The Coupling Hanbook: Part VII

Selecting the Right Coupling - General Characteristics & Application Considerations
General Coupling Characteristics

An understanding of the general characteristics of couplings will help in selecting the correct coupling for an application and will help evaluate competitive coupling proposals.

Finite Life and Infinite Life Couplings

All flexible couplings fall into one of two categories, "finite life" or "infinite life.”

Finite-life couplings are those that wear in normal operation, because of using sliding or rubbing parts to transmit torque and compensate for misalignment. This group includes jaw, gear, grid, sleeve (shear), Nylon sleeve gear, chain, offset and pin & bushing types. All usually have lower purchase costs than infinite-life couplings. They won't last as long, but their life span may be sufficient for the life expectancy of the application. Periodic maintenance is required.
Infinite-life is something of a misnomer, as these couplings do not necessarily last forever. It simply means the couplings do not wear in normal operation and by design the acceptable loads do not exceed the fatigue life of the parts. This is because they transmit torque and compensate for misalignment through distortion within their flexing elements rather than by the sliding or rubbing movement of loosely fitted parts. This group includes tire, disc, diaphragm, some donut types, wrapped-spring, flex-link, and most motion-control types. (Sleeve types are excluded here because their torque and misalignment capabilities are served by the flexing of their elastomeric element, the interface between the element and its hubs is a loose gear-like fit that wears.)

Distortions of the flexible element results in fatigue stresses rather than wear. Infinite life in couplings remains infinite only as long as the operating load stresses, considering misalignment is kept within the fatigue capabilities of the coupling's material. Elastomeric couplings do not have the same fatigue capabilities as metal couplings and they also experience reduced load capability as time passes. For that reason, the shelf life of the elastomer must be factored into the couplings design rating.

An overload that will fail an infinite-life coupling might only reduce the life of a comparably rated finite-life coupling. Accordingly infinite-life designs are most often used on maintenance-free systems where maximum torque requirements (including transient, cyclic and start-up torque) are known.

Single Flex, 3 Bearing Systems and Two Flex Plane 4 Bearing Systems

We have previously mentioned that some couplings, the metallic flex type in particular can be built as single flex element or two flex element couplings. Single flex element couplings were noted to be limited to angular misalignment and possibly axial displacement whereas the two flex element units were needed to achieve the additional parallel (radial) misalignment capabilities. Couplings of the single flex element type could be expected to have a lower cost. Elastomeric couplings may provide parallel misalignment in a single element through distortion of the element.

There are applications that require two elements and therefore two flex planes, and other applications that either allow or require the single element. The coupling installed in a four bearing system will be of the two flex plane type or of a type that allows radial misalignment. The four bearing system consists of two pieces of rotating equipment, each having a set of two bearings. Each set of bearings will hold the associated shaft in a straight line when the equipment is installed on its foundation. Alignment of the two pieces of equipment will make the shafts close to coaxial and coplanar. However, since some misalignment will occur, a flexible coupling is needed. Unless one piece of equipment can swivel about a point, parallel misalignment will eventually show up in the system and a coupling with that capability will be required.

The coupling installed in a three bearing system will be of the single flex type. The single bearing is a self aligning type which provides the swivel possibilities. (It does not have to be a three dimensional swivel.) The system only needs an angular misalignment capability as associated with a single flex coupling. There are two types of single bearing systems. Note that both types have a radial load that is carried across the coupling. Most elastomeric couplings will not be able to carry that radial load and should not be used in the system unless checked for radial capabilities. Two flex plane couplings will be unstable in these systems and cause vibrations or wobble.

The first type of a single bearing system is one that places the load between the coupling and the outboard single bearing. This is typical of a three bearing generator coupled to a driver. The load can be heavy. Usually the flex half of the coupling is mounted near to the driver bearing to reduce the overhung moment.

The second type of single bearing system is the overhung pulley application. The pulley has one side open to allow for easy changing of the belts. The bending moment caused by the pulley load has to be passed through the coupling. The bearing between the coupling and the pulley is a pivot point and a load carrying position.

The floating shaft or floating tube coupling is a special case of using two single flex couplings in a four bearing system. The connection between the two single flex couplings is a long unsupported shaft or tube. The length of the shaft or tube is limited by critical speed, the diameter is a function of the torque. Tubes are used to lighten the weight and improve the critical speed. The flex halves can be on the center shaft, a marine type, or next to the equipment bearing, a reduced moment type. Mixed coupling designs with one side being a reduced moment and the other a marine style is acceptable. Vertical floating shafts are available. Floating shafts that use full flex couplings on both ends of the floating shaft are unstable when operating and should be avoided. Elastomeric floating shaft couplings are possible but must be reviewed and approved by the coupling manufacturer. Floating shafts are used when the connected equipment has offset shafts and space is available for the long shaft. They are found in paper and steel mills.

Some systems have a mix of floating shafts and semi-floating shafts. Usually single flex couplings are needed to provide stability in the rotating system. The flex half should be mounted nearest to a bearing for best results.

Torque - Limited and Bore - Limited Couplings

Some coupling designs are limited by the torque capability of the flexing element. They are called "torque-limited" couplings. Other couplings are limited by the hub bore size because the flex element is capable of transmitting all the torque that shaft size will normally deliver. These are termed "bore-limited".

The elastomeric coupling is considered a torque limited coupling device because the flexing element uns out of torque carrying capacity before the connecting shafts reach their full torque potential. This is because elastomers have much lower tensile and compressive strength than the metals otherwise used in flexing elements. Consequently, elastomeric couplings must become larger in diameter to achieve higher torque-carrying capabilities. The hub naturally follows the elastomer in becoming large, giving the hub a bore capability that is unnecessarily large in relation to the torque capability of the coupling. Enterprising designers use that extra bore capability to fit tapered bushings and other easy-assembly devices into the hubs. (For more discussion on these devices see the chapter on mounting the coupling hubs to the shafts.) All this means that elastomeric couplings must always be checked for both torque and bore capability.

Metallic element couplings tend to keep a close relationship between hub, bore and torque capability. One notable exception is the gear coupling which is truly bore-limited because it can transmit more torque than its maximum shaft size will normally deliver.

Some composite materials offer strength capabilities somewhere between elastomers and metals. These materials sometimes offer weight-to-strength advantages that can be important.
Coupling selection always needs consideration of torque, speed, misalignment, connecting shaft sizes, and appropriate service factors. However, in old installations needing coupling replacement, the real torque values might be unknown or uncertain. In such situations the gear coupling could be selected purely on shaft diameter and speed, with limited risk.

Selecting elastomeric couplings purely on shaft diameter and speed is very risky. In some cases, however, that risk can be an advantage. When overloaded, the elastomeric coupling will fail before the rotating equipment shaft fails, provided the overall design is correct, thus sacrificing the less expensive coupling to protect the more expensive rotating equipment. When using this strategy, the overall design considerations should include the wear life of the coupling and the damping energy to be absorbed by the coupling.

The fact that the coupling can be the weakest element does not necessarily mean that the coupling will provide a fusible link. To have the coupling serve that function, it is necessary to pick the type of coupling with that feature. These types are termed non-failsafe. In failsafe design, coupling failure does not automatically disconnect the two rotating shafts, but will require the coupling to be maintained as soon as possible. If the coupling is a wearable device, as are most elastomeric couplings, both load and misalignment are factors in total life. The end of usable life of the coupling might not be the result of equipment problems when wear is a consideration.

Application Considerations

1. Determining Torque Requirements

Coupling torque requirements can be defined many ways, and specifiers need to decide which definition to use. We will first review the various definitions, then discuss how they are used in coupling selection.

System Torque

Normal Operating Torque - The steady state torque required by the system when operating at normal design conditions. This is usually the level at which the equipment designer certifies the equipment performance.

Starting Torque - The torque needed when the system starts its operation. This torque can be greater or less than the normal operating torque.

Peak Torque - The maximum torque required by the system. This torque is normally a one time event or limited to a specified number of occasions. In torsional vibration coupling systems it is the maximum vibratory response torque that could pass through the coupling.

Cyclic Torque - It is any torque requirement of the system that varies with time. It can be of a smooth, periodic variation like a sine wave or could be an erratic variation. It does not go through zero to a negative value, but can be equal to zero. In torsional vibrating systems it is the vibratory torque that occurs at the operating speed.

Reversing Torque - This is a cyclic torque that passes through zero and becomes negative or "reverses" to the opposite direction.

Transient Torque - A transient torque is of short duration, not necessarily expected, not happening on a regular basis but occurring when a system is upset. It may or may not be equal to or greater than peak torque.

Normal Braking Torque - It is the torque used to decelerate or reduce the speed of the equipment when the brakes are applied in a normal manner. The torque is time dependent, and moves through the system.

Emergency Braking Torque - In this case the brakes are applied to stop the equipment in a very short time. The torque will exceed the normal braking torque by the inverse ratio of the time required to stop in each case.

Stall or Lockup Torque - This is the torque that passes through the system when the system stalls or otherwise come to a stop because of some activity within the driven system.

Shutdown Torque - The torque required to bring the equipment from operating conditions to a shut down condition. This can be the normal braking torque or could be a result of friction or load in a system that is coasting to a stop.

Torque to Accelerate or to Decelerate - The torque required to increase or to decrease the equipment operating speed. In the case of acceleration, the available torque for acceleration is the difference between the driver capability and the system requirements at the current speed. Decelerating torque comes from braking devices or from frictional drag or other energy drains within the system that cannot be overcome by the driver. A formula for calculating this torque is found at the end of this section.

Driver Horsepower (Torque)

Nameplate Rated Horsepower (Torque) - The torque value is derived from the driver capability shown on the nameplate as a horsepower and a speed. It is based on specific inputs to the driver such as voltage, and amps or kVA if it is an electric motor. A formula to convert horsepower and speed to torque is found at the end of this section.

Service Factor Rated Horsepower (Torque) - Some drivers have additional capabilities beyond the name plate rating. The nameplate capabilities are multiplied by the service factor. The service factor is also shown on the nameplate.

Start-Up Torque - The driver torque capability at start-up available to accelerate the driven equipment to operating speed. Some drivers have a fixed percentage of the rated torque available at start-up. It can be greater than 100%.

Peak Torque - This is the maximum torque available from the driver, it may not be able to operate for extended time periods at this torque.

Stall Torque - This is the system torque requirement that will cause the driver to come to a stop.
While all the torque values defined previously may exist within the system at some point in time, the torque requirements of the driven equipment are the primary consideration. The driver will not supply more torque than the driven equipment will absorb or the driver can produce. Under some conditions the maximum torque within the system may exceed the driver capability, for example when brakes are energized.

A piece of driven equipment operating at its full speed capability requires a certain amount of torque. If the driven equipment is not operating at full speed the driver will supply additional torque until equilibrium is reached for torque and speed. The driver could still have additional capability, but it will not transmit it to the driven equipment. Other than at start up, the speed variation is small and subject to driver speed limits.

Drivers have speed limits that are imposed by physics or by trip devices. The physical limits can include the effects of frequency on an electric motor, or the effects of fuel restriction on an internal combustion engine, or steam availability to a steam turbine. Trip devices can include governors and over speed switches. The speed-torque capabilities of the driver are fixed by the design of the driver and the inputs to the driver.

Coupling Selection Torque

Using the Driver Torque

The coupling can be selected based on the driver capabilities, using nameplate values or start-up torque. The capability requirements can be increased by an application service factor before choosing the coupling. This method of coupling selection usually results in a coupling that is oversized for the application, even if the service factor is 1.0. This translates into high cost and other problems. The reason oversizing results is twofold. First the driven loads may include equipment service factors that have already increased the torque value. Second, the driver is usually oversized. Drivers such as electric motors, come in standard sizes. If a piece of driven equipment requires a horsepower that is in between two standard sizes, the larger is chosen. Even when the requirements are right on the nose, the designer will usually pick a larger size out of conservatism.

When the coupling is chosen by driver horsepower one must be sure there is no gear reducer between the driver and the driven load. Gearboxes are constant horsepower devices that increase the torque or decrease the torque depending on the gear ratio input to output. Other power transmission devices may do the same. In any case those types of devices must be accounted for in the coupling selection. Couplings selected using driver torque are normally mounted with one half on the driver shaft.

Using Driven Equipment Torque and a Service Factor

The coupling can be selected by using the normal operating torque of the driven equipment, adjusted for coupling location, multiplied by a service factor. Service factors are used to account for unknowns in the driven equipment system.

Service Factors

Sometimes "Service Factors" are called "Application Factors" or "Experience Factors". They have been empirically developed for most applications, or are known by their designer based on experience with their systems. Coupling manufacturers publish Service Factors based on their experience with their couplings on various systems. The factors are listed in coupling catalogs. Manufacturers may publish different service factors by product line. The catalog service factors will include factors for the application and the type of driver. Elastomer couplings sometimes include an environmental temperature service factor, and if intended for dampening vibratory torque, will have a frequency service factor as well.

AGMA Standard 9922-A96 lists service factors for many different applications. Service Factors are not the same as design Factors of Safety. Service factors deal with the unpredictable nature of the application, not with unknowns in the design of the coupling.
Depending on the selection of service factor this method also could result in an oversize coupling. Oversize couplings cost more and can result in bearing overload, excess inertia, premature wear and more maintenance.

Using System Torque with Little or No Service Factor

A coupling can be selected based on the exact requirements of the system. In this case the requirements must include all the torque values to be transmitted through the coupling. That can include starting requirements, braking requirements, peaks, transients and any others listed at the beginning of this section. Check the coupling manufacturers catalog as the coupling can have various torque capabilities. It may have one rating based on normal operation with another simultaneous rating for low cycles of peak torque. It may be acceptable to compare the peak system torque with a 1.15 Service Factor, to the yield strength of the coupling, and allow that as part of the acceptable selection. The coupling manufacturer should be consulted when the coupling selection is based on peak torque, emergency torque or a high transient that comes along only once. The coupling may already have sufficient reserve to satisfy those requirements on a limited number of occurrences.

If the coupling has only one published torque value, the coupling would have to be selected to meet the maximum torque expected in that part of the system. However, some types of couplings have torque ratings based on wear life, maximum misalignment combined with torque, or conservative considerations.

If the coupling is subject to cyclic torque or reversing torque, the selection should be based on those torque values. In the case of cyclic torque, use the high value. In the case of reversing torque, it will be necessary to check the coupling's fatigue life against the torque peaks and the acceleration/deceleration requirements associated with reversing operation.

The most economical selection will be based on the exact torque requirements of the system including peak, transients, breaking, or other expected torque values. Of course, this approach requires that all of the torque values be known with certainty. When the coupling has been sized to meet torque, it must also be checked for bore capability. Some bore-limited couplings might have the needed torque capacity but not enough bore capability to accept the shaft that will deliver it. Likewise, some torque-limited couplings might have sufficient bore capability to accept the shaft but not be able to carry all the torque that the shaft will deliver.

Using Torque Information Coupling Catalogs

Coupling manufacturers have several methods of listing the coupling capabilities in their catalogs. These capabilities vary on each manufacturer's experience, design requirements, and testing capabilities. Torque capabilities found in the catalogs may have to be factored or reduced for misalignment, vibration frequency, temperature (elastomers), life (including elastomeric shelf life), or maximum torque. Such factors, if they are to be used, should be shown in the same catalog.

Most often the value shown in the catalog is the normal torque capability that the coupling can transmit over its design life. Some couplings have a listed maximum torque. Usually that maximum value is used when the application might involve short cycle fatigue on couplings that have infinite life. Couplings that wear over time, such as a gear coupling, may have maximum capabilities that are quite large as long as their application keeps wear low. Couplings that wear may also offer alternate materials for reduced wear and longer life or for higher torque.
Because some coupling torque capabilities are limited by wear of the flex element and others limited by on fatigue of the flex element, it is best to understand the type of coupling that is to be used in the system before selecting the size. In addition to the flex element, coupling torque capability is affected by the method of securing shaft to hub, and any other joint in the unit, bolted or otherwise. Usually it is the flex element that is the limiting factor for the catalog torque values.

Useful torque equations:

Converting horsepower to torque:
T = BHP x 63025 / RPM
T = the torque in inch-pounds
BHP = the motor or other horsepower
RPM = the operating speed in revolutions per minute
63025 = a constant used for inch-pounds, use 5252 for foot-pounds, and 7121 for Newton-meters

Converting kW to torque:
T = BHP x 84518 / RPM
T = the torque in inch-pounds
kW = the motor or other kilowatts
RPM = the operating speed in revolutions per minute
84518 = a constant used for inch-pounds, use 7043 for foot-pounds, and 9550 for Newton-meters

Determining the acceleration or deceleration torque:
T = (Wk^2 x N) / (307 x t)
T = the torque to accelerate or decelerate in foot-pounds
Wk2 = the inertia of the piece to be accelerated or decelerated in pound
feet squared
N = the absolute change of speed in RPM
t = the time for the speed change in seconds
307 = a constant that allows the speed to be in RPM, the time to be in seconds and the torque and inertia to be in pounds and feet. It is a common form of the equation.

2. Motion Control

While all couplings claim constant RPM transfer, not all can meet the rigorous demands of motion control, for two shafts to be synchronized, moving at exactly the same speed to exactly the same location. Such demands are found in applications such as shaft encoders, resolvers, all forms of servo devices, linear and ball screw actuators, robots, stepmotors, light duty pumps and metering devices, plotters, medical equipment, positioning tables, computers and radar.
Coupling characteristics most important for motion control include high torsional stiffness but low radial stiffness, low inertia, constant velocity, no wind-up, zero backlash in coupling components, shaft interface and corrosion resistance. Highly accurate machine tools, robotic systems and printing presses need extremely stiff couplings, as do encoders, which provide positioning feedback to the system.

Coupling torsional stiffness often is related more to the torque used by the system than to the capability of the coupling. Lightly loaded couplings can act like very stiff couplings, but this usually means they are oversized for the job. This oversizing effect is often seen when low backlash curved jaw couplings are used for motion control.

Another required attribute for the motion control coupling is to withstand peak torque loads that are high relative to the nominal torque and size of the coupling. High peak loads result from reversals. In these applications couplings should be sized for the reversing torque rather than the normal torque. The reversing torque may in fact be the normal operating torque. One way to reduce the start-up and reversing torque peaks is to reduce the inertia of the two halves of the system, including the couplings. For this reason motion control couplings are designed for low inertia.

Fortunately, most of the high-precision end of motion control applications call for small 
equipment with small shaft diameters and small couplings. As a result, nominal torque values are low in absolute terms even if not in relative terms.

Small shafts must be aligned properly too, because reactionary loading from misalignment will be detrimental to both shaft and bearing systems. Motion control couplings are designed to minimize reactionary loads even though they are stiff couplings. That might seem contradictory since stiffer couplings generate higher reactionary forces. However, bellows and beam couplings provide a good example of being radially resilient while torsionally stiff.

Finally the system could be subject to lateral critical (vibratory) speeds if the coupling is not stiff enough in that direction. Once again, just because the systems are usually small does not mean they can't experience these problems.

3. Torsional Vibrations

One class of coupling applications is unique in that a secondary load is transferred through the power transmission system and the equipment connected to the system. That secondary load is torsional vibration. Torsional vibrations are associated with internal combustion engines, reciprocating (piston) type compressors, vane passing frequencies of some centrifugal pumps, grinding mill drives, kiln drives, rolling mill drives, variable speed motors, and the start up of synchronous motors. Diesel engines represent the most significant unit volume of torsional coupling applications, and will be discussed in separate detail later.

One class of coupling applications is unique in that a secondary load is transferred through the power transmission system and the equipment connected to the system. That secondary load is torsional vibration. Torsional vibrations are associated with internal combustion engines, reciprocating (piston) type compressors, vane passing frequencies of some centrifugal pumps, grinding mill drives, kiln drives, rolling mill drives, variable speed motors, and the start up of synchronous motors. Diesel engines represent the most significant unit volume of torsional coupling applications, and will be discussed in separate detail later.

Torsional vibrations cause equipment breakdowns such as wear or chatter on loose connections like spline pump shafts, or complete fatigue failure of the shaft or some other element. These harmonic torsional pulses are difficult to detect, because they do not bounce the equipment up and down, as would a lateral vibration. Nor can they be felt by touching the equipment. Usually, the result of the vibrations is known before the vibration is known. Often something else is blamed.

If the torsional vibratory frequency matches a system torsional natural frequency, the system reaches a harmonic or becomes resonant. That's because the natural frequency is an energy balance point at which additional forces will set off uncontrolled vibration. From a technical standpoint, it is the frequency at which the kinetic energy of spinning inertia blocks is equal to the potential energy of the torsional spring connecting the inertia blocks.

In such systems, inertia blocks can be impellers, pistons, mill rolls, motor rotors or any other device that is mounted on the shaft, which all rotate together as a single wheel. The torsional spring is a combination of the shaft and coupling's flexible element, plus other potentially flexing components such as a spacer or floating shaft.

When the wheel and spring rotate as parts of the same system, the inertia of the spinning wheel is balanced against the windup of the spring. Any additional forward pulsing force on the wheel will cause the spring to windup more and that will in turn react with a reverse force to the wheel. Between pulses, when that additional force is removed the spring unwinds, and the wheel surges forward. When the pulsing force returns, the spring winds up again, reapplying the reverse force to the wheel, etc. That pulsing force which is being applied at some time cycle or frequency at or related to the operating RPM, is the torsional vibration. If the timing is right, the winding and unwinding of the spring and the energy changes in the wheel resonate back and forth. The point where the timing is right is the system's natural frequency.

Determining the Natural Frequency

All rotating systems have a torsional natural frequency. It is a function of the driven inertia, driver inertia and the torsional stiffness of the shaft, spacer and/or coupling connecting the two. There is a natural frequency for each combination of inertia and spring. Aside from the kinds of torsionally sensitive systems discussed in this section, most systems have torsional natural frequencies so high as to be inconsequential. By itself, the natural frequency is harmless and does not generate torsional vibration, but is simply a sensitive spot along the systems RPM curve. It is a "forcing frequency", i.e. it is not self-initiating or self-sustaining, rather it must be triggered by a vibratory force pulsing at that frequency.

Many systems can be reduced to a two-mass system. For a two-mass system, the frequency can be determined mathematically from the following equation.

CPM= (60/2π) SqRt (Ctdyn x (JA + JL) / (JA x JL))
CPM is the frequency in "cycles per minute".
JA is the polar inertia of the driver
JL is the polar inertia of the driven
Ctdyn is the dynamic torsional stiffness of the coupling.
60/2π is a constant.

Reducing a system to a two-mass system is done by lumping inertias connected by torsionally stiff shaft elements. For example the lumped polar moment of inertia of the driver JA and the lumped polar moment of inertia of the driven equipment JL are determined by adding all the individual inertias that are connected by stiff shafts. When a gear reducer or increaser is involved, the downstream inertia must be factored by the square of the gear ratio (speed). It is an inverse function.

A coupling is between the driver and the driven. The coupling stiffness Ctdyn is obtained from the coupling manufacturer. It is called the dynamic torsional stiffness, which is higher than the static torsional stiffness.

Inertia is marked by the symbol "J", the units in the English system are inch-pounds second squared. It is related to WR2 by "g" the acceleration due to gravity. For a method of calculating the inertia value and the stiffness of connecting pieces refer to AGMA Standard 9004.
In a multi-mass system that includes more than two inertias connected by torsionally soft shafts, couplings, or sections, the natural frequency can be determined using the Holzer method. Refer to a textbook for an example of the Holzer analysis.

As long as the torsional natural frequency is more than 40% above or 30% below (.7 Nc to 1.4 Nc, where Nc is the critical numerical value) the system's operating frequency or idling frequencies (RPM) or associated torsional vibration frequencies (CPM) no resonance problems should occur. If it is in between those values there is a good chance the system vibratory response will cause damage to one or more components. If it is close to any of those frequencies, resonance is likely to occur.

Campbell diagrams are graphic plots of operating speeds and pulse frequency. They are used to identify the potential trouble spots where operating or idle RPM is equal to a torsional pulse frequency in CPM, (cycles per minute).

If it is decided to operate the system normally at an RPM above the torsional critical speed, (natural frequency) then the driver must have enough torque available to accelerate the load quickly through the critical speed zone (RPM). Comparing the speed torque capabilities of the driver and the load will determine the system's ability to accelerate through the critical zone quickly enough.

Using the Coupling to Tune Critical Frequency

In the torsionally sensitive system, couplings take on an important extra role beyond the transfer of driving torque and the handling of misalignment. They have the ability to move the natural frequency away from those levels that will be occupied by the torsional vibratory frequency at normal operating or idling speeds. This is called "tuning" the critical frequency. It works as long as the coupling is the controlling element for the critical frequency. That is not the case when long slender shafts are in the torque path. They also can be used to damp the energy of torsional vibration to reduce its potential for damage. The coupling torsional stiffness/softness is an attribute that is important in serving these functions.

Couplings with the highest levels of torsional stiffness are not used here. Those designs primarily serve systems that must transfer motion without windup or backlash, as previously discussed under motion control. Torsionally soft systems have a normal operating speed above the torsional critical speed while torsionally stiff systems have a normal operating speed well below the torsional critical speed. Because the coupling is usually the softest torsional element in either system, the system tends to be stiff when the coupling has a relatively high torsional stiffness and soft when the coupling has relatively high torsional softness.

Stiff couplings have elastomers of the Zytel® and Hytrel® type of plastic or their flex elements are metal. Soft couplings are rubber elastomers in compression or in shear.

Changing to a torsionally stiffer coupling raises the system's natural (critical) frequency, and reduces or eliminates the coupling's capacity to damp vibratory energy.

Using stiffer couplings to drive the critical frequency above the operating speed is as effective on simple systems like a single hydraulic pump driven by a diesel engine as it is on sophisticated high-speed couplings that are found on turbine driven rotating equipment. 

When the coupling is used in the regimen of keeping the critical frequency high, it is usually just a matter of making sure the coupling is sufficiently torsionally stiff. That could be accomplished by using a stiff spacer piece with a metallic-element coupling, or by using a very stiff elastomeric element on a flywheel coupling. The coupling manufacturer can provide the necessary information on coupling and spacer piece stiffness.

An exception would occur when a system has a long slender shaft, which usually means the lowest critical frequency would be the result of that shaft. That type of system can become complex because the coupling is no longer the element that controls the stiffness.

The torsionally stiff elastomeric coupling and the torsionally stiff metallic element coupling offer no damping between the driver and the driven equipment. That means torsional vibrations are passed into the driven system. In such stiff systems, loose parts or parts with backlash will vibrate and rattle, and may have wear problems. Typically spline shafts on hydraulic pumps and gears with backlash suffer the wear.

Changing to a torsionally softer coupling lowers the system's natural (critical) frequency, but also may increase the coupling's capacity to damp vibratory energy, so that function and the heat it will generate through hysteresis needs to be considered in the selection. Elastomeric couplings expected to damp torsional energy must be designed to reject the resulting heat to a heat sink. Otherwise the heat will fail the elastomer by melting from the inside out.

Elastomeric torsional couplings can be either compression type or shear types. The more common compression types are of the donut or torus configuration. However, some use elastomer blocks or elastomer cylinders. The compression block types are most often found in the high torque applications. The shear types are shaped to equalize stresses from torque and misalignment.

Torsional softness and torque capabilities are opposite coupling characteristics. A soft coupling tends to have lower torque capabilities than similar sizes of stiff couplings. The softer, lower-torque couplings generally are used on applications that require 100 HP at 2,000 RPM or less. Torque capability increases with torsional stiffness of the flex elements.

The coupling designer must balance the various attributes to achieve the desired coupling for the specific application, or to devise a coupling with broad capabilities as a standard unit that serves many applications. Dual stage torsional couplings can also be obtained. They incorporate two different elements. One is soft for low or idle speed and a stiffer one for high or operational speed.

Some torsional coupling types utilize viscous friction damping This method is found in hydraulic torque converters, which mechanically isolate the driven system from the driver, and transmit torque between them through the motion of a viscous fluid. When a system uses a torque converter, it becomes two separate torsional systems. Torsional vibrations do not pass through the torque converter, except when a lock up device is engaged to mechanically connect the two halves. Hydraulic torque converters are not included in this handbook's discussion of flexible couplings.

Refer to the torsional coupling section and the metallic element section of this handbook for a more detailed description of the couplings used to damp torsional vibration and/or tune critical frequencies. Also refer to the bibliography for more publications on this subject.

Torsionally Sensitive Systems

Torsional vibration problems appear primarily in four types of applications briefly discussed here.

High Speed Machines

High-speed machines have torsional pulses or vibrations at high frequencies, therefore the natural (critical) frequencies must be kept even higher. A discussion about high-speed special purpose couplings and the associated equipment torsional problems can be found in many of the coupling textbooks. They are a sophisticated coupling application, which is not covered in this handbook.

Variable Frequency Drives

The VFD will produce a torsional pulse at low speeds that is larger than those generated at faster speeds. Keeping the operating speed above 10% of the maximum speed, i.e. no lower than 90% below maximum will alleviate the problem in that type of system.

Synchronous Motors

Synchronous motor start-up is a unique situation. At start-up the motor produces torque pulses at a frequency equal to two times the slip frequency. (Slip frequency is numerically equal to full synchronous speed minus operating speed.) The magnitude of the pulse is related to the torque developed by the motor. As the unit accelerates to full speed, the torque pulses drop in frequency reaching zero at full synchronous speed. The torsional vibrations or vibratory torque ceases at that point. A problem will occur if a torsional natural frequency is less than two times the AC power line frequency, as the start-up torque pulse frequency must then pass through the critical frequency. When going from startup to the running speed the driver must accelerate the load through the critical speed quickly. Acceleration through the critical frequency is a function of the torque available from the motor at starting.

High torque synchronous motors will also have high vibratory pulses that need the damping of torsionally soft couplings, but soft torsional couplings have a high vibratory response when passing through the critical speed, as well as difficulty carrying the high torque loads. The relationship between the two functions therefore must be a compromise. The coupling must be soft enough at startup to dampen some torsional vibration energy, but stiff enough to carry the high torque at running speed.

Reciprocating Internal Combustion Engine Drives

There are three main types of engines in common use. They are gasoline engines, gas engines (natural or LPG or propane or other), and diesel engines. Gasoline and natural gas engines are spark-ignited low cylinder pressure types as compared to the compression-ignited diesel engine, which requires very high cylinder pressure.

The diesel is the most efficient of the three so it is very popular for continuous duty applications in those regions of the world that have high fuel prices. Gas engines (Natural, LPG or Propane) are most popular where these gases are readily available or where air pollution is a serious problem like the inner cities.

All internal combustion engines generate a torsional vibratory pulse. The magnitude of the pulse is a function of the cylinder pressure, turbo charging, engine's displacement, internal damping, the engine geometry, and whether it is a two or four stroke engine. The diesel drive rotating system accounts for the majority of the torsional vibration problems due to its high cylinder pressures and resulting high magnitude of torsional harmonic pulse compounded by its widespread popularity. The engine itself is designed to tolerate its internally generated forces from torsional vibration and may include some internal damping. The problems start when these harmonic vibrations pass to the driven equipment. Special attention must then be given to selecting couplings that can help reduce these problems

Diesel drives range from the simple low-horsepower single-unit hydraulic pump to a marine installation in which the diesel will drive the propeller and generators through a gear reducer. The preponderance of diesel drive systems can utilize a simple analysis to select the right coupling, however the marine system should be analyzed by an expert in that field.

While the magnitude of the torsional pulse is important, it is also necessary to know the frequency of the pulse. Like magnitude, pulse frequency is dependent on many factors. Those factors can include the number of cylinders, the configuration, such as "V" or inline, the stroke (two or four) and the firing order.

Also note that diesels typically have several torsional pulse frequencies, established at harmonic intervals. A 6-cylinder 4-stroke inline engine will have major harmonic orders of 3 and 6. Pulse frequencies are the RPM multiplied by the order. For example an engine running at 2100 RPM will have pulse frequencies of 6300 and 12600 CPM. If the natural frequency were also 6300 or 12600 CPM, the engine should not be operated at 2100 RPM. Note the frequency in CPM and speed in RPM is the same units in this case.

If any of the torsional frequencies are equal to a natural frequency the system will vibrate at resonance.

Coupling Selection for Torsional Systems

In addition to the damping possibilities, the coupling is selected with three torque values in mind. The first would be the continuous running torque. The coupling should be capable of handling this torque under all environmental conditions of the applications. The second is continuous vibratory torque. The coupling should damp this torque without a meltdown from heat generation. The third is the maximum torque pulse or peak torque. The pulse occurs as a vibratory response torque at critical speed. The coupling rating is a fatigue life in that case. The manufacturer will publish the torque value at 100,000 non-reversing cycles.

Continuous Running Torque

This is the design torque for the system. Usually it is the driver horsepower and operating speed. That value is normally in excess of the load requirements or is tied closely to the load requirements. Since the coupling also will be judged against peak or maximum transients in the system, a service factor is redundant except for high starting torque. Couplings that are oversized by using service factors can also be too stiff. Elastomer couplings may require derate factors on the coupling capabilities for temperature or frequency or speed. A derate factor is not a service factor. For more discussion on the various torque values found in an operating system see the chapter called "Applications ".

Maximum or Peak and Vibratory Torque

It is important when analyzing the torsionally sensitive coupling application to know the value for the generated vibratory torque. That value becomes the forcing torque that puts the natural frequency into critical resonant vibration. In a diesel drive system the torque pulse is a function of cylinder pressure, number of cylinders, use of turbocharging, number of strokes for firing, etc.
Lloyds Register of Shipping publishes a pamphlet that is a good source of harmonic pulse factors used to determine the harmonic vibratory torque of diesel engines. The engine manufacturers could also provide the information. The manufacturers of other drivers or driven equipment should be able to provide the similar forcing torque values for their equipment.
Once the initial pulse torque is known, it is then possible to calculate the values for the vibratory response.

If the values are plotted on a graph of torque vs. speed, the peak will occur at the critical RPM. All values to the left of peak (below critical) are higher than the initial value. Once past peak the coupling will dampen the vibratory response starting at about 1.4 times critical RPM. Actually there are several damping possibilities in a system, but the damping type coupling is the best bet. Because of the damping, the torque pulse transmitted downstream to the system is reduced from the original value.

The torque pulse transmitted down the system can trigger other forced responses or vibrations. Thus an undamped pulse, like the type transmitted through the stiff coupling system, has the potential to damage downstream components. Loose connections, such as a hydraulic pump spline shaft, are susceptible to this damage unless they are protected. It is also likely that more than one pulse is generated in the operating range. This is very true of diesel engines. All the vibrations must be accounted for if they are in or near the operating range. The Campbell diagram shows the ones in the operating range.

At continuous operating speeds the vibratory torque capability of the coupling must be greater than the vibratory response torque pulse. The damping is energy absorbed by the coupling through hystersis, which results in heat generation. The coupling must dissipate the heat to survive. Its capability to dissipate heat is reflected in the published continuous vibratory torque rating.

The peak torque generated at critical speed must not exceed the maximum torque capability of the coupling. That value is shown in the coupling capabilities as the Tkmax for 100,000 cycles or 50,000 reversing cycles.

Torsional Conclusions

Torsional systems are a special case for coupling applications. Equipment that is driven directly off the diesel flywheel or by synchronous motors should always be given an extended 
system analysis for torsional vibrations.

Go To Next Section - Part 8: Selecting the Right Coupling - Mounting, Alignment, and (Un)Balance
Go Back To Handbook Index

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