Engineering - Tech Notes

ENGINEERING

VMC Groups’ engineering staff works seamlessly with our Sales and Manufacturing Departments. This is one of the key organizational elements that allow VMC to provide a high level of technical support to every customer and every product. We operate along the lines of an Integrated Product Team (IPT) structure. VMC employs engineers who have industry-recognized credentials in disciplines such as structural analysis, elastomer development, machine design, and system dynamics, providing a total professional experience exceeding 230 years. We have licensed Professional Engineers on staff.

VMC Groups’ engineers have a number of specialized computer-based dynamic simulation programs available to solve customer application problems. Some of these programs have been specially created for or tailored to our use. We also utilize a number of finite-element and structural analysis programs. VMC Group’s history has provided us with a unique library of an isolator, equipment, and environmental characteristics.

VMC operates an on-site engineering lab that supports product development, application validation, and on-going manufacturing quality assurance. Combined with specialized outside labs, we can provide most any type of testing necessary, including system dynamic response, static properties, and standard ASTM component material tests.

SHOCK AND VIBRATION MANAGEMENT

Many experienced designers have come to believe that the science of mechanical shock and vibration is simply a technique for overcoming an annoying quirk of physics with a few drop-in catalog items. This misconception will more than likely result in a disappointing result. Rather than attempt to defeat a fundamental law of physics, VMC Group's approach is to manage it. Everyone has experienced the unwanted effects of mechanical, structure-borne shock, and vibration. The annoying buzz of a vehicle floorboard underfoot, rattling pipes in a building, or the damage sustained by something that has been dropped are familiar cases. There are also desirable shocks and vibrations designed into devices that must be kept under control. The perceivable problem associated with shock and vibration is a two-way street. The “machine” may disturb us in the “outside world” and equally the “outside world” may disturb the “machine”. The “machine” may be almost anything, a solid object, a building, even a person. “The outside world” can be anything, including another machine and the earth itself. In a general sense, we can say that we have two or more objects with a connection between them. To one or more of these objects, we apply a disturbance. This disturbance may be in the form of a force, velocity, acceleration, or displacement. 

SHOCK AND VIBRATION MANAGEMENT: THE CONCEPTS OF THE SIMPLE AND ROBUST SYSTEM

The equations that describe the full array of possible real-world motions are complicated and can be intimidating to solve. The real world is very complex. The applied science of shock and vibration management can be thought of as the simplification and control of a very small portion of the real world. From this desire for simplification, comes the concept of a “robust system”.

In the days before computers, engineers simplified calculations to make their tasks doable within the time allowed. The wholesale trimming of the mathematics is usually sufficient so long as the designer succeeds in keeping both the design and the world around it simple. By terming it as “simple”, it is not to say that the design is not sophisticated. In our general definition, we said that we have two or more objects. In the simple design, our goal is to keep the number of objects to a minimum, preferably only two. We want to keep them clearly defined with sharp boundaries. 

We say that these objects will have some manner of a physical connection. Like the objects themselves, we like to see the connections limited in number and with clearly defined characteristics and boundaries. The same can be said for the physical motion. We would like to work with motion in only one direction at a time. We want to work with a motion that can be described by a single, manageable equation. A good example of the simple system is a heavy block hanging from a strong beam by a soft coil spring. All of the system mass is placed in the “heavy” block. All of the system compliance is placed in the “soft” spring. By calling the beam “strong” we have taken away all of the attributes of motion, spring rate, and mass from it and left an immovable attachment point in space. We can pull straight down in one direction on the block and the system will respond along that same one direction according to a simple mathematical equation. That equation is a sinusoidal function.

The real world cannot always be made that simple. The spring may become so heavy that its mass can no longer be ignored. The block may be somewhat spongy and contain compliance of its own. The strong beam may not always be as strong as we would like. We can have more than one block and more than one spring. When we apply a disturbance it may be simultaneously in more than one direction. The system may respond in a direction different from that in which we applied the disturbance.

The simple system is a goal. The goal cannot be reached by merely assuming a complex system is simple and ignoring mass and compliance that are in inconvenient locations. This is where the concept of a robust system enters. The distinct separation of masses, springs, and supports must be designed in upfront, not analyzed in later. Moreover, this distinction between masses, springs, and supports must hold true time after time as manufacturing continues to build less than perfect copies of the original design. It must hold true as the product experiences the wear and tear of a life cycle of use and abuse. This is the concept of a robust design. Designs still must be functional, innovative, and cost-effective. The envelope of size, weight, and power will always be pushed. These will always challenge the notion of the robust system and invariably lead to compromises. The key element to remember is that considerations for shock and vibration management must be designed in as early as possible. There are no “magic pills” which absorb shock and block vibration that takes up zero space and is free of charge.

THE VARYING SHADES OF GRAY IN MOTION: STEADY, HARMONIC AND TRANSIENT

The term harmonic motion is used extensively when speaking of vibration. The word harmonic simply means that the motion is predictably repetitive. In simple harmonic motion, the repetitive motion follows a simple mathematical formula. This almost always is a sinusoid in the world of engineered machines. Consider a long straight road. There are two lanes going in opposite directions. Between them is a straight centerline and to the sides are the road’s shoulders. You are traveling in a lane at a constant speed. You have been doing so for quite some time and not much is changing. We call this condition a steady state. After a while, you begin to drift over into the opposite lane, and since the road is clear for as far as the eye can see, you stay there for a while. We can still say that you are at a steady-state, just in a different state.

Now if you begin to repeat this over and over we could say that you are no longer at steady state in either lane but rather repeatedly and regularly drifting from side to side. At what point you switched from steady-state to a repetitive (harmonic) position is subject to interpretation. 

The same matter of interpretation holds true for machine motion. Just as what passes for the steady-state and alternating state on a long empty road is different from what is tolerated on a busy city street, so is the determination between steady-state and harmonic motion in a machine.

Now that you are repetitively (harmonically) swerving from side to side of the road, we can calculate the frequency of that motion. Starting on the westbound side, you move to the east and then back to the west exactly where you started from. Reaching that point, you have completed one cycle. If it took 10 seconds to accomplish this, we could say that you are moving side to side at a frequency of 10 seconds per cycle, or in other words, 0.1 cycles per second (or CPS). Another name for this unit of measurement is hertz (Hz). If we put this in a circular sense, it could be expressed as revolutions per second and mean the same thing nonetheless. Revolutions per minute (RPM) differs only in that it is the number of cycles in a minute instead of in a second. There should be no problem in working with RPM so long as we remember to divide by 60. Radians per second is the language of physicists and we must divide it by 2π so that we can work in the engineering units of hertz.

Motion is described in terms of frequency and amplitude. In our example, moving from shoulder to shoulder on the road, your double amplitude is one road-width. We call this double amplitude (DA) because the motion is a mirror image around the centerline of the road and because we are measuring from extreme to extreme, or peak to peak (p-p), across that centerline. We could have just as easily said that the amplitude was plus or minus (±) half road width, single amplitude (SA), or zero to peak (0-p). Leaving out the plus or minus (±) would describe a motion which is not a sinusoidal mirror image about the centerline but rather a series bumps all on one side of the centerline. Many vibration measurement results have been reported incorrectly and off by a factor of two by failure to grasp and properly communicate these concepts. 

If we were to go aloft over the road and look down we would see the road and centerline extending out, and the car moving regularly side to side over the centerline. As we get higher, the car reduces to a dot, and its progression down the road at constant speed begins to resemble the progression of time. Returning to the road, on one of the excursions near the shoulder you hit the guardrail and bounce off. The car, now careening both forward and sideways, is forced near the opposite shoulder, you begin to recover control, try to maintain your lane but oversteer a little across the centerline. Finally, you recover full control of the vehicle and proceed onward. This is, as you hope, a one-time, single event that lasted only a short duration. In mathematical language, it is a transient occurrence. It was a single event followed by a recovery reaction. Besides being a shock to you, the driver, its single event nature, and transient duration make it a shock in the mechanical sense. 

Now perhaps this shock appeared violent down in the car, but moving back up in the air high above the road it may have been barely discernible from the driver’s repetitive weaving across the lanes. Perhaps, for reasons unknown, you repetitively slam the car from guardrail to guardrail. Again, high up in the air this may appear to be just another repetitive (harmonic) but not quite simple or regular motion. Just as the question of steady-state motion versus harmonic motion is a matter of interpretation, so is the question of harmonic versus transient motion. Those who fail to recognize the overlapping nature of harmonic (vibration) motion and transient (shock) motion may lose the overlapping benefits of vibration attenuation systems and shock attenuation systems. Many incorrectly believe that shock mounts and vibration mounts are two completely different technologies. This statement, if true, would present problems. Nothing in nature prevents shocks and vibration from occurring simultaneously.

We can hold onto the car on the road analogy a little longer to define three descriptive terms associated with transients (shocks). If the driver of the car that just bounced off the guardrail were a good race car driver, he would recover control almost immediately and return to his lane. Let's call this “overdamped”. The average driver may take a little longer to recover and perhaps swerve about 1 1/2 cycles, each smaller than the last, to get back into the lane. Let's call this “critically damped”. A poor driver may take a long time to recover, swerving back and forth, still with each cycle a little smaller than the last. Let's call this “underdamped”. In a structural sense, we can call the last condition “ringing” just as an underdamped bell rings for some time after being struck. In the bell’s case, it is what the designer intended. In most other system designs, it is not. The difference between underdamped, critically damped, and overdamped in the car analogy is a function of the spring in the driver’s hands, the mass of his car, and the damping control that his brain imparts on the controls. In the mechanical system, although more impersonal, it is mass, spring rate, and damping that determine this same response.

MASS AND SPRINGS: CONCEPTS OF SIMPLE, DEFINED PACKAGING

It is important for the designer to recognize that mass and weight are different terms with different units of measure. Mass is a fundamental building block in the universe. Weight is a term of convenience to satisfy human perception. Weight is what mass looks like to us only when exposed to the downward acceleration of Earth’s gravity. Weight rarely has use in engineering calculations. Weight has units of pounds (lbs), sometimes called pounds-force (lbf). When divided by gravity (g); 32.2 ft/sec2 or 386.4 in/sec2, we have the correct mass term in the English inch-pound-second system of measurement. Its units are lb-sec2/ft or lb/sec2/in. Some will call this pounds-mass (lbm), but using this term leaves the question of inches versus feet open. In the metric system, weight is a force and, strictly speaking, should be in terms of Newtons or dynes. Grams and kilograms are direct mass terms. Use of grams as a measure of weight is common but incorrect. Failure to grasp this concept may result in a mathematical error that is a function of g. Not all shock and vibration applications occur on the surface of the earth where weight and g are valid. An important consideration of mass in simple, robust dynamic systems is the recognition that in the real world it is spread throughout the system. It is in the spring element, in the foundation, even in the connection that applies the disturbance. In the simplified model, we try to push the mass into defined and convenient packages. 

We call a compliant element a spring. We can apply a unit of force. The spring will respond by deflecting away from that force by some measurable amount. Our spring rate or spring constant (K) is expressed as the applied force (pounds, dynes, or Newtons) per measured deflection. There are linear springs in which this number is reasonably the same regardless of what load is applied. On a plot of load versus deflection, the response curve is a straight line rising to the right. The spring rate, K, is the slope of this curve and it is constant (linear or first-order). The best example of a linear spring is a steel coil spring. 

Most things in nature are not linear. A block of rubber in compression will get “stiffer” as more force is applied. A plot of its load-deflection response will look like a line curving upward to the right. This response may be related to a squared or exponential mathematical function, or in other words, second order. If we were only interested in working in a very small portion along this curve, we could take a local slope (tangent) and use its value for our simplified spring rate (K). We have springs that are structural bending, buckling, and shear elements. These will take on a more complicated third-order response shape. To tailor a spring’s response over its usable range, designers build these first, second, and third-order responses into the element by intelligent manipulation of its shape. Like mass, we strive to push springs into defined packages in convenient locations.

NATURAL FREQUENCY AND TRANSMISSIBILITY: BASIC TOOLS FOR VIBRATION MANAGEMENT

In a simple system consisting of a mass supported by a spring, the natural frequency is the frequency at which the mass will respond when displaced and released. The term simple system tells us that the mass and spring are in defined, discrete packages. The excitation is a step input. In other words, it came, moved the mass, and then it was gone. The equation that describes the response of this simple system reduces to:

Where:

K is spring rate in terms of force/distance.

m is mass in terms of either force-time2/distance or metric grams.

?n is frequency in engineering terms of CPS or hertz (Hz).

This is a fixed characteristic of a particular dynamic system just as the tone of a tuning fork is always the same and a characteristic of that fork. 

When struck by a simple step input, the simple system responded with its unique natural frequency. Now let's grasp onto the system and instead of just striking it, we will push and pull on it in a regular (harmonic) fashion. Just as with the car and road analogy, our motion input will have frequency (?) and amplitude (A). We now have an input frequency (?i ), an input amplitude (Ai), and a natural frequency (?n) associated with our simple system. We can develop a ratio between the input amplitude and the response or output amplitude. When this ratio is developed as a function of the input frequency and the system’s unique natural frequency, the result is called the transmissibility of the system. The equation for transmissibility in its simplest form reduces to:

Transmissibility (T) is a unitless ratio that is always positive. Both frequencies are typically in hertz, but being a ratio it does not matter what units they are expressed in so long as they are both the same. To make this equation even simpler, most texts and catalogs reduce this to a graphic known as the classical single degree of freedom undamped transmissibility curve. 

It is easier to see from the graphic than the equation that for frequency inputs that are less than the natural frequency, the response (output) amplitude is about the same or slightly greater than the input amplitude (slight amplification). For frequency inputs greater than the natural frequency, the response (output) is less, and sometimes far less than the input (attenuation). For inputs at or near the natural frequency, there is a dramatic increase in the response amplitude over the input amplitude or amplification. It is easiest to see from the graphic that if we control the natural frequency and the input frequency we can make the system behave in some predetermined, intelligent manner. If we force the input frequency to be well below the system’s natural frequency we can be assured of a response that tracks the input. If we were designing a crank arm to drive a machine that may be our goal. If we force the input frequency to be near the natural frequency (also called resonant frequency) we can be assured of a large-amplitude response to a much smaller input. In machine design, this is usually considered a condition to be avoided unless the design was a musical instrument or loudspeaker. Since the goal for the products that VMC manufactures is shock and vibration attenuation, the portion of the curve well above the system’s natural frequency is where we look to operate. It is these two equations that form the basis for applied shock and vibration management.

THE CONCEPT OF THE ENERGY CONVERTER: REPLACING ABSORBERS, ISOLATORS AND DAMPERS

We often use the terms attenuator, isolator and shock absorber to describe the hardware associated with shock and vibration management. We filter, block, absorb, and isolate shock and vibration, but we never have to clean the filter or empty the absorber. These terms lead designers into a false sense of security, that a magic pill exists, that when placed under the equipment, destroys unwanted shocks and vibrations. Shock and vibration represent energy, and the laws of physics prevent energy’s destruction. We can, however, convert it into a form that we can tolerate. Energy of motion has two faces, kinetic and potential. Kinetic is dynamic, associated with the velocity of motion like a rock expelled from a slingshot. Potential is static, associated with a position like that same rock pulled back against the stretched elastic band of the sling slot just prior to release. The kinetic and potential energy of a system may trade-off between each other so long as their sum is conserved. Moving along the curve of the transmissibility graphic, we are trading off kinetic and potential energy but keeping their sum unchanged. What we have in commonly known shock absorbers and vibration isolators are energy converters.

At times, we say that we “filter” vibration. Electrical engineers employ filters. They are no more of a filter in the electrical sense than they are in the mechanical. They behave according to a mathematical function very similar to our mechanical transmissibility curve. In an electrical system, resistance and inductance are akin to our spring and mass. An electrical system has a natural frequency. It can be forced to move by a voltage or current input. An electrical engineer’s filter trades off the kinetic and potential electrical energy. Similarly, our single degree of freedom, first-order undamped transmissibility curve is the mechanical equivalent of an electrical low-pass filter. In this conceptual filter, frequencies that are low relative to the natural frequency seem to “pass” through. Frequencies that are high relative to the natural frequency seem not to “pass”. 

In the road analogy, we presented shock as nothing more than a subset of the same family that contained simple harmonic (vibration) motion. The development of the concept of an energy converter holds just as true for the shock subset as for vibration. We are taking a high amplitude high-frequency input, dominated by kinetic energy, and converting it to a low amplitude low-frequency output dominated by potential energy. The total energy must remain the same. A shock pulse is defined by its shape, height (amplitude), and width (time period). When inverted, time is frequency. As time goes by we are moving over distance. We can say that we are spreading the energy out over distance to get a lower amplitude. This brings us to a few simplified equations, derived from the same basic equations of motion that describe vibration. These can be used to relate input and output for transients (shocks).

All three expressions are the same equation expressed in different ways. For a given system having a natural frequency, ?n, we can apply an input in terms of a velocity step and obtain a response in terms of a peak acceleration amplitude and a displacement. There is the power behind the use of a single equivalent velocity step to represent a shock pulse input. It reduces the two-dimensional pulse that has features of acceleration amplitude, time duration, and shape into something related to its pure kinetic energy content. An equivalent velocity step can be approximated for various Common pulse shapes as follow:

It is important to recognize that in spreading out energy over time we are spreading it out over distance. On the output end, the isolated element is expected to move a greater distance than the input. This applies to both shock and vibration management. 

DEVELOPING THE ISOLATED SUSPENSION: ESTABLISHING LIMITS BASED ON FUNCTION

Let us take an example of a simple machine sitting on a bed of steel coil springs. The machine has a rotating shaft and may not be perfectly balanced. Its shaft speed is 1800 RPM. That translates to 30 Hz. This is the excitation for the system, or in other words the input or forcing function. As a rotating device, its sinusoidal nature fits perfectly into our simplified model. If left to sit directly on the floor, this 30 Hz disturbance may cause some annoyance in the building, so the machine is placed on springs. The floor can only respond to a simple up and down motion on it, so the single axis nature of coil springs makes them a perfect choice.

We go to our transmissibility curve and find that if the spring suspension natural frequency were about one-third of the disturbance frequency of 10 Hz, the transmissibility would only be about 0.2. Another way of saying this is that the transmissibility would be about 20% or conversely that the isolation efficiency would be about 80%. Knowing the mass of the machine, the desired frequency, and the total number of springs supporting the machine, we can calculate the spring rate of the spring to be purchased. Remember that the spring rate of springs in parallel adds together. When we select springs from a catalog, we find that what is available is considerably softer. After verifying from catalog data that the springs are rated to bear the load, we recalculate our suspension natural frequency and isolation efficiency finding it to be about 3 Hz and 98%.

For the machine sitting in a building, our problem is not only solved but also solved better than our minimum goal. If we take this same spring-mounted machine and install it on a skid to move it down the hall, we find that the machine bounces and sways. With every turn to the side, even a slow (as in steady-state) turn, the machine leans over dangerously on its soft springs. The overly soft 3 Hz suspension, while an added benefit to the original stationary application, would now be better replaced by our original 10 Hz design. Our suspension resonance point, or in other words filter point, is trapped between two competing limits on its upper and lower bounds. The robust design provides a sufficient margin between the competing limits to allow us to select a spring suspension that will work in all cases even when variations of tolerances and time are considered. Real equipment, particularly mobile equipment, may face upper and lower limits in more than one direction simultaneously. A good example of this is a vehicle engine. 

When the machine in our example was moved across the floor and hit a floor joint it bounced violently. This single event can be considered a shock input. There was a sudden change in velocity over a short period of time. The machine was accelerated once and then settled out. If we could measure the input from the floor joint, we may find that it had a high acceleration peak and lasted only a few milliseconds. To reach that velocity in such a short period of time required high acceleration. Looking at the skid, you may have never seen the effect of hitting the floor joint. The motion was so small and it went by so quickly. An accelerometer on the skid would have sensed high acceleration and therefore high forces. The soft spring-mounted machine moved several inches over a second or two. Following that, the machine continued to bob up and down in several diminishing cycles until coming to rest. The soft spring suspension took a short duration, high acceleration peak input, and converted it into a long duration, low peak acceleration output. 

Here we come to a design trade-off. The displacement necessary to meet the goal for shock attenuation may be more than the mechanical packaging will allow. The level of softness necessary to meet the shock or vibration attenuation goal may result in an unstable system. By unstable, we mean that the system will respond in undesirable modes. Usually, this entails large motions in other directions that cannot be controlled. The level of shock attenuation is only a function of allowable response time and travel. If one-inch of response travel is needed to reduce a certain input velocity to a certain response acceleration, then it will take this same one-inch of travel whether the subject is a 100,000-lb. generator or a 1-lb. circuit card.

DEVELOPING THE CONCEPT OF DAMPING

In our example of the machine mounted on springs, after receiving the floor-joint shock, the suspension required a few cycles to return to rest. This is the same condition found in the car on the road analogy. We had three skills of drivers who regained control of their cars at different rates. In the machine, on springs example we also have the ability to control the rate at which the system returns to rest. In our machine on springs system, we rely upon material properties to provide damping. The type of damping mechanism typical of mechanical resilient suspensions is a function that provides a force opposing motion proportional to the velocity of that motion. 

Damping reduces the time and number of cycles needed for the system to return to rest after a transient by limiting velocity response and therefore overshoot.

Damping makes the dynamic system look stiffer; in other words, the total spring rate appears to be higher when calculating an actual natural frequency.

Damping lowers the peak at resonance by limiting response velocity; in doing so, it is reducing the kinetic energy of the system by converting it to another form. 

Most passive mechanical dampers convert kinetic energy into heat energy. In a general statement, dampers can also convert kinetic energy into sound, plastic deformation, and electric current to name a few others. Like softness and displacement, the level of desirable damping in a real system has upper and lower bounds. 

If the time and number of cycles needed for the system to return to rest after a transient are too short because of increased damping, the system may never find a true null position. This may also be called hysteresis. If hysteresis is too great, the system tends to latch into unanticipated positions.

Damping is a mathematical term in the equations for natural frequency and transmissibility that was omitted from our previous simplifications. Including the term makes the apparent dynamic spring rate and natural frequency number greater. The damping term is non-linear and a function of velocity. What this means is that damping becomes more significant generally as input amplitude and/or input frequency increases.

With apparent spring rate changing on the fly, the system response at one input may not be the same as its response at another input. This is something that must be considered. The damping term also tends to shift the phase angle between the output response and the input function.

Most engineered passive damped isolators convert some amount of kinetic energy into heat. The more damping, the more heat. If the flow of heat under all conditions is poorly considered, elastic isolators may eventually break down, char, and even burn.

The common concept of a damper is an automotive shock absorber. In this type of design, a separate and distinct damping device is installed in parallel with the spring element. Keeping the elements separate gives the automotive designer latitude in selecting the damping rate and the spring rate independently. The isolators that VMC manufactures typically rely upon material damping that is integral with the elastic material. This works well with most of our applications that require damping controlled to only qualitative limits. Steel coil springs have no damping to speak of. When placed in a housing, friction-damping elements can be added. These are usually adjustable for mechanical “drag” by the user on site. Being adjustable, almost any damping factor can be attained to the point that the isolator is solidly locked. Molded elastomer provides damping by virtue of elastomers’s viscous fluid nature. Typical industrial elastomeric compounds provide a damping factor between 5% and 10% of critical damping. This makes most elastomers mildly damped. Specialty highly damped elastomeric materials may provide up to 15% and 25% damping factor. Wire rope isolators provide coulomb, or friction damping, by virtue of relative motion between wire strands. Damping factor may run 20% to 25% depending on the character of the input.

SELECTING AN ISOLATOR

With system loads, frequencies and basic suspension requirements established, we are faced with the task of selecting real-world mounts from this catalog. The science of shock and vibration management provides several very different technologies to choose from. VMC perhaps offers the most of these technologies all under one roof.

VMC Group's Family Tree of Mounting Technologies

Molded Elastomer Isolator Choices:

? Housed and Un-housed

? Failsafe (captive, restrained, seismic) and Non-Failsafe

? Amount of side thrust and uplift that can be tolerated

? Single directional, bi-directional, all-attitude, and axial to a radial ratio

? Flush mount and Non-flush mount

? Degree of deflection available

? Degree of dynamic damping

? Material selection with respect to the environment (temperature, sunlight, ozone, chemical, mechanical stress level)

Pad Choices:

? Material selection with respect to the environment

? Stacking to provide desired spring rate and deflection

? Interleaving with shims to control stresses and cross-axis distortions

? Engineered shapes

Steel Coil Spring Isolator Choices:

? Housed and Un-housed

? Failsafe (captive, restrained, seismic) and Non-Failsafe

? Level to which isolator can withstand side thrust and uplift (seismic rating)

? Jacking capability or fixed height

? Adjustable mechanical snubbing or fixed

? Provisions for lagging into concrete or bolting/ welding to steel

? Option of elastomer “sound pad” on mounting surfaces

? Surface finish of springs, housings, and hardware to meet service environment

? Large linear deflection capability

Wire Rope Isolator Choices:

? Choices between Helical, Circular Arch and Arch to obtain various axial to cross-axis performance ratios in a given volume

? Customization of materials and interfaces to meet system requirements

In most cases, there is not one single isolator or isolator technology for every application. It is more likely that the designer will be faced with a trade-off of different isolators that can meet the customer’s needs.

SOME BROAD GENERALITIES ON APPLICATIONS BY TYPE OF ISOLATOR

STEEL COIL SPRING ISOLATORS

Steel coil spring isolators find popular use in fixed industrial, HVAC, and architectural applications. For the most part, the disturbances involved are in a single, usually vertical direction. Steel coil springs can offer some very large deflections, up to 5 inches to rated load. This translates into a very soft suspension, down to about 3 Hz. Being stationary, such a soft suspension can be tolerated so long as the underlying foundation is much stiffer. Such a soft suspension offers excellent attenuation of fundamental machine vibrations due to shaft rotation. This is typically in the 20 to 60 Hz band. Steel coil springs are near perfectly linear almost up to solid compression. The dynamic properties of the isolator are predictable as load is applied. A loaded coil spring in itself is somewhat unstable. It is only a spring in one direction; those offered by VMC are compression springs. It is a tall, slender column subject to buckling. Without side restraint, the simple open spring has limited, usually light-duty application. Housings provide the restraint necessary not only to avoid buckling but to provide some other features as well.

Housings provide restraint, or snubbing, against side thrusts that would otherwise knock the machine off of open springs. Housings can incorporate dedicated snubbing blocks and can further combine features to adjust the gaps before the snubbing block is contacted. When the gap is adjusted to near zero, or an interference fit, frictional drag is added. Steel coil springs in themselves provide virtually no damping.

Housings around steel coil springs provide restraint against side thrusts. Machines may generate moderate side thrusts during operation. The magnitude of the thrust and the criticality of the application dictates the type of housing necessary. Gray iron castings are sufficient for low to moderate service loads. Welded steel plate structures are necessary for the loads associated with heavily unbalanced machines, earthquakes, and high winds. To meet seismic requirements, the housing must also provide restraint against uplift. Housed steel spring isolators without uplift restraint can be lifted off of their spring support. In the absence of earthquakes, high winds, and heavy unbalanced forces, it is assumed that the weight of stationary equipment is sufficient to keep the machine on its isolators. The top and bottom housings may be bolted or welded to the machine and its foundation as an assurance that it will not “walk”, but not all installations are truly affixed unless provisions for high side thrust and uplift forces have been made. 

There are special considerations to be taken for mobile steel spring-mounted equipment. The isolator should be housed, with full restraint in all directions. The super-soft suspensions achievable in stationary equipment will most likely present a stability problem when moved. The travel or road suspension onto which the isolated equipment rides is also a soft suspension. Two soft suspensions in series may couple into one another. The result may be amplification instead of attenuation. Mobile spring isolators, some known as marine isolators, compromise vibration isolation efficiency by using stiffer springs. Perhaps suspension natural frequencies not less than 7 Hz should be attempted. The isolators also must provide a good measure of frictional damping.

In this simple form, the elastomeric spring resembles the steel coil spring. If we could bond a “handle” on the faces of the elastic block, we then could not only push but also pull and shear on it. Unlike the steel coil spring, the block of elastic material is elastic in all directions simultaneously so long as there are “handles” in all these directions through which to apply load. The art of tailoring the properties in these directions is in the design of these handles. In VMC Group’s line of engineered elastomeric isolators, the handles are a variety of metal housings, tubes and rings molded or bonded onto and into the elastomer. Some of these metal features provide attachment to the equipment. Intelligent design can yield a compression-only isolator such as a pad, a compression isolator with moderate shear and tension capabilities, or a compression isolator that can equally bear load in shear and tension. Intelligent design can also address relative elasticity (spring rate), travel limits, and ultimate limits.

isolator that is held together only by its elastomer is not considered fail-safe. If the metals are designed to interfere with each other when relative motion becomes too great, then the isolator can be called fail-safe or captive. This is the same approach used in-housed steel spring isolators. Captive fail-safe elastomeric isolators, with all-directional elastic properties, find extensive application in mobile equipment. Given sufficient strength in the restraining metal parts, they can meet seismic ratings.

Where elastomeric isolators differ from steel spring isolators is in their deflection capability in relation to their size. Where a 4-inch tall coil spring may deflect 3 inches, a 4-inch thick section of elastomer may only deflect a half-inch. Where the steel spring follows a linear load-deflection curve, the elastomer section becomes increasingly stiffer with increasing load (a second-order or stiffening curve). Where the steel spring comes to rest at solid compression, the elastomer section continues to deform until it fails unless otherwise restrained. This is not to say that elastomer is inferior to the steel spring. In fact, these characteristics make it more suited to some applications. The limited deflection capability per unit volume can easily yield engineered isolators that produce multi-directional suspensions that are 7 Hz and higher. This band is desirable for mounting mobile equipment. The stiffening load-deflection curve produces an inherent snubbing effect desirable on equipment subject to periodic load spikes. The isolator’s failure limit can be avoided with an external or internal snubber if necessary. 

Materials used in elastomeric isolators must be properly selected for the expected service environment. Most machinery applications fall in a temperature range between -55 F to +300 F. The spring rate of steel is unaffected within this range. The characteristics of most polymer and natural elastomers will change. We rely on a wide variety of rubbers as well as plastics, cork, and composite materials as elastomers. Elastomer chemistry must be properly selected to perform to the required temperature just as to perform against chemical exposure, sunlight, ozone, and stress.

As the pad stack becomes taller, the stack becomes softer. Reasonable stacks of 1 to 4 layers will provide a mid-range suspension capable of attenuating a machine’s higher frequency disturbances. Pads are a simple, inexpensive means of blocking the transmission of noise from high speed, well-balanced equipment, and high-frequency structural resonances arising in the machine’s structure. If a bolt is driven through the pad to fix a machine in place, there must be some type of resilient material under the head of the bolt and clearance around the shank of the bolt or a “short-circuit” of vibration energy will be created. This will limit or defeat the effectiveness of the pad isolator.

Engineered pad systems are a cost-effective option to massive inertia blocks, large coil spring isolators, and mechanical dampers for mounting forging hammers and roll grinders weighing upwards of 100,000 pounds. Specialized composite materials capable of bearing loads of 1000 psi, properly sectioned and layered in pits up to 18 inches deep, can provide good isolation at low frequencies.

WIRE ROPE ISOLATORS

VMC pioneered the wire rope isolator more than forty years ago. A length of wire rope can be bent and will spring back to its original shape. This is the same mechanism that occurs when wire rope, or cable, is bent over a pulley when used as a tension element. Stranded wire rope can be bent to an extreme repeatedly without issue because it is comprised of many individual small wires. A single steel bar cannot be deformed very far 

The wire rope bending element is as much an elastic element as any tempered steel coil spring and molded elastomer or pad. As such, it can be used to limit vibration and shock transmission. Wire rope can provide a significant level of dynamic damping; typically 15% to 20% of critical damping. This comes from the frictional forces that arise between the individual wire strands in the rope bundle. Just as with damped elastomers and housed spring isolators with tight snubbing blocks, the damping makes wire rope attractive for applications that involve sweeps through resonance and transients such as shock. Like rubber, the damping is a property of the material and a function of the dynamic input. It is not adjustable. 

Two important characteristics of wire rope isolators come out of this shape of response curve. Shock is attenuated by spreading the input energy over time and distance. The flattened section of the curve is excellent for doing this. The load deflection curve of a wire rope is very long given the isolator’s physical size. The isolator is a hollow, slender device capable of collapsing in on itself. For its size, it can deflect far more than elastomer and even more than a coil spring. This is the characteristic most desirable for shock attenuation. This gives rise to a misconception – that wire rope isolators are only suitable for shock environments. As an elastic element in a spring-mass system, it will exhibit a natural frequency and thereby form a low-pass filter for vibration energy in the same manner as any coil spring or elastomer.

As said previously, stranded wire rope exhibits perhaps unmatched ability to repeatedly bend elastically to a great degree without fatigue becoming an issue. Drawn steel wire, out of which the rope is wound, provides tremendous tensile strength. Elastomers exhibit good compressive and shear strength, but very poor tensile strength. Bending is a part of buckling and bending results in tensile loads. There are elastomeric buckling isolators on the market. Because of elastomer’s limitations to tensile stresses, elastomeric buckling or bending mounts have limited applicability.

The most obvious difference between wire rope isolators and other technologies is in how they are presented on VMC Group’s website. We do not list load ratings for individual wire rope isolators and we publish two different average spring rates. In order to determine how much load can be placed on a wire rope isolator, we must first ask what the customer intends to do with the isolator. If small amplitude vibration is the input, we can place the static load along much of the lower two thirds of the curve. The effective static spring rate is the tangent of the curve at that load point. If large amplitudes, particularly deep shocks are to be the input, we place the static load down in the linear first third of the curve. This allows the load to ride high up onto the curve in response to the shock. In this case, the effective average spring rate is a global straight-line end-to-end slope of the curve over the excursion. 

To provide average values in the catalog for design purposes, we take the vibration spring rate as the tangent slope near zero and the shock spring rate as the overall end-to-end straight-line slope over the curve. Due to the complexity of the spring rate, VMC recommends that our engineering department be consulted for assistance when selecting wire rope isolators.

Another characteristic of wire rope isolators that is a reason for the user to consult with VMC before selecting is the interrelationship between the axes of the isolator. Wire rope isolators are elastic elements in all directions simultaneously. This makes them suited for all-attitude and mobile applications and applications that involve complex, off-axis inputs. What makes them different from elastomeric isolators that provide this same benefit is that an input in one direction can generate a cross-coupled response in another. This is a side effect of buckling. Unless unique external structures are added, we cannot infinitely adjust the induced cross-axis response. We can manage it, in most cases, using properly engineered solutions that take all axes into account. It should be noted as a caveat to the all-axis elasticity claim that use of the tension direction for primary shock attenuation is not recommended. This is due to the predominance of tensile loading within the cable that results in a stiffening curve. A rebound from a compressive shock; back down the compression curve and snubbing into the tension curve is usually not a problem.

By their nature, wire rope isolators are self-snubbing at some point; they are fail-safe and captive to the ultimate limits of the metals. They are insensitive to temperature from cryogenic up to near anneal. They resist most industrial and natural environments, and this resistance can be enhanced with special materials and coatings. VMC Group’s manufacturing process is set up to create special winding configurations to customize spring rate and deflection.

Acceleration – The time rate change of velocity, typically expressed in units of inches per second per second (in/ sec2), or g’s (percentage of acceleration due to earth’s gravity, 386.4 in/sec2). In seismic applications, multiply this value by a unit’s mass (or weight, when using g’s), to obtain an applied force.

Amplification – The increase of an output amplitude proportional to the input amplitude. Amplitude is typically acceleration, velocity, force, or displacement in a dynamic mechanical system. Also characterized by a transmissibility greater than 1.0 and associated with a resonance condition.

Attenuation – The decrease of an output amplitude proportional to the input amplitude. Also characterized by a transmissibility less than 1.0. Sometimes referred to as isolation.

Center of Gravity – The point of support at which a body would be in balance. Also known as the center of mass and inertial center.

Compression – The act of applying a load to an object to shorten its length. Conversely, a compressive load.

Damping – Generally, the dissipation of energy out of a dynamic system. Typically, the dissipation of energy by conversion from kinetic energy into heat. The rate of damping is typically proportional to the velocity of the system.

Damping Factor – A dimensionless ratio defining the amount of damping in a system. Usually expressed as a percentage of critical damping.

Decade Band – An interval between two discrete frequency ratios of ten. For example, frequencies of 60 Hz and 70 Hz are one decade apart.

Decibel – A dimensionless unit of amplitude level that denotes the ratio between two quantities, such as power, pressure, or acceleration.

Deflection – The distance an elastic body or spring moves when subjected to a static or dynamic force. Typical units are inches or millimeters.

Displacement – The change of position of a body, usually measured from the means or rest position. Common units are inches or millimeters and must be qualified as either double amplitude (DA) or single amplitude (SA) depending on whether or not the motion is centered about the mean position. Displacement is related to acceleration by frequency.

Elastomer – A generic term that encompasses all types of natural and synthetic rubber, plastics, and selected composite materials. The type of elastomer chosen for an application depends on many factors including loading, life cycle, dynamic characteristics such as spring rate and damping, as well as environmental considerations such as temperature, chemical exposure, and the elements of nature.

Fragility – The maximum amount of load that a piece of equipment can withstand before failure. This may be in terms of maximum amount of transmitted acceleration (g’s), maximum amount of transmitted force, or maximum vibration amplitude (acceleration or displacement) at one or more defined frequencies. Isolation systems are designed or selected to limit the transmission of force or acceleration to below the stated fragility.

Free Vibration – The oscillation of a system when there are no externally applied forces. This oscillation will occur at the natural frequency of the system.

Frequency – The number of complete cycles of oscillations per unit of time. The reciprocal of frequency is the period, or the time required to travel one complete cycle. Frequency is commonly expressed in units of hertz (Hz) or cycles per second (cps). Common machine rotation expressed in revolutions per minute (rpm) can be stated in Hz by dividing by 60.

Mass – The fundamental building block of the universe and the mathematics that describe it. Most dynamic equations require a mass term unless they have been adjusted to use weight, which is a force term. Mass can be derived from measured weight by dividing weight by the gravitational constant, g (g=32.2 ft./sec2 or 386 in./sec2). In the American-English system of measurement, weight and force are in terms of pounds (lbs) or pounds-force. Mass is in terms of lb-sec2/in or lb-sec2/ft. In the metric system, weight and force are in terms of dynes or Newtons. Mass is in terms of grams, kilograms, etc. Use of grams and kilograms to refer to weight, as measured off of a gram scale, is a shorthand approach that assumes that the measurement is taken in earth’s 1-g environment. Similarly, some people will express weight divided by g as “pounds-mass”. Both shorthand approaches can cause problems if the units of measure are not properly understood and accounted for.

Modulus – A material characteristic that is related to its stiffness. Modulus is the ratio of stress to strain in the elastomer at a given loading condition. Typical units are lb/in2.

Moment of Inertia – Another fundamental building block of the universe and its mathematics, it combines attributes of the physical geometry of an object with its mass. It is a term of importance particularly in systems that contain some amount of rotation. Typical units of mass moments of inertia in the American-English system are inch-pound-sec2 and in the Metric system kilogrammeters2.

Natural Frequency – Any object possessing mass and some degree of compliance (spring) when disturbed from rest by a transient input, will oscillate freely. The frequency of this free oscillation is termed the object’s natural frequency or resonant frequency. In an oscillating system, the frequency at which the system will vibrate. Typically designated as ?n. Common units are hertz (Hz) or cycles per second (cps).

Octave Band – An octave is the interval between two discrete frequencies having a frequency ratio of two. For instance, frequencies of 25 Hz and 50 Hz are separated by one octave.

Period – The period is the time required for a periodic motion to repeat itself. It is the inverse of frequency and the common unit is seconds.

Random Vibration – An energy spectrum comprised of oscillations occurring at many frequencies each with unique amplitudes simultaneously. Also known as complex motion and white noise, it is most representative of the real world. Random vibration must be specified over a defined frequency range and with either a graphical plot or mathematical equation describing the amplitude. Units are typically in terms of power spectral density (PSD) and termed g2/Hz.

Resonance – Resonance occurs when the frequency of excitation is equal to the natural frequency of the system. When this happens, the amplitude of vibration increases and is only limited by the amount of damping present in the isolation system.

Rotation – Although most of what has been said here applies to objects moving along a straight line, the same applies to objects in rotation. In a rotational system, mass is replaced by mass moment of inertia. Rotational displacement must be in terms of radians (rad). Rotational spring rate is torque per unit rotational displacement such as inch-pounds per radian. The resulting rotational frequency remains in terms of hertz or cycles per second.

Shear – When a body, such as rubber mount, is subject to equal and opposite forces that are not in line, the forces tend to shear the body in two. The stiffness of an elastomeric isolator subjected to this type of loading is referred to as shear stiffness.

Shock – Shock is a transient condition where the equilibrium of a system is disrupted by a sudden applied force or increment of force, or by sudden change in the direction or magnitude of a velocity vector. Shock is defined by the character of the shock pulse.

Shock Pulse – A primary disturbance characterized by a rise and decay of acceleration in a relatively short time. Shock pulse is generally shown as a plot of acceleration vs. time. Peak amplitude in terms of acceleration, time duration, and shape are necessary to fully define a shock pulse input.

Sinusoidal Vibration – Oscillations in which motion is periodic with time in the form of a sine curve. Rotating equipment generates vibrations that are frequently considered as sinusoidal. This also can be termed Simple Harmonic Motion when only a single frequency and a single amplitude are involved at any one instance in time.

Stiffness – The force required to deflect an elastic element, such as an isolator, a unit distance. Stiffness is the slope of a curve showing force on the y-axis and deflection on the x-axis. Typical units are lbs/in.

Transmissibility – Transmissibility is the ratio of the transmitted (or responding or output) force, displacement or acceleration, to the imposed (driving, applied or input) force, displacement, or acceleration.

Velocity – Velocity is a vector that defines the time rate of change of displacement. Typical units are in/sec.

Weight – The measurable sensation of the bearing force resulting from a mass under a gravitational pull, as in a mass on a scale. See mass for more details.

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