Isolator Selection Guide – dB Engineering

Isolator Selection Guide – dB Engineering

Mechanical vibration and shock are present in varying degrees in virtually all locations where equipment and people function. The adverse effect of these disturbances can range from negligible to catastrophic depending on the severity of the disturbance and the sensitivity of the equipment.

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Introduction

In one extreme, the vibration environment may consist of low-level seismic disturbances present everywhere on earth, which present operating problems to highly sensitive items such as delicate optical equipment. When other disturbances are superimposed on the seismic disturbances, a wide range of precision equipment is adversely affected.

These other disturbances are caused by things like vehicular and foot traffic, passing trains, air conditioning systems, and nearby rotating and reciprocating machinery. They cause resolution problems in electron microscopes, disturb other optical systems, cause surface finish problems on precision grinders and jig borers, and hamper delicate work on microcircuitry.

Another concept is the detrimental effect of vibrating internal components of certain equipment such as motors, blowers, and fans in computers or similar systems. These components transmit noise and vibration to the surrounding structure resulting in fatigue, reduced reliability, and a "noisy" product.

When compared to stationary applications, vehicular installations subject equipment to much more severe shock and vibration. Vibration from a propulsion engine is present in air, sea, and road vehicles, as well as shock and vibration effects from the media in which they travel.

Common phenomena like air turbulence and rough roads impart severe dynamic transients to the vehicles traveling on them. In addition to rough seas, military ships are also subjected to very severe mechanical shock when they encounter near-miss air and underwater explosions in combat.

Vibration-control techniques in the form of shock and vibration isolators have been devised to provide dynamic protection to all types of equipment.

When discussing vibration protection, it is useful to identify the three basic elements of dynamic systems:

1. The equipment (component, machine motor, instrument, part, etc.);
2. The support structure (floor, baseplate, concrete foundation, etc.); and
3. The resilient member referred to as an isolator or mount (rubber pad, air column, spring, etc.) which is interposed between the equipment and the support structure.

If the equipment is the source of the vibration and/or shock, the purpose of the isolator is to reduce the force transmitted from the equipment to the support structure. The direction of force transmission is from the equipment to the support structure. This is illustrated in Figure 1, where M represents the mass of a motor which is the vibrating source, and K, which is located between the motor and the support structure, represents the isolator.

If the support structure is the source of the vibration and/or shock, the purpose of the isolator is to reduce the dynamic disturbance transmitted from the support structure to the equipment. The direction of motion transmission is from the support structure to the equipment. This occurs, for instance, in protecting delicate measuring instruments from vibrating floors. This condition is illustrated in Figure 2, where M represents the mass of a delicate measuring instrument which is protected from a vibrating floor by an isolator signified as K.

In either case, the principle of isolation is the same. The isolator, being a resilient element, stores the incoming energy at a time interval which affords a reduction of the disturbance to the equipment or support structure. The purpose of this Design Guide is to help the design engineer select the proper isolator to reduce the amount of vibration and/or shock that is transmitted to or from equipment.

Definitions

Although a vibration isolator will provide some degree of shock isolation, and vice versa, the principles of isolation are different, and shock and vibration requirements should be analyzed separately. The most potentially troublesome environment, whether it be vibration or shock, generally dictates the design of the isolator. In other applications, where both are potentially troublesome, a compromise solution is possible.

Before a selection of a vibration and/or shock isolator can be made, the engineer should have a basic understanding of the following definitions, symbols, and terms:

Vibration: A magnitude (force, displacement, or acceleration) which oscillates about some specified reference where the magnitude of the force, displacement, or acceleration is alternately smaller and greater than the reference. Vibration is commonly expressed in terms of frequency (cycles per second or Hz) and amplitude, which is the magnitude of the force, displacement, or acceleration.

Frequency: Frequency may be defined as the number of complete cycles of oscillations which occur per unit of time.

Period: The time required to complete one cycle of vibration.

Forcing Frequency: Defined as the number of oscillations per unit time of an external force or displacement applied to a system.

Natural Frequency: Natural frequency may be defined as the number of oscillations that a system will carry out in unit time if displaced from its equilibrium position and allowed to vibrate freely.

Amplitude: The zero to peak value corresponding to the maximum magnitude of a harmonic vibration time-history.

Displacement: A vector quantity that specifies the change of the position of a body or particle and is usually measured from the mean position or equilibrium position.

Velocity: A vector that specifies the time rate of change of displacement with respect to a frame of reference.

Acceleration: A vector that specifies the time rate of change of velocity with respect to a frame of reference. The acceleration produced by the force of gravity is given by g = 980.665 centimeters per second² = 386.093 in/sec² = 32.1739 ft/sec², which is chosen as a standard acceleration due to gravity.

Deflection: The distance a body or spring will move when subjected to a static or dynamic force, F.

Spring Stiffness: Described as a constant which is the ratio of a force increment to a corresponding deflection increment of the spring.

Elastic Center: The single point at which the stiffness of an isolator or system of isolators can be represented by a single stiffness value.

Damping: The phenomenon by which energy is dissipated in a vibratory system. Three types of damping generally encountered are: coulomb, hysteresis, and viscous.

Coulomb Damping: If the damping force in a vibratory system is constant and independent of the position or velocity of the system, the system is said to have coulomb or dry friction damping.

Hysteresis (Inherent) Damping: Damping which results from the molecular structure of a material when that material is subjected to motion is referred to as hysteresis damping. Elastomers are good examples of materials which possess this type of damping.

Viscous Damping: If any particle in a vibrating body encounters a force which has a magnitude proportional to the magnitude of the velocity of the particle in a direction opposite to the direction of the velocity of the particle, the particle is said to be viscously damped. This is the easiest type of damping to model mathematically. Most of the equations in this text are based on the use of a viscous damping coefficient.

Damping Coefficient: Damping for a material is expressed by its damping coefficient.

Critical Damping: A system is said to be critically damped when it is displaced from its static position and returns to this initial static position without any over-oscillation. The damping coefficient required for critical damping can be calculated using:

Damping Factor: The non-dimensionless ratio which defines the amount of damping in a system.

Resonance: When the forcing frequency coincides with the natural frequency of a suspension system, this condition is known as resonance.

Transmissibility: Defined as the ratio of the dynamic output to the dynamic input.

Shock: Defined as a motion in which there is a sharp, nearly sudden change in velocity. Examples include a hammer blow on an anvil or a package falling to the ground. Shock may be expressed mathematically as a motion in which the velocity changes very suddenly.

Shock Pulse: A primary disturbance characterized by a rise and decay of acceleration from a constant value in a very short period. Shock pulses are normally displayed graphically as acceleration vs. time curves.

Shock Transmission: Shock transmitted to the object subjected to the shock. This can be calculated with the following equation:

The associated dynamic linear deflection of an isolator under shock can be determined by the use of the following equation:

Design Considerations

Vertical Vibration: In the general introduction of this Guide, it was pointed out that vibration and shock can have gross detrimental effects on the performance and reliability of a particular product. The vibration which a unit transmits to a supporting structure or the vibration which a unit feels when it is being excited by a vibrating structure can be reduced or attenuated by an isolator if properly selected. The design example section of this Guide contains problem solutions which use the equations and graphs presented in this section.

The function of an isolator may be best understood by first reducing it to its simplest form, as illustrated in Figure 4. The system of Figure 4 includes a rigid mass M supported by a spring K and constrained by guides to move only in vertical translation without rotation about a vertical axis. A damper C is arranged in parallel with the spring between the support and the mass. The mounted equipment is simulated by the mass while the spring and damper taken together simulate the elasticity and damping of the conventional isolator. The system shown in Figure 4 is said to be a single-degree-of-freedom system because its configuration at any time may be specified by a single coordinate; e.g., by the height of the mass M with respect to the fixed support.

Isolation is attained primarily by maintaining the proper relationship between the disturbing frequency and the system’s natural frequency. The characteristics of the isolator include its natural frequency, or more properly, the natural frequency of the system consisting of isolator and mounted equipment. In general, a system has a natural frequency for each degree of freedom; the single-degree-of-freedom system illustrated in Figure 4 thus has one natural frequency.

A critical damped system returns without oscillation to equilibrium if displaced; it has no natural frequency of oscillation.

In most circumstances, the value of the damping coefficient is relatively small. The influence of damping on the natural frequency may then be neglected. Setting the damping coefficient C equal to zero, the system becomes an undamped single-degree-of-freedom system.

This expression is sufficiently accurate for calculating the actual natural frequency in most instances.

The concept of static deflection often is used to define the characteristics of an isolator. Static deflection is the deflection of the isolator under the static or deadweight load of the mounted equipment.

Metallic springs generally meet this requirement, but many organic materials used in isolators do not. The dynamic modulus of elasticity of these materials is higher than the static modulus; the natural frequency of the isolator is thus somewhat greater than that calculated on the basis of static deflection alone.

Dynamic stiffness may be obtained indirectly by determining the natural frequency when the isolator is vibrated with a known load and calculating the dynamic stiffness from the natural frequency.

Effectiveness of isolators in reducing vibration is indicated by the transmissibility of the system. When the system is excited at its natural frequency, the system will be in resonance and the disturbance forces will be amplified rather than reduced. Therefore, it is very desirable to select the proper isolator so that its natural frequency will not coincide with any critical frequencies of the equipment.

Referring to Figure 6, it can be seen that when the ratio of the disturbing frequency fd over the natural frequency fn is less than or 1.4, the transmissibility is greater than 1, or the equipment experiences amplification of the input. Simply expressed, when the input excitation frequency is below 1.4 times the natural frequency of the mount, transmissibility will be greater than 1, resulting in amplification of the input.

Isolation begins when the input excitation frequency is 1.4 times the natural frequency of the mount. When the input excitation frequency is higher than 1.4 times the natural frequency of the mount, the output Xo is less than the input Xi, and the mounted unit is said to be isolated.

Damping: The majority of isolators possess damping in varying degrees. Here are damping factor C/Cc values for various materials. Damping is advantageous when the mounted system is operating at or near its natural frequency because it helps to reduce transmissibility. For example, consider an internal combustion engine mounted on steel springs which possess very little damping. Upon start-up of the engine and as the engine RPM increases, the disturbing frequency of the engine will at some point correspond with the natural frequency of the spring-mass system. With light damping, the buildup of forces from the engine to the support will be very large; that is, transmissibility will be very high. If the idle RPM of the engine falls in the range of the natural frequency of the spring-mass system, serious damage may result to the engine or support chassis. If, on the other hand, the designer selects an elastomeric isolator which possesses a higher degree of damping, amplification at resonance would be much less.

The relationship between a highly damped and a lightly damped system is illustrated in Figure 8. This figure shows that as damping is increased, isolation efficiency is somewhat reduced in the isolation region. High values of damping cause significant reduction of transmissibility at resonance, while in the isolation region this effect is only a small increase in transmissibility.

A family of curves which relate fn, fd, transmissibility, and damping are shown in Figure 8.

Horizontal Vibration: When an isolation system is excited horizontally, two natural frequencies result if the center of gravity of the unit is not in line with the elastic center of the isolators. A typical transmissibility curve illustrating this horizontal vibration output is shown in Figure 9. Two natural frequencies involved include a lower mode wherein the equipment rocks about a point well below the elastic center of the isolators and a higher mode where the equipment oscillates about a point near the center of gravity.

Figure 10 can be used to determine the approximate frequencies of these modes as a function of spring stiffness and equipment dimensions. These curves assume that the equipment is solid, of uniform mass, and that the isolators are attached at the extreme corners. Under horizontal excitation, the equipment may be made to translate only by lining up the center of gravity of the equipment with the elastic center of the isolators instead of installing the isolators at the bottom corners of the equipment. In this case, Figure 10 may be applied by letting H/W = 0, resulting in only one mode of vibration, that of translation. A second mode can only be excited by torsional excitation.

Structure-Borne Noise: The demand on equipment today is to maximize its output which generally requires faster operation and more complex mechanical motions. As a result, noise is sometimes generated. High-frequency disturbances are excited because the moving components within the equipment impose vibratory inputs to the internal structures. These vibrations are amplified and structure-borne noise is encountered. Complete pieces of equipment bolted to their support foundations also cause similar noisy conditions.

An effective and low-cost means of alleviating structure-borne noise problems is to physically separate the solid structures and interpose a resilient material between them. In this manner, a mechanical attachment is provided, but the resilient media prevents vibration forces from being transmitted and structure-borne noise is substantially reduced.

Elastomeric materials are generally best suited for structure-borne noise reduction. They exhibit desirable characteristics like shape flexibility and inherent damping to avoid spring-like response which might produce violent resonances at critical frequencies. They afford high-frequency isolation. Many isolators suitable for the attenuation of structure-borne noise problems are available from dB Engineering.

Shock: Shock is normally classified as a transient phenomenon, while a typical vibration input is classified as a steady-state phenomenon. A shock input pulse is normally described by its peak amplitude A expressed in g’s, its duration t normally expressed in milliseconds, and its overall shape, such as half-sine, triangular, (initial peak sawtooth, symmetrical and terminal peak sawtooth), versed sine, rectangular, and the form most likely to occur in nature, a more or less random-shaped complex waveform force, and acceleration impulse. Since there are many types of shock pulses encountered in nature, there are many types of shock tests specified for testing a piece of equipment. The different shock tests are normally associated with the environment that the equipment will encounter during its lifetime.

Equipment installed in aircraft is normally tested on a free-fall shock machine, which will generate either a half-sine or terminal peak sawtooth form. A typical test is an 11-millisecond half-sine waveform with a peak acceleration of 15 g’s. For components in some areas of missiles where large shock pulses will be felt due to the explosive separation of stages, a 6-millisecond sawtooth at 100 g’s may be specified. If a piece of equipment is going on board a Navy vessel, the normal test will be the hammer blow specified in MIL-S-901, which exhibits a velocity shock of approximately 120 in./sec. Shipping containers are normally tested by dropping the container on a concrete floor or by suspending it by some suitable support mechanism and letting it swing against a concrete abutment. Other tests pertaining to shipment are edge and corner drops from various drop heights. All of these tests attempt to simulate the shock pulse which will be encountered in the normal environment of the equipment.

The isolation of shock inputs is considerably different from that of a vibration input. The shock isolator is characterized as a storage device wherein the input energy, usually with a very steep wave front, is instantaneously absorbed by the isolator. This energy is stored in the isolator and released at the natural frequency of the spring-mass system.

The most common procedure for predicting shock isolation is a mathematical approach utilizing equations for determining the velocity and calculating transmitted accelerations.

Another means is through the use