The Coupling Handbook: Part VIII

Selecting the Right Coupling - Mounting, Alignment, and (Un)Balance

Mounting the Coupling on the Shaft

In order for the coupling to be effective it must first be secured to the shafts of the connected equipment. There are several ways to do this. Most shafts are cylindrical at the point of coupling attachment, but it is not uncommon to find taper shafts, flanged shafts, polygon shafts, spline shafts and others that the coupling must match. The interface of the coupling hub and the shaft must be able to transmit torque and reactionary loads without slipping, without backlash, without contributing to unbalance and without causing vibration. Therefore, the coupling hub-to-shaft interface is an important part of the coupling design.

Most couplings mount with one of two basic types of interface, either clearance fit or interference fit. In clearance fits, the coupling bore is sized so the shaft will slide snugly but freely into the hole. Obviously, this does not provide meaningful friction so additional devices are needed to keep the hub in place and transfer torque. Interference fits, also known as shrink fits, mean the hub bore is slightly smaller than the shaft, and binds tightly to the shaft by means of the size difference. Both types of fit are discussed below in more detail under "Coupling Attachment and Torque Transmission". Before delving into that topic, it's helpful to understand the basics of shaft sizing. 

Shaft Size

Shaft size is one of the first considerations in coupling selection. Equipment designers, through their trade associations or via common practice, develop shaft standards in the U.S. market. The metric marketplace uses ISO standards for the most part, or JIS standards in Japanese-influenced marketplaces. JIS standards are similar to metric standards. In U.S. standards, the hole-to-shaft fit is expressed on a shaft basis. For the metric markets it is expressed as a hole basis. Shaft basis means the maximum shaft size is basic. Hole basis means the minimum hole size is basic. Basic means that it is the starting dimension to which tolerances are applied. Which one should be used? To quote from the ANSI B4.2 standard "normally the hole system is preferred, however, when a common shaft mates with several holes, the shaft basis system should be used." Most rotating equipment has a shaft that mates with several holes, such as wheels, impellers and bearings as well as couplings. Of course the coupling has to mate with the shafts of two different rotors. Typically the shaft system in the US market is defined by the motor manufacturer through NEMA, by the gear box manufacturer or by the manufacturer of equipment such as pumps or compressors.

On a shaft basis system, if the preferred shaft diameter is 1¼ inches, its maximum diameter is 1.250 inches. The tolerance, if chosen from the motor manufacturers NEMA standard, would be +0.0000 -0.0005. Under these conditions, the acceptable shaft diameter range becomes 1.2500/1.2495 inches. A less precise standard allowing a tolerance +0.000-0.001 would accept a shaft diameter range of 1.250/1.249 inches. The coupling hub bore would take its beginning dimension from the shaft depending on the type of fit being used. It would have a hole (bore) diameter that starts with 1.250 inches, but could be as big as 1.252 inches for a clearance fit or is as small as 1.249 inches for an interference fit. Those coupling hub bores would be defined by a standard such as AGMA 9002-A86 Bores and Keyways for Flexible Couplings (Inch Series).

When the shaft basis system is used in metric measurements, if the preferred shaft diameter is 30mm, its maximum diameter is 30mm. The tolerance (h6 is usually chosen) would be +0.0000 - 0.0130 mm. The coupling hub bore would take its beginning dimension from the shaft, depending on the type of fit being used. For a clearance fit it would have a hole (bore) diameter that starts at 30.000 mm, but could be as big as 30.021 mm (H7). If an interference fit is desired, a P7 hub tolerance is usually chosen. That would result in a hub that is bored to 29.986/29.952 mm. Note that shaft fits are defined with lower case letters such as h6 and bore fits are defined with upper case letters such as H7. The complete description would be 30h6 for a shaft diameter and 30H7 for a bore diameter.

Standard metric coupling hubs are bored, by the manufacturer, to an H7 tolerance unless specified to a different dimension. Other common hub bore tolerances are H6 and P7. They are matched to an equipment shaft that is h6, j6, k6, or m6. The fit of shaft to hub would then depend on the shaft size and would range from clearance to interference. If a specific fit is desired the coupling manufacturer and the equipment manufacturer must agree on the hub bore tolerance. These shaft and bore dimensions would be defined by a standard such as ANSI B4.2-1978 Preferred Metric Limits and Fits or (when available) an AGMA standard.

Coupling manufacturers' catalogs have charts and tables that define shaft/bore combinations for their products. New applications of couplings on newly designed equipment follow the lead of the equipment designer's shaft system and fit requirements. Some difficulty might occur when replacing an old coupling with a new one, especially when the new coupling is a different type or from a different manufacturer.

When facing this situation, first determine whether shaft dimensions are metric or inch type. If measuring with an inch type instrument, leads to a strange dimension, measure again with a metric instrument to see if perhaps it meets a preferred metric size. Nameplates can also provide assistance. It is usually a good bet to assume that the designer used a preferred shaft size, then selected a coupling bore to match. An exception would occur when a shaft has been dressed or repaired.

Shaft shapes other than cylindrical or spline present a problem for coupling selection. The equipment designer and the coupling manufacturer must agree on the applicable standard or the proper interface dimensions. The spline shaft is also a torque transmission device and is discussed later in this section.

Coupling Attachment and Torque Transmission

Several different techniques are used to hold the coupling hub to its shaft, secure against reactionary loads, gravity, speed and/or other forces, and to assure effective torque transfer between shaft and hub. In most cases, the functions are interrelated so we will discuss them together. Although several parts of the coupling system affect the amount of torque transmitted (including the flexible element, the way it is attached to the hubs , and any bolted connections between the hubs). This discussion will focus on hub-to-shaft mounting considerations only.
The capability of the shaft/hub juncture to transmit torque is indicated by the length of hub covering the shaft (called length through bore or LTB) and the ratio hub OD to the bore diameter. The length of hub covering the shaft usually ranges from 0.5 to 1.5 times the bore diameter. This depends on the type of interface, with splines able to use small values and clearance fits tending toward the higher values. The hub OD to bore diameter ratio typically ranges from 1.3 to 1.5. That ratio assures that the hub will not split from the loading.
Over-bored clearance hubs fail from fatigue at the corner of the keyway or at the setscrew hole, whereas over-bored shrink fit and bushing-type hubs will split in the process of mounting on the shaft. Sometimes a larger bore (smaller ratio) is safe when the torque is low in relation to shaft diameter. It is best to have the coupling manufacturer check the stress levels on all over-bored specifications.

Most industrial applications use keys to transmit torque from shaft to coupling hub. The number and type of coupling hub keyways vary widely. A single square keyway is most popular on industrial coupling applications up to 6.5 inches diameter, a rectangular key is used on larger bores. Woodruff keys are used on small-diameter shafts. Woodruff keys are thin and have a circular keyseat in the shaft. Two rectangular keyways are also used on very large hub bores. Polygon shafts, D shaped shafts, square shaft ends and hexagonal shafts can all transfer the torque directly to the hub without keys. They are chosen by rotating equipment designers for many reasons including ease of assembly and ease of maintenance.

Clearance fit hubs with keys commonly use a setscrew tightened radially against the key to hold both key and hub in place. In clearance fit hubs used without keys, the setscrew is usually tightened against a flat seat machined into the shaft circumference. Dual setscrews, placed one over the key way and one around the circumference of the shaft in the same axial plane, improve the effect of limiting backlash and holding the hub tight to the key under stop-start conditions. The clearance fit with setscrews generally can be used on shafts up to 4 inches in diameter. In applications with round shafts and no keys, splines or setscrews, torque transmission from the shaft to the coupling hub relies on friction. One frictional method used on some small or low torque devices is the axially split hub drawn together with clamping screws. Another method used on high torque transmission applications is a clamping ring or a
shrink disc. These are described in a following section.

Interference (shrink) fits offer a third method for securing the hub to the shaft. They are used with gear and disc and other high torque couplings on both straight and tapered shafts. Interference fits are used with keyed shafts and heavy shrink fits are used with keyless shafts. For keyed fits the torque is transmitted by the key. The friction resulting from the interference keeps the hub in place when subject to various loads such as reactionary forces. Shrink fits involve heating the hub to expand the bore so it will fit over the shaft, then letting it cool and shrink into a secure grip. The temperature differential used for shrink-fit installation usually ranges from 200°F to 400°F. It can be calculated at 160°F per 0.001 inches of shrink per inch of shaft diameter plus 50° to 75°. Differential here refers to the relative temperatures of hub and shaft. Shrink fits are also accomplished by using hydraulic force to expand the hub and slide it on the shaft.

Shrink fits with keys to provide torque transfer use a shrink of 0.003 to 0.00075 inches per inch of shaft diameter. Shrink fits without keys, which rely solely on the fit friction to transmit torque, use shrink rates of 0.0015 to 0.003 inches per inch of shaft diameter. Known as a heavy shrink fit, the keyless type offers an obvious advantage for applications where balance is important. It should also be noted that heavy shrink fits are used with hub materials of sufficient strength. Consult the coupling manufacturer when contemplating this type of fit.

The tapered shaft uses an interference fit. It can be the keyed type or the keyless type. For light interference it is accomplished by pushing a hub (with a matching tapered bore) on to the tapered shaft until the desired interference is reached. The hub can be pushed onto the shaft using a end plate and nut. Medium interference will require that the hub be heated to be installed as the friction can not be overcome otherwise. Heavy interference requires heating or hydraulic force. The hydraulic force expands the hub and pushes the hub onto the shaft. The end plate and bolts or nut will serve to prevent axial movement under loads. Tapered shafts are used for ease of maintenance. A popular tapered shaft device is the mill motor that uses a standard tapered shaft with key.

Shaft Locking Devices: Bushings, and Shrink Disks

Shaft locking devices can use a combination of friction and keys to transfer the torque from shaft to coupling hub. Shrink discs are more popular in metric applications, but are growing in use on inch applications. All these devices were developed to make the attachment of the coupling hub to equipment shaft easy while still transmitting the proper torque. The devices also prevent fretting, wobble, sliding, and backlash in the hubs.

When extra bore capacity is available, the coupling can use a tapered bushing. When a bushing is used, the shaft size capability of the hub is reduced because the bushing takes up some of the hub's bore space normally available for the shaft. Since the hub must maintain the hub OD-to-bore-diameter ratio range of 1.3 to 1.5, adding a bushing makes the hub-OD-to-shaft-diameter raise to a range of 1.9 to 3.0 and sometimes more.

Bushings require that a taper bore be machined into the hub. The taper can be in either direction depending on the installation. The bushing, essentially a split ring with a matching taper, is inserted from the wide side of the taper and drawn into the bore by setscrews or cap screws threaded into the hub. As the bushing moves into the tapered bore, the taper forces the split halves of the bushing together, which clamps the bushing tightly to the shaft and wedges it into the tapered bore of the hub. Torque is transferred by friction from shaft to bushing to hub. Setscrews and cap screws are tightened to a specified torque value.

There are external and internal frictional locking devices that use opposing tapers to develop radial forces that lock hubs to shafts without using keys. The devices can be installed and removed without heat, are free of backlash, do not require a taper bore in the hub and are able to transmit high torque. The devices are locked to the hub and shaft until deliberately released.
They are commonly called shrink discs, locking assemblies, locking elements or clamping bushings. Shrink discs and clamping bushings are external hub locking devices.Locking assemblies or locking elements are internal devices mounted into a counter bore in the hub. Both use built-in opposing tapers or inclined planes as the means to squeeze the hub onto the shaft or to expand into an internal locking position between the hub and the shaft. The locking assembly is activated by cap screws that are tightened to provide an axial load which then becomes a radial pressure between hub and shaft. Another version uses hydraulic pressure to activate the locking force.

The dimensions of the hub are modified to allow the device to work properly. The devices are a self-contained part that is added to the basic coupling. The hub must be checked to determine if it is strong enough to accommodate the device at the expected torque transmission values.

Flywheel Attachments

Couplings used for diesel engine applications mount on the engine flywheel. This can be accomplished by either attaching the hub to a flat plate or by making one hub in the form of a flat plate. The plate thickness is designed to transmit the required torque from the flywheel to the coupling. The plate has a pilot OD and holes of the proper size on a bolt circle that matches the engine flywheel. These are in accordance with standards for the dimensions on flywheels that were originally made for use with mechanical clutches. The more popular standard in North America and Europe is the SAE flywheel standard J620d.

Misalignment on these applications is usually limited to a tolerance stackup of the connected parts, all of which are attached to the engine block.

Some OEM applications involve enough production quantity to justify having the flywheel and the coupling hub matched to each other. In these cases the flywheel is not dimensioned for a mechanical clutch, but is sized for a specific inertia. The coupling hub has bolt holes that match a set of holes on the flywheel eliminating the need for a mounting plate or a special plate type hub.


Splines can be considered as parallel keys cut axially around the end of the shaft, which fit into corresponding grooves, or teeth, cut axially inside the bore of the coupling hub. Their big advantage is ease of assembly, even blind assembly. The spline is used to locate shaft and hub with respect to each other, and to transmit torque from one to the other without intentional relative motion or intentional misalignment. Splines can be involute tooth or straight-sided teeth. Splines are also flat root or fillet root.

Involute teeth are considered to have greater torque carrying capacities than straight-sided teeth. Spline involutes can have 30°, 37½°, or 45° pressure angles (PA), with 30° by far being the most common. That pressure angle is chosen for strength of tooth as well as manufacturing considerations. The pitch diameter (Pd) is usually dictated by the geometry of the parts to be assembled, such as the shaft OD. Many teeth rather than fewer teeth ensure multiple tooth shaft-to-hub contact under load. Splines utilize seventeen specific pitches from 2.5 to 128 teeth per inch of pitch diameter. Pitch is designated with a numerator and denominator such as 4/8 with the ratio for spline pitches as 1 to 2. This means the spline tooth is one-half the height of a standard gear tooth. Under this system, splines always have stub teeth that allow easier assembly. Spline tooth length, on the shaft, is a function of torque-carrying needs and tooth contact. Full contact of all teeth normally would allow a length equal to 1/3 the Pd. Only 50% contact can be counted on, so to ensure sufficient torque-carrying capability, the effective length usually is 2/3 the Pd and can equal the Pd. For comparison, a key-driven shaft-to-hub assembly usually uses a key length of 1 to 1½ times the shaft OD on clearance fits.

Splines are usually slide fits and can be locational as side fit or major diameter fit. Some machine tool and automotive splines fit on the minor diameter because grinding equipment more easily accesses that diameter. These are usually SAE straight-sided splines.

Splines have 4 tolerance levels, designated Class 4, 5, 6, and 7 with Class 5 considered as the base. The hub spline is usually a class 5 tolerance, while the external spline (shaft spline) is modifiable across the other tolerance classes. While these tolerances effect the precision of the teeth they do not dictate the fit between two pieces. Splines have major diameter fits that are always loose. Depending on the shaft spline tolerance the hub will be very loose or tight, but not line to line or tighter. Hub splines always have the same tolerance. Torque is always transmitted side to side between teeth. All tolerances are fixed so that the spacing between the teeth and the width of the teeth are equal at the maximum tooth and minimum space. The shaft is always supposed to fit into the hub no matter the tolerance match.

Splines present a problem for holding the hub in place because their normal tolerances tend to promote axial hub movement and backlash, which can destroy the spline profile, stress other system components and reduce operating efficiency. There is a need to limit axial movement and backlash movement. A collar and/or a snap ring might be used to limit axial movement. Setscrews are used, but tend to cause the shaft spline to be scored, distorted or otherwise damaged. Spline hubs can use the split hub clamping technique described previously, or other proprietary methods.

Coupling Alignment

The coupling should never be the basis for allowable misalignment because it can accommodate far more misalignment than can be tolerated by the other connected pieces of equip. The coupling may have ten times the capability for misalignment that can be tolerated by the rotating equipment. System alignment should be based first on the minimum requirements of the driven equipment, or the driver, and then the coupling.

It is always important that the equipment be aligned as close as possible, keeping within the economics and sophistication of the system. Misalignment is a leading cause of bearing and seal failures, vibration, oil leakage from bearing frames, broken shafts and coupling failures.

Planes of Flexibility
We could look at the plane of flexibility as pivot points within the coupling. A full flex coupling has two pivot points with one attached to each of the connected shafts. A coupling with a pivot point on one side and a rigid shaft attachment on the other is called a single flex, flex rigid, or half coupling. Note that the pivot point can be in the loose fit between separate parts, such as the hub tooth to sleeve tooth interface in a gear coupling, or in the bending of a continuous flexing element such as used in disc or diaphragm, or link coupling. The flex plane of an elastomeric coupling is within the elastomer itself. For other types of couplings you should refer to the literature, as no two coupling types are alike.

There are three variations to shaft misalignment. They are parallel offset (radial) misalignment, angular misalignment and the combination of angular and parallel offset. Axial displacement is considered a form of misalignment that the coupling may need to deal with.

Radial or Parallel Misalignment

Parallel (radial) misalignment occurs when the driving and driven shafts are parallel, but with some offset between their axial centers. Accommodating such offset requires either a full flex coupling (with two flex planes) or two single flex couplings in series. In either case, the greater the axial distance between the two flex planes, the greater the coupling's parallel (radial) capability. Typical full flex couplings include gear, grid, and dual element disc or diaphragm types. Spacer couplings are good for extra radial displacement and close-coupled couplings such as a standard flanged sleeve gear coupling provide the minimum. Spindle couplings and floating shaft couplings provide the maximum capability by further spreading the flex planes. Although the elastomeric type has only one flex plane, the elastomer can distort enough in some cases to provide significant parallel offset capability if it has sufficient resilience. Elastomeric couplings can also be made as spacer or floating shaft types to a limited extent.

Angular Misalignment

Angular misalignment occurs when the axial centers of driving and driven shafts intersect. Flex-rigid or half couplings provide only angular misalignment, because there is only one flex plane. Single element disc or diaphragm couplings provide for angular misalignment only. Single element couplings are used on three bearing systems and on one end of floating shaft systems.

Axial Displacement

Axial misalignment or in-out movement is often associated with thermal shaft growth and floating rotors. Thermal growth is the result of high temperature in the rotating equipment causing an unconfined growth along the length of its shaft. Sometimes a thrust bearing at the coupling end of the shaft will direct axial movement or growth away from the coupling, but sometimes the thrust bearing is at the other end of the shaft. The location of a thrust bearing is a factor in the determination of axial containment. Another well-known source of axial movement is the rotor that seeks its magnetic centers. The coupling must either accommodate axial movement or contain it by transferring the thrust to the bearing system of the rotor. Those that contain it are called limited end float couplings. Sometimes axial thrust is deliberately transferred to another machine through the coupling. Limited end float may or may not be invoked in such a case.

Gear couplings exhibit the best capability to handle axial misalignment or movement. In the gear coupling the hub teeth are free to slide axially within the sleeve while in mesh. Axial displacement is available from either the full-flex or the flex-rigid unit. The amount available depends on many factors, and in fact specials are available for long sliding applications. Gear couplings can be made to limit end float with the addition of a plate and/or button between the coupling halves. The elastomeric coupling is not very tolerant of axial displacement.
Other types such as the diaphragm coupling can flex or stretch to allow some axial displacement. The disc coupling can also, but to a lesser degree than the diaphragm coupling. In both the disc and the diaphragm coupling, axial movement is met with resistance that increases as the displacement increases.

The elastomeric coupling is not a good unit for axial float or axial displacement. Sometimes the unit can slide in one direction, but there are no limiters that stop the slide and the coupling disengages. In other types of elastomeric coupling axial distortion would overload the elastomer when combined with normal misalignment and nominal torque transmission.

Misalignment Comparison by Coupling Type

The coupling manufacturers' full line catalog is a good starting point for a comparison of misalignment capabilities. Coupling misalignment is usually given in terms of angular misalignment that can be converted to radial or parallel when two flex planes are used.
The conversion of angular to radial misalignment capability is a matter of plane geometry. The radial offset distance is the product of the tangent of the angle of misalignment and the distance between flex points.

In the case of elastomeric couplings, where parallel offset capability results from distortion within a single flex plane, parallel capability is listed in conjunction with the angular.
It is true that misalignment, torque capabilities and coupling life are intertwined. The torque capability of a coupling is reduced when the coupling is misaligned. The reduction in life can come from higher wear and the reduction in torque from high fatigue forces. Misalignment will cause fatigue forces. Some manufacturers publish their torque ratings as a maximum value and require that the user de-rate by some factor to determine usable nominal torque. Others publish their torque ratings at rated full misalignment. When the coupling is selected it should be able to carry the nominal torque while misaligned per the application.

Gear couplings are capable of 1½° of misalignment per gear mesh, although the gear coupling needs some misalignment to push the lubricant to the friction surfaces of the teeth. With tooth modification that misalignment can be increase to as much as 6°. At that much misalignment you may decide to change the pressure angle to strengthen the tooth. That would be the method for spindle couplings. High-speed gear coupling units might be reduced to ¼° per mesh.

Other metallic element flexible couplings have a wide range of angular capabilities. The flexing link coupling is suitable for 6° while the torsional spring coupling can be used up to 4½° of angular. Published data for the disc and diaphragm coupling types range from ¼° to 1°.
The elastomer couplings such as the jaw types and the unclamped donut elastomer in shear type couplings are limited to 1° or 1½°. Donut type elastomer couplings are suitable for 3° of angular misalignment.

The coupling manufacturers' catalog or published information should always be consulted for actual values of misalignment and torque derating requirements. Misalignment capabilities and torque capabilities are interrelated.

Acceptable Misalignment

A high speed, high power system requires close alignment, general-purpose equipment is aligned to a looser specification. For example high speed equipment (running at 3000 RPM or more), needs alignment to .0005 inch (or better) per inch of flex point separation. General-purpose equipment can be acceptable at .001 inches per inch of separation. Smaller values will improve the operation but should be consistent with the equipment manufacturer recommendation.

The preceding recommendations are usually used with "close coupled" equipment. When 
spacers and floating shafts are chosen for the ability to allow radial displacements of two pieces of equipment, these rules of thumb would not necessarily apply.

It is sometimes necessary to have large amounts of parallel displacement built into the equipment installation. Special design alterations to the couplings and the connected equipment can also be required in those cases. The drivers and driven equipment must have sufficient design strength to deal with the increased reactionary load. Equipment with spacer couplings or even floating shafts may be designed for ease of maintenance rather than for the increased misalignment capability that would be possible. In such situations, always remember that acceptable system misalignment is still dictated by equipment capabilities, not the coupling's ability to withstand the misalignment.

Exceeding acceptable misalignment contributes to vibration problems. Severe misalignment will impose a heavy vibratory force on the equipment. Large amounts of parallel misalignment are acceptable only on machines operating at slow speed. High-speed machines, even those with spacers and floating shafts must be aligned closely to limit the vibration and the reactionary loads.

Reactionary Loads from Misalignment

Shaft to shaft misalignment causes couplings to impose reactionary loads on the connected equipment. The greater the misalignment the greater the reactionary load. Different types of couplings produce different reactionary loads.

In gear couplings, reactionary forces result from the sliding friction of the tooth to tooth movement. The sliding friction is considerable when dealing with metal-to-metal contact. There is some lubricant but it is a very thin film.

When a gear coupling is misaligned, the friction or drag forces become a bending moment on the system. The bending moment reactionary load can be 10% of the value of the torque transmitted. At that value it is many times the reaction load of a disc coupling.

Disc and diaphragm couplings utilize the flexing of thin metal elements to handle the misalignment, both angular and axial. The thinner the element the less force it takes to bend the metal. The force to bend becomes the force of the reaction in the classic physics truth about equal and opposite reaction forces. Link couplings and spring couplings also provide a reactionary force in proportion to the loading force.

Elastomeric couplings exhibit different kinds of forces depending on the type of coupling. Elastomeric couplings in shear will impose a thrust (axial) load on the adjacent machine parts. Distortion of a elastomeric donut or misalignment in a jaw coupling will impose a bending moment. Tire type couplings exert a thrust load also as the centrifugal force acts on the tire. Reaction forces in the elastomer coupling are a function of the resiliency and may also have some friction components. The friction is not unlike the sliding of gear teeth and occurs on couplings like the jaw units.

The reactionary loads include the weight of the coupling. Because weight usually reflects size, the more power intensive couplings (those with higher torque capacity for smaller size, such as gear couplings) will have the advantage of lower reactionary forces at comparable torque loads. Large size couplings, (less power intensive types) may also be made from light materials to reduce their weight and their inertia.

The loads imposed by the coupling are related to the point of loading. The pivot point or flex plane is the location of the loading for the coupling. Those couplings that move the pivot point closer to the next available bearing are termed "reduced moment" couplings, because they reduce the reactionary load imposed on the bearing. After all it is the machinery bearings that ultimately carry the extra loading.

Alignment Occurs at Installation

Alignment is accomplished at the final installation point of the equipment. Alignment is done when the coupling is installed. Equipment can be aligned when the driver and the driven equipment is assembled at the manufacturer, however the alignment still must be checked and likely adjusted at the final installation.

When aligning the coupling, the installer must take into account the conditions affecting the rotating machinery. Not only is it important to understand where the equipment is at standstill, but also it is important to know where the equipment will move when in operation. For example, hot operating equipment grows when it is brought up to operating temperature. The coupling is aligned cold at one location with the expectation that movement will bring it to closer alignment. The initial cold alignment should be within the coupling and rotating equipment capabilities. Sometimes the determining the position of the rotating equipment at operating temperature is the most difficult part of alignment and installation.

A motor rotor will seek its magnetic center causing a thrust that must be transmitted through the coupling to the next thrust bearing. That axial displacement is a misalignment problem for the equipment.

In addition to temperature considerations the rotating equipment alignment can be affected by tolerance stackup, pipe loading, the foundation and conditions such as bent shafts or soft foot. Before aligning the equipment it is best to check for those occurrences.

Alignment can be measured by use of a straight edge and feeler gage (or calipers or taper gage). That would be the simplest method, but the least accurate. Dial indicators are used with the reverse indicator and the face and rim method. The most modern method uses a laser alignment system. Each method has its strengths and weakness and all can be satisfactory depending on the skill of the installer.

There are many books and papers written on the "how to" of alignment. Some are listed in the bibliography. The reader should see those for details of alignment. The following paragraphs are for the purpose of general descriptions of the processes.

Methods to Check Alignment

Straight Edge and Taper Gage Alignment

A straight edge is used to determine the shaft offset by eye. It is used for both vertical and horizontal planes. The taper gage (or calipers or feeler gage) is used for angular misalignment. The shaft separation or "BSE" dimension is measured with a ruler. It is a trial and error process.

Dial Indicator Alignment

Dial indicators are used with the reverse indicator or the face and rim method. The dial indicators are mounted on the shaft opposite to the reading to be taken. These indicators are accurate to ± 1 mil.

In the reverse indicator method, readings are taken from coupling hub on shaft "A" to the rim of the coupling hub on shaft "B". A second set of readings are taken from the coupling hub on shaft "B" to the rim of the coupling hub on shaft "A". Both sets of readings are plotted on graph paper or become the input to a personal computer program. With the proper calculations in plane geometry, the misalignment of both parallel offset, and angularity of the shafts can be determined.

The face and rim method uses the dial indicator mounted on one coupling hub to take readings on the face and the rim of the second coupling hub. Again with graphical plotting or a computer and plane geometry the misalignment of both types can be determined.

This method can be very accurate if done with graphical assistance or computer assistance. Other commercial mechanical and electrical devices can obtain the results by measuring the positions of two shafts.

Laser Beam Alignment

Laser beam alignment uses the laser to replace the dial indicator. It is a little more accurate, but is much more costly. Included with the laser package is the means of direct input to a computer program that calculates the moves necessary to align the equipment. Lasers are accurate to ± 3 micron or better.

The laser is a light beam that is very narrow and focused. The beam generating equipment is mounted on the equipment shaft and aimed at a device on the opposite shaft. The device can be a reflector or can be the photodiode target cell that will generate a voltage. The amount of voltage that is generated will depend on the position of the light beam as it hits the cell. A reflector will cause the beam to return to a target cell that is mounted with the laser generator. The generated voltage becomes the input to a system that calculates the misalignment and needed corrections.

Alignment Conclusions

Proper installation and alignment procedures are included with the installation instructions of rotating equipment and couplings. Often the coupling manufacturer can provide further guidelines for installing the coupling and aligning the rotating equipment. There are many published papers and pamphlets on the subject. High speed high powered equipment often is ordered with the services of installation start up supervision from the manufacturer. That service is well worth its extra cost. Also there are many companies within specific industries that provide alignment service.

There are many combinations of angles and spacing which can be calculated by plane geometry to obtain the ideal situation for an application. Always keep in mind that equipment should be aligned to the rotating equipment manufacturers' standards and requirements, not the coupling manufacturers. When operating misaligned, the coupling can transmit reactionary loads and vibration that are within the coupling capabilities, but not the equipment capabilities.

Coupling (Un) Balance

Balance in any rotating system is important because without it the system vibrates. Vibration in rotating systems invariably results in problems ranging from premature wear to severe damage and failure in all parts of the system. But perfect balance is not achievable, so instead we talk about how much unbalance is acceptable. The rotor designer and rotating equipment specialist determines the amount of acceptable unbalance. There are standards to help them. The standards have been developed through empirical data generated over years of service conditions as well as design and testing.

Vibration can occur in lateral, torsional or axial directions, but only lateral vibration involves coupling unbalance so the others will not be discussed here. Lateral vibration refers to sideways movement (radial, or perpendicular to the axis of rotation). It occurs regardless of whether the axis is vertical or horizontal. Reducing the rotor unbalance is an important method of reducing vibration.

Because coupling unbalance forces contribute to vibration, reducing coupling unbalance can be an important means of preventing these kinds of problems. But we cannot discuss coupling unbalance without first understanding a little bit about the relationship between vibration, unbalance, and critical speeds.


Vibration is cyclic force acting on the rotor. One of the causes of lateral vibration is an unbalanced mass within the rotor, the coupling or both. Other forces that are vibratory in nature include vane passing frequencies, misalignment, gears meshing, external system variations, pressure pulsation, and internal machine functions. Coupling unbalance can be a serious contributor to vibratory forces for two reasons. First, the coupling is overhung outside the bearings where the shaft might be more vulnerable to unbalance forces. Second, the coupling might be added later in the application without the benefit of being balanced to the same standards as the rotor. Coupling and rotor unbalance can be corrected by manufacturing process or by utilizing a balancing machine. Other vibratory forces should be minimized or damped by the equipment system.

Unbalance, where the center of mass of the rotor is not the same as the center of rotation, causes the shaft to whirl as it rotates. The force from the unbalance mass increases with increasing speed.

The unbalance force is equal to:

F = 1.77 x (RPM/1000)^2 x U
F = the unbalance force in pounds
RPM = operating speed in revolutions/minute.
U = the unbalance in ounce-inches

A 50-pound coupling with center of mass .002 inches from its center of rotation has 1.6 oz-ins of unbalance. 1.6 oz-inches of unbalance at 1800 RPM are 9 lbs. of untamed force. That same unbalance at 3600 RPM becomes 36 lbs. of force. It shows as vibration and wear on the rotor bearings. A .004 TIR on the bore concentricity would displace the mass center by .002 inch. 

As the system rotates, the combined unbalance of the rotor and coupling causes the shaft to deflect or whirl. The system tries to rotate about its mass center rather than its shaft centerline. The magnitude of the unbalance forces increase as shaft RPM increases, and at some point, these forces become strong enough to seriously damage the bearings and/or fatigue the shaft. Still higher magnitudes can cause the machinery to jump around (or try to), and that will lead to fatigue failures in machine housings and moorings. A severe unbalance will impact the rotor and bearings at virtually any speed and must be avoided. The cyclic forces are always present, and will cause a vibratory response. That vibratory response will be reflective of the ratio of running speed to critical speed. At a ratio of 1:1 the response is infinite and resonance occurs.

Critical Speed

All systems, including the rotating shaft with one half of a coupling have at least one lateral natural frequency. When this frequency (in cycles per minute) matches RPM, it may also be called the critical speed. The critical frequency or speed is defined as the point where the kinetic energy of the rotating masses equals the potential energy stored in the shaft acting as a spring.

The natural frequency becomes a critical frequency, which is resonating, when an external force is applied cyclically at the same frequency. Since the system is rotating at this frequency or RPM, there are many available forces to trigger resonance. Since the system must be triggered or forced, it is called a forcing frequency. At resonance the system could fly apart.
The lateral natural frequency is a function of the deflection of the shaft and the masses attached. The amount of deflection (amplitude) at any point along the shaft will depend upon the location and weight of rotor attachments, length of shaft span, shaft overhang, diameter of shaft, and material stiffness. Shafts with relatively large diameters and short spans don't deflect much, and so are termed "rigid rotors". While we would like all rotors to be rigid, it may not be possible for economic or geometric reasons. Shafts with smaller diameters and larger spans deflect more, and so are termed "limber rotors". 

Generally the more rigid the rotor, the higher the lateral natural (critical) frequency. It will take a greater force to cause deflection. The more limber the rotor, the lower the natural (critical) frequency will be. Because of all the variables involved, lateral vibration can become complex. There may be more than one point of deflection along the shaft, both between the bearings and in the overhung portion, and thus more than one natural (critical) frequency. So, the terms rigid and limber have roots in flexibility just like they do outside of engineering.

Another type of critical speed is the self-induced critical speed that is caused by unbalance. The deflection from the unbalance forces increases with increasing speed until the critical frequency is reached. This frequency is the same value as the natural frequency of the shaft system. At this point the shaft will whirl like a child's jump rope. This critical and the response is self-induced by the unbalanced mass, as opposed to the lateral frequency that needs to be triggered by external forces. Unbalance does not change the natural frequency or the critical frequency of the system. It does add another force to the system. The added force can be large in comparison to other forces. The unbalance force can be reduced by efforts to balance the rotor and the coupling as opposed to trying to dampen the forces.

When the lateral critical frequency and the self-induced critical frequency are equal to the operating or forcing frequency (operating speed) the vibratory response is infinite and the system resonates (vibrates out of control). Note two different effects are happening at the same time. One is the natural frequency being forced by an external trigger, and the other a induced force from the out of center mass. The combined effect is disastrous to the system. There are two solutions to the problem. The first and obvious one is to always operate the system below the critical speeds. The second would be to operate above the first critical and below the second critical. The driver must have enough torque to accelerate through the critical very quickly, the unbalance must be very low and the forcing or trigger forces must be damped in order to pass through without incident.

Rigid rotors, with deflection so slight as to approach zero, have natural frequencies so high that normal operating speeds typically don't come anywhere close to critical speeds. These are usually rugged, slowspeed systems such as found in mill applications. They are not affected by adding a normal amount of coupling unbalance. Limber rotors and rotors with overhung loads are more likely to have natural frequencies uncomfortably close to their normal operating speeds. These are often found in multistage pump compressors and other equipment that operates at speeds of 3000 RPM or higher.

The term "sensitive" is used to identify systems in which adding coupling unbalance can adversely affect rotor unbalance. For example a relatively light coupling mounted on a rigid (stiff) rotor is not a sensitive situation. On the other hand a relatively heavy coupling mounted with a long overhang to the first bearing, with an overhung machine load and operating at a high speed (close to critical most likely) is a sensitive situation. Everything else is in between.
Typically the lateral critical speed calculation for each piece of rotating equipment is calculated by its manufacturer. This means that critical speeds for driving and driven equipment are calculated separately. For this reason it is common practice for the rotor manufacturer to consider one-half of the coupling as a part of the rotor for purposes of critical speed calculation. The coupling manufacturer could calculate the critical speed of the spacer piece or floating shaft in the center of that type of coupling. To determine the critical speed of the complete equipment train is a complicated issue, well beyond the scope of the coupling supplier.

Issues for Coupling Balance

The coupling is an integral part of the rotating system and, as a part of the system, it must be balanced to the same criteria as the other elements of the system. The coupling cannot be the balancing device to solve problems in these two systems, but neither should it be the unbalancing device.

Balancing is an expensive option for the coupling and possibly the system. It usually does not pay to put severe unbalance restrictions on a coupling, unless it is a coupling for a high-speed sensitive rotor. In those cases, reducing the couplings vibratory forces due to unbalance is usually worth the expense, because those forces increase by the square of the speed. A doubling of the speed increases the force by four times. High-speed equipment therefore has more reasons to include strict balancing criteria. Long floating shaft couplings should also be considered a candidate for a critical speed check, and if necessary, a more strict balancing criteria.

Sometimes vibration can be damped with bearings, bushings or fluids (in the case of pumps). However, even with some damping and good balance criteria, the rotor should never be operated near a lateral critical speed.

In equipment with sensitive rotors, it's the rotating equipment designer's responsibility to keep the bigger picture in view. The couplings should be selected not only for size and torque/misalignment capabilities, but also for the more subtle criteria of weight, balance, moment arm, spring stiffness and reactionary loads.

Coupling balance should be accounted for at the onset of the equipment selection and design. If a machine begins vibrating after operating smoothly for a period of time, it is not because an unbalanced coupling suddenly came to light. The first suspect in that case would be the alignment which should always be checked first. Second, find out what changes occurred between smooth operation and vibration. It is important that all changes be accounted for in the system. There is also a good chance that something has become worn or has broken. Discovering the problem could be so costly in time and resources that commissioning a vibration analysis could be cheaper in the long run. Don't assume that reducing a coupling's unbalance will solve the problem by itself.

Balancing the Coupling

Good coupling balance originates in the design and manufacturing stages. As a practical matter, however, all standard couplings are manufactured with a certain amount of unbalance called "inherent unbalance". The final exact unbalance of the coupling will be related to this, but cannot be determined until each half of the coupling is ultimately mounted on a rotor shaft that, in effect, becomes part of that half of the coupling.

The amount of unbalance permitted in new couplings is a matter of tolerances applied at the factory and balance categories selected by the coupling manufacturer or the coupling specifications provided by the system designer or user. AGMA, ISO and API have developed standards for coupling balance.

Each coupling has a unique potential unbalance resulting from the displacement of the center of mass with respect to the center of rotation. Displacement of mass can occur by non-uniform density of the material, by non-concentric shapes, non-symmetric geometry such as keyways or by machining tolerance stack up. Elastomeric couplings have the problem of parts that change shape under load and at speed, which has the effect of mass displacement

To understand the causes of mass displacement, envision the coupling as a perfectly shaped cylinder on its side. Each end is a perfect circle, the top and bottom sides are straight lines of equal length, and the cylinder is solid with uniform density throughout. This cylinder would have a center of mass in the horizontal direction that is a line lengthwise through the geometric center of the cylinder. If we attach a perfect axle to each end of the cylinder exactly in the middle of the end circle, we could then rotate the cylinder on that axis with no unbalance forces. The center of rotation would be coincident with the center of mass. All centrifugal forces resulting from rotation of the mass particles would be equal and opposite in a radial line from the center.

The perfect cylinder described above cannot be practically achieved. The material, if a casting, would very likely have internal voids or spots of high density. Our axles, as represented by the coupling's shaft bore holes, would not be placed exactly in the geometric center of each end and coincident with each other. Instead, each would be slightly off center by a tolerance normally allowed for manufacturing capabilities. With these bores not exactly concentric with the outer wall of the coupling cylinder, there is now more coupling mass on one side of the shaft than on the other. Because the shaft is the center of rotation, the side with more mass will generate a higher centrifugal force than the other side, resulting in an unbalance force, or vibration.

In our perfect cylinder the end circles were perpendicular to the side walls. Again, manufacturing tolerances would allow the ends to be somewhat skewed. That means one side of the cylinder is longer than the other side. The long side has more mass so our mass center is not at the geometric center anymore and possibly even further from the center of rotation as defined by the axles. That means more out-of-balance centrifugal forces.

If our cylinder were made up of many pieces bolted together, as many couplings are, every bolted joint would have the potential to displace the center of mass with respect to the center of rotation. That is because the bolt holes have a clearance with respect to the body of the bolt, the bolt holes are not perfectly placed on the bolt circle and the bolt circle is not perfectly concentric with the center of the part. More mass displacement will occur.

Every piece of the bolted-together cylinder would have its own manufacturing tolerance that would stack up and cause the center of mass to be different from the center of rotation. The unbalance forces they create would be spread all around the center of rotation, some canceling each other out and others reinforcing each other. With good luck all forces would be equal and opposite and cancel each other out. No unbalance forces would exist. Of course the situation with the greatest chance is that there will be a net residual non-canceled force called unbalance.

When the coupling is assembled, our cylinder will also become longer along the axis compared to the diameter perpendicular to the axis. That complicates the unbalance, and is of special concern with spacer type couplings. Our opposing forces are no longer in line with each other so they become a force couple rather than canceling each other out. In
effect we have two unbalance forces acting on the coupling one at each end of a long span. The vibration becomes complicated.

These special concerns regarding multi-piece bolted together couplings emphasize the importance of match marking the coupling. Match marking allows the parts to be put back exactly where they came from when disassembling and reassembling the coupling for maintenance. Thus eliminating the chances of introducing more unbalance into the system.

The best way to resolve the balance issue calls for design of the coupling parts with low manufacturing tolerance consistent with cost and with the application requirements. The design and manufacturing features for good balance include bores and cylindrical surfaces that are concentric with the center of the coupling, hub faces that are perpendicular to the center line, and bolt circles that are true positioned. The design can also include pilot fits to place the components in the proper plane. Bolts and bolt holes can be tight fits too. Some applications allow for high-cost couplings that have tighter tolerances and fits. On those high cost special couplings everything including the weight of individual bolts, the keys, and the keyways must be accounted for. Remember that the unbalance force is a function of speed, so that the need for tighter tolerances to minimize unbalance is more important for high speed rotors.

Balance Machine Balancing

While close attention to design and manufacturing can result in very low unbalance forces, it is sometimes necessary to fine-tune or further reduce the coupling unbalance. This is done by adding or removing weights (mass) equal and opposite to the unbalance, as directed by the use of balancing machines. The balance machine is not a substitute for good design practice and manufacturing tolerances. It can provide about 5% to 20% adjustment on the balance built into the coupling through design and manufacturing. Some couplings also include devices that can adjust the unbalance once the coupling is mounted on the rotor. This is called trim balancing, and is used on couplings for very high speed or sensitive rotors.

The coupling manufacturer talks about single plane and two plane balancing, static and dynamic balancing, or spin balancing. Let's examine these terms.

Static balancing consists of placing the part with its shaft on knife-edges so that the heavy side rotates to the bottom. By trial and error one can place weight or remove weight to the point where the piece no longer rotates to the "low side". This is a crude method, and seeks to compensate for unbalance as a single point in a single plane of rotation.

A more sophisticated method is to spin the coupling on a turntable or between two bearing supports, with either device spring-loaded so as to be displaced as the heavy side passes, and instrumented to report the amount and location of the unbalance mass. Turntables are single plane units used for testing full round coupling components whose diameter is equal to or larger than the parts axial length, such as hubs, flanges or collars. A dual bearing balancing machine is used for testing coupling assemblies in which axial length may exceed diameter. The two-plane approach is needed to account for the unbalanced-mass "couples" that are formed on long parts as mentioned earlier, which do not cancel each other out but act independently on whichever end of the coupling is closest.

Mounting the coupling or the coupling part on the balance machine is an art in itself. The arbor, mandrel or shaft substitute could be "unbalanced" and must be accounted for in the balance work. The coupling has to be rigidified to allow the balance machine to work properly. Gear couplings must be made with a tight fit on the major diameter for the balancing process and then relieved for actual installation in a system. Disc couplings use a clamping screw to hold the discs tight. Some couplings cannot be balanced as an assembly, only as components.
After components are balanced, the high sides are marked so that the coupling can be assembled with high sides properly located versus other high sides. The couplings can also be assembly check-balanced once the components are assembled. Component balanced couplings should only utilize substitute parts that are balanced to the same criteria.

When a coupling has been balanced as a complete assembly, its components are "match marked" to guide future assembly. Assembly balanced couplings cannot have substitute parts installed unless the whole assembly is re-balanced. Otherwise the balance will be compromised.

When a coupling has been machine balanced, and is still mounted in the machine, the result is described in terms of how much residual unbalance remains. Once removed from the machine the unbalance is called potential unbalance.

Continue to second page of Part 8 (continued)
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