementsGardner, Ross. "The Reduction of High Frequency Vibration and Noise by Using E-A-R ISODAMP Isolation Materials." Indianapolis: E-A-R Division, Cabot Corporation, 1976. Inmann Daniel. Engineering Vibration. Englewood Cliffs, N.J.: Prentice-Hall, Inc., 1994. Lord, Harold, William Gatley and Harold Evensen. Noise Control for Engineers. New York: |
), transmissibility will once again drop to 1. This is known as the crossover frequency, and the area below this frequency is known as the amplification region. Above this frequency lies the isolation region, where transmissibility is less than 1. As a goal, the isolator designer tries to design a mounting system that puts the primary operating frequencies of the system in the isolation region. Many systems must operate at a number of primary frequencies or must frequently go through a startup or slowdown as part of the operation cycle. For these systems, damping in the mount becomes increasingly important when it must function at or near resonance.
Shapes in parallel:
